Initial value formulation of dynamical Chern-Simons gravity

NASA Astrophysics Data System (ADS)

Delsate, Térence; Hilditch, David; Witek, Helvi

2015-01-01

We derive an initial value formulation for dynamical Chern-Simons gravity, a modification of general relativity involving parity-violating higher derivative terms. We investigate the structure of the resulting system of partial differential equations thinking about linearization around arbitrary backgrounds. This type of consideration is necessary if we are to establish well-posedness of the Cauchy problem. Treating the field equations as an effective field theory we find that weak necessary conditions for hyperbolicity are satisfied. For the full field equations we find that there are states from which subsequent evolution is not determined. Generically the evolution system closes, but is not hyperbolic in any sense that requires a first order pseudodifferential reduction. In a cursory mode analysis we find that the equations of motion contain terms that may cause ill-posedness of the initial value problem.

Dynamic colloidal assembly pathways via low dimensional models

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

Yang, Yuguang; Bevan, Michael A., E-mail: mabevan@jhu.edu; Thyagarajan, Raghuram

2016-05-28

Here we construct a low-dimensional Smoluchowski model for electric field mediated colloidal crystallization using Brownian dynamic simulations, which were previously matched to experiments. Diffusion mapping is used to infer dimensionality and confirm the use of two order parameters, one for degree of condensation and one for global crystallinity. Free energy and diffusivity landscapes are obtained as the coefficients of a low-dimensional Smoluchowski equation to capture the thermodynamics and kinetics of microstructure evolution. The resulting low-dimensional model quantitatively captures the dynamics of different assembly pathways between fluid, polycrystal, and single crystals states, in agreement with the full N-dimensional data as characterizedmore » by first passage time distributions. Numerical solution of the low-dimensional Smoluchowski equation reveals statistical properties of the dynamic evolution of states vs. applied field amplitude and system size. The low-dimensional Smoluchowski equation and associated landscapes calculated here can serve as models for predictive control of electric field mediated assembly of colloidal ensembles into two-dimensional crystalline objects.« less

From crater functions to partial differential equations: a new approach to ion bombardment induced nonequilibrium pattern formation.

PubMed

Norris, Scott A; Brenner, Michael P; Aziz, Michael J

2009-06-03

We develop a methodology for deriving continuum partial differential equations for the evolution of large-scale surface morphology directly from molecular dynamics simulations of the craters formed from individual ion impacts. Our formalism relies on the separation between the length scale of ion impact and the characteristic scale of pattern formation, and expresses the surface evolution in terms of the moments of the crater function. We demonstrate that the formalism reproduces the classical Bradley-Harper results, as well as ballistic atomic drift, under the appropriate simplifying assumptions. Given an actual set of converged molecular dynamics moments and their derivatives with respect to the incidence angle, our approach can be applied directly to predict the presence and absence of surface morphological instabilities. This analysis represents the first work systematically connecting molecular dynamics simulations of ion bombardment to partial differential equations that govern topographic pattern-forming instabilities.

Self-Supervised Dynamical Systems

NASA Technical Reports Server (NTRS)

Zak, Michail

2003-01-01

Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and metal aspects of a monad is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. This feedback is what makes the evolution of probability densities nonlinear. The deviation from linear evolution can be characterized, in a sense, as an expression of free will. It has been demonstrated that probability densities can approach prescribed attractors while exhibiting such patterns as shock waves, solitons, and chaos in probability space. The concept of self-supervised dynamical systems has been considered for application to diverse phenomena, including information-based neural networks, cooperation, competition, deception, games, and control of chaos. In addition, a formal similarity between the mathematical structures of self-supervised dynamical systems and of quantum-mechanical systems has been investigated.

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

Bisio, Alessandro; D’Ariano, Giacomo Mauro; Tosini, Alessandro, E-mail: alessandro.tosini@unipv.it

We present a quantum cellular automaton model in one space-dimension which has the Dirac equation as emergent. This model, a discrete-time and causal unitary evolution of a lattice of quantum systems, is derived from the assumptions of homogeneity, parity and time-reversal invariance. The comparison between the automaton and the Dirac evolutions is rigorously set as a discrimination problem between unitary channels. We derive an exact lower bound for the probability of error in the discrimination as an explicit function of the mass, the number and the momentum of the particles, and the duration of the evolution. Computing this bound withmore » experimentally achievable values, we see that in that regime the QCA model cannot be discriminated from the usual Dirac evolution. Finally, we show that the evolution of one-particle states with narrow-band in momentum can be efficiently simulated by a dispersive differential equation for any regime. This analysis allows for a comparison with the dynamics of wave-packets as it is described by the usual Dirac equation. This paper is a first step in exploring the idea that quantum field theory could be grounded on a more fundamental quantum cellular automaton model and that physical dynamics could emerge from quantum information processing. In this framework, the discretization is a central ingredient and not only a tool for performing non-perturbative calculation as in lattice gauge theory. The automaton model, endowed with a precise notion of local observables and a full probabilistic interpretation, could lead to a coherent unification of a hypothetical discrete Planck scale with the usual Fermi scale of high-energy physics. - Highlights: • The free Dirac field in one space dimension as a quantum cellular automaton. • Large scale limit of the automaton and the emergence of the Dirac equation. • Dispersive differential equation for the evolution of smooth states on the automaton. • Optimal discrimination between the automaton evolution and the Dirac equation.« less

Generalized Landau Equation for a System with a Self-Consistent Mean Field - Derivation from an N-Particle Liouville Equation

NASA Astrophysics Data System (ADS)

Kandrup, H.

1981-02-01

Assume that the evolution of a system is determined by an N-particle Liouville equation. Suppose, moreover, that the particles which compose the system interact via a long range force like gravity so that the system will be spatially inhomogeneous. In this case, the mean force acting upon a test particle does not vanish, so that one wishes to isolate a self-consistent mean field and distinguish its "systematic" effects from the effects of "fluctuations." This is done here. The time-dependent projection operator formalism of Willis and Picard is used to obtain an exact equation for the time evolution of an appropriately defined one-particle probability density. If one implements the assumption that the "fluctuation" time scale is much shorter than both the relaxation and dynamical time scales, this exact equation can be approximated as a closed Markovian equation. In the limiting case of spatial homogeneity, one recovers precisely the standard Landau equation, which is customarily derived by a stochastic binary-encounter argument. This equation is contrasted with the standard heuristic equation for a mean field theory, as formulated for a Newtonian r-1 gravitational potential in stellar dynamics.

Selected Aspects of Markovian and Non-Markovian Quantum Master Equations

NASA Astrophysics Data System (ADS)

Lendi, K.

A few particular marked properties of quantum dynamical equations accounting for general relaxation and dissipation are selected and summarized in brief. Most results derive from the universal concept of complete positivity. The considerations mainly regard genuinely irreversible processes as characterized by a unique asymptotically stationary final state for arbitrary initial conditions. From ordinary Markovian master equations and associated quantum dynamical semigroup time-evolution, derivations of higher order Onsager coefficients and related entropy production are discussed. For general processes including non-faithful states a regularized version of quantum relative entropy is introduced. Further considerations extend to time-dependent infinitesimal generators of time-evolution and to a possible description of propagation of initial states entangled between open system and environment. In the coherence-vector representation of the full non-Markovian equations including entangled initial states, first results are outlined towards identifying mathematical properties of a restricted class of trial integral-kernel functions suited to phenomenological applications.

Statistical Decoupling of a Lagrangian Fluid Parcel in Newtonian Cosmology

NASA Astrophysics Data System (ADS)

Wang, Xin; Szalay, Alex

2016-03-01

The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differential equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.

STATISTICAL DECOUPLING OF A LAGRANGIAN FLUID PARCEL IN NEWTONIAN COSMOLOGY

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

Wang, Xin; Szalay, Alex, E-mail: xwang@cita.utoronto.ca

The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differentialmore » equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.« less

Ohm's law in the fast lane: general relatiivistic charge dynamics

NASA Technical Reports Server (NTRS)

Meier, D.

2004-01-01

Fully relativistic and causal equations for the flow of charge in curved spacetime are derived. It is believed that this is the first set of equations to be published that correctly describes the flow of charge, as well as the evolution of the electromagnetic field, in highly dynamical relativistic environments on timescales much shorter than the collapse time (GM/c3).

Chaotic universe model.

PubMed

Aydiner, Ekrem

2018-01-15

In this study, we consider nonlinear interactions between components such as dark energy, dark matter, matter and radiation in the framework of the Friedman-Robertson-Walker space-time and propose a simple interaction model based on the time evolution of the densities of these components. By using this model we show that these interactions can be given by Lotka-Volterra type equations. We numerically solve these coupling equations and show that interaction dynamics between dark energy-dark matter-matter or dark energy-dark matter-matter-radiation has a strange attractor for 0 > w de  >-1, w dm  ≥ 0, w m  ≥ 0 and w r  ≥ 0 values. These strange attractors with the positive Lyapunov exponent clearly show that chaotic dynamics appears in the time evolution of the densities. These results provide that the time evolution of the universe is chaotic. The present model may have potential to solve some of the cosmological problems such as the singularity, cosmic coincidence, big crunch, big rip, horizon, oscillation, the emergence of the galaxies, matter distribution and large-scale organization of the universe. The model also connects between dynamics of the competing species in biological systems and dynamics of the time evolution of the universe and offers a new perspective and a new different scenario for the universe evolution.

Propagation of nonlinear shock waves for the generalised Oskolkov equation and its dynamic motions in the presence of an external periodic perturbation

NASA Astrophysics Data System (ADS)

Ak, Turgut; Aydemir, Tugba; Saha, Asit; Kara, Abdul Hamid

2018-06-01

Propagation of nonlinear shock waves for the generalised Oskolkov equation and dynamic motions of the perturbed Oskolkov equation are investigated. Employing the unified method, a collection of exact shock wave solutions for the generalised Oskolkov equations is presented. Collocation finite element method is applied to the generalised Oskolkov equation for checking the accuracy of the proposed method by two test problems including the motion of shock wave and evolution of waves with Gaussian and undular bore initial conditions. Considering an external periodic perturbation, the dynamic motions of the perturbed generalised Oskolkov equation are studied depending on the system parameters with the help of phase portrait and time series plot. The perturbed generalised Oskolkov equation exhibits period-3, quasiperiodic and chaotic motions for some special values of the system parameters, whereas the generalised Oskolkov equation presents shock waves in the absence of external periodic perturbation.

The evolution of dispersal in a Levins' type metapopulation model.

PubMed

Jansen, Vincent A A; Vitalis, Renaud

2007-10-01

We study the evolution of the dispersal rate in a metapopulation model with extinction and colonization dynamics, akin to the model as originally described by Levins. To do so we extend the metapopulation model with a description of the within patch dynamics. By means of a separation of time scales we analytically derive a fitness expression from first principles for this model. The fitness function can be written as an inclusive fitness equation (Hamilton's rule). By recasting this equation in a form that emphasizes the effects of competition we show the effect of the local competition and the local population size on the evolution of dispersal. We find that the evolution of dispersal cannot be easily interpreted in terms of avoidance of kin competition, but rather that increased dispersal reduces the competitive ability. Our model also yields a testable prediction in term of relatedness and life-history parameters.

Time-evolution of quantum systems via a complex nonlinear Riccati equation. I. Conservative systems with time-independent Hamiltonian

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

Cruz, Hans, E-mail: hans@ciencias.unam.mx; Schuch, Dieter; Castaños, Octavio, E-mail: ocasta@nucleares.unam.mx

2015-09-15

The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.

Computing generalized Langevin equations and generalized Fokker-Planck equations.

PubMed

Darve, Eric; Solomon, Jose; Kia, Amirali

2009-07-07

The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

Modelling of hyperconcentrated flood and channel evolution in a braided reach using a dynamically coupled one-dimensional approach

NASA Astrophysics Data System (ADS)

Xia, Junqiang; Zhang, Xiaolei; Wang, Zenghui; Li, Jie; Zhou, Meirong

2018-06-01

Hyperconcentrated sediment-laden floods often occur in a braided reach of the Lower Yellow River, usually leading to significant channel evolution. A one-dimensional (1D) morphodynamic model using a dynamically coupled solution approach is developed to simulate hyperconcentrated flood and channel evolution in the braided reach with an extremely irregular cross-sectional geometry. In the model, the improved equations for hydrodynamics account for the effects of sediment concentration and bed evolution, which are coupled with the equations of non-equilibrium sediment transport and bed evolution. The model was validated using measurements from the 1977 and 2004 hyperconcentrated floods. Furthermore, the effects were investigated of different cross-sectional spacings and allocation modes of channel deformation area on the model results. It was found that a suitable cross-sectional distance of less than 3 km should be adopted when simulating hyperconcentrated floods, and the results using the uniform allocation mode can agree better with measurements than other two allocation modes.

Equation-free multiscale computation: algorithms and applications.

PubMed

Kevrekidis, Ioannis G; Samaey, Giovanni

2009-01-01

In traditional physicochemical modeling, one derives evolution equations at the (macroscopic, coarse) scale of interest; these are used to perform a variety of tasks (simulation, bifurcation analysis, optimization) using an arsenal of analytical and numerical techniques. For many complex systems, however, although one observes evolution at a macroscopic scale of interest, accurate models are only given at a more detailed (fine-scale, microscopic) level of description (e.g., lattice Boltzmann, kinetic Monte Carlo, molecular dynamics). Here, we review a framework for computer-aided multiscale analysis, which enables macroscopic computational tasks (over extended spatiotemporal scales) using only appropriately initialized microscopic simulation on short time and length scales. The methodology bypasses the derivation of macroscopic evolution equations when these equations conceptually exist but are not available in closed form-hence the term equation-free. We selectively discuss basic algorithms and underlying principles and illustrate the approach through representative applications. We also discuss potential difficulties and outline areas for future research.

Schrödinger–Langevin equation with quantum trajectories for photodissociation dynamics

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

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

The Schrödinger–Langevin equation is integrated to study the wave packet dynamics of quantum systems subject to frictional effects by propagating an ensemble of quantum trajectories. The equations of motion for the complex action and quantum trajectories are derived from the Schrödinger–Langevin equation. The moving least squares approach is used to evaluate the spatial derivatives of the complex action required for the integration of the equations of motion. Computational results are presented and analyzed for the evolution of a free Gaussian wave packet, a two-dimensional barrier model, and the photodissociation dynamics of NOCl. The absorption spectrum of NOCl obtained from themore » Schrödinger–Langevin equation displays a redshift when frictional effects increase. This computational result agrees qualitatively with the experimental results in the solution-phase photochemistry of NOCl.« less

Time-dependent spectral renormalization method

NASA Astrophysics Data System (ADS)

Cole, Justin T.; Musslimani, Ziad H.

2017-11-01

The spectral renormalization method was introduced by Ablowitz and Musslimani (2005) as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems. In this paper, we extend those ideas to the time domain and introduce a time-dependent spectral renormalization method as a numerical means to simulate linear and nonlinear evolution equations. The essence of the method is to convert the underlying evolution equation from its partial or ordinary differential form (using Duhamel's principle) into an integral equation. The solution sought is then viewed as a fixed point in both space and time. The resulting integral equation is then numerically solved using a simple renormalized fixed-point iteration method. Convergence is achieved by introducing a time-dependent renormalization factor which is numerically computed from the physical properties of the governing evolution equation. The proposed method has the ability to incorporate physics into the simulations in the form of conservation laws or dissipation rates. This novel scheme is implemented on benchmark evolution equations: the classical nonlinear Schrödinger (NLS), integrable PT symmetric nonlocal NLS and the viscous Burgers' equations, each of which being a prototypical example of a conservative and dissipative dynamical system. Numerical implementation and algorithm performance are also discussed.

Complexity of life via collective mind

NASA Technical Reports Server (NTRS)

Zak, Michail

2004-01-01

e mind is introduced as a set of simple intelligent units (say, neurons, or interacting agents), which can communicate by exchange of information without explicit global control. Incomplete information is compensated by a sequence of random guesses symmetrically distributed around expectations with prescribed variances. Both the expectations and variances are the invariants characterizing the whole class of agents. These invariants are stored as parameters of the collective mind, while they contribute into dynamical formalism of the agents' evolution, and in particular, into the reflective chains of their nested abstract images of the selves and non-selves. The proposed model consists of the system of stochastic differential equations in the Langevin form representing the motor dynamics, and the corresponding Fokker-Planck equation representing the mental dynamics (Motor dynamics describes the motion in physical space, while mental dynamics simulates the evolution of initial errors in terms of the probability density). The main departure of this model from Newtonian and statistical physics is due to a feedback from the mental to the motor dynamics which makes the Fokker-Planck equation nonlinear. Interpretation of this model from mathematical and physical viewpoints, as well as possible interpretation from biological, psychological, and social viewpoints are discussed. The model is illustrated by the dynamics of a dialog.

Designing non-Hermitian dynamics for conservative state evolution on the Bloch sphere

NASA Astrophysics Data System (ADS)

Yu, Sunkyu; Piao, Xianji; Park, Namkyoo

2018-03-01

An evolution on the Bloch sphere is the fundamental state transition, including optical polarization controls and qubit operations. Conventional evolution of a polarization state or qubit is implemented within a closed system that automatically satisfies energy conservation from the Hermitian formalism. Although particular forms of static non-Hermitian Hamiltonians, such as parity-time-symmetric Hamiltonians, allow conservative states in an open system, the criteria for the energy conservation in a dynamical open system have not been fully explored. Here, we derive the condition of conservative state evolution in open-system dynamics and its inverse design method, by developing the non-Hermitian modification of the Larmor precession equation. We show that the geometrically designed locus on the Bloch sphere can be realized by different forms of dynamics, leading to the isolocus family of non-Hermitian dynamics. This increased degree of freedom allows the complementary phenomena of error-robust and highly sensitive evolutions on the Bloch sphere, which could be applicable to stable polarizers, quantum gates, and optimized sensors in dynamical open systems.

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

NASA Astrophysics Data System (ADS)

Galitski, Victor

2012-02-01

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

Evolution and End Point of the Black String Instability: Large D Solution.

PubMed

Emparan, Roberto; Suzuki, Ryotaku; Tanabe, Kentaro

2015-08-28

We derive a simple set of nonlinear, (1+1)-dimensional partial differential equations that describe the dynamical evolution of black strings and branes to leading order in the expansion in the inverse of the number of dimensions D. These equations are easily solved numerically. Their solution shows that thin enough black strings are unstable to developing inhomogeneities along their length, and at late times they asymptote to stable nonuniform black strings. This proves an earlier conjecture about the end point of the instability of black strings in a large enough number of dimensions. If the initial black string is very thin, the final configuration is highly nonuniform and resembles a periodic array of localized black holes joined by short necks. We also present the equations that describe the nonlinear dynamics of anti-de Sitter black branes at large D.

An Inverse Problem for a Class of Conditional Probability Measure-Dependent Evolution Equations

PubMed Central

Mirzaev, Inom; Byrne, Erin C.; Bortz, David M.

2016-01-01

We investigate the inverse problem of identifying a conditional probability measure in measure-dependent evolution equations arising in size-structured population modeling. We formulate the inverse problem as a least squares problem for the probability measure estimation. Using the Prohorov metric framework, we prove existence and consistency of the least squares estimates and outline a discretization scheme for approximating a conditional probability measure. For this scheme, we prove general method stability. The work is motivated by Partial Differential Equation (PDE) models of flocculation for which the shape of the post-fragmentation conditional probability measure greatly impacts the solution dynamics. To illustrate our methodology, we apply the theory to a particular PDE model that arises in the study of population dynamics for flocculating bacterial aggregates in suspension, and provide numerical evidence for the utility of the approach. PMID:28316360

Ring Current Ion Coupling with Electromagnetic Ion Cyclotron Waves

NASA Technical Reports Server (NTRS)

Khazanov, George V.

2002-01-01

A new ring current global model has been developed for the first time that couples the system of two kinetic equations: one equation describes the ring current (RC) ion dynamic, and another equation describes wave evolution of electromagnetic ion cyclotron waves (EMIC). The coupled model is able to simulate, for the first time self-consistently calculated RC ion kinetic and evolution of EMIC waves that propagate along geomagnetic field lines and reflect from the ionosphere. Ionospheric properties affect the reflection index through the integral Pedersen and Hall coductivities. The structure and dynamics of the ring current proton precipitating flux regions, intensities of EMIC, global RC energy balance, and some other parameters will be studied in detail for the selected geomagnetic storms. The space whether aspects of RC modelling and comparison with the data will also be discussed.

Nonlinear evolution of coarse-grained quantum systems with generalized purity constraints

NASA Astrophysics Data System (ADS)

Burić, Nikola

2010-12-01

Constrained quantum dynamics is used to propose a nonlinear dynamical equation for pure states of a generalized coarse-grained system. The relevant constraint is given either by the generalized purity or by the generalized invariant fluctuation, and the coarse-grained pure states correspond to the generalized coherent, i.e. generalized nonentangled states. Open system model of the coarse-graining is discussed. It is shown that in this model and in the weak coupling limit the constrained dynamical equations coincide with an equation for pointer states, based on Hilbert-Schmidt distance, that was previously suggested in the context of the decoherence theory.

Semistable extremal ground states for nonlinear evolution equations in unbounded domains

NASA Astrophysics Data System (ADS)

Rodríguez-Bernal, Aníbal; Vidal-López, Alejandro

2008-02-01

In this paper we show that dissipative reaction-diffusion equations in unbounded domains posses extremal semistable ground states equilibria, which bound asymptotically the global dynamics. Uniqueness of such positive ground state and their approximation by extremal equilibria in bounded domains is also studied. The results are then applied to the important case of logistic equations.

Evolution of complex dynamics

NASA Astrophysics Data System (ADS)

Wilds, Roy; Kauffman, Stuart A.; Glass, Leon

2008-09-01

We study the evolution of complex dynamics in a model of a genetic regulatory network. The fitness is associated with the topological entropy in a class of piecewise linear equations, and the mutations are associated with changes in the logical structure of the network. We compare hill climbing evolution, in which only mutations that increase the fitness are allowed, with neutral evolution, in which mutations that leave the fitness unchanged are allowed. The simple structure of the fitness landscape enables us to estimate analytically the rates of hill climbing and neutral evolution. In this model, allowing neutral mutations accelerates the rate of evolutionary advancement for low mutation frequencies. These results are applicable to evolution in natural and technological systems.

Quantum theory of open systems based on stochastic differential equations of generalized Langevin (non-Wiener) type

NASA Astrophysics Data System (ADS)

Basharov, A. M.

2012-09-01

It is shown that the effective Hamiltonian representation, as it is formulated in author's papers, serves as a basis for distinguishing, in a broadband environment of an open quantum system, independent noise sources that determine, in terms of the stationary quantum Wiener and Poisson processes in the Markov approximation, the effective Hamiltonian and the equation for the evolution operator of the open system and its environment. General stochastic differential equations of generalized Langevin (non-Wiener) type for the evolution operator and the kinetic equation for the density matrix of an open system are obtained, which allow one to analyze the dynamics of a wide class of localized open systems in the Markov approximation. The main distinctive features of the dynamics of open quantum systems described in this way are the stabilization of excited states with respect to collective processes and an additional frequency shift of the spectrum of the open system. As an illustration of the general approach developed, the photon dynamics in a single-mode cavity without losses on the mirrors is considered, which contains identical intracavity atoms coupled to the external vacuum electromagnetic field. For some atomic densities, the photons of the cavity mode are "locked" inside the cavity, thus exhibiting a new phenomenon of radiation trapping and non-Wiener dynamics.

The spectrum of density perturbations in an expanding universe

NASA Technical Reports Server (NTRS)

Silk, J.

1974-01-01

The basic dynamic equations that govern the evolution of perturbations in a Friedmann-Lemaitre universe are derived. General solutions describing the evolution of adiabatic perturbations in the density of matter are obtained, and the choice of the appropriate initial conditions is examined. The various perturbation modes are compared, and the effects of decoupling on the perturbation spectrum are studied. The scheme used to follow the evolution of density perturbations through decoupling is based on an extension of the Eddington approximation to the radiative transfer equation, and is strictly valid in both optically thick and thin limits.

Development of linear projecting in studies of non-linear flow. Acoustic heating induced by non-periodic sound

NASA Astrophysics Data System (ADS)

Perelomova, Anna

2006-08-01

The equation of energy balance is subdivided into two dynamics equations, one describing evolution of the dominative sound, and the second one responsible for acoustic heating. The first one is the famous KZK equation, and the second one is a novel equation governing acoustic heating. The novel dynamic equation considers both periodic and non-periodic sound. Quasi-plane geometry of flow is supposed. Subdividing is provided on the base of specific links of every mode. Media with arbitrary thermic T(p,ρ) and caloric e(p,ρ) equations of state are considered. Individual roles of thermal conductivity and viscosity in the heating induced by aperiodic sound in the ideal gases and media different from ideal gases are discussed.

Dynamical networks with topological self-organization

NASA Technical Reports Server (NTRS)

Zak, M.

2001-01-01

Coupled evolution of state and topology of dynamical networks is introduced. Due to the well organized tensor structure, the governing equations are presented in a canonical form, and required attractors as well as their basins can be easily implanted and controlled.

General framework for fluctuating dynamic density functional theory

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

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

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

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

New Perspectives: Wave Mechanical Interpretations of Dark Matter, Baryon and Dark Energy

NASA Astrophysics Data System (ADS)

Russell, Esra

We model the cosmic components: dark matter, dark energy and baryon distributions in the Cosmic Web by means of highly nonlinear Schrodinger type and reaction diffusion type wave mechanical descriptions. The construction of these wave mechanical models of the structure formation is achieved by introducing the Fisher information measure and its comparison with highly nonlinear term which has dynamical analogy to infamous quantum potential in the wave equations. Strikingly, the comparison of this nonlinear term and the Fisher information measure provides a dynamical distinction between lack of self-organization and self-organization in the dynamical evolution of the cosmic components. Mathematically equivalent to the standard cosmic fluid equations, these approaches make it possible to follow the evolution of the matter distribution even into the highly nonlinear regime by circumventing singularities. Also, numerical realizations of the emerging web-like patterns are presented from the nonlinear dynamics of the baryon component while dark energy component shows Gaussian type dynamics corresponding to soliton-like solutions.

A Watched Ocean World Never Boils: Inspecting the Geochemical Impact on Ocean Worlds from Their Thermal Evolution

NASA Astrophysics Data System (ADS)

Spiers, E. M.; Schmidt, B. E.

2018-05-01

I aim to acquire better understanding of coupled thermal evolution and geochemical fluxes of an ocean world through a box model. A box model divides the system into plainer elements with realistically-solvable, dynamic equations.

Molecular representation of molar domain (volume), evolution equations, and linear constitutive relations for volume transport.

PubMed

Eu, Byung Chan

2008-09-07

In the traditional theories of irreversible thermodynamics and fluid mechanics, the specific volume and molar volume have been interchangeably used for pure fluids, but in this work we show that they should be distinguished from each other and given distinctive statistical mechanical representations. In this paper, we present a general formula for the statistical mechanical representation of molecular domain (volume or space) by using the Voronoi volume and its mean value that may be regarded as molar domain (volume) and also the statistical mechanical representation of volume flux. By using their statistical mechanical formulas, the evolution equations of volume transport are derived from the generalized Boltzmann equation of fluids. Approximate solutions of the evolution equations of volume transport provides kinetic theory formulas for the molecular domain, the constitutive equations for molar domain (volume) and volume flux, and the dissipation of energy associated with volume transport. Together with the constitutive equation for the mean velocity of the fluid obtained in a previous paper, the evolution equations for volume transport not only shed a fresh light on, and insight into, irreversible phenomena in fluids but also can be applied to study fluid flow problems in a manner hitherto unavailable in fluid dynamics and irreversible thermodynamics. Their roles in the generalized hydrodynamics will be considered in the sequel.

Effect of EMIC Wave Normal Angle Distribution on Relativistic Electron Scattering Based on the Newly Developed Self-consistent RC/EMIC Waves Model by Khazanov et al. [2006

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Gallagher, D. L.; Gamayunov, K.

2007-01-01

It is well known that the effects of EMIC waves on RC ion and RB electron dynamics strongly depend on such particle/wave characteristics as the phase-space distribution function, frequency, wave-normal angle, wave energy, and the form of wave spectral energy density. Therefore, realistic characteristics of EMIC waves should be properly determined by modeling the RC-EMIC waves evolution self-consistently. Such a selfconsistent model progressively has been developing by Khaznnov et al. [2002-2006]. It solves a system of two coupled kinetic equations: one equation describes the RC ion dynamics and another equation describes the energy density evolution of EMIC waves. Using this model, we present the effectiveness of relativistic electron scattering and compare our results with previous work in this area of research.

Perturbative dynamics of thin-shell wormholes beyond general relativity: An alternative approach

NASA Astrophysics Data System (ADS)

Rubín de Celis, Emilio; Tomasini, Cecilia; Simeone, Claudio

Recent studies relating the approximations for the equations-of-state for thin shells and their consequent perturbative evolution are extended to thin-shell wormholes in theories beyond general relativity and more than four spacetime dimensions. The assumption of equations-of-state of the same form for static and slowly evolving shells appears as a strong restriction excluding the possibility of oscillatory evolutions. Then the new results considerably differ from previous ones obtained within the usual linearized approach.

Hydrodynamical processes in coalescing binary stars

NASA Astrophysics Data System (ADS)

Lai, Dong

1994-01-01

Coalescing neutron star binaries are considered to be the most promising sources of gravitational waves that could be detected by the planned laser-interferometer LIGO/VIRGO detectors. Extracting gravity wave signals from noisy data requires accurate theoretical waveforms in the frequency range 10-1000 Hz end detailed understanding of the dynamics of the binary orbits. We investigate the quasi-equilibrium and dynamical tidal interactions in coalescing binary stars, with particular focus on binary neutron stars. We develop a new formalism to study the equilibrium and dynamics of fluid stars in binary systems. The stars are modeled as compressible ellipsoids, and satisfy polytropic equation of state. The hydrodynamic equations are reduced to a set of ordinary differential equations for the evolution of the principal axes and other global quantities. The equilibrium binary structure is determined by a set of algebraic equations. We consider both synchronized and nonsynchronized systems, obtaining the generalizations to compressible fluid of the classical results for the ellipsoidal binary configurations. Our method can be applied to a wide variety of astrophysical binary systems containing neutron stars, white dwarfs, main-sequence stars and planets. We find that both secular and dynamical instabilities can develop in close binaries. The quasi-static (secular) orbital evolution, as well as the dynamical evolution of binaries driven by viscous dissipation and gravitational radiation reaction are studied. The development of the dynamical instability accelerates the binary coalescence at small separation, leading to appreciable radial infall velocity near contact. We also study resonant excitations of g-mode oscillations in coalescing binary neutron stars. A resonance occurs when the frequency of the tidal driving force equals one of the intrinsic g-mode frequencies. Using realistic microscopic nuclear equations of state, we determine the g-modes in a cold neutron atar. Resonant excitations of these g-modes during the last few minutes of the binary coalescence result in energy transfer and angular momentum transfer from the binary orbit to the neutron star. Because of the weak coupling between the g-modes and the tidal potential, the induced orbital phase errors due to resonances are small. However, resonant excitations of the g-modes play an important role in the tidal heating of binary neutron stars.

Turbulence and the Stabilization Principle

NASA Technical Reports Server (NTRS)

Zak, Michail

2010-01-01

Further results of research, reported in several previous NASA Tech Briefs articles, were obtained on a mathematical formalism for postinstability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence). To recapitulate: Fictitious control forces are introduced to couple the dynamical equations with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in ordinary perceived three-dimensional space is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. Con sequently, the postinstability motion is represented by a set of functions describing the evolution of such statistical quantities as expectations and higher moments, and this representation is stable. The previously reported findings are analyzed from the perspective of the authors Stabilization Principle, according to which (1) stability is recognized as an attribute of mathematical formalism rather than of underlying physics and (2) a dynamical system that appears unstable when modeled by differentiable functions only can be rendered stable by modifying the dynamical equations to incorporate intrinsic stochasticity.

Probabilistic density function method for nonlinear dynamical systems driven by colored noise

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

Barajas-Solano, David A.; Tartakovsky, Alexandre M.

2016-05-01

We present a probability density function (PDF) method for a system of nonlinear stochastic ordinary differential equations driven by colored noise. The method provides an integro-differential equation for the temporal evolution of the joint PDF of the system's state, which we close by means of a modified Large-Eddy-Diffusivity-type closure. Additionally, we introduce the generalized local linearization (LL) approximation for deriving a computable PDF equation in the form of the second-order partial differential equation (PDE). We demonstrate the proposed closure and localization accurately describe the dynamics of the PDF in phase space for systems driven by noise with arbitrary auto-correlation time.more » We apply the proposed PDF method to the analysis of a set of Kramers equations driven by exponentially auto-correlated Gaussian colored noise to study the dynamics and stability of a power grid.« less

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.

Nonlinear stability of oscillatory core-annular flow: A generalized Kuramoto-Sivashinsky equation with time periodic coefficients

NASA Technical Reports Server (NTRS)

Coward, Adrian V.; Papageorgiou, Demetrios T.; Smyrlis, Yiorgos S.

1994-01-01

In this paper the nonlinear stability of two-phase core-annular flow in a pipe is examined when the acting pressure gradient is modulated by time harmonic oscillations and viscosity stratification and interfacial tension is present. An exact solution of the Navier-Stokes equations is used as the background state to develop an asymptotic theory valid for thin annular layers, which leads to a novel nonlinear evolution describing the spatio-temporal evolution of the interface. The evolution equation is an extension of the equation found for constant pressure gradients and generalizes the Kuramoto-Sivashinsky equation with dispersive effects found by Papageorgiou, Maldarelli & Rumschitzki, Phys. Fluids A 2(3), 1990, pp. 340-352, to a similar system with time periodic coefficients. The distinct regimes of slow and moderate flow are considered and the corresponding evolution is derived. Certain solutions are described analytically in the neighborhood of the first bifurcation point by use of multiple scales asymptotics. Extensive numerical experiments, using dynamical systems ideas, are carried out in order to evaluate the effect of the oscillatory pressure gradient on the solutions in the presence of a constant pressure gradient.

Influence of Initial Correlations on Evolution of a Subsystem in a Heat Bath and Polaron Mobility

NASA Astrophysics Data System (ADS)

Los, Victor F.

2017-08-01

A regular approach to accounting for initial correlations, which allows to go beyond the unrealistic random phase (initial product state) approximation in deriving the evolution equations, is suggested. An exact homogeneous (time-convolution and time-convolutionless) equations for a relevant part of the two-time equilibrium correlation function for the dynamic variables of a subsystem interacting with a boson field (heat bath) are obtained. No conventional approximation like RPA or Bogoliubov's principle of weakening of initial correlations is used. The obtained equations take into account the initial correlations in the kernel governing their evolution. The solution to these equations is found in the second order of the kernel expansion in the electron-phonon interaction, which demonstrates that generally the initial correlations influence the correlation function's evolution in time. It is explicitly shown that this influence vanishes on a large timescale (actually at t→ ∞) and the evolution process enters an irreversible kinetic regime. The developed approach is applied to the Fröhlich polaron and the low-temperature polaron mobility (which was under a long-time debate) is found with a correction due to initial correlations.

The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts

NASA Astrophysics Data System (ADS)

Neill, Duff

2017-01-01

We develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. This equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We compute the decay width analytically, giving a closed form expression, and find it to be jet geometry independent, up to the number of legs of the dipole in the active jet. Enabling the asymptotic expansion is the correct perturbative seed, where we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures. Indeed, we recover the equations of saturation physics in the final state dynamics of QCD.

Kinematic validation of a quasi-geostrophic model for the fast dynamics in the Earth's outer core

NASA Astrophysics Data System (ADS)

Maffei, S.; Jackson, A.

2017-09-01

We derive a quasi-geostrophic (QG) system of equations suitable for the description of the Earth's core dynamics on interannual to decadal timescales. Over these timescales, rotation is assumed to be the dominant force and fluid motions are strongly invariant along the direction parallel to the rotation axis. The diffusion-free, QG system derived here is similar to the one derived in Canet et al. but the projection of the governing equations on the equatorial disc is handled via vertical integration and mass conservation is applied to the velocity field. Here we carefully analyse the properties of the resulting equations and we validate them neglecting the action of the Lorentz force in the momentum equation. We derive a novel analytical solution describing the evolution of the magnetic field under these assumptions in the presence of a purely azimuthal flow and an alternative formulation that allows us to numerically solve the evolution equations with a finite element method. The excellent agreement we found with the analytical solution proves that numerical integration of the QG system is possible and that it preserves important physical properties of the magnetic field. Implementation of magnetic diffusion is also briefly considered.

The formulation of dynamical contact problems with friction in the case of systems of rigid bodies and general discrete mechanical systems—Painlevé and Kane paradoxes revisited

NASA Astrophysics Data System (ADS)

Charles, Alexandre; Ballard, Patrick

2016-08-01

The dynamics of mechanical systems with a finite number of degrees of freedom (discrete mechanical systems) is governed by the Lagrange equation which is a second-order differential equation on a Riemannian manifold (the configuration manifold). The handling of perfect (frictionless) unilateral constraints in this framework (that of Lagrange's analytical dynamics) was undertaken by Schatzman and Moreau at the beginning of the 1980s. A mathematically sound and consistent evolution problem was obtained, paving the road for many subsequent theoretical investigations. In this general evolution problem, the only reaction force which is involved is a generalized reaction force, consistently with the virtual power philosophy of Lagrange. Surprisingly, such a general formulation was never derived in the case of frictional unilateral multibody dynamics. Instead, the paradigm of the Coulomb law applying to reaction forces in the real world is generally invoked. So far, this paradigm has only enabled to obtain a consistent evolution problem in only some very few specific examples and to suggest numerical algorithms to produce computational examples (numerical modeling). In particular, it is not clear what is the evolution problem underlying the computational examples. Moreover, some of the few specific cases in which this paradigm enables to write down a precise evolution problem are known to show paradoxes: the Painlevé paradox (indeterminacy) and the Kane paradox (increase in kinetic energy due to friction). In this paper, we follow Lagrange's philosophy and formulate the frictional unilateral multibody dynamics in terms of the generalized reaction force and not in terms of the real-world reaction force. A general evolution problem that governs the dynamics is obtained for the first time. We prove that all the solutions are dissipative; that is, this new formulation is free of Kane paradox. We also prove that some indeterminacy of the Painlevé paradox is fixed in this formulation.

Exact solution for a non-Markovian dissipative quantum dynamics.

PubMed

Ferialdi, Luca; Bassi, Angelo

2012-04-27

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

Simple waves in a two-component Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Ivanov, S. K.; Kamchatnov, A. M.

2018-04-01

We study the dynamics of so-called simple waves in a two-component Bose-Einstein condensate. The evolution of the condensate is described by Gross-Pitaevskii equations which can be reduced for these simple wave solutions to a system of ordinary differential equations which coincide with those derived by Ovsyannikov for the two-layer fluid dynamics. We solve the Ovsyannikov system for two typical situations of large and small difference between interspecies and intraspecies nonlinear interaction constants. Our analytic results are confirmed by numerical simulations.

On an aggregation in birth-and-death stochastic dynamics

NASA Astrophysics Data System (ADS)

Finkelshtein, Dmitri; Kondratiev, Yuri; Kutoviy, Oleksandr; Zhizhina, Elena

2014-06-01

We consider birth-and-death stochastic dynamics of particle systems with attractive interaction. The heuristic generator of the dynamics has a constant birth rate and density-dependent decreasing death rate. The corresponding statistical dynamics is constructed. Using the Vlasov-type scaling we derive the limiting mesoscopic evolution and prove that this evolution propagates chaos. We study a nonlinear non-local kinetic equation for the first correlation function (density of population). The existence of uniformly bounded solutions as well as solutions growing inside of a bounded domain and expanding in the space are shown. These solutions describe two regimes in the mesoscopic system: regulation and aggregation.

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

DOE PAGES

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; ...

2015-11-12

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

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

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

Model dynamics for quantum computing

NASA Astrophysics Data System (ADS)

Tabakin, Frank

2017-08-01

A model master equation suitable for quantum computing dynamics is presented. In an ideal quantum computer (QC), a system of qubits evolves in time unitarily and, by virtue of their entanglement, interfere quantum mechanically to solve otherwise intractable problems. In the real situation, a QC is subject to decoherence and attenuation effects due to interaction with an environment and with possible short-term random disturbances and gate deficiencies. The stability of a QC under such attacks is a key issue for the development of realistic devices. We assume that the influence of the environment can be incorporated by a master equation that includes unitary evolution with gates, supplemented by a Lindblad term. Lindblad operators of various types are explored; namely, steady, pulsed, gate friction, and measurement operators. In the master equation, we use the Lindblad term to describe short time intrusions by random Lindblad pulses. The phenomenological master equation is then extended to include a nonlinear Beretta term that describes the evolution of a closed system with increasing entropy. An external Bath environment is stipulated by a fixed temperature in two different ways. Here we explore the case of a simple one-qubit system in preparation for generalization to multi-qubit, qutrit and hybrid qubit-qutrit systems. This model master equation can be used to test the stability of memory and the efficacy of quantum gates. The properties of such hybrid master equations are explored, with emphasis on the role of thermal equilibrium and entropy constraints. Several significant properties of time-dependent qubit evolution are revealed by this simple study.

The Dynamics of a Viscous Gas Ring around a Kerr Black Hole

NASA Astrophysics Data System (ADS)

Riffert, H.

2000-01-01

The dynamics of a rotationally symmetric viscous gas ring around a Kerr black hole is calculated in the thin-disk approximation. An evolution equation for the surface density Σ(t,r) is derived, which is the relativistic extension of a classical equation obtained by R. Lüst. A singular point appears at the radius of the last stable circular orbit r=rc. The nature of this point is investigated, and it turns out that the solution is always bounded at rc, and no boundary condition can be obtained at this radius. A unique solution of an initial value problem requires a matching condition at rc which follows from the flow structure between rc and the horizon. In the model presented here, the density in this domain is zero, and the resulting boundary condition leads to a vanishing shear stress at r=rc, which is the condition used in the standard stationary thin-disk model of Novikov & Thorne. Numerical solutions of the evolution equation are presented for two different angular momenta of the black hole. The time evolution of the resulting accretion rate depends strongly on this angular momentum.

CFD modeling of space-time evolution of fast pyrolysis products in a bench-scale fluidized-bed reactor

USDA-ARS?s Scientific Manuscript database

A model for the evolution of pyrolysis products in a fluidized bed has been developed. In this study the unsteady constitutive transport equations for inert gas flow and decomposition kinetics were modeled using the commercial computational fluid dynamics (CFD) software FLUENT-12. The model system d...

Qubit models of weak continuous measurements: markovian conditional and open-system dynamics

NASA Astrophysics Data System (ADS)

Gross, Jonathan A.; Caves, Carlton M.; Milburn, Gerard J.; Combes, Joshua

2018-04-01

In this paper we approach the theory of continuous measurements and the associated unconditional and conditional (stochastic) master equations from the perspective of quantum information and quantum computing. We do so by showing how the continuous-time evolution of these master equations arises from discretizing in time the interaction between a system and a probe field and by formulating quantum-circuit diagrams for the discretized evolution. We then reformulate this interaction by replacing the probe field with a bath of qubits, one for each discretized time segment, reproducing all of the standard quantum-optical master equations. This provides an economical formulation of the theory, highlighting its fundamental underlying assumptions.

Rosenzweig instability in a thin layer of a magnetic fluid

NASA Astrophysics Data System (ADS)

Korovin, V. M.

2013-12-01

A simple mathematical model of the initial stage of nonlinear evolution of the Rosenzweig instability in a thin layer of a nonlinearly magnetized viscous ferrofluid coating a horizontal nonmagnetizable plate is constructed on the basis of the system of equations and boundary conditions of ferrofluid dynamics. A dispersion relation is derived and analyzed using the linearized equations of this model. The critical magnetization of the initial layer with a flat free surface, the threshold wavenumber, and the characteristic time of evolution of the most rapidly growing mode are determined. The equation for the neutral stability curve, which is applicable for any physically admissible law of magnetization of a ferrofluid, is derived analytically.

Parametric resonant triad interactions in a free shear layer

NASA Technical Reports Server (NTRS)

Mallier, R.; Maslowe, S. A.

1993-01-01

We investigate the weakly nonlinear evolution of a triad of nearly-neutral modes superimposed on a mixing layer with velocity profile u bar equals Um + tanh y. The perturbation consists of a plane wave and a pair of oblique waves each inclined at approximately 60 degrees to the mean flow direction. Because the evolution occurs on a relatively fast time scale, the critical layer dynamics dominate the process and the amplitude evolution of the oblique waves is governed by an integro-differential equation. The long-time solution of this equation predicts very rapid (exponential of an exponential) amplification and we discuss the pertinence of this result to vortex pairing phenomena in mixing layers.

Dynamic similarity in erosional processes

USGS Publications Warehouse

Scheidegger, A.E.

1963-01-01

A study is made of the dynamic similarity conditions obtaining in a variety of erosional processes. The pertinent equations for each type of process are written in dimensionless form; the similarity conditions can then easily be deduced. The processes treated are: raindrop action, slope evolution and river erosion. ?? 1963 Istituto Geofisico Italiano.

On the reduced dynamics of a subset of interacting bosonic particles

NASA Astrophysics Data System (ADS)

Gessner, Manuel; Buchleitner, Andreas

2018-03-01

The quantum dynamics of a subset of interacting bosons in a subspace of fixed particle number is described in terms of symmetrized many-particle states. A suitable partial trace operation over the von Neumann equation of an N-particle system produces a hierarchical expansion for the subdynamics of M ≤ N particles. Truncating this hierarchy with a pure product state ansatz yields the general, nonlinear coherent mean-field equation of motion. In the special case of a contact interaction potential, this reproduces the Gross-Pitaevskii equation. To account for incoherent effects on top of the mean-field evolution, we discuss possible extensions towards a second-order perturbation theory that accounts for interaction-induced decoherence in form of a nonlinear Lindblad-type master equation.

The evolution of hyperboloidal data with the dual foliation formalism: mathematical analysis and wave equation tests

NASA Astrophysics Data System (ADS)

Hilditch, David; Harms, Enno; Bugner, Marcus; Rüter, Hannes; Brügmann, Bernd

2018-03-01

A long-standing problem in numerical relativity is the satisfactory treatment of future null-infinity. We propose an approach for the evolution of hyperboloidal initial data in which the outer boundary of the computational domain is placed at infinity. The main idea is to apply the ‘dual foliation’ formalism in combination with hyperboloidal coordinates and the generalized harmonic gauge formulation. The strength of the present approach is that, following the ideas of Zenginoğlu, a hyperboloidal layer can be naturally attached to a central region using standard coordinates of numerical relativity applications. Employing a generalization of the standard hyperboloidal slices, developed by Calabrese et al, we find that all formally singular terms take a trivial limit as we head to null-infinity. A byproduct is a numerical approach for hyperboloidal evolution of nonlinear wave equations violating the null-condition. The height-function method, used often for fixed background spacetimes, is generalized in such a way that the slices can be dynamically ‘waggled’ to maintain the desired outgoing coordinate lightspeed precisely. This is achieved by dynamically solving the eikonal equation. As a first numerical test of the new approach we solve the 3D flat space scalar wave equation. The simulations, performed with the pseudospectral bamps code, show that outgoing waves are cleanly absorbed at null-infinity and that errors converge away rapidly as resolution is increased.

Analogy between the Navier-Stokes equations and Maxwell's equations: Application to turbulence

NASA Astrophysics Data System (ADS)

Marmanis, Haralambos

1998-06-01

A new theory of turbulence is initiated, based on the analogy between electromagnetism and turbulent hydrodynamics, for the purpose of describing the dynamical behavior of averaged flow quantities in incompressible fluid flows of high Reynolds numbers. The starting point is the recognition that the vorticity (w=∇×u) and the Lamb vector (l=w×u) should be taken as the kernel of a dynamical theory of turbulence. The governing equations for these fields can be obtained by the Navier-Stokes equations, which underlie the whole evolution. Then whatever parts are not explicitly expressed as a function of w or l only are gathered and treated as source terms. This is done by introducing the concepts of turbulent charge and turbulent current. Thus we are led to a closed set of linear equations for the averaged field quantities. The premise is that the earlier introduced sources will be apt for modeling, in the sense that their distribution will depend only on the geometry and the total energetics of the flow. The dynamics described in the preceding manner is what we call the metafluid dynamics.

An evolution infinity Laplace equation modelling dynamic elasto-plastic torsion

NASA Astrophysics Data System (ADS)

Messelmi, Farid

2017-12-01

We consider in this paper a parabolic partial differential equation involving the infinity Laplace operator and a Leray-Lions operator with no coercitive assumption. We prove the existence and uniqueness of the corresponding approached problem and we show that at the limit the solution solves the parabolic variational inequality arising in the elasto-plastic torsion problem.

Estimating the time evolution of NMR systems via a quantum-speed-limit-like expression

NASA Astrophysics Data System (ADS)

Villamizar, D. V.; Duzzioni, E. I.; Leal, A. C. S.; Auccaise, R.

2018-05-01

Finding the solutions of the equations that describe the dynamics of a given physical system is crucial in order to obtain important information about its evolution. However, by using estimation theory, it is possible to obtain, under certain limitations, some information on its dynamics. The quantum-speed-limit (QSL) theory was originally used to estimate the shortest time in which a Hamiltonian drives an initial state to a final one for a given fidelity. Using the QSL theory in a slightly different way, we are able to estimate the running time of a given quantum process. For that purpose, we impose the saturation of the Anandan-Aharonov bound in a rotating frame of reference where the state of the system travels slower than in the original frame (laboratory frame). Through this procedure it is possible to estimate the actual evolution time in the laboratory frame of reference with good accuracy when compared to previous methods. Our method is tested successfully to predict the time spent in the evolution of nuclear spins 1/2 and 3/2 in NMR systems. We find that the estimated time according to our method is better than previous approaches by up to four orders of magnitude. One disadvantage of our method is that we need to solve a number of transcendental equations, which increases with the system dimension and parameter discretization used to solve such equations numerically.

Stochastic modeling of mode interactions via linear parabolized stability equations

NASA Astrophysics Data System (ADS)

Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo

2017-11-01

Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.

Comet Gas and Dust Dynamics Modeling

NASA Technical Reports Server (NTRS)

Von Allmen, Paul A.; Lee, Seungwon

2010-01-01

This software models the gas and dust dynamics of comet coma (the head region of a comet) in order to support the Microwave Instrument for Rosetta Orbiter (MIRO) project. MIRO will study the evolution of the comet 67P/Churyumov-Gerasimenko's coma system. The instrument will measure surface temperature, gas-production rates and relative abundances, and velocity and excitation temperatures of each species along with their spatial temporal variability. This software will use these measurements to improve the understanding of coma dynamics. The modeling tool solves the equation of motion of a dust particle, the energy balance equation of the dust particle, the continuity equation for the dust and gas flow, and the dust and gas mixture energy equation. By solving these equations numerically, the software calculates the temperature and velocity of gas and dust as a function of time for a given initial gas and dust production rate, and a dust characteristic parameter that measures the ability of a dust particle to adjust its velocity to the local gas velocity. The software is written in a modular manner, thereby allowing the addition of more dynamics equations as needed. All of the numerical algorithms are added in-house and no third-party libraries are used.

The Dominance of Dynamic Barlike Instabilities in the Evolution of a Massive Stellar Core Collapse That ``Fizzles''

NASA Astrophysics Data System (ADS)

Imamura, James N.; Durisen, Richard H.

2001-03-01

Core collapse in a massive rotating star may halt at subnuclear density if the core contains angular momentum J>~1049 g cm2 s-1. An aborted collapse can lead to the formation of a rapidly rotating equilibrium object, which, because of its high electron fraction, Ye>0.4, and high entropy per baryon, Sb/k~1-2, is secularly and dynamically stable. The further evolution of such a ``fizzler'' is driven by deleptonization and cooling of the hot, dense material. These processes cause the fizzler both to contract toward neutron star densities and to spin up, driving it toward instability points of the barlike modes. Using linear stability analyses to study the latter case, we find that the stability properties of fizzlers are similar to those of Maclaurin spheroids and polytropes despite the nonpolytropic nature and extreme compressibility of the fizzler equation of state. For fizzlers with the specific angular momentum distribution of the Maclaurin spheroids, secular and dynamic barlike instabilities set in at T/|W|~0.14 and 0.27, respectively, where T is the rotational kinetic energy and W is the gravitational energy of the fizzler, the same limits as found for Maclaurin spheroids. For fizzlers in which angular momentum is more concentrated toward the equator, the secular stability limits drop dramatically. For the most extreme angular momentum distribution we consider, the secular stability limit for the barlike modes falls to T/|W|~0.038, compared with T/|W|~0.09-0.10 for the most extreme polytropic cases known previously (Imamura et al.). For fixed equation-of-state parameters, the secular and dynamic stability limits occur at roughly constant mass over the range of typical fizzler central densities. Deleptonization and cooling decrease the limiting masses on timescales shorter than the growth time for secular instability. Consequently, unless an evolving fizzler reaches neutron star densities first, it will always encounter dynamic barlike instabilities before secular instabilities have time to grow. Quasi-linear analysis shows that the angular momentum loss during the early nonlinear evolution of the dynamic barlike instability is dominated by Newtonian self-interaction gravitational torques rather than by the emission of gravitational wave (GW) radiation. GW emission may dominate after the initial dynamic evolutionary phase ends. Nonlinear hydrodynamics simulations with a proper equation of state will be required to determine the ultimate outcome of such evolutions and to refine predictions of GW production by barlike instabilities.

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.

A Korteweg-de Vries description of dark solitons in polariton superfluids

NASA Astrophysics Data System (ADS)

Carretero-González, R.; Cuevas-Maraver, J.; Frantzeskakis, D. J.; Horikis, T. P.; Kevrekidis, P. G.; Rodrigues, A. S.

2017-12-01

We study the dynamics of dark solitons in an incoherently pumped exciton-polariton condensate by means of a system composed of a generalized open-dissipative Gross-Pitaevskii equation for the polaritons' wavefunction and a rate equation for the exciton reservoir density. Considering a perturbative regime of sufficiently small reservoir excitations, we use the reductive perturbation method, to reduce the system to a Korteweg-de Vries (KdV) equation with linear loss. This model is used to describe the analytical form and the dynamics of dark solitons. We show that the polariton field supports decaying dark soliton solutions with a decay rate determined analytically in the weak pumping regime. We also find that the dark soliton evolution is accompanied by a shelf, whose dynamics follows qualitatively the effective KdV picture.

The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts

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

Neill, Duff

Here, we develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. Furthermore, this equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We also compute the decay width analytically, giving a closed form expression, and find it to be jet geometrymore » independent, up to the number of legs of the dipole in the active jet. By enabling the asymptotic expansion we find that the perturbative seed is correct; we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures. Indeed, we recover the equations of saturation physics in the final state dynamics of QCD.« less

The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts

DOE PAGES

Neill, Duff

2017-01-25

Here, we develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. Furthermore, this equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We also compute the decay width analytically, giving a closed form expression, and find it to be jet geometrymore » independent, up to the number of legs of the dipole in the active jet. By enabling the asymptotic expansion we find that the perturbative seed is correct; we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures. Indeed, we recover the equations of saturation physics in the final state dynamics of QCD.« less

Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements

NASA Astrophysics Data System (ADS)

Zander, C.; Plastino, A. R.; Díaz-Alonso, J.

2015-11-01

We investigate time-dependent solutions for a non-linear Schrödinger equation recently proposed by Nassar and Miret-Artés (NM) to describe the continuous measurement of the position of a quantum particle (Nassar, 2013; Nassar and Miret-Artés, 2013). Here we extend these previous studies in two different directions. On the one hand, we incorporate a potential energy term in the NM equation and explore the corresponding wave packet dynamics, while in the previous works the analysis was restricted to the free-particle case. On the other hand, we investigate time-dependent solutions while previous studies focused on a stationary one. We obtain exact wave packet solutions for linear and quadratic potentials, and approximate solutions for the Morse potential. The free-particle case is also revisited from a time-dependent point of view. Our analysis of time-dependent solutions allows us to determine the stability properties of the stationary solution considered in Nassar (2013), Nassar and Miret-Artés (2013). On the basis of these results we reconsider the Bohmian approach to the NM equation, taking into account the fact that the evolution equation for the probability density ρ =| ψ | 2 is not a continuity equation. We show that the effect of the source term appearing in the evolution equation for ρ has to be explicitly taken into account when interpreting the NM equation from a Bohmian point of view.

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

Evolution of wealth in a non-conservative economy driven by local Nash equilibria.

PubMed

Degond, Pierre; Liu, Jian-Guo; Ringhofer, Christian

2014-11-13

We develop a model for the evolution of wealth in a non-conservative economic environment, extending a theory developed in Degond et al. (2014 J. Stat. Phys. 154, 751-780 (doi:10.1007/s10955-013-0888-4)). The model considers a system of rational agents interacting in a game-theoretical framework. This evolution drives the dynamics of the agents in both wealth and economic configuration variables. The cost function is chosen to represent a risk-averse strategy of each agent. That is, the agent is more likely to interact with the market, the more predictable the market, and therefore the smaller its individual risk. This yields a kinetic equation for an effective single particle agent density with a Nash equilibrium serving as the local thermodynamic equilibrium. We consider a regime of scale separation where the large-scale dynamics is given by a hydrodynamic closure with this local equilibrium. A class of generalized collision invariants is developed to overcome the difficulty of the non-conservative property in the hydrodynamic closure derivation of the large-scale dynamics for the evolution of wealth distribution. The result is a system of gas dynamics-type equations for the density and average wealth of the agents on large scales. We recover the inverse Gamma distribution, which has been previously considered in the literature, as a local equilibrium for particular choices of the cost function. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Continuous measurement of an atomic current

NASA Astrophysics Data System (ADS)

Laflamme, C.; Yang, D.; Zoller, P.

2017-04-01

We are interested in dynamics of quantum many-body systems under continuous observation, and its physical realizations involving cold atoms in lattices. In the present work we focus on continuous measurement of atomic currents in lattice models, including the Hubbard model. We describe a Cavity QED setup, where measurement of a homodyne current provides a faithful representation of the atomic current as a function of time. We employ the quantum optical description in terms of a diffusive stochastic Schrödinger equation to follow the time evolution of the atomic system conditional to observing a given homodyne current trajectory, thus accounting for the competition between the Hamiltonian evolution and measurement back action. As an illustration, we discuss minimal models of atomic dynamics and continuous current measurement on rings with synthetic gauge fields, involving both real space and synthetic dimension lattices (represented by internal atomic states). Finally, by "not reading" the current measurements the time evolution of the atomic system is governed by a master equation, where—depending on the microscopic details of our CQED setups—we effectively engineer a current coupling of our system to a quantum reservoir. This provides interesting scenarios of dissipative dynamics generating "dark" pure quantum many-body states.

Aging dynamics of quantum spin glasses of rotors

NASA Astrophysics Data System (ADS)

Kennett, Malcolm P.; Chamon, Claudio; Ye, Jinwu

2001-12-01

We study the long time dynamics of quantum spin glasses of rotors using the nonequilibrium Schwinger-Keldysh formalism. These models are known to have a quantum phase transition from a paramagnetic to a spin-glass phase, which we approach by looking at the divergence of the spin-relaxation rate at the transition point. In the aging regime, we determine the dynamical equations governing the time evolution of the spin response and correlation functions, and show that all terms in the equations that arise solely from quantum effects are irrelevant at long times under time reparametrization group (RPG) transformations. At long times, quantum effects enter only through the renormalization of the parameters in the dynamical equations for the classical counterpart of the rotor model. Consequently, quantum effects only modify the out-of-equilibrium fluctuation-dissipation relation (OEFDR), i.e. the ratio X between the temperature and the effective temperature, but not the form of the classical OEFDR.

On a generalized Ablowitz-Kaup-Newell-Segur hierarchy in inhomogeneities of media: soliton solutions and wave propagation influenced from coefficient functions and scattering data

NASA Astrophysics Data System (ADS)

Zhang, Sheng; Hong, Siyu

2018-07-01

In this paper, a generalized Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy in inhomogeneities of media described by variable coefficients is investigated, which includes some important nonlinear evolution equations as special cases, for example, the celebrated Korteweg-de Vries equation modeling waves on shallow water surfaces. To be specific, the known AKNS spectral problem and its time evolution equation are first generalized by embedding a finite number of differentiable and time-dependent functions. Starting from the generalized AKNS spectral problem and its generalized time evolution equation, a generalized AKNS hierarchy with variable coefficients is then derived. Furthermore, based on a systematic analysis on the time dependence of related scattering data of the generalized AKNS spectral problem, exact solutions of the generalized AKNS hierarchy are formulated through the inverse scattering transform method. In the case of reflectionless potentials, the obtained exact solutions are reduced to n-soliton solutions. It is graphically shown that the dynamical evolutions of such soliton solutions are influenced by not only the time-dependent coefficients but also the related scattering data in the process of propagations.

Solutions of the KPI equation with smooth initial data

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A.

1994-06-01

The solution $u(t,x,y)$ of the Kadomtsev--Petviashvili I (KPI) equation with given initial data $u(0,x,y)$ belonging to the Schwartz space is considered. No additional special constraints, usually considered in literature, as $\\int\\!dx\\,u(0,x,y)=0$ are required to be satisfied by the initial data. The problem is completely solved in the framework of the spectral transform theory and it is shown that $u(t,x,y)$ satisfies a special evolution version of the KPI equation and that, in general, $\\partial_t u(t,x,y)$ has different left and right limits at the initial time $t=0$. The conditions of the type $\\int\\!dx\\,u(t,x,y)=0$, $\\int\\!dx\\,xu_y(t,x,y)=0$ and so on (first, second, etc. `constraints') are dynamically generated by the evolution equation for $t\

Anisotropic evolution of 5D Friedmann-Robertson-Walker spacetime

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

Middleton, Chad A.; Stanley, Ethan

2011-10-15

We examine the time evolution of the five-dimensional Einstein field equations subjected to a flat, anisotropic Robertson-Walker metric, where the 3D and higher-dimensional scale factors are allowed to dynamically evolve at different rates. By adopting equations of state relating the 3D and higher-dimensional pressures to the density, we obtain an exact expression relating the higher-dimensional scale factor to a function of the 3D scale factor. This relation allows us to write the Friedmann-Robertson-Walker field equations exclusively in terms of the 3D scale factor, thus yielding a set of 4D effective Friedmann-Robertson-Walker field equations. We examine the effective field equations inmore » the general case and obtain an exact expression relating a function of the 3D scale factor to the time. This expression involves a hypergeometric function and cannot, in general, be inverted to yield an analytical expression for the 3D scale factor as a function of time. When the hypergeometric function is expanded for small and large arguments, we obtain a generalized treatment of the dynamical compactification scenario of Mohammedi [Phys. Rev. D 65, 104018 (2002)] and the 5D vacuum solution of Chodos and Detweiler [Phys. Rev. D 21, 2167 (1980)], respectively. By expanding the hypergeometric function near a branch point, we obtain the perturbative solution for the 3D scale factor in the small time regime. This solution exhibits accelerated expansion, which, remarkably, is independent of the value of the 4D equation of state parameter w. This early-time epoch of accelerated expansion arises naturally out of the anisotropic evolution of 5D spacetime when the pressure in the extra dimension is negative and offers a possible alternative to scalar field inflationary theory.« less

Quasi-static evolution of coronal magnetic fields

NASA Technical Reports Server (NTRS)

Longcope, D. W.; Sudan, R. N.

1992-01-01

A formalism is developed to describe the purely quasi-static part of the evolution of a coronal loop driven by its footpoints. This is accomplished under assumptions of a long, thin loop. The quasi-static equations reveal the possibility for sudden 'loss of equilibrium' at which time the system evolves dynamically rather than quasi-statically. Such quasi-static crises produce high-frequency Alfven waves and, in conjunction with Alfven wave dissipation models, form a viable coronal heating mechanism. Furthermore, an approximate solution to the quasi-static equations by perturbation method verifies the development of small-scale spatial current structure.

Conditional and unconditional Gaussian quantum dynamics

NASA Astrophysics Data System (ADS)

Genoni, Marco G.; Lami, Ludovico; Serafini, Alessio

2016-07-01

This article focuses on the general theory of open quantum systems in the Gaussian regime and explores a number of diverse ramifications and consequences of the theory. We shall first introduce the Gaussian framework in its full generality, including a classification of Gaussian (also known as 'general-dyne') quantum measurements. In doing so, we will give a compact proof for the parametrisation of the most general Gaussian completely positive map, which we believe to be missing in the existing literature. We will then move on to consider the linear coupling with a white noise bath, and derive the diffusion equations that describe the evolution of Gaussian states under such circumstances. Starting from these equations, we outline a constructive method to derive general master equations that apply outside the Gaussian regime. Next, we include the general-dyne monitoring of the environmental degrees of freedom and recover the Riccati equation for the conditional evolution of Gaussian states. Our derivation relies exclusively on the standard quantum mechanical update of the system state, through the evaluation of Gaussian overlaps. The parametrisation of the conditional dynamics we obtain is novel and, at variance with existing alternatives, directly ties in to physical detection schemes. We conclude our study with two examples of conditional dynamics that can be dealt with conveniently through our formalism, demonstrating how monitoring can suppress the noise in optical parametric processes as well as stabilise systems subject to diffusive scattering.

The Evolution of Finite Amplitude Wavetrains in Plane Channel Flow

NASA Technical Reports Server (NTRS)

Hewitt, R. E.; Hall, P.

1996-01-01

We consider a viscous incompressible fluid flow driven between two parallel plates by a constant pressure gradient. The flow is at a finite Reynolds number, with an 0(l) disturbance in the form of a traveling wave. A phase equation approach is used to discuss the evolution of slowly varying fully nonlinear two dimensional wavetrains. We consider uniform wavetrains in detail, showing that the development of a wavenumber perturbation is governed by Burgers equation in most cases. The wavenumber perturbation theory, constructed using the phase equation approach for a uniform wavetrain, is shown to be distinct from an amplitude perturbation expansion about the periodic flow. In fact we show that the amplitude equation contains only linear terms and is simply the heat equation. We review, briefly, the well known dynamics of Burgers equation, which imply that both shock structures and finite time singularities of the wavenumber perturbation can occur with respect to the slow scales. Numerical computations have been performed to identify areas of the (wavenumber, Reynolds number, energy) neutral surface for which each of these possibilities can occur. We note that the evolution equations will breakdown under certain circumstances, in particular for a weakly nonlinear secondary flow. Finally we extend the theory to three dimensions and discuss the limit of a weak spanwise dependence for uniform wavetrains, showing that two functions are required to describe the evolution. These unknowns are a phase and a pressure function which satisfy a pair of linearly coupled partial differential equations. The results obtained from applying the same analysis to the fully three dimensional problem are included as an appendix.

Generalized Master Equation with Non-Markovian Multichromophoric Förster Resonance Energy Transfer for Modular Exciton Densities

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

Jang, Seogjoo; Hoyer, Stephan; Fleming, Graham

2014-10-31

A generalized master equation (GME) governing quantum evolution of modular exciton density (MED) is derived for large scale light harvesting systems composed of weakly interacting modules of multiple chromophores. The GME-MED offers a practical framework to incorporate real time coherent quantum dynamics calculations of small length scales into dynamics over large length scales, and also provides a non-Markovian generalization and rigorous derivation of the Pauli master equation employing multichromophoric Förster resonance energy transfer rates. A test of the GME-MED for four sites of the Fenna-Matthews-Olson complex demonstrates how coherent dynamics of excitonic populations over coupled chromophores can be accurately describedmore » by transitions between subgroups (modules) of delocalized excitons. Application of the GME-MED to the exciton dynamics between a pair of light harvesting complexes in purple bacteria demonstrates its promise as a computationally efficient tool to investigate large scale exciton dynamics in complex environments.« less

Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations.

PubMed

Schüler, D; Alonso, S; Torcini, A; Bär, M

2014-12-01

Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexisting static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.

Interactive mixture of inhomogeneous dark fluids driven by dark energy: a dynamical system analysis

NASA Astrophysics Data System (ADS)

Izquierdo, Germán; Blanquet-Jaramillo, Roberto C.; Sussman, Roberto A.

2018-03-01

We examine the evolution of an inhomogeneous mixture of non-relativistic pressureless cold dark matter (CDM), coupled to dark energy (DE) characterised by the equation of state parameter w<-1/3, with the interaction term proportional to the DE density. This coupled mixture is the source of a spherically symmetric Lemaître-Tolman-Bondi (LTB) metric admitting an asymptotic Friedman-Lemaître-Robertson-Walker (FLRW) background. Einstein's equations reduce to a 5-dimensional autonomous dynamical system involving quasi-local variables related to suitable averages of covariant scalars and their fluctuations. The phase space evolution around the critical points (past/future attractors and five saddles) is examined in detail. For all parameter values and both directions of energy flow (CDM to DE and DE to CDM) the phase space trajectories are compatible with a physically plausible early cosmic times behaviour near the past attractor. This result compares favourably with mixtures with interaction driven by the CDM density, whose past evolution is unphysical for DE to CDM energy flow. Numerical examples are provided describing the evolution of an initial profile that can be associated with idealised structure formation scenarios.

Relations between nonlinear Riccati equations and other equations in fundamental physics

NASA Astrophysics Data System (ADS)

Schuch, Dieter

2014-10-01

Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract "quantizations" such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown.

Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations.

PubMed

Vorobev, Anatoliy

2010-11-01

We use the Cahn-Hilliard approach to model the slow dissolution dynamics of binary mixtures. An important peculiarity of the Cahn-Hilliard-Navier-Stokes equations is the necessity to use the full continuity equation even for a binary mixture of two incompressible liquids due to dependence of mixture density on concentration. The quasicompressibility of the governing equations brings a short time-scale (quasiacoustic) process that may not affect the slow dynamics but may significantly complicate the numerical treatment. Using the multiple-scale method we separate the physical processes occurring on different time scales and, ultimately, derive the equations with the filtered-out quasiacoustics. The derived equations represent the Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations. This approximation can be further employed as a universal theoretical model for an analysis of slow thermodynamic and hydrodynamic evolution of the multiphase systems with strongly evolving and diffusing interfacial boundaries, i.e., for the processes involving dissolution/nucleation, evaporation/condensation, solidification/melting, polymerization, etc.

Dynamics of one- and two-dimensional fronts in a bistable equation with time-delayed global feedback: Propagation failure and control mechanisms

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

Boubendir, Yassine; Mendez, Vicenc; Rotstein, Horacio G.

2010-09-15

We study the evolution of fronts in a bistable equation with time-delayed global feedback in the fast reaction and slow diffusion regime. This equation generalizes the Hodgkin-Grafstein and Allen-Cahn equations. We derive a nonlinear equation governing the motion of fronts, which includes a term with delay. In the one-dimensional case this equation is linear. We study the motion of one- and two-dimensional fronts, finding a much richer dynamics than for the previously studied cases (without time-delayed global feedback). We explain the mechanism by which localized fronts created by inhibitory global coupling loose stability in a Hopf bifurcation as the delaymore » time increases. We show that for certain delay times, the prevailing phase is different from that corresponding to the system in the absence of global coupling. Numerical simulations of the partial differential equation are in agreement with the analytical predictions.« less

Using some results about the Lie evolution of differential operators to obtain the Fokker-Planck equation for non-Hamiltonian dynamical systems of interest

NASA Astrophysics Data System (ADS)

Bianucci, Marco

2018-05-01

Finding the generalized Fokker-Planck Equation (FPE) for the reduced probability density function of a subpart of a given complex system is a classical issue of statistical mechanics. Zwanzig projection perturbation approach to this issue leads to the trouble of resumming a series of commutators of differential operators that we show to correspond to solving the Lie evolution of first order differential operators along the unperturbed Liouvillian of the dynamical system of interest. In this paper, we develop in a systematic way the procedure to formally solve this problem. In particular, here we show which the basic assumptions are, concerning the dynamical system of interest, necessary for the Lie evolution to be a group on the space of first order differential operators, and we obtain the coefficients of the so-evolved operators. It is thus demonstrated that if the Liouvillian of the system of interest is not a first order differential operator, in general, the FPE structure breaks down and the master equation contains all the power of the partial derivatives, up to infinity. Therefore, this work shed some light on the trouble of the ubiquitous emergence of both thermodynamics from microscopic systems and regular regression laws at macroscopic scales. However these results are very general and can be applied also in other contexts that are non-Hamiltonian as, for example, geophysical fluid dynamics, where important events, like El Niño, can be considered as large time scale phenomena emerging from the observation of few ocean degrees of freedom of a more complex system, including the interaction with the atmosphere.

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.

Numerical modeling of the Madison Dynamo Experiment.

NASA Astrophysics Data System (ADS)

Bayliss, R. A.; Wright, J. C.; Forest, C. B.; O'Connell, R.

2002-11-01

Growth, saturation and turbulent evolution of the Madison dynamo experiment is investigated numerically using a 3-D pseudo-spectral simulation of the MHD equations; results of the simulations will be compared to results obtained from the experiment. The code, Dynamo (Fortran90), allows for full evolution of the magnetic and velocity fields. The induction equation governing B and the curl of the momentum equation governing V are separately or simultaneously solved. The code uses a spectral representation via spherical harmonic basis functions of the vector fields in longitude and latitude, and fourth order finite differences in the radial direction. The magnetic field evolution has been benchmarked against the laminar kinematic dynamo predicted by M.L. Dudley and R.W. James (M.L. Dudley and R.W. James, Time-dependent kinematic dynamos with stationary flows, Proc. R. Soc. Lond. A 425, p. 407 (1989)). Power balance in the system has been verified in both mechanically driven and perturbed hydrodynamic, kinematic, and dynamic cases. Evolution of the vacuum magnetic field has been added to facilitate comparison with the experiment. Modeling of the Madison Dynamo eXperiment will be presented.

On the breakup of viscous liquid threads

NASA Technical Reports Server (NTRS)

Papageorgiou, Demetrios T.

1995-01-01

A one-dimensional model evolution equation is used to describe the nonlinear dynamics that can lead to the breakup of a cylindrical thread of Newtonian fluid when capillary forces drive the motion. The model is derived from the Stokes equations by use of rational asymptotic expansions and under a slender jet approximation. The equations are solved numerically and the jet radius is found to vanish after a finite time yielding breakup. The slender jet approximation is valid throughout the evolution leading to pinching. The model admits self-similar pinching solutions which yield symmetric shapes at breakup. These solutions are shown to be the ones selected by the initial boundary value problem, for general initial conditions. Further more, the terminal state of the model equation is shown to be identical to that predicted by a theory which looks for singular pinching solutions directly from the Stokes equations without invoking the slender jet approximation throughout the evolution. It is shown quantitatively, therefore, that the one-dimensional model gives a consistent terminal state with the jet shape being locally symmetric at breakup. The asymptotic expansion scheme is also extended to include unsteady and inerticial forces in the momentum equations to derive an evolution system modelling the breakup of Navier-Stokes jets. The model is employed in extensive simulations to compute breakup times for different initial conditions; satellite drop formation is also supported by the model and the dependence of satellite drop volumes on initial conditions is studied.

Control of ITBs in Fusion Self-Heated Plasmas

NASA Astrophysics Data System (ADS)

Panta, Soma; Newman, David; Terry, Paul; Sanchez, Raul

2015-11-01

Simple dynamical models have been able to capture a remarkable amount of the dynamics of the transport barriers found in many devices, including the often disconnected nature of the electron thermal transport channel sometimes observed in the presence of a standard (``ion channel'') barrier. By including in this rich though simple dynamic transport model an evolution equation for electron fluctuations we have previously investigated the interaction between the formation of the standard ion channel barrier and the somewhat less common electron channel barrier. The electron channel formation and evolution is even more sensitive to the alignment of the various gradients making up the sheared radial electric field then the ion barrier is. Because of this sensitivity and coupling of the barrier dynamics, the dynamic evolution of the fusion self-heating profile can have a significant impact on the barrier location and dynamics. To investigate this, self-heating has been added this model and the impact of the self-heating on the formation and controllability of the various barriers is explored. It has been found that the evolution of the heating profiles can suppress or collapse the electron channel barrier. NBI and RF schemes will be investigated for profile/barrier control.

About Tidal Evolution of Quasi-Periodic Orbits of Satellites

NASA Astrophysics Data System (ADS)

Ershkov, Sergey V.

2017-06-01

Tidal interactions between Planet and its satellites are known to be the main phenomena, which are determining the orbital evolution of the satellites. The modern ansatz in the theory of tidal dissipation in Saturn was developed previously by the international team of scientists from various countries in the field of celestial mechanics. Our applying to the theory of tidal dissipation concerns the investigating of the system of ODE-equations (ordinary differential equations) that govern the orbital evolution of the satellites; such an extremely non-linear system of 2 ordinary differential equations describes the mutual internal dynamics for the eccentricity of the orbit along with involving the semi-major axis of the proper satellite into such a monstrous equations. In our derivation, we have presented the elegant analytical solutions to the system above; so, the motivation of our ansatz is to transform the previously presented system of equations to the convenient form, in which the minimum of numerical calculations are required to obtain the final solutions. Preferably, it should be the analytical solutions; we have presented the solution as a set of quasi- periodic cycles via re-inversing of the proper ultra- elliptical integral. It means a quasi-periodic character of the evolution of the eccentricity, of the semi-major axis for the satellite orbit as well as of the quasi-periodic character of the tidal dissipation in the Planet.

An Optimization Principle for Deriving Nonequilibrium Statistical Models of Hamiltonian Dynamics

NASA Astrophysics Data System (ADS)

Turkington, Bruce

2013-08-01

A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. Given a vector of resolved variables, selected to describe the macroscopic state of the system, a family of quasi-equilibrium probability densities on phase space corresponding to the resolved variables is employed as a statistical model, and the evolution of the mean resolved vector is estimated by optimizing over paths of these densities. Specifically, a cost function is constructed to quantify the lack-of-fit to the microscopic dynamics of any feasible path of densities from the statistical model; it is an ensemble-averaged, weighted, squared-norm of the residual that results from submitting the path of densities to the Liouville equation. The path that minimizes the time integral of the cost function determines the best-fit evolution of the mean resolved vector. The closed reduced equations satisfied by the optimal path are derived by Hamilton-Jacobi theory. When expressed in terms of the macroscopic variables, these equations have the generic structure of governing equations for nonequilibrium thermodynamics. In particular, the value function for the optimization principle coincides with the dissipation potential that defines the relation between thermodynamic forces and fluxes. The adjustable closure parameters in the best-fit reduced equations depend explicitly on the arbitrary weights that enter into the lack-of-fit cost function. Two particular model reductions are outlined to illustrate the general method. In each example the set of weights in the optimization principle contracts into a single effective closure parameter.

From the big five to the general factor of personality: a dynamic approach.

PubMed

Micó, Joan C; Amigó, Salvador; Caselles, Antonio

2014-10-28

An integrating and dynamic model of personality that allows predicting the response of the basic factors of personality, such as the Big Five Factors (B5F) or the general factor of personality (GFP) to acute doses of drug is presented in this paper. Personality has a dynamic nature, i.e., as a consequence of a stimulus, the GFP dynamics as well as each one of the B5F of personality dynamics can be explained by the same model (a system of three coupled differential equations). From this invariance hypothesis, a partial differential equation, whose solution relates the GFP with each one of the B5F, is deduced. From this dynamic approach, a co-evolution of the GFP and each one of the B5F occurs, rather than an unconnected evolution, as a consequence of the same stimulus. The hypotheses and deductions are validated through an experimental design centered on the individual, where caffeine is the considered stimulus. Thus, as much from a theoretical point of view as from an applied one, the models here proposed open a new perspective in the understanding and study of personality like a global system that interacts intimately with the environment, being a clear bet for the high level inter-disciplinary research.

Deducing multiple interfacial dynamics during polymeric foaming.

PubMed

Chandan, Mohammed Rehaan; Naskar, Nilanjon; Das, Anuja; Mukherjee, Rabibrata; Harikrishnan, Gopalakrishna Pillai

2018-06-15

Several interfacial phenomena are active during polymeric foaming, the dynamics of which significantly influence terminal stability, cell structure and in turn the thermo-mechanical properties of temporally evolved foam. Understanding these dynamics is important in achieving desired foam properties. Here, we introduce a method to simultaneously portray the time evolution of bubble growth, lamella thinning and Plateau border drainage, occurring during reactive polymeric foaming. In this method, we initially conduct bulk and surface shear rheology under polymerizing and non-foaming conditions. In a subsequent step, foaming experiments were conducted in a rheometer. The microscopic structural dimensions pertaining to the terminal values of the dynamics of each interfacial phenomena are then measured using a combination of scanning electron microscopy, optical microscopy and imaging ellipsometry, after the foaming is over. The measured surface and bulk rheological parameters are incorporated in time evolution equations that are derived from mass and momentum transport occurring when a model viscoelastic fluid is foamed by gas dispersion. Analytical and numerical solutions to these equations portray the dynamics. We demonstrate this method for a series of reactive polyurethane foams generated from different chemical sources. The effectiveness of our method is in simultaneously obtaining these dynamics that are difficult to directly monitor due to short active durations over multiple length scales.

Soliton switching in a site-dependent ferromagnet

NASA Astrophysics Data System (ADS)

Senjudarvannan, R.; Sathishkumar, P.; Vijayalakshmi, S.

2017-02-01

Switching of soliton in a ferromagnetic medium offers the possibility of developing a new innovative approach for information storage technologies. The nonlinear spin dynamics of a site-dependent Heisenberg ferromagnetic spin chain with Gilbert damping under the influence of external magnetic field is expressed in the form of the Landau-Lifshitz-Gilbert equation in the classical continuum limit. The corresponding evolution equation is developed through stereographic projection technique by projecting the unit sphere of spin onto a complex plane. The exact soliton solutions are constructed by solving the associated evolution equation through the modified extended tanh-function method. The impact of damping and external magnetic field on the magnetic soliton under the invariant inhomogeneity is investigated and finally, the magnetization switching in the form of shape changing solitons are demonstrated.

Three-dimensional simulations of thin ferro-fluid films and drops in magnetic fields

NASA Astrophysics Data System (ADS)

Conroy, Devin; Wray, Alex; Matar, Omar

2016-11-01

We consider the interfacial dynamics of a thin, ferrofluidic film flowing down an inclined substrate, under the action of a magnetic field, bounded above by an inviscid gas. The fluid is assumed to be weakly-conducting. Its dynamics are governed by a coupled system of the steady Maxwell's, the Navier-Stokes, and continuity equations. The magnetisation of the film is a function of the magnetic field, and is prescribed by a Langevin function. We make use of a long-wave reduction in order to solve for the dynamics of the pressure, velocity, and magnetic fields inside the film. The potential in the gas phase is solved with the use of Fourier Transforms. Imposition of appropriate interfacial conditions allows for the construction of an evolution equation for the interfacial shape, via use of the kinematic condition, and the magnetic field. We consider the three-dimensional evolution of the film to spawise perturbations by solving the non-linear equations numerically. The constant flux configuration is considered, which corresponds to a thin film and drop flowing down an incline, and a parametric study is performed to understand the effect of a magnetic field on the stability and structure of the formed drops. EPSRC UK platform Grant MACIPh (EP/L020564/1) and programme Grant MEMPHIS (EP/K003976/1).

A coarse-grained biophysical model of sequence evolution and the population size dependence of the speciation rate

PubMed Central

Khatri, Bhavin S.; Goldstein, Richard A.

2015-01-01

Speciation is fundamental to understanding the huge diversity of life on Earth. Although still controversial, empirical evidence suggests that the rate of speciation is larger for smaller populations. Here, we explore a biophysical model of speciation by developing a simple coarse-grained theory of transcription factor-DNA binding and how their co-evolution in two geographically isolated lineages leads to incompatibilities. To develop a tractable analytical theory, we derive a Smoluchowski equation for the dynamics of binding energy evolution that accounts for the fact that natural selection acts on phenotypes, but variation arises from mutations in sequences; the Smoluchowski equation includes selection due to both gradients in fitness and gradients in sequence entropy, which is the logarithm of the number of sequences that correspond to a particular binding energy. This simple consideration predicts that smaller populations develop incompatibilities more quickly in the weak mutation regime; this trend arises as sequence entropy poises smaller populations closer to incompatible regions of phenotype space. These results suggest a generic coarse-grained approach to evolutionary stochastic dynamics, allowing realistic modelling at the phenotypic level. PMID:25936759

Evolution of rogue waves in dusty plasmas

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

Tolba, R. E., E-mail: tolba-math@yahoo.com; El-Bedwehy, N. A., E-mail: nab-elbedwehy@yahoo.com; Moslem, W. M., E-mail: wmmoslem@hotmail.com

2015-04-15

The evolution of rogue waves associated with the dynamics of positively charged dust grains that interact with streaming electrons and ions is investigated. Using a perturbation method, the basic set of fluid equations is reduced to a nonlinear Schrödinger equation (NLSE). The rational solution of the NLSE is presented, which proposed as an effective tool for studying the rogue waves in Jupiter. It is found that the existence region of rogue waves depends on the dust-acoustic speed and the streaming densities of the ions and electrons. Furthermore, the supersonic rogue waves are much taller than the subsonic rogue waves bymore » ∼25 times.« less

Black hole evolution by spectral methods

NASA Astrophysics Data System (ADS)

Kidder, Lawrence E.; Scheel, Mark A.; Teukolsky, Saul A.; Carlson, Eric D.; Cook, Gregory B.

2000-10-01

Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite differencing. In this paper, we explore the use of a pseudospectral collocation (PSC) method for the evolution of a spherically symmetric black hole spacetime in one dimension using a hyperbolic formulation of Einstein's equations. We demonstrate that our PSC method is able to evolve a spherically symmetric black hole spacetime forever without enforcing constraints, even if we add dynamics via a Klein-Gordon scalar field. We find that, in contrast with finite-differencing methods, black hole excision is a trivial operation using PSC applied to a hyperbolic formulation of Einstein's equations. We discuss the extension of this method to three spatial dimensions.

Learning the dynamics of objects by optimal functional interpolation.

PubMed

Ahn, Jong-Hoon; Kim, In Young

2012-09-01

Many areas of science and engineering rely on functional data and their numerical analysis. The need to analyze time-varying functional data raises the general problem of interpolation, that is, how to learn a smooth time evolution from a finite number of observations. Here, we introduce optimal functional interpolation (OFI), a numerical algorithm that interpolates functional data over time. Unlike the usual interpolation or learning algorithms, the OFI algorithm obeys the continuity equation, which describes the transport of some types of conserved quantities, and its implementation shows smooth, continuous flows of quantities. Without the need to take into account equations of motion such as the Navier-Stokes equation or the diffusion equation, OFI is capable of learning the dynamics of objects such as those represented by mass, image intensity, particle concentration, heat, spectral density, and probability density.

A Self-Consistent Model of the Interacting Ring Current Ions and Electromagnetic Ion Cyclotron Waves, Initial Results: Waves and Precipitating Fluxes

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Gamayunov, K. V.; Jordanova, V. K.; Krivorutsky, E. N.

2002-01-01

Initial results from a newly developed model of the interacting ring current ions and ion cyclotron waves are presented. The model is based on the system of two kinetic equations: one equation describes the ring current ion dynamics, and another equation describes wave evolution. The system gives a self-consistent description of the ring current ions and ion cyclotron waves in a quasilinear approach. These equations for the ion phase space distribution function and for the wave power spectral density were solved on aglobal magnetospheric scale undernonsteady state conditions during the 2-5 May 1998 storm. The structure and dynamics of the ring current proton precipitating flux regions and the ion cyclotron wave-active zones during extreme geomagnetic disturbances on 4 May 1998 are presented and discussed in detail.

Dynamical analysis on f(R, G) cosmology

NASA Astrophysics Data System (ADS)

Santos da Costa, S.; Roig, F. V.; Alcaniz, J. S.; Capozziello, S.; De Laurentis, M.; Benetti, M.

2018-04-01

We use a dynamical system approach to study the cosmological viability of f(R, G) gravity theories. The method consists of formulating the evolution equations as an autonomous system of ordinary differential equations, using suitable variables. The formalism is applied to a class of models in which f(R, G)\\propto RnG1-n and its solutions and corresponding stability are analysed in detail. New accelerating solutions that can be attractors in the phase space are found. We also find that this class of models does not exhibit a matter-dominated epoch, a solution which is inconsistent with current cosmological observations.

Complexity for Survival of Living Systems

NASA Technical Reports Server (NTRS)

Zak, Michail

2009-01-01

A logical connection between the survivability of living systems and the complexity of their behavior (equivalently, mental complexity) has been established. This connection is an important intermediate result of continuing research on mathematical models that could constitute a unified representation of the evolution of both living and non-living systems. Earlier results of this research were reported in several prior NASA Tech Briefs articles, the two most relevant being Characteristics of Dynamics of Intelligent Systems (NPO- 21037), NASA Tech Briefs, Vol. 26, No. 12 (December 2002), page 48; and Self-Supervised Dynamical Systems (NPO- 30634) NASA Tech Briefs, Vol. 27, No. 3 (March 2003), page 72. As used here, living systems is synonymous with active systems and intelligent systems. The quoted terms can signify artificial agents (e.g., suitably programmed computers) or natural biological systems ranging from single-cell organisms at one extreme to the whole of human society at the other extreme. One of the requirements that must be satisfied in mathematical modeling of living systems is reconciliation of evolution of life with the second law of thermodynamics. In the approach followed in this research, this reconciliation is effected by means of a model, inspired partly by quantum mechanics, in which the quantum potential is replaced with an information potential. The model captures the most fundamental property of life - the ability to evolve from disorder to order without any external interference. The model incorporates the equations of classical dynamics, including Newton s equations of motion and equations for random components caused by uncertainties in initial conditions and by Langevin forces. The equations of classical dynamics are coupled with corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces that are gradients of the information potential, which, in turn, is a function of the probability densities. The probability densities are associated with mental images both self-image and nonself images (images of external objects that can include other agents). The evolution of the probability densities represents mental dynamics. Then the interaction between the physical and metal aspects of behavior is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. The interaction of a system with its self and nonself images affords unlimited capacity for increase of complexity. There is a biological basis for this model of mental dynamics in the discovery of mirror neurons that learn by imitation. The levels of complexity attained by use of this model match those observed in living systems. To establish a mechanism for increasing the complexity of dynamics of an active system, the model enables exploitation of a chain of reflections exemplified by questions of the form, "What do you think that I think that you think...?" Mathematically, each level of reflection is represented in the form of an attractor performing the corresponding level of abstraction with more details removed from higher levels. The model can be used to describe the behaviors, not only of biological systems, but also of ecological, social, and economics ones.

The Soil Foam Drainage Equation - an alternative model for unsaturated flow in porous media

NASA Astrophysics Data System (ADS)

Assouline, Shmuel; Lehmann, Peter; Hoogland, Frouke; Or, Dani

2017-04-01

The analogy between the geometry and dynamics of wet foam drainage and gravity drainage of unsaturated porous media expands modeling capabilities for capillary flows and supplements the standard Richards equation representation. The governing equation for draining foam (or a soil variant termed the soil foam drainage equation - SFDE) obviates the need for macroscopic unsaturated hydraulic conductivity function by an explicit account of diminishing flow pathway sizes as the medium gradually drains. Potential advantages of the proposed drainage foam formalism include direct description of transient flow without requiring constitutive functions; evolution of capillary cross sections that provides consistent description of self-regulating internal fluxes (e.g., towards field capacity); and a more intuitive geometrical picture of capillary flow across textural boundaries. We will present new and simple analytical expressions for drainage rates and volumes from unsaturated porous media subjected to different boundary conditions that are in good agreement with the numerical solution of the SFDE and experimental results. The foam drainage methodology expands the range of tools available for describing and quantifying unsaturated flows and provides geometrically tractable links between evolution of liquid configuration and flow dynamics in unsaturated porous media. The resulting geometrical representation of capillary drainage could improve understanding of colloid and pathogen transport. The explicit geometrical interpretation of flow pathways underlying the hydraulic functions used by the Richards equation offers new insights that benefit both approaches.

Simulation of Stochastic Processes by Coupled ODE-PDE

NASA Technical Reports Server (NTRS)

Zak, Michail

2008-01-01

A document discusses the emergence of randomness in solutions of coupled, fully deterministic ODE-PDE (ordinary differential equations-partial differential equations) due to failure of the Lipschitz condition as a new phenomenon. It is possible to exploit the special properties of ordinary differential equations (represented by an arbitrarily chosen, dynamical system) coupled with the corresponding Liouville equations (used to describe the evolution of initial uncertainties in terms of joint probability distribution) in order to simulate stochastic processes with the proscribed probability distributions. The important advantage of the proposed approach is that the simulation does not require a random-number generator.

A stochastic differential equation analysis of cerebrospinal fluid dynamics.

PubMed

Raman, Kalyan

2011-01-18

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

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.

Explosive magnetorotational instability in Keplerian disks

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

Shtemler, Yu., E-mail: shtemler@bgu.ac.il; Liverts, E., E-mail: eliverts@bgu.ac.il; Mond, M., E-mail: mond@bgu.ac.il

Differentially rotating disks under the effect of axial magnetic field are prone to a nonlinear explosive magnetorotational instability (EMRI). The dynamic equations that govern the temporal evolution of the amplitudes of three weakly detuned resonantly interacting modes are derived. As distinct from exponential growth in the strict resonance triads, EMRI occurs due to the resonant interactions of an MRI mode with stable Alfvén–Coriolis and magnetosonic modes. Numerical solutions of the dynamic equations for amplitudes of a triad indicate that two types of perturbations behavior can be excited for resonance conditions: (i) EMRI which leads to infinite values of the threemore » amplitudes within a finite time, and (ii) bounded irregular oscillations of all three amplitudes. Asymptotic explicit solutions of the dynamic equations are obtained for EMRI regimes and are shown to match the numerical solutions near the explosion time.« less

On whole Abelian model dynamics

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

Chauca, J.; Doria, R.; Aprendanet, Petropolis, 25600

2012-09-24

Physics challenge is to determine the objects dynamics. However, there are two ways for deciphering the part. The first one is to search for the ultimate constituents; the second one is to understand its behaviour in whole terms. Therefore, the parts can be defined either from elementary constituents or as whole functions. Historically, science has been moving through the first aspect, however, quarks confinement and complexity are interrupting this usual approach. These relevant facts are supporting for a systemic vision be introduced. Our effort here is to study on the whole meaning through gauge theory. Consider a systemic dynamics orientedmore » through the U(1) - systemic gauge parameter which function is to collect a fields set {l_brace}A{sub {mu}I}{r_brace}. Derive the corresponding whole gauge invariant Lagrangian, equations of motion, Bianchi identities, Noether relationships, charges and Ward-Takahashi equations. Whole Lorentz force and BRST symmetry are also studied. These expressions bring new interpretations further than the usual abelian model. They are generating a systemic system governed by 2N+ 10 classical equations plus Ward-Takahashi identities. A whole dynamics based on the notions of directive and circumstance is producing a set determinism where the parts dynamics are inserted in the whole evolution. A dynamics based on state, collective and individual equations with a systemic interdependence.« less

Diffusion of non-Gaussianity in heavy ion collisions

NASA Astrophysics Data System (ADS)

Kitazawa, Masakiyo; Asakawa, Masayuki; Ono, Hirosato

2014-05-01

We investigate the time evolution of higher order cumulants of bulk fluctuations of conserved charges in the hadronic stage in relativistic heavy ion collisions. The dynamical evolution of non-Gaussian fluctuations is modeled by the diffusion master equation. Using this model we predict that the fourth-order cumulant of net-electric charge is suppressed compared with the recently observed second-order one at ALICE for a reasonable parameter range. Significance of the measurements of various cumulants as functions of rapidity window to probe dynamical history of the hot medium created by heavy ion collisions is emphasized.

Dynamical Casimir-Polder force on a partially dressed atom near a conducting wall

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

Messina, Riccardo; Vasile, Ruggero; Passante, Roberto

2010-12-15

We study the time evolution of the Casimir-Polder force acting on a neutral atom in front of a perfectly conducting plate, when the system starts its unitary evolution from a partially dressed state. We solve the Heisenberg equations for both atomic and field quantum operators, exploiting a series expansion with respect to the electric charge and an iterative technique. After discussing the behavior of the time-dependent force on an initially partially dressed atom, we analyze a possible experimental scheme to prepare the partially dressed state and the observability of this new dynamical effect.

Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations

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

Schüler, D.; Alonso, S.; Bär, M.

2014-12-15

Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexistingmore » static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.« less

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

PubMed

Salis, Howard; Kaznessis, Yiannis N

2005-12-01

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

Lagrangian Perturbation Approach to the Formation of Large-scale Structure

NASA Astrophysics Data System (ADS)

Buchert, Thomas

The present lecture notes address three columns on which the Lagrangian perturbation approach to cosmological dynamics is based: 1. the formulation of a Lagrangian theory of self-gravitating flows in which the dynamics is described in terms of a single field variable; 2. the procedure, how to obtain the dynamics of Eulerian fields from the Lagrangian picture, and 3. a precise definition of a Newtonian cosmology framework in which Lagrangian perturbation solutions can be studied. While the first is a discussion of the basic equations obtained by transforming the Eulerian evolution and field equations to the Lagrangian picture, the second exemplifies how the Lagrangian theory determines the evolution of Eulerian fields including kinematical variables like expansion, vorticity, as well as the shear and tidal tensors. The third column is based on a specification of initial and boundary conditions, and in particular on the identification of the average flow of an inhomogeneous cosmology with a `Hubble-flow'. Here, we also look at the limits of the Lagrangian perturbation approach as inferred from comparisons with N-body simulations and illustrate some striking properties of the solutions.

Polynomial f (R ) Palatini cosmology: Dynamical system approach

NASA Astrophysics Data System (ADS)

Szydłowski, Marek; Stachowski, Aleksander

2018-05-01

We investigate cosmological dynamics based on f (R ) gravity in the Palatini formulation. In this study, we use the dynamical system methods. We show that the evolution of the Friedmann equation reduces to the form of the piecewise smooth dynamical system. This system is reduced to a 2D dynamical system of the Newtonian type. We demonstrate how the trajectories can be sewn to guarantee C0 extendibility of the metric similarly as "Milne-like" Friedmann-Lemaître-Robertson-Walker spacetimes are C0-extendible. We point out that importance of the dynamical system of the Newtonian type with nonsmooth right-hand sides in the context of Palatini cosmology. In this framework, we can investigate singularities which appear in the past and future of the cosmic evolution. We consider cosmological systems in both Einstein and Jordan frames. We show that at each frame the topological structures of phase space are different.

Evolution analysis of EUV radiation from laser-produced tin plasmas based on a radiation hydrodynamics model

PubMed Central

Su, M. G.; Min, Q.; Cao, S. Q.; Sun, D. X.; Hayden, P.; O’Sullivan, G.; Dong, C. Z.

2017-01-01

One of fundamental aims of extreme ultraviolet (EUV) lithography is to maximize brightness or conversion efficiency of laser energy to radiation at specific wavelengths from laser produced plasmas (LPPs) of specific elements for matching to available multilayer optical systems. Tin LPPs have been chosen for operation at a wavelength of 13.5 nm. For an investigation of EUV radiation of laser-produced tin plasmas, it is crucial to study the related atomic processes and their evolution so as to reliably predict the optimum plasma and experimental conditions. Here, we present a simplified radiation hydrodynamic model based on the fluid dynamic equations and the radiative transfer equation to rapidly investigate the evolution of radiation properties and dynamics in laser-produced tin plasmas. The self-absorption features of EUV spectra measured at an angle of 45° to the direction of plasma expansion have been successfully simulated and explained, and the evolution of some parameters, such as the plasma temperature, ion distribution and density, expansion size and velocity, have also been evaluated. Our results should be useful for further understanding of current research on extreme ultraviolet and soft X-ray source development for applications such as lithography, metrology and biological imaging. PMID:28332621

Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion

NASA Astrophysics Data System (ADS)

Congy, T.; Ivanov, S. K.; Kamchatnov, A. M.; Pavloff, N.

2017-08-01

We consider the space-time evolution of initial discontinuities of depth and flow velocity for an integrable version of the shallow water Boussinesq system introduced by Kaup. We focus on a specific version of this "Kaup-Boussinesq model" for which a flat water surface is modulationally stable, we speak below of "positive dispersion" model. This model also appears as an approximation to the equations governing the dynamics of polarisation waves in two-component Bose-Einstein condensates. We describe its periodic solutions and the corresponding Whitham modulation equations. The self-similar, one-phase wave structures are composed of different building blocks, which are studied in detail. This makes it possible to establish a classification of all the possible wave configurations evolving from initial discontinuities. The analytic results are confirmed by numerical simulations.

Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion.

PubMed

Congy, T; Ivanov, S K; Kamchatnov, A M; Pavloff, N

2017-08-01

We consider the space-time evolution of initial discontinuities of depth and flow velocity for an integrable version of the shallow water Boussinesq system introduced by Kaup. We focus on a specific version of this "Kaup-Boussinesq model" for which a flat water surface is modulationally stable, we speak below of "positive dispersion" model. This model also appears as an approximation to the equations governing the dynamics of polarisation waves in two-component Bose-Einstein condensates. We describe its periodic solutions and the corresponding Whitham modulation equations. The self-similar, one-phase wave structures are composed of different building blocks, which are studied in detail. This makes it possible to establish a classification of all the possible wave configurations evolving from initial discontinuities. The analytic results are confirmed by numerical simulations.

A note on a nonlinear equation arising in discussions of the steady fall of a resistive, viscous, isothermal fluid across a magnetic field

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

Tautz, R. C., E-mail: robert.c.tautz@gmail.com; Lerche, I., E-mail: lercheian@yahoo.com

2015-11-15

This note considers the evolution of steady isothermal flow across a uniform magnetic field from an analytic standpoint. This problem is of concern in developments of magnetic fields in the solar corona and for prominence dynamics. Limiting behaviors are obtained to the nonlinear equation describing the flow depending on the value of a single parameter. For the situation where the viscous drag is a small correction to the inviscid flow limiting structures are also outlined. The purpose of the note is to show how one can evaluate some of the analytic properties of the highly nonlinear equation that are ofmore » use in considering the numerical evolution as done in Low and Egan [Phys. Plasmas 21, 062105 (2014)].« less

Numerical computation of linear instability of detonations

NASA Astrophysics Data System (ADS)

Kabanov, Dmitry; Kasimov, Aslan

2017-11-01

We propose a method to study linear stability of detonations by direct numerical computation. The linearized governing equations together with the shock-evolution equation are solved in the shock-attached frame using a high-resolution numerical algorithm. The computed results are processed by the Dynamic Mode Decomposition technique to generate dispersion relations. The method is applied to the reactive Euler equations with simple-depletion chemistry as well as more complex multistep chemistry. The results are compared with those known from normal-mode analysis. We acknowledge financial support from King Abdullah University of Science and Technology.

Dynamic optimization and its relation to classical and quantum constrained systems

NASA Astrophysics Data System (ADS)

Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo

2017-08-01

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

Dynamic of charged planar geometry in tilted and non-tilted frames

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

Sharif, M., E-mail: msharif.math@pu.edu.pk; Zaeem Ul Haq Bhatti, M., E-mail: mzaeem.math@pu.edu.pk

2015-05-15

We investigate the dynamics of charged planar symmetry with an anisotropic matter field subject to a radially moving observer called a tilted observer. The Einstein-Maxwell field equations are used to obtain a relation between non-tilted and tilted frames and between kinematical and dynamical quantities. Using the Taub mass formalism and conservation laws, two evolution equations are developed to analyze the inhomogeneities in the tilted congruence. It is found that the radial velocity (due to the tilted observer) and the electric charge have a crucial effect on the inhomogeneity factor. Finally, we discuss the stability in the non-tilted frame in themore » pure diffusion case and examine the effects of the electromagnetic field.« less

Stochastic Feshbach Projection for the Dynamics of Open Quantum Systems

NASA Astrophysics Data System (ADS)

Link, Valentin; Strunz, Walter T.

2017-11-01

We present a stochastic projection formalism for the description of quantum dynamics in bosonic or spin environments. The Schrödinger equation in the coherent state representation with respect to the environmental degrees of freedom can be reformulated by employing the Feshbach partitioning technique for open quantum systems based on the introduction of suitable non-Hermitian projection operators. In this picture the reduced state of the system can be obtained as a stochastic average over pure state trajectories, for any temperature of the bath. The corresponding non-Markovian stochastic Schrödinger equations include a memory integral over the past states. In the case of harmonic environments and linear coupling the approach gives a new form of the established non-Markovian quantum state diffusion stochastic Schrödinger equation without functional derivatives. Utilizing spin coherent states, the evolution equation for spin environments resembles the bosonic case with, however, a non-Gaussian average for the reduced density operator.

Describing the dynamics of processes consisting simultaneously of Poissonian and non-Poissonian kinetics

NASA Astrophysics Data System (ADS)

Eule, S.; Friedrich, R.

2013-03-01

Dynamical processes exhibiting non-Poissonian kinetics with nonexponential waiting times are frequently encountered in nature. Examples are biochemical processes like gene transcription which are known to involve multiple intermediate steps. However, often a second process, obeying Poissonian statistics, affects the first one simultaneously, such as the degradation of mRNA in the above example. The aim of the present article is to provide a concise treatment of such random systems which are affected by regular and non-Poissonian kinetics at the same time. We derive the governing master equation and provide a controlled approximation scheme for this equation. The simplest approximation leads to generalized reaction rate equations. For a simple model of gene transcription we solve the resulting equation and show how the time evolution is influenced significantly by the type of waiting time distribution assumed for the non-Poissonian process.

A Self-Consistent Model of the Interacting Ring Current Ions with Electromagnetic ICWs

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Gamayunov, K. V.; Jordanova, V. K.; Krivorutsky, E. N.; Whitaker, Ann F. (Technical Monitor)

2001-01-01

Initial results from a newly developed model of the interacting ring current ions and ion cyclotron waves are presented. The model is based on the system of two bound kinetic equations: one equation describes the ring current ion dynamics, and another equation describes wave evolution. The system gives a self-consistent description of ring current ions and ion cyclotron waves in a quasilinear approach. These two equations were solved on a global scale under non steady-state conditions during the May 2-5, 1998 storm. The structure and dynamics of the ring current proton precipitating flux regions and the wave active zones at three time cuts around initial, main, and late recovery phases of the May 4, 1998 storm phase are presented and discussed in detail. Comparisons of the model wave-ion data with the Polar/HYDRA and Polar/MFE instruments results are presented..

Spherically symmetric Einstein-aether perfect fluid models

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

Coley, Alan A.; Latta, Joey; Leon, Genly

We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which form a well-posed system of first order partial differential equations in two variables. We then introduce normalized variables. The formalism is particularly well-suited for numerical computations and the study of the qualitative properties of the models, which are also solutions of Horava gravity. We study the local stability of the equilibrium points of the resulting dynamical system corresponding to physically realistic inhomogeneous cosmological models and astrophysicalmore » objects with values for the parameters which are consistent with current constraints. In particular, we consider dust models in (β−) normalized variables and derive a reduced (closed) evolution system and we obtain the general evolution equations for the spatially homogeneous Kantowski-Sachs models using appropriate bounded normalized variables. We then analyse these models, with special emphasis on the future asymptotic behaviour for different values of the parameters. Finally, we investigate static models for a mixture of a (necessarily non-tilted) perfect fluid with a barotropic equations of state and a scalar field.« less

Studying relaxation phenomena via effective master equations

NASA Astrophysics Data System (ADS)

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

2000-04-01

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

Dynamic stiffness of chemically and physically ageing rubber vibration isolators in the audible frequency range. Part 1: constitutive equations

NASA Astrophysics Data System (ADS)

Kari, Leif

2017-09-01

The constitutive equations of chemically and physically ageing rubber in the audible frequency range are modelled as a function of ageing temperature, ageing time, actual temperature, time and frequency. The constitutive equations are derived by assuming nearly incompressible material with elastic spherical response and viscoelastic deviatoric response, using Mittag-Leffler relaxation function of fractional derivative type, the main advantage being the minimum material parameters needed to successfully fit experimental data over a broad frequency range. The material is furthermore assumed essentially entropic and thermo-mechanically simple while using a modified William-Landel-Ferry shift function to take into account temperature dependence and physical ageing, with fractional free volume evolution modelled by a nonlinear, fractional differential equation with relaxation time identical to that of the stress response and related to the fractional free volume by Doolittle equation. Physical ageing is a reversible ageing process, including trapping and freeing of polymer chain ends, polymer chain reorganizations and free volume changes. In contrast, chemical ageing is an irreversible process, mainly attributed to oxygen reaction with polymer network either damaging the network by scission or reformation of new polymer links. The chemical ageing is modelled by inner variables that are determined by inner fractional evolution equations. Finally, the model parameters are fitted to measurements results of natural rubber over a broad audible frequency range, and various parameter studies are performed including comparison with results obtained by ordinary, non-fractional ageing evolution differential equations.

Time Evolution of Modeled Reynolds Stresses in Planar Homogeneous Flows

NASA Technical Reports Server (NTRS)

Jongen, T.; Gatski, T. B.

1997-01-01

The analytic expression of the time evolution of the Reynolds stress anisotropy tensor in all planar homogeneous flows is obtained by exact integration of the modeled differential Reynolds stress equations. The procedure is based on results of tensor representation theory, is applicable for general pressure-strain correlation tensors, and can account for any additional turbulence anisotropy effects included in the closure. An explicit solution of the resulting system of scalar ordinary differential equations is obtained for the case of a linear pressure-strain correlation tensor. The properties of this solution are discussed, and the dynamic behavior of the Reynolds stresses is studied, including limit cycles and sensitivity to initial anisotropies.

Modeling tree crown dynamics with 3D partial differential equations.

PubMed

Beyer, Robert; Letort, Véronique; Cournède, Paul-Henry

2014-01-01

We characterize a tree's spatial foliage distribution by the local leaf area density. Considering this spatially continuous variable allows to describe the spatiotemporal evolution of the tree crown by means of 3D partial differential equations. These offer a framework to rigorously take locally and adaptively acting effects into account, notably the growth toward light. Biomass production through photosynthesis and the allocation to foliage and wood are readily included in this model framework. The system of equations stands out due to its inherent dynamic property of self-organization and spontaneous adaptation, generating complex behavior from even only a few parameters. The density-based approach yields spatially structured tree crowns without relying on detailed geometry. We present the methodological fundamentals of such a modeling approach and discuss further prospects and applications.

What is general relativity?

NASA Astrophysics Data System (ADS)

Coley, Alan A.; Wiltshire, David L.

2017-05-01

General relativity is a set of physical and geometric principles, which lead to a set of (Einstein) field equations that determine the gravitational field and to the geodesic equations that describe light propagation and the motion of particles on the background. But open questions remain, including: what is the scale on which matter and geometry are dynamically coupled in the Einstein equations? Are the field equations valid on small and large scales? What is the largest scale on which matter can be coarse grained while following a geodesic of a solution to Einstein’s equations? We address these questions. If the field equations are causal evolution equations, whose average on cosmological scales is not an exact solution of the Einstein equations, then some simplifying physical principle is required to explain the statistical homogeneity of the late epoch Universe. Such a principle may have its origin in the dynamical coupling between matter and geometry at the quantum level in the early Universe. This possibility is hinted at by diverse approaches to quantum gravity which find a dynamical reduction to two effective dimensions at high energies on one hand, and by cosmological observations which are beginning to strongly restrict the class of viable inflationary phenomenologies on the other. We suggest that the foundational principles of general relativity will play a central role in reformulating the theory of spacetime structure to meet the challenges of cosmology in the 21st century.

Dynamical Signatures of Living Systems

NASA Technical Reports Server (NTRS)

Zak, M.

1999-01-01

One of the main challenges in modeling living systems is to distinguish a random walk of physical origin (for instance, Brownian motions) from those of biological origin and that will constitute the starting point of the proposed approach. As conjectured, the biological random walk must be nonlinear. Indeed, any stochastic Markov process can be described by linear Fokker-Planck equation (or its discretized version), only that type of process has been observed in the inanimate world. However, all such processes always converge to a stable (ergodic or periodic) state, i.e., to the states of a lower complexity and high entropy. At the same time, the evolution of living systems directed toward a higher level of complexity if complexity is associated with a number of structural variations. The simplest way to mimic such a tendency is to incorporate a nonlinearity into the random walk; then the probability evolution will attain the features of diffusion equation: the formation and dissipation of shock waves initiated by small shallow wave disturbances. As a result, the evolution never "dies:" it produces new different configurations which are accompanied by an increase or decrease of entropy (the decrease takes place during formation of shock waves, the increase-during their dissipation). In other words, the evolution can be directed "against the second law of thermodynamics" by forming patterns outside of equilibrium in the probability space. Due to that, a specie is not locked up in a certain pattern of behavior: it still can perform a variety of motions, and only the statistics of these motions is constrained by this pattern. It should be emphasized that such a "twist" is based upon the concept of reflection, i.e., the existence of the self-image (adopted from psychology). The model consists of a generator of stochastic processes which represents the motor dynamics in the form of nonlinear random walks, and a simulator of the nonlinear version of the diffusion equation which represents the mental dynamics. It has been demonstrated that coupled mental-motor dynamics can simulate emerging self-organization, prey-predator games, collaboration and competition, "collective brain," etc.

Optimization of CW Fiber Lasers With Strong Nonlinear Cavity Dynamics

NASA Astrophysics Data System (ADS)

Shtyrina, O. V.; Efremov, S. A.; Yarutkina, I. A.; Skidin, A. S.; Fedoruk, M. P.

2018-04-01

In present work the equation for the saturated gain is derived from one-level gain equations describing the energy evolution inside the laser cavity. It is shown how to derive the parameters of the mathematical model from the experimental results. The numerically-estimated energy and spectrum of the signal are in good agreement with the experiment. Also, the optimization of the output energy is performed for a given set of model parameters.

Dynamic optimization of open-loop input signals for ramp-up current profiles in tokamak plasmas

NASA Astrophysics Data System (ADS)

Ren, Zhigang; Xu, Chao; Lin, Qun; Loxton, Ryan; Teo, Kok Lay

2016-03-01

Establishing a good current spatial profile in tokamak fusion reactors is crucial to effective steady-state operation. The evolution of the current spatial profile is related to the evolution of the poloidal magnetic flux, which can be modeled in the normalized cylindrical coordinates using a parabolic partial differential equation (PDE) called the magnetic diffusion equation. In this paper, we consider the dynamic optimization problem of attaining the best possible current spatial profile during the ramp-up phase of the tokamak. We first use the Galerkin method to obtain a finite-dimensional ordinary differential equation (ODE) model based on the original magnetic diffusion PDE. Then, we combine the control parameterization method with a novel time-scaling transformation to obtain an approximate optimal parameter selection problem, which can be solved using gradient-based optimization techniques such as sequential quadratic programming (SQP). This control parameterization approach involves approximating the tokamak input signals by piecewise-linear functions whose slopes and break-points are decision variables to be optimized. We show that the gradient of the objective function with respect to the decision variables can be computed by solving an auxiliary dynamic system governing the state sensitivity matrix. Finally, we conclude the paper with simulation results for an example problem based on experimental data from the DIII-D tokamak in San Diego, California.

Dynamics of tethered satellites in the vicinity of the Lagrangian point L2 of the Earth-Moon system

NASA Astrophysics Data System (ADS)

Baião, M. F.; Stuchi, T. J.

2017-08-01

This paper analyzes the dynamical evolution of satellites formed by two masses connected by a cable— tethered satellites. We derive the Lagrangian equations of motion in the neighborhood of the collinear equilibrium points, especially for the L2 , of the restricted problem of three bodies. The rigid body configuration is expanded in Legendre polynomials up to fourth degree. We present some numerical simulations of the influence of the parameters such as cable length, mass ratio and initial conditions in the behavior of the tethered satellites. The equation for the collinear equilibrium point is derived and numerically solved. The evolution of the equilibria with the variation of the cable length as a parameter is studied. We also present a discussion of the linear stability around these equilibria. Based on this analysis calculate some unstable Lyapunov orbits associated to these equilibrium points. We found periodic orbits in which the tether travels parallel to itself without involving the angular motion. The numerical applications are focused on the Earth-Moon system. However, the general character of the equations allows applications to the L1 equilibrium and obviously to systems other than the Earth-Moon.

Coarse-grained description of cosmic structure from Szekeres models

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

Sussman, Roberto A.; Gaspar, I. Delgado; Hidalgo, Juan Carlos, E-mail: sussman@nucleares.unam.mx, E-mail: ismael.delgadog@uaem.edu.mx, E-mail: hidalgo@fis.unam.mx

2016-03-01

We show that the full dynamical freedom of the well known Szekeres models allows for the description of elaborated 3-dimensional networks of cold dark matter structures (over-densities and/or density voids) undergoing ''pancake'' collapse. By reducing Einstein's field equations to a set of evolution equations, which themselves reduce in the linear limit to evolution equations for linear perturbations, we determine the dynamics of such structures, with the spatial comoving location of each structure uniquely specified by standard early Universe initial conditions. By means of a representative example we examine in detail the density contrast, the Hubble flow and peculiar velocities ofmore » structures that evolved, from linear initial data at the last scattering surface, to fully non-linear 10–20 Mpc scale configurations today. To motivate further research, we provide a qualitative discussion on the connection of Szekeres models with linear perturbations and the pancake collapse of the Zeldovich approximation. This type of structure modelling provides a coarse grained—but fully relativistic non-linear and non-perturbative —description of evolving large scale cosmic structures before their virialisation, and as such it has an enormous potential for applications in cosmological research.« less

Bound states of moving potential wells in discrete wave mechanics

NASA Astrophysics Data System (ADS)

Longhi, S.

2017-10-01

Discrete wave mechanics describes the evolution of classical or matter waves on a lattice, which is governed by a discretized version of the Schrödinger equation. While for a vanishing lattice spacing wave evolution of the continuous Schrödinger equation is retrieved, spatial discretization and lattice effects can deeply modify wave dynamics. Here we discuss implications of breakdown of exact Galilean invariance of the discrete Schrödinger equation on the bound states sustained by a smooth potential well which is uniformly moving on the lattice with a drift velocity v. While in the continuous limit the number of bound states does not depend on the drift velocity v, as one expects from the covariance of ordinary Schrödinger equation for a Galilean boost, lattice effects can lead to a larger number of bound states for the moving potential well as compared to the potential well at rest. Moreover, for a moving potential bound states on a lattice become rather generally quasi-bound (resonance) states.

4-wave dynamics in kinetic wave turbulence

NASA Astrophysics Data System (ADS)

Chibbaro, Sergio; Dematteis, Giovanni; Rondoni, Lamberto

2018-01-01

A general Hamiltonian wave system with quartic resonances is considered, in the standard kinetic limit of a continuum of weakly interacting dispersive waves with random phases. The evolution equation for the multimode characteristic function Z is obtained within an ;interaction representation; and a perturbation expansion in the small nonlinearity parameter. A frequency renormalization is performed to remove linear terms that do not appear in the 3-wave case. Feynman-Wyld diagrams are used to average over phases, leading to a first order differential evolution equation for Z. A hierarchy of equations, analogous to the Boltzmann hierarchy for low density gases is derived, which preserves in time the property of random phases and amplitudes. This amounts to a general formalism for both the N-mode and the 1-mode PDF equations for 4-wave turbulent systems, suitable for numerical simulations and for investigating intermittency. Some of the main results which are developed here in detail have been tested numerically in a recent work.

Modelling of squall with the generalised kinetic equation

NASA Astrophysics Data System (ADS)

Annenkov, Sergei; Shrira, Victor

2014-05-01

We study the long-term evolution of random wind waves using the new generalised kinetic equation (GKE). The GKE derivation [1] does not assume the quasi-stationarity of a random wave field. In contrast with the Hasselmann kinetic equation, the GKE can describe fast spectral changes occurring when a wave field is driven out of a quasi-equilibrium state by a fast increase or decrease of wind, or by other factors. In these cases, a random wave field evolves on the dynamic timescale typical of coherent wave processes, rather than on the kinetic timescale predicted by the conventional statistical theory. Besides that, the generalised theory allows to trace the evolution of higher statistical moments of the field, notably the kurtosis, which is important for assessing the risk of freak waves and other applications. A new efficient and highly parallelised algorithm for the numerical simulation of the generalised kinetic equation is presented and discussed. Unlike in the case of the Hasselmann equation, the algorithm takes into account all (resonant and non-resonant) nonlinear wave interactions, but only approximately resonant interactions contribute to the spectral evolution. However, counter-intuitively, all interactions contribute to the kurtosis. Without forcing or dissipation, the algorithm is shown to conserve the relevant integrals. We show that under steady wind forcing the wave field evolution predicted by the GKE is close to the predictions of the conventional statistical theory, which is applicable in this case. In particular, we demonstrate the known long-term asymptotics for the evolution of the spectrum. When the wind forcing is not steady (in the simplest case, an instant increase or decrease of wind occurs), the generalised theory is the only way to study the spectral evolution, apart from the direct numerical simulation. The focus of the work is a detailed analysis of the fast evolution after an instant change of forcing, and of the subsequent transition to the new quasi-stationary state of a wave field. It is shown that both increase and decrease of wind lead to a significant transient increase of the dynamic kurtosis, although these changes remain small compared to the changes of the other component of the kurtosis, which is due to bound harmonics. A special consideration is given to the case of the squall, i.e. an instant and large (by a factor of 2-4) increase of wind, which lasts for O(102) characteristic wave periods. We show that fast adjustment processes lead to the formation of a transient spectrum, which has a considerably narrower peak than the spectra developed under a steady forcing. These transient spectra differ qualitatively from those predicted by the Hasselmann kinetic equation under the squall with the same parameters. 1. S.Annenkov, V.Shrira (2006) Role of non-resonant interactions in evolution of nonlinear random water wave fields, J. Fluid Mech. 561, 181-207.

Universality in the nonlinear leveling of capillary films

NASA Astrophysics Data System (ADS)

Zheng, Zhong; Fontelos, Marco A.; Shin, Sangwoo; Stone, Howard A.

2018-03-01

Many material science, coating, and manufacturing problems involve liquid films where defects that span the film thickness must be removed. Here, we study the surface-tension-driven leveling dynamics of a thin viscous film following closure of an initial hole. The dynamics of the film shape is described by a nonlinear evolution equation, for which we obtain a self-similar solution. The analytical results are verified using time-dependent numerical and experimental results for the profile shapes and the minimum film thickness at the center. The universal behavior we identify can be useful for characterizing the time evolution of the leveling process and estimating material properties from experiments.

KvN mechanics approach to the time-dependent frequency harmonic oscillator.

PubMed

Ramos-Prieto, Irán; Urzúa-Pineda, Alejandro R; Soto-Eguibar, Francisco; Moya-Cessa, Héctor M

2018-05-30

Using the Ermakov-Lewis invariants appearing in KvN mechanics, the time-dependent frequency harmonic oscillator is studied. The analysis builds upon the operational dynamical model, from which it is possible to infer quantum or classical dynamics; thus, the mathematical structure governing the evolution will be the same in both cases. The Liouville operator associated with the time-dependent frequency harmonic oscillator can be transformed using an Ermakov-Lewis invariant, which is also time dependent and commutes with itself at any time. Finally, because the solution of the Ermakov equation is involved in the evolution of the classical state vector, we explore some analytical and numerical solutions.

Probabilistic density function method for nonlinear dynamical systems driven by colored noise.

PubMed

Barajas-Solano, David A; Tartakovsky, Alexandre M

2016-05-01

We present a probability density function (PDF) method for a system of nonlinear stochastic ordinary differential equations driven by colored noise. The method provides an integrodifferential equation for the temporal evolution of the joint PDF of the system's state, which we close by means of a modified large-eddy-diffusivity (LED) closure. In contrast to the classical LED closure, the proposed closure accounts for advective transport of the PDF in the approximate temporal deconvolution of the integrodifferential equation. In addition, we introduce the generalized local linearization approximation for deriving a computable PDF equation in the form of a second-order partial differential equation. We demonstrate that the proposed closure and localization accurately describe the dynamics of the PDF in phase space for systems driven by noise with arbitrary autocorrelation time. We apply the proposed PDF method to analyze a set of Kramers equations driven by exponentially autocorrelated Gaussian colored noise to study nonlinear oscillators and the dynamics and stability of a power grid. Numerical experiments show the PDF method is accurate when the noise autocorrelation time is either much shorter or longer than the system's relaxation time, while the accuracy decreases as the ratio of the two timescales approaches unity. Similarly, the PDF method accuracy decreases with increasing standard deviation of the noise.

Extension of the Schrodinger equation

NASA Astrophysics Data System (ADS)

Somsikov, Vyacheslav

2017-03-01

Extension of the Schrodinger equation is submitted by removing its limitations appearing due to the limitations of the formalism of Hamilton, based on which this equation was obtained. For this purpose the problems of quantum mechanics arising from the limitations of classical mechanics are discussed. These limitations, in particular, preclude the use of the Schrodinger equation to describe the time symmetry violation. The extension of the Schrodinger equation is realized based on the principle of duality symmetry. According to this principle the dynamics of the systems is determined by the symmetry of the system and by the symmetry of the space. The extension of the Schrodinger equation was obtained from the dual expression of energy, represented in operator form. For this purpose the independent micro - and macro-variables that determine respectively the dynamics of quantum particle system relative to its center of mass and the movement of the center of mass in space are used. The solution of the extended Schrodinger equation for the system near equilibrium is submitted. The main advantage of the extended Schrodinger equation is that it is applicable to describe the interaction and evolution of quantum systems in inhomogeneous field of external forces.

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

Sharif, M., E-mail: msharif.math@pu.edu.pk; Manzoor, Rubab, E-mail: rubab.manzoor@umt.edu.pk; Department of Mathematics, University of Management and Technology, Johar Town Campus, Lahore-54782

This paper explores the influences of dark energy on the shear-free axially symmetric evolution by considering self-interacting Brans–Dicke gravity as a dark energy candidate. We describe energy source of the model and derive all the effective dynamical variables as well as effective structure scalars. It is found that scalar field is one of the sources of anisotropy and dissipation. The resulting effective structure scalars help to study the dynamics associated with dark energy in any axial configuration. In order to investigate shear-free evolution, we formulate a set of governing equations along with heat transport equation. We discuss consequences of shear-freemore » condition upon different SBD fluid models like dissipative non-geodesic and geodesic models. For dissipative non-geodesic case, the rotational distribution turns out to be the necessary and sufficient condition for radiating model. The dissipation depends upon inhomogeneous expansion. The geodesic model is found to be irrotational and non-radiating. The non-dissipative geodesic model leads to FRW model for positive values of the expansion parameter.« less

A three-dimensional model of corotating streams in the solar wind. 1: Theoretical foundations

NASA Technical Reports Server (NTRS)

Pizzo, V. J.

1978-01-01

The theoretical and mathematical background pertinent to the study of steady, corotating solar wind structure in all three spatial dimensions (3-D) is discussed. The dynamical evolution of the plasma in interplanetary space (defined as the region beyond roughly 35 solar radii where the flow is supersonic) is approximately described by the nonlinear, single fluid, polytropic (magneto-) hydrodynamic equations. Efficient numerical techniques for solving this complex system of coupled, hyperbolic partial differential equations are outlined. The formulation is inviscid and nonmagnetic, but methods allow for the potential inclusion of both features with only modest modifications. One simple, highly idealized, hydrodynamic model stream is examined to illustrate the fundamental processes involved in the 3-D dynamics of stream evolution. Spatial variations in the rotational stream interaction mechanism were found to produce small nonradial flows on a global scale that lead to the transport of mass, energy, and momentum away from regions of relative compression and into regions of relative rarefaction.

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

PubMed Central

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

2014-01-01

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

The Nonlinear Magnetosphere: Expressions in MHD and in Kinetic Models

NASA Technical Reports Server (NTRS)

Hesse, Michael; Birn, Joachim

2011-01-01

Like most plasma systems, the magnetosphere of the Earth is governed by nonlinear dynamic evolution equations. The impact of nonlinearities ranges from large scales, where overall dynamics features are exhibiting nonlinear behavior, to small scale, kinetic, processes, where nonlinear behavior governs, among others, energy conversion and dissipation. In this talk we present a select set of examples of such behavior, with a specific emphasis on how nonlinear effects manifest themselves in MHD and in kinetic models of magnetospheric plasma dynamics.

Homogeneous quantum electrodynamic turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1992-01-01

The electromagnetic field equations and Dirac equations for oppositely charged wave functions are numerically time-integrated using a spatial Fourier method. The numerical approach used, a spectral transform technique, is based on a continuum representation of physical space. The coupled classical field equations contain a dimensionless parameter which sets the strength of the nonlinear interaction (as the parameter increases, interaction volume decreases). For a parameter value of unity, highly nonlinear behavior in the time-evolution of an individual wave function, analogous to ideal fluid turbulence, is observed. In the truncated Fourier representation which is numerically implemented here, the quantum turbulence is homogeneous but anisotropic and manifests itself in the nonlinear evolution of equilibrium modal spatial spectra for the probability density of each particle and also for the electromagnetic energy density. The results show that nonlinearly interacting fermionic wave functions quickly approach a multi-mode, dynamic equilibrium state, and that this state can be determined by numerical means.

The Arrow of Time in the Collapse of Collisionless Self-gravitating Systems: Non-validity of the Vlasov-Poisson Equation during Violent Relaxation

NASA Astrophysics Data System (ADS)

Beraldo e Silva, Leandro; de Siqueira Pedra, Walter; Sodré, Laerte; Perico, Eder L. D.; Lima, Marcos

2017-09-01

The collapse of a collisionless self-gravitating system, with the fast achievement of a quasi-stationary state, is driven by violent relaxation, with a typical particle interacting with the time-changing collective potential. It is traditionally assumed that this evolution is governed by the Vlasov-Poisson equation, in which case entropy must be conserved. We run N-body simulations of isolated self-gravitating systems, using three simulation codes, NBODY-6 (direct summation without softening), NBODY-2 (direct summation with softening), and GADGET-2 (tree code with softening), for different numbers of particles and initial conditions. At each snapshot, we estimate the Shannon entropy of the distribution function with three different techniques: Kernel, Nearest Neighbor, and EnBiD. For all simulation codes and estimators, the entropy evolution converges to the same limit as N increases. During violent relaxation, the entropy has a fast increase followed by damping oscillations, indicating that violent relaxation must be described by a kinetic equation other than the Vlasov-Poisson equation, even for N as large as that of astronomical structures. This indicates that violent relaxation cannot be described by a time-reversible equation, shedding some light on the so-called “fundamental paradox of stellar dynamics.” The long-term evolution is well-described by the orbit-averaged Fokker-Planck model, with Coulomb logarithm values in the expected range 10{--}12. By means of NBODY-2, we also study the dependence of the two-body relaxation timescale on the softening length. The approach presented in the current work can potentially provide a general method for testing any kinetic equation intended to describe the macroscopic evolution of N-body systems.

A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations

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

Liu, Chang, E-mail: cliuaa@ust.hk; Xu, Kun, E-mail: makxu@ust.hk; Sun, Quanhua, E-mail: qsun@imech.ac.cn

Fluid dynamic equations are valid in their respective modeling scales, such as the particle mean free path scale of the Boltzmann equation and the hydrodynamic scale of the Navier–Stokes (NS) equations. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. Even though the Boltzmann equation is claimed to be valid in all scales, many Boltzmann solvers, including direct simulation Monte Carlo method, require the cell resolution to the order of particle mean free path scale. Therefore, they are still single scale methods. In order to study multiscale flow evolution efficiently, themore » dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. Even though the UGKS is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time, it still has space to develop more accurate flow solver in the region, where the time step is comparable with the local particle mean free time. In such a scale, there is dynamic difference from the full Boltzmann collision term and the model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region where it is needed. The central ingredient of the UGKS is the coupled treatment of particle transport and collision in the flux evaluation across a cell interface, where a continuous flow dynamics from kinetic to hydrodynamic scales is modeled. The newly developed UGKS has the asymptotic preserving (AP) property of recovering the NS solutions in the continuum flow regime, and the full Boltzmann solution in the rarefied regime. In the mostly unexplored transition regime, the UGKS itself provides a valuable tool for the non-equilibrium flow study. The mathematical properties of the scheme, such as stability, accuracy, and the asymptotic preserving, will be analyzed in this paper as well.« less

On the non-stationary generalized Langevin equation

NASA Astrophysics Data System (ADS)

Meyer, Hugues; Voigtmann, Thomas; Schilling, Tanja

2017-12-01

In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble ("bundle") of trajectories. Under stationary conditions, the time-evolution of such averages is described by the generalized Langevin equation. By contrast, if the dynamics is not stationary, it is not a priori clear which form the equation of motion for an averaged observable has. We employ the formalism of time-dependent projection operator techniques to derive the equation of motion for a non-equilibrium trajectory-averaged observable as well as for its non-stationary auto-correlation function. The equation is similar in structure to the generalized Langevin equation but exhibits a time-dependent memory kernel as well as a fluctuating force that implicitly depends on the initial conditions of the process. We also derive a relation between this memory kernel and the autocorrelation function of the fluctuating force that has a structure similar to a fluctuation-dissipation relation. In addition, we show how the choice of the projection operator allows us to relate the Taylor expansion of the memory kernel to data that are accessible in MD simulations and experiments, thus allowing us to construct the equation of motion. As a numerical example, the procedure is applied to Brownian motion initialized in non-equilibrium conditions and is shown to be consistent with direct measurements from simulations.

On the numeric integration of dynamic attitude equations

NASA Technical Reports Server (NTRS)

Crouch, P. E.; Yan, Y.; Grossman, Robert

1992-01-01

We describe new types of numerical integration algorithms developed by the authors. The main aim of the algorithms is to numerically integrate differential equations which evolve on geometric objects, such as the rotation group. The algorithms provide iterates which lie on the prescribed geometric object, either exactly, or to some prescribed accuracy, independent of the order of the algorithm. This paper describes applications of these algorithms to the evolution of the attitude of a rigid body.

A depth-averaged debris-flow model that includes the effects of evolving dilatancy: II. Numerical predictions and experimental tests.

USGS Publications Warehouse

George, David L.; Iverson, Richard M.

2014-01-01

We evaluate a new depth-averaged mathematical model that is designed to simulate all stages of debris-flow motion, from initiation to deposition. A companion paper shows how the model’s five governing equations describe simultaneous evolution of flow thickness, solid volume fraction, basal pore-fluid pressure, and two components of flow momentum. Each equation contains a source term that represents the influence of state-dependent granular dilatancy. Here we recapitulate the equations and analyze their eigenstructure to show that they form a hyperbolic system with desirable stability properties. To solve the equations we use a shock-capturing numerical scheme with adaptive mesh refinement, implemented in an open-source software package we call D-Claw. As tests of D-Claw, we compare model output with results from two sets of large-scale debris-flow experiments. One set focuses on flow initiation from landslides triggered by rising pore-water pressures, and the other focuses on downstream flow dynamics, runout, and deposition. D-Claw performs well in predicting evolution of flow speeds, thicknesses, and basal pore-fluid pressures measured in each type of experiment. Computational results illustrate the critical role of dilatancy in linking coevolution of the solid volume fraction and pore-fluid pressure, which mediates basal Coulomb friction and thereby regulates debris-flow dynamics.

Evolution of quantum-like modeling in decision making processes

NASA Astrophysics Data System (ADS)

Khrennikova, Polina

2012-12-01

The application of the mathematical formalism of quantum mechanics to model behavioral patterns in social science and economics is a novel and constantly emerging field. The aim of the so called 'quantum like' models is to model the decision making processes in a macroscopic setting, capturing the particular 'context' in which the decisions are taken. Several subsequent empirical findings proved that when making a decision people tend to violate the axioms of expected utility theory and Savage's Sure Thing principle, thus violating the law of total probability. A quantum probability formula was devised to describe more accurately the decision making processes. A next step in the development of QL-modeling in decision making was the application of Schrödinger equation to describe the evolution of people's mental states. A shortcoming of Schrödinger equation is its inability to capture dynamics of an open system; the brain of the decision maker can be regarded as such, actively interacting with the external environment. Recently the master equation, by which quantum physics describes the process of decoherence as the result of interaction of the mental state with the environmental 'bath', was introduced for modeling the human decision making. The external environment and memory can be referred to as a complex 'context' influencing the final decision outcomes. The master equation can be considered as a pioneering and promising apparatus for modeling the dynamics of decision making in different contexts.

Inverse problem of HIV cell dynamics using Genetic Algorithms

NASA Astrophysics Data System (ADS)

González, J. A.; Guzmán, F. S.

2017-01-01

In order to describe the cell dynamics of T-cells in a patient infected with HIV, we use a flavour of Perelson's model. This is a non-linear system of Ordinary Differential Equations that describes the evolution of healthy, latently infected, infected T-cell concentrations and the free viral cells. Different parameters in the equations give different dynamics. Considering the concentration of these types of cells is known for a particular patient, the inverse problem consists in estimating the parameters in the model. We solve this inverse problem using a Genetic Algorithm (GA) that minimizes the error between the solutions of the model and the data from the patient. These errors depend on the parameters of the GA, like mutation rate and population, although a detailed analysis of this dependence will be described elsewhere.

Nonlinear viscosity in brane-world cosmology with a Gauss–Bonnet term

NASA Astrophysics Data System (ADS)

Debnath, P. S.; Beesham, A.; Paul, B. C.

2018-06-01

Cosmological solutions are obtained with nonlinear bulk viscous cosmological fluid in the Randall–Sundrum type II (RS) brane-world model with or without Gauss–Bonnet (GB) terms. To describe such a viscous fluid, we consider the nonlinear transport equation which may be used far from equilibrium during inflation or reheating. Cosmological models are explored for both (i) power law and (ii) exponential evolution of the early universe in the presence of an imperfect fluid described by the non-linear Israel and Stewart theory (nIS). We obtain analytic solutions and the complex field equations are also analyzed numerically to study the evolution of the universe. The stability analysis of the equilibrium points of the dynamical system associated with the evolution of the nonlinear bulk viscous fluid in the RS Brane in the presence (or absence) of a GB term are also studied.

Effective long wavelength scalar dynamics in de Sitter

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

Moss, Ian; Rigopoulos, Gerasimos, E-mail: ian.moss@newcastle.ac.uk, E-mail: gerasimos.rigopoulos@ncl.ac.uk

We discuss the effective infrared theory governing a light scalar's long wavelength dynamics in de Sitter spacetime. We show how the separation of scales around the physical curvature radius k / a ∼ H can be performed consistently with a window function and how short wavelengths can be integrated out in the Schwinger-Keldysh path integral formalism. At leading order, and for time scales Δ t >> H {sup −1}, this results in the well-known Starobinsky stochastic evolution. However, our approach allows for the computation of quantum UV corrections, generating an effective potential on which the stochastic dynamics takes place. Themore » long wavelength stochastic dynamical equations are now second order in time, incorporating temporal scales Δ t ∼ H {sup −1} and resulting in a Kramers equation for the probability distribution—more precisely the Wigner function—in contrast to the more usual Fokker-Planck equation. This feature allows us to non-perturbatively evaluate, within the stochastic formalism, not only expectation values of field correlators, but also the stress-energy tensor of φ.« less

Role of phase synchronisation in turbulence

NASA Astrophysics Data System (ADS)

Moradi, Sara; Teaca, Bogdan; Anderson, Johan

2017-11-01

The role of the phase dynamics in turbulence is investigated. As a demonstration of the importance of the phase dynamics, a simplified system is used, namely the one-dimensional Burgers equation, which is evolved numerically. The system is forced via a known external force, with two components that are added into the evolution equations of the amplitudes and the phase of the Fourier modes, separately. In this way, we are able to control the impact of the force on the dynamics of the phases. In the absence of the direct forcing in the phase equation, it is observed that the phases are not stochastic as assumed in the Random Phase Approximation (RPA) models, and in contrast, the non-linear couplings result in intermittent locking of the phases to ± π/2. The impact of the force, applied purely on the phases, is to increase the occurrence of the phase locking events in which the phases of the modes in a wide k range are now locked to ± π/2, leading to a change in the dynamics of both phases and amplitudes, with a significant localization of the real space flow structures.

Quantum power functional theory for many-body dynamics

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

Schmidt, Matthias, E-mail: Matthias.Schmidt@uni-bayreuth.de

2015-11-07

We construct a one-body variational theory for the time evolution of nonrelativistic quantum many-body systems. The position- and time-dependent one-body density, particle current, and time derivative of the current act as three variational fields. The generating (power rate) functional is minimized by the true current time derivative. The corresponding Euler-Lagrange equation, together with the continuity equation for the density, forms a closed set of one-body equations of motion. Space- and time-nonlocal one-body forces are generated by the superadiabatic contribution to the functional. The theory applies to many-electron systems.

The Dynamics and Evolution of Poles and Rogue Waves for Nonlinear Schrödinger Equations*

NASA Astrophysics Data System (ADS)

Chiu, Tin Lok; Liu, Tian Yang; Chan, Hiu Ning; Wing Chow, Kwok

2017-09-01

Rogue waves are unexpectedly large deviations from equilibrium or otherwise calm positions in physical systems, e.g. hydrodynamic waves and optical beam intensities. The profiles and points of maximum displacements of these rogue waves are correlated with the movement of poles of the exact solutions extended to the complex plane through analytic continuation. Such links are shown to be surprisingly precise for the first order rogue wave of the nonlinear Schrödinger (NLS) and the derivative NLS equations. A computational study on the second order rogue waves of the NLS equation also displays remarkable agreements.

Physics of Life: A Model for Non-Newtonian Properties of Living Systems

NASA Technical Reports Server (NTRS)

Zak, Michail

2010-01-01

This innovation proposes the reconciliation of the evolution of life with the second law of thermodynamics via the introduction of the First Principle for modeling behavior of living systems. The structure of the model is quantum-inspired: it acquires the topology of the Madelung equation in which the quantum potential is replaced with the information potential. As a result, the model captures the most fundamental property of life: the progressive evolution; i.e. the ability to evolve from disorder to order without any external interference. The mathematical structure of the model can be obtained from the Newtonian equations of motion (representing the motor dynamics) coupled with the corresponding Liouville equation (representing the mental dynamics) via information forces. All these specific non-Newtonian properties equip the model with the levels of complexity that matches the complexity of life, and that makes the model applicable for description of behaviors of ecological, social, and economical systems. Rather than addressing the six aspects of life (organization, metabolism, growth, adaptation, response to stimuli, and reproduction), this work focuses only on biosignature ; i.e. the mechanical invariants of life, and in particular, the geometry and kinematics of behavior of living things. Living things obey the First Principles of Newtonian mechanics. One main objective of this model is to extend the First Principles of classical physics to include phenomenological behavior on living systems; to develop a new mathematical formalism within the framework of classical dynamics that would allow one to capture the specific properties of natural or artificial living systems such as formation of the collective mind based upon abstract images of the selves and non-selves; exploitation of this collective mind for communications and predictions of future expected characteristics of evolution; and for making decisions and implementing the corresponding corrections if the expected scenario is different from the originally planned one. This approach postulates that even a primitive living species possesses additional, non-Newtonian properties that are not included in the laws of Newtonian or statistical mechanics. These properties follow from a privileged ability of living systems to possess a self-image (a concept introduced in psychology) and to interact with it. The proposed mathematical system is based on the coupling of the classical dynamical system representing the motor dynamics with the corresponding Liouville equation describing the evolution of initial uncertainties in terms of the probability density and representing the mental dynamics. The coupling is implemented by the information-based supervising forces that can be associated with self-awareness. These forces fundamentally change the pattern of the probability evolution, and therefore, lead to a major departure of the behavior of living systems from the patterns of both Newtonian and statistical mechanics. This innovation is meant to capture the signature of life based only on observable behavior, not on any biochemistry. This will not prevent the use of this model for developing artificial living systems, as well as for studying some general properties of behavior of natural, living systems.

Structure and Dynamics of Replication-Mutation Systems

NASA Astrophysics Data System (ADS)

Schuster, Peter

1987-03-01

The kinetic equations of polynucleotide replication can be brought into fairly simple form provided certain environmental conditions are fulfilled. Two flow reactors, the continuously stirred tank reactor (CSTR) and a special dialysis reactor are particularly suitable for the analysis of replication kinetics. An experimental setup to study the chemical reaction network of RNA synthesis was derived from the bacteriophage Qβ. It consists of a virus specific RNA polymerase, Qβ replicase, the activated ribonucleosides GTP, ATP, CTP and UTP as well as a template suitable for replication. The ordinary differential equations for replication and mutation under the conditions of the flow reactors were analysed by the qualitative methods of bifurcation theory as well as by numerical integration. The various kinetic equations are classified according to their dynamical properties: we distinguish "quasilinear systems" which have uniquely stable point attractors and "nonlinear systems" with inherent nonlinearities which lead to multiple steady states, Hopf bifuractions, Feigenbaum-like sequences and chaotic dynamics for certain parameter ranges. Some examples which are relevant in molecular evolution and population genetics are discussed in detail.

General high-order breathers and rogue waves in the (3 + 1) -dimensional KP-Boussinesq equation

NASA Astrophysics Data System (ADS)

Sun, Baonan; Wazwaz, Abdul-Majid

2018-11-01

In this work, we investigate the (3 + 1) -dimensional KP-Boussinesq equation, which can be used to describe the nonlinear dynamic behavior in scientific and engineering applications. We derive general high-order soliton solutions by using the Hirota's bilinear method combined with the perturbation expansion technique. We also obtain periodic solutions comprising of high-order breathers, periodic line waves, and mixed solutions consisting of breathers and periodic line waves upon selecting particular parameter constraints of the obtained soliton solutions. Furthermore, smooth rational solutions are generated by taking a long wave limit of the soliton solutions. These smooth rational solutions include high-order rogue waves, high-order lumps, and hybrid solutions consisting of lumps and line rogue waves. To better understand the dynamical behaviors of these solutions, we discuss some illustrative graphical analyses. It is expected that our results can enrich the dynamical behavior of the (3 + 1) -dimensional nonlinear evolution equations of other forms.

Generation of localized patterns in anharmonic lattices with cubic-quintic nonlinearities and fourth-order dispersion via a variational approach

NASA Astrophysics Data System (ADS)

Wamba, Etienne; Tchakoutio Nguetcho, Aurélien S.

2018-05-01

We use the time-dependent variational method to examine the formation of localized patterns in dynamically unstable anharmonic lattices with cubic-quintic nonlinearities and fourth-order dispersion. The governing equation is an extended nonlinear Schrödinger equation known for modified Frankel-Kontorova models of atomic lattices and here derived from an extended Bose-Hubbard model of bosonic lattices with local three-body interactions. In presence of modulated waves, we derive and investigate the ordinary differential equations for the time evolution of the amplitude and phase of dynamical perturbation. Through an effective potential, we find the modulationally unstable domains of the lattice and discuss the effect of the fourth-order dispersion in the dynamics. Direct numerical simulations are performed to support our analytical results, and a good agreement is found. Various types of localized patterns, including breathers and solitonic chirped-like pulses, form in the system as a result of interplay between the cubic-quintic nonlinearities and the second- and fourth-order dispersions.

Nonlinear Dynamics, Artificial Cognition and Galactic Export

NASA Astrophysics Data System (ADS)

Rössler, Otto E.

2004-08-01

The field of nonlinear dynamics focuses on function rather than structure. Evolution and brain function are examples. An equation for a brain, described in 1973, is explained. Then, a principle of interactional function change between two coupled equations of this type is described. However, all of this is not done in an abstract manner but in close contact with the meaning of these equations in a biological context. Ethological motivation theory and Batesonian interaction theory are reencountered. So is a fairly unknown finding by van Hooff on the indistinguishability of smile and laughter in a single primate species. Personhood and evil, two human characteristics, are described abstractly. Therapies and the question of whether it is ethically allowed to export benevolence are discussed. The whole dynamic approach is couched in terms of the Cartesian narrative, invented in the 17th century and later called Enlightenment. Whether or not it is true that a "second Enlightenment" is around the corner is the main question raised in the present paper.

Stochastic Representation of Chaos Using Terminal Attractors

NASA Technical Reports Server (NTRS)

Zak, Michail

2006-01-01

A nonlinear version of the Liouville equation based on terminal attractors is part of a mathematical formalism for describing postinstability motions of dynamical systems characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism can be applied to both conservative systems (e.g., multibody systems in celestial mechanics) and dissipative systems (e.g., viscous fluids). The development of the present formalism was undertaken in an effort to remove positive Lyapunov exponents. The means chosen to accomplish this is coupling of the governing dynamical equations with the corresponding Liouville equation that describes the evolution of the flow of error probability. The underlying idea is to suppress the divergences of different trajectories that correspond to different initial conditions, without affecting a target trajectory, which is one that starts with prescribed initial conditions.

Dynamics of localized structures in reaction-diffusion systems induced by delayed feedback

NASA Astrophysics Data System (ADS)

Gurevich, Svetlana V.

2013-05-01

We are interested in stability properties of a single localized structure in a three-component reaction-diffusion system subjected to the time-delayed feedback. We shall show that variation in the product of the delay time and the feedback strength leads to complex dynamical behavior of the system, including formation of target patterns, spontaneous motion, and spontaneous breathing as well as various complex structures, arising from combination of different oscillatory instabilities. In the case of spontaneous motion, we provide a bifurcation analysis of the delayed system and derive an order parameter equation for the position of the localized structure, explicitly describing its temporal evolution in the vicinity of the bifurcation point. This equation is a subject to a nonlinear delay differential equation, which can be transformed to the normal form of the pitchfork drift bifurcation.

Derivation of a generalized Schrödinger equation from the theory of scale relativity

NASA Astrophysics Data System (ADS)

Chavanis, Pierre-Henri

2017-06-01

Using Nottale's theory of scale relativity relying on a fractal space-time, we derive a generalized Schrödinger equation taking into account the interaction of the system with the external environment. This equation describes the irreversible evolution of the system towards a static quantum state. We first interpret the scale-covariant equation of dynamics stemming from Nottale's theory as a hydrodynamic viscous Burgers equation for a potential flow involving a complex velocity field and an imaginary viscosity. We show that the Schrödinger equation can be directly obtained from this equation by performing a Cole-Hopf transformation equivalent to the WKB transformation. We then introduce a friction force proportional and opposite to the complex velocity in the scale-covariant equation of dynamics in a way that preserves the local conservation of the normalization condition. We find that the resulting generalized Schrödinger equation, or the corresponding fluid equations obtained from the Madelung transformation, involve not only a damping term but also an effective thermal term. The friction coefficient and the temperature are related to the real and imaginary parts of the complex friction coefficient in the scale-covariant equation of dynamics. This may be viewed as a form of fluctuation-dissipation theorem. We show that our generalized Schrödinger equation satisfies an H-theorem for the quantum Boltzmann free energy. As a result, the probability distribution relaxes towards an equilibrium state which can be viewed as a Boltzmann distribution including a quantum potential. We propose to apply this generalized Schrödinger equation to dark matter halos in the Universe, possibly made of self-gravitating Bose-Einstein condensates.

Asymptotic behavior of dynamical variables and naked singularity formation in spherically symmetric gravitational collapse

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

Kawakami, Hayato; Mitsuda, Eiji; Nambu, Yasusada

In considering the gravitational collapse of matter, it is an important problem to clarify what kind of conditions leads to the formation of naked singularity. For this purpose, we apply the 1+3 orthonormal frame formalism introduced by Uggla et al. to the spherically symmetric gravitational collapse of a perfect fluid. This formalism allows us to construct an autonomous system of evolution and constraint equations for scale-invariant dynamical variables normalized by the volume expansion rate of the timelike orthonormal frame vector. We investigate the asymptotic evolution of such dynamical variables towards the formation of a central singularity and present a conjecturemore » that the steep spatial gradient for the normalized density function is a characteristic of the naked singularity formation.« less

Strong-field gravitational-wave emission in Schwarzschild and Kerr geometries: some general considerations

NASA Astrophysics Data System (ADS)

Rodríguez, J. F.; Rueda, J. A.; Ruffini, R.

2018-01-01

We have used the perturbations of the exact solutions of the Einstein equations to estimate the relativistic wave emission of a test particle orbiting around a black hole. We show how the hamiltonian equations of motion of a test particle augmented with the radiation-reaction force can establish a priori constraints on the possible phenomena occurring in the merger of compact objects. The dynamical evolution consists of a helicoidal sequence of quasi-circular orbits, induced by the radiation-reaction and the background spacetime. Near the innermost stable circular orbit the evolution is followed by a smooth transition and finally plunges geodesically into the black hole horizon. This analysis gives physical insight of the merger of two equal masses objects.

Axisymmetric contour dynamics for buoyant vortex rings

NASA Astrophysics Data System (ADS)

Chang, Ching; Llewellyn Smith, Stefan

2017-11-01

Vortex rings are important in many fluid flows in engineering and environmental applications. A family of steady propagating vortex rings including thin-core rings and Hill's spherical vortex was obtained by Norbury (1973). However, the dynamics of vortex rings in the presence of buoyancy has not been investigated yet in detail. When the core of a ring is thin, we may formulate reduced equations using momentum balance for vortex filaments, but that is not the case for ``fat'' rings. In our study, we use contour dynamics to study the time evolution of axisymmetric vortex rings when the density of the fluid inside the ring differs from that of the ambient. Axisymmetry leads to an almost-conserved material variable when the Boussinesq approximation is made. A set of integro-differential equations is solved numerically for these buoyant vortex rings. The same physical settings are also used to run a DNS code and compare to the results from contour dynamics.

Wetting dynamics of a collapsing fluid hole

NASA Astrophysics Data System (ADS)

Bostwick, J. B.; Dijksman, J. A.; Shearer, M.

2017-01-01

The collapse dynamics of an axisymmetric fluid cavity that wets the bottom of a rotating bucket bound by vertical sidewalls are studied. Lubrication theory is applied to the governing field equations for the thin film to yield an evolution equation that captures the effect of capillary, gravitational, and centrifugal forces on this converging flow. The focus is on the quasistatic spreading regime, whereby contact-line motion is governed by a constitutive law relating the contact-angle to the contact-line speed. Surface tension forces dominate the collapse dynamics for small holes with the collapse time appearing as a power law whose exponent compares favorably to experiments in the literature. Gravity accelerates the collapse process. Volume dependence is predicted and compared with experiment. Centrifugal forces slow the collapse process and lead to complex dynamics characterized by stalled spreading behavior that separates the large and small hole asymptotic regimes.

On the physically based modeling of surface tension and moving contact lines with dynamic contact angles on the continuum scale

NASA Astrophysics Data System (ADS)

Huber, M.; Keller, F.; Säckel, W.; Hirschler, M.; Kunz, P.; Hassanizadeh, S. M.; Nieken, U.

2016-04-01

The description of wetting phenomena is a challenging problem on every considerable length-scale. The behavior of interfaces and contact lines on the continuum scale is caused by intermolecular interactions like the Van der Waals forces. Therefore, to describe surface tension and the resulting dynamics of interfaces and contact lines on the continuum scale, appropriate formulations must be developed. While the Continuum Surface Force (CSF) model is well-engineered for the description of interfaces, there is still a lack of treatment of contact lines, which are defined by the intersection of an ending fluid interface and a solid boundary surface. In our approach we use a balance equation for the contact line and extend the Navier-Stokes equations in analogy to the extension of a two-phase interface in the CSF model. Since this model depicts a physically motivated approach on the continuum scale, no fitting parameters are introduced and the deterministic description leads to a dynamical evolution of the system. As verification of our theory, we show a Smoothed Particle Hydrodynamics (SPH) model and simulate the evolution of droplet shapes and their corresponding contact angles.

Nonlinear waves in solids with slow dynamics: an internal-variable model.

PubMed

Berjamin, H; Favrie, N; Lombard, B; Chiavassa, G

2017-05-01

In heterogeneous solids such as rocks and concrete, the speed of sound diminishes with the strain amplitude of a dynamic loading (softening). This decrease, known as 'slow dynamics', occurs at time scales larger than the period of the forcing. Also, hysteresis is observed in the steady-state response. The phenomenological model by Vakhnenko et al. (2004 Phys. Rev. E 70, 015602. (doi:10.1103/PhysRevE.70.015602)) is based on a variable that describes the softening of the material. However, this model is one dimensional and it is not thermodynamically admissible. In the present article, a three-dimensional model is derived in the framework of the finite-strain theory. An internal variable that describes the softening of the material is introduced, as well as an expression of the specific internal energy. A mechanical constitutive law is deduced from the Clausius-Duhem inequality. Moreover, a family of evolution equations for the internal variable is proposed. Here, an evolution equation with one relaxation time is chosen. By construction, this new model of the continuum is thermodynamically admissible and dissipative (inelastic). In the case of small uniaxial deformations, it is shown analytically that the model reproduces qualitatively the main features of real experiments.

Spectral evolution of weakly nonlinear random waves: kinetic description vs direct numerical simulations

NASA Astrophysics Data System (ADS)

Annenkov, Sergei; Shrira, Victor

2016-04-01

We study numerically the long-term evolution of water wave spectra without wind forcing, using three different models, aiming at understanding the role of different sets of assumptions. The first model is the classical Hasselmann kinetic equation (KE). We employ the WRT code kindly provided by G. van Vledder. Two other models are new. As the second model, we use the generalised kinetic equation (gKE), derived without the assumption of quasi-stationarity. Thus, unlike the KE, the gKE is valid in the cases when a wave spectrum is changing rapidly (e.g. at the initial stage of evolution of a narrow spectrum). However, the gKE employs the same statistical closure as the KE. The third model is based on the Zakharov integrodifferential equation for water waves and does not depend on any statistical assumptions. Since the Zakharov equation plays the role of the primitive equation of the theory of wave turbulence, we refer to this model as direct numerical simulation of spectral evolution (DNS-ZE). For initial conditions, we choose two narrow-banded spectra with the same frequency distribution (a JONSWAP spectrum with high peakedness γ = 6) and different degrees of directionality. These spectra are from the set of observations collected in a directional wave tank by Onorato et al (2009). Spectrum A is very narrow in angle (corresponding to N = 840 in the cosN directional model). Spectrum B is initially wider in angle (corresponds to N = 24). Short-term evolution of both spectra (O(102) wave periods) has been studied numerically by Xiao et al (2013) using two other approaches (broad-band modified nonlinear Schrödinger equation and direct numerical simulation based on the high-order spectral method). We use these results to verify the initial stage of our DNS-ZE simulations. However, the advantage of the DNS-ZE method is that it allows to study long-term spectral evolution (up to O(104) periods), which was previously possible only with the KE. In the short-term evolution, we find a good agreement between our DNS-ZE results and simulations by Xiao et al (2013), both for the evolution of frequency spectra and for the directional spreading. In the long term, all three approaches demonstrate very close evolution of integral characteristics of spectra, approaching for large time the theoretical asymptotes of the self-similar stage of evolution. However, the detailed comparison of the spectral evolution shows certain notable differences. Both kinetic equations give virtually identical evolution of spectrum B, but in the case of initially nearly one-dimensional spectrum A the KE overestimates the amplitude of the spectral peak. Meanwhile, the DNS-ZE results show considerably wider spectra with less pronounced peak. There is a striking difference for the rate of spectral broadening, which is much larger for the gKE and especially for the KE, than for the DNS-ZE. We show that the rates of change of the spectra obtained with the DNS-ZE are proportional to the fourth power of nonlinearity, corresponding to the dynamical timescale of evolution, rather than the statistical timescale of both kinetic equations.

Spatial evolutionary epidemiology of spreading epidemics

PubMed Central

2016-01-01

Most spatial models of host–parasite interactions either neglect the possibility of pathogen evolution or consider that this process is slow enough for epidemiological dynamics to reach an equilibrium on a fast timescale. Here, we propose a novel approach to jointly model the epidemiological and evolutionary dynamics of spatially structured host and pathogen populations. Starting from a multi-strain epidemiological model, we use a combination of spatial moment equations and quantitative genetics to analyse the dynamics of mean transmission and virulence in the population. A key insight of our approach is that, even in the absence of long-term evolutionary consequences, spatial structure can affect the short-term evolution of pathogens because of the build-up of spatial differentiation in mean virulence. We show that spatial differentiation is driven by a balance between epidemiological and genetic effects, and this quantity is related to the effect of kin competition discussed in previous studies of parasite evolution in spatially structured host populations. Our analysis can be used to understand and predict the transient evolutionary dynamics of pathogens and the emergence of spatial patterns of phenotypic variation. PMID:27798295

Spatial evolutionary epidemiology of spreading epidemics.

PubMed

Lion, S; Gandon, S

2016-10-26

Most spatial models of host-parasite interactions either neglect the possibility of pathogen evolution or consider that this process is slow enough for epidemiological dynamics to reach an equilibrium on a fast timescale. Here, we propose a novel approach to jointly model the epidemiological and evolutionary dynamics of spatially structured host and pathogen populations. Starting from a multi-strain epidemiological model, we use a combination of spatial moment equations and quantitative genetics to analyse the dynamics of mean transmission and virulence in the population. A key insight of our approach is that, even in the absence of long-term evolutionary consequences, spatial structure can affect the short-term evolution of pathogens because of the build-up of spatial differentiation in mean virulence. We show that spatial differentiation is driven by a balance between epidemiological and genetic effects, and this quantity is related to the effect of kin competition discussed in previous studies of parasite evolution in spatially structured host populations. Our analysis can be used to understand and predict the transient evolutionary dynamics of pathogens and the emergence of spatial patterns of phenotypic variation. © 2016 The Author(s).

Modeling Day-to-day Flow Dynamics on Degradable Transport Network

PubMed Central

Gao, Bo; Zhang, Ronghui; Lou, Xiaoming

2016-01-01

Stochastic link capacity degradations are common phenomena in transport network which can cause travel time variations and further can affect travelers’ daily route choice behaviors. This paper formulates a deterministic dynamic model, to capture the day-to-day (DTD) flow evolution process in the presence of degraded link capacity degradations. The aggregated network flow dynamics are driven by travelers’ study of uncertain travel time and their choice of risky routes. This paper applies the exponential-smoothing filter to describe travelers’ study of travel time variations, and meanwhile formulates risk attitude parameter updating equation to reflect travelers’ endogenous risk attitude evolution schema. In addition, this paper conducts theoretical analyses to investigate several significant mathematical characteristics implied in the proposed DTD model, including fixed point existence, uniqueness, stability and irreversibility. Numerical experiments are used to demonstrate the effectiveness of the DTD model and verify some important dynamic system properties. PMID:27959903

Evolutionary optimization with data collocation for reverse engineering of biological networks.

PubMed

Tsai, Kuan-Yao; Wang, Feng-Sheng

2005-04-01

Modern experimental biology is moving away from analyses of single elements to whole-organism measurements. Such measured time-course data contain a wealth of information about the structure and dynamic of the pathway or network. The dynamic modeling of the whole systems is formulated as a reverse problem that requires a well-suited mathematical model and a very efficient computational method to identify the model structure and parameters. Numerical integration for differential equations and finding global parameter values are still two major challenges in this field of the parameter estimation of nonlinear dynamic biological systems. We compare three techniques of parameter estimation for nonlinear dynamic biological systems. In the proposed scheme, the modified collocation method is applied to convert the differential equations to the system of algebraic equations. The observed time-course data are then substituted into the algebraic system equations to decouple system interactions in order to obtain the approximate model profiles. Hybrid differential evolution (HDE) with population size of five is able to find a global solution. The method is not only suited for parameter estimation but also can be applied for structure identification. The solution obtained by HDE is then used as the starting point for a local search method to yield the refined estimates.

Algorithm for Stabilizing a POD-Based Dynamical System

NASA Technical Reports Server (NTRS)

Kalb, Virginia L.

2010-01-01

This algorithm provides a new way to improve the accuracy and asymptotic behavior of a low-dimensional system based on the proper orthogonal decomposition (POD). Given a data set representing the evolution of a system of partial differential equations (PDEs), such as the Navier-Stokes equations for incompressible flow, one may obtain a low-dimensional model in the form of ordinary differential equations (ODEs) that should model the dynamics of the flow. Temporal sampling of the direct numerical simulation of the PDEs produces a spatial time series. The POD extracts the temporal and spatial eigenfunctions of this data set. Truncated to retain only the most energetic modes followed by Galerkin projection of these modes onto the PDEs obtains a dynamical system of ordinary differential equations for the time-dependent behavior of the flow. In practice, the steps leading to this system of ODEs entail numerically computing first-order derivatives of the mean data field and the eigenfunctions, and the computation of many inner products. This is far from a perfect process, and often results in the lack of long-term stability of the system and incorrect asymptotic behavior of the model. This algorithm describes a new stabilization method that utilizes the temporal eigenfunctions to derive correction terms for the coefficients of the dynamical system to significantly reduce these errors.

Dynamics of entropic uncertainty for atoms immersed in thermal fluctuating massless scalar field

NASA Astrophysics Data System (ADS)

Huang, Zhiming

2018-04-01

In this article, the dynamics of quantum memory-assisted entropic uncertainty relation for two atoms immersed in a thermal bath of fluctuating massless scalar field is investigated. The master equation that governs the system evolution process is derived. It is found that the mixedness is closely associated with entropic uncertainty. For equilibrium state, the tightness of uncertainty vanishes. For the initial maximum entangled state, the tightness of uncertainty undergoes a slight increase and then declines to zero with evolution time. It is found that temperature can increase the uncertainty, but two-atom separation does not always increase the uncertainty. The uncertainty evolves to different relatively stable values for different temperatures and converges to a fixed value for different two-atom distances with evolution time. Furthermore, weak measurement reversal is employed to control the entropic uncertainty.

Gravity-Wave Dynamics in the Atmosphere

DTIC Science & Technology

2010-02-01

boundaries of domain. The viscous boundary layers are used as an artificial radiation condition. 25 The inclusion of viscous terms in an explicit temporal... evolution equations become Volterra equations of the second kind given by Kc11aT +K c 12bT + ˆ x −∞ dx′ (K11xa ′ T +K12xb ′ T )− 1 2 α2a + bxY = 0...nonlinear wavepackets arising from shear-flow instabilities. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18

Stability and bifurcation in a model for the dynamics of stem-like cells in leukemia under treatment

NASA Astrophysics Data System (ADS)

Rǎdulescu, I. R.; Cândea, D.; Halanay, A.

2012-11-01

A mathematical model for the dynamics of leukemic cells during treatment is introduced. Delay differential equations are used to model cells' evolution and are based on the Mackey-Glass approach, incorporating Goldie-Coldman law. Since resistance is propagated by cells that have the capacity of self-renewal, a population of stem-like cells is studied. Equilibrium points are calculated and their stability properties are investigated.

Generalized quantum Fokker-Planck equation for photoinduced nonequilibrium processes with positive definiteness condition

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

Jang, Seogjoo, E-mail: sjang@qc.cuny.edu

2016-06-07

This work provides a detailed derivation of a generalized quantum Fokker-Planck equation (GQFPE) appropriate for photo-induced quantum dynamical processes. The path integral method pioneered by Caldeira and Leggett (CL) [Physica A 121, 587 (1983)] is extended by utilizing a nonequilibrium influence functional applicable to different baths for the ground and the excited electronic states. Both nonequilibrium and non-Markovian effects are accounted for consistently by expanding the paths in the exponents of the influence functional up to the second order with respect to time. This procedure results in approximations involving only single time integrations for the exponents of the influence functionalmore » but with additional time dependent boundary terms that have been ignored in previous works. The boundary terms complicate the derivation of a time evolution equation but do not affect position dependent physical observables or the dynamics in the steady state limit. For an effective density operator with the boundary terms factored out, a time evolution equation is derived, through short time expansion of the effective action and Gaussian integration in analytically continued complex domain of space. This leads to a compact form of the GQFPE with time dependent kernels and additional terms, which renders the resulting equation to be in the Dekker form [Phys. Rep. 80, 1 (1981)]. Major terms of the equation are analyzed for the case of Ohmic spectral density with Drude cutoff, which shows that the new GQFPE satisfies the positive definiteness condition in medium to high temperature limit. Steady state limit of the GQFPE is shown to approach the well-known expression derived by CL in the high temperature and Markovian bath limit and also provides additional corrections due to quantum and non-Markovian effects of the bath.« less

Generalized quantum Fokker-Planck equation for photoinduced nonequilibrium processes with positive definiteness condition

NASA Astrophysics Data System (ADS)

Jang, Seogjoo

2016-06-01

This work provides a detailed derivation of a generalized quantum Fokker-Planck equation (GQFPE) appropriate for photo-induced quantum dynamical processes. The path integral method pioneered by Caldeira and Leggett (CL) [Physica A 121, 587 (1983)] is extended by utilizing a nonequilibrium influence functional applicable to different baths for the ground and the excited electronic states. Both nonequilibrium and non-Markovian effects are accounted for consistently by expanding the paths in the exponents of the influence functional up to the second order with respect to time. This procedure results in approximations involving only single time integrations for the exponents of the influence functional but with additional time dependent boundary terms that have been ignored in previous works. The boundary terms complicate the derivation of a time evolution equation but do not affect position dependent physical observables or the dynamics in the steady state limit. For an effective density operator with the boundary terms factored out, a time evolution equation is derived, through short time expansion of the effective action and Gaussian integration in analytically continued complex domain of space. This leads to a compact form of the GQFPE with time dependent kernels and additional terms, which renders the resulting equation to be in the Dekker form [Phys. Rep. 80, 1 (1981)]. Major terms of the equation are analyzed for the case of Ohmic spectral density with Drude cutoff, which shows that the new GQFPE satisfies the positive definiteness condition in medium to high temperature limit. Steady state limit of the GQFPE is shown to approach the well-known expression derived by CL in the high temperature and Markovian bath limit and also provides additional corrections due to quantum and non-Markovian effects of the bath.

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.

Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems.

PubMed

Venturi, D; Karniadakis, G E

2014-06-08

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima-Zwanzig-Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection-reaction problems.

Two-dimensional electronic spectra from the hierarchical equations of motion method: Application to model dimers

NASA Astrophysics Data System (ADS)

Chen, Liping; Zheng, Renhui; Shi, Qiang; Yan, YiJing

2010-01-01

We extend our previous study of absorption line shapes of molecular aggregates using the Liouville space hierarchical equations of motion (HEOM) method [L. P. Chen, R. H. Zheng, Q. Shi, and Y. J. Yan, J. Chem. Phys. 131, 094502 (2009)] to calculate third order optical response functions and two-dimensional electronic spectra of model dimers. As in our previous work, we have focused on the applicability of several approximate methods related to the HEOM method. We show that while the second order perturbative quantum master equations are generally inaccurate in describing the peak shapes and solvation dynamics, they can give reasonable peak amplitude evolution even in the intermediate coupling regime. The stochastic Liouville equation results in good peak shapes, but does not properly describe the excited state dynamics due to the lack of detailed balance. A modified version of the high temperature approximation to the HEOM gives the best agreement with the exact result.

Convolutionless Nakajima–Zwanzig equations for stochastic analysis in nonlinear dynamical systems

PubMed Central

Venturi, D.; Karniadakis, G. E.

2014-01-01

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima–Zwanzig–Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection–reaction problems. PMID:24910519

Essential equivalence of the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) and steepest-entropy-ascent models of dissipation for nonequilibrium thermodynamics.

PubMed

Montefusco, Alberto; Consonni, Francesco; Beretta, Gian Paolo

2015-04-01

By reformulating the steepest-entropy-ascent (SEA) dynamical model for nonequilibrium thermodynamics in the mathematical language of differential geometry, we compare it with the primitive formulation of the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) model and discuss the main technical differences of the two approaches. In both dynamical models the description of dissipation is of the "entropy-gradient" type. SEA focuses only on the dissipative, i.e., entropy generating, component of the time evolution, chooses a sub-Riemannian metric tensor as dissipative structure, and uses the local entropy density field as potential. GENERIC emphasizes the coupling between the dissipative and nondissipative components of the time evolution, chooses two compatible degenerate structures (Poisson and degenerate co-Riemannian), and uses the global energy and entropy functionals as potentials. As an illustration, we rewrite the known GENERIC formulation of the Boltzmann equation in terms of the square root of the distribution function adopted by the SEA formulation. We then provide a formal proof that in more general frameworks, whenever all degeneracies in the GENERIC framework are related to conservation laws, the SEA and GENERIC models of the dissipative component of the dynamics are essentially interchangeable, provided of course they assume the same kinematics. As part of the discussion, we note that equipping the dissipative structure of GENERIC with the Leibniz identity makes it automatically SEA on metric leaves.

Stochastic description of quantum Brownian dynamics

NASA Astrophysics Data System (ADS)

Yan, Yun-An; Shao, Jiushu

2016-08-01

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

Coalescing neutron stars - gravitational waves from polytropic models.

NASA Astrophysics Data System (ADS)

Ruffert, M.; Rampp, M.; Janka, H.-T.

1997-05-01

The dynamics, time evolution of the mass distribution, and gravitational wave signature of coalescing neutron stars described by polytropes are compared with three simulations published previously: (a) "Run 2" of Zhuge et al. (1994PhRvD..50.6247Z), (b) "Model III" of Shibata et al. (1992, Prog, Theor. Phys. 88, 1079), and (c) "Model A64" of Ruffert et al. (1996A&A...311..532R). We aim at studying the differences due to the use of different numerical methods, different implementations of the gravitational wave backreaction, and different equations of state. We integrate the three-dimensional Newtonian equations of hydrodynamics by the Riemann-solver based "Piecewise Parabolic Method" on an equidistant Cartesian grid. Comparison (a) confronts the results of our grid-based PPM scheme with those from an SPH code. We find that due to the lower numerical viscosity of the PPM code, the post-merging oscillations and pulsations can be followed for a longer time and lead to larger secondary and tertiary maxima of the gravitational wave luminosity and to a stronger peak of the gravitational wave spectrum at a frequency of about f=~1.8KHz when compared to the results of Zhuge et al. (1994PhRvD..50.6247Z). In case (b) two grid based codes with the same backreaction formalism but differing hydrodynamic integrators and slightly different initial conditions are compared. Instead of rotationally deformed initial neutron stars we use spherically shaped stars. Satisfactory agreement of the amplitude of the gravitational wave luminosity is established, although due to the different initial conditions a small time delay develops in the onset of the dynamical instability setting in when the two stars come very close. In (c) we find that using a polytropic equation of state instead of the high-density equation of state of Lattimer & Swesty (1991, Nucl. Phys. A535, 331) employed by Ruffert et al. (1996A&A...311..532R) does not change the overall dynamical evolution of the merger and yields agreement of the gravitational wave signature to within 20% accuracy. Whereas the polytropic law describes the dynamical behaviour of the bulk of the matter at and above nuclear density sufficiently well, we, however, find clear differences of the structure and evolution of the outer layers of the neutron stars where the stiffness of the equation of state is largely overestimated. This has important implications for questions like mass loss and disk formation during the merging of binary neutron stars.

Capture of Small Bodies After Tidal Disruption

NASA Astrophysics Data System (ADS)

Ershova, A.; Medvedev, Yu.

2017-09-01

The subject of the current work is the phisical and dynamical evolution of the small comets group formed by tidal disruption of the protocomet while passing near the large body (Sun, Jupiter). The equations of motion were integrated numericaly. In case of the Sun the evolution of the sun-grazing orbits were discussed and the typical lifetime of such comets was estimated. Nongravitational acceleration and the size reduction of fragments due to sublimation were taking into account using the Marsden formula.

Tidal evolution of close binary stars. I - Revisiting the theory of the equilibrium tide

NASA Technical Reports Server (NTRS)

Zahn, J.-P.

1989-01-01

The theory of the equilibrium tide in stars that possess a convective envelope is reexamined critically, taking recent developments into account and treating thermal convection in the most consistent way within the mixing-length approach. The weak points are identified and discussed, in particular, the reduction of the turbulent viscosity when the tidal period becomes shorter than the convective turnover time. An improved version is derived for the secular equations governing the dynamical evolution of close binaries of such type.

Dynamical analysis of an n‑H‑T cosmological quintessence real gas model with a general equation of state

NASA Astrophysics Data System (ADS)

Ivanov, Rossen I.; Prodanov, Emil M.

2018-01-01

The cosmological dynamics of a quintessence model based on real gas with general equation of state is presented within the framework of a three-dimensional dynamical system describing the time evolution of the number density, the Hubble parameter and the temperature. Two global first integrals are found and examples for gas with virial expansion and van der Waals gas are presented. The van der Waals system is completely integrable. In addition to the unbounded trajectories, stemming from the presence of the conserved quantities, stable periodic solutions (closed orbits) also exist under certain conditions and these represent models of a cyclic Universe. The cyclic solutions exhibit regions characterized by inflation and deflation, while the open trajectories are characterized by inflation in a “fly-by” near an unstable critical point.

Dynamic recrystallization behavior of an as-cast TiAl alloy during hot compression

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

Li, Jianbo, E-mail: lijianbo1205@163.com; Liu, Yong, E-mail: yonliu@csu.edu.cn; Wang, Yan, E-mail: wangyan@csu.edu.cn

2014-11-15

High temperature compressive deformation behaviors of as-cast Ti–43Al–4Nb–1.4W–0.6B alloy were investigated at temperatures ranging from 1050 °C to 1200 °C, and strain rates from 0.001 s{sup −1} to 1 s{sup −1}. Electron back scattered diffraction technique, scanning electron microscopy and transmission electron microscopy were employed to investigate the microstructural evolutions and nucleation mechanisms of the dynamic recrystallization. The results indicated that the true stress–true strain curves show a dynamic flow softening behavior. The dependence of the peak stress on the deformation temperature and the strain rate can well be expressed by a hyperbolic-sine type equation. The activation energy decreases withmore » increasing the strain. The size of the dynamically recrystallized β grains decreases with increasing the value of the Zener–Hollomon parameter (Z). When the flow stress reaches a steady state, the size of β grains almost remains constant with increasing the deformation strain. The continuous dynamic recrystallization plays a dominant role in the deformation. In order to characterize the evolution of dynamic recrystallization volume fraction, the dynamic recrystallization kinetics was studied by Avrami-type equation. Besides, the role of β phase and the softening mechanism during the hot deformation was also discussed in details. - Highlights: • The size of DRXed β grains decreases with increasing the value of the Z. • The CDRX plays a dominant role in the deformation. • The broken TiB{sub 2} particles can promote the nucleation of DRX.« less

Pyroclastic flow transport dynamics for a Montserrat volcano eruption

NASA Astrophysics Data System (ADS)

Cordoba, G.; Sparks, S.; del Risco, E.

2003-04-01

A two phase model of pyroclastic flows dynamics which account for the bed load and suspended load is shown. The model uses the compressible Navier-Stokes equations coupled with the convection-diffusion equation in order to take into account for the sedimentation. The skin friction is taken into account by using the wall functions. In despite of the complex mathematical formulation of the model, it has been implemented in a Personal Computer due to an assumption of two phase one velocity model which reduce the number of equations in the system. This non-linear equation system is solved numerically by using the Finite Element Method. This numerical method let us move the mesh in the direction of the deposition and then accounting for the shape of the bed and the thickness of the deposit The model is applied to the Montserrat's White River basin which extend from the dome to the sea, located about 4 Km away and then compared with the field data from the Boxing Day (26 December, 1997) eruption. Additionally some features as the temporary evolution of the dynamical pressure, particle concentration and temperature along the path at each time step is shown.

Yang-Baxter maps, discrete integrable equations and quantum groups

NASA Astrophysics Data System (ADS)

Bazhanov, Vladimir V.; Sergeev, Sergey M.

2018-01-01

For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang-Baxter equation. This map allows one to define an integrable discrete quantum evolution system on quadrilateral lattices, where local degrees of freedom (dynamical variables) take values in a tensor power of the quantized Lie algebra. The corresponding equations of motion admit the zero curvature representation. The commuting Integrals of Motion are defined in the standard way via the Quantum Inverse Problem Method, utilizing Baxter's famous commuting transfer matrix approach. All elements of the above construction have a meaningful quasi-classical limit. As a result one obtains an integrable discrete Hamiltonian evolution system, where the local equation of motion are determined by a classical Yang-Baxter map and the action functional is determined by the quasi-classical asymptotics of the universal R-matrix of the underlying quantum algebra. In this paper we present detailed considerations of the above scheme on the example of the algebra Uq (sl (2)) leading to discrete Liouville equations, however the approach is rather general and can be applied to any quantized Lie algebra.

Dynamics and elastic interactions of the discrete multi-dark soliton solutions for the Kaup-Newell lattice equation

NASA Astrophysics Data System (ADS)

Liu, Nan; Wen, Xiao-Yong

2018-03-01

Under consideration in this paper is the Kaup-Newell (KN) lattice equation which is an integrable discretization of the KN equation. Infinitely, many conservation laws and discrete N-fold Darboux transformation (DT) for this system are constructed and established based on its Lax representation. Via the resulting N-fold DT, the discrete multi-dark soliton solutions in terms of determinants are derived from non-vanishing background. Propagation and elastic interaction structures of such solitons are shown graphically. Overtaking interaction phenomena between/among the two, three and four solitons are discussed. Numerical simulations are used to explore their dynamical behaviors of such multi-dark solitons. Numerical results show that their evolutions are stable against a small noise. Results in this paper might be helpful for understanding the propagation of nonlinear Alfvén waves in plasmas.

Determining Selection across Heterogeneous Landscapes: A Perturbation-Based Method and Its Application to Modeling Evolution in Space.

PubMed

Wickman, Jonas; Diehl, Sebastian; Blasius, Bernd; Klausmeier, Christopher A; Ryabov, Alexey B; Brännström, Åke

2017-04-01

Spatial structure can decisively influence the way evolutionary processes unfold. To date, several methods have been used to study evolution in spatial systems, including population genetics, quantitative genetics, moment-closure approximations, and individual-based models. Here we extend the study of spatial evolutionary dynamics to eco-evolutionary models based on reaction-diffusion equations and adaptive dynamics. Specifically, we derive expressions for the strength of directional and stabilizing/disruptive selection that apply both in continuous space and to metacommunities with symmetrical dispersal between patches. For directional selection on a quantitative trait, this yields a way to integrate local directional selection across space and determine whether the trait value will increase or decrease. The robustness of this prediction is validated against quantitative genetics. For stabilizing/disruptive selection, we show that spatial heterogeneity always contributes to disruptive selection and hence always promotes evolutionary branching. The expression for directional selection is numerically very efficient and hence lends itself to simulation studies of evolutionary community assembly. We illustrate the application and utility of the expressions for this purpose with two examples of the evolution of resource utilization. Finally, we outline the domain of applicability of reaction-diffusion equations as a modeling framework and discuss their limitations.

Elliptic-type soliton combs in optical ring microresonators

NASA Astrophysics Data System (ADS)

Dikandé Bitha, Rodrigues D.; Dikandé, Alain M.

2018-03-01

Soliton crystals are periodic patterns of multispot optical fields formed from either time or space entanglements of equally separated identical high-intensity pulses. These specific nonlinear optical structures have gained interest in recent years with the advent and progress in nonlinear optical fibers and fiber lasers, photonic crystals, wave-guided wave systems, and most recently optical ring microresonator devices. In this work an extensive analysis of characteristic features of soliton crystals is carried out, with an emphasis on their one-to-one correspondence with elliptic solitons. With this purpose in mind, we examine their formation, their stability, and their dynamics in ring-shaped nonlinear optical media within the framework of the Lugiato-Lefever equation. The stability analysis deals with internal modes of the system via a 2 ×2 -matrix Lamé-type eigenvalue problem, the spectrum of which is shown to possess a rich set of bound states consisting of stable zero-fequency modes and unstable decaying as well as growing modes. Turning towards the dynamics of elliptic solitons in ring-shaped fiber resonators with Kerr nonlinearity, we first propose a collective-coordinate approach, based on a Lagrangian formalism suitable for elliptic-soliton solutions to the nonlinear Schrödinger equation with an arbitrary perturbation. Next we derive time evolutions of elliptic-soliton parameters in the specific context of ring-shaped optical fiber resonators, where the optical field evolution is thought to be governed by the Lugiato-Lefever equation. By solving numerically the collective-coordinate equations an analysis of the amplitude, the position, the phase of internal oscillations, the phase velocity, the energy, and phase portraits of the amplitude is carried out and reveals a complex dynamics of the elliptic soliton in ring-shaped optical microresonators. Direct numerical simulations of the Lugiato-Lefever equation are also carried out seeking for stationary-wave solutions, and the numerical results are in very good agreement with the collective-coordinate approach.

Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses.

PubMed

Ocker, Gabriel Koch; Litwin-Kumar, Ashok; Doiron, Brent

2015-08-01

The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their joint spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent theory for the evolution of network structure by combining fast spiking covariance with a slow evolution of synaptic weights. Through a finite-size expansion of network dynamics we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse connectivity motifs. With this theory in hand, we explore how the form of the plasticity rule drives the evolution of microcircuits in cortical networks. When potentiation and depression are in approximate balance, synaptic dynamics depend on weighted divergent, convergent, and chain motifs. For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure. Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.

Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses

PubMed Central

Ocker, Gabriel Koch; Litwin-Kumar, Ashok; Doiron, Brent

2015-01-01

The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their joint spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent theory for the evolution of network structure by combining fast spiking covariance with a slow evolution of synaptic weights. Through a finite-size expansion of network dynamics we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse connectivity motifs. With this theory in hand, we explore how the form of the plasticity rule drives the evolution of microcircuits in cortical networks. When potentiation and depression are in approximate balance, synaptic dynamics depend on weighted divergent, convergent, and chain motifs. For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure. Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure. PMID:26291697

The equilibrium tide in stars and giant planets. I. The coplanar case

NASA Astrophysics Data System (ADS)

Remus, F.; Mathis, S.; Zahn, J.-P.

2012-08-01

Context. Since 1995, more than 500 extrasolar planets have been discovered orbiting very close to their parent star, where they experience strong tidal interactions. Their orbital evolution depends on the physical mechanisms that cause tidal dissipation, which remain poorly understood. Aims: We refine the theory of the equilibrium tide in fluid bodies that are partly or entirely convective, to predict the dynamical evolution of the systems. In particular, we examine the validity of modeling the tidal dissipation using the quality factor Q, which is commonly done. We consider here the simplest case where the considered star or planet rotates uniformly, all spins are aligned, and the companion is reduced to a point mass. Methods: We expand the tidal potential as a Fourier series, and express the hydrodynamical equations in the reference frame, which rotates with the corresponding Fourier component. The results are cast in the form of a complex disturbing function, which may be implemented directly in the equations governing the dynamical evolution of the system. Results: The first manifestation of the tide is to distort the shape of the star or planet adiabatically along the line of centers. This generates the divergence-free velocity field of the adiabatic equilibrium tide, which is stationary in the frame rotating with the considered Fourier component of the tidal potential; this large-scale velocity field is decoupled from the dynamical tide. The tidal kinetic energy is dissipated into heat by means of turbulent friction, which is modeled here as an eddy-viscosity acting on the adiabatic tidal flow. This dissipation induces a second velocity field, the dissipative equilibrium tide, which is in quadrature with the exciting potential; this field is responsible for the imaginary part of the disturbing function, which is implemented in the dynamical evolution equations, from which one derives the characteristic evolutionary times. Conclusions: The rate at which the system evolves depends on the physical properties of the tidal dissipation, and specifically on both how the eddy viscosity varies with tidal frequency and the thickness of the convective envelope for the fluid equilibrium tide. At low frequency, this tide is retarded by a constant time delay, whereas it lags behind by a constant angle when the tidal frequency exceeds the convective turnover rate.

Super-rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations.

PubMed

Slunyaev, A; Pelinovsky, E; Sergeeva, A; Chabchoub, A; Hoffmann, N; Onorato, M; Akhmediev, N

2013-07-01

The rogue wave solutions (rational multibreathers) of the nonlinear Schrödinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation, also known as the Dysthe equation. This numerical modeling allowed us to directly compare simulations with recent results of laboratory measurements in Chabchoub et al. [Phys. Rev. E 86, 056601 (2012)]. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near-breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.

Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(-ϕ(ξ))-expansion method.

PubMed

Roshid, Harun-Or; Kabir, Md Rashed; Bhowmik, Rajandra Chadra; Datta, Bimal Kumar

2014-01-01

In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(-ϕ(ξ)) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko- Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.

Adaptive focusing of laser radiation onto a rough reflecting surface through the turbulent and nonlinear atmosphere

NASA Astrophysics Data System (ADS)

Vorontsov, Mikhail A.; Kolosov, Valeriy V.

2004-12-01

Target-in-the-loop (TIL) wave propagation geometry represents perhaps the most challenging case for adaptive optics applications that are related with maximization of irradiance power density on extended remotely located surfaces in the presence of dynamically changing refractive index inhomogeneities in the propagation medium. We introduce a TIL propagation model that uses a combination of the parabolic equation describing outgoing wave propagation, and the equation describing evolution of the mutual coherence function (MCF) for the backscattered (returned) wave. The resulting evolution equation for the MCF is further simplified by the use of the smooth refractive index approximation. This approximation enables derivation of the transport equation for the returned wave brightness function, analyzed here using method characteristics (brightness function trajectories). The equations for the brightness function trajectories (ray equations) can be efficiently integrated numerically. We also consider wavefront sensors that perform sensing of speckle-averaged characteristics of the wavefront phase (TIL sensors). Analysis of the wavefront phase reconstructed from Shack-Hartmann TIL sensor measurements shows that an extended target introduces a phase modulation (target-induced phase) that cannot be easily separated from the atmospheric turbulence-related phase aberrations. We also show that wavefront sensing results depend on the extended target shape, surface roughness, and the outgoing beam intensity distribution on the target surface.

Analysis of wave propagation and wavefront sensing in target-in-the-loop beam control systems

NASA Astrophysics Data System (ADS)

Vorontsov, Mikhail A.; Kolosov, Valeri V.

2004-10-01

Target-in-the-loop (TIL) wave propagation geometry represents perhaps the most challenging case for adaptive optics applications that are related with maximization of irradiance power density on extended remotely located surfaces in the presence of dynamically changing refractive index inhomogeneities in the propagation medium. We introduce a TIL propagation model that uses a combination of the parabolic equation describing outgoing wave propagation, and the equation describing evolution of the mutual intensity function (MIF) for the backscattered (returned) wave. The resulting evolution equation for the MIF is further simplified by the use of the smooth refractive index approximation. This approximation enables derivation of the transport equation for the returned wave brightness function, analyzed here using method characteristics (brightness function trajectories). The equations for the brightness function trajectories (ray equations) can be efficiently integrated numerically. We also consider wavefront sensors that perform sensing of speckle-averaged characteristics of the wavefront phase (TIL sensors). Analysis of the wavefront phase reconstructed from Shack-Hartmann TIL sensor measurements shows that an extended target introduces a phase modulation (target-induced phase) that cannot be easily separated from the atmospheric turbulence-related phase aberrations. We also show that wavefront sensing results depend on the extended target shape, surface roughness, and the outgoing beam intensity distribution on the target surface.

Relativistic fluid dynamics with spin

NASA Astrophysics Data System (ADS)

Florkowski, Wojciech; Friman, Bengt; Jaiswal, Amaresh; Speranza, Enrico

2018-04-01

Using the conservation laws for charge, energy, momentum, and angular momentum, we derive hydrodynamic equations for the charge density, local temperature, and fluid velocity, as well as for the polarization tensor, starting from local equilibrium distribution functions for particles and antiparticles with spin 1/2. The resulting set of differential equations extends the standard picture of perfect-fluid hydrodynamics with a conserved entropy current in a minimal way. This framework can be used in space-time analyses of the evolution of spin and polarization in various physical systems including high-energy nuclear collisions. We demonstrate that a stationary vortex, which exhibits vorticity-spin alignment, corresponds to a special solution of the spin-hydrodynamical equations.

Numerical computations of the dynamics of fluidic membranes and vesicles

NASA Astrophysics Data System (ADS)

Barrett, John W.; Garcke, Harald; Nürnberg, Robert

2015-11-01

Vesicles and many biological membranes are made of two monolayers of lipid molecules and form closed lipid bilayers. The dynamical behavior of vesicles is very complex and a variety of forms and shapes appear. Lipid bilayers can be considered as a surface fluid and hence the governing equations for the evolution include the surface (Navier-)Stokes equations, which in particular take the membrane viscosity into account. The evolution is driven by forces stemming from the curvature elasticity of the membrane. In addition, the surface fluid equations are coupled to bulk (Navier-)Stokes equations. We introduce a parametric finite-element method to solve this complex free boundary problem and present the first three-dimensional numerical computations based on the full (Navier-)Stokes system for several different scenarios. For example, the effects of the membrane viscosity, spontaneous curvature, and area difference elasticity (ADE) are studied. In particular, it turns out, that even in the case of no viscosity contrast between the bulk fluids, the tank treading to tumbling transition can be obtained by increasing the membrane viscosity. Besides the classical tank treading and tumbling motions, another mode (called the transition mode in this paper, but originally called the vacillating-breathing mode and subsequently also called trembling, transition, and swinging mode) separating these classical modes appears and is studied by us numerically. We also study how features of equilibrium shapes in the ADE and spontaneous curvature models, like budding behavior or starfish forms, behave in a shear flow.

Dynamical systems for modeling the evolution of the magnetic field of stars and Earth

NASA Astrophysics Data System (ADS)

Popova, H.

2016-02-01

The cycles of solar magnetic activity are connected with a solar dynamo that operates in the convective zone. Solar dynamo mechanism is based on the combined action of the differential rotation and the alpha-effect. Application of these concepts allows us to get an oscillating solution as a wave of the toroidal field propagating from middle latitudes to the equator. We investigated the dynamo model with the meridional circulation by the low-mode approach. This approach is based on an assumption that the solar magnetic field can be described by non-linear dynamical systems with a relatively small number of parameters. Such non-linear dynamical systems are based on the equations of dynamo models. With this method dynamical systems have been built for media which contains the meridional flow and thickness of the convection zone of the star. It was shown the possibility of coexistence of quiasi-biennial and 22-year cycle. We obtained the different regimes (oscillations, vacillations, dynamo-bursts) depending on the value of the dynamo-number, the meridional circulation, and thickness of the convection zone. We discuss the features of these regimes and compare them with the observed features of evolution of the solar and geo magnetic fields. We built theoretical paleomagnetic time scale and butterfly-diagrams for the helicity and toroidal magnetic field for different regimes.

Controlled Quantum Packets

NASA Technical Reports Server (NTRS)

DeMartino, Salvatore; DeSiena, Silvio

1996-01-01

We look at time evolution of a physical system from the point of view of dynamical control theory. Normally we solve motion equation with a given external potential and we obtain time evolution. Standard examples are the trajectories in classical mechanics or the wave functions in Quantum Mechanics. In the control theory, we have the configurational variables of a physical system, we choose a velocity field and with a suited strategy we force the physical system to have a well defined evolution. The evolution of the system is the 'premium' that the controller receives if he has adopted the right strategy. The strategy is given by well suited laboratory devices. The control mechanisms are in many cases non linear; it is necessary, namely, a feedback mechanism to retain in time the selected evolution. Our aim is to introduce a scheme to obtain Quantum wave packets by control theory. The program is to choose the characteristics of a packet, that is, the equation of evolution for its centre and a controlled dispersion, and to give a building scheme from some initial state (for example a solution of stationary Schroedinger equation). It seems natural in this view to use stochastic approach to Quantum Mechanics, that is, Stochastic Mechanics [S.M.]. It is a quantization scheme different from ordinary ones only formally. This approach introduces in quantum theory the whole mathematical apparatus of stochastic control theory. Stochastic Mechanics, in our view, is more intuitive when we want to study all the classical-like problems. We apply our scheme to build two classes of quantum packets both derived generalizing some properties of coherent states.

Effect of surface roughness on contact line dynamics of a thin droplet

NASA Astrophysics Data System (ADS)

Bhattacharjee, Debanik; Soltannia, Babak; Nazaripoor, Hadi; Sadrzadeh, Mohtada

2017-11-01

Any surface possesses inherent roughness. Droplet spreading on a surface is an example of a contact line problem. The tri-phase contact line is prone to stress singularity which can be relieved by using precursor film assumption and disjoining pressure. In this study, an axisymmetric, incompressible, Newtonian droplet spreading on a surface was investigated. An evolution equation which tracks the droplet height over time was obtained considering the lubrication approximation. The nonlinear PDE of evolution equation was solved using finite difference scheme. A simplified Gaussian model was used as a starting point to assess the role of roughness in the dynamics of contact line. The preliminary results revealed that, for both impermeable and permeable surfaces, the apparent contact angle increased in the presence of defects whereas the equilibrium stage remained unaffected. The apparent contact angle, however, was more strongly dependent on the nature and density of defects for impermeable surfaces due to the longer droplet lifetime. Furthermore, random self-affine and non-Gaussian models are employed. The mathematical model results are finally compared with theoretical models like the Cassie-Baxter, Wenzel, and Penetration modes. NSERC.

Stochastic dynamic programming illuminates the link between environment, physiology, and evolution.

PubMed

Mangel, Marc

2015-05-01

I describe how stochastic dynamic programming (SDP), a method for stochastic optimization that evolved from the work of Hamilton and Jacobi on variational problems, allows us to connect the physiological state of organisms, the environment in which they live, and how evolution by natural selection acts on trade-offs that all organisms face. I first derive the two canonical equations of SDP. These are valuable because although they apply to no system in particular, they share commonalities with many systems (as do frictionless springs). After that, I show how we used SDP in insect behavioral ecology. I describe the puzzles that needed to be solved, the SDP equations we used to solve the puzzles, and the experiments that we used to test the predictions of the models. I then briefly describe two other applications of SDP in biology: first, understanding the developmental pathways followed by steelhead trout in California and second skipped spawning by Norwegian cod. In both cases, modeling and empirical work were closely connected. I close with lessons learned and advice for the young mathematical biologists.

SPH Modelling of Sea-ice Pack Dynamics

NASA Astrophysics Data System (ADS)

Staroszczyk, Ryszard

2017-12-01

The paper is concerned with the problem of sea-ice pack motion and deformation under the action of wind and water currents. Differential equations describing the dynamics of ice, with its very distinct mateFfigrial responses in converging and diverging flows, express the mass and linear momentum balances on the horizontal plane (the free surface of the ocean). These equations are solved by the fully Lagrangian method of smoothed particle hydrodynamics (SPH). Assuming that the ice behaviour can be approximated by a non-linearly viscous rheology, the proposed SPH model has been used to simulate the evolution of a sea-ice pack driven by wind drag stresses. The results of numerical simulations illustrate the evolution of an ice pack, including variations in ice thickness and ice area fraction in space and time. The effects of different initial ice pack configurations and of different conditions assumed at the coast-ice interface are examined. In particular, the SPH model is applied to a pack flow driven by a vortex wind to demonstrate how well the Lagrangian formulation can capture large deformations and displacements of sea ice.

Structural Evolutions of STOCK Markets Controlled by Generalized Entropy Principles of Complex Systems

NASA Astrophysics Data System (ADS)

Wang, Yi Jiao; Feng, Qing Yi; Chai, Li He

As one of the most important financial markets and one of the main parts of economic system, the stock market has become the research focus in economics. The stock market is a typical complex open system far from equilibrium. Many available models that make huge contribution to researches on market are strong in describing the market however, ignoring strong nonlinear interactions among active agents and weak in reveal underlying dynamic mechanisms of structural evolutions of market. From econophysical perspectives, this paper analyzes the complex interactions among agents and defines the generalized entropy in stock markets. Nonlinear evolutionary dynamic equation for the stock markets is then derived from Maximum Generalized Entropy Principle. Simulations are accordingly conducted for a typical case with the given data, by which the structural evolution of the stock market system is demonstrated. Some discussions and implications are finally provided.

Cosmological Ohm's law and dynamics of non-minimal electromagnetism

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

Hollenstein, Lukas; Jain, Rajeev Kumar; Urban, Federico R., E-mail: lukas.hollenstein@cea.fr, E-mail: jain@cp3.dias.sdu.dk, E-mail: furban@ulb.ac.be

2013-01-01

The origin of large-scale magnetic fields in cosmic structures and the intergalactic medium is still poorly understood. We explore the effects of non-minimal couplings of electromagnetism on the cosmological evolution of currents and magnetic fields. In this context, we revisit the mildly non-linear plasma dynamics around recombination that are known to generate weak magnetic fields. We use the covariant approach to obtain a fully general and non-linear evolution equation for the plasma currents and derive a generalised Ohm law valid on large scales as well as in the presence of non-minimal couplings to cosmological (pseudo-)scalar fields. Due to the sizeablemore » conductivity of the plasma and the stringent observational bounds on such couplings, we conclude that modifications of the standard (adiabatic) evolution of magnetic fields are severely limited in these scenarios. Even at scales well beyond a Mpc, any departure from flux freezing behaviour is inhibited.« less

Computational modelling of mesoscale dislocation patterning and plastic deformation of single crystals

NASA Astrophysics Data System (ADS)

Xia, Shengxu; El-Azab, Anter

2015-07-01

We present a continuum dislocation dynamics model that predicts the formation of dislocation cell structure in single crystals at low strains. The model features a set of kinetic equations of the curl type that govern the space and time evolution of the dislocation density in the crystal. These kinetic equations are coupled to stress equilibrium and deformation kinematics using the eigenstrain approach. A custom finite element method has been developed to solve the coupled system of equations of dislocation kinetics and crystal mechanics. The results show that, in general, dislocations self-organize in patterns under their mutual interactions. However, the famous dislocation cell structure has been found to form only when cross slip is implemented in the model. Cross slip is also found to lower the yield point, increase the hardening rate, and sustain an increase in the dislocation density over the hardening regime. Analysis of the cell structure evolution reveals that the average cell size decreases with the applied stress, which is consistent with the similitude principle.

Magnetic Flux Transport at the Solar Surface

NASA Astrophysics Data System (ADS)

Jiang, J.; Hathaway, D. H.; Cameron, R. H.; Solanki, S. K.; Gizon, L.; Upton, L.

2014-12-01

After emerging to the solar surface, the Sun's magnetic field displays a complex and intricate evolution. The evolution of the surface field is important for several reasons. One is that the surface field, and its dynamics, sets the boundary condition for the coronal and heliospheric magnetic fields. Another is that the surface evolution gives us insight into the dynamo process. In particular, it plays an essential role in the Babcock-Leighton model of the solar dynamo. Describing this evolution is the aim of the surface flux transport model. The model starts from the emergence of magnetic bipoles. Thereafter, the model is based on the induction equation and the fact that after emergence the magnetic field is observed to evolve as if it were purely radial. The induction equation then describes how the surface flows—differential rotation, meridional circulation, granular, supergranular flows, and active region inflows—determine the evolution of the field (now taken to be purely radial). In this paper, we review the modeling of the various processes that determine the evolution of the surface field. We restrict our attention to their role in the surface flux transport model. We also discuss the success of the model and some of the results that have been obtained using this model.

Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics

NASA Astrophysics Data System (ADS)

Roca, Carlos P.; Cuesta, José A.; Sánchez, Angel

2009-12-01

Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator equation, that describes mathematically the idea that those individuals performing better have more offspring and thus their frequency in the population grows. While very many interesting results have been obtained with this equation in the three decades elapsed since it was first proposed, it is important to realize the limits of its applicability. One particularly relevant issue in this respect is that of non-mean-field effects, that may arise from temporal fluctuations or from spatial correlations, both neglected in the replicator equation. This review discusses these temporal and spatial effects focusing on the non-trivial modifications they induce when compared to the outcome of replicator dynamics. Alongside this question, the hypothesis of linearity and its relation to the choice of the rule for strategy update is also analyzed. The discussion is presented in terms of the emergence of cooperation, as one of the current key problems in Biology and in other disciplines.

Impact of nearest-neighbor repulsion on superconducting pairing in 2D extended Hubbard model

NASA Astrophysics Data System (ADS)

Jiang, Mi; Hahner, U. R.; Maier, T. A.; Schulthess, T. C.

Using dynamical cluster approximation (DCA) with an continuous-time QMC solver for the two-dimensional extended Hubbard model, we studied the impact of nearest-neighbor Coulomb repulsion V on d-wave superconducting pairing dynamics. By solving Bethe-Salpeter equation for particle-particle superconducting channel, we focused on the evolution of leading d-wave eigenvalue with V and the momentum and frequency dependence of the corresponding eigenfunction. The comparison with the evolution of both spin and charge susceptibilities versus V is presented showing the competition between spin and charge fluctuations. This research received generous support from the MARVEL NCCR and used resources of the Swiss National Supercomputing Center, as well as (INCITE) program in Oak Ridge Leadership Computing Facility.

Relativistic longitudinal self-compression of ultrashort time-domain hollow Gaussian pulses in plasma

NASA Astrophysics Data System (ADS)

Cao, Xiaochao; Fang, Feiyun; Wang, Zhaoying; Lin, Qiang

2017-10-01

We report a study on dynamical evolution of the ultrashort time-domain dark hollow Gaussian (TDHG) pulses beyond the slowly varying envelope approximation in homogenous plasma. Using the complex-source-point model, an analytical formula is proposed for describing TDHG pulses based on the oscillating electric dipoles, which is the exact solution of the Maxwell's equations. The numerical simulations show the relativistic longitudinal self-compression (RSC) due to the relativistic mass variation of moving electrons. The influences of plasma oscillation frequency and collision effect on dynamics of the TDHG pulses in plasma have been considered. Furthermore, we analyze the evolution of instantaneous energy density of the TDHG pulses on axis as well as the off axis condition.

Dynamics of one-dimensional self-gravitating systems using Hermite-Legendre polynomials

NASA Astrophysics Data System (ADS)

Barnes, Eric I.; Ragan, Robert J.

2014-01-01

The current paradigm for understanding galaxy formation in the Universe depends on the existence of self-gravitating collisionless dark matter. Modelling such dark matter systems has been a major focus of astrophysicists, with much of that effort directed at computational techniques. Not surprisingly, a comprehensive understanding of the evolution of these self-gravitating systems still eludes us, since it involves the collective non-linear dynamics of many particle systems interacting via long-range forces described by the Vlasov equation. As a step towards developing a clearer picture of collisionless self-gravitating relaxation, we analyse the linearized dynamics of isolated one-dimensional systems near thermal equilibrium by expanding their phase-space distribution functions f(x, v) in terms of Hermite functions in the velocity variable, and Legendre functions involving the position variable. This approach produces a picture of phase-space evolution in terms of expansion coefficients, rather than spatial and velocity variables. We obtain equations of motion for the expansion coefficients for both test-particle distributions and self-gravitating linear perturbations of thermal equilibrium. N-body simulations of perturbed equilibria are performed and found to be in excellent agreement with the expansion coefficient approach over a time duration that depends on the size of the expansion series used.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Summer Study Program in Geophysical Fluid Dynamics - The Influence of Convection on Large-Scale Circulations - 1988

DTIC Science & Technology

1989-07-01

the vector of the body force." lo., ,P /’P l> 16 __ __ _ __ ___P . 19 U In the first lecture we define the buoyancy force, develop a simplified...force and l’is a unit vector along the motion vector . Integrating Bernoulli’s law over a closed loop one gets: I also [ C by integrating along the...convection. It is conveiient to write these equations as evolution equations for a atate vector U(x, z, t) where x is the horizontal coordinate vector

Novel asymmetric representation method for solving the higher-order Ginzburg-Landau equation

PubMed Central

Wong, Pring; Pang, Lihui; Wu, Ye; Lei, Ming; Liu, Wenjun

2016-01-01

In ultrafast optics, optical pulses are generated to be of shorter pulse duration, which has enormous significance to industrial applications and scientific research. The ultrashort pulse evolution in fiber lasers can be described by the higher-order Ginzburg-Landau (GL) equation. However, analytic soliton solutions for this equation have not been obtained by use of existing methods. In this paper, a novel method is proposed to deal with this equation. The analytic soliton solution is obtained for the first time, and is proved to be stable against amplitude perturbations. Through the split-step Fourier method, the bright soliton solution is studied numerically. The analytic results here may extend the integrable methods, and could be used to study soliton dynamics for some equations in other disciplines. It may also provide the other way to obtain two-soliton solutions for higher-order GL equations. PMID:27086841

From the nonlinear Fokker-Planck equation to the Vlasov description and back: Confined interacting particles with drag

NASA Astrophysics Data System (ADS)

Plastino, A. R.; Curado, E. M. F.; Nobre, F. D.; Tsallis, C.

2018-02-01

Nonlinear Fokker-Planck equations endowed with power-law diffusion terms have proven to be valuable tools for the study of diverse complex systems in physics, biology, and other fields. The nonlinearity appearing in these evolution equations can be interpreted as providing an effective description of a system of particles interacting via short-range forces while performing overdamped motion under the effect of an external confining potential. This point of view has been recently applied to the study of thermodynamical features of interacting vortices in type II superconductors. In the present work we explore an embedding of the nonlinear Fokker-Planck equation within a Vlasov equation, thus incorporating inertial effects to the concomitant particle dynamics. Exact time-dependent solutions of the q -Gaussian form (with compact support) are obtained for the Vlasov equation in the case of quadratic confining potentials.

Stochastic and Boltzmann-like models for behavioral changes, and their relation to game theory

NASA Astrophysics Data System (ADS)

Helbing, Dirk

1993-03-01

In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is developed. Three kinds of social pair interactions are distinguished: Avoidance processes, compromising processes, and imitative processes. Computational results are presented for a special case of imitative processes: the competition of two equivalent strategies. They show a phase transition that describes the self-organization of a behavioral convention. This phase transition is further analyzed by examining the equations for the most probable behavioral distribution, which are Boltzmann-like equations. Special cases of Boltzmann-like equations do not obey the H-theorem and have oscillatory or even chaotic solutions. A suitable Taylor approximation leads to the so-called game dynamical equations (also known as selection-mutation equations in the theory of evolution).

Derivation of a continuum model and the energy law for moving contact lines with insoluble surfactants

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

Zhang, Zhen, E-mail: matzz@nus.edu.sg; Xu, Shixin, E-mail: matxs@nus.edu.sg; Ren, Weiqing, E-mail: matrw@nus.edu.sg

2014-06-15

A continuous model is derived for the dynamics of two immiscible fluids with moving contact lines and insoluble surfactants based on thermodynamic principles. The continuum model consists of the Navier-Stokes equations for the dynamics of the two fluids and a convection-diffusion equation for the evolution of the surfactant on the fluid interface. The interface condition, the boundary condition for the slip velocity, and the condition for the dynamic contact angle are derived from the consideration of energy dissipations. Different types of energy dissipations, including the viscous dissipation, the dissipations on the solid wall and at the contact line, as wellmore » as the dissipation due to the diffusion of surfactant, are identified from the analysis. A finite element method is developed for the continuum model. Numerical experiments are performed to demonstrate the influence of surfactant on the contact line dynamics. The different types of energy dissipations are compared numerically.« less

Expectation-Based Control of Noise and Chaos

NASA Technical Reports Server (NTRS)

Zak, Michael

2006-01-01

A proposed approach to control of noise and chaos in dynamic systems would supplement conventional methods. The approach is based on fictitious forces composed of expectations governed by Fokker-Planck or Liouville equations that describe the evolution of the probability densities of the controlled parameters. These forces would be utilized as feedback control forces that would suppress the undesired diffusion of the controlled parameters. Examples of dynamic systems in which the approach is expected to prove beneficial include spacecraft, electronic systems, and coupled lasers.

Optimal Control for Stochastic Delay Evolution Equations

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

Meng, Qingxin, E-mail: mqx@hutc.zj.cn; Shen, Yang, E-mail: skyshen87@gmail.com

2016-08-15

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we applymore » stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.« less

A Few New 2+1-Dimensional Nonlinear Dynamics and the Representation of Riemann Curvature Tensors

NASA Astrophysics Data System (ADS)

Wang, Yan; Zhang, Yufeng; Zhang, Xiangzhi

2016-09-01

We first introduced a linear stationary equation with a quadratic operator in ∂x and ∂y, then a linear evolution equation is given by N-order polynomials of eigenfunctions. As applications, by taking N=2, we derived a (2+1)-dimensional generalized linear heat equation with two constant parameters associative with a symmetric space. When taking N=3, a pair of generalized Kadomtsev-Petviashvili equations with the same eigenvalues with the case of N=2 are generated. Similarly, a second-order flow associative with a homogeneous space is derived from the integrability condition of the two linear equations, which is a (2+1)-dimensional hyperbolic equation. When N=3, the third second flow associative with the homogeneous space is generated, which is a pair of new generalized Kadomtsev-Petviashvili equations. Finally, as an application of a Hermitian symmetric space, we established a pair of spectral problems to obtain a new (2+1)-dimensional generalized Schrödinger equation, which is expressed by the Riemann curvature tensors.

Analytic study of solutions for a (3 + 1) -dimensional generalized KP equation

NASA Astrophysics Data System (ADS)

Gao, Hui; Cheng, Wenguang; Xu, Tianzhou; Wang, Gangwei

2018-03-01

The (3 + 1) -dimensional generalized KP (gKP) equation is an important nonlinear partial differential equation in theoretical and mathematical physics which can be used to describe nonlinear wave motion. Through the Hirota bilinear method, one-solition, two-solition and N-solition solutions are derived via symbolic computation. Two classes of lump solutions, rationally localized in all directions in space, to the dimensionally reduced cases in (2 + 1)-dimensions, are constructed by using a direct method based on the Hirota bilinear form of the equation. It implies that we can derive the lump solutions of the reduced gKP equation from positive quadratic function solutions to the aforementioned bilinear equation. Meanwhile, we get interaction solutions between a lump and a kink of the gKP equation. The lump appears from a kink and is swallowed by it with the change of time. This work offers a possibility which can enrich the variety of the dynamical features of solutions for higher-dimensional nonlinear evolution equations.

Protecting quantum Fisher information in curved space-time

NASA Astrophysics Data System (ADS)

Huang, Zhiming

2018-03-01

In this work, we investigate the quantum Fisher information (QFI) dynamics of a two-level atom interacting with quantized conformally coupled massless scalar fields in de Sitter-invariant vacuum. We first derive the master equation that governs its evolution. It is found that the QFI decays with evolution time. Furthermore, we propose two schemes to protect QFI by employing prior weak measurement (WM) and post measurement reversal (MR). We find that the first scheme can not always protect QFI and the second scheme has prominent advantage over the first scheme.

Urey Prize Lecture - Chaotic dynamics in the solar system

NASA Technical Reports Server (NTRS)

Wisdom, Jack

1987-01-01

Attention is given to solar system cases in which chaotic solutions of Newton's equations are important, as in chaotic rotation and orbital evolution. Hyperion is noted to be tumbling chaotically; chaotic orbital evolution is suggested to be of fundamental importance to an accounting for the Kirkwood gaps in asteroid distribution and for the phase space boundary of the chaotic zone at the 3/1 mean-motion commensurability with Jupiter. In addition, chaotic trajectories in the 2/1 chaotic zone reach very high eccentricities by a route that carries them to high inclinations temporarily.

Transition from Direct to Inverse Cascade in Three-Dimensional Turbulence

NASA Astrophysics Data System (ADS)

Sahoo, Ganapati; Alexakis, Alexandros; Biferale, Luca

2017-11-01

We study a model system where the triadic interactions in Navier-Stokes equations are enhanced or suppressed in a controlled manner without affecting neither the total number of degrees of freedom nor the ideal invariants and without breaking any of the symmetries of original equations. Our numerical simulations are based on the helical decomposition of velocity Fourier modes. We introduced a parameter (0 <= λ <= 1) that controls the relative weight among homochiral and heterochiral triads in the nonlinear evolution. We show that by using this weighting protocol the turbulent evolution displays a sharp transition, for a critical value of the control parameter, from forward to backward energy transfer but still keeping the dynamics fully three dimensional, isotropic, and parity invariant. AtMath Collaboration of University of Helsinki and ERC Grant No. 339032 `NewTurb'.

Dynamical modeling and free vibration analysis of spinning pipes conveying fluid with axial deployment

NASA Astrophysics Data System (ADS)

Liang, Feng; Yang, Xiao-Dong; Zhang, Wei; Qian, Ying-Jing

2018-03-01

In this paper, a dynamical model of simply-supported spinning pipes conveying fluid with axial deployment is proposed and the transverse free vibration and stability for such a doubly gyroscopic system involving time-dependent parameters are investigated. The partial differential equations of motion are derived by the extended Hamilton principle and then truncated by the Galerkin technique. The time-variant frequencies, mode shapes and responses to initial conditions are comprehensively investigated to reveal the dynamical essence of the system. It is indicated that the qualitative stability evolution of the system mainly depends on the effect of fluid-structure interaction (FSI), while the spinning motion will enhance the pipe rigidity and eliminate the buckling instability. The dynamical evolution of a retracting pipe is almost inverse to that of the deploying one. The pipe possesses different mode configurations of spatial curves as the pipe length increases and some modal and response characteristics of the present system are found rather distinct from those of deploying cantilevered structures.

Non-Markovian electron dynamics in nanostructures coupled to dissipative contacts

NASA Astrophysics Data System (ADS)

Novakovic, B.; Knezevic, I.

2013-02-01

In quasiballistic semiconductor nanostructures, carrier exchange between the active region and dissipative contacts is the mechanism that governs relaxation. In this paper, we present a theoretical treatment of transient quantum transport in quasiballistic semiconductor nanostructures, which is based on the open system theory and valid on timescales much longer than the characteristic relaxation time in the contacts. The approach relies on a model interaction between the current-limiting active region and the contacts, given in the scattering-state basis. We derive a non-Markovian master equation for the irreversible evolution of the active region's many-body statistical operator by coarse-graining the exact dynamical map over the contact relaxation time. In order to obtain the response quantities of a nanostructure under bias, such as the potential and the charge and current densities, the non-Markovian master equation must be solved numerically together with the Schr\\"{o}dinger, Poisson, and continuity equations. We discuss how to numerically solve this coupled system of equations and illustrate the approach on the example of a silicon nin diode.

Koopman decomposition of Burgers' equation: What can we learn?

NASA Astrophysics Data System (ADS)

Page, Jacob; Kerswell, Rich

2017-11-01

Burgers' equation is a well known 1D model of the Navier-Stokes equations and admits a selection of equilibria and travelling wave solutions. A series of Burgers' trajectories are examined with Dynamic Mode Decomposition (DMD) to probe the capability of the method to extract coherent structures from ``run-down'' simulations. The performance of the method depends critically on the choice of observable. We use the Cole-Hopf transformation to derive an observable which has linear, autonomous dynamics and for which the DMD modes overlap exactly with Koopman modes. This observable can accurately predict the flow evolution beyond the time window of the data used in the DMD, and in that sense outperforms other observables motivated by the nonlinearity in the governing equation. The linearizing observable also allows us to make informed decisions about often ambiguous choices in nonlinear problems, such as rank truncation and snapshot spacing. A number of rules of thumb for connecting DMD with the Koopman operator for nonlinear PDEs are distilled from the results. Related problems in low Reynolds number fluid turbulence are also discussed.

Dynamical stochastic processes of returns in financial markets

NASA Astrophysics Data System (ADS)

Lim, Gyuchang; Kim, SooYong; Yoon, Seong-Min; Jung, Jae-Won; Kim, Kyungsik

2007-03-01

We study the evolution of probability distribution functions of returns, from the tick data of the Korean treasury bond (KTB) futures and the S&P 500 stock index, which can be described by means of the Fokker-Planck equation. We show that the Fokker-Planck equation and the Langevin equation from the estimated Kramers-Moyal coefficients can be estimated directly from the empirical data. By analyzing the statistics of the returns, we present quantitatively the deterministic and random influences on financial time series for both markets, for which we can give a simple physical interpretation. We particularly focus on the diffusion coefficient, which may be important for the creation of a portfolio.

Linear analysis of auto-organization in Hebbian neural networks.

PubMed

Carlos Letelier, J; Mpodozis, J

1995-01-01

The self-organization of neurotopies where neural connections follow Hebbian dynamics is framed in terms of linear operator theory. A general and exact equation describing the time evolution of the overall synaptic strength connecting two neural laminae is derived. This linear matricial equation, which is similar to the equations used to describe oscillating systems in physics, is modified by the introduction of non-linear terms, in order to capture self-organizing (or auto-organizing) processes. The behavior of a simple and small system, that contains a non-linearity that mimics a metabolic constraint, is analyzed by computer simulations. The emergence of a simple "order" (or degree of organization) in this low-dimensionality model system is discussed.

Multidimensional discrete compactons in nonlinear Schrödinger lattices with strong nonlinearity management

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

D'Ambroise, J.; Salerno, M.; Kevrekidis, P. G.

The existence of multidimensional lattice compactons in the discrete nonlinear Schrödinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. By averaging over the period of the fast modulations, an effective averaged dynamical equation arises with coupling constants involving Bessel functions of the first and zeroth kinds. We show that these terms allow one to solve, at this averaged level, for exact discrete compacton solution configurations in the corresponding stationary equation. We focus on seven types of compacton solutions. Single-site and vortex solutions are found to be always stable in the parametric regimes we examined.more » We also found that other solutions such as double-site in- and out-of-phase, four-site symmetric and antisymmetric, and a five-site compacton solution are found to have regions of stability and instability in two-dimensional parametric planes, involving variations of the strength of the coupling and of the nonlinearity. We also explore the time evolution of the solutions and compare the dynamics according to the averaged equations with those of the original dynamical system. Finally, the possible observation of compactons in Bose-Einstein condensates loaded in a deep two-dimensional optical lattice with interactions modulated periodically in time is also discussed.« less

Multidimensional discrete compactons in nonlinear Schrödinger lattices with strong nonlinearity management

DOE PAGES

D'Ambroise, J.; Salerno, M.; Kevrekidis, P. G.; ...

2015-11-19

The existence of multidimensional lattice compactons in the discrete nonlinear Schrödinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. By averaging over the period of the fast modulations, an effective averaged dynamical equation arises with coupling constants involving Bessel functions of the first and zeroth kinds. We show that these terms allow one to solve, at this averaged level, for exact discrete compacton solution configurations in the corresponding stationary equation. We focus on seven types of compacton solutions. Single-site and vortex solutions are found to be always stable in the parametric regimes we examined.more » We also found that other solutions such as double-site in- and out-of-phase, four-site symmetric and antisymmetric, and a five-site compacton solution are found to have regions of stability and instability in two-dimensional parametric planes, involving variations of the strength of the coupling and of the nonlinearity. We also explore the time evolution of the solutions and compare the dynamics according to the averaged equations with those of the original dynamical system. Finally, the possible observation of compactons in Bose-Einstein condensates loaded in a deep two-dimensional optical lattice with interactions modulated periodically in time is also discussed.« less

Direct modeling for computational fluid dynamics

NASA Astrophysics Data System (ADS)

Xu, Kun

2015-06-01

All fluid dynamic equations are valid under their modeling scales, such as the particle mean free path and mean collision time scale of the Boltzmann equation and the hydrodynamic scale of the Navier-Stokes (NS) equations. The current computational fluid dynamics (CFD) focuses on the numerical solution of partial differential equations (PDEs), and its aim is to get the accurate solution of these governing equations. Under such a CFD practice, it is hard to develop a unified scheme that covers flow physics from kinetic to hydrodynamic scales continuously because there is no such governing equation which could make a smooth transition from the Boltzmann to the NS modeling. The study of fluid dynamics needs to go beyond the traditional numerical partial differential equations. The emerging engineering applications, such as air-vehicle design for near-space flight and flow and heat transfer in micro-devices, do require further expansion of the concept of gas dynamics to a larger domain of physical reality, rather than the traditional distinguishable governing equations. At the current stage, the non-equilibrium flow physics has not yet been well explored or clearly understood due to the lack of appropriate tools. Unfortunately, under the current numerical PDE approach, it is hard to develop such a meaningful tool due to the absence of valid PDEs. In order to construct multiscale and multiphysics simulation methods similar to the modeling process of constructing the Boltzmann or the NS governing equations, the development of a numerical algorithm should be based on the first principle of physical modeling. In this paper, instead of following the traditional numerical PDE path, we introduce direct modeling as a principle for CFD algorithm development. Since all computations are conducted in a discretized space with limited cell resolution, the flow physics to be modeled has to be done in the mesh size and time step scales. Here, the CFD is more or less a direct construction of discrete numerical evolution equations, where the mesh size and time step will play dynamic roles in the modeling process. With the variation of the ratio between mesh size and local particle mean free path, the scheme will capture flow physics from the kinetic particle transport and collision to the hydrodynamic wave propagation. Based on the direct modeling, a continuous dynamics of flow motion will be captured in the unified gas-kinetic scheme. This scheme can be faithfully used to study the unexplored non-equilibrium flow physics in the transition regime.

Long-term evolution of electron distribution function due to nonlinear resonant interaction with whistler mode waves

NASA Astrophysics Data System (ADS)

Artemyev, Anton V.; Neishtadt, Anatoly I.; Vasiliev, Alexei A.

2018-04-01

Accurately modelling and forecasting of the dynamics of the Earth's radiation belts with the available computer resources represents an important challenge that still requires significant advances in the theoretical plasma physics field of wave-particle resonant interaction. Energetic electron acceleration or scattering into the Earth's atmosphere are essentially controlled by their resonances with electromagnetic whistler mode waves. The quasi-linear diffusion equation describes well this resonant interaction for low intensity waves. During the last decade, however, spacecraft observations in the radiation belts have revealed a large number of whistler mode waves with sufficiently high intensity to interact with electrons in the nonlinear regime. A kinetic equation including such nonlinear wave-particle interactions and describing the long-term evolution of the electron distribution is the focus of the present paper. Using the Hamiltonian theory of resonant phenomena, we describe individual electron resonance with an intense coherent whistler mode wave. The derived characteristics of such a resonance are incorporated into a generalized kinetic equation which includes non-local transport in energy space. This transport is produced by resonant electron trapping and nonlinear acceleration. We describe the methods allowing the construction of nonlinear resonant terms in the kinetic equation and discuss possible applications of this equation.

How Markovian is exciton dynamics in purple bacteria?

NASA Astrophysics Data System (ADS)

Vaughan, Felix; Linden, Noah; Manby, Frederick R.

2017-03-01

We investigate the extent to which the dynamics of excitons in the light-harvesting complex LH2 of purple bacteria can be described using a Markovian approximation. To analyse the degree of non-Markovianity in these systems, we introduce a measure based on fitting Lindblad dynamics, as well as employing a recently introduced trace-distance measure. We apply these measures to a chromophore-dimer model of exciton dynamics and use the hierarchical equation-of-motion method to take into account the broad, low-frequency phonon bath. With a smooth phonon bath, small amounts of non-Markovianity are present according to the trace-distance measure, but the dynamics is poorly described by a Lindblad master equation unless the excitonic dimer coupling strength is modified. Inclusion of underdamped, high-frequency modes leads to significant deviations from Markovian evolution in both measures. In particular, we find that modes that are nearly resonant with gaps in the excitonic spectrum produce dynamics that deviate most strongly from the Lindblad approximation, despite the trace distance measuring larger amounts of non-Markovianity for higher frequency modes. Overall we find that the detailed structure in the high-frequency region of the spectral density has a significant impact on the nature of the dynamics of excitons.

A boundary integral approach in primitive variables for free surface flows

NASA Astrophysics Data System (ADS)

Casciola, C.; Piva, R.

The boundary integral formulation, very efficient for free surface potential flows, was considered for its possible extension to rotational flows either inviscid or viscous. We first analyze a general formulation for unsteady Navier-Stokes equations in primitive variables, which reduces to a representation for the Euler equations in the limiting case of Reynolds infinity. A first simplified model for rotational flows, obtained by decoupling kinematics and dynamics, reduces the integral equations to a known kinematical form whose mathematical and numerical properties have been studied. The dynamics equations to complete the model are obtained for the free surface and the wake. A simple and efficient scheme for the study of the non linear evolution of the wave system and its interaction with the body wake is presented. A steady state version for the calculation of the wave resistance is also reported. A second model was proposed for the simulation of rotational separated regions, by coupling the integral equations in velocity with an integral equation for the vorticity at the body boundary. The same procedure may be extended to include the diffusion of the vorticity in the flowfield. The vortex shedding from a cylindrical body in unsteady motion is discussed, as a first application of the model.

Multiphase Equation of State and Strength Properties of Beryllium from AB INITIO and Quantum Molecular Dynamics Calculations.

NASA Astrophysics Data System (ADS)

Robert, G.; Sollier, A.; Legrand, Ph.

2007-12-01

In the framework of density functional theory, static properties and phonon spectra of beryllium have been calculated under high compression (for pressures up to 4 Mbar) for two solid phases: hexagonal compact (hcp) and body-centered cubic (bcc). The melting curve and some isotherms in the liquid phase have been calculated using quantum molecular dynamics. The coupling of these theoretical data to a quasi-harmonic approach (phonon moments) allows us to suggest a new theoretical phase diagram and to build a multiphase equation of state (EOS) valid in a large range of pressure and temperature. The resulting Hugoniot curves as well as the evolution of the longitudinal sound speed with both pressure and temperature are in good agreement with available experimental data.

Implications of causality for quantum biology - I: topology change

NASA Astrophysics Data System (ADS)

Scofield, D. F.; Collins, T. C.

2018-06-01

A framework for describing the causal, topology changing, evolution of interacting biomolecules is developed. The quantum dynamical manifold equations (QDMEs) derived from this framework can be related to the causality restrictions implied by a finite speed of light and to Planck's constant to set a transition frequency scale. The QDMEs imply conserved stress-energy, angular-momentum and Noether currents. The functional whose extremisation leads to this result provides a causal, time-dependent, non-equilibrium generalisation of the Hohenberg-Kohn theorem. The system of dynamical equations derived from this functional and the currents J derived from the QDMEs are shown to be causal and consistent with the first and second laws of thermodynamics. This has the potential of allowing living systems to be quantum mechanically distinguished from non-living ones.

Liquid film drag out in the presence of molecular forces

NASA Astrophysics Data System (ADS)

Schmidhalter, I.; Cerro, R. L.; Giavedoni, M. D.; Saita, F. A.

2013-03-01

From a practical as well as a conceptual point of view, one of the most interesting problems of physicochemical hydrodynamics is the drag out of a liquid film by a moving solid out of a pool of liquid. The basic problem, sometimes denoted the Landau-Levich problem [L. Landau and B. Levich, "Dragging of a liquid by a moving plate," Acta Physicochim. USSR 17, 42-54 (1942)], involves an interesting blend of capillary and viscous forces plus a matching of the static solution for capillary rise with a numerical solution of the film evolution equation, neglecting gravity, on the downstream region of the flow field. The original solution describes experimental data for a wide range of Capillary numbers but fails to match results for large and very small Capillary numbers. Molecular level forces are introduced to create an augmented version of the film evolution equation to show the effect of van der Waals forces at the lower range of Capillary numbers. A closed form solution for static capillary rise, including molecular forces, was matched with a numerical solution of the augmented film evolution equation in the dynamic meniscus region. Molecular forces do not sensibly modify the static capillary rise region, since film thicknesses are larger than the range of influence of van der Waals forces, but are determinant in shaping the downstream dynamic meniscus of the very thin liquid films. As expected, a quantitatively different level of disjoining pressure for different values of molecular constants remains in the very thin liquid film far downstream. Computational results for a wide range of Capillary numbers and Hamaker constants show a clear transition towards a region where the film thickness becomes independent of the coating speed.

Utility Rate Equations of Group Population Dynamics in Biological and Social Systems

PubMed Central

Yukalov, Vyacheslav I.; Yukalova, Elizaveta P.; Sornette, Didier

2013-01-01

We present a novel system of equations to describe the evolution of self-organized structured societies (biological or human) composed of several trait groups. The suggested approach is based on the combination of ideas employed in the theory of biological populations, system theory, and utility theory. The evolution equations are defined as utility rate equations, whose parameters are characterized by the utility of each group with respect to the society as a whole and by the mutual utilities of groups with respect to each other. We analyze in detail the cases of two groups (cooperators and defectors) and of three groups (cooperators, defectors, and regulators) and find that, in a self-organized society, neither defectors nor regulators can overpass the maximal fractions of about each. This is in agreement with the data for bee and ant colonies. The classification of societies by their distance from equilibrium is proposed. We apply the formalism to rank the countries according to the introduced metric quantifying their relative stability, which depends on the cost of defectors and regulators as well as their respective population fractions. We find a remarkable concordance with more standard economic ranking based, for instance, on GDP per capita. PMID:24386163

Building 1D resonance broadened quasilinear (RBQ) code for fast ions Alfvénic relaxations

NASA Astrophysics Data System (ADS)

Gorelenkov, Nikolai; Duarte, Vinicius; Berk, Herbert

2016-10-01

The performance of the burning plasma is limited by the confinement of superalfvenic fusion products, e.g. alpha particles, which are capable of resonating with the Alfvénic eigenmodes (AEs). The effect of AEs on fast ions is evaluated using a resonance line broadened diffusion coefficient. The interaction of fast ions and AEs is captured for cases where there are either isolated or overlapping modes. A new code RBQ1D is being built which constructs diffusion coefficients based on realistic eigenfunctions that are determined by the ideal MHD code NOVA. The wave particle interaction can be reduced to one-dimensional dynamics where for the Alfvénic modes typically the particle kinetic energy is nearly constant. Hence to a good approximation the Quasi-Linear (QL) diffusion equation only contains derivatives in the angular momentum. The diffusion equation is then one dimensional that is efficiently solved simultaneously for all particles with the equation for the evolution of the wave angular momentum. The evolution of fast ion constants of motion is governed by the QL diffusion equations which are adapted to find the ion distribution function.

Utility rate equations of group population dynamics in biological and social systems.

PubMed

Yukalov, Vyacheslav I; Yukalova, Elizaveta P; Sornette, Didier

2013-01-01

We present a novel system of equations to describe the evolution of self-organized structured societies (biological or human) composed of several trait groups. The suggested approach is based on the combination of ideas employed in the theory of biological populations, system theory, and utility theory. The evolution equations are defined as utility rate equations, whose parameters are characterized by the utility of each group with respect to the society as a whole and by the mutual utilities of groups with respect to each other. We analyze in detail the cases of two groups (cooperators and defectors) and of three groups (cooperators, defectors, and regulators) and find that, in a self-organized society, neither defectors nor regulators can overpass the maximal fractions of about [Formula: see text] each. This is in agreement with the data for bee and ant colonies. The classification of societies by their distance from equilibrium is proposed. We apply the formalism to rank the countries according to the introduced metric quantifying their relative stability, which depends on the cost of defectors and regulators as well as their respective population fractions. We find a remarkable concordance with more standard economic ranking based, for instance, on GDP per capita.

The Master Equation for Two-Level Accelerated Systems at Finite Temperature

NASA Astrophysics Data System (ADS)

Tomazelli, J. L.; Cunha, R. O.

2016-10-01

In this work, we study the behaviour of two weakly coupled quantum systems, described by a separable density operator; one of them is a single oscillator, representing a microscopic system, while the other is a set of oscillators which perform the role of a reservoir in thermal equilibrium. From the Liouville-Von Neumann equation for the reduced density operator, we devise the master equation that governs the evolution of the microscopic system, incorporating the effects of temperature via Thermofield Dynamics formalism by suitably redefining the vacuum of the macroscopic system. As applications, we initially investigate the behaviour of a Fermi oscillator in the presence of a heat bath consisting of a set of Fermi oscillators and that of an atomic two-level system interacting with a scalar radiation field, considered as a reservoir, by constructing the corresponding master equation which governs the time evolution of both sub-systems at finite temperature. Finally, we calculate the energy variation rates for the atom and the field, as well as the atomic population levels, both in the inertial case and at constant proper acceleration, considering the two-level system as a prototype of an Unruh detector, for admissible couplings of the radiation field.

Modeling and 2-D discrete simulation of dislocation dynamics for plastic deformation of metal

NASA Astrophysics Data System (ADS)

Liu, Juan; Cui, Zhenshan; Ou, Hengan; Ruan, Liqun

2013-05-01

Two methods are employed in this paper to investigate the dislocation evolution during plastic deformation of metal. One method is dislocation dynamic simulation of two-dimensional discrete dislocation dynamics (2D-DDD), and the other is dislocation dynamics modeling by means of nonlinear analysis. As screw dislocation is prone to disappear by cross-slip, only edge dislocation is taken into account in simulation. First, an approach of 2D-DDD is used to graphically simulate and exhibit the collective motion of a large number of discrete dislocations. In the beginning, initial grains are generated in the simulation cells according to the mechanism of grain growth and the initial dislocation is randomly distributed in grains and relaxed under the internal stress. During the simulation process, the externally imposed stress, the long range stress contribution of all dislocations and the short range stress caused by the grain boundaries are calculated. Under the action of these forces, dislocations begin to glide, climb, multiply, annihilate and react with each other. Besides, thermal activation process is included. Through the simulation, the distribution of dislocation and the stress-strain curves can be obtained. On the other hand, based on the classic dislocation theory, the variation of the dislocation density with time is described by nonlinear differential equations. Finite difference method (FDM) is used to solve the built differential equations. The dislocation evolution at a constant strain rate is taken as an example to verify the rationality of the model.

On order and chaos in the mergers of galaxies

NASA Astrophysics Data System (ADS)

Vandervoort, Peter O.

2018-03-01

This paper describes a low-dimensional model of the merger of two galaxies. The governing equations are the complete sets of moment equations of the first and second orders derived from the collisionless Boltzmann equations representing the galaxies. The moment equations reduce to an equation governing the relative motion of the galaxies, tensor virial equations, and equations governing the kinetic energy tensors. We represent the galaxies as heterogeneous ellipsoids with Gaussian stratifications of their densities, and we represent the mean stellar motions in terms of velocity fields that sustain those densities consistently with the equation of continuity. We reduce and solve the governing equations for a head-on encounter of a dwarf galaxy with a giant galaxy. That reduction includes the effect of dynamical friction on the relative motion of the galaxies. Our criterion for chaotic behaviour is sensitivity of the motion to small changes in the initial conditions. In a survey of encounters and mergers of a dwarf galaxy with a giant galaxy, chaotic behaviour arises mainly in non-linear oscillations of the dwarf galaxy. The encounter disrupts the dwarf, excites chaotic oscillations of the dwarf, or excites regular oscillations. Dynamical friction can drive a merger to completion within a Hubble time only if the dwarf is sufficiently massive. The survey of encounters and mergers is the basis for a simple model of the evolution of a `Local Group' consisting of a giant galaxy and a population of dwarf galaxies bound to the giant as satellites on radial orbits.

Evolution equation for quantum entanglement

NASA Astrophysics Data System (ADS)

Konrad, Thomas; de Melo, Fernando; Tiersch, Markus; Kasztelan, Christian; Aragão, Adriano; Buchleitner, Andreas

2008-02-01

Quantum information technology largely relies on a precious and fragile resource, quantum entanglement, a highly non-trivial manifestation of the coherent superposition of states of composite quantum systems. However, our knowledge of the time evolution of this resource under realistic conditions-that is, when corrupted by environment-induced decoherence-is so far limited, and general statements on entanglement dynamics in open systems are scarce. Here we prove a simple and general factorization law for quantum systems shared by two parties, which describes the time evolution of entanglement on passage of either component through an arbitrary noisy channel. The robustness of entanglement-based quantum information processing protocols is thus easily and fully characterized by a single quantity.

Preface of the "Symposium on Mathematical Models and Methods to investigate Heterogeneity in Cell and Cell Population Biology"

NASA Astrophysics Data System (ADS)

Clairambault, Jean

2016-06-01

This session investigates hot topics related to mathematical representations of cell and cell population dynamics in biology and medicine, in particular, but not only, with applications to cancer. Methods in mathematical modelling and analysis, and in statistical inference using single-cell and cell population data, should contribute to focus this session on heterogeneity in cell populations. Among other methods are proposed: a) Intracellular protein dynamics and gene regulatory networks using ordinary/partial/delay differential equations (ODEs, PDEs, DDEs); b) Representation of cell population dynamics using agent-based models (ABMs) and/or PDEs; c) Hybrid models and multiscale models to integrate single-cell dynamics into cell population behaviour; d) Structured cell population dynamics and asymptotic evolution w.r.t. relevant traits; e) Heterogeneity in cancer cell populations: origin, evolution, phylogeny and methods of reconstruction; f) Drug resistance as an evolutionary phenotype: predicting and overcoming it in therapeutics; g) Theoretical therapeutic optimisation of combined drug treatments in cancer cell populations and in populations of other organisms, such as bacteria.

Nonlinear dynamic evolution and control in CCFN with mixed attachment mechanisms

NASA Astrophysics Data System (ADS)

Wang, Jianrong; Wang, Jianping; Han, Dun

2017-01-01

In recent years, wireless communication plays an important role in our lives. Cooperative communication, is used by a mobile station with single antenna to share with each other forming a virtual MIMO antenna system, will become a development with a diversity gain for wireless communication in tendency future. In this paper, a fitness model of evolution network based on complex networks with mixed attachment mechanisms is devised in order to study an actual network-CCFN (cooperative communication fitness network). Firstly, the evolution of CCFN is given by four cases with different probabilities, and the rate equations of nodes degree are presented to analyze the evolution of CCFN. Secondly, the degree distribution is analyzed by calculating the rate equation and numerical simulation with the examples of four fitness distributions such as power law, uniform fitness distribution, exponential fitness distribution and Rayleigh fitness distribution. Finally, the robustness of CCFN is studied by numerical simulation with four fitness distributions under random attack and intentional attack to analyze the effects of degree distribution, average path length and average degree. The results of this paper offers insights for building CCFN systems in order to program communication resources.

Ecological and evolutionary dynamics of interconnectedness and modularity

PubMed Central

Nordbotten, Jan M.; Levin, Simon A.; Szathmáry, Eörs; Stenseth, Nils C.

2018-01-01

In this contribution, we develop a theoretical framework for linking microprocesses (i.e., population dynamics and evolution through natural selection) with macrophenomena (such as interconnectedness and modularity within an ecological system). This is achieved by developing a measure of interconnectedness for population distributions defined on a trait space (generalizing the notion of modularity on graphs), in combination with an evolution equation for the population distribution. With this contribution, we provide a platform for understanding under what environmental, ecological, and evolutionary conditions ecosystems evolve toward being more or less modular. A major contribution of this work is that we are able to decompose the overall driver of changes at the macro level (such as interconnectedness) into three components: (i) ecologically driven change, (ii) evolutionarily driven change, and (iii) environmentally driven change. PMID:29311333

Integrating Evolutionary Game Theory into Mechanistic Genotype-Phenotype Mapping.

PubMed

Zhu, Xuli; Jiang, Libo; Ye, Meixia; Sun, Lidan; Gragnoli, Claudia; Wu, Rongling

2016-05-01

Natural selection has shaped the evolution of organisms toward optimizing their structural and functional design. However, how this universal principle can enhance genotype-phenotype mapping of quantitative traits has remained unexplored. Here we show that the integration of this principle and functional mapping through evolutionary game theory gains new insight into the genetic architecture of complex traits. By viewing phenotype formation as an evolutionary system, we formulate mathematical equations to model the ecological mechanisms that drive the interaction and coordination of its constituent components toward population dynamics and stability. Functional mapping provides a procedure for estimating the genetic parameters that specify the dynamic relationship of competition and cooperation and predicting how genes mediate the evolution of this relationship during trait formation. Copyright © 2016 Elsevier Ltd. All rights reserved.

Alternative descriptions of wave and particle aspects of the harmonic oscillator

NASA Technical Reports Server (NTRS)

Schuch, Dieter

1993-01-01

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

Three kinds of particles on a single rationally parameterized world line

NASA Astrophysics Data System (ADS)

Kassandrov, V. V.; Markova, N. V.

2016-10-01

We consider the light cone (`retardation') equation (LCE) of an inertially moving observer and a single worldline parameterized by arbitrary rational functions. Then a set of apparent copies, R- or C-particles, defined by the (real or complex conjugate) roots of the LCE will be detected by the observer. For any rational worldline the collective R-C dynamics is manifestly Lorentz-invariant and conservative; the latter property follows directly from the structure of Vieta formulas for the LCE roots. In particular, two Lorentz invariants, the square of total 4-momentum and total rest mass, are distinct and both integer-valued. Asymptotically, at large values of the observer's proper time, one distinguishes three types of the LCE roots and associated R-C particles, with specific locations and evolutions; each of three kinds of particles can assemble into compact large groups - clusters. Throughout the paper, we make no use of differential equations of motion, field equations, etc.: the collective R-C dynamics is purely algebraic

The Nonlinear Coupling of Electromagnetic Ion Cyclotron and Lower Hybrid Waves in the Ring Current Region: The Magnetic Storm May 1-7 1998

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Krivorutsky, E.; Gamayunov, K.; Avanov, L.

2003-01-01

The excitation of lower hybrid waves (LHWs) is a widely discussed mechanism of interaction between plasma species in space, and is one of the unresolved questions of magnetospheric multi-ion plasmas. In this paper we present the morphology, dynamics, and level of LHW activity generated by electromagnetic ion cyclotron (EMIC) waves during the May 2-7, 1998 storm period on the global scale. The LHWs were calculated based on our newly developed self-consistent model that couples the system of two kinetic equations: one equation describes the ring current (RC) ion dynamic, and another equation describes the evolution of EMIC waves. It is found that the LHWs are excited by helium ions due to their mass dependent drift in the electric field of EMIC waves. The level of LHW activity is calculated assuming that the induced scattering process is the main saturation mechanism for these waves. The calculated LHWs electric fields are consistent with the observational data.

The Nonlinear Coupling of Electromagnetic Ion Cyclotron and Lower Hybrid Waves in the Ring Current Region

NASA Technical Reports Server (NTRS)

Khazanov, G. V.

2004-01-01

The excitation of lower hybrid waves (LHWs) is a widely discussed mechanism of interaction between plasma species in space, and is one of the unresolved questions of magnetospheric multi-ion plasmas. In this paper we present the morphology, dynamics, and level of LHW activity generated by electromagnetic ion cyclotron (EMIC) waves during the May 2-7, 1998 storm period on the global scale. The LHWs were calculated based on a newly developed self-consistent model (Khazanov et. al., 2002, 2003) that couples the system of two kinetic equations: one equation describes the ring current (RC) ion dynamic, and another equation describes the evolution of EMIC waves. It is found that the LHWs are excited by helium ions due to their mass dependent drift in the electric field of EMIC waves. The level of LHW activity is calculated assuming that the induced scattering process is the main saturation mechanism for these waves. The calculated LHWs electric fields are consistent with the observational data.

Helicity evolution at small-x

DOE PAGES

Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.

2016-01-13

We construct small-x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the g1 structure function. These evolution equations resum powers of α s ln 2(1/x) in the polarization-dependent evolution along with the powers of α s ln(1/x) in the unpolarized evolution which includes saturation efects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-N c and large-N c & N f limits. As a cross-check,more » in the ladder approximation, our equations map onto the same ladder limit of the infrared evolution equations for g 1 structure function derived previously by Bartels, Ermolaev and Ryskin.« less

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

NASA Astrophysics Data System (ADS)

Laurie, Nathan S.

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

Self-Consistent Frequency Sweeping of TAE mode

NASA Astrophysics Data System (ADS)

Wang, Ge

2012-03-01

We have extended our intuitive Toroidal Alfven Wave (TAE) model [1] for describing spontaneous frequency sweeping by a destabilizing component of energetic particles. Now a fully developed self-consistent description for frequency sweeping of an isolated TAE mode has been developed. As in [1], we use the Rosenbluth, Berk,Van Dam tip theory [2], valid for low beta, large aspect ratio, circular tokamaks, to describe the evolution of the TAE wave equation. The wave is coupled to the particle dynamics that uses the Berk, Breizman, Ye map model [3] to construct the particle/wave Lagrangian associated with a phase space dependent mode structure. Then together with the appropriate Vlasov equation for describing the particle dynamics, a set of equations determining the dynamics of the system has been formulated. Adiabatic solutions have been obtained and work is underway in simulating the exact nonlinear dynamics. A status report of our results will be given at the meeting. [4pt] [1] G. Wang and H. L. Berk, Communication in Nonlinear Science and Numerical Simulation 17, 2179 (2012) [0pt] [2] M. N. Rosenbluth,; H. L. Berk, J. Van Dam and D. M. Lingberg, Phys. Rev. Lett. 68, 596 (1992). [0pt] [3] Berk, H.L.; Breizman, B.N.; Ye, H. In: Physics of Fluids B 51993, 1506 (1993)

Propagation dynamics of super-Gaussian beams in fractional Schrödinger equation: from linear to nonlinear regimes.

PubMed

Zhang, Lifu; Li, Chuxin; Zhong, Haizhe; Xu, Changwen; Lei, Dajun; Li, Ying; Fan, Dianyuan

2016-06-27

We have investigated the propagation dynamics of super-Gaussian optical beams in fractional Schrödinger equation. We have identified the difference between the propagation dynamics of super-Gaussian beams and that of Gaussian beams. We show that, the linear propagation dynamics of the super-Gaussian beams with order m > 1 undergo an initial compression phase before they split into two sub-beams. The sub-beams with saddle shape separate each other and their interval increases linearly with propagation distance. In the nonlinear regime, the super-Gaussian beams evolve to become a single soliton, breathing soliton or soliton pair depending on the order of super-Gaussian beams, nonlinearity, as well as the Lévy index. In two dimensions, the linear evolution of super-Gaussian beams is similar to that for one dimension case, but the initial compression of the input super-Gaussian beams and the diffraction of the splitting beams are much stronger than that for one dimension case. While the nonlinear propagation of the super-Gaussian beams becomes much more unstable compared with that for the case of one dimension. Our results show the nonlinear effects can be tuned by varying the Lévy index in the fractional Schrödinger equation for a fixed input power.

Extension of Liouville Formalism to Postinstability Dynamics

NASA Technical Reports Server (NTRS)

Zak, Michail

2003-01-01

A mathematical formalism has been developed for predicting the postinstability motions of a dynamic system governed by a system of nonlinear equations and subject to initial conditions. Previously, there was no general method for prediction and mathematical modeling of postinstability behaviors (e.g., chaos and turbulence) in such a system. The formalism of nonlinear dynamics does not afford means to discriminate between stable and unstable motions: an additional stability analysis is necessary for such discrimination. However, an additional stability analysis does not suggest any modifications of a mathematical model that would enable the model to describe postinstability motions efficiently. The most important type of instability that necessitates a postinstability description is associated with positive Lyapunov exponents. Such an instability leads to exponential growth of small errors in initial conditions or, equivalently, exponential divergence of neighboring trajectories. The development of the present formalism was undertaken in an effort to remove positive Lyapunov exponents. The means chosen to accomplish this is coupling of the governing dynamical equations with the corresponding Liouville equation that describes the evolution of the flow of error probability. The underlying idea is to suppress the divergences of different trajectories that correspond to different initial conditions, without affecting a target trajectory, which is one that starts with prescribed initial conditions.

Far-from-equilibrium magnetic granular layers: dynamic patterns, magnetic order and self-assembled swimmers

NASA Astrophysics Data System (ADS)

Snezhko, Alexey

2010-03-01

Ensembles of interacting particles subject to an external periodic forcing often develop nontrivial collective behavior and self-assembled dynamic patterns. We study emergent phenomena in magnetic granular ensembles suspended at a liquid-air and liquid-liquid interfaces and subjected to a transversal alternating magnetic field. Experiments reveal a new type of nontrivially ordered dynamic self-assembled structures (in particular, ``magnetic snakes'', ``asters'', ``clams'') emerging in such systems in a certain range of excitation parameters. These non-equilibrium dynamic structures emerge as a result of the competition between magnetic and hydrodynamic forces and have complex magnetic ordering. Transition between different self-assembled phases with parameters of external driving magnetic field is observed. I will show that above some frequency threshold magnetic snakes spontaneously break the symmetry of the self-induced surface flows (symmetry breaking instability) and turn into swimmers. Self-induced surface flows symmetry can be also broken in a controlled fashion by introduction of a large bead to a magnetic snake (bead-snake hybrid), that transforms it into a robust self-locomoting entity. Some features of the self-localized structures can be understood in the framework of an amplitude equation for parametric waves coupled to the conservation law equation describing the evolution of the magnetic particle density and the Navier-Stokes equation for hydrodynamic flows.

New methodology for fast prediction of wheel wear evolution

NASA Astrophysics Data System (ADS)

Apezetxea, I. S.; Perez, X.; Casanueva, C.; Alonso, A.

2017-07-01

In railway applications wear prediction in the wheel-rail interface is a fundamental matter in order to study problems such as wheel lifespan and the evolution of vehicle dynamic characteristic with time. However, one of the principal drawbacks of the existing methodologies for calculating the wear evolution is the computational cost. This paper proposes a new wear prediction methodology with a reduced computational cost. This methodology is based on two main steps: the first one is the substitution of the calculations over the whole network by the calculation of the contact conditions in certain characteristic point from whose result the wheel wear evolution can be inferred. The second one is the substitution of the dynamic calculation (time integration calculations) by the quasi-static calculation (the solution of the quasi-static situation of a vehicle at a certain point which is the same that neglecting the acceleration terms in the dynamic equations). These simplifications allow a significant reduction of computational cost to be obtained while maintaining an acceptable level of accuracy (error order of 5-10%). Several case studies are analysed along the paper with the objective of assessing the proposed methodology. The results obtained in the case studies allow concluding that the proposed methodology is valid for an arbitrary vehicle running through an arbitrary track layout.

A GLOBAL GALACTIC DYNAMO WITH A CORONA CONSTRAINED BY RELATIVE HELICITY

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

Prasad, A.; Mangalam, A., E-mail: avijeet@iiap.res.in, E-mail: mangalam@iiap.res.in

We present a model for a global axisymmetric turbulent dynamo operating in a galaxy with a corona that treats the parameters of turbulence driven by supernovae and by magneto-rotational instability under a common formalism. The nonlinear quenching of the dynamo is alleviated by the inclusion of small-scale advective and diffusive magnetic helicity fluxes, which allow the gauge-invariant magnetic helicity to be transferred outside the disk and consequently to build up a corona during the course of dynamo action. The time-dependent dynamo equations are expressed in a separable form and solved through an eigenvector expansion constructed using the steady-state solutions ofmore » the dynamo equation. The parametric evolution of the dynamo solution allows us to estimate the final structure of the global magnetic field and the saturated value of the turbulence parameter α{sub m}, even before solving the dynamical equations for evolution of magnetic fields in the disk and the corona, along with α-quenching. We then solve these equations simultaneously to study the saturation of the large-scale magnetic field, its dependence on the small-scale magnetic helicity fluxes, and the corresponding evolution of the force-free field in the corona. The quadrupolar large-scale magnetic field in the disk is found to reach equipartition strength within a timescale of 1 Gyr. The large-scale magnetic field in the corona obtained is much weaker than the field inside the disk and has only a weak impact on the dynamo operation.« less

Dynamical Models of Elliptical Galaxies in z = 0.5 Clusters. I. Data-Model Comparison and Evolution of Galaxy Rotation

NASA Astrophysics Data System (ADS)

van der Marel, Roeland P.; van Dokkum, Pieter G.

2007-10-01

We present spatially resolved stellar rotation velocity and velocity dispersion profiles from Keck/LRIS absorption-line spectra for 25 galaxies, mostly visually classified ellipticals, in three clusters at z~0.5. We interpret the kinematical data and HST photometry using oblate axisymmetric two-integral f(E,Lz) dynamical models based on the Jeans equations. This yields good fits, provided that the seeing and observational characteristics are carefully modeled. The fits yield for each galaxy the dynamical mass-to-light ratio (M/L) and a measure of the galaxy rotation rate. Paper II addresses the implied M/L evolution. Here we study the rotation-rate evolution by comparison to a sample of local elliptical galaxies of similar present-day luminosity. The brightest galaxies in the sample all rotate too slowly to account for their flattening, as is also observed at z=0. But the average rotation rate is higher at z~0.5 than locally. This may be due to a higher fraction of misclassified S0 galaxies (although this effect is insufficient to explain the observed strong evolution of the cluster S0 fraction with redshift). Alternatively, dry mergers between early-type galaxies may have decreased the average rotation rate over time. It is unclear whether such mergers are numerous enough in clusters to explain the observed trend quantitatively. Disk-disk mergers may affect the comparison through the so-called ``progenitor bias,'' but this cannot explain the direction of the observed rotation-rate evolution. Additional samples are needed to constrain possible environmental dependencies and cosmic variance in galaxy rotation rates. Either way, studies of the internal stellar dynamics of distant galaxies provide a valuable new approach for exploring galaxy evolution.

Portent of Heine's Reciprocal Square Root Identity

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

Cohl, H W

Precise efforts in theoretical astrophysics are needed to fully understand the mechanisms that govern the structure, stability, dynamics, formation, and evolution of differentially rotating stars. Direct computation of the physical attributes of a star can be facilitated by the use of highly compact azimuthal and separation angle Fourier formulations of the Green's functions for the linear partial differential equations of mathematical physics.

Evolutionary game dynamics of controlled and automatic decision-making

NASA Astrophysics Data System (ADS)

Toupo, Danielle F. P.; Strogatz, Steven H.; Cohen, Jonathan D.; Rand, David G.

2015-07-01

We integrate dual-process theories of human cognition with evolutionary game theory to study the evolution of automatic and controlled decision-making processes. We introduce a model in which agents who make decisions using either automatic or controlled processing compete with each other for survival. Agents using automatic processing act quickly and so are more likely to acquire resources, but agents using controlled processing are better planners and so make more effective use of the resources they have. Using the replicator equation, we characterize the conditions under which automatic or controlled agents dominate, when coexistence is possible and when bistability occurs. We then extend the replicator equation to consider feedback between the state of the population and the environment. Under conditions in which having a greater proportion of controlled agents either enriches the environment or enhances the competitive advantage of automatic agents, we find that limit cycles can occur, leading to persistent oscillations in the population dynamics. Critically, however, these limit cycles only emerge when feedback occurs on a sufficiently long time scale. Our results shed light on the connection between evolution and human cognition and suggest necessary conditions for the rise and fall of rationality.

Evolutionary game dynamics of controlled and automatic decision-making.

PubMed

Toupo, Danielle F P; Strogatz, Steven H; Cohen, Jonathan D; Rand, David G

2015-07-01

We integrate dual-process theories of human cognition with evolutionary game theory to study the evolution of automatic and controlled decision-making processes. We introduce a model in which agents who make decisions using either automatic or controlled processing compete with each other for survival. Agents using automatic processing act quickly and so are more likely to acquire resources, but agents using controlled processing are better planners and so make more effective use of the resources they have. Using the replicator equation, we characterize the conditions under which automatic or controlled agents dominate, when coexistence is possible and when bistability occurs. We then extend the replicator equation to consider feedback between the state of the population and the environment. Under conditions in which having a greater proportion of controlled agents either enriches the environment or enhances the competitive advantage of automatic agents, we find that limit cycles can occur, leading to persistent oscillations in the population dynamics. Critically, however, these limit cycles only emerge when feedback occurs on a sufficiently long time scale. Our results shed light on the connection between evolution and human cognition and suggest necessary conditions for the rise and fall of rationality.

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

NASA Astrophysics Data System (ADS)

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

2001-01-01

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

BINARY CORRELATIONS IN IONIZED GASES

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

Balescu, R.; Taylor, H.S.

1961-01-01

An equation of evolution for the binary distribution function in a classical homogeneous, nonequilibrium plasma was derived. It is shown that the asymptotic (long-time) solution of this equation is the Debye distribution, thus providing a rigorous dynamical derivation of the equilibrium distribution. This proof is free from the fundamental conceptual difficulties of conventional equilibrium derivations. Out of equilibrium, a closed formula was obtained for the long living correlations, in terms of the momentum distribution function. These results should form an appropriate starting point for a rigorous theory of transport phenomena in plasmas, including the effect of molecular correlations. (auth)

Dynamical Stochastic Processes of Returns in Financial Markets

NASA Astrophysics Data System (ADS)

Kim, Kyungsik; Kim, Soo Yong; Lim, Gyuchang; Zhou, Junyuan; Yoon, Seung-Min

2006-03-01

We show how the evolution of probability distribution functions of the returns from the tick data of the Korean treasury bond futures (KTB) and the S&P 500 stock index can be described by means of the Fokker-Planck equation. We derive the Fokker- Planck equation from the estimated Kramers-Moyal coefficients estimated directly from the empirical data. By analyzing the statistics of the returns, we present the quantitative deterministic and random influences on both financial time series, for which we can give a simple physical interpretation. Finally, we remark that the diffusion coefficient should be significantly considered to make a portfolio.

Comparing an analytical spacetime metric for a merging binary to a fully nonlinear numerical evolution using curvature scalars

NASA Astrophysics Data System (ADS)

Sadiq, Jam; Zlochower, Yosef; Nakano, Hiroyuki

2018-04-01

We introduce a new geometrically invariant prescription for comparing two different spacetimes based on geodesic deviation. We use this method to compare a family of recently introduced analytical spacetime representing inspiraling black-hole binaries to fully nonlinear numerical solutions to the Einstein equations. Our method can be used to improve analytical spacetime models by providing a local measure of the effects that violations of the Einstein equations will have on timelike geodesics, and indirectly, gas dynamics. We also discuss the advantages and limitations of this method.

Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Tikan, Alexey; Billet, Cyril; El, Gennady; Tovbis, Alexander; Bertola, Marco; Sylvestre, Thibaut; Gustave, Francois; Randoux, Stephane; Genty, Goëry; Suret, Pierre; Dudley, John M.

2017-07-01

We report experimental confirmation of the universal emergence of the Peregrine soliton predicted to occur during pulse propagation in the semiclassical limit of the focusing nonlinear Schrödinger equation. Using an optical fiber based system, measurements of temporal focusing of high power pulses reveal both intensity and phase signatures of the Peregrine soliton during the initial nonlinear evolution stage. Experimental and numerical results are in very good agreement, and show that the universal mechanism that yields the Peregrine soliton structure is highly robust and can be observed over a broad range of parameters.

Surge dynamics coupled to pore-pressure evolution in debris flows

USGS Publications Warehouse

Savage, S.B.; Iverson, R.M.; ,

2003-01-01

Temporally and spatially varying pore-fluid pressures exert strong controls on debris-flow motion by mediating internal and basal friction at grain contacts. We analyze these effects by deriving a one-dimensional model of pore-pressure diffusion explicitly coupled to changes in debris-flow thickness. The new pore-pressure equation is combined with Iverson's (1997) extension of the depth-averaged Savage-Hutter (1989, 1991) granular avalanche equations to predict motion of unsteady debris-flow surges with evolving pore-pressure distributions. Computational results illustrate the profound effects of pore-pressure diffusivities on debris-flow surge depths and velocities. ?? 2003 Millpress,.

Concise calculation of the scaling function, exponents, and probability functional of the Edwards-Wilkinson equation with correlated noise

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

Yu, Y.; Pang, N.; Halpin-Healy, T.

1994-12-01

The linear Langevin equation proposed by Edwards and Wilkinson [Proc. R. Soc. London A 381, 17 (1982)] is solved in closed form for noise of arbitrary space and time correlation. Furthermore, the temporal development of the full probability functional describing the height fluctuations is derived exactly, exhibiting an interesting evolution between two distinct Gaussian forms. We determine explicitly the dynamic scaling function for the interfacial width for any given initial condition, isolate the early-time behavior, and discover an invariance that was unsuspected in this problem of arbitrary spatiotemporal noise.

Propagation of hydroclimatic variability through the critical zone

NASA Astrophysics Data System (ADS)

Porporato, A. M.; Calabrese, S.; Parolari, A.

2016-12-01

The interaction between soil moisture dynamics and mineral-weathering reactions (e.g., ion exchange, precipitation-dissolution) affects the availability of nutrients to plants, composition of soils, soil acidification, as well as CO2 sequestration. Across the critical zone (CZ), this interaction is responsible for propagating hydroclimatic fluctuations to deeper soil layers, controlling weathering rates via leaching events which intermittently alter the alkalinity levels. In this contribution, we analyze these dynamics using a stochastic modeling approach based on spatially lumped description of soil hydrology and chemical weathering reactions forced by multi-scale temporal hydrologic variability. We quantify the role of soil moisture dynamics in filtering the rainfall fluctuations through its impacts on soil water chemistry, described by a system of ordinary differential equations (and algebraic equations, for the equilibrium reactions), driving the evolution of alkalinity, pH, the chemical species of the soil solution, and the mineral-weathering rate. A probabilistic description of the evolution of the critical zone is thus obtained, allowing us to describe the CZ response to long-term climate fluctuations, ecosystem and land-use conditions, in terms of key variables groups. The model is applied to the weathering rate of albite in the Calhoun CZ observatory and then extended to explore similarities and differences across other CZs. Typical time scales of response and degrees of sensitivities of CZ to hydroclimatic fluctuations and human forcing are also explored.

Dodging the dark matter degeneracy while determining the dynamics of dark energy

NASA Astrophysics Data System (ADS)

Busti, Vinicius C.; Clarkson, Chris

2016-05-01

One of the key issues in cosmology is to establish the nature of dark energy, and to determine whether the equation of state evolves with time. When estimating this from distance measurements there is a degeneracy with the matter density. We show that there exists a simple function of the dark energy equation of state and its first derivative which is independent of this degeneracy at all redshifts, and so is a much more robust determinant of the evolution of dark energy than just its derivative. We show that this function can be well determined at low redshift from supernovae using Gaussian Processes, and that this method is far superior to a variety of parameterisations which are also subject to priors on the matter density. This shows that parametrised models give very biased constraints on the evolution of dark energy.

Nonlinear spatial evolution of inviscid instabilities on hypersonic boundary layers

NASA Technical Reports Server (NTRS)

Wundrow, David W.

1996-01-01

The spatial development of an initially linear vorticity-mode instability on a compressible flat-plate boundary layer is considered. The analysis is done in the framework of the hypersonic limit where the free-stream Mach number M approaches infinity. Nonlinearity is shown to become important locally, in a thin critical layer, when sigma, the deviation of the phase speed from unity, becomes o(M(exp -8/7)) and the magnitude of the pressure fluctuations becomes 0(sigma(exp 5/2)M(exp 2)). The unsteady flow outside the critical layer takes the form of a linear instability wave but with its amplitude completely determined by the nonlinear flow within the critical layer. The coupled set of equations which govern the critical-layer dynamics reflect a balance between spatial-evolution, (linear and nonlinear) convection and nonlinear vorticity-generation terms. The numerical solution to these equations shows that nonlinear effects produce a dramatic reduction in the instability-wave amplitude.

Modeling of dynamic bipolar plasma sheaths

NASA Astrophysics Data System (ADS)

Grossmann, J. M.; Swanekamp, S. B.; Ottinger, P. F.

1991-08-01

The behavior of a one dimensional plasma sheath is described in regimes where the sheath is not in equilibrium because it carries current densities that are either time dependent, or larger than the bipolar Child-Langmuir level determined from the injected ion flux. Earlier models of dynamic bipolar sheaths assumed that ions and electrons evolve in a series of quasi-equilibria. In addition, sheath growth was described by the equation Zenoxs = (ji)-Zenouo, where xs is the velocity of the sheath edge, ji is the ion current density, nouo is the injected ion flux density, and Ze is the ion charge. In this paper, a generalization of the bipolar electron-to-ion current density ratio formula is derived to study regimes where ions are not in equilibrium. A generalization of the above sheath growth equation is also developed which is consistent with the ion continuity equation and which reveals new physics of sheath behavior associated with the emitted electrons and their evolution. Based on these findings, two new models of dynamic bipolar sheaths are developed. Larger sheath sizes and potentials than those of earlier models are found. In certain regimes, explosive sheath growth is predicted.

Dynamical interpretation of conditional patterns

NASA Technical Reports Server (NTRS)

Adrian, R. J.; Moser, R. D.; Moin, P.

1988-01-01

While great progress is being made in characterizing the 3-D structure of organized turbulent motions using conditional averaging analysis, there is a lack of theoretical guidance regarding the interpretation and utilization of such information. Questions concerning the significance of the structures, their contributions to various transport properties, and their dynamics cannot be answered without recourse to appropriate dynamical governing equations. One approach which addresses some of these questions uses the conditional fields as initial conditions and calculates their evolution from the Navier-Stokes equations, yielding valuable information about stability, growth, and longevity of the mean structure. To interpret statistical aspects of the structures, a different type of theory which deals with the structures in the context of their contributions to the statistics of the flow is needed. As a first step toward this end, an effort was made to integrate the structural information from the study of organized structures with a suitable statistical theory. This is done by stochastically estimating the two-point conditional averages that appear in the equation for the one-point probability density function, and relating the structures to the conditional stresses. Salient features of the estimates are identified, and the structure of the one-point estimates in channel flow is defined.

Effects of grain size evolution on mantle dynamics

NASA Astrophysics Data System (ADS)

Schulz, Falko; Tosi, Nicola; Plesa, Ana-Catalina; Breuer, Doris

2016-04-01

The rheology of planetary mantle materials is strongly dependent on temperature, pressure, strain-rate, and grain size. In particular, the rheology of olivine, the most abundant mineral of the Earth's upper mantle, has been extensively studied in the laboratory (e.g., Karato and Wu, 1993; Hirth and Kohlstedt, 2003). Two main mechanisms control olivine's deformation: dislocation and diffusion creep. While the former implies a power-law dependence of the viscosity on the strain-rate that leads to a non-Newtonian behaviour, the latter is sensitively dependent on the grain size. The dynamics of planetary interiors is locally controlled by the deformation mechanism that delivers the lowest viscosity. Models of the dynamics and evolution of planetary mantles should thus be capable to self-consistently distinguish which of the two mechanisms dominates at given conditions of temperature, pressure, strain-rate and grain size. As the grain size can affect the viscosity associated with diffusion creep by several orders of magnitude, it can strongly influence the dominant deformation mechanism. The vast majority of numerical, global-scale models of mantle convection, however, are based on the use of a linear diffusion-creep rheology with constant grain-size. Nevertheless, in recent studies, a new equation has been proposed to properly model the time-dependent evolution of the grain size (Austin and Evens, 2007; Rozel et al., 2010). We implemented this equation in our mantle convection code Gaia (Hüttig et al., 2013). In the framework of simple models of stagnant lid convection, we compared simulations based on the fully time-dependent equation of grain-size evolution with simulations based on its steady-state version. In addition, we tested a number of different parameters in order to identify those that affects the grain size to the first order and, in turn, control the conditions at which mantle deformation is dominated by diffusion or dislocation creep. References Austin, N. J. and Evans, B. (2007). Geology, 35(4):343. Hirth, G. and Kohlstedt, D. (2003). Geophysical Monograph Series, page 83105. Hüttig, C., Tosi, N., and Moore, W. B. (2013). Physics of the Earth and Planetary Interiors, 220:11-18. Karato, S.-i. and Wu, P. (1993). Science, 260(5109):771778. Rozel, A., Ricard, Y., and Bercovici, D. (2010). Geophysical Journal International, 184(2):719728.

Binary Black Hole Mergers from Field Triples: Properties, Rates, and the Impact of Stellar Evolution

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

Antonini, Fabio; Toonen, Silvia; Hamers, Adrian S.

We consider the formation of binary black hole (BH) mergers through the evolution of field massive triple stars. In this scenario, favorable conditions for the inspiral of a BH binary are initiated by its gravitational interaction with a distant companion, rather than by a common-envelope phase invoked in standard binary evolution models. We use a code that follows self-consistently the evolution of massive triple stars, combining the secular triple dynamics (Lidov–Kozai cycles) with stellar evolution. After a BH triple is formed, its dynamical evolution is computed using either the orbit-averaged equations of motion, or a high-precision direct integrator for triplesmore » with weaker hierarchies for which the secular perturbation theory breaks down. Most BH mergers in our models are produced in the latter non-secular dynamical regime. We derive the properties of the merging binaries and compute a BH merger rate in the range (0.3–1.3) Gpc{sup −3} yr{sup −1}, or up to ≈2.5 Gpc{sup −3} yr{sup −1} if the BH orbital planes have initially random orientation. Finally, we show that BH mergers from the triple channel have significantly higher eccentricities than those formed through the evolution of massive binaries or in dense star clusters. Measured eccentricities could therefore be used to uniquely identify binary mergers formed through the evolution of triple stars. While our results suggest up to ≈10 detections per year with Advanced-LIGO, the high eccentricities could render the merging binaries harder to detect with planned space based interferometers such as LISA.« less

Buoyancy-driven convection around chemical fronts traveling in covered horizontal solution layers.

PubMed

Rongy, L; Goyal, N; Meiburg, E; De Wit, A

2007-09-21

Density differences across an autocatalytic chemical front traveling horizontally in covered thin layers of solution trigger hydrodynamic flows which can alter the concentration profile. We theoretically investigate the spatiotemporal evolution and asymptotic dynamics resulting from such an interplay between isothermal chemical reactions, diffusion, and buoyancy-driven convection. The studied model couples the reaction-diffusion-convection evolution equation for the concentration of an autocatalytic species to the incompressible Stokes equations ruling the evolution of the flow velocity in a two-dimensional geometry. The dimensionless parameter of the problem is a solutal Rayleigh number constructed upon the characteristic reaction-diffusion length scale. We show numerically that the asymptotic dynamics is one steady vortex surrounding, deforming, and accelerating the chemical front. This chemohydrodynamic structure propagating at a constant speed is quite different from the one obtained in the case of a pure hydrodynamic flow resulting from the contact between two solutions of different density or from the pure reaction-diffusion planar traveling front. The dynamics is symmetric with regard to the middle of the layer thickness for positive and negative Rayleigh numbers corresponding to products, respectively, lighter or heavier than the reactants. A parametric study shows that the intensity of the flow, the propagation speed, and the deformation of the front are increasing functions of the Rayleigh number and of the layer thickness. In particular, the asymptotic mixing length and reaction-diffusion-convection speed both scale as square root Ra for Ra>5. The velocity and concentration fields in the asymptotic dynamics are also found to exhibit self-similar properties with Ra. A comparison of the dynamics in the case of a monostable versus bistable kinetics is provided. Good agreement is obtained with experimental data on the speed of iodate-arsenous acid fronts propagating in horizontal capillaries. We furthermore compare the buoyancy-driven dynamics studied here to Marangoni-driven deformation of traveling chemical fronts in solution open to the air in the absence of gravity previously studied in the same geometry [L. Rongy and A. De Wit, J. Chem. Phys. 124, 164705 (2006)].

Two-dimensional evolution equation of finite-amplitude internal gravity waves in a uniformly stratified fluid

PubMed

Kataoka; Tsutahara; Akuzawa

2000-02-14

We derive a fully nonlinear evolution equation that can describe the two-dimensional motion of finite-amplitude long internal waves in a uniformly stratified three-dimensional fluid of finite depth. The derived equation is the two-dimensional counterpart of the evolution equation obtained by Grimshaw and Yi [J. Fluid Mech. 229, 603 (1991)]. In the small-amplitude limit, our equation is reduced to the celebrated Kadomtsev-Petviashvili equation.

Characteristics of 3-D transport simulations of the stratosphere and mesosphere

NASA Technical Reports Server (NTRS)

Fairlie, T. D. A.; Siskind, D. E.; Turner, R. E.; Fisher, M.

1992-01-01

A 3D mechanistic, primitive-equation model of the stratosphere and mesosphere is coupled to an offline spectral transport model. The dynamics model is initialized with and forced by observations so that the coupled models may be used to study specific episodes. Results are compared with those obtained by transport online in the dynamics model. Although some differences are apparent, the results suggest that coupling of the models to a comprehensive photochemical package will provide a useful tool for studying the evolution of constituents in the middle atmosphere during specific episodes.

Dynamical Evolution of a Doubly Quantized Vortex Imprinted in a Bose-Einstein Condensate

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

Mateo, A. Munoz; Delgado, V.

2006-11-03

The recent experiment by Shin et al. [Phys. Rev. Lett. 93, 160406 (2004)] on the decay of a doubly quantized vortex is analyzed by numerically solving the Gross-Pitaevskii equation. Our results demonstrate that the vortex decay is mainly a consequence of dynamical instability. The monotonic increase observed in the vortex lifetimes is a consequence of the fact that the measured lifetimes incorporate the time it takes for the initial perturbation to reach the central slice. When considered locally, the splitting occurs approximately at the same time in every condensate.

Satellite recovery - Attitude dynamics of the targets

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

Quantum simulation of dissipative processes without reservoir engineering

DOE PAGES

Di Candia, R.; Pedernales, J. S.; del Campo, A.; ...

2015-05-29

We present a quantum algorithm to simulate general finite dimensional Lindblad master equations without the requirement of engineering the system-environment interactions. The proposed method is able to simulate both Markovian and non-Markovian quantum dynamics. It consists in the quantum computation of the dissipative corrections to the unitary evolution of the system of interest, via the reconstruction of the response functions associated with the Lindblad operators. Our approach is equally applicable to dynamics generated by effectively non-Hermitian Hamiltonians. We confirm the quality of our method providing specific error bounds that quantify its accuracy.

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Spatio-temporal dynamics of an active, polar, viscoelastic ring.

PubMed

Marcq, Philippe

2014-04-01

Constitutive equations for a one-dimensional, active, polar, viscoelastic liquid are derived by treating the strain field as a slow hydrodynamic variable. Taking into account the couplings between strain and polarity allowed by symmetry, the hydrodynamics of an active, polar, viscoelastic body include an evolution equation for the polarity field that generalizes the damped Kuramoto-Sivashinsky equation. Beyond thresholds of the active coupling coefficients between the polarity and the stress or the strain rate, bifurcations of the homogeneous state lead first to stationary waves, then to propagating waves of the strain, stress and polarity fields. I argue that these results are relevant to living matter, and may explain rotating actomyosin rings in cells and mechanical waves in epithelial cell monolayers.

Supercomputations and big-data analysis in strong-field ultrafast optical physics: filamentation of high-peak-power ultrashort laser pulses

NASA Astrophysics Data System (ADS)

Voronin, A. A.; Panchenko, V. Ya; Zheltikov, A. M.

2016-06-01

High-intensity ultrashort laser pulses propagating in gas media or in condensed matter undergo complex nonlinear spatiotemporal evolution where temporal transformations of optical field waveforms are strongly coupled to an intricate beam dynamics and ultrafast field-induced ionization processes. At the level of laser peak powers orders of magnitude above the critical power of self-focusing, the beam exhibits modulation instabilities, producing random field hot spots and breaking up into multiple noise-seeded filaments. This problem is described by a (3  +  1)-dimensional nonlinear field evolution equation, which needs to be solved jointly with the equation for ultrafast ionization of a medium. Analysis of this problem, which is equivalent to solving a billion-dimensional evolution problem, is only possible by means of supercomputer simulations augmented with coordinated big-data processing of large volumes of information acquired through theory-guiding experiments and supercomputations. Here, we review the main challenges of supercomputations and big-data processing encountered in strong-field ultrafast optical physics and discuss strategies to confront these challenges.

Effects of stochastic noise on dynamical decoupling procedures

NASA Astrophysics Data System (ADS)

Bernád, J. Z.; Frydrych, H.

2014-06-01

Dynamical decoupling is an important tool to counter decoherence and dissipation effects in quantum systems originating from environmental interactions. It has been used successfully in many experiments; however, there is still a gap between fidelity improvements achieved in practice compared to theoretical predictions. We propose a model for imperfect dynamical decoupling based on a stochastic Ito differential equation which could explain the observed gap. We discuss the impact of our model on the time evolution of various quantum systems in finite- and infinite-dimensional Hilbert spaces. Analytical results are given for the limit of continuous control, whereas we present numerical simulations and upper bounds for the case of finite control.

A study of the adequacy of quasi-geostrophic dynamics for modeling the effect of frontal cyclones on the larger scale flow

NASA Technical Reports Server (NTRS)

Mudrick, Stephen

1987-01-01

The evolution of individual cyclone waves is studied in order to see how well quasi-geostrophic (QG) dynamics can simulate the behavior of primitive equations (PE) dynamics. This work is an extension of a similar study (Mudrick, 1982); emphasis is placed here on adding a frontal zone and other more diverse features to the basic states used. In addition, sets of PE integrations, with and without friction, are used to study the formation of surface occluded fronts within the evolving cyclones. Results of the study are summarized at the beginning of the report.

Social evolution and genetic interactions in the short and long term.

PubMed

Van Cleve, Jeremy

2015-08-01

The evolution of social traits remains one of the most fascinating and feisty topics in evolutionary biology even after half a century of theoretical research. W.D. Hamilton shaped much of the field initially with his 1964 papers that laid out the foundation for understanding the effect of genetic relatedness on the evolution of social behavior. Early theoretical investigations revealed two critical assumptions required for Hamilton's rule to hold in dynamical models: weak selection and additive genetic interactions. However, only recently have analytical approaches from population genetics and evolutionary game theory developed sufficiently so that social evolution can be studied under the joint action of selection, mutation, and genetic drift. We review how these approaches suggest two timescales for evolution under weak mutation: (i) a short-term timescale where evolution occurs between a finite set of alleles, and (ii) a long-term timescale where a continuum of alleles are possible and populations evolve continuously from one monomorphic trait to another. We show how Hamilton's rule emerges from the short-term analysis under additivity and how non-additive genetic interactions can be accounted for more generally. This short-term approach reproduces, synthesizes, and generalizes many previous results including the one-third law from evolutionary game theory and risk dominance from economic game theory. Using the long-term approach, we illustrate how trait evolution can be described with a diffusion equation that is a stochastic analogue of the canonical equation of adaptive dynamics. Peaks in the stationary distribution of the diffusion capture classic notions of convergence stability from evolutionary game theory and generally depend on the additive genetic interactions inherent in Hamilton's rule. Surprisingly, the peaks of the long-term stationary distribution can predict the effects of simple kinds of non-additive interactions. Additionally, the peaks capture both weak and strong effects of social payoffs in a manner difficult to replicate with the short-term approach. Together, the results from the short and long-term approaches suggest both how Hamilton's insight may be robust in unexpected ways and how current analytical approaches can expand our understanding of social evolution far beyond Hamilton's original work. Copyright © 2015 Elsevier Inc. All rights reserved.

Exact traveling wave solutions for system of nonlinear evolution equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H

2016-01-01

In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.

Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Opanchuk, B.; Drummond, P. D.

2013-04-01

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved using conventional stochastic methods. The technique is valid for large mode occupation numbers. We give a detailed derivation of methods of functional Wigner representation appropriate for quantum fields. Our approach describes spatial evolution of spinor components and properly accounts for nonlinear losses. Such techniques are applicable to calculating the leading quantum corrections, including effects such as quantum squeezing, entanglement, EPR correlations, and interactions with engineered nonlinear reservoirs. By using a consistent expansion in the inverse density, we are able to explain an inconsistency in the nonlinear loss equations found by earlier authors.

Time-Reversal Generation of Rogue Waves

NASA Astrophysics Data System (ADS)

Chabchoub, Amin; Fink, Mathias

2014-03-01

The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schrödinger equation (NLS). Within the class of exact NLS breather solutions on a finite background, which describe the modulational instability of monochromatic wave trains, the hierarchy of rational solutions localized in both time and space is considered to provide appropriate prototypes to model rogue wave dynamics. Here, we use the time-reversal invariance of the NLS to propose and experimentally demonstrate a new approach to constructing strongly nonlinear localized waves focused in both time and space. The potential applications of this time-reversal approach include remote sensing and motivated analogous experimental analysis in other nonlinear dispersive media, such as optics, Bose-Einstein condensates, and plasma, where the wave motion dynamics is governed by the NLS.

Computationally efficient statistical differential equation modeling using homogenization

USGS Publications Warehouse

Hooten, Mevin B.; Garlick, Martha J.; Powell, James A.

2013-01-01

Statistical models using partial differential equations (PDEs) to describe dynamically evolving natural systems are appearing in the scientific literature with some regularity in recent years. Often such studies seek to characterize the dynamics of temporal or spatio-temporal phenomena such as invasive species, consumer-resource interactions, community evolution, and resource selection. Specifically, in the spatial setting, data are often available at varying spatial and temporal scales. Additionally, the necessary numerical integration of a PDE may be computationally infeasible over the spatial support of interest. We present an approach to impose computationally advantageous changes of support in statistical implementations of PDE models and demonstrate its utility through simulation using a form of PDE known as “ecological diffusion.” We also apply a statistical ecological diffusion model to a data set involving the spread of mountain pine beetle (Dendroctonus ponderosae) in Idaho, USA.

A Self-Consistent Model of the Interacting Ring Current Ions and Electromagnetic ICWs. Initial Results: Waves and Precipitation Fluxes

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Gamayunov, K. V.; Jordanova, V. K.; Krivorutsky, E. N.; Whitaker, Ann F. (Technical Monitor)

2001-01-01

Initial results from the new developed model of the interacting ring current ions and ion cyclotron waves are presented. The model described by the system of two bound kinetic equations: one equation describes the ring current ion dynamics, and another one gives wave evolution. Such system gives a self-consistent description of the ring current ions and ion cyclotron waves in a quasilinear approach. Calculating ion-wave relationships, on a global scale under non steady-state conditions during May 2-5, 1998 storm, we presented the data at three time cuts around initial, main, and late recovery phases of May 4, 1998 storm phase. The structure and dynamics of the ring current proton precipitating flux regions and the wave active ones are discussed in detail.

Lie symmetries for systems of evolution equations

NASA Astrophysics Data System (ADS)

Paliathanasis, Andronikos; Tsamparlis, Michael

2018-01-01

The Lie symmetries for a class of systems of evolution equations are studied. The evolution equations are defined in a bimetric space with two Riemannian metrics corresponding to the space of the independent and dependent variables of the differential equations. The exact relation of the Lie symmetries with the collineations of the bimetric space is determined.

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.

Higher-order stochastic differential equations and the positive Wigner function

NASA Astrophysics Data System (ADS)

Drummond, P. D.

2017-12-01

General higher-order stochastic processes that correspond to any diffusion-type tensor of higher than second order are obtained. The relationship of multivariate higher-order stochastic differential equations with tensor decomposition theory and tensor rank is explained. Techniques for generating the requisite complex higher-order noise are proved to exist either using polar coordinates and γ distributions, or from products of Gaussian variates. This method is shown to allow the calculation of the dynamics of the Wigner function, after it is extended to a complex phase space. The results are illustrated physically through dynamical calculations of the positive Wigner distribution for three-mode parametric downconversion, widely used in quantum optics. The approach eliminates paradoxes arising from truncation of the higher derivative terms in Wigner function time evolution. Anomalous results of negative populations and vacuum scattering found in truncated Wigner quantum simulations in quantum optics and Bose-Einstein condensate dynamics are shown not to occur with this type of stochastic theory.

Experimental and theoretical investigation of radiation and dynamics properties in laser-produced carbon plasmas

NASA Astrophysics Data System (ADS)

Min, Qi; Su, Maogen; Wang, Bo; Cao, Shiquan; Sun, Duixiong; Dong, Chenzhong

2018-05-01

The radiation and dynamics properties of laser-produced carbon plasma in vacuum were studied experimentally with aid of a spatio-temporally resolved emission spectroscopy technique. In addition, a radiation hydrodynamics model based on the fluid dynamic equations and the radiative transfer equation was presented, and calculation of the charge states was performed within the time-dependent collisional radiative model. Detailed temporal and spatial evolution behavior about plasma parameters have been analyzed, such as velocity, electron temperature, charge state distribution, energy level population, and various atomic processes. At the same time, the effects of different atomic processes on the charge state distribution were examined. Finally, the validity of assuming a local thermodynamic equilibrium in the carbon plasma expansion was checked, and the results clearly indicate that the assumption was valid only at the initial (<80 ns) stage of plasma expansion. At longer delay times, it was not applicable near the plasma boundary because of a sharp drop of plasma temperature and electron density.

Algebraic aspects of the driven dynamics in the density operator and correlation functions calculation for multi-level open quantum systems

NASA Astrophysics Data System (ADS)

Bogolubov, Nikolai N.; Soldatov, Andrey V.

2017-12-01

Exact and approximate master equations were derived by the projection operator method for the reduced statistical operator of a multi-level quantum system with finite number N of quantum eigenstates interacting with arbitrary external classical fields and dissipative environment simultaneously. It was shown that the structure of these equations can be simplified significantly if the free Hamiltonian driven dynamics of an arbitrary quantum multi-level system under the influence of the external driving fields as well as its Markovian and non-Markovian evolution, stipulated by the interaction with the environment, are described in terms of the SU(N) algebra representation. As a consequence, efficient numerical methods can be developed and employed to analyze these master equations for real problems in various fields of theoretical and applied physics. It was also shown that literally the same master equations hold not only for the reduced density operator but also for arbitrary nonequilibrium multi-time correlation functions as well under the only assumption that the system and the environment are uncorrelated at some initial moment of time. A calculational scheme was proposed to account for these lost correlations in a regular perturbative way, thus providing additional computable terms to the correspondent master equations for the correlation functions.

Evolution of an electron plasma vortex in a strain flow

NASA Astrophysics Data System (ADS)

Danielson, J. R.

2016-10-01

Coherent vortex structures are ubiquitous in fluids and plasmas and are examples of self-organized structures in nonlinear dynamical systems. The fate of these structures in strain and shear flows is an important issue in many physical systems, including geophysical fluids and shear suppression of turbulence in plasmas. In two-dimensions, an inviscid, incompressible, ideal fluid can be modeled with the Euler equations, which is perhaps the simplest system that supports vortices. The Drift-Poisson equations for pure electron plasmas in a strong, uniform magnetic field are isomorphic to the Euler equations, and so electron plasmas are an excellent test bed for the study of 2D vortex dynamics. This talk will describe results from a new experiment using pure electron plasmas in a specially designed Penning-Malmberg (PM) trap to study the evolution of an initially axisymmetric 2D vortex subject to externally imposed strains. Complementary vortex-in-cell simulations are conducted to validate the 2D nature of the experimental results and to extend the parameter range of these studies. Data for vortex destruction using both instantaneously applied and time dependent strains with flat (constant vorticity) and extended radial profiles will be presented. The role of vortex self-organization will be discussed. A simple 2D model works well for flat vorticity profiles. However, extended profiles exhibit more complicated behavior, such as filamentation and stripping; and these effects and their consequences will be discussed. Work done in collaboration with N. C. Hurst, D. H. E. Dubin, and C. M. Surko.

OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS

PubMed Central

OTT, WILLIAM; RIVAS, MAURICIO A.; WEST, JAMES

2016-01-01

Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝN using a ‘typical’ nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time-T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence). PMID:28066028

OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.

PubMed

Ott, William; Rivas, Mauricio A; West, James

2015-12-01

Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ N using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C 1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time- T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).

Ecological and evolutionary dynamics of interconnectedness and modularity.

PubMed

Nordbotten, Jan M; Levin, Simon A; Szathmáry, Eörs; Stenseth, Nils C

2018-01-23

In this contribution, we develop a theoretical framework for linking microprocesses (i.e., population dynamics and evolution through natural selection) with macrophenomena (such as interconnectedness and modularity within an ecological system). This is achieved by developing a measure of interconnectedness for population distributions defined on a trait space (generalizing the notion of modularity on graphs), in combination with an evolution equation for the population distribution. With this contribution, we provide a platform for understanding under what environmental, ecological, and evolutionary conditions ecosystems evolve toward being more or less modular. A major contribution of this work is that we are able to decompose the overall driver of changes at the macro level (such as interconnectedness) into three components: ( i ) ecologically driven change, ( ii ) evolutionarily driven change, and ( iii ) environmentally driven change. Copyright © 2018 the Author(s). Published by PNAS.

Incomplete Thermalization from Trap-Induced Integrability Breaking: Lessons from Classical Hard Rods

NASA Astrophysics Data System (ADS)

Cao, Xiangyu; Bulchandani, Vir B.; Moore, Joel E.

2018-04-01

We study a one-dimensional gas of hard rods trapped in a harmonic potential, which breaks integrability of the hard-rod interaction in a nonuniform way. We explore the consequences of such broken integrability for the dynamics of a large number of particles and find three distinct regimes: initial, chaotic, and stationary. The initial regime is captured by an evolution equation for the phase-space distribution function. For any finite number of particles, this hydrodynamics breaks down and the dynamics becomes chaotic after a characteristic timescale determined by the interparticle distance and scattering length. The system fails to thermalize over the timescale studied (1 04 natural units), but the time-averaged ensemble is a stationary state of the hydrodynamic evolution. We close by discussing logical extensions of the results to similar systems of quantum particles.

Convective radiation fluid-dynamics: formation and early evolution of ultra low-mass objects

NASA Astrophysics Data System (ADS)

Wuchterl, G.

2005-12-01

The formation process of ultra low-mass objects is some kind of extension of the star formation process. The physical changes towards lower mass are discussed by investigating the collapse of cloud cores that are modelled as Bonnor-Ebert spheres. Their collapse is followed by solving the equations of fluid dynamics with radiation and a model of time-dependent convection that has been calibrated to the Sun. For a sequence of cloud-cores with 1 to 0.01 solar masses, evolutionary tracks and isochrones are shown in the mass-radius diagram, the Hertzsprung-Russel diagram and the effective temperature-surface gravity or Kiel diagram. The collapse and the early hydrostatic evolution to ages of few Ma are briefly discussed and compared to observations of objects in Upper Scorpius and the low-mass components of GG Tau.

Glassy dynamics of landscape evolution

PubMed Central

Ortiz, Carlos P.; Jerolmack, Douglas J.

2018-01-01

Soil creeps imperceptibly downhill, but also fails catastrophically to create landslides. Despite the importance of these processes as hazards and in sculpting landscapes, there is no agreed-upon model that captures the full range of behavior. Here we examine the granular origins of hillslope soil transport by discrete element method simulations and reanalysis of measurements in natural landscapes. We find creep for slopes below a critical gradient, where average particle velocity (sediment flux) increases exponentially with friction coefficient (gradient). At critical gradient there is a continuous transition to a dense-granular flow rheology. Slow earthflows and landslides thus exhibit glassy dynamics characteristic of a wide range of disordered materials; they are described by a two-phase flux equation that emerges from grain-scale friction alone. This glassy model reproduces topographic profiles of natural hillslopes, showing its promise for predicting hillslope evolution over geologic timescales. PMID:29686102

Dynamic evolution of double Λ five-level atom interacting with one-mode electromagnetic cavity field

NASA Astrophysics Data System (ADS)

Abdel-Wahab, N. H.; Salah, Ahmed

2017-12-01

In this paper, the model describing a double Λ five-level atom interacting with a single mode electromagnetic cavity field in the (off) non-resonate case is studied. We obtained the constants of motion for the considered model. Also, the state vector of the wave function is given by using the Schrödinger equation when the atom is initially prepared in its excited state. The dynamical evolutions for the collapse revivals, the antibunching of photons and the field squeezing phenomena are investigated when the field is considered in a coherent state. The influence of detuning parameters on these phenomena is investigated. We noticed that the atom-field properties are influenced by changing the detuning parameters. The investigation of these aspects by numerical simulations is carried out using the Quantum Toolbox in Python (QuTip).

Non-equilibrium time evolution of higher order cumulants of conserved charges and event-by-event analysis

NASA Astrophysics Data System (ADS)

Kitazawa, Masakiyo; Asakawa, Masayuki; Ono, Hirosato

2014-01-01

We investigate the time evolution of higher order cumulants of conserved charges in a volume with the diffusion master equation. Applying the result to the diffusion of non-Gaussian fluctuations in the hadronic stage of relativistic heavy ion collisions, we show that the fourth-order cumulant of net-electric charge at LHC energy is suppressed compared with the recently observed second-order cumulant at ALICE, if the higher order cumulants at hadronization are suppressed compared with their values in the hadron phase in equilibrium. The significance of the experimental information on the rapidity window dependence of various cumulants in investigating the history of the dynamical evolution of the hot medium created in relativistic heavy ion collisions is emphasized.

Modeling self-consistent multi-class dynamic traffic flow

NASA Astrophysics Data System (ADS)

Cho, Hsun-Jung; Lo, Shih-Ching

2002-09-01

In this study, we present a systematic self-consistent multiclass multilane traffic model derived from the vehicular Boltzmann equation and the traffic dispersion model. The multilane domain is considered as a two-dimensional space and the interaction among vehicles in the domain is described by a dispersion model. The reason we consider a multilane domain as a two-dimensional space is that the driving behavior of road users may not be restricted by lanes, especially motorcyclists. The dispersion model, which is a nonlinear Poisson equation, is derived from the car-following theory and the equilibrium assumption. Under the concept that all kinds of users share the finite section, the density is distributed on a road by the dispersion model. In addition, the dynamic evolution of the traffic flow is determined by the systematic gas-kinetic model derived from the Boltzmann equation. Multiplying Boltzmann equation by the zeroth, first- and second-order moment functions, integrating both side of the equation and using chain rules, we can derive continuity, motion and variance equation, respectively. However, the second-order moment function, which is the square of the individual velocity, is employed by previous researches does not have physical meaning in traffic flow. Although the second-order expansion results in the velocity variance equation, additional terms may be generated. The velocity variance equation we propose is derived from multiplying Boltzmann equation by the individual velocity variance. It modifies the previous model and presents a new gas-kinetic traffic flow model. By coupling the gas-kinetic model and the dispersion model, a self-consistent system is presented.

On the account of gravitational perturbations in computer simulation technology of meteoroid complex formation and evolution

NASA Astrophysics Data System (ADS)

Kulikova, N. V.; Chepurova, V. M.

2009-10-01

So far we investigated the nonperturbation dynamics of meteoroid complexes. The numerical integration of the differential equations of motion in the N-body problem by the Everhart algorithm (N=2-6) and introduction of the intermediate hyperbolic orbits build on the base of the generalized problem of two fixed centers permit to take into account some gravitational perturbations.

MHD Forces in Quasi-Static Evolution, Catastrophe, and ``Failed'' Eruption of Solar Flux Ropes

NASA Astrophysics Data System (ADS)

Chen, James

2017-08-01

This paper presents the first unified theoretical model of flux rope dynamics---a single set of flux-rope equations in ideal MHD---to describe as one dynamical process the quasi-static evolution, catastrophic transition to eruption, cessation (``failure'') of eruption, and the post-eruption quasi-equilibria. The model is defined by the major radial {\\it and} minor radial equations of motion including pressure. The initial equilibrium is a flux rope in a background plasma with pressure $p_c(Z)$ and an overlying magnetic field $B_c(Z)$. The flux rope is initially force-free, but theevolution is not required to be force- free. A single quasi-static control parameter, the rate of increase in poloidal flux, is used for the entire process. As this parameter is slowly increased, the flux rope rises, following a sequence of quasi-static equilibria. As the apex of the flux rope rises past a critical height $Z_{crt}$, it expands on a dynamical (Alfvénic) timescale. The eruption rapidly ceases, as the stored magnetic energy of eruption is exhausted, and a new equilibrium is established at height $Z_1 > Z_{crt}$. The calculated velocity profile resembles the observed velocity profiles in ``failed'' eruptions including a damped oscillation. In the post-eruption equilibria, the outward hoop force is balanced by the tension of the toroidal self magnetic field and pressure gradient force. Thus, the flux rope does not evolve in a force-free manner. The flux rope may also expand without reaching a new equilibrium, provided a sufficient amount of poloidal flux is injected on the timescale of eruption. This scenario results in a full CME eruption. It is shown that the minor radial expansion critically couples the evolution of the toroidal self-field and pressure gradient force. No parameter regime is found in which the commonly used simplifications---near-equilibrium minor radial expansion, force-free expansion, and constant aspect ratio $R/a$ (e.g., the torus instability equation)---are valid.Work supported by the Naval Research Laboratory Base Research Program

Feedback coupling in dynamical systems

NASA Astrophysics Data System (ADS)

Trimper, Steffen; Zabrocki, Knud

2003-05-01

Different evolution models are considered with feedback-couplings. In particular, we study the Lotka-Volterra system under the influence of a cumulative term, the Ginzburg-Landau model with a convolution memory term and chemical rate equations with time delay. The memory leads to a modified dynamical behavior. In case of a positive coupling the generalized Lotka-Volterra system exhibits a maximum gain achieved after a finite time, but the population will die out in the long time limit. In the opposite case, the time evolution is terminated in a crash. Due to the nonlinear feedback coupling the two branches of a bistable model are controlled by the the strength and the sign of the memory. For a negative coupling the system is able to switch over between both branches of the stationary solution. The dynamics of the system is further controlled by the initial condition. The diffusion-limited reaction is likewise studied in case the reacting entities are not available simultaneously. Whereas for an external feedback the dynamics is altered, but the stationary solution remain unchanged, a self-organized internal feedback leads to a time persistent solution.

Self-consistent modeling of the dynamic evolution of magnetic island growth in the presence of stabilizing electron-cyclotron current drive

NASA Astrophysics Data System (ADS)

Chatziantonaki, Ioanna; Tsironis, Christos; Isliker, Heinz; Vlahos, Loukas

2013-11-01

The most promising technique for the control of neoclassical tearing modes in tokamak experiments is the compensation of the missing bootstrap current with an electron-cyclotron current drive (ECCD). In this frame, the dynamics of magnetic islands has been studied extensively in terms of the modified Rutherford equation (MRE), including the presence of a current drive, either analytically described or computed by numerical methods. In this article, a self-consistent model for the dynamic evolution of the magnetic island and the driven current is derived, which takes into account the island's magnetic topology and its effect on the current drive. The model combines the MRE with a ray-tracing approach to electron-cyclotron wave-propagation and absorption. Numerical results exhibit a decrease in the time required for complete stabilization with respect to the conventional computation (not taking into account the island geometry), which increases by increasing the initial island size and radial misalignment of the deposition.

Fluid dynamic propagation of initial baryon number perturbations on a Bjorken flow background

DOE PAGES

Floerchinger, Stefan; Martinez, Mauricio

2015-12-11

Baryon number density perturbations offer a possible route to experimentally measure baryon number susceptibilities and heat conductivity of the quark gluon plasma. We study the fluid dynamical evolution of local and event-by-event fluctuations of baryon number density, flow velocity, and energy density on top of a (generalized) Bjorken expansion. To that end we use a background-fluctuation splitting and a Bessel-Fourier decomposition for the fluctuating part of the fluid dynamical fields with respect to the azimuthal angle, the radius in the transverse plane, and rapidity. Here, we examine how the time evolution of linear perturbations depends on the equation of statemore » as well as on shear viscosity, bulk viscosity, and heat conductivity for modes with different azimuthal, radial, and rapidity wave numbers. Finally we discuss how this information is accessible to experiments in terms of the transverse and rapidity dependence of correlation functions for baryonic particles in high energy nuclear collisions.« less

Dynamics of the quantum search and quench-induced first-order phase transitions.

PubMed

Coulamy, Ivan B; Saguia, Andreia; Sarandy, Marcelo S

2017-02-01

We investigate the excitation dynamics at a first-order quantum phase transition (QPT). More specifically, we consider the quench-induced QPT in the quantum search algorithm, which aims at finding out a marked element in an unstructured list. We begin by deriving the exact dynamics of the model, which is shown to obey a Riccati differential equation. Then, we discuss the probabilities of success by adopting either global or local adiabaticity strategies. Moreover, we determine the disturbance of the quantum criticality as a function of the system size. In particular, we show that the critical point exponentially converges to its thermodynamic limit even in a fast evolution regime, which is characterized by both entanglement QPT estimators and the Schmidt gap. The excitation pattern is manifested in terms of quantum domain walls separated by kinks. The kink density is then shown to follow an exponential scaling as a function of the evolution speed, which can be interpreted as a Kibble-Zurek mechanism for first-order QPTs.

Non-minimally coupled quintessence dark energy model with a cubic galileon term: a dynamical system analysis

NASA Astrophysics Data System (ADS)

Bhattacharya, Somnath; Mukherjee, Pradip; Roy, Amit Singha; Saha, Anirban

2018-03-01

We consider a scalar field which is generally non-minimally coupled to gravity and has a characteristic cubic Galilean-like term and a generic self-interaction, as a candidate of a Dark Energy model. The system is dynamically analyzed and novel fixed points with perturbative stability are demonstrated. Evolution of the system is numerically studied near a novel fixed point which owes its existence to the Galileon character of the model. It turns out that demanding the stability of this novel fixed point puts a strong restriction on the allowed non-minimal coupling and the choice of the self-interaction. The evolution of the equation of state parameter is studied, which shows that our model predicts an accelerated universe throughout and the phantom limit is only approached closely but never crossed. Our result thus extends the findings of Coley, Dynamical systems and cosmology. Kluwer Academic Publishers, Boston (2013) for more general NMC than linear and quadratic couplings.

Evolution of axis ratios from phase space dynamics of triaxial collapse

NASA Astrophysics Data System (ADS)

Nadkarni-Ghosh, Sharvari; Arya, Bhaskar

2018-04-01

We investigate the evolution of axis ratios of triaxial haloes using the phase space description of triaxial collapse. In this formulation, the evolution of the triaxial ellipsoid is described in terms of the dynamics of eigenvalues of three important tensors: the Hessian of the gravitational potential, the tensor of velocity derivatives, and the deformation tensor. The eigenvalues of the deformation tensor are directly related to the parameters that describe triaxiality, namely, the minor-to-major and intermediate-to-major axes ratios (s and q) and the triaxiality parameter T. Using the phase space equations, we evolve the eigenvalues and examine the evolution of the probability distribution function (PDF) of the axes ratios as a function of mass scale and redshift for Gaussian initial conditions. We find that the ellipticity and prolateness increase with decreasing mass scale and decreasing redshift. These trends agree with previous analytic studies but differ from numerical simulations. However, the PDF of the scaled parameter {\\tilde{q}} = (q-s)/(1-s) follows a universal distribution over two decades in mass range and redshifts which is in qualitative agreement with the universality for conditional PDF reported in simulations. We further show using the phase space dynamics that, in fact, {\\tilde{q}} is a phase space invariant and is conserved individually for each halo. These results demonstrate that the phase space analysis is a useful tool that provides a different perspective on the evolution of perturbations and can be applied to more sophisticated models in the future.

Asymmetry in Time Evolution of Magnetization in Magnetic Nanostructures

DOE PAGES

Tóbik, Jaroslav; Cambel, Vladimir; Karapetrov, Goran

2015-07-22

Strong interest in nanomagnetism stems from the promise of high storage densities of information through control of ever smaller and smaller ensembles of spins. There is a broad consensus that the Landau-Lifshitz-Gilbert equation reliably describes the magnetization dynamics on classical phenomenological level. On the other hand, it is not so evident that the magnetization dynamics governed by this equation contains built-in asymmetry in the case of broad topology sets of symmetric total energy functional surfaces. The magnetization dynamics in such cases shows preference for one particular state from many energetically equivalent available minima. Here, we demonstrate this behavior on amore » simple one-spin model which can be treated analytically. Depending on the ferromagnet geometry and material parameters, this asymmetric behavior can be robust enough to survive even at high temperatures opening simplified venues for controlling magnetic states of nanodevices in practical applications. Using micromagnetic simulations we demonstrate the asymmetry in magnetization dynamics in a real system with reduced symmetry such as Pacman-like nanodot. Finally, exploiting the built-in asymmetry in the dynamics could lead to practical methods of preparing desired spin configurations on nanoscale. Introduction« less

Extinction rates in tumour public goods games.

PubMed

Gerlee, Philip; Altrock, Philipp M

2017-09-01

Cancer evolution and progression are shaped by cellular interactions and Darwinian selection. Evolutionary game theory incorporates both of these principles, and has been proposed as a framework to understand tumour cell population dynamics. A cornerstone of evolutionary dynamics is the replicator equation, which describes changes in the relative abundance of different cell types, and is able to predict evolutionary equilibria. Typically, the replicator equation focuses on differences in relative fitness. We here show that this framework might not be sufficient under all circumstances, as it neglects important aspects of population growth. Standard replicator dynamics might miss critical differences in the time it takes to reach an equilibrium, as this time also depends on cellular turnover in growing but bounded populations. As the system reaches a stable manifold, the time to reach equilibrium depends on cellular death and birth rates. These rates shape the time scales, in particular, in coevolutionary dynamics of growth factor producers and free-riders. Replicator dynamics might be an appropriate framework only when birth and death rates are of similar magnitude. Otherwise, population growth effects cannot be neglected when predicting the time to reach an equilibrium, and cell-type-specific rates have to be accounted for explicitly. © 2017 The Authors.

Hierarchical Multiscale Modeling of Macromolecules and their Assemblies

PubMed Central

Ortoleva, P.; Singharoy, A.; Pankavich, S.

2013-01-01

Soft materials (e.g., enveloped viruses, liposomes, membranes and supercooled liquids) simultaneously deform or display collective behaviors, while undergoing atomic scale vibrations and collisions. While the multiple space-time character of such systems often makes traditional molecular dynamics simulation impractical, a multiscale approach has been presented that allows for long-time simulation with atomic detail based on the co-evolution of slowly-varying order parameters (OPs) with the quasi-equilibrium probability density of atomic configurations. However, this approach breaks down when the structural change is extreme, or when nearest-neighbor connectivity of atoms is not maintained. In the current study, a self-consistent approach is presented wherein OPs and a reference structure co-evolve slowly to yield long-time simulation for dynamical soft-matter phenomena such as structural transitions and self-assembly. The development begins with the Liouville equation for N classical atoms and an ansatz on the form of the associated N-atom probability density. Multiscale techniques are used to derive Langevin equations for the coupled OP-configurational dynamics. The net result is a set of equations for the coupled stochastic dynamics of the OPs and centers of mass of the subsystems that constitute a soft material body. The theory is based on an all-atom methodology and an interatomic force field, and therefore enables calibration-free simulations of soft matter, such as macromolecular assemblies. PMID:23671457

Stochastic Averaging Principle for Spatial Birth-and-Death Evolutions in the Continuum

NASA Astrophysics Data System (ADS)

Friesen, Martin; Kondratiev, Yuri

2018-06-01

We study a spatial birth-and-death process on the phase space of locally finite configurations Γ^+ × Γ^- over R}^d. Dynamics is described by an non-equilibrium evolution of states obtained from the Fokker-Planck equation and associated with the Markov operator L^+(γ ^-) + 1/ɛ L^-, ɛ > 0. Here L^- describes the environment process on Γ^- and L^+(γ ^-) describes the system process on Γ^+, where γ ^- indicates that the corresponding birth-and-death rates depend on another locally finite configuration γ ^- \\in Γ^-. We prove that, for a certain class of birth-and-death rates, the corresponding Fokker-Planck equation is well-posed, i.e. there exists a unique evolution of states μ _t^{ɛ } on Γ^+ × Γ^-. Moreover, we give a sufficient condition such that the environment is ergodic with exponential rate. Let μ _{inv} be the invariant measure for the environment process on Γ^-. In the main part of this work we establish the stochastic averaging principle, i.e. we prove that the marginal of μ _t^{ɛ } onto Γ^+ converges weakly to an evolution of states on {Γ}^+ associated with the averaged Markov birth-and-death operator {\\overline{L}} = \\int _{Γ}^- L^+(γ ^-)d μ _{inv}(γ ^-).

Stochastic Averaging Principle for Spatial Birth-and-Death Evolutions in the Continuum

NASA Astrophysics Data System (ADS)

Friesen, Martin; Kondratiev, Yuri

2018-04-01

We study a spatial birth-and-death process on the phase space of locally finite configurations Γ^+ × Γ^- over R^d . Dynamics is described by an non-equilibrium evolution of states obtained from the Fokker-Planck equation and associated with the Markov operator L^+(γ ^-) + 1/ɛ L^- , ɛ > 0 . Here L^- describes the environment process on Γ^- and L^+(γ ^-) describes the system process on Γ^+ , where γ ^- indicates that the corresponding birth-and-death rates depend on another locally finite configuration γ ^- \\in Γ^- . We prove that, for a certain class of birth-and-death rates, the corresponding Fokker-Planck equation is well-posed, i.e. there exists a unique evolution of states μ _t^{ɛ } on Γ^+ × Γ^- . Moreover, we give a sufficient condition such that the environment is ergodic with exponential rate. Let μ _{inv} be the invariant measure for the environment process on Γ^- . In the main part of this work we establish the stochastic averaging principle, i.e. we prove that the marginal of μ _t^{ɛ } onto Γ^+ converges weakly to an evolution of states on Γ^+ associated with the averaged Markov birth-and-death operator \\overline{L} = \\int _{Γ}^-}L^+(γ ^-)d μ _{inv}(γ ^-).

Circularly polarized few-cycle optical rogue waves: rotating reduced Maxwell-Bloch equations.

PubMed

Xu, Shuwei; Porsezian, K; He, Jingsong; Cheng, Yi

2013-12-01

The rotating reduced Maxwell-Bloch (RMB) equations, which describe the propagation of few-cycle optical pulses in a transparent media with two isotropic polarized electronic field components, are derived from a system of complete Maxwell-Bloch equations without using the slowly varying envelope approximations. Two hierarchies of the obtained rational solutions, including rogue waves, which are also called few-cycle optical rogue waves, of the rotating RMB equations are constructed explicitly through degenerate Darboux transformation. In addition to the above, the dynamical evolution of the first-, second-, and third-order few-cycle optical rogue waves are constructed with different patterns. For an electric field E in the three lower-order rogue waves, we find that rogue waves correspond to localized large amplitude oscillations of the polarized electric fields. Further a complementary relationship of two electric field components of rogue waves is discussed in terms of analytical formulas as well as numerical figures.

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

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

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

Pacemakers in large arrays of oscillators with nonlocal coupling

NASA Astrophysics Data System (ADS)

Jaramillo, Gabriela; Scheel, Arnd

2016-02-01

We model pacemaker effects of an algebraically localized heterogeneity in a 1 dimensional array of oscillators with nonlocal coupling. We assume the oscillators obey simple phase dynamics and that the array is large enough so that it can be approximated by a continuous nonlocal evolution equation. We concentrate on the case of heterogeneities with positive average and show that steady solutions to the nonlocal problem exist. In particular, we show that these heterogeneities act as a wave source. This effect is not possible in 3 dimensional systems, such as the complex Ginzburg-Landau equation, where the wavenumber of weak sources decays at infinity. To obtain our results we use a series of isomorphisms to relate the nonlocal problem to the viscous eikonal equation. We then use Fredholm properties of the Laplace operator in Kondratiev spaces to obtain solutions to the eikonal equation, and by extension to the nonlocal problem.

Asymptotic theory of time-varying social networks with heterogeneous activity and tie allocation.

PubMed

Ubaldi, Enrico; Perra, Nicola; Karsai, Márton; Vezzani, Alessandro; Burioni, Raffaella; Vespignani, Alessandro

2016-10-24

The dynamic of social networks is driven by the interplay between diverse mechanisms that still challenge our theoretical and modelling efforts. Amongst them, two are known to play a central role in shaping the networks evolution, namely the heterogeneous propensity of individuals to i) be socially active and ii) establish a new social relationships with their alters. Here, we empirically characterise these two mechanisms in seven real networks describing temporal human interactions in three different settings: scientific collaborations, Twitter mentions, and mobile phone calls. We find that the individuals' social activity and their strategy in choosing ties where to allocate their social interactions can be quantitatively described and encoded in a simple stochastic network modelling framework. The Master Equation of the model can be solved in the asymptotic limit. The analytical solutions provide an explicit description of both the system dynamic and the dynamical scaling laws characterising crucial aspects about the evolution of the networks. The analytical predictions match with accuracy the empirical observations, thus validating the theoretical approach. Our results provide a rigorous dynamical system framework that can be extended to include other processes shaping social dynamics and to generate data driven predictions for the asymptotic behaviour of social networks.

Self-consistent analysis of radiation and relativistic electron beam dynamics in a helical wiggler using Lienard-Wiechert fields

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

Tecimer, M.; Elias, L.R.

1995-12-31

Lienard-Wiechert (LW) fields, which are exact solutions of the Wave Equation for a point charge in free space, are employed to formulate a self-consistent treatment of the electron beam dynamics and the evolution of the generated radiation in long undulators. In a relativistic electron beam the internal forces leading to the interaction of the electrons with each other can be computed by means of retarded LW fields. The resulting electron beam dynamics enables us to obtain three dimensional radiation fields starting from an initial incoherent spontaneous emission, without introducing a seed wave at start-up. Based on the formalism employed here,more » both the evolution of the multi-bucket electron phase space dynamics in the beam body as well as edges and the relative slippage of the radiation with respect to the electrons in the considered short bunch are naturally embedded into the simulation model. In this paper, we present electromagnetic radiation studies, including multi-bucket electron phase dynamics and angular distribution of radiation in the time and frequency domain produced by a relativistic short electron beam bunch interacting with a circularly polarized magnetic undulator.« less

Asymptotic theory of time-varying social networks with heterogeneous activity and tie allocation

NASA Astrophysics Data System (ADS)

Ubaldi, Enrico; Perra, Nicola; Karsai, Márton; Vezzani, Alessandro; Burioni, Raffaella; Vespignani, Alessandro

2016-10-01

The dynamic of social networks is driven by the interplay between diverse mechanisms that still challenge our theoretical and modelling efforts. Amongst them, two are known to play a central role in shaping the networks evolution, namely the heterogeneous propensity of individuals to i) be socially active and ii) establish a new social relationships with their alters. Here, we empirically characterise these two mechanisms in seven real networks describing temporal human interactions in three different settings: scientific collaborations, Twitter mentions, and mobile phone calls. We find that the individuals’ social activity and their strategy in choosing ties where to allocate their social interactions can be quantitatively described and encoded in a simple stochastic network modelling framework. The Master Equation of the model can be solved in the asymptotic limit. The analytical solutions provide an explicit description of both the system dynamic and the dynamical scaling laws characterising crucial aspects about the evolution of the networks. The analytical predictions match with accuracy the empirical observations, thus validating the theoretical approach. Our results provide a rigorous dynamical system framework that can be extended to include other processes shaping social dynamics and to generate data driven predictions for the asymptotic behaviour of social networks.

Dynamics of quantum correlation and coherence for two atoms coupled with a bath of fluctuating massless scalar field

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

Huang, Zhiming, E-mail: 465609785@qq.com; Situ, Haozhen, E-mail: situhaozhen@gmail.com

In this article, the dynamics of quantum correlation and coherence for two atoms interacting with a bath of fluctuating massless scalar field in the Minkowski vacuum is investigated. We firstly derive the master equation that describes the system evolution with initial Bell-diagonal state. Then we discuss the system evolution for three cases of different initial states: non-zero correlation separable state, maximally entangled state and zero correlation state. For non-zero correlation initial separable state, quantum correlation and coherence can be protected from vacuum fluctuations during long time evolution when the separation between the two atoms is relatively small. For maximally entangledmore » initial state, quantum correlation and coherence overall decrease with evolution time. However, for the zero correlation initial state, quantum correlation and coherence are firstly generated and then drop with evolution time; when separation is sufficiently small, they can survive from vacuum fluctuations. For three cases, quantum correlation and coherence first undergo decline and then fluctuate to relatively stable values with the increasing distance between the two atoms. Specially, for the case of zero correlation initial state, quantum correlation and coherence occur periodically revival at fixed zero points and revival amplitude declines gradually with increasing separation of two atoms.« less

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

Umansky, M. V.; Ryutov, D. D.

Reduced MHD equations are used for studying toroidally symmetric plasma dynamics near the divertor null point. Numerical solution of these equations exhibits a plasma vortex localized at the null point with the time-evolution defined by interplay of the curvature drive, magnetic restoring force, and dissipation. Convective motion is easier to achieve for a second-order null (snowflake) divertor than for a regular x-point configuration, and the size of the convection zone in a snowflake configuration grows with plasma pressure at the null point. In conclusion, the trends in simulations are consistent with tokamak experiments which indicate the presence of enhanced transportmore » at the null point.« less

The polarized Debye sheath effect on Kadomtsev-Petviashvili electrostatic structures in strongly coupled dusty plasma

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

Shahmansouri, M.; Alinejad, H.

2015-04-15

We give a theoretical investigation on the dynamics of nonlinear electrostatic waves in a strongly coupled dusty plasma with strong electrostatic interaction between dust grains in the presence of the polarization force (i.e., the force due to the polarized Debye sheath). Adopting a reductive perturbation method, we derived a three-dimensional Kadomtsev-Petviashvili equation that describes the evolution of weakly nonlinear electrostatic localized waves. The energy integral equation is used to study the existence domains of the localized structures. The analysis provides the localized structure existence region, in terms of the effects of strong interaction between the dust particles and polarization force.

Remote monitoring of environmental particulate pollution - A problem in inversion of first-kind integral equations

NASA Technical Reports Server (NTRS)

Fymat, A. L.

1975-01-01

The determination of the microstructure, chemical nature, and dynamical evolution of scattering particulates in the atmosphere is considered. A description is given of indirect sampling techniques which can circumvent most of the difficulties associated with direct sampling techniques, taking into account methods based on scattering, extinction, and diffraction of an incident light beam. Approaches for reconstructing the particulate size distribution from the direct and the scattered radiation are discussed. A new method is proposed for determining the chemical composition of the particulates and attention is given to the relevance of methods of solution involving first kind Fredholm integral equations.

Why do Electrons with "Anomalous Energies" appear in High-Pressure Gas Discharges?

NASA Astrophysics Data System (ADS)

Kozyrev, Andrey; Kozhevnikov, Vasily; Semeniuk, Natalia

2018-01-01

Experimental studies connected with runaway electron beams generation convincingly shows the existence of electrons with energies above the maximum voltage applied to the discharge gap. Such electrons are also known as electrons with "anomalous energies". We explain the presence of runaway electrons having so-called "anomalous energies" according to physical kinetics principles, namely, we describe the total ensemble of electrons with the distribution function. Its evolution obeys Boltzmann kinetic equation. The dynamics of self-consistent electromagnetic field is taken into the account by adding complete Maxwell's equation set to the resulting system of equations. The electrodynamic mechanism of the interaction of electrons with a travelling-wave electric field is analyzed in details. It is responsible for the appearance of electrons with high energies in real discharges.

Boltzmann equations for a binary one-dimensional ideal gas.

PubMed

Boozer, A D

2011-09-01

We consider a time-reversal invariant dynamical model of a binary ideal gas of N molecules in one spatial dimension. By making time-asymmetric assumptions about the behavior of the gas, we derive Boltzmann and anti-Boltzmann equations that describe the evolution of the single-molecule velocity distribution functions for an ensemble of such systems. We show that for a special class of initial states of the ensemble one can obtain an exact expression for the N-molecule velocity distribution function, and we use this expression to rigorously prove that the time-asymmetric assumptions needed to derive the Boltzmann and anti-Boltzmann equations hold in the limit of large N. Our results clarify some subtle issues regarding the origin of the time asymmetry of Boltzmann's H theorem.

Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

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

Opanchuk, B.; Drummond, P. D.

2013-04-15

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved using conventional stochastic methods. The technique is valid for large mode occupation numbers. We give a detailed derivation of methods of functional Wigner representation appropriate for quantum fields. Our approach describes spatial evolution of spinor components and properly accounts for nonlinear losses. Such techniques are applicable to calculating the leading quantum corrections, including effects such asmore » quantum squeezing, entanglement, EPR correlations, and interactions with engineered nonlinear reservoirs. By using a consistent expansion in the inverse density, we are able to explain an inconsistency in the nonlinear loss equations found by earlier authors.« less

Two-phase vesicles: a study on evolutionary and stationary models.

PubMed

Sahebifard, MohammadMahdi; Shahidi, Alireza; Ziaei-Rad, Saeed

2017-05-01

In the current article, the dynamic evolution of two-phase vesicles is presented as an extension to a previous stationary model and based on an equilibrium of local forces. In the simplified model, ignoring the effects of membrane inertia, a dynamic equilibrium between the membrane bending potential and local fluid friction is considered in each phase. The equilibrium equations at the domain borders are completed by extended introduction of membrane section reactions. We show that in some cases, the results of stationary and evolutionary models are in agreement with each other and also with experimental observations, while in others the two models differ markedly. The value of our approach is that we can account for unresponsive points of uncertainty using our equations with the local velocity of the lipid membranes and calculating the intermediate states (shapes) in the consequent evolutionary, or response, path.

Bacterial Cheating Limits the Evolution of Antibiotic Resistance

NASA Astrophysics Data System (ADS)

Yurtsev, Eugene; Xiao Chao, Hui; Datta, Manoshi; Artemova, Tatiana; Gore, Jeff

2012-02-01

The emergence of antibiotic resistance in bacteria is a significant health concern. Bacteria can gain resistance to the antibiotic ampicillin by acquiring a plasmid carrying the gene beta-lactamase, which inactivates the antibiotic. This inactivation may represent a cooperative behavior, as the entire bacterial population benefits from removal of the antibiotic. The presence of a cooperative mechanism of resistance suggests that a cheater strain - which does not contribute to breaking down the antibiotic - may be able to take advantage of resistant cells. We find experimentally that a ``sensitive'' bacterial strain lacking the plasmid conferring resistance can invade a population of resistant bacteria, even in antibiotic concentrations that should kill the sensitive strain. We use a simple model in conjunction with difference equations to explain the observed population dynamics as a function of cell density and antibiotic concentration. Our experimental difference equations resemble the logistic map, raising the possibility of oscillations or even chaotic dynamics.

Dynamics in a Maximally Symmetric Universe

NASA Astrophysics Data System (ADS)

Bewketu, Asnakew

2016-03-01

Our present understanding of the evolution of the universe relies upon the Friedmann- Robertson- Walker cosmological models. This model is so successful that it is now being considered as the Standard Model of Cosmology. So in this work we derive the Fried- mann equations using the Friedmann-Robertson-Walker metric together with Einstein field equation and then we give a simple method to reduce Friedmann equations to a second order linear differential equation when it is supplemented with a time dependent equation of state. Furthermore, as illustrative examples, we solve this equation for some specific time dependent equation of states. And also by using the Friedmann equations with some time dependent equation of state we try to determine the cosmic scale factor(the rate at which the universe expands) and age of the Friedmann universe, for the matter dominated era, radiation dominated era and for both matter and radiation dominated era by considering different cases. We have finally discussed the observable quantities that can be evidences for the accelerated expansion of the Friedmann universe. I would like to acknowledge Addis Ababa University for its financial and material support to my work on the title mentioned above.

Non linear dynamics of flame cusps: from experiments to modeling

NASA Astrophysics Data System (ADS)

Almarcha, Christophe; Radisson, Basile; Al-Sarraf, Elias; Quinard, Joel; Villermaux, Emmanuel; Denet, Bruno; Joulin, Guy

2016-11-01

The propagation of premixed flames in a medium initially at rest exhibits the appearance and competition of elementary local singularities called cusps. We investigate this problem both experimentally and numerically. An analytical solution of the two-dimensional Michelson Sivashinsky equation is obtained as a composition of pole solutions, which is compared with experimental flames fronts propagating between glass plates separated by a thin gap width. We demonstrate that the front dynamics can be reproduced numerically with a good accuracy, from the linear stages of destabilization to its late time evolution, using this model-equation. In particular, the model accounts for the experimentally observed steady distribution of distances between cusps, which is well-described by a one-parameter Gamma distribution, reflecting the aggregation type of interaction between the cusps. A modification of the Michelson Sivashinsky equation taking into account gravity allows to reproduce some other special features of these fronts. Aix-Marseille Univ., IRPHE, UMR 7342 CNRS, Centrale Marseille, Technopole de Château Gombert, 49 rue F. Joliot Curie, 13384 Marseille Cedex 13, France.

Parametrically excited helicopter ground resonance dynamics with high blade asymmetries

NASA Astrophysics Data System (ADS)

Sanches, L.; Michon, G.; Berlioz, A.; Alazard, D.

2012-07-01

The present work is aimed at verifying the influence of high asymmetries in the variation of in-plane lead-lag stiffness of one blade on the ground resonance phenomenon in helicopters. The periodical equations of motions are analyzed by using Floquet's Theory (FM) and the boundaries of instabilities predicted. The stability chart obtained as a function of asymmetry parameters and rotor speed reveals a complex evolution of critical zones and the existence of bifurcation points at low rotor speed values. Additionally, it is known that when treated as parametric excitations; periodic terms may cause parametric resonances in dynamic systems, some of which can become unstable. Therefore, the helicopter is later considered as a parametrically excited system and the equations are treated analytically by applying the Method of Multiple Scales (MMS). A stability analysis is used to verify the existence of unstable parametric resonances with first and second-order sets of equations. The results are compared and validated with those obtained by Floquet's Theory. Moreover, an explanation is given for the presence of unstable motion at low rotor speeds due to parametric instabilities of the second order.

a Statistical Dynamic Approach to Structural Evolution of Complex Capital Market Systems

NASA Astrophysics Data System (ADS)

Shao, Xiao; Chai, Li H.

As an important part of modern financial systems, capital market has played a crucial role on diverse social resource allocations and economical exchanges. Beyond traditional models and/or theories based on neoclassical economics, considering capital markets as typical complex open systems, this paper attempts to develop a new approach to overcome some shortcomings of the available researches. By defining the generalized entropy of capital market systems, a theoretical model and nonlinear dynamic equation on the operations of capital market are proposed from statistical dynamic perspectives. The US security market from 1995 to 2001 is then simulated and analyzed as a typical case. Some instructive results are discussed and summarized.

Dynamics of bright-bright solitons in Bose-Einstein condensate with Raman-induced one-dimensional spin-orbit coupling

NASA Astrophysics Data System (ADS)

Wen, Lin; Zhang, Xiao-Fei; Hu, Ai-Yuan; Zhou, Jing; Yu, Peng; Xia, Lei; Sun, Qing; Ji, An-Chun

2018-03-01

We investigate the dynamics of bright-bright solitons in one-dimensional two-component Bose-Einstein condensates with Raman-induced spin-orbit coupling, via the variational approximation and the numerical simulation of Gross-Pitaevskii equations. For the uniform system without trapping potential, we obtain two population balanced stationary solitons. By performing the linear stability analysis, we find a Goldstone eigenmode and an oscillation eigenmode around these stationary solitons. Moreover, we derive a general dynamical solution to describe the center-of-mass motion and spin evolution of the solitons under the action of spin-orbit coupling. The effects of a harmonic trap have also been discussed.

Fisher equation for anisotropic diffusion: simulating South American human dispersals.

PubMed

Martino, Luis A; Osella, Ana; Dorso, Claudio; Lanata, José L

2007-09-01

The Fisher equation is commonly used to model population dynamics. This equation allows describing reaction-diffusion processes, considering both population growth and diffusion mechanism. Some results have been reported about modeling human dispersion, always assuming isotropic diffusion. Nevertheless, it is well-known that dispersion depends not only on the characteristics of the habitats where individuals are but also on the properties of the places where they intend to move, then isotropic approaches cannot adequately reproduce the evolution of the wave of advance of populations. Solutions to a Fisher equation are difficult to obtain for complex geometries, moreover, when anisotropy has to be considered and so few studies have been conducted in this direction. With this scope in mind, we present in this paper a solution for a Fisher equation, introducing anisotropy. We apply a finite difference method using the Crank-Nicholson approximation and analyze the results as a function of the characteristic parameters. Finally, this methodology is applied to model South American human dispersal.

H theorem for generalized entropic forms within a master-equation framework

NASA Astrophysics Data System (ADS)

Casas, Gabriela A.; Nobre, Fernando D.; Curado, Evaldo M. F.

2016-03-01

The H theorem is proven for generalized entropic forms, in the case of a discrete set of states. The associated probability distributions evolve in time according to a master equation, for which the corresponding transition rates depend on these entropic forms. An important equation describing the time evolution of the transition rates and probabilities in such a way as to drive the system towards an equilibrium state is found. In the particular case of Boltzmann-Gibbs entropy, it is shown that this equation is satisfied in the microcanonical ensemble only for symmetric probability transition rates, characterizing a single path to the equilibrium state. This equation fulfils the proof of the H theorem for generalized entropic forms, associated with systems characterized by complex dynamics, e.g., presenting nonsymmetric probability transition rates and more than one path towards the same equilibrium state. Some examples considering generalized entropies of the literature are discussed, showing that they should be applicable to a wide range of natural phenomena, mainly those within the realm of complex systems.

Dark solitons in laser radiation build-up dynamics.

PubMed

Woodward, R I; Kelleher, E J R

2016-03-01

We reveal the existence of slowly decaying dark solitons in the radiation build-up dynamics of bright pulses in all-normal dispersion mode-locked fiber lasers, numerically modeled in the framework of a generalized nonlinear Schrödinger equation. The evolution of noise perturbations to quasistationary dark solitons is examined, and the significance of background shape and soliton-soliton collisions on the eventual soliton decay is established. We demonstrate the role of a restoring force in extending soliton interactions in conservative systems to include the effects of dissipation, as encountered in laser cavities, and generalize our observations to other nonlinear systems.

Fractal attractors and singular invariant measures in two-sector growth models with random factor shares

NASA Astrophysics Data System (ADS)

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

2018-05-01

We analyze a multi-sector growth model subject to random shocks affecting the two sector-specific production functions twofold: the evolution of both productivity and factor shares is the result of such exogenous shocks. We determine the optimal dynamics via Euler-Lagrange equations, and show how these dynamics can be described in terms of an iterated function system with probability. We also provide conditions that imply the singularity of the invariant measure associated with the fractal attractor. Numerical examples show how specific parameter configurations might generate distorted copies of the Barnsley's fern attractor.

Non-uniform Erosion and Surface Evolution of Plasma-Facing Materials for Electric Propulsion

NASA Astrophysics Data System (ADS)

Matthes, Christopher Stanley Rutter

A study regarding the surface evolution of plasma-facing materials is presented. Experimental efforts were performed in the UCLA Pi Facility, designed to explore the physics of plasma-surface interactions. The influence of micro-architectured surfaces on the effects of plasma sputtering is compared with the response of planar samples. Ballistic deposition of sputtered atoms as a result of geometric re-trapping is observed. This provides a self-healing mechanism of micro-architectured surfaces during plasma exposure. This result is quantified using a QCM to demonstrate the evolution of surface features and the corresponding influence on the instantaneous sputtering yield. The sputtering yield of textured molybdenum samples exposed to 300 eV Ar plasma is found to be roughly 1 of the 2 corresponding value of flat samples, and increases with ion fluence. Mo samples exhibited a sputtering yield initially as low as 0.22+/-8%, converging to 0.4+/-8% at high fluence. Although the yield is dependent on the initial surface structure, it is shown to be transient, reaching a steady-state value that is independent of initial surface conditions. A continuum model of surface evolution resulting from sputtering, deposition and surface diffusion is also derived to resemble the damped Kuramoto-Sivashinsky (KS) equation of non-linear dynamics. Linear stability analysis of the evolution equation provides an estimate of the selected wavelength, and its dependence on the ion energy and angle of incidence. The analytical results are confirmed by numerical simulations of the equation with a Fast Fourier Transform method. It is shown that for an initially flat surface, small perturbations lead to the evolution of a selected surface pattern that has nano- scale wavelength. When the surface is initially patterned by other means, the final resulting pattern is a competition between the "templated" pattern and the "self-organized" structure. Potential future routes of research are also discussed, corresponding to a design analysis of the current experimental study.

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.

On the Use of a Standard Spreadsheet to Model Physical Systems in School Teaching

ERIC Educational Resources Information Center

Quale, Andreas

2012-01-01

In the teaching of physics at upper secondary school level (K10-K12), the students are generally taught to solve problems analytically, i.e. using the dynamics describing a system (typically in the form of differential equations) to compute its evolution in time, e.g. the motion of a body along a straight line or in a plane. This reduces the scope…

Periodicity in cell dynamics in some mathematical models for the treatment of leukemia

NASA Astrophysics Data System (ADS)

Halanay, A.

2012-11-01

A model for the evolution of short-term hematopoietic stem cells and of leukocytes in leucemia under periodic treatment is introduced. It consists of a system of periodic delay differential equations and takes into consideration the asymmetric division. A guiding function is used, together with a theorem of Krasnoselskii, to prove the existence of a strictly positive periodic solution and its stability is investigated.

Numerical investigation on the batch characteristics of liquid encapsulated vertical Bridgman crystal growth

NASA Astrophysics Data System (ADS)

Lan, C. W.; Ting, C. C.

1995-04-01

Since the liquid encapsulated vertical Bridgman (LEVB) crystal growth is a batch process, it is time dependent in nature. A numerical simulation is conducted to study the unsteady features of the process, including the dynamic evolution of heat flow, growth rate, and interface morphology during crystal growth. The numerical model, which is governed by time-dependent equations for momentum and energy transport, and the conditions for evolution of melt/crystal and melt/encapsulant interfaces, is approximated by a body-fitted coordinate finite-volume method. The resulting differential/algebraic equations are then solved by the ILU (0) preconditioned DASPK code. Sample calculations are mainly conducted for GaAs. Dynamic effects of some process parameters, such as the growth speed, the ambient temperature profile, and ampoule design, are illustrated through calculated results. Due to the heat of fusion release and time-dependent end effects, in some cases a near steady-state operation is not possible. The control of growth front by modifying the ambient temperature profile is also demonstrated. Calculations are also performed for a 4.8 cm diameter InP crystal. The calculated melt/seed interface shape is compared with the measured one from Matsumoto et al. [J. Crystal Growth 132 (1993) 348] and they are in good agreement.

Nonlinear waves in solids with slow dynamics: an internal-variable model

PubMed Central

Berjamin, H.; Favrie, N.; Chiavassa, G.

2017-01-01

In heterogeneous solids such as rocks and concrete, the speed of sound diminishes with the strain amplitude of a dynamic loading (softening). This decrease, known as ‘slow dynamics’, occurs at time scales larger than the period of the forcing. Also, hysteresis is observed in the steady-state response. The phenomenological model by Vakhnenko et al. (2004 Phys. Rev. E 70, 015602. (doi:10.1103/PhysRevE.70.015602)) is based on a variable that describes the softening of the material. However, this model is one dimensional and it is not thermodynamically admissible. In the present article, a three-dimensional model is derived in the framework of the finite-strain theory. An internal variable that describes the softening of the material is introduced, as well as an expression of the specific internal energy. A mechanical constitutive law is deduced from the Clausius–Duhem inequality. Moreover, a family of evolution equations for the internal variable is proposed. Here, an evolution equation with one relaxation time is chosen. By construction, this new model of the continuum is thermodynamically admissible and dissipative (inelastic). In the case of small uniaxial deformations, it is shown analytically that the model reproduces qualitatively the main features of real experiments. PMID:28588408

Forging property, processing map, and mesoscale microstructural evolution modeling of a Ti-17 alloy with a lamellar (α+β) starting microstructure

NASA Astrophysics Data System (ADS)

Matsumoto, Hiroaki; Naito, Daiki; Miyoshi, Kento; Yamanaka, Kenta; Chiba, Akihiko; Yamabe-Mitarai, Yoko

2017-12-01

This work identifies microstructural conversion mechanisms during hot deformation (at temperatures ranging from 750 °C to 1050 °C and strain rates ranging from 10-3 s-1 to 1 s-1) of a Ti-5Al-2Sn-2Zr-4Mo-4Cr (Ti-17) alloy with a lamellar starting microstructure and establishes constitutive formulae for predicting the microstructural evolution using finite-element analysis. In the α phase, lamellae kinking is the dominant mode in the higher strain rate region and dynamic globularization frequently occurs at higher temperatures. In the β phase, continuous dynamic recrystallization is the dominant mode below the transition temperature, Tβ (880 890 °C). Dynamic recovery tends to be more active at conditions of lower strain rates and higher temperatures. At temperatures above Tβ, continuous dynamic recrystallization of the β phase frequently occurs, especially in the lower strain rate region. A set of constitutive equations modeling the microstructural evolution and processing map characteristic are established by optimizing the experimental data and were later implemented in the DEFORM-3D software package. There is a satisfactory agreement between the experimental and simulated results, indicating that the established series of constitutive models can be used to reliably predict the properties of a Ti-17 alloy after forging in the (α+β) region.

Forging property, processing map, and mesoscale microstructural evolution modeling of a Ti-17 alloy with a lamellar (α+β) starting microstructure

PubMed Central

Matsumoto, Hiroaki; Naito, Daiki; Miyoshi, Kento; Yamanaka, Kenta; Chiba, Akihiko; Yamabe-Mitarai, Yoko

2017-01-01

Abstract This work identifies microstructural conversion mechanisms during hot deformation (at temperatures ranging from 750 °C to 1050 °C and strain rates ranging from 10−3 s−1 to 1 s−1) of a Ti-5Al-2Sn-2Zr-4Mo-4Cr (Ti-17) alloy with a lamellar starting microstructure and establishes constitutive formulae for predicting the microstructural evolution using finite-element analysis. In the α phase, lamellae kinking is the dominant mode in the higher strain rate region and dynamic globularization frequently occurs at higher temperatures. In the β phase, continuous dynamic recrystallization is the dominant mode below the transition temperature, T β (880~890 °C). Dynamic recovery tends to be more active at conditions of lower strain rates and higher temperatures. At temperatures above T β, continuous dynamic recrystallization of the β phase frequently occurs, especially in the lower strain rate region. A set of constitutive equations modeling the microstructural evolution and processing map characteristic are established by optimizing the experimental data and were later implemented in the DEFORM-3D software package. There is a satisfactory agreement between the experimental and simulated results, indicating that the established series of constitutive models can be used to reliably predict the properties of a Ti-17 alloy after forging in the (α+β) region. PMID:29152021

Forging property, processing map, and mesoscale microstructural evolution modeling of a Ti-17 alloy with a lamellar (α+β) starting microstructure.

PubMed

Matsumoto, Hiroaki; Naito, Daiki; Miyoshi, Kento; Yamanaka, Kenta; Chiba, Akihiko; Yamabe-Mitarai, Yoko

2017-01-01

This work identifies microstructural conversion mechanisms during hot deformation (at temperatures ranging from 750 °C to 1050 °C and strain rates ranging from 10 -3  s -1 to 1 s -1 ) of a Ti-5Al-2Sn-2Zr-4Mo-4Cr (Ti-17) alloy with a lamellar starting microstructure and establishes constitutive formulae for predicting the microstructural evolution using finite-element analysis. In the α phase, lamellae kinking is the dominant mode in the higher strain rate region and dynamic globularization frequently occurs at higher temperatures. In the β phase, continuous dynamic recrystallization is the dominant mode below the transition temperature, T β (880~890 °C). Dynamic recovery tends to be more active at conditions of lower strain rates and higher temperatures. At temperatures above T β , continuous dynamic recrystallization of the β phase frequently occurs, especially in the lower strain rate region. A set of constitutive equations modeling the microstructural evolution and processing map characteristic are established by optimizing the experimental data and were later implemented in the DEFORM-3D software package. There is a satisfactory agreement between the experimental and simulated results, indicating that the established series of constitutive models can be used to reliably predict the properties of a Ti-17 alloy after forging in the (α+ β ) region.

Glassy dynamics of landscape evolution.

PubMed

Ferdowsi, Behrooz; Ortiz, Carlos P; Jerolmack, Douglas J

2018-05-08

Soil creeps imperceptibly downhill, but also fails catastrophically to create landslides. Despite the importance of these processes as hazards and in sculpting landscapes, there is no agreed-upon model that captures the full range of behavior. Here we examine the granular origins of hillslope soil transport by discrete element method simulations and reanalysis of measurements in natural landscapes. We find creep for slopes below a critical gradient, where average particle velocity (sediment flux) increases exponentially with friction coefficient (gradient). At critical gradient there is a continuous transition to a dense-granular flow rheology. Slow earthflows and landslides thus exhibit glassy dynamics characteristic of a wide range of disordered materials; they are described by a two-phase flux equation that emerges from grain-scale friction alone. This glassy model reproduces topographic profiles of natural hillslopes, showing its promise for predicting hillslope evolution over geologic timescales. Copyright © 2018 the Author(s). Published by PNAS.

Collective effects and dynamics of non-adiabatic flame balls

NASA Astrophysics Data System (ADS)

D'Angelo, Yves; Joulin, Guy

2001-03-01

The dynamics of a homogeneous, polydisperse collection of non-adiabatic flame balls (FBs) is investigated by analytical/numerical means. A strongly temperature-dependent Arrhenius reaction rate is assumed, along with a light enough reactant characterized by a markedly less than unity Lewis number (Le). Combining activation-energy asymptotics with a mean-field type of treatment, the analysis yields a nonlinear integro-differential evolution equation (EE) for the FB population. The EE accounts for heat losses inside each FB and unsteadiness around it, as well as for its interactions with the entire FB population, namely mutual heating and faster (Le<1) consumption of the reactant pool. The initial FB number density and size distribution enter the EE explicitly. The latter is studied analytically at early times, then for small total FB number densities; it is subsequently solved numerically, yielding the whole population evolution and its lifetime. Generalizations and open questions relating to `spotty' turbulent combustion are finally evoked.

Predictive modeling of multicellular structure formation by using Cellular Particle Dynamics simulations

NASA Astrophysics Data System (ADS)

McCune, Matthew; Shafiee, Ashkan; Forgacs, Gabor; Kosztin, Ioan

2014-03-01

Cellular Particle Dynamics (CPD) is an effective computational method for describing and predicting the time evolution of biomechanical relaxation processes of multicellular systems. A typical example is the fusion of spheroidal bioink particles during post bioprinting structure formation. In CPD cells are modeled as an ensemble of cellular particles (CPs) that interact via short-range contact interactions, characterized by an attractive (adhesive interaction) and a repulsive (excluded volume interaction) component. The time evolution of the spatial conformation of the multicellular system is determined by following the trajectories of all CPs through integration of their equations of motion. CPD was successfully applied to describe and predict the fusion of 3D tissue construct involving identical spherical aggregates. Here, we demonstrate that CPD can also predict tissue formation involving uneven spherical aggregates whose volumes decrease during the fusion process. Work supported by NSF [PHY-0957914]. Computer time provided by the University of Missouri Bioinformatics Consortium.

Wave kinetics of random fibre lasers

PubMed Central

Churkin, D V.; Kolokolov, I V.; Podivilov, E V.; Vatnik, I D.; Nikulin, M A.; Vergeles, S S.; Terekhov, I S.; Lebedev, V V.; Falkovich, G.; Babin, S A.; Turitsyn, S K.

2015-01-01

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-uniform double-scale dynamics with strong periodic changes of the energy spectrum and slow evolution from cycle to cycle to a statistically steady state. Taking a practically important example—random fibre laser—we show that a model describing such a system is close to integrable non-linear Schrödinger equation and needs a new formalism of wave kinetics, developed here. We derive a non-linear kinetic theory of the laser spectrum, generalizing the seminal linear model of Schawlow and Townes. Experimental results agree with our theory. The work has implications for describing kinetics of cyclical systems beyond photonics. PMID:25645177

Lozenge Tiling Dynamics and Convergence to the Hydrodynamic Equation

NASA Astrophysics Data System (ADS)

Laslier, Benoît; Toninelli, Fabio Lucio

2018-03-01

We study a reversible continuous-time Markov dynamics of a discrete (2 + 1)-dimensional interface. This can be alternatively viewed as a dynamics of lozenge tilings of the {L× L} torus, or as a conservative dynamics for a two-dimensional system of interlaced particles. The particle interlacement constraints imply that the equilibrium measures are far from being product Bernoulli: particle correlations decay like the inverse distance squared and interface height fluctuations behave on large scales like a massless Gaussian field. We consider a particular choice of the transition rates, originally proposed in Luby et al. (SIAM J Comput 31:167-192, 2001): in terms of interlaced particles, a particle jump of length n that preserves the interlacement constraints has rate 1/(2 n). This dynamics presents special features: the average mutual volume between two interface configurations decreases with time (Luby et al. 2001) and a certain one-dimensional projection of the dynamics is described by the heat equation (Wilson in Ann Appl Probab 14:274-325, 2004). In this work we prove a hydrodynamic limit: after a diffusive rescaling of time and space, the height function evolution tends as L\\to∞ to the solution of a non-linear parabolic PDE. The initial profile is assumed to be C 2 differentiable and to contain no "frozen region". The explicit form of the PDE was recently conjectured (Laslier and Toninelli in Ann Henri Poincaré Theor Math Phys 18:2007-2043, 2017) on the basis of local equilibrium considerations. In contrast with the hydrodynamic equation for the Langevin dynamics of the Ginzburg-Landau model (Funaki and Spohn in Commun Math Phys 85:1-36, 1997; Nishikawa in Commun Math Phys 127:205-227, 2003), here the mobility coefficient turns out to be a non-trivial function of the interface slope.

Progress in the development of PDF turbulence models for combustion

NASA Technical Reports Server (NTRS)

Hsu, Andrew T.

1991-01-01

A combined Monte Carlo-computational fluid dynamic (CFD) algorithm was developed recently at Lewis Research Center (LeRC) for turbulent reacting flows. In this algorithm, conventional CFD schemes are employed to obtain the velocity field and other velocity related turbulent quantities, and a Monte Carlo scheme is used to solve the evolution equation for the probability density function (pdf) of species mass fraction and temperature. In combustion computations, the predictions of chemical reaction rates (the source terms in the species conservation equation) are poor if conventional turbulence modles are used. The main difficulty lies in the fact that the reaction rate is highly nonlinear, and the use of averaged temperature produces excessively large errors. Moment closure models for the source terms have attained only limited success. The probability density function (pdf) method seems to be the only alternative at the present time that uses local instantaneous values of the temperature, density, etc., in predicting chemical reaction rates, and thus may be the only viable approach for more accurate turbulent combustion calculations. Assumed pdf's are useful in simple problems; however, for more general combustion problems, the solution of an evolution equation for the pdf is necessary.

Early universe with modified scalar-tensor theory of gravity

NASA Astrophysics Data System (ADS)

Mandal, Ranajit; Sarkar, Chandramouli; Sanyal, Abhik Kumar

2018-05-01

Scalar-tensor theory of gravity with non-minimal coupling is a fairly good candidate for dark energy, required to explain late-time cosmic evolution. Here we study the very early stage of evolution of the universe with a modified version of the theory, which includes scalar curvature squared term. One of the key aspects of the present study is that, the quantum dynamics of the action under consideration ends up generically with de-Sitter expansion under semiclassical approximation, rather than power-law. This justifies the analysis of inflationary regime with de-Sitter expansion. The other key aspect is that, while studying gravitational perturbation, the perturbed generalized scalar field equation obtained from the perturbed action, when matched with the perturbed form of the background scalar field equation, relates the coupling parameter and the potential exactly in the same manner as the solution of classical field equations does, assuming de-Sitter expansion. The study also reveals that the quantum theory is well behaved, inflationary parameters fall well within the observational limit and quantum perturbation analysis shows that the power-spectrum does not deviate considerably from the standard one obtained from minimally coupled theory.

Modelling language evolution: Examples and predictions

NASA Astrophysics Data System (ADS)

Gong, Tao; Shuai, Lan; Zhang, Menghan

2014-06-01

We survey recent computer modelling research of language evolution, focusing on a rule-based model simulating the lexicon-syntax coevolution and an equation-based model quantifying the language competition dynamics. We discuss four predictions of these models: (a) correlation between domain-general abilities (e.g. sequential learning) and language-specific mechanisms (e.g. word order processing); (b) coevolution of language and relevant competences (e.g. joint attention); (c) effects of cultural transmission and social structure on linguistic understandability; and (d) commonalities between linguistic, biological, and physical phenomena. All these contribute significantly to our understanding of the evolutions of language structures, individual learning mechanisms, and relevant biological and socio-cultural factors. We conclude the survey by highlighting three future directions of modelling studies of language evolution: (a) adopting experimental approaches for model evaluation; (b) consolidating empirical foundations of models; and (c) multi-disciplinary collaboration among modelling, linguistics, and other relevant disciplines.

Coronal evolution due to shear motion

NASA Technical Reports Server (NTRS)

Steinolfson, R. S.

1991-01-01

Numerical solutions of the compressible MHD equations are used here to simulate the evolution of an initially force-free magnetic field in a static corona as a result of slow photospheric motion of the magnetic field footpoints. Simulations have been completed for values of plasma beta from 0.1 to 0.5, maximum shear velocities from 0.5 to 10.3 km/s, and with various amounts of resistive and viscous dissipation. In all cases the evolution proceeds in two qualitatively different stages. In the earlier stage, the field evolves gradually with the field lines, expanding outward at a velocity not unlike the shear velocity. Then, the field begins to expand much more rapidly until it reaches velocities exceeding a characteristic Alfven velocity. Inclusion of the thermodynamics, gravity, and compressibility is shown to have only a quantitative effect on the onset of the eruptive phase, illustrating that the primary interactions are between the dynamics and the magnetic field evolution.

Electron quantum dynamics in atom-ion interaction

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

Sabzyan, H., E-mail: sabzyan@sci.ui.ac.ir; Jenabi, M. J.

2016-04-07

Electron transfer (ET) process and its dependence on the system parameters are investigated by solving two-dimensional time-dependent Schrödinger equation numerically using split operator technique. Evolution of the electron wavepacket occurs from the one-electron species hydrogen atom to another bare nucleus of charge Z > 1. This evolution is quantified by partitioning the simulation box and defining regional densities belonging to the two nuclei of the system. It is found that the functional form of the time-variations of these regional densities and the extent of ET process depend strongly on the inter-nuclear distance and relative values of the nuclear charges, whichmore » define the potential energy surface governing the electron wavepacket evolution. Also, the initial electronic state of the single-electron atom has critical effect on this evolution and its consequent (partial) electron transfer depending on its spreading extent and orientation with respect to the inter-nuclear axis.« less

Anomalous diffusion and long-range correlations in the score evolution of the game of cricket

NASA Astrophysics Data System (ADS)

Ribeiro, Haroldo V.; Mukherjee, Satyam; Zeng, Xiao Han T.

2012-08-01

We investigate the time evolution of the scores of the second most popular sport in the world: the game of cricket. By analyzing, event by event, the scores of more than 2000 matches, we point out that the score dynamics is an anomalous diffusive process. Our analysis reveals that the variance of the process is described by a power-law dependence with a superdiffusive exponent, that the scores are statistically self-similar following a universal Gaussian distribution, and that there are long-range correlations in the score evolution. We employ a generalized Langevin equation with a power-law correlated noise that describes all the empirical findings very well. These observations suggest that competition among agents may be a mechanism leading to anomalous diffusion and long-range correlation.

Single-bubble sonoluminescence in sulfuric acid and water: bubble dynamics, stability, and continuous spectra.

PubMed

Puente, Gabriela F; García-Martínez, Pablo; Bonetto, Fabián J

2007-01-01

We present theoretical calculations of an argon bubble in a liquid solution of 85%wt sulfuric acid and 15%wt water in single-bubble sonoluminescence. We used a model without free parameters to be adjusted. We predict from first principles the region in parameter space for stable bubble evolution, the temporal evolution of the bubble radius, the maximum temperature, pressures, and the light spectra due to thermal emissions. We also used a partial differential equation based model (hydrocode) to compute the temperature and pressure evolutions at the center of the bubble during maximum compression. We found the behavior of this liquid mixture to be very different from water in several aspects. Most of the models in sonoluminescence were compared with water experimental results.

Target-in-the-loop beam control: basic considerations for analysis and wave-front sensing

NASA Astrophysics Data System (ADS)

Vorontsov, Mikhail A.; Kolosov, Valeriy

2005-01-01

Target-in-the-loop (TIL) wave propagation geometry represents perhaps the most challenging case for adaptive optics applications that are related to maximization of irradiance power density on extended remotely located surfaces in the presence of dynamically changing refractive-index inhomogeneities in the propagation medium. We introduce a TIL propagation model that uses a combination of the parabolic equation describing coherent outgoing-wave propagation, and the equation describing evolution of the mutual correlation function (MCF) for the backscattered wave (return wave). The resulting evolution equation for the MCF is further simplified by use of the smooth-refractive-index approximation. This approximation permits derivation of the transport equation for the return-wave brightness function, analyzed here by the method of characteristics (brightness function trajectories). The equations for the brightness function trajectories (ray equations) can be efficiently integrated numerically. We also consider wave-front sensors that perform sensing of speckle-averaged characteristics of the wave-front phase (TIL sensors). Analysis of the wave-front phase reconstructed from Shack-Hartmann TIL sensor measurements shows that an extended target introduces a phase modulation (target-induced phase) that cannot be easily separated from the atmospheric-turbulence-related phase aberrations. We also show that wave-front sensing results depend on the extended target shape, surface roughness, and outgoing-beam intensity distribution on the target surface. For targets with smooth surfaces and nonflat shapes, the target-induced phase can contain aberrations. The presence of target-induced aberrations in the conjugated phase may result in a deterioration of adaptive system performance.

Target-in-the-loop beam control: basic considerations for analysis and wave-front sensing.

PubMed

Vorontsov, Mikhail A; Kolosov, Valeriy

2005-01-01

Target-in-the-loop (TIL) wave propagation geometry represents perhaps the most challenging case for adaptive optics applications that are related to maximization of irradiance power density on extended remotely located surfaces in the presence of dynamically changing refractive-index inhomogeneities in the propagation medium. We introduce a TIL propagation model that uses a combination of the parabolic equation describing coherent outgoing-wave propagation, and the equation describing evolution of the mutual correlation function (MCF) for the backscattered wave (return wave). The resulting evolution equation for the MCF is further simplified by use of the smooth-refractive-index approximation. This approximation permits derivation of the transport equation for the return-wave brightness function, analyzed here by the method of characteristics (brightness function trajectories). The equations for the brightness function trajectories (ray equations) can be efficiently integrated numerically. We also consider wave-front sensors that perform sensing of speckle-averaged characteristics of the wave-front phase (TIL sensors). Analysis of the wave-front phase reconstructed from Shack-Hartmann TIL sensor measurements shows that an extended target introduces a phase modulation (target-induced phase) that cannot be easily separated from the atmospheric-turbulence-related phase aberrations. We also show that wave-front sensing results depend on the extended target shape, surface roughness, and outgoing-beam intensity distribution on the target surface. For targets with smooth surfaces and nonflat shapes, the target-induced phase can contain aberrations. The presence of target-induced aberrations in the conjugated phase may result in a deterioration of adaptive system performance.

Modeling of the flow behavior of SAE 8620H combing microstructure evolution in hot forming

NASA Astrophysics Data System (ADS)

Fu, Xiaobin; Wang, Baoyu; Tang, Xuefeng

2017-10-01

With the development of net-shape forming technology, hot forming process is widely applied to manufacturing gear parts, during which, materials suffer severe plastic distortion and microstructure changes continually. In this paper, to understand and model the flow behavior and microstructure evolution, SAE 8620H, a widely used gear steel, is selected as the object and the flow behavior and microstructure evolution are observed by an isothermal hot compression tests at 1273-1373 K with a strain rate of 0.1-10 s-1. Depending on the results of the compression test, a set of internal-state-variable based unified constitutive equations is put forward to describe the flow behavior and microstructure evaluation of SAE 8620H. Moreover, the evaluation of the dislocation density and the fraction of dynamic recrystallization based on the theory of thermal activation is modeled and reincorporated into the constitutive law. The material parameters in the constitutive model are calculated based on the measured flow stress and dynamic recrystallization fraction. The predicted flow stress under different deformation conditions has a good agreement with the measured results.

On the long-period evolution of the sun-synchronous orbits

NASA Astrophysics Data System (ADS)

Kuznetsov, E. D.; Jasim, A. T.

2016-05-01

The dynamic evolution of sun-synchronous orbits at a time interval of 20 years is considered. The numerical motion simulation has been carried out using the Celestial Mechanics software package developed at the Institute of Astronomy of the University of Bern. The dependence of the dynamic evolution on the initial value of the ascending node longitude is examined for two families of sun-synchronous orbits with altitudes of 751 and 1191 km. Variations of the semimajor axis and orbit inclination are obtained depending on the initial value of the ascending node longitude. Recommendations on the selection of orbits, in which spent sun-synchronous satellites can be moved, are formulated. Minimal changes of elements over a time interval of 20 years have been observed for orbits in which at the initial time the angle between the orbit ascending node and the direction of the Sun measured along the equator have been close to 90° or 270°. In this case, the semimajor axis of the orbit is not experiencing secular perturbations arising from the satellite's passage through the Earth's shadow.

Dynamics of double-polarity subduction: application to the Western Mediterranean

NASA Astrophysics Data System (ADS)

Peral, M.; Zlotnik, S.; Fernandez, M.; Verges, J.; Jiménez-Munt, I.; Torne, M.

2015-12-01

The evolution of the Western Mediterranean is a highly debated question by geologists and geophysicists. Even though most scientists agree in considering slab roll-back to be the driving mechanism of the tectonic evolution of this area, there is still no consensus about the initial setup and its time evolution. A recent model proposed by Vergés and Fernàndez (2012) suggests a lateral change in subduction polarity of the Ligurian-Thetys oceanic domain to explain the formation and evolution of the Betic-Rif orogenic system and the associated Alboran back-arc basin. Such geodynamic scenario is also proposed for different converging regions. The aim of this study is to analyze the dynamic evolution of a double-polarity subduction process and its consequences in order to test the physical feasibility of this interaction and provide geometries and evolutions comparable to those proposed for the Western Mediterranean. The 3D numerical model of double-polarity subduction is carried out via the Underworld framework. Tectonic plate behavior is described by equations of fluid dynamics in the presence of several different phases. Underworld solves a non-linear Stokes flow problem using Finite Elements combined with particle-in-cell approach, thus the discretization combines a standard Eulerian Finite Element mesh with Lagrangian particles to track the location of the phases. The final model consists of two oceanic plates with viscoplastic rheology subducting into the upper mantle and the problem is driven by Rayleigh-Taylor instability. The main factors to be studied are the interaction between the two plates, the poloidal and toroidal mantle fluxes, the velocity variations of slabs, the stress distribution and the variations in the trench morphology.

The Liouville equation for flavour evolution of neutrinos and neutrino wave packets

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

Hansen, Rasmus Sloth Lundkvist; Smirnov, Alexei Yu., E-mail: rasmus@mpi-hd.mpg.de, E-mail: smirnov@mpi-hd.mpg.de

We consider several aspects related to the form, derivation and applications of the Liouville equation (LE) for flavour evolution of neutrinos. To take into account the quantum nature of neutrinos we derive the evolution equation for the matrix of densities using wave packets instead of Wigner functions. The obtained equation differs from the standard LE by an additional term which is proportional to the difference of group velocities. We show that this term describes loss of the propagation coherence in the system. In absence of momentum changing collisions, the LE can be reduced to a single derivative equation over amore » trajectory coordinate. Additional time and spatial dependence may stem from initial (production) conditions. The transition from single neutrino evolution to the evolution of a neutrino gas is considered.« less

The role of the global phase in the spatio-temporal evolution of strong-coupling Brillouin scattering

NASA Astrophysics Data System (ADS)

Amiranoff, F.; Riconda, C.; Chiaramello, M.; Lancia, L.; Marquès, J. R.; Weber, S.

2018-01-01

The role of the global phase in the spatio-temporal evolution of the 3-wave coupled equations for backscattering is analyzed in the strong-coupling regime of Brillouin scattering. This is of particular interest for controlled backscattering in the case of plasma-based amplification to produce short and intense laser pulses. It is shown that the analysis of the envelope equations of the three waves involved, pump, seed, and ion wave, in terms of phase and amplitude fully describes the coupling dynamics. In particular, it helps understanding the role of the chirp of the laser beams and of the plasma density profile. The results can be used to optimize or quench the coupling mechanism. It is found that the directionality of the energy transfer is imposed by the phase relation at the leading edge of the pulse. This actually ensures continued energy transfer even if the intensity of the seed pulse is already higher than the pump pulse intensity.

Observational constraint on dynamical evolution of dark energy

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

Gong, Yungui; Cai, Rong-Gen; Chen, Yun

2010-01-01

We use the Constitution supernova, the baryon acoustic oscillation, the cosmic microwave background, and the Hubble parameter data to analyze the evolution property of dark energy. We obtain different results when we fit different baryon acoustic oscillation data combined with the Constitution supernova data to the Chevallier-Polarski-Linder model. We find that the difference stems from the different values of Ω{sub m0}. We also fit the observational data to the model independent piecewise constant parametrization. Four redshift bins with boundaries at z = 0.22, 0.53, 0.85 and 1.8 were chosen for the piecewise constant parametrization of the equation of state parametermore » w(z) of dark energy. We find no significant evidence for evolving w(z). With the addition of the Hubble parameter, the constraint on the equation of state parameter at high redshift is improved by 70%. The marginalization of the nuisance parameter connected to the supernova distance modulus is discussed.« less

Stochastic dynamics of dengue epidemics.

PubMed

de Souza, David R; Tomé, Tânia; Pinho, Suani T R; Barreto, Florisneide R; de Oliveira, Mário J

2013-01-01

We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, such as dengue, and the threshold of the disease. The coexistence space is composed of two structures representing the human and mosquito populations. The human population follows a susceptible-infected-recovered (SIR) type dynamics and the mosquito population follows a susceptible-infected-susceptible (SIS) type dynamics. The human infection is caused by infected mosquitoes and vice versa, so that the SIS and SIR dynamics are interconnected. We develop a truncation scheme to solve the evolution equations from which we get the threshold of the disease and the reproductive ratio. The threshold of the disease is also obtained by performing numerical simulations. We found that for certain values of the infection rates the spreading of the disease is impossible, for any death rate of infected mosquitoes.

Comprehensive solutions to the Bloch equations and dynamical models for open two-level systems

NASA Astrophysics Data System (ADS)

Skinner, Thomas E.

2018-01-01

The Bloch equation and its variants constitute the fundamental dynamical model for arbitrary two-level systems. Many important processes, including those in more complicated systems, can be modeled and understood through the two-level approximation. It is therefore of widespread relevance, especially as it relates to understanding dissipative processes in current cutting-edge applications of quantum mechanics. Although the Bloch equation has been the subject of considerable analysis in the 70 years since its inception, there is still, perhaps surprisingly, significant work that can be done. This paper extends the scope of previous analyses. It provides a framework for more fully understanding the dynamics of dissipative two-level systems. A solution is derived that is compact, tractable, and completely general, in contrast to previous results. Any solution of the Bloch equation depends on three roots of a cubic polynomial that are crucial to the time dependence of the system. The roots are typically only sketched out qualitatively, with no indication of their dependence on the physical parameters of the problem. Degenerate roots, which modify the solutions, have been ignored altogether. Here the roots are obtained explicitly in terms of a single real-valued root that is expressed as a simple function of the system parameters. For the conventional Bloch equation, a simple graphical representation of this root is presented that makes evident the explicit time dependence of the system for each point in the parameter space. Several intuitive, visual models of system dynamics are developed. A Euclidean coordinate system is identified in which any generalized Bloch equation is separable, i.e., the sum of commuting rotation and relaxation operators. The time evolution in this frame is simply a rotation followed by relaxation at modified rates that play a role similar to the standard longitudinal and transverse rates. These rates are functions of the applied field, which provides information towards control of the dissipative process. The Bloch equation also describes a system of three coupled harmonic oscillators, providing additional perspective on dissipative systems.

Dynamical and Mechanistic Reconstructive Approaches of T Lymphocyte Dynamics: Using Visual Modeling Languages to Bridge the Gap between Immunologists, Theoreticians, and Programmers

PubMed Central

Thomas-Vaslin, Véronique; Six, Adrien; Ganascia, Jean-Gabriel; Bersini, Hugues

2013-01-01

Dynamic modeling of lymphocyte behavior has primarily been based on populations based differential equations or on cellular agents moving in space and interacting each other. The final steps of this modeling effort are expressed in a code written in a programing language. On account of the complete lack of standardization of the different steps to proceed, we have to deplore poor communication and sharing between experimentalists, theoreticians and programmers. The adoption of diagrammatic visual computer language should however greatly help the immunologists to better communicate, to more easily identify the models similarities and facilitate the reuse and extension of existing software models. Since immunologists often conceptualize the dynamical evolution of immune systems in terms of “state-transitions” of biological objects, we promote the use of unified modeling language (UML) state-transition diagram. To demonstrate the feasibility of this approach, we present a UML refactoring of two published models on thymocyte differentiation. Originally built with different modeling strategies, a mathematical ordinary differential equation-based model and a cellular automata model, the two models are now in the same visual formalism and can be compared. PMID:24101919

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

NASA Astrophysics Data System (ADS)

Lacroix, Denis

2005-06-01

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

Applicability of transfer tensor method for open quantum system dynamics.

PubMed

Gelzinis, Andrius; Rybakovas, Edvardas; Valkunas, Leonas

2017-12-21

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

Soliton evolution and radiation loss for the sine-Gordon equation.

PubMed

Smyth, N F; Worthy, A L

1999-08-01

An approximate method for describing the evolution of solitonlike initial conditions to solitons for the sine-Gordon equation is developed. This method is based on using a solitonlike pulse with variable parameters in an averaged Lagrangian for the sine-Gordon equation. This averaged Lagrangian is then used to determine ordinary differential equations governing the evolution of the pulse parameters. The pulse evolves to a steady soliton by shedding dispersive radiation. The effect of this radiation is determined by examining the linearized sine-Gordon equation and loss terms are added to the variational equations derived from the averaged Lagrangian by using the momentum and energy conservation equations for the sine-Gordon equation. Solutions of the resulting approximate equations, which include loss, are found to be in good agreement with full numerical solutions of the sine-Gordon equation.

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

Yan Changshuo; Wang Jianmin, E-mail: wangjm@ihep.ac.c

High spatial resolution observations show that high-redshift galaxies are undergoing intensive evolution of dynamical structure and morphologies displayed by the H{alpha}, H{beta}, [O III], and [N II] images. It has been shown that supernova explosion (SNexp) of young massive stars during the star formation epoch, as kinetic feedback to host galaxies, can efficiently excite the turbulent viscosity. We incorporate the feedback into the dynamical equations through mass dropout and angular momentum transportation driven by the SNexp-excited turbulent viscosity. The empirical Kennicutt-Schmidt law is used for star formation rates (SFRs). We numerically solve the equations and show that there can bemore » intensive evolution of structure of the gaseous disk. Secular evolution of the disk shows interesting characteristics: (1) high viscosity excited by SNexp can efficiently transport the gas from 10 kpc to {approx}1 kpc forming a stellar disk whereas a stellar ring forms for the case with low viscosity; (2) starbursts trigger SMBH activity with a lag of {approx}10{sup 8} yr depending on SFRs, prompting the joint evolution of SMBHs and bulges; and (3) the velocity dispersion is as high as {approx}100 km s{sup -1} in the gaseous disk. These results are likely to vary with the initial mass function (IMF) that the SNexp rates rely on. Given the IMF, we use the GALAXEV code to compute the spectral evolution of stellar populations based on the dynamical structure. In order to compare the present models with the observed dynamical structure and images, we use the incident continuum from the simple stellar synthesis and CLOUDY to calculate emission line ratios of H{alpha}, H{beta}, [O III], and [N II], and H{alpha} brightness of gas photoionized by young massive stars formed on the disks. The models can produce the main features of emission from star-forming galaxies. We apply the present model to two galaxies, BX 389 and BX 482 observed in the SINS high-z sample, which are bulge and disk-dominated, respectively. Two successive rings independently evolving are able to reproduce the main dynamical and emission properties of the two galaxies, such as the Baldwin-Phillips-Terlevich diagram, the relation between line ratios, and H{alpha} brightness. The observed relation between turbulent velocity and the H{alpha} brightness can be explained by the present model. High viscosity excited by SNexp is able to efficiently transport the gas into a bulge to maintain high SFRs or to form a stellar ring close enough to the bulge so that it immigrates into the bulge of its host galaxy. This leads to a fast growing bulge. Implications and future work of the present models have been extensively discussed for galaxy formation in high-z universe.« less

Theory and observation of electromagnetic ion cyclotron triggered emissions in the magnetosphere

NASA Astrophysics Data System (ADS)

Omura, Yoshiharu; Pickett, Jolene; Grison, Benjamin; Santolik, Ondrej; Dandouras, Iannis; Engebretson, Mark; Décréau, Pierrette M. E.; Masson, Arnaud

2010-07-01

We develop a nonlinear wave growth theory of electromagnetic ion cyclotron (EMIC) triggered emissions observed in the inner magnetosphere. We first derive the basic wave equations from Maxwell's equations and the momentum equations for the electrons and ions. We then obtain equations that describe the nonlinear dynamics of resonant protons interacting with an EMIC wave. The frequency sweep rate of the wave plays an important role in forming the resonant current that controls the wave growth. Assuming an optimum condition for the maximum growth rate as an absolute instability at the magnetic equator and a self-sustaining growth condition for the wave propagating from the magnetic equator, we obtain a set of ordinary differential equations that describe the nonlinear evolution of a rising tone emission generated at the magnetic equator. Using the physical parameters inferred from the wave, particle, and magnetic field data measured by the Cluster spacecraft, we determine the dispersion relation for the EMIC waves. Integrating the differential equations numerically, we obtain a solution for the time variation of the amplitude and frequency of a rising tone emission at the equator. Assuming saturation of the wave amplitude, as is found in the observations, we find good agreement between the numerical solutions and the wave spectrum of the EMIC triggered emissions.

Externally driven magnetic granular layers at a liquid/air interface: self-organization, flows and magnetic order

NASA Astrophysics Data System (ADS)

Snezhko, Alexey

2007-03-01

Collective dynamics and pattern formation in ensembles of magnetic microparticles suspended at the liquid/air interface and subjected to an alternating magnetic field are studied. Experiments reveal a new type of nontrivially ordered dynamic self-assembled structures (``snakes'') emerging in such systems in a certain range of field magnitudes and frequencies. These remarkable structures are directly related to surface waves in the liquid generated by the collective response of magnetic microparticles to the alternating magnetic field. In addition, a large-scale vortex flows are induced in the vicinity of the dynamic structures. Some features of the self-localized snake structures can be understood in the framework of an amplitude equation for parametric waves coupled to the conservation law equation describing the evolution of the magnetic particle density. Self-assembled snakes have a complex magnetic order: the segments of the snake exhibit long-range antiferromagnetic ordering mediated by the surface wave, while each segment is composed of ferromagnetically aligned chains of microparticles. A phenomenological model describing magnetic behavior of the magnetic snakes in external magnetic fields is proposed.

Selection by consequences, behavioral evolution, and the price equation.

PubMed

Baum, William M

2017-05-01

Price's equation describes evolution across time in simple mathematical terms. Although it is not a theory, but a derived identity, it is useful as an analytical tool. It affords lucid descriptions of genetic evolution, cultural evolution, and behavioral evolution (often called "selection by consequences") at different levels (e.g., individual vs. group) and at different time scales (local and extended). The importance of the Price equation for behavior analysis lies in its ability to precisely restate selection by consequences, thereby restating, or even replacing, the law of effect. Beyond this, the equation may be useful whenever one regards ontogenetic behavioral change as evolutionary change, because it describes evolutionary change in abstract, general terms. As an analytical tool, the behavioral Price equation is an excellent aid in understanding how behavior changes within organisms' lifetimes. For example, it illuminates evolution of response rate, analyses of choice in concurrent schedules, negative contingencies, and dilemmas of self-control. © 2017 Society for the Experimental Analysis of Behavior.

Rotation and magnetism in intermediate-mass stars

NASA Astrophysics Data System (ADS)

Quentin, Léo G.; Tout, Christopher A.

2018-06-01

Rotation and magnetism are increasingly recognized as important phenomena in stellar evolution. Surface magnetic fields from a few to 20 000 G have been observed and models have suggested that magnetohydrodynamic transport of angular momentum and chemical composition could explain the peculiar composition of some stars. Stellar remnants such as white dwarfs have been observed with fields from a few to more than 109 G. We investigate the origin of and the evolution, on thermal and nuclear rather than dynamical time-scales, of an averaged large-scale magnetic field throughout a star's life and its coupling to stellar rotation. Large-scale magnetic fields sustained until late stages of stellar evolution with conservation of magnetic flux could explain the very high fields observed in white dwarfs. We include these effects in the Cambridge stellar evolution code using three time-dependant advection-diffusion equations coupled to the structural and composition equations of stars to model the evolution of angular momentum and the two components of the magnetic field. We present the evolution in various cases for a 3 M_{⊙} star from the beginning to the late stages of its life. Our particular model assumes that turbulent motions, including convection, favour small-scale field at the expense of large-scale field. As a result, the large-scale field concentrates in radiative zones of the star and so is exchanged between the core and the envelope of the star as it evolves. The field is sustained until the end of the asymptotic giant branch, when it concentrates in the degenerate core.

On the Global Regularity of a Helical-Decimated Version of the 3D Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Biferale, Luca; Titi, Edriss S.

2013-06-01

We study the global regularity, for all time and all initial data in H 1/2, of a recently introduced decimated version of the incompressible 3D Navier-Stokes (dNS) equations. The model is based on a projection of the dynamical evolution of Navier-Stokes (NS) equations into the subspace where helicity (the L 2-scalar product of velocity and vorticity) is sign-definite. The presence of a second (beside energy) sign-definite inviscid conserved quadratic quantity, which is equivalent to the H 1/2-Sobolev norm, allows us to demonstrate global existence and uniqueness, of space-periodic solutions, together with continuity with respect to the initial conditions, for this decimated 3D model. This is achieved thanks to the establishment of two new estimates, for this 3D model, which show that the H 1/2 and the time average of the square of the H 3/2 norms of the velocity field remain finite. Such two additional bounds are known, in the spirit of the work of H. Fujita and T. Kato (Arch. Ration. Mech. Anal. 16:269-315, 1964; Rend. Semin. Mat. Univ. Padova 32:243-260, 1962), to be sufficient for showing well-posedness for the 3D NS equations. Furthermore, they are directly linked to the helicity evolution for the dNS model, and therefore with a clear physical meaning and consequences.

Hydrodynamics of bacterial colonies: A model

NASA Astrophysics Data System (ADS)

Lega, J.; Passot, T.

2003-03-01

We propose a hydrodynamic model for the evolution of bacterial colonies growing on soft agar plates. This model consists of reaction-diffusion equations for the concentrations of nutrients, water, and bacteria, coupled to a single hydrodynamic equation for the velocity field of the bacteria-water mixture. It captures the dynamics inside the colony as well as on its boundary and allows us to identify a mechanism for collective motion towards fresh nutrients, which, in its modeling aspects, is similar to classical chemotaxis. As shown in numerical simulations, our model reproduces both usual colony shapes and typical hydrodynamic motions, such as the whirls and jets recently observed in wet colonies of Bacillus subtilis. The approach presented here could be extended to different experimental situations and provides a general framework for the use of advection-reaction-diffusion equations in modeling bacterial colonies.

On a hierarchy of nonlinearly dispersive generalized Korteweg - de Vries evolution equations

DOE PAGES

Christov, Ivan C.

2015-08-20

We propose a hierarchy of nonlinearly dispersive generalized Korteweg–de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. Two recent nonlinear evolution equations describing wave propagation in certain generalized continua with an inherent material length scale are members of the proposed hierarchy. Like KdV, the equations from the proposed hierarchy possess Hamiltonian structure. Unlike KdV, the solutions to these equations can be compact (i.e., they vanish outside of some open interval) and, in addition, peaked. Implicit solutions for these peaked, compact traveling waves (“peakompactons”) are presented.

Surface plasmon polariton Akhmediev Breather in a dielectric-metal-dielectric geometry with subwavelength thickness

NASA Astrophysics Data System (ADS)

Devi, Koijam Monika; Porsezian, K.; Sarma, Amarendra K.

2018-05-01

We report Akhmediev Breather solutions in a nonlinear multilayer structure comprising of a metal sandwiched between two semi-infinite dielectric layers with subwavelength thickness. These nonlinear solutions inherit the properties of Surface plasmon polaritons and its dynamics is governed by the Nonlinear Schrodinger equation. The breather evolution is studied for specific values of nonlinear and dispersion parameters. An experimental scheme to observe these breathers is also proposed.

Matching-pursuit/split-operator-Fourier-transform computations of thermal correlation functions.

PubMed

Chen, Xin; Wu, Yinghua; Batista, Victor S

2005-02-08

A rigorous and practical methodology for evaluating thermal-equilibrium density matrices, finite-temperature time-dependent expectation values, and time-correlation functions is described. The method involves an extension of the matching-pursuit/split-operator-Fourier-transform method to the solution of the Bloch equation via imaginary-time propagation of the density matrix and the evaluation of Heisenberg time-evolution operators through real-time propagation in dynamically adaptive coherent-state representations.

Functional thermo-dynamics: a generalization of dynamic density functional theory to non-isothermal situations.

PubMed

Anero, Jesús G; Español, Pep; Tarazona, Pedro

2013-07-21

We present a generalization of Density Functional Theory (DFT) to non-equilibrium non-isothermal situations. By using the original approach set forth by Gibbs in his consideration of Macroscopic Thermodynamics (MT), we consider a Functional Thermo-Dynamics (FTD) description based on the density field and the energy density field. A crucial ingredient of the theory is an entropy functional, which is a concave functional. Therefore, there is a one to one connection between the density and energy fields with the conjugate thermodynamic fields. The connection between the three levels of description (MT, DFT, FTD) is clarified through a bridge theorem that relates the entropy of different levels of description and that constitutes a generalization of Mermin's theorem to arbitrary levels of description whose relevant variables are connected linearly. Although the FTD level of description does not provide any new information about averages and correlations at equilibrium, it is a crucial ingredient for the dynamics in non-equilibrium states. We obtain with the technique of projection operators the set of dynamic equations that describe the evolution of the density and energy density fields from an initial non-equilibrium state towards equilibrium. These equations generalize time dependent density functional theory to non-isothermal situations. We also present an explicit model for the entropy functional for hard spheres.

Stochastic dynamics of time correlation in complex systems with discrete time

NASA Astrophysics Data System (ADS)

Yulmetyev, Renat; Hänggi, Peter; Gafarov, Fail

2000-11-01

In this paper we present the concept of description of random processes in complex systems with discrete time. It involves the description of kinetics of discrete processes by means of the chain of finite-difference non-Markov equations for time correlation functions (TCFs). We have introduced the dynamic (time dependent) information Shannon entropy Si(t) where i=0,1,2,3,..., as an information measure of stochastic dynamics of time correlation (i=0) and time memory (i=1,2,3,...). The set of functions Si(t) constitute the quantitative measure of time correlation disorder (i=0) and time memory disorder (i=1,2,3,...) in complex system. The theory developed started from the careful analysis of time correlation involving dynamics of vectors set of various chaotic states. We examine two stochastic processes involving the creation and annihilation of time correlation (or time memory) in details. We carry out the analysis of vectors' dynamics employing finite-difference equations for random variables and the evolution operator describing their natural motion. The existence of TCF results in the construction of the set of projection operators by the usage of scalar product operation. Harnessing the infinite set of orthogonal dynamic random variables on a basis of Gram-Shmidt orthogonalization procedure tends to creation of infinite chain of finite-difference non-Markov kinetic equations for discrete TCFs and memory functions (MFs). The solution of the equations above thereof brings to the recurrence relations between the TCF and MF of senior and junior orders. This offers new opportunities for detecting the frequency spectra of power of entropy function Si(t) for time correlation (i=0) and time memory (i=1,2,3,...). The results obtained offer considerable scope for attack on stochastic dynamics of discrete random processes in a complex systems. Application of this technique on the analysis of stochastic dynamics of RR intervals from human ECG's shows convincing evidence for a non-Markovian phenomemena associated with a peculiarities in short- and long-range scaling. This method may be of use in distinguishing healthy from pathologic data sets based in differences in these non-Markovian properties.

Controlled exciton transfer between quantum dots with acoustic phonons taken into account

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

Golovinski, P. A., E-mail: golovinski@bk.ru

2015-09-15

A system of excitons in two quantum dots coupled by the dipole–dipole interaction is investigated. The excitation transfer process controlled by the optical Stark effect at nonresonant frequencies is considered and the effect of the interaction between excitons and acoustic phonons in a medium on this process is taken into account. The system evolution is described using quantum Heisenberg equations. A truncated set of equations is obtained and the transfer dynamics is numerically simulated. High-efficiency picosecond switching of the excitation transfer by a laser pulse with a rectangular envelope is demonstrated. The dependence of picosecond switching on the quantum-dot parametersmore » and optical-pulse length is presented.« less

Toroidally symmetric plasma vortex at tokamak divertor null point

DOE PAGES

Umansky, M. V.; Ryutov, D. D.

2016-03-09

Reduced MHD equations are used for studying toroidally symmetric plasma dynamics near the divertor null point. Numerical solution of these equations exhibits a plasma vortex localized at the null point with the time-evolution defined by interplay of the curvature drive, magnetic restoring force, and dissipation. Convective motion is easier to achieve for a second-order null (snowflake) divertor than for a regular x-point configuration, and the size of the convection zone in a snowflake configuration grows with plasma pressure at the null point. In conclusion, the trends in simulations are consistent with tokamak experiments which indicate the presence of enhanced transportmore » at the null point.« less

Averaged variational principle for autoresonant Bernstein-Greene-Kruskal modes

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

Khain, P.; Friedland, L.

2010-10-15

Whitham's averaged variational principle is applied in studying dynamics of formation of autoresonant (continuously phase-locked) Bernstein-Greene-Kruskal (BGK) modes in a plasma driven by a chirped frequency ponderomotive wave. A flat-top electron velocity distribution is used as a model allowing a variational formulation within the water bag theory. The corresponding Lagrangian, averaged over the fast phase variable yields evolution equations for the slow field variables, allows uniform description of all stages of excitation of driven-chirped BGK modes, and predicts modulational stability of these nonlinear phase-space structures. Numerical solutions of the system of slow variational equations are in good agreement with Vlasov-Poissonmore » simulations.« less

Dynamic screening in a two-species asymmetric exclusion process

NASA Astrophysics Data System (ADS)

Kim, Kyung Hyuk; den Nijs, Marcel

2007-08-01

The dynamic scaling properties of the one-dimensional Burgers equation are expected to change with the inclusion of additional conserved degrees of freedom. We study this by means of one-dimensional (1D) driven lattice gas models that conserve both mass and momentum. The most elementary version of this is the Arndt-Heinzel-Rittenberg (AHR) process, which is usually presented as a two-species diffusion process, with particles of opposite charge hopping in opposite directions and with a variable passing probability. From the hydrodynamics perspective this can be viewed as two coupled Burgers equations, with the number of positive and negative momentum quanta individually conserved. We determine the dynamic scaling dimension of the AHR process from the time evolution of the two-point correlation functions, and find numerically that the dynamic critical exponent is consistent with simple Kardar-Parisi-Zhang- (KPZ) type scaling. We establish that this is the result of perfect screening of fluctuations in the stationary state. The two-point correlations decay exponentially in our simulations and in such a manner that in terms of quasiparticles, fluctuations fully screen each other at coarse grained length scales. We prove this screening rigorously using the analytic matrix product structure of the stationary state. The proof suggests the existence of a topological invariant. The process remains in the KPZ universality class but only in the sense of a factorization, as (KPZ)2 . The two Burgers equations decouple at large length scales due to the perfect screening.

Globally coupled stochastic two-state oscillators: fluctuations due to finite numbers.

PubMed

Pinto, Italo'Ivo Lima Dias; Escaff, Daniel; Harbola, Upendra; Rosas, Alexandre; Lindenberg, Katja

2014-05-01

Infinite arrays of coupled two-state stochastic oscillators exhibit well-defined steady states. We study the fluctuations that occur when the number N of oscillators in the array is finite. We choose a particular form of global coupling that in the infinite array leads to a pitchfork bifurcation from a monostable to a bistable steady state, the latter with two equally probable stationary states. The control parameter for this bifurcation is the coupling strength. In finite arrays these states become metastable: The fluctuations lead to distributions around the most probable states, with one maximum in the monostable regime and two maxima in the bistable regime. In the latter regime, the fluctuations lead to transitions between the two peak regions of the distribution. Also, we find that the fluctuations break the symmetry in the bimodal regime, that is, one metastable state becomes more probable than the other, increasingly so with increasing array size. To arrive at these results, we start from microscopic dynamical evolution equations from which we derive a Langevin equation that exhibits an interesting multiplicative noise structure. We also present a master equation description of the dynamics. Both of these equations lead to the same Fokker-Planck equation, the master equation via a 1/N expansion and the Langevin equation via standard methods of Itô calculus for multiplicative noise. From the Fokker-Planck equation we obtain an effective potential that reflects the transition from the monomodal to the bimodal distribution as a function of a control parameter. We present a variety of numerical and analytic results that illustrate the strong effects of the fluctuations. We also show that the limits N → ∞ and t → ∞ (t is the time) do not commute. In fact, the two orders of implementation lead to drastically different results.

Globally coupled stochastic two-state oscillators: Fluctuations due to finite numbers

NASA Astrophysics Data System (ADS)

Pinto, Italo'Ivo Lima Dias; Escaff, Daniel; Harbola, Upendra; Rosas, Alexandre; Lindenberg, Katja

2014-05-01

Infinite arrays of coupled two-state stochastic oscillators exhibit well-defined steady states. We study the fluctuations that occur when the number N of oscillators in the array is finite. We choose a particular form of global coupling that in the infinite array leads to a pitchfork bifurcation from a monostable to a bistable steady state, the latter with two equally probable stationary states. The control parameter for this bifurcation is the coupling strength. In finite arrays these states become metastable: The fluctuations lead to distributions around the most probable states, with one maximum in the monostable regime and two maxima in the bistable regime. In the latter regime, the fluctuations lead to transitions between the two peak regions of the distribution. Also, we find that the fluctuations break the symmetry in the bimodal regime, that is, one metastable state becomes more probable than the other, increasingly so with increasing array size. To arrive at these results, we start from microscopic dynamical evolution equations from which we derive a Langevin equation that exhibits an interesting multiplicative noise structure. We also present a master equation description of the dynamics. Both of these equations lead to the same Fokker-Planck equation, the master equation via a 1/N expansion and the Langevin equation via standard methods of Itô calculus for multiplicative noise. From the Fokker-Planck equation we obtain an effective potential that reflects the transition from the monomodal to the bimodal distribution as a function of a control parameter. We present a variety of numerical and analytic results that illustrate the strong effects of the fluctuations. We also show that the limits N →∞ and t →∞ (t is the time) do not commute. In fact, the two orders of implementation lead to drastically different results.

Asymptotic Representation for the Eigenvalues of a Non-selfadjoint Operator Governing the Dynamics of an Energy Harvesting Model

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

Shubov, Marianna A., E-mail: marianna.shubov@gmail.com

2016-06-15

We consider a well known model of a piezoelectric energy harvester. The harvester is designed as a beam with a piezoceramic layer attached to its top face (unimorph configuration). A pair of thin perfectly conductive electrodes is covering the top and the bottom faces of the piezoceramic layer. These electrodes are connected to a resistive load. The model is governed by a system consisting of two equations. The first of them is the equation of the Euler–Bernoulli model for the transverse vibrations of the beam and the second one represents the Kirchhoff’s law for the electric circuit. Both equations aremore » coupled due to the direct and converse piezoelectric effects. The boundary conditions for the beam equations are of clamped-free type. We represent the system as a single operator evolution equation in a Hilbert space. The dynamics generator of this system is a non-selfadjoint operator with compact resolvent. Our main result is an explicit asymptotic formula for the eigenvalues of this generator, i.e., we perform the modal analysis for electrically loaded (not short-circuit) system. We show that the spectrum splits into an infinite sequence of stable eigenvalues that approaches a vertical line in the left half plane and possibly of a finite number of unstable eigenvalues. This paper is the first in a series of three works. In the second one we will prove that the generalized eigenvectors of the dynamics generator form a Riesz basis (and, moreover, a Bari basis) in the energy space. In the third paper we will apply the results of the first two to control problems for this model.« less

Microscopic modeling of gas-surface scattering. I. A combined molecular dynamics-rate equation approach

NASA Astrophysics Data System (ADS)

Filinov, A.; Bonitz, M.; Loffhagen, D.

2018-06-01

A combination of first principle molecular dynamics (MD) simulations with a rate equation model (MD-RE approach) is presented to study the trapping and the scattering of rare gas atoms from metal surfaces. The temporal evolution of the atom fractions that are either adsorbed or scattered into the continuum is investigated in detail. We demonstrate that for this description one has to consider trapped, quasi-trapped and scattering states, and present an energetic definition of these states. The rate equations contain the transition probabilities between the states. We demonstrate how these rate equations can be derived from kinetic theory. Moreover, we present a rigorous way to determine the transition probabilities from a microscopic analysis of the particle trajectories generated by MD simulations. Once the system reaches quasi-equilibrium, the rates converge to stationary values, and the subsequent thermal adsorption/desorption dynamics is completely described by the rate equations without the need to perform further time-consuming MD simulations. As a proof of concept of our approach, MD simulations for argon atoms interacting with a platinum (111) surface are presented. A detailed deterministic trajectory analysis is performed, and the transition rates are constructed. The dependence of the rates on the incidence conditions and the lattice temperature is analyzed. Based on this example, we analyze the time scale of the gas-surface system to approach the quasi-stationary state. The MD-RE model has great relevance for the plasma-surface modeling as it makes an extension of accurate simulations to long, experimentally relevant time scales possible. Its application to the computation of atomic sticking probabilities is given in the second part (paper II).

Weight of fitness deviation governs strict physical chaos in replicator dynamics.

PubMed

Pandit, Varun; Mukhopadhyay, Archan; Chakraborty, Sagar

2018-03-01

Replicator equation-a paradigm equation in evolutionary game dynamics-mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the average fitnesses of the evolving population under consideration. In this paper, we deal with two discrete versions of the replicator equation employed to study evolution in a population where any two players' interaction is modelled by a two-strategy symmetric normal-form game. There are twelve distinct classes of such games, each typified by a particular ordinal relationship among the elements of the corresponding payoff matrix. Here, we find the sufficient conditions for the existence of asymptotic solutions of the replicator equations such that the solutions-fixed points, periodic orbits, and chaotic trajectories-are all strictly physical, meaning that the frequency of any strategy lies inside the closed interval zero to one at all times. Thus, we elaborate on which of the twelve types of games are capable of showing meaningful physical solutions and for which of the two types of replicator equation. Subsequently, we introduce the concept of the weight of fitness deviation that is the scaling factor in a positive affine transformation connecting two payoff matrices such that the corresponding one-shot games have exactly same Nash equilibria and evolutionary stable states. The weight also quantifies how much the excess of fitness of a strategy over the average fitness of the population affects the per capita change in the frequency of the strategy. Intriguingly, the weight's variation is capable of making the Nash equilibria and the evolutionary stable states, useless by introducing strict physical chaos in the replicator dynamics based on the normal-form game.

Vortex Dynamics and Shear-Layer Instability in High-Intensity Cyclotrons.

PubMed

Cerfon, Antoine J

2016-04-29

We show that the space-charge dynamics of high-intensity beams in the plane perpendicular to the magnetic field in cyclotrons is described by the two-dimensional Euler equations for an incompressible fluid. This analogy with fluid dynamics gives a unified and intuitive framework to explain the beam spiraling and beam breakup behavior observed in experiments and in simulations. Specifically, we demonstrate that beam breakup is the result of a classical instability occurring in fluids subject to a sheared flow. We give scaling laws for the instability and predict the nonlinear evolution of beams subject to it. Our work suggests that cyclotrons may be uniquely suited for the experimental study of shear layers and vortex distributions that are not achievable in Penning-Malmberg traps.

Classical and quantum dynamics of a kicked relativistic particle in a box

NASA Astrophysics Data System (ADS)

Yusupov, J. R.; Otajanov, D. M.; Eshniyazov, V. E.; Matrasulov, D. U.

2018-03-01

We study classical and quantum dynamics of a kicked relativistic particle confined in a one dimensional box. It is found that in classical case for chaotic motion the average kinetic energy grows in time, while for mixed regime the growth is suppressed. However, in case of regular motion energy fluctuates around certain value. Quantum dynamics is treated by solving the time-dependent Dirac equation with delta-kicking potential, whose exact solution is obtained for single kicking period. In quantum case, depending on the values of the kicking parameters, the average kinetic energy can be quasi periodic, or fluctuating around some value. Particle transport is studied by considering spatio-temporal evolution of the Gaussian wave packet and by analyzing the trembling motion.

Three-dimensional wave evolution on electrified falling films

NASA Astrophysics Data System (ADS)

Tomlin, Ruben; Papageorgiou, Demetrios; Pavliotis, Greg

2016-11-01

We consider the full three-dimensional model for a thin viscous liquid film completely wetting a flat infinite solid substrate at some non-zero angle to the horizontal, with an electric field normal to the substrate far from the flow. Thin film flows have applications in cooling processes. Many studies have shown that the presence of interfacial waves increases heat transfer by orders of magnitude due to film thinning and convection effects. A long-wave asymptotics procedure yields a Kuramoto-Sivashinsky equation with a non-local term to model the weakly nonlinear evolution of the interface dynamics for overlying film arrangements, with a restriction on the electric field strength. The non-local term is always linearly destabilising and produces growth rates proportional to the cube of the magnitude of the wavenumber vector. A sufficiently strong electric field is able promote non-trivial dynamics for subcritical Reynolds number flows where the flat interface is stable in the absence of an electric field. We present numerical simulations where we observe rich dynamical behavior with competing attractors, including "snaking" travelling waves and other fully three-dimensional wave formations. EPSRC studentship (RJT).

Governing Laws of Complex System Predictability under Co-evolving Uncertainty Sources: Theory and Nonlinear Geophysical Applications

NASA Astrophysics Data System (ADS)

Perdigão, R. A. P.

2017-12-01

Predictability assessments are traditionally made on a case-by-case basis, often by running the particular model of interest with randomly perturbed initial/boundary conditions and parameters, producing computationally expensive ensembles. These approaches provide a lumped statistical view of uncertainty evolution, without eliciting the fundamental processes and interactions at play in the uncertainty dynamics. In order to address these limitations, we introduce a systematic dynamical framework for predictability assessment and forecast, by analytically deriving governing equations of predictability in terms of the fundamental architecture of dynamical systems, independent of any particular problem under consideration. The framework further relates multiple uncertainty sources along with their coevolutionary interplay, enabling a comprehensive and explicit treatment of uncertainty dynamics along time, without requiring the actual model to be run. In doing so, computational resources are freed and a quick and effective a-priori systematic dynamic evaluation is made of predictability evolution and its challenges, including aspects in the model architecture and intervening variables that may require optimization ahead of initiating any model runs. It further brings out universal dynamic features in the error dynamics elusive to any case specific treatment, ultimately shedding fundamental light on the challenging issue of predictability. The formulated approach, framed with broad mathematical physics generality in mind, is then implemented in dynamic models of nonlinear geophysical systems with various degrees of complexity, in order to evaluate their limitations and provide informed assistance on how to optimize their design and improve their predictability in fundamental dynamical terms.

Emergence and analysis of Kuramoto-Sakaguchi-like models as an effective description for the dynamics of coupled Wien-bridge oscillators.

PubMed

English, L Q; Mertens, David; Abdoulkary, Saidou; Fritz, C B; Skowronski, K; Kevrekidis, P G

2016-12-01

We derive the Kuramoto-Sakaguchi model from the basic circuit equations governing two coupled Wien-bridge oscillators. A Wien-bridge oscillator is a particular realization of a tunable autonomous oscillator that makes use of frequency filtering (via an RC bandpass filter) and positive feedback (via an operational amplifier). In the past few years, such oscillators have started to be utilized in synchronization studies. We first show that the Wien-bridge circuit equations can be cast in the form of a coupled pair of van der Pol equations. Subsequently, by applying the method of multiple time scales, we derive the differential equations that govern the slow evolution of the oscillator phases and amplitudes. These equations are directly reminiscent of the Kuramoto-Sakaguchi-type models for the study of synchronization. We analyze the resulting system in terms of the existence and stability of various coupled oscillator solutions and explain on that basis how their synchronization emerges. The phase-amplitude equations are also compared numerically to the original circuit equations and good agreement is found. Finally, we report on experimental measurements of two coupled Wien-bridge oscillators and relate the results to the theoretical predictions.

Falling films on flexible inclines

NASA Astrophysics Data System (ADS)

Matar, O. K.; Craster, R. V.; Kumar, S.

2007-11-01

The nonlinear stability and dynamic behavior of falling fluid films is studied for flow over a flexible substrate. We use asymptotic methods to deduce governing equations valid in various limits. Long-wave theory is used to derive Benney-like coupled equations for the film thickness and substrate deflection. Weakly nonlinear equations are then derived from these equations that, in the limit of large wall damping and/or large wall tension, reduce to the Kuramoto-Sivashinsky equation. These models break down when inertia becomes more significant, so we also use a long-wave approximation in conjunction with integral theory to derive three strongly coupled nonlinear evolution equations for the film thickness, substrate deflection, and film volumetric flow rate valid at higher Reynolds numbers. These equations, accounting for inertia, capillary, viscous, wall tension, and damping effects, are solved over a wide range of parameters. Our results suggest that decreasing wall damping and/or wall tension can promote the development of chaos in the weakly nonlinear regime and lead to severe substrate deformations in the strongly nonlinear regime; these can give rise to situations in which the free surface and underlying substrate come into contact in finite time.

A Pressure-Dependent Damage Model for Energetic Materials

DTIC Science & Technology

2013-04-01

appropriate damage nucleation and evolution laws, and the equation of state ) with its reactive response. 15. SUBJECT TERMS pressure-dependent...evolution laws, and the equation of state ) with its reactive response. INTRODUCTION Explosions and deflagrations are classifications of sub-detonative...energetic material’s mechanical response (through the yield criterion, damage evolution and equation of state ) with its reactive response. DAMAGE-FREE

A note on the evolution equations from the area fraction and the thickness of a floating ice cover

NASA Astrophysics Data System (ADS)

Schulkes, R. M. S. M.

1995-03-01

In this paper, two sets of evolution equations for the area fraction and the ice thickness are investigated. First of all, a simplified alternative derivation of the evolution equations as presented by Gray and Morland (1994) is given. In addition, it is shown that with proper identification of ridging functions, there is a close connection between the derived equations and the thickness distribution model introduced by Thorndike et al. (1975).

Dynamics and stability of light-like tachyon condensation

NASA Astrophysics Data System (ADS)

Barnaby, Neil; Mulryne, David J.; Nunes, Nelson J.; Robinson, Patrick

2009-03-01

Recently, Hellerman and Schnabl considered the dynamics of unstable D-branes in the background of a linear dilaton. Remarkably, they were able to construct light-like tachyon solutions which interpolate smoothly between the perturbative and nonperturbative vacua, without undergoing the wild oscillations that plague time-like solutions. In their analysis, however, the full structure of the initial value problem for the nonlocal dynamical equations was not considered. In this paper, therefore, we reexamine the nonlinear dynamics of light-like tachyon condensation using a combination of numerical and analytical techniques. We find that for the p-adic string the monotonic behaviour obtained previously relied on a special choice of initial conditions near the unstable maximum. For generic initial conditions the wild oscillations come back to haunt us. Interestingly, we find an ``island of stability'' in initial condition space that leads to sensible evolution at late times. For the string field theory case, on the other hand, we find that the evolution is completely stable for generic choices of initial data. This provides an explicit example of a string theoretic system that admits infinitely many initial data but is nevertheless nonperturbatively stable. Qualitatively similar dynamics are obtained in nonlocal cosmologies where the Hubble damping plays a role very analogous to the dilaton gradient.

Pressure evolution equation for the particulate phase in inhomogeneous compressible disperse multiphase flows

NASA Astrophysics Data System (ADS)

Annamalai, Subramanian; Balachandar, S.; Sridharan, P.; Jackson, T. L.

2017-02-01

An analytical expression describing the unsteady pressure evolution of the dispersed phase driven by variations in the carrier phase is presented. In this article, the term "dispersed phase" represents rigid particles, droplets, or bubbles. Letting both the dispersed and continuous phases be inhomogeneous, unsteady, and compressible, the developed pressure equation describes the particle response and its eventual equilibration with that of the carrier fluid. The study involves impingement of a plane traveling wave of a given frequency and subsequent volume-averaged particle pressure calculation due to a single wave. The ambient or continuous fluid's pressure and density-weighted normal velocity are identified as the source terms governing the particle pressure. Analogous to the generalized Faxén theorem, which is applicable to the particle equation of motion, the pressure expression is also written in terms of the surface average of time-varying incoming flow properties. The surface average allows the current formulation to be generalized for any complex incident flow, including situations where the particle size is comparable to that of the incoming flow. Further, the particle pressure is also found to depend on the dispersed-to-continuous fluid density ratio and speed of sound ratio in addition to dynamic viscosities of both fluids. The model is applied to predict the unsteady pressure variation inside an aluminum particle subjected to normal shock waves. The results are compared against numerical simulations and found to be in good agreement. Furthermore, it is shown that, although the analysis is conducted in the limit of negligible flow Reynolds and Mach numbers, it can be used to compute the density and volume of the dispersed phase to reasonable accuracy. Finally, analogous to the pressure evolution expression, an equation describing the time-dependent particle radius is deduced and is shown to reduce to the Rayleigh-Plesset equation in the linear limit.

Spatial evolution of quantum mechanical states

NASA Astrophysics Data System (ADS)

Christensen, N. D.; Unger, J. E.; Pinto, S.; Su, Q.; Grobe, R.

2018-02-01

The time-dependent Schrödinger equation is solved traditionally as an initial-time value problem, where its solution is obtained by the action of the unitary time-evolution propagator on the quantum state that is known at all spatial locations but only at t = 0. We generalize this approach by examining the spatial evolution from a state that is, by contrast, known at all times t, but only at one specific location. The corresponding spatial-evolution propagator turns out to be pseudo-unitary. In contrast to the real energies that govern the usual (unitary) time evolution, the spatial evolution can therefore require complex phases associated with dynamically relevant solutions that grow exponentially. By introducing a generalized scalar product, for which the spatial generator is Hermitian, one can show that the temporal integral over the probability current density is spatially conserved, in full analogy to the usual norm of the state, which is temporally conserved. As an application of the spatial propagation formalism, we introduce a spatial backtracking technique that permits us to reconstruct any quantum information about an atom from the ionization data measured at a detector outside the interaction region.

On star formation in stellar systems. I - Photoionization effects in protoglobular clusters

NASA Technical Reports Server (NTRS)

Tenorio-Tagle, G.; Bodenheimer, P.; Lin, D. N. C.; Noriega-Crespo, A.

1986-01-01

The progressive ionization and subsequent dynamical evolution of nonhomogeneously distributed low-metal-abundance diffuse gas after star formation in globular clusters are investigated analytically, taking the gravitational acceleration due to the stars into account. The basic equations are derived; the underlying assumptions, input parameters, and solution methods are explained; and numerical results for three standard cases (ionization during star formation, ionization during expansion, and evolution resulting in a stable H II region at its equilibrium Stromgren radius) are presented in graphs and characterized in detail. The time scale of residual-gas loss in typical clusters is found to be about the same as the lifetime of a massive star on the main sequence.

A modified Lotka-Volterra model for the evolution of coordinate symbiosis in energy enterprise

NASA Astrophysics Data System (ADS)

Zhou, Li; Wang, Teng; Lyu, Xiaohuan; Yu, Jing

2018-02-01

Recent developments in energy markets make the operating industries more dynamic and complex, and energy enterprises cooperate more closely in the industrial chain and symbiosis. In order to further discuss the evolution of coordinate symbiosis in energy enterprises, a modified Lotka-Volterra equation is introduced to develop a symbiosis analysis model of energy groups. According to the equilibrium and stability analysis, a conclusion is obtained that if the upstream energy group and the downstream energy group are in symbiotic state, the growth of their utility will be greater than their independent value. Energy enterprises can get mutual benefits and positive promotions in industrial chain by their cooperation.

Observation of Fermi-Pasta-Ulam Recurrence Induced by Breather Solitons in an Optical Microresonator

NASA Astrophysics Data System (ADS)

Bao, Chengying; Jaramillo-Villegas, Jose A.; Xuan, Yi; Leaird, Daniel E.; Qi, Minghao; Weiner, Andrew M.

2016-10-01

We present, experimentally and numerically, the observation of Fermi-Pasta-Ulam recurrence induced by breather solitons in a high-Q SiN microresonator. Breather solitons can be excited by increasing the pump power at a relatively small pump phase detuning in microresonators. Out of phase power evolution is observed for groups of comb lines around the center of the spectrum compared to groups of lines in the spectral wings. The evolution of the power spectrum is not symmetric with respect to the spectrum center. Numerical simulations based on the generalized Lugiato-Lefever equation are in good agreement with the experimental results and unveil the role of stimulated Raman scattering in the symmetry breaking of the power spectrum evolution. Our results show that optical microresonators can be exploited as a powerful platform for the exploration of soliton dynamics.

Critical spaces for quasilinear parabolic evolution equations and applications

NASA Astrophysics Data System (ADS)

Prüss, Jan; Simonett, Gieri; Wilke, Mathias

2018-02-01

We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal Lp-regularity in time-weighted function spaces. It is shown that our notion of critical spaces coincides with the concept of scaling invariant spaces in case that the underlying partial differential equation enjoys a scaling invariance. Applications to the vorticity equations for the Navier-Stokes problem, convection-diffusion equations, the Nernst-Planck-Poisson equations in electro-chemistry, chemotaxis equations, the MHD equations, and some other well-known parabolic equations are given.

Dynamical evolution of spectator systems produced in ultrarelativistic heavy-ion collisions

NASA Astrophysics Data System (ADS)

Mazurek, K.; Szczurek, A.; Schmitt, C.; Nadtochy, P. N.

2018-02-01

In peripheral heavy-ion collisions at ultrarelativistic energies, usually only parts of the colliding nuclei effectively interact with each other. In the overlapping zone, a fireball or quark-gluon plasma is produced. The excitation energy of the heavy remnant can range from a few tens to several hundreds of MeV, depending on the impact parameter. The decay of these excited spectators is investigated in this work for the first time within a dynamical approach based on the multidimensional stochastic Langevin equation. The potential of this exploratory work to understand the connection between electromagnetic fields generated by the heavy spectators and measured pion distributions is discussed.

Nonlinear calculations of the time evolution of black hole accretion disks

NASA Technical Reports Server (NTRS)

Luo, C.

1994-01-01

Based on previous works on black hole accretion disks, I continue to explore the disk dynamics using the finite difference method to solve the highly nonlinear problem of time-dependent alpha disk equations. Here a radially zoned model is used to develop a computational scheme in order to accommodate functional dependence of the viscosity parameter alpha on the disk scale height and/or surface density. This work is based on the author's previous work on the steady disk structure and the linear analysis of disk dynamics to try to apply to x-ray emissions from black candidates (i.e., multiple-state spectra, instabilities, QPO's, etc.).

Convergence Time towards Periodic Orbits in Discrete Dynamical Systems

PubMed Central

San Martín, Jesús; Porter, Mason A.

2014-01-01

We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we use linearized equations to examine the evolution near that neighborhood. The underlying idea is that points of stable periodic orbit are associated with intervals. We state and prove a theorem that details what regions of phase space are mapped into these intervals (once they are known) and how many iterations are required to get there. We also construct algorithms that allow our theoretical results to be implemented successfully in practice. PMID:24736594

Swinging motion of active deformable particles in Poiseuille flow

NASA Astrophysics Data System (ADS)

Tarama, Mitsusuke

2017-08-01

Dynamics of active deformable particles in an external Poiseuille flow is investigated. To make the analysis general, we employ time-evolution equations derived from symmetry considerations that take into account an elliptical shape deformation. First, we clarify the relation of our model to that of rigid active particles. Then, we study the dynamical modes that active deformable particles exhibit by changing the strength of the external flow. We emphasize the difference between the active particles that tend to self-propel parallel to the elliptical shape deformation and those self-propelling perpendicularly. In particular, a swinging motion around the centerline far from the channel walls is discussed in detail.

The fast kinematic magnetic dynamo and the dissipationless limit

NASA Technical Reports Server (NTRS)

Finn, John M.; Ott, Edward

1990-01-01

The evolution of the magnetic field in models that incorporate chaotic field line stretching, field cancellation, and finite magnetic Reynolds number is examined analytically and numerically. Although the models used here are highly idealized, it is claimed that they display and illustrate typical behavior relevant to fast magnetic dynamic behavior. It is shown, in particular, that consideration of magnetic flux through a finite fixed surface provides a simple and effective way of deducing fast dynamo behavior from the zero resistivity equation. Certain aspects of the fast dynamo problem can thus be reduced to a study of nonlinear dynamic properties of the underlying flow.

Mesoscopic Dynamical Differences from Quantum State Preparation in a Bose-Hubbard Trimer

NASA Astrophysics Data System (ADS)

Olsen, M. K.; Neely, T. W.; Bradley, A. S.

2018-06-01

Conventional wisdom is that quantum effects will tend to disappear as the number of quanta in a system increases, and the evolution of a system will become closer to that described by mean-field classical equations. In this Letter we combine newly developed theoretical and experimental techniques to propose and analyze an experiment using a Bose-Hubbard trimer where the opposite is the case. We find that differences in the preparation of a centrally evacuated trimer can lead to readily observable differences in the subsequent dynamics which increase with system size. Importantly, these differences can be detected by the simple measurements of atomic number.

Multiscale equation-free algorithms for molecular dynamics

NASA Astrophysics Data System (ADS)

Abi Mansour, Andrew

Molecular dynamics is a physics-based computational tool that has been widely employed to study the dynamics and structure of macromolecules and their assemblies at the atomic scale. However, the efficiency of molecular dynamics simulation is limited because of the broad spectrum of timescales involved. To overcome this limitation, an equation-free algorithm is presented for simulating these systems using a multiscale model cast in terms of atomistic and coarse-grained variables. Both variables are evolved in time in such a way that the cross-talk between short and long scales is preserved. In this way, the coarse-grained variables guide the evolution of the atom-resolved states, while the latter provide the Newtonian physics for the former. While the atomistic variables are evolved using short molecular dynamics runs, time advancement at the coarse-grained level is achieved with a scheme that uses information from past and future states of the system while accounting for both the stochastic and deterministic features of the coarse-grained dynamics. To complete the multiscale cycle, an atom-resolved state consistent with the updated coarse-grained variables is recovered using algorithms from mathematical optimization. This multiscale paradigm is extended to nanofluidics using concepts from hydrodynamics, and it is demonstrated for macromolecular and nanofluidic systems. A toolkit is developed for prototyping these algorithms, which are then implemented within the GROMACS simulation package and released as an open source multiscale simulator.

Variational study of fermionic and bosonic systems with non-Gaussian states: Theory and applications

NASA Astrophysics Data System (ADS)

Shi, Tao; Demler, Eugene; Ignacio Cirac, J.

2018-03-01

We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian states by including generalized canonical transformations between the fields. The key advantage of such states compared to simple Gaussian states is presence of non-factorizable correlations and the possibility of describing states with strong entanglement between particles. In contrast to the commonly used canonical transformations, such as the polaron or Lang-Firsov transformations, we allow parameters of the transformations to be time dependent, which extends their regions of applicability. We derive equations of motion for the parameters characterizing the states both in real and imaginary time using the differential structure of the variational manifold. The ground state can be found by following the imaginary time evolution until it converges to a steady state. Collective excitations in the system can be obtained by linearizing the real-time equations of motion in the vicinity of the imaginary time steady-state solution. Our formalism allows us not only to determine the energy spectrum of quasiparticles and their lifetime, but to obtain the complete spectral functions and to explore far out of equilibrium dynamics such as coherent evolution following a quantum quench. We illustrate and benchmark this framework with several examples: a single polaron in the Holstein and Su-Schrieffer-Heeger models, non-equilibrium dynamics in the spin-boson and Kondo models, the superconducting to charge density wave phase transitions in the Holstein model.

Gravitational collapse of dark energy field configurations and supermassive black hole formation

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

Jhalani, V.; Kharkwal, H.; Singh, A., E-mail: anupamsingh.iitk@gmail.com

Dark energy is the dominant component of the total energy density of our Universe. The primary interaction of dark energy with the rest of the Universe is gravitational. It is therefore important to understand the gravitational dynamics of dark energy. Since dark energy is a low-energy phenomenon from the perspective of particle physics and field theory, a fundamental approach based on fields in curved space should be sufficient to understand the current dynamics of dark energy. Here, we take a field theory approach to dark energy. We discuss the evolution equations for a generic dark energy field in curved space-timemore » and then discuss the gravitational collapse for dark energy field configurations. We describe the 3 + 1 BSSN formalism to study the gravitational collapse of fields for any general potential for the fields and apply this formalism to models of dark energy motivated by particle physics considerations. We solve the resulting equations for the time evolution of field configurations and the dynamics of space-time. Our results show that gravitational collapse of dark energy field configurations occurs and must be considered in any complete picture of our Universe. We also demonstrate the black hole formation as a result of the gravitational collapse of the dark energy field configurations. The black holes produced by the collapse of dark energy fields are in the supermassive black hole category with the masses of these black holes being comparable to the masses of black holes at the centers of galaxies.« less

Nonlinear dynamics of the 3D FMS and Alfven wave beams propagating in plasma of ionosphere and magnetosphere

NASA Astrophysics Data System (ADS)

Belashov, Vasily

We study the formation, structure, stability and dynamics of the multidimensional soliton-like beam structures forming on the low-frequency branch of oscillation in the ionospheric and magnetospheric plasma for cases when beta=4pinT/B(2) <<1 and beta>1. In first case with the conditions omega>{k_{yz}}(2,) v_{x}$<

Macroscopic dielectric function within time-dependent density functional theory—Real time evolution versus the Casida approach

NASA Astrophysics Data System (ADS)

Sander, Tobias; Kresse, Georg

2017-02-01

Linear optical properties can be calculated by solving the time-dependent density functional theory equations. Linearization of the equation of motion around the ground state orbitals results in the so-called Casida equation, which is formally very similar to the Bethe-Salpeter equation. Alternatively one can determine the spectral functions by applying an infinitely short electric field in time and then following the evolution of the electron orbitals and the evolution of the dipole moments. The long wavelength response function is then given by the Fourier transformation of the evolution of the dipole moments in time. In this work, we compare the results and performance of these two approaches for the projector augmented wave method. To allow for large time steps and still rely on a simple difference scheme to solve the differential equation, we correct for the errors in the frequency domain, using a simple analytic equation. In general, we find that both approaches yield virtually indistinguishable results. For standard density functionals, the time evolution approach is, with respect to the computational performance, clearly superior compared to the solution of the Casida equation. However, for functionals including nonlocal exchange, the direct solution of the Casida equation is usually much more efficient, even though it scales less beneficial with the system size. We relate this to the large computational prefactors in evaluating the nonlocal exchange, which renders the time evolution algorithm fairly inefficient.

Evolution dynamics of a model for gene duplication under adaptive conflict

NASA Astrophysics Data System (ADS)

Ancliff, Mark; Park, Jeong-Man

2014-06-01

We present and solve the dynamics of a model for gene duplication showing escape from adaptive conflict. We use a Crow-Kimura quasispecies model of evolution where the fitness landscape is a function of Hamming distances from two reference sequences, which are assumed to optimize two different gene functions, to describe the dynamics of a mixed population of individuals with single and double copies of a pleiotropic gene. The evolution equations are solved through a spin coherent state path integral, and we find two phases: one is an escape from an adaptive conflict phase, where each copy of a duplicated gene evolves toward subfunctionalization, and the other is a duplication loss of function phase, where one copy maintains its pleiotropic form and the other copy undergoes neutral mutation. The phase is determined by a competition between the fitness benefits of subfunctionalization and the greater mutational load associated with maintaining two gene copies. In the escape phase, we find a dynamics of an initial population of single gene sequences only which escape adaptive conflict through gene duplication and find that there are two time regimes: until a time t* single gene sequences dominate, and after t* double gene sequences outgrow single gene sequences. The time t* is identified as the time necessary for subfunctionalization to evolve and spread throughout the double gene sequences, and we show that there is an optimum mutation rate which minimizes this time scale.

Self-Consistent Ring Current Modeling with Propagating Electromagnetic Ion Cyclotron Waves in the Presence of Heavy Ions

NASA Technical Reports Server (NTRS)

Khazanov, George V.

2006-01-01

The self-consistent treatment of the RC ion dynamics and EMIC waves, which are thought to exert important influences on the ion dynamical evolution, is an important missing element in our understanding of the storm-and recovery-time ring current evolution. Under certain conditions, relativistic electrons, with energies 21 MeV, can be removed from the outer radiation belt by EMIC wave scattering during a magnetic storm. That is why the modeling of EMIC waves is critical and timely issue in magnetospheric physics. To describe the RC evolution itself this study uses the ring current-atmosphere interaction model (RAM). RAM solves the gyration and bounce-averaged Boltzmann-Landau equation inside of geosynchronous orbit. Originally developed at the University of Michigan, there are now several branches of this model currently in use as describe by Liemohn namely those at NASA Goddard Space Flight Center This study will generalize the self-consistent theoretical description of RC ions and EMIC waves that has been developed by Khazanov and include the heavy ions and propagation effects of EMIC waves in the global dynamic of self-consistent RC - EMIC waves coupling. The results of our newly developed model that will be presented at GEM meeting, focusing mainly on the dynamic of EMIC waves and comparison of these results with the previous global RC modeling studies devoted to EMIC waves formation. We also discuss RC ion precipitations and wave induced thermal electron fluxes into the ionosphere.

Cylindrical and spherical solitary waves in an electron-acoustic plasma with vortex electron distribution

NASA Astrophysics Data System (ADS)

Demiray, Hilmi; El-Zahar, Essam R.

2018-04-01

We consider the nonlinear propagation of electron-acoustic waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The basic nonlinear equations of the above described plasma are re-examined in the cylindrical (spherical) coordinates by employing the reductive perturbation technique. The modified cylindrical (spherical) KdV equation with fractional power nonlinearity is obtained as the evolution equation. Due to the nature of nonlinearity, this evolution equation cannot be reduced to the conventional KdV equation. A new family of closed form analytical approximate solution to the evolution equation and a comparison with numerical solution are presented and the results are depicted in some 2D and 3D figures. The results reveal that both solutions are in good agreement and the method can be used to obtain a new progressive wave solution for such evolution equations. Moreover, the resulting closed form analytical solution allows us to carry out a parametric study to investigate the effect of the physical parameters on the solution behavior of the modified cylindrical (spherical) KdV equation.

Dark energy as a fixed point of the Einstein Yang-Mills Higgs equations

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

Rinaldi, Massimiliano, E-mail: massimiliano.rinaldi@unitn.it

We study the Einstein Yang-Mills Higgs equations in the SO(3) representation on a isotropic and homogeneous flat Universe, in the presence of radiation and matter fluids. We map the equations of motion into an autonomous dynamical system of first-order differential equations and we find the equilibrium points. We show that there is only one stable fixed point that corresponds to an accelerated expanding Universe in the future. In the past, instead, there is an unstable fixed point that implies a stiff-matter domination. In between, we find three other unstable fixed points, corresponding, in chronological order, to radiation domination, to mattermore » domination, and, finally, to a transition from decelerated expansion to accelerated expansion. We solve the system numerically and we confirm that there are smooth trajectories that correctly describe the evolution of the Universe, from a remote past dominated by radiation to a remote future dominated by dark energy, passing through a matter-dominated phase.« less

Dark energy as a fixed point of the Einstein Yang-Mills Higgs equations

NASA Astrophysics Data System (ADS)

Rinaldi, Massimiliano

2015-10-01

We study the Einstein Yang-Mills Higgs equations in the SO(3) representation on a isotropic and homogeneous flat Universe, in the presence of radiation and matter fluids. We map the equations of motion into an autonomous dynamical system of first-order differential equations and we find the equilibrium points. We show that there is only one stable fixed point that corresponds to an accelerated expanding Universe in the future. In the past, instead, there is an unstable fixed point that implies a stiff-matter domination. In between, we find three other unstable fixed points, corresponding, in chronological order, to radiation domination, to matter domination, and, finally, to a transition from decelerated expansion to accelerated expansion. We solve the system numerically and we confirm that there are smooth trajectories that correctly describe the evolution of the Universe, from a remote past dominated by radiation to a remote future dominated by dark energy, passing through a matter-dominated phase.

Semi-classical statistical description of Fröhlich condensation.

PubMed

Preto, Jordane

2017-06-01

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

Simulation study of the thermal and the thermoelastic effects induced by pulsed laser absorption in human skin

NASA Astrophysics Data System (ADS)

Kim, Jae-Young; Jang, Kyungmin; Yang, Seung-Jin; Baek, Jun-Hyeok; Park, Jong-Rak; Yeom, Dong-Il; Kim, Ji-Sun; Kim, Hyung-Sik; Jun, Jae-Hoon; Chung, Soon-Cheol

2016-04-01

We studied the thermal and the mechanical effects induced by pulsed laser absorption in human skin by numerically solving the heat-transfer and the thermoelastic wave equations. The simulation of the heat-transfer equation yielded the spatiotemporal distribution of the temperature increase in the skin, which was then used in the driving term of the thermoelastic wave equation. We compared our simulation results for the temperature increase and the skin displacements with the measured and numerical results, respectively. For the comparison, we used a recent report by Jun et al. [Sci. Rep. 5, 11016 (2015)], who measured in vivo skin temperature and performed numerical simulation of the thermoelastic wave equation using a simple assumption about the temporal evolution of the temperature distribution, and found their results to be in good agreement with our results. In addition, we obtained solutions for the stresses in the human skin and analyzed their dynamic behaviors in detail.

A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations

PubMed Central

Motsa, S. S.; Magagula, V. M.; Sibanda, P.

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252

A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations.

PubMed

Motsa, S S; Magagula, V M; Sibanda, P

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.

A continuous stochastic model for non-equilibrium dense gases

NASA Astrophysics Data System (ADS)

Sadr, M.; Gorji, M. H.

2017-12-01

While accurate simulations of dense gas flows far from the equilibrium can be achieved by direct simulation adapted to the Enskog equation, the significant computational demand required for collisions appears as a major constraint. In order to cope with that, an efficient yet accurate solution algorithm based on the Fokker-Planck approximation of the Enskog equation is devised in this paper; the approximation is very much associated with the Fokker-Planck model derived from the Boltzmann equation by Jenny et al. ["A solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion," J. Comput. Phys. 229, 1077-1098 (2010)] and Gorji et al. ["Fokker-Planck model for computational studies of monatomic rarefied gas flows," J. Fluid Mech. 680, 574-601 (2011)]. The idea behind these Fokker-Planck descriptions is to project the dynamics of discrete collisions implied by the molecular encounters into a set of continuous Markovian processes subject to the drift and diffusion. Thereby, the evolution of particles representing the governing stochastic process becomes independent from each other and thus very efficient numerical schemes can be constructed. By close inspection of the Enskog operator, it is observed that the dense gas effects contribute further to the advection of molecular quantities. That motivates a modelling approach where the dense gas corrections can be cast in the extra advection of particles. Therefore, the corresponding Fokker-Planck approximation is derived such that the evolution in the physical space accounts for the dense effects present in the pressure, stress tensor, and heat fluxes. Hence the consistency between the devised Fokker-Planck approximation and the Enskog operator is shown for the velocity moments up to the heat fluxes. For validation studies, a homogeneous gas inside a box besides Fourier, Couette, and lid-driven cavity flow setups is considered. The results based on the Fokker-Planck model are compared with respect to benchmark simulations, where good agreement is found for the flow field along with the transport properties.

Organization of the cytokeratin network in an epithelial cell.

PubMed

Portet, Stéphanie; Arino, Ovide; Vassy, Jany; Schoëvaërt, Damien

2003-08-07

The cytoskeleton is a dynamic three-dimensional structure mainly located in the cytoplasm. It is involved in many cell functions such as mechanical signal transduction and maintenance of cell integrity. Among the three cytoskeletal components, intermediate filaments (the cytokeratin in epithelial cells) are the best candidates for this mechanical role. A model of the establishment of the cytokeratin network of an epithelial cell is proposed to study the dependence of its structural organization on extracellular mechanical environment. To implicitly describe the latter and its effects on the intracellular domain, we use mechanically regulated protein synthesis. Our model is a hybrid of a partial differential equation of parabolic type, governing the evolution of the concentration of cytokeratin, and a set of stochastic differential equations describing the dynamics of filaments. Each filament is described by a stochastic differential equation that reflects both the local interactions with the environment and the non-local interactions via the past history of the filament. A three-dimensional simulation model is derived from this mathematical model. This simulation model is then used to obtain examples of cytokeratin network architectures under given mechanical conditions, and to study the influence of several parameters.

Dynamics of double-polarity subduction: application to the Western Mediterranean

NASA Astrophysics Data System (ADS)

Peral, Mireia; Zlotnik, Sergio; Fernandez, Manel; Vergés, Jaume; Jiménez-Munt, Ivone; Torne, Montserrat

2016-04-01

The evolution of the Western Mediterranean is a highly debated question by geologists and geophysicists. Even though most scientists agree in considering slab roll-back to be the driving mechanism of the tectonic evolution of this area, there is still no consensus about the initial setup and its time evolution. A recent model suggests a lateral change in subduction polarity of the Ligurian-Thetys oceanic domain to explain the formation and evolution of the Betic-Rif orogenic system and the associated Alboran back-arc basin. Such geodynamic scenario is also proposed for different converging regions. The aim of this study is to analyze the dynamic evolution of a double-polarity subduction process and its consequences in order to test the physical feasibility of this interaction and provide geometries and evolutions comparable to those proposed for the Western Mediterranean. The 3D numerical model is carried out via the Underworld framework. Tectonic plate behavior is described by equations of fluid dynamics in the presence of several different phases. Underworld solves a non-linear Stokes flow problem using Finite Elements combined with particle-in-cell approach, thus the discretization combines a standard Eulerian Finite Element mesh with Lagrangian particles to track the location of the phases. The final model consists of two oceanic plates with viscoplastic rheology subducting into the upper mantle in opposite direction and the problem is driven by Rayleigh-Taylor instability. We study the influence of the boundary conditions in the model evolution, and the slab deformation produced by the proximity between both plates. Moreover the case of asymmetric friction on the lateral sides of slabs is also considered. Simulations of single subduction models are used as a reference, to compare results and understand the influence of the second plate. We observe slight differences in the trench retreat velocity and the slab morphology near the contact area when plates are spaced less than 100 km.

Quantum critical probing and simulation of colored quantum noise

NASA Astrophysics Data System (ADS)

Mascarenhas, Eduardo; de Vega, Inés

2017-12-01

We propose a protocol to simulate the evolution of a non-Markovian open quantum system by considering a collisional process with a many-body system, which plays the role of an environment. As a result of our protocol, the environment spatial correlations are mapped into the time correlations of a noise that drives the dynamics of the open system. Considering the weak coupling limit, the open system can also be considered as a probe of the environment properties. In this regard, when preparing the environment in its ground state, a measurement of the dynamics of the open system allows to determine the length of the environment spatial correlations and therefore its critical properties. To illustrate our proposal we simulate the full system dynamics with matrix-product-states and compare this to the reduced dynamics obtained with an approximated variational master equation.

Historical evolution of vortex-lattice methods

NASA Technical Reports Server (NTRS)

Deyoung, J.

1976-01-01

A review of the beginning and some orientation of the vortex-lattice method were given. The historical course of this method was followed in conjunction with its field of computational fluid dynamics, spanning the period from L.F. Richardson's paper in 1910 to 1975. The following landmarks were pointed out: numerical analysis of partial differential equations, lifting-line theory, finite-difference method, 1/4-3/4 rule, block relaxation technique, application of electronic computers, and advanced panel methods.

Computational models for the berry phase in semiconductor quantum dots

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

Prabhakar, S., E-mail: rmelnik@wlu.ca; Melnik, R. V. N., E-mail: rmelnik@wlu.ca; Sebetci, A.

2014-10-06

By developing a new model and its finite element implementation, we analyze the Berry phase low-dimensional semiconductor nanostructures, focusing on quantum dots (QDs). In particular, we solve the Schrödinger equation and investigate the evolution of the spin dynamics during the adiabatic transport of the QDs in the 2D plane along circular trajectory. Based on this study, we reveal that the Berry phase is highly sensitive to the Rashba and Dresselhaus spin-orbit lengths.

Taking side effects into account for HIV medication.

PubMed

Costanza, Vicente; Rivadeneira, Pablo S; Biafore, Federico L; D'Attellis, Carlos E

2010-09-01

A control-theoretic approach to the problem of designing "low-side-effects" therapies for HIV patients based on highly active drugs is substantiated here. The evolution of side effects during treatment is modeled by an extra differential equation coupled to the dynamics of virions, healthy T-cells, and infected ones. The new equation reflects the dependence of collateral damages on the amount of each dose administered to the patient and on the evolution of the viral load detected by periodical blood analysis. The cost objective accounts for recommended bounds on healthy cells and virions, and also penalizes the appearance of collateral morbidities caused by the medication. The optimization problem is solved by a hybrid dynamic programming scheme that adhere to discrete-time observation and control actions, but by maintaining the continuous-time setup for predicting states and side effects. The resulting optimal strategies employ less drugs than those prescribed by previous optimization studies, but maintaining high doses at the beginning and the end of each period of six months. If an inverse discount rate is applied to favor early actions, and under a mild penalization of the final viral load, then the optimal doses are found to be high at the beginning and decrease afterward, thus causing an apparent stabilization of the main variables. But in this case, the final viral load turns higher than acceptable.

Cooperation, Norms, and Revolutions: A Unified Game-Theoretical Approach

PubMed Central

Helbing, Dirk; Johansson, Anders

2010-01-01

Background Cooperation is of utmost importance to society as a whole, but is often challenged by individual self-interests. While game theory has studied this problem extensively, there is little work on interactions within and across groups with different preferences or beliefs. Yet, people from different social or cultural backgrounds often meet and interact. This can yield conflict, since behavior that is considered cooperative by one population might be perceived as non-cooperative from the viewpoint of another. Methodology and Principal Findings To understand the dynamics and outcome of the competitive interactions within and between groups, we study game-dynamical replicator equations for multiple populations with incompatible interests and different power (be this due to different population sizes, material resources, social capital, or other factors). These equations allow us to address various important questions: For example, can cooperation in the prisoner's dilemma be promoted, when two interacting groups have different preferences? Under what conditions can costly punishment, or other mechanisms, foster the evolution of norms? When does cooperation fail, leading to antagonistic behavior, conflict, or even revolutions? And what incentives are needed to reach peaceful agreements between groups with conflicting interests? Conclusions and Significance Our detailed quantitative analysis reveals a large variety of interesting results, which are relevant for society, law and economics, and have implications for the evolution of language and culture as well. PMID:20967256

Discrete and Continuum Approximations for Collective Cell Migration in a Scratch Assay with Cell Size Dynamics.

PubMed

Matsiaka, Oleksii M; Penington, Catherine J; Baker, Ruth E; Simpson, Matthew J

2018-04-01

Scratch assays are routinely used to study the collective spreading of cell populations. In general, the rate at which a population of cells spreads is driven by the combined effects of cell migration and proliferation. To examine the effects of cell migration separately from the effects of cell proliferation, scratch assays are often performed after treating the cells with a drug that inhibits proliferation. Mitomycin-C is a drug that is commonly used to suppress cell proliferation in this context. However, in addition to suppressing cell proliferation, mitomycin-C also causes cells to change size during the experiment, as each cell in the population approximately doubles in size as a result of treatment. Therefore, to describe a scratch assay that incorporates the effects of cell-to-cell crowding, cell-to-cell adhesion, and dynamic changes in cell size, we present a new stochastic model that incorporates these mechanisms. Our agent-based stochastic model takes the form of a system of Langevin equations that is the system of stochastic differential equations governing the evolution of the population of agents. We incorporate a time-dependent interaction force that is used to mimic the dynamic increase in size of the agents. To provide a mathematical description of the average behaviour of the stochastic model we present continuum limit descriptions using both a standard mean-field approximation and a more sophisticated moment dynamics approximation that accounts for the density of agents and density of pairs of agents in the stochastic model. Comparing the accuracy of the two continuum descriptions for a typical scratch assay geometry shows that the incorporation of agent growth in the system is associated with a decrease in accuracy of the standard mean-field description. In contrast, the moment dynamics description provides a more accurate prediction of the evolution of the scratch assay when the increase in size of individual agents is included in the model.

Dynamic Characteristics of Positive Pulsed Dielectric Barrier Discharge for Ozone Generation in Air

NASA Astrophysics Data System (ADS)

Wei, Linsheng; Peng, Bangfa; Li, Ming; Zhang, Yafang; Hu, Zhaoji

2016-02-01

A comprehensive dynamic model consisting of 66 reactions and 24 species is developed to investigate the dynamic characteristics of ozone generation by positive pulsed dielectric barrier discharge (DBD) using parallel-plate reactor in air. The electron energy conservation equation is coupled to the electron continuity equation, the heavy species continuity equation, and Poisson's equation for a better description. The reliability of the model is experimentally confirmed. The model can be used to predict the temporal and spatial evolution of species, as well as streamer propagation. The simulation results show that electron density increases nearly exponentially in the direction to the anode at the electron avalanche. Streamer propagation velocity is about 5.26 × 104 m/s from anode to cathode in the simulated condition. The primary positive ion, negative ion, and excited species are O2+, O3- and O2(1Δg) in pulsed DBD in air, respectively. N2O has the largest density among nitrogen oxides. e and N2+ densities in the streamer head increase gradually to maximum values with the development of the streamer. Meanwhile, the O2+, O, O3, N2(A3Σ) and N2O densities reach maximum values in the vicinity of the anode. supported by National Natural Science Foundation of China (Nos. 51366012 and 11105067), Jiangxi Province Young Scientists (Jinggang Star) Cultivation Plan of China (No. 20133BCB23008), Natural Science Foundation of Jiangxi, China (No. 20151BAB206047) and Jiangxi Province Higher School Science and Technology Landing Plan of China (No. KJLD-14015)

Why there is no Newtonian backreaction

NASA Astrophysics Data System (ADS)

Kaiser, Nick

2017-07-01

In the conventional framework for cosmological dynamics, the scalefactor a(t) is assumed to obey the 'background' Friedmann equation for a perfectly homogeneous universe while particles move according to equations of motions driven by the gravity of the density fluctuations. It has recently been suggested that the emergence of structure modifies the evolution of a(t) via Newtonian (or 'kinematic') backreaction and that this may avoid the need for dark energy. Here, we point out that the conventional system of equations is exact in Newtonian gravity and there is no approximation in the use of the homogeneous universe equation for a(t). The recently proposed modification of Rácz et al. does not reduce to Newtonian gravity in the limit of low velocities. We discuss the relation of this to the 'generalized Friedmann equation' of Buchert and Ehlers. These are quite different things; their formula describes individual regions and is obtained under the restrictive assumption that the matter behaves like a pressure-free fluid, whereas our result is exact for collisionless dynamics and is an auxiliary relation appearing in the structure equations. We use the symmetry of the general velocity autocorrelation function to show how Buchert's Q tends very rapidly to zero for large volume and that this does not simply arise 'by construction' through the adoption of periodic boundary conditions as has been claimed. We conclude that, to the extent that Newtonian gravity accurately describes the low-z universe, there is no backreaction of structure on a(t) and that the need for dark energy cannot be avoided in this way.

Instability of 2D Flows to Hydrostatic 3D Perturbations.

NASA Astrophysics Data System (ADS)

Straub, David N.

2003-01-01

Considered here is the evolution of three-dimensional perturbations to the hydrostatic equations linearized about a two-dimensional base state U. Motivated by an argument by T. Warn, this study begins with the nonrotating, unstratified case, and draws analogies between the perturbation equations and equations describing evolution of material line elements and scalar gradients embedded in the same 2D flow. When U is chaotic, both scalar gradients and line elements are characterized by rapid growth, and this leads one to suspect that the perturbations behave similarly. A generalized Okubo-Weiss parameter is proposed, and it is argued that this gives a reasonable litmus test for identifying regions where growth is most probable. Rotation modifies the generalized Okubo-Weiss parameter and tends to curb growth of the perturbation fields, as expected. It is also pointed out that, in realistic geophysical settings, the stability parameter can be suggestive of growth locally, even when a globally defined Rossby number is small.Also considered is the effect of a constant stratification. The perturbation equations can then be separated into vertical modes that have simple sinusoidal structures. The equations describing the evolution of a given mode take a form analogous to the shallow water equations, linearized about U. Numerical simulations of these, assuming a simple but chaotic prescription of U, are carried out. For sufficiently strong stratification, a balance dynamics similar to that suggested by Riley, Metcalfe, and Weissman is recovered. For a given value of the buoyancy frequency N, however, this balance breaks down at high vertical wavenumbers. For high vertical wavenumbers, the modified Okubo-Weiss parameter once again appears to give a potentially useful indication of when growth should be expected. When the Rossby number is small, this criterion predicts stability, and growth occurs only when stratification effects are comparable to or larger than rotational effects. More specifically, growth is seen when the relevant Rossby radius is comparable to or larger than the characteristic length scale of U. It is also found in this limit that approximate geostrophic adjustment occurs prior to growth.

A Pair of Resonance Stripe Solitons and Lump Solutions to a Reduced (3+1)-Dimensional Nonlinear Evolution Equation

NASA Astrophysics Data System (ADS)

Chen, Mei-Dan; Li, Xian; Wang, Yao; Li, Biao

2017-06-01

With symbolic computation, some lump solutions are presented to a (3+1)-dimensional nonlinear evolution equation by searching the positive quadratic function from the Hirota bilinear form of equation. The quadratic function contains six free parameters, four of which satisfy two determinant conditions guaranteeing analyticity and rational localization of the solutions, while the others are free. Then, by combining positive quadratic function with exponential function, the interaction solutions between lump solutions and the stripe solitons are presented on the basis of some conditions. Furthermore, we extend this method to obtain more general solutions by combining of positive quadratic function and hyperbolic cosine function. Thus the interaction solutions between lump solutions and a pair of resonance stripe solitons are derived and asymptotic property of the interaction solutions are analyzed under some specific conditions. Finally, the dynamic properties of these solutions are shown in figures by choosing the values of the parameters. Supported by National Natural Science Foundation of China under Grant Nos. 11271211, 11275072, and 11435005, Ningbo Natural Science Foundation under Grant No. 2015A610159 and the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No. xkzw11502 and K.C. Wong Magna Fund in Ningbo University

Continued-fraction representation of the Kraus map for non-Markovian reservoir damping

NASA Astrophysics Data System (ADS)

van Wonderen, A. J.; Suttorp, L. G.

2018-04-01

Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative dynamics as determined by the unitary evolution of system and reservoir is described by a Kraus map consisting of an infinite number of matrices. For all Laplace-transformed Kraus matrices exact solutions are constructed in terms of continued fractions that depend on the pair correlation functions of the reservoir. By performing factorizations in the Kraus map a perturbation theory is set up that conserves in arbitrary perturbative order both positivity and probability of the density matrix. The latter is determined by an integral equation for a bitemporal matrix and a finite hierarchy for Kraus matrices. In the lowest perturbative order this hierarchy reduces to one equation for one Kraus matrix. Its solution is given by a continued fraction of a much simpler structure as compared to the non-perturbative case. In the lowest perturbative order our non-Markovian evolution equations are applied to the damped Jaynes–Cummings model. From the solution for the atomic density matrix it is found that the atom may remain in the state of maximum entropy for a significant time span that depends on the initial energy of the radiation field.

Time Asymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

Bohm, Arno R.; Gadella, Manuel; Kielanowski, Piotr

2011-09-01

The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t0≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.

Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves

NASA Astrophysics Data System (ADS)

El, G. A.; Khamis, E. G.; Tovbis, A.

2016-09-01

We propose a novel, analytically tractable, scenario of the rogue wave formation in the framework of the small-dispersion focusing nonlinear Schrödinger (NLS) equation with the initial condition in the form of a rectangular barrier (a ‘box’). We use the Whitham modulation theory combined with the nonlinear steepest descent for the semi-classical inverse scattering transform, to describe the evolution and interaction of two counter-propagating nonlinear wave trains—the dispersive dam break flows—generated in the NLS box problem. We show that the interaction dynamics results in the emergence of modulated large-amplitude quasi-periodic breather lattices whose amplitude profiles are closely approximated by the Akhmediev and Peregrine breathers within certain space-time domain. Our semi-classical analytical results are shown to be in excellent agreement with the results of direct numerical simulations of the small-dispersion focusing NLS equation.

Hydrodynamical Aspects of the Formation of Spiral-Vortical Structures in Rotating Gaseous Disks

NASA Astrophysics Data System (ADS)

Elizarova, T. G.; Zlotnik, A. A.; Istomina, M. A.

2018-01-01

This paper is dedicated to numerical simulations of spiral-vortical structures in rotating gaseous disks using a simple model based on two-dimensional, non-stationary, barotropic Euler equations with a body force. The results suggest the possibility of a purely hydrodynamical basis for the formation and evolution of such structures. New, axially symmetric, stationary solutions of these equations are derived that modify known approximate solutions. These solutions with added small perturbations are used as initial data in the non-stationary problem, whose solution demonstrates the formation of density arms with bifurcation. The associated redistribution of angular momentum is analyzed. The correctness of laboratory experiments using shallow water to describe the formation of large-scale vortical structures in thin gaseous disks is confirmed. The computations are based on a special quasi-gas-dynamical regularization of the Euler equations in polar coordinates.

A numerical relativity scheme for cosmological simulations

NASA Astrophysics Data System (ADS)

Daverio, David; Dirian, Yves; Mitsou, Ermis

2017-12-01

Cosmological simulations involving the fully covariant gravitational dynamics may prove relevant in understanding relativistic/non-linear features and, therefore, in taking better advantage of the upcoming large scale structure survey data. We propose a new 3  +  1 integration scheme for general relativity in the case where the matter sector contains a minimally-coupled perfect fluid field. The original feature is that we completely eliminate the fluid components through the constraint equations, thus remaining with a set of unconstrained evolution equations for the rest of the fields. This procedure does not constrain the lapse function and shift vector, so it holds in arbitrary gauge and also works for arbitrary equation of state. An important advantage of this scheme is that it allows one to define and pass an adaptation of the robustness test to the cosmological context, at least in the case of pressureless perfect fluid matter, which is the relevant one for late-time cosmology.

Phase space of modified Gauss-Bonnet gravity.

PubMed

Carloni, Sante; Mimoso, José P

2017-01-01

We investigate the evolution of non-vacuum Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes with any spatial curvature in the context of Gauss-Bonnet gravity. The analysis employs a new method which enables us to explore the phase space of any specific theory of this class. We consider several examples, discussing the transition from a decelerating into an acceleration universe within these theories. We also deduce from the dynamical equations some general conditions on the form of the action which guarantee the presence of specific behaviours like the emergence of accelerated expansion. As in f ( R ) gravity, our analysis shows that there is a set of initial conditions for which these models have a finite time singularity which can be an attractor. The presence of this instability also in the Gauss-Bonnet gravity is to be ascribed to the fourth-order derivative in the field equations, i.e., is the direct consequence of the higher order of the equations.

Entanglement dynamics in random media

NASA Astrophysics Data System (ADS)

Menezes, G.; Svaiter, N. F.; Zarro, C. A. D.

2017-12-01

We study how the entanglement dynamics between two-level atoms is impacted by random fluctuations of the light cone. In our model the two-atom system is envisaged as an open system coupled with an electromagnetic field in the vacuum state. We employ the quantum master equation in the Born-Markov approximation in order to describe the completely positive time evolution of the atomic system. We restrict our investigations to the situation in which the atoms are coupled individually to two spatially separated cavities, one of which displays the emergence of light-cone fluctuations. In such a disordered cavity, we assume that the coefficients of the Klein-Gordon equation are random functions of the spatial coordinates. The disordered medium is modeled by a centered, stationary, and Gaussian process. We demonstrate that disorder has the effect of slowing down the entanglement decay. We conjecture that in a strong-disorder environment the mean life of entangled states can be enhanced in such a way as to almost completely suppress quantum nonlocal decoherence.

A master equation approach to actin polymerization applied to endocytosis in yeast.

PubMed

Wang, Xinxin; Carlsson, Anders E

2017-12-01

We present a Master Equation approach to calculating polymerization dynamics and force generation by branched actin networks at membranes. The method treats the time evolution of the F-actin distribution in three dimensions, with branching included as a directional spreading term. It is validated by comparison with stochastic simulations of force generation by actin polymerization at obstacles coated with actin "nucleation promoting factors" (NPFs). The method is then used to treat the dynamics of actin polymerization and force generation during endocytosis in yeast, using a model in which NPFs form a ring around the endocytic site, centered by a spot of molecules attaching the actin network strongly to the membrane. We find that a spontaneous actin filament nucleation mechanism is required for adequate forces to drive the process, that partial inhibition of branching and polymerization lead to different characteristic responses, and that a limited range of polymerization-rate values provide effective invagination and obtain correct predictions for the effects of mutations in the active regions of the NPFs.

Reconstructing the intermittent dynamics of the torque in wind turbines

NASA Astrophysics Data System (ADS)

Lind, Pedro G.; Wächter, Matthias; Peinke, Joachim

2014-06-01

We apply a framework introduced in the late nineties to analyze load measurements in off-shore wind energy converters (WEC). The framework is borrowed from statistical physics and properly adapted to the analysis of multivariate data comprising wind velocity, power production and torque measurements, taken at one single WEC. In particular, we assume that wind statistics drives the fluctuations of the torque produced in the wind turbine and show how to extract an evolution equation of the Langevin type for the torque driven by the wind velocity. It is known that the intermittent nature of the atmosphere, i.e. of the wind field, is transferred to the power production of a wind energy converter and consequently to the shaft torque. We show that the derived stochastic differential equation quantifies the dynamical coupling of the measured fluctuating properties as well as it reproduces the intermittency observed in the data. Finally, we discuss our approach in the light of turbine monitoring, a particular important issue in off-shore wind farms.

Cluster dynamics of pulse coupled oscillators

NASA Astrophysics Data System (ADS)

O'Keeffe, Kevin; Strogatz, Steven; Krapivsky, Paul

2015-03-01

We study the dynamics of networks of pulse coupled oscillators. Much attention has been devoted to the ultimate fate of the system: which conditions lead to a steady state in which all the oscillators are firing synchronously. But little is known about how synchrony builds up from an initially incoherent state. The current work addresses this question. Oscillators start to synchronize by forming clusters of different sizes that fire in unison. First pairs of oscillators, then triplets and so on. These clusters progressively grow by coalescing with others, eventually resulting in the fully synchronized state. We study the mean field model in which the coupling between oscillators is all to all. We use probabilistic arguments to derive a recursive set of evolution equations for these clusters. Using a generating function formalism, we derive simple equations for the moments of these clusters. Our results are in good agreement simulation. We then numerically explore the effects of non-trivial connectivity. Our results have potential application to ultra-low power ``impulse radio'' & sensor networks.

Kinetic Analysis of Weakly ionized Plasmas in presence of collecting walls

NASA Astrophysics Data System (ADS)

Gonzalez, J.; Donoso, J. M.

2018-02-01

Description of plasmas in contact with a wall able to collecting or emitting charged particles is a research topic of great importance. This situation arises in a great variety of phenomena such as the characterization of plasmas by means of electric probes, in the surface treatment of materials and in the service-life of coatings in electric thrusters. In particular, in this work we devote attention to the dynamics of an argon weakly ionized plasma in the presence of a collecting wall. It is proposed a kinetic model in a 1D1V planar phase-space geometry. The model accounts for the electric field coupled to the system by solving the associated Poisson’s equation. To solve numerically the resulting non-linear system of equations, the Propagator Integral Method is used in conjunction with a slabbing method. On each interrelating plasma slab the integral advancing scheme operates in velocity space, in such a way that the all the species dynamics dominating the system evolution are kinetically described.

Stability analysis of confined V-shaped flames in high-velocity streams.

PubMed

El-Rabii, Hazem; Joulin, Guy; Kazakov, Kirill A

2010-06-01

The problem of linear stability of confined V-shaped flames with arbitrary gas expansion is addressed. Using the on-shell description of flame dynamics, a general equation governing propagation of disturbances of an anchored flame is obtained. This equation is solved analytically for V-flames anchored in high-velocity channel streams. It is demonstrated that dynamics of the flame disturbances in this case is controlled by the memory effects associated with vorticity generated by the perturbed flame. The perturbation growth rate spectrum is determined, and explicit analytical expressions for the eigenfunctions are given. It is found that the piecewise linear V structure is unstable for all values of the gas expansion coefficient. Despite the linearity of the basic pattern, however, evolutions of the V-flame disturbances are completely different from those found for freely propagating planar flames or open anchored flames. The obtained results reveal strong influence of the basic flow and the channel walls on the stability properties of confined V-flames.