Interacting particle systems in time-dependent geometries

NASA Astrophysics Data System (ADS)

Ali, A.; Ball, R. C.; Grosskinsky, S.; Somfai, E.

2013-09-01

Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be described effectively by space-time trajectories of interacting particles, such as domain boundaries in two-dimensional growth or river networks. We study trajectories embedded in time-dependent geometries, and the main focus is on uniformly expanding or decreasing domains for which we obtain an exact mapping to simple fixed domain systems while preserving the local scale invariance properties. This approach was recently introduced in Ali et al (2013 Phys. Rev. E 87 020102(R)) and here we provide a detailed discussion on its applicability for self-affine Markovian models, and how it can be adapted to self-affine models with memory or explicit time dependence. The mapping corresponds to a nonlinear time transformation which converges to a finite value for a large class of trajectories, enabling an exact analysis of asymptotic properties in expanding domains. We further provide a detailed discussion of different particle interactions and generalized geometries. All our findings are based on exact computations and are illustrated numerically for various examples, including Lévy processes and fractional Brownian motion.

Exact synchronization bound for coupled time-delay systems.

PubMed

Senthilkumar, D V; Pesquera, Luis; Banerjee, Santo; Ortín, Silvia; Kurths, J

2013-04-01

We obtain an exact bound for synchronization in coupled time-delay systems using the generalized Halanay inequality for the general case of time-dependent delay, coupling, and coefficients. Furthermore, we show that the same analysis is applicable to both uni- and bidirectionally coupled time-delay systems with an appropriate evolution equation for their synchronization manifold, which can also be defined for different types of synchronization. The exact synchronization bound assures an exponential stabilization of the synchronization manifold which is crucial for applications. The analytical synchronization bound is independent of the nature of the modulation and can be applied to any time-delay system satisfying a Lipschitz condition. The analytical results are corroborated numerically using the Ikeda system.

Exact Time-Dependent Exchange-Correlation Potential in Electron Scattering Processes

NASA Astrophysics Data System (ADS)

Suzuki, Yasumitsu; Lacombe, Lionel; Watanabe, Kazuyuki; Maitra, Neepa T.

2017-12-01

We identify peak and valley structures in the exact exchange-correlation potential of time-dependent density functional theory that are crucial for time-resolved electron scattering in a model one-dimensional system. These structures are completely missed by adiabatic approximations that, consequently, significantly underestimate the scattering probability. A recently proposed nonadiabatic approximation is shown to correctly capture the approach of the electron to the target when the initial Kohn-Sham state is chosen judiciously, and it is more accurate than standard adiabatic functionals but ultimately fails to accurately capture reflection. These results may explain the underestimation of scattering probabilities in some recent studies on molecules and surfaces.

Numerically exact full counting statistics of the nonequilibrium Anderson impurity model

NASA Astrophysics Data System (ADS)

Ridley, Michael; Singh, Viveka N.; Gull, Emanuel; Cohen, Guy

2018-03-01

The time-dependent full counting statistics of charge transport through an interacting quantum junction is evaluated from its generating function, controllably computed with the inchworm Monte Carlo method. Exact noninteracting results are reproduced; then, we continue to explore the effect of electron-electron interactions on the time-dependent charge cumulants, first-passage time distributions, and n -electron transfer distributions. We observe a crossover in the noise from Coulomb blockade to Kondo-dominated physics as the temperature is decreased. In addition, we uncover long-tailed spin distributions in the Kondo regime and analyze queuing behavior caused by correlations between single-electron transfer events.

Numerically exact full counting statistics of the nonequilibrium Anderson impurity model

DOE PAGES

Ridley, Michael; Singh, Viveka N.; Gull, Emanuel; ...

2018-03-06

The time-dependent full counting statistics of charge transport through an interacting quantum junction is evaluated from its generating function, controllably computed with the inchworm Monte Carlo method. Exact noninteracting results are reproduced; then, we continue to explore the effect of electron-electron interactions on the time-dependent charge cumulants, first-passage time distributions, and n-electron transfer distributions. We observe a crossover in the noise from Coulomb blockade to Kondo-dominated physics as the temperature is decreased. In addition, we uncover long-tailed spin distributions in the Kondo regime and analyze queuing behavior caused by correlations between single-electron transfer events

Numerically exact full counting statistics of the nonequilibrium Anderson impurity model

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

Ridley, Michael; Singh, Viveka N.; Gull, Emanuel

The time-dependent full counting statistics of charge transport through an interacting quantum junction is evaluated from its generating function, controllably computed with the inchworm Monte Carlo method. Exact noninteracting results are reproduced; then, we continue to explore the effect of electron-electron interactions on the time-dependent charge cumulants, first-passage time distributions, and n-electron transfer distributions. We observe a crossover in the noise from Coulomb blockade to Kondo-dominated physics as the temperature is decreased. In addition, we uncover long-tailed spin distributions in the Kondo regime and analyze queuing behavior caused by correlations between single-electron transfer events

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

NASA Astrophysics Data System (ADS)

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

2009-12-01

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

Wave Functions for Time-Dependent Dirac Equation under GUP

NASA Astrophysics Data System (ADS)

Zhang, Meng-Yao; Long, Chao-Yun; Long, Zheng-Wen

2018-04-01

In this work, the time-dependent Dirac equation is investigated under generalized uncertainty principle (GUP) framework. It is possible to construct the exact solutions of Dirac equation when the time-dependent potentials satisfied the proper conditions. In (1+1) dimensions, the analytical wave functions of the Dirac equation under GUP have been obtained for the two kinds time-dependent potentials. Supported by the National Natural Science Foundation of China under Grant No. 11565009

Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

NASA Astrophysics Data System (ADS)

Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan

2018-01-01

In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

Exact time-dependent nonlinear dispersive wave solutions in compressible magnetized plasmas exhibiting collapse.

PubMed

Chakrabarti, Nikhil; Maity, Chandan; Schamel, Hans

2011-04-08

Compressional waves in a magnetized plasma of arbitrary resistivity are treated with the lagrangian fluid approach. An exact nonlinear solution with a nontrivial space and time dependence is obtained with boundary conditions as in Harris' current sheet. The solution shows competition among hydrodynamic convection, magnetic field diffusion, and dispersion. This results in a collapse of density and the magnetic field in the absence of dispersion. The dispersion effects arrest the collapse of density but not of the magnetic field. A possible application is in the early stage of magnetic star formation.

Simulation of biochemical reactions with time-dependent rates by the rejection-based algorithm

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

Thanh, Vo Hong, E-mail: vo@cosbi.eu; Priami, Corrado, E-mail: priami@cosbi.eu; Department of Mathematics, University of Trento, Trento

We address the problem of simulating biochemical reaction networks with time-dependent rates and propose a new algorithm based on our rejection-based stochastic simulation algorithm (RSSA) [Thanh et al., J. Chem. Phys. 141(13), 134116 (2014)]. The computation for selecting next reaction firings by our time-dependent RSSA (tRSSA) is computationally efficient. Furthermore, the generated trajectory is exact by exploiting the rejection-based mechanism. We benchmark tRSSA on different biological systems with varying forms of reaction rates to demonstrate its applicability and efficiency. We reveal that for nontrivial cases, the selection of reaction firings in existing algorithms introduces approximations because the integration of reactionmore » rates is very computationally demanding and simplifying assumptions are introduced. The selection of the next reaction firing by our approach is easier while preserving the exactness.« less

A large class of solvable multistate Landau–Zener models and quantum integrability

NASA Astrophysics Data System (ADS)

Chernyak, Vladimir Y.; Sinitsyn, Nikolai A.; Sun, Chen

2018-06-01

The concept of quantum integrability has been introduced recently for quantum systems with explicitly time-dependent Hamiltonians (Sinitsyn et al 2018 Phys. Rev. Lett. 120 190402). Within the multistate Landau–Zener (MLZ) theory, however, there has been a successful alternative approach to identify and solve complex time-dependent models (Sinitsyn and Chernyak 2017 J. Phys. A: Math. Theor. 50 255203). Here we compare both methods by applying them to a new class of exactly solvable MLZ models. This class contains systems with an arbitrary number of interacting states and shows quick growth with N number of exact adiabatic energy crossing points, which appear at different moments of time. At each N, transition probabilities in these systems can be found analytically and exactly but complexity and variety of solutions in this class also grow with N quickly. We illustrate how common features of solvable MLZ systems appear from quantum integrability and develop an approach to further classification of solvable MLZ problems.

Numerical simulations of piecewise deterministic Markov processes with an application to the stochastic Hodgkin-Huxley model.

PubMed

Ding, Shaojie; Qian, Min; Qian, Hong; Zhang, Xuejuan

2016-12-28

The stochastic Hodgkin-Huxley model is one of the best-known examples of piecewise deterministic Markov processes (PDMPs), in which the electrical potential across a cell membrane, V(t), is coupled with a mesoscopic Markov jump process representing the stochastic opening and closing of ion channels embedded in the membrane. The rates of the channel kinetics, in turn, are voltage-dependent. Due to this interdependence, an accurate and efficient sampling of the time evolution of the hybrid stochastic systems has been challenging. The current exact simulation methods require solving a voltage-dependent hitting time problem for multiple path-dependent intensity functions with random thresholds. This paper proposes a simulation algorithm that approximates an alternative representation of the exact solution by fitting the log-survival function of the inter-jump dwell time, H(t), with a piecewise linear one. The latter uses interpolation points that are chosen according to the time evolution of the H(t), as the numerical solution to the coupled ordinary differential equations of V(t) and H(t). This computational method can be applied to all PDMPs. Pathwise convergence of the approximated sample trajectories to the exact solution is proven, and error estimates are provided. Comparison with a previous algorithm that is based on piecewise constant approximation is also presented.

Generalized Success-Breeds-Success Principle Leading to Time-Dependent Informetric Distributions.

ERIC Educational Resources Information Center

Egghe, Leo; Rousseau, Ronald

1995-01-01

Reformulates the success-breeds-success (SBS) principle in informetrics in order to generate a general theory of source-item relationships. Topics include a time-dependent probability, a new model for the expected probability that is compared with the SBS principle with exact combinatorial calculations, classical frequency distributions, and…

Discontinuous functional for linear-response time-dependent density-functional theory: The exact-exchange kernel and approximate forms

NASA Astrophysics Data System (ADS)

Hellgren, Maria; Gross, E. K. U.

2013-11-01

We present a detailed study of the exact-exchange (EXX) kernel of time-dependent density-functional theory with an emphasis on its discontinuity at integer particle numbers. It was recently found that this exact property leads to sharp peaks and step features in the kernel that diverge in the dissociation limit of diatomic systems [Hellgren and Gross, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.85.022514 85, 022514 (2012)]. To further analyze the discontinuity of the kernel, we here make use of two different approximations to the EXX kernel: the Petersilka Gossmann Gross (PGG) approximation and a common energy denominator approximation (CEDA). It is demonstrated that whereas the PGG approximation neglects the discontinuity, the CEDA includes it explicitly. By studying model molecular systems it is shown that the so-called field-counteracting effect in the density-functional description of molecular chains can be viewed in terms of the discontinuity of the static kernel. The role of the frequency dependence is also investigated, highlighting its importance for long-range charge-transfer excitations as well as inner-shell excitations.

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

NASA Astrophysics Data System (ADS)

Kovchegov, Yuri V.; Wu, Bin

2018-03-01

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

Electron localisation in static and time-dependent one-dimensional model systems

NASA Astrophysics Data System (ADS)

Durrant, T. R.; Hodgson, M. J. P.; Ramsden, J. D.; Godby, R. W.

2018-02-01

The most direct signature of electron localisation is the tendency of an electron in a many-body system to exclude other same-spin electrons from its vicinity. By applying this concept directly to the exact many-body wavefunction, we find that localisation can vary considerably between different ground-state systems, and can also be strongly disrupted, as a function of time, when a system is driven by an applied electric field. We use this measure to assess the well-known electron localisation function (ELF), both in its approximate single-particle form (often applied within density-functional theory) and its full many-particle form. The full ELF always gives an excellent description of localisation, but the approximate ELF fails in time-dependent situations, even when the exact Kohn-Sham orbitals are employed.

Entanglement dynamics following a sudden quench: An exact solution

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Exact solutions to force-free electrodynamics in black hole backgrounds

NASA Astrophysics Data System (ADS)

Brennan, T. Daniel; Gralla, Samuel E.; Jacobson, Ted

2013-10-01

A shared property of several of the known exact solutions to the equations of force-free electrodynamics is that their charge-current four-vector is null. We examine the general properties of null-current solutions and then focus on the principal congruences of the Kerr black hole spacetime. We obtain a large class of exact solutions, which are in general time-dependent and non-axisymmetric. These solutions include waves that, surprisingly, propagate without scattering on the curvature of the black hole’s background. They may be understood as generalizations to Robinson’s solutions to vacuum electrodynamics associated with a shear-free congruence of null geodesics. When stationary and axisymmetric, our solutions reduce to those of Menon and Dermer, the only previously known solutions in Kerr. In Kerr, all of our solutions have null electromagnetic fields (\\vec{E} \\cdot \\vec{B} = 0 and E2 = B2). However, in Schwarzschild or flat spacetime there is freedom to add a magnetic monopole field, making the solutions magnetically dominated (B2 > E2). This freedom may be used to reproduce the various flat-spacetime and Schwarzschild-spacetime (split) monopole solutions available in the literature (due to Michel and later authors), and to obtain a large class of time-dependent, non-axisymmetric generalizations. These generalizations may be used to model the magnetosphere of a conducting star that rotates with arbitrary prescribed time-dependent rotation axis and speed. We thus significantly enlarge the class of known exact solutions, while organizing and unifying previously discovered solutions in terms of their null structure.

Integrable Time-Dependent Quantum Hamiltonians

NASA Astrophysics Data System (ADS)

Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.; Patra, Aniket; Sun, Chen

2018-05-01

We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.

Ultrafast strong-field photoelectron emission from biased metal surfaces: exact solution to time-dependent Schrödinger Equation

PubMed Central

Zhang, Peng; Lau, Y. Y.

2016-01-01

Laser-driven ultrafast electron emission offers the possibility of manipulation and control of coherent electron motion in ultrashort spatiotemporal scales. Here, an analytical solution is constructed for the highly nonlinear electron emission from a dc biased metal surface illuminated by a single frequency laser, by solving the time-dependent Schrödinger equation exactly. The solution is valid for arbitrary combinations of dc electric field, laser electric field, laser frequency, metal work function and Fermi level. Various emission mechanisms, such as multiphoton absorption or emission, optical or dc field emission, are all included in this single formulation. The transition between different emission processes is analyzed in detail. The time-dependent emission current reveals that intense current modulation may be possible even with a low intensity laser, by merely increasing the applied dc bias. The results provide insights into the electron pulse generation and manipulation for many novel applications based on ultrafast laser-induced electron emission. PMID:26818710

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

NASA Astrophysics Data System (ADS)

Scopa, Stefano; Unterberger, Jéremie; Karevski, Dragi

2018-05-01

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

Zone clearance in an infinite TASEP with a step initial condition

NASA Astrophysics Data System (ADS)

Cividini, Julien; Appert-Rolland, Cécile

2017-06-01

The TASEP is a paradigmatic model of out-of-equilibrium statistical physics, for which many quantities have been computed, either exactly or by approximate methods. In this work we study two new kinds of observables that have some relevance in biological or traffic models. They represent the probability for a given clearance zone of the lattice to be empty (for the first time) at a given time, starting from a step density profile. Exact expressions are obtained for single-time quantities, while more involved history-dependent observables are studied by Monte Carlo simulation, and partially predicted by a phenomenological approach.

LETTER TO THE EDITOR: Exact energy distribution function in a time-dependent harmonic oscillator

NASA Astrophysics Data System (ADS)

Robnik, Marko; Romanovski, Valery G.; Stöckmann, Hans-Jürgen

2006-09-01

Following a recent work by Robnik and Romanovski (2006 J. Phys. A: Math. Gen. 39 L35, 2006 Open Syst. Inf. Dyn. 13 197-222), we derive an explicit formula for the universal distribution function of the final energies in a time-dependent 1D harmonic oscillator, whose functional form does not depend on the details of the frequency ω(t) and is closely related to the conservation of the adiabatic invariant. The normalized distribution function is P(x) = \\pi^{-1} (2\\mu^2 - x^2)^{-\\frac{1}{2}} , where x=E_1- \\skew3\\bar{E}_1 ; E1 is the final energy, \\skew3\\bar{E}_1 is its average value and µ2 is the variance of E1. \\skew3\\bar{E}_1 and µ2 can be calculated exactly using the WKB approach to all orders.

Wide localized solutions of the parity-time-symmetric nonautonomous nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Meza, L. E. Arroyo; Dutra, A. de Souza; Hott, M. B.; Roy, P.

2015-01-01

By using canonical transformations we obtain localized (in space) exact solutions of the nonlinear Schrödinger equation (NLSE) with cubic and quintic space and time modulated nonlinearities and in the presence of time-dependent and inhomogeneous external potentials and amplification or absorption (source or drain) coefficients. We obtain a class of wide localized exact solutions of NLSE in the presence of a number of non-Hermitian parity-time (PT )-symmetric external potentials, which are constituted by a mixing of external potentials and source or drain terms. The exact solutions found here can be applied to theoretical studies of ultrashort pulse propagation in optical fibers with focusing and defocusing nonlinearities. We show that, even in the presence of gain or loss terms, stable solutions can be found and that the PT symmetry is an important feature to guarantee the conservation of the average energy of the system.

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

NASA Astrophysics Data System (ADS)

Kurzweil, Yair; Head-Gordon, Martin

2009-07-01

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

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

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

Kurzweil, Yair; Head-Gordon, Martin

2009-07-15

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

Exact analytic solution for non-linear density fluctuation in a ΛCDM universe

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

Yoo, Jaiyul; Gong, Jinn-Ouk, E-mail: jyoo@physik.uzh.ch, E-mail: jinn-ouk.gong@apctp.org

We derive the exact third-order analytic solution of the matter density fluctuation in the proper-time hypersurface in a ΛCDM universe, accounting for the explicit time-dependence and clarifying the relation to the initial condition. Furthermore, we compare our analytic solution to the previous calculation in the comoving gauge, and to the standard Newtonian perturbation theory by providing Fourier kernels for the relativistic effects. Our results provide an essential ingredient for a complete description of galaxy bias in the relativistic context.

Optimized effective potential in real time: Problems and prospects in time-dependent density-functional theory

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

Mundt, Michael; Kuemmel, Stephan

2006-08-15

The integral equation for the time-dependent optimized effective potential (TDOEP) in time-dependent density-functional theory is transformed into a set of partial-differential equations. These equations only involve occupied Kohn-Sham orbitals and orbital shifts resulting from the difference between the exchange-correlation potential and the orbital-dependent potential. Due to the success of an analog scheme in the static case, a scheme that propagates orbitals and orbital shifts in real time is a natural candidate for an exact solution of the TDOEP equation. We investigate the numerical stability of such a scheme. An approximation beyond the Krieger-Li-Iafrate approximation for the time-dependent exchange-correlation potential ismore » analyzed.« less

The degenerate parametric oscillator and Ince's equation

NASA Astrophysics Data System (ADS)

Cordero-Soto, Ricardo; Suslov, Sergei K.

2011-01-01

We construct Green's function for the quantum degenerate parametric oscillator in the coordinate representation in terms of standard solutions of Ince's equation in a framework of a general approach to variable quadratic Hamiltonians. Exact time-dependent wavefunctions and their connections with dynamical invariants and SU(1, 1) group are also discussed. An extension to the degenerate parametric oscillator with time-dependent amplitude and phase is also mentioned.

Observation of 1-D time dependent non-propagating laser plasma structures using fluid and PIC codes

NASA Astrophysics Data System (ADS)

Verma, Deepa; Bera, Ratan Kumar; Kumar, Atul; Patel, Bhavesh; Das, Amita

2017-12-01

The manuscript reports the observation of time dependent localized and non-propagating structures in the coupled laser plasma system through 1-D fluid and Particle-In-Cell (PIC) simulations. It is reported that such structures form spontaneously as a result of collision amongst certain exact solitonic solutions. They are seen to survive as coherent entities for a long time up to several hundreds of plasma periods. Furthermore, it is shown that such time dependence can also be artificially recreated by significantly disturbing the delicate balance between the radiation and the density fields required for the exact non-propagating solution obtained by Esirkepov et al., JETP 68(1), 36-41 (1998). The ensuing time evolution is an interesting interplay between kinetic and field energies of the system. The electrostatic plasma oscillations are coupled with oscillations in the electromagnetic field. The inhomogeneity of the background and the relativistic nature, however, invariably produces large amplitude density perturbations leading to its wave breaking. In the fluid simulations, the signature of wave breaking can be discerned by a drop in the total energy which evidently gets lost to the grid. The PIC simulations are observed to closely follow the fluid simulations till the point of wave breaking. However, the total energy in the case of PIC simulations is seen to remain conserved throughout the simulations. At the wave breaking, the particles are observed to acquire thermal kinetic energy in the case of PIC. Interestingly, even after wave breaking, compact coherent structures with trapped radiation inside high-density peaks continue to exist both in PIC and fluid simulations. Although the time evolution does not exactly match in the two simulations as it does prior to the process of wave breaking, the time-dependent features exhibited by the remnant structures are characteristically similar.

Time-dependent flow model of a generalized Burgers' fluid with fractional derivatives through a cylindrical domain: An exact and numerical approach

NASA Astrophysics Data System (ADS)

Safdar, Rabia; Imran, M.; Khalique, Chaudry Masood

2018-06-01

Exact solutions for velocity field and tangential stress for rotational flow of a generalized Burgers' fluid within an infinite circular pipe are derived by using the methods of Laplace and finite Hankel transformations. Firstly we take the position of fluid at rest and then the fluid flow due to the rotation of the pipe around the axis of flow having time dependant angular velocity. The exact solutions are presented in terms of the generalized Ga,b,c (., t) -functions. The corresponding results can be freely specified for the same results of Burgers', Oldroyd B, Maxwell, second grade and Newtonian fluids (performing the same motion) as particular cases of the results obtained earlier. The impact of the different parameters, individually and in comparison, are represented by graphical demonstrations. Secondly the numerical solutions for velocity and stress are also obtained with the help of Laplace transformation, Gaver Stehfest's algorithm and MATHCAD. Finally a comparison of both methods for the same problem is done and shows the consistency of results.

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.

Landau problem with time dependent mass in time dependent electric and harmonic background fields

NASA Astrophysics Data System (ADS)

Lawson, Latévi M.; Avossevou, Gabriel Y. H.

2018-04-01

The spectrum of a Hamiltonian describing the dynamics of a Landau particle with time-dependent mass and frequency undergoing the influence of a uniform time-dependent electric field is obtained. The configuration space wave function of the model is expressed in terms of the generalised Laguerre polynomials. To diagonalize the time-dependent Hamiltonian, we employ the Lewis-Riesenfeld method of invariants. To this end, we introduce a unitary transformation in the framework of the algebraic formalism to construct the invariant operator of the system and then to obtain the exact solution of the Hamiltonian. We recover the solutions of the ordinary Landau problem in the absence of the electric and harmonic fields for a constant particle mass.

Exact results for models of multichannel quantum nonadiabatic transitions

DOE PAGES

Sinitsyn, N. A.

2014-12-11

We consider nonadiabatic transitions in explicitly time-dependent systems with Hamiltonians of the form Hˆ(t)=Aˆ+Bˆt+Cˆ/t, where t is time and Aˆ,Bˆ,Cˆ are Hermitian N × N matrices. We show that in any model of this type, scattering matrix elements satisfy nontrivial exact constraints that follow from the absence of the Stokes phenomenon for solutions with specific conditions at t→–∞. This allows one to continue such solutions analytically to t→+∞, and connect their asymptotic behavior at t→–∞ and t→+∞. This property becomes particularly useful when a model shows additional discrete symmetries. Specifically, we derive a number of simple exact constraints and explicitmore » expressions for scattering probabilities in such systems.« less

Exact probability distribution functions for Parrondo's games

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Exact probability distribution functions for Parrondo's games.

PubMed

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

2016-12-01

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

Theoretical Studies of Defects in Tetrahedral Semiconductors.

DTIC Science & Technology

1980-08-01

pulse. The exact time of the maximal sur- has been measured by Shvarev et al. [I I at 1.0, face temperature depends on pulse duration, thermal 0.7 and...0.4 lAn from 57.50 off normal incidence. diffusivity (which is generally T dependent ), pulse Auston et al. (81 reported the time resolved reflec- shape...surface occur 30 to 40 ns after the peak of their 25 ns HWHM or ripples on the surface or a temperature depend - gaussian pulse rather than within

Time-dependent quantum transport and power-law decay of the transient current in a nano-relay and nano-oscillator

NASA Astrophysics Data System (ADS)

Cuansing, Eduardo C.; Liang, Gengchiau

2011-10-01

Time-dependent nonequilibrium Green's functions are used to study electron transport properties in a device consisting of two linear chain leads and a time-dependent interlead coupling that is switched on non-adiabatically. We derive a numerically exact expression for the particle current and examine its characteristics as it evolves in time from the transient regime to the long-time steady-state regime. We find that just after switch-on, the current initially overshoots the expected long-time steady-state value, oscillates and decays as a power law, and eventually settles to a steady-state value consistent with the value calculated using the Landauer formula. The power-law parameters depend on the values of the applied bias voltage, the strength of the couplings, and the speed of the switch-on. In particular, the oscillating transient current decays away longer for lower bias voltages. Furthermore, the power-law decay nature of the current suggests an equivalent series resistor-inductor-capacitor circuit wherein all of the components have time-dependent properties. Such dynamical resistive, inductive, and capacitive influences are generic in nano-circuits where dynamical switches are incorporated. We also examine the characteristics of the dynamical current in a nano-oscillator modeled by introducing a sinusoidally modulated interlead coupling between the two leads. We find that the current does not strictly follow the sinusoidal form of the coupling. In particular, the maximum current does not occur during times when the leads are exactly aligned. Instead, the times when the maximum current occurs depend on the values of the bias potential, nearest-neighbor coupling, and the interlead coupling.

Composite recovery type curves in normalized time from Theis' exact solution

USGS Publications Warehouse

Goode, Daniel J.

1997-01-01

Type curves derived from Theis’ exact nonequilibrium well function solution are proposed for graphical estimation of aquifer hydraulic properties, transmissivity (T), and storage coefficient (S), from water-level recovery data after cessation of a constant-rate discharge test. Drawdown (on log scale) is plotted versus the ratio of time since pumping stopped to duration of pumping, a normalized time. Under Theis conditions, individual type curves depend on only the dimensionless pumping duration, which depends in turn on S and radial distance from the pumping well. Type curve matching, in contrast to the Theis procedure for pumping data, is performed by shifting only the drawdown axis; the time axis is fixed because it is a relative or normalized time. The match-point for the drawdown axis is used to compute T, and S is determined from matching the curve shape, which depends on early dimensionless-time data. Multiple well data can be plotted and matched simultaneously (a composite plot), with drawdown at different radial distances matching different curves. The ratio of dimensionless pumping durations for any two matched curves is equal to one over the squared ratio of radial distances. Application to two recovery datasets from the literature confirm the utility of these type curves in normalized time for composite estimation of T and S.

Exact solutions for coupled Einstein, Dirac, Maxwell, and zero-mass scalar fields

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

Patra, A.C.; Ray, D.

1987-12-01

Coupled equations for Einstein, Maxwell, Dirac, and zero-mass scalar fields studied by Krori, Bhattacharya, and Nandi are integrated for plane-symmetric time-independent case. It is shown that solutions do not exist for the plane-symmetric time-dependent case.

Optimised effective potential for ground states, excited states, and time-dependent phenomena

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

Gross, E.K.U.

1996-12-31

(1) The optimized effective potential method is a variant of the traditional Kohn-Sham scheme. In this variant, the exchange-correlation energy E{sub xc} is an explicit functional of single-particle orbitals. The exchange-correlation potential, given as usual by the functional derivative v{sub xc} = {delta}E{sub xc}/{delta}{rho}, then satisfies as integral equation involving the single-particle orbitals. This integral equation in solved semi-analytically using a scheme recently proposed by Krieger, Li and Iafrate. If the exact (Fock) exchange-energy functional is employed together with the Colle-Salvetti orbital functional for the correlation energy, the mean absolute deviation of the resulting ground-state energies from the exact nonrelativisticmore » values is CT mH for the first-row atoms, as compared to 4.5 mH in a state-of-the-art CI calculation. The proposed scheme is thus significantly more accurate than the conventional Kohn-Sham method while the numerical effort involved is about the same as for an ordinary Hanree-Fock calculation. (2) A time-dependent generalization of the optimized-potential method is presented and applied to the linear-response regime. Since time-dependent density functional theory leads to a formally exact representation of the frequency-dependent linear density response and since the latter, as a function of frequency, has poles at the excitation energies of the fully interacting system, the formalism is suitable for the calculation of excitation energies. A simple additive correction to the Kohn-Sham single-particle excitation energies will be deduced and first results for atomic and molecular singlet and triplet excitation energies will be presented. (3) Beyond the regime of linear response, the time-dependent optimized-potential method is employed to describe atoms in strong emtosecond laser pulses. Ionization yields and harmonic spectra will be presented and compared with experimental data.« less

Exact folded-band chaotic oscillator.

PubMed

Corron, Ned J; Blakely, Jonathan N

2012-06-01

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

Time-Harmonic Gaussian Beams: Exact Solutions of the Helmhotz Equation in Free Space

NASA Astrophysics Data System (ADS)

Kiselev, A. P.

2017-12-01

An exact solution of the Helmholtz equation u xx + u yy + u zz + k 2 u = 0 is presented, which describes propagation of monochromatic waves in the free space. The solution has the form of a superposition of plane waves with a specific weight function dependent on a certain free parameter a. If ka→∞, the solution is localized in the Gaussian manner in a vicinity of a certain straight line and asymptotically coincides with the famous approximate solution known as the fundamental mode of a paraxial Gaussian beam. The asymptotics of the aforementioned exact solution does not include a backward wave.

Exact Solutions of Schrödinger Equation with Improved Ring-Shaped Non-Spherical Harmonic Oscillator and Coulomb Potential

NASA Astrophysics Data System (ADS)

Ndem Ikot, Akpan; Akpan, Ita O.; Abbey, T. M.; Hassanabadi, Hassan

2016-05-01

We propose improved ring shaped like potential of the form, V(r, θ) = V(r) + (ħ2/2Mr2)[(β sin2 θ + γ cos2 θ + λ) / sin θ cos θ]2 and its exact solutions are presented via the Nikiforov-Uvarov method. The angle dependent part V(θ) = (ħ2 / 2 Mr2)[(β sin2 θ + γ cos2 θ + λ) / sin θ cos θ]2, which is reported for the first time embodied the novel angle dependent (NAD) potential and harmonic novel angle dependent potential (HNAD) as special cases. We discuss in detail the effects of the improved ring shaped like potential on the radial parts of the spherical harmonic and Coulomb potentials.

Time-dependent corona models - Scaling laws

NASA Technical Reports Server (NTRS)

Korevaar, P.; Martens, P. C. H.

1989-01-01

Scaling laws are derived for the one-dimensional time-dependent Euler equations that describe the evolution of a spherically symmetric stellar atmosphere. With these scaling laws the results of the time-dependent calculations by Korevaar (1989) obtained for one star are applicable over the whole Hertzsprung-Russell diagram and even to elliptic galaxies. The scaling is exact for stars with the same M/R-ratio and a good approximation for stars with a different M/R-ratio. The global relaxation oscillation found by Korevaar (1989) is scaled to main sequence stars, a solar coronal hole, cool giants and elliptic galaxies.

Using permutations to detect dependence between time series

NASA Astrophysics Data System (ADS)

Cánovas, Jose S.; Guillamón, Antonio; Ruíz, María del Carmen

2011-07-01

In this paper, we propose an independence test between two time series which is based on permutations. The proposed test can be carried out by means of different common statistics such as Pearson’s chi-square or the likelihood ratio. We also point out why an exact test is necessary. Simulated and real data (return exchange rates between several currencies) reveal the capacity of this test to detect linear and nonlinear dependences.

Time Dependent Models of Grain Formation Around Carbon Stars

NASA Technical Reports Server (NTRS)

Egan, M. P.; Shipman, R. F.

1996-01-01

Carbon-rich Asymptotic Giant Branch stars are sites of dust formation and undergo mass loss at rates ranging from 10(exp -7) to 10(exp -4) solar mass/yr. The state-of-the-art in modeling these processes is time-dependent models which simultaneously solve the grain formation and gas dynamics problem. We present results from such a model, which also includes an exact solution of the radiative transfer within the system.

Interplay between gravity and quintessence: a set of new GR solutions

NASA Astrophysics Data System (ADS)

Chernin, Arthur D.; Santiago, David I.; Silbergleit, Alexander S.

2002-02-01

A set of new exact analytical general relativity (GR) solutions with time-dependent and spatially inhomogeneous quintessence demonstrate (1) a static non-empty space-time with a horizon-type singular surface; (2) time-dependent spatially homogeneous `spheres' which are completely different in geometry from the Friedmann isotropic models; (3) infinitely strong anti-gravity at a `true' singularity where the density is infinitely large. It is also found that (4) the GR solutions allow for an extreme `density-free' form of energy that can generate regular space-time geometries.

Multispecies reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Aghamohammadi, A.; Fatollahi, A. H.; Khorrami, M.; Shariati, A.

2000-10-01

Multispecies reaction-diffusion systems, for which the time evolution equations of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time dependence of the average densities in these cases are also studied. For the general case, the large-time behavior of the average densities has also been obtained.

Anomalous diffusion associated with nonlinear fractional derivative fokker-planck-like equation: exact time-dependent solutions

PubMed

Bologna; Tsallis; Grigolini

2000-08-01

We consider the d=1 nonlinear Fokker-Planck-like equation with fractional derivatives ( partial differential/ partial differentialt)P(x,t)=D( partial differential(gamma)/ partial differentialx(gamma))[P(x,t)](nu). Exact time-dependent solutions are found for nu=(2-gamma)/(1+gamma)(-infinity

Molecular Excitation Energies from Time-Dependent Density Functional Theory Employing Random-Phase Approximation Hessians with Exact Exchange.

PubMed

Heßelmann, Andreas

2015-04-14

Molecular excitation energies have been calculated with time-dependent density-functional theory (TDDFT) using random-phase approximation Hessians augmented with exact exchange contributions in various orders. It has been observed that this approach yields fairly accurate local valence excitations if combined with accurate asymptotically corrected exchange-correlation potentials used in the ground-state Kohn-Sham calculations. The inclusion of long-range particle-particle with hole-hole interactions in the kernel leads to errors of 0.14 eV only for the lowest excitations of a selection of three alkene, three carbonyl, and five azabenzene molecules, thus surpassing the accuracy of a number of common TDDFT and even some wave function correlation methods. In the case of long-range charge-transfer excitations, the method typically underestimates accurate reference excitation energies by 8% on average, which is better than with standard hybrid-GGA functionals but worse compared to range-separated functional approximations.

Drude weight of the spin-(1)/(2) XXZ chain: Density matrix renormalization group versus exact diagonalization

NASA Astrophysics Data System (ADS)

Karrasch, C.; Hauschild, J.; Langer, S.; Heidrich-Meisner, F.

2013-06-01

We revisit the problem of the spin Drude weight D of the integrable spin-1/2 XXZ chain using two complementary approaches, exact diagonalization (ED) and the time-dependent density-matrix renormalization group (tDMRG). We pursue two main goals. First, we present extensive results for the temperature dependence of D. By exploiting time translation invariance within tDMRG, one can extract D for significantly lower temperatures than in previous tDMRG studies. Second, we discuss the numerical quality of the tDMRG data and elaborate on details of the finite-size scaling of the ED results, comparing calculations carried out in the canonical and grand-canonical ensembles. Furthermore, we analyze the behavior of the Drude weight as the point with SU(2)-symmetric exchange is approached and discuss the relative contribution of the Drude weight to the sum rule as a function of temperature.

Radially Symmetric Motions of Nonlinearly Viscoelastic Bodies Under Live Loads

NASA Astrophysics Data System (ADS)

Stepanov, Alexey B.; Antman, Stuart S.

2017-12-01

This paper treats radially symmetric motions of nonlinearly viscoelastic circular-cylindrical and spherical shells subjected to the live loads of centrifugal force and (time-dependent) hydrostatic pressures. The governing equations are exact versions of those for 3-dimensional continuum mechanics (so shell does not connote an approximate via some shell theory). These motions are governed by quasilinear third-order parabolic-hyperbolic equations having but one independent spatial variable. The principal part of such a partial differential equation is determined by a general family of nonlinear constitutive equations. The presence of strains in two orthogonal directions requires a careful treatment of constitutive restrictions that are physically natural and support the analysis. The interaction of geometrically exact formulations, the compatible use of general constitutive equations for material response, and the presence of live loads show how these factors play crucial roles in the behavior of solutions. In particular, for different kinds of live loads there are thresholds separating materials that produce qualitatively different dynamical behavior. The analysis (using classical methods) covers infinite-time blowup for cylindrical shells subject to centrifugal forces, infinite-time blowup for cylindrical shells subject to steady and time-dependent hydrostatic pressures, finite-time blowup for spherical shells subject to steady and time-dependent hydrostatic pressures, and the preclusion of total compression. This paper concludes with a sketch (using some modern methods) of the existence of regular solutions until the time of blowup.

Exact combinatorial approach to finite coagulating systems

NASA Astrophysics Data System (ADS)

Fronczak, Agata; Chmiel, Anna; Fronczak, Piotr

2018-02-01

This paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete and the binary aggregation alone governs the time evolution of the systems. By considering the growth histories of all possible clusters, an exact expression is derived for the probability of a coagulating system with an arbitrary kernel being found in a given cluster configuration when monodisperse initial conditions are applied. Then this probability is used to calculate the time-dependent distribution for the number of clusters of a given size, the average number of such clusters, and that average's standard deviation. The correctness of our general expressions is proved based on the (analytical and numerical) results obtained for systems with the constant kernel. In addition, the results obtained are compared with the results arising from the solutions to the mean-field Smoluchowski coagulation equation, indicating its weak points. The paper closes with a brief discussion on the extensibility to other systems of the approach presented herein, emphasizing the issue of arbitrary initial conditions.

Ideal quantum gas in an expanding cavity: nature of nonadiabatic force.

PubMed

Nakamura, K; Avazbaev, S K; Sobirov, Z A; Matrasulov, D U; Monnai, T

2011-04-01

We consider a quantum gas of noninteracting particles confined in the expanding cavity and investigate the nature of the nonadiabatic force which is generated from the gas and acts on the cavity wall. First, with use of the time-dependent canonical transformation, which transforms the expanding cavity to the nonexpanding one, we can define the force operator. Second, applying the perturbative theory, which works when the cavity wall begins to move at time origin, we find that the nonadiabatic force is quadratic in the wall velocity and thereby does not break the time-reversal symmetry, in contrast with general belief. Finally, using an assembly of the transitionless quantum states, we obtain the nonadiabatic force exactly. The exact result justifies the validity of both the definition of the force operator and the issue of the perturbative theory. The mysterious mechanism of nonadiabatic transition with the use of transitionless quantum states is also explained. The study is done for both cases of the hard- and soft-wall confinement with the time-dependent confining length. ©2011 American Physical Society

Watching excitons move: the time-dependent transition density matrix

NASA Astrophysics Data System (ADS)

Ullrich, Carsten

2012-02-01

Time-dependent density-functional theory allows one to calculate excitation energies and the associated transition densities in principle exactly. The transition density matrix (TDM) provides additional information on electron-hole localization and coherence of specific excitations of the many-body system. We have extended the TDM concept into the real-time domain in order to visualize the excited-state dynamics in conjugated molecules. The time-dependent TDM is defined as an implicit density functional, and can be approximately obtained from the time-dependent Kohn-Sham orbitals. The quality of this approximation is assessed in simple model systems. A computational scheme for real molecular systems is presented: the time-dependent Kohn-Sham equations are solved with the OCTOPUS code and the time-dependent Kohn-Sham TDM is calculated using a spatial partitioning scheme. The method is applied to show in real time how locally created electron-hole pairs spread out over neighboring conjugated molecular chains. The coupling mechanism, electron-hole coherence, and the possibility of charge separation are discussed.

On One Possible Generalization of the Regression Theorem

NASA Astrophysics Data System (ADS)

Bogolubov, N. N.; Soldatov, A. V.

2018-03-01

A general approach to derivation of formally exact closed time-local or time-nonlocal evolution equations for non-equilibrium multi-time correlations functions made of observables of an open quantum system interacting simultaneously with external time-dependent classical fields and dissipative environment is discussed. The approach allows for the subsequent treatment of these equations within a perturbative scheme assuming that the system-environment interaction is weak.

Quantum and classical dissipation of charged particles

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

Ibarra-Sierra, V.G.; Anzaldo-Meneses, A.; Cardoso, J.L.

2013-08-15

A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases using canonical transformations applied to Hamiltonians for a particle with variable mass. Green’s function is constructed and, from it, the motion of a Gaussian wave packet is studied in detail. -- Highlights: •Hamiltonian of a damped charged particle in time dependent electromagnetic fields. •Exact Green’s function of a charged particle in time dependent electromagnetic fields. •Time evolution of a Gaussian wave packet of a damped charged particle.more » •Classical and quantum dynamics of a damped electric charge.« less

Exact axially symmetric galactic dynamos

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

Agostini, Federica; Abedi, Ali; Suzuki, Yasumitsu

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

Linearly exact parallel closures for slab geometry

NASA Astrophysics Data System (ADS)

Ji, Jeong-Young; Held, Eric D.; Jhang, Hogun

2013-08-01

Parallel closures are obtained by solving a linearized kinetic equation with a model collision operator using the Fourier transform method. The closures expressed in wave number space are exact for time-dependent linear problems to within the limits of the model collision operator. In the adiabatic, collisionless limit, an inverse Fourier transform is performed to obtain integral (nonlocal) parallel closures in real space; parallel heat flow and viscosity closures for density, temperature, and flow velocity equations replace Braginskii's parallel closure relations, and parallel flow velocity and heat flow closures for density and temperature equations replace Spitzer's parallel transport relations. It is verified that the closures reproduce the exact linear response function of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] for Landau damping given a temperature gradient. In contrast to their approximate closures where the vanishing viscosity coefficient numerically gives an exact response, our closures relate the heat flow and nonvanishing viscosity to temperature and flow velocity (gradients).

Transcriptional dynamics with time-dependent reaction rates

NASA Astrophysics Data System (ADS)

Nandi, Shubhendu; Ghosh, Anandamohan

2015-02-01

Transcription is the first step in the process of gene regulation that controls cell response to varying environmental conditions. Transcription is a stochastic process, involving synthesis and degradation of mRNAs, that can be modeled as a birth-death process. We consider a generic stochastic model, where the fluctuating environment is encoded in the time-dependent reaction rates. We obtain an exact analytical expression for the mRNA probability distribution and are able to analyze the response for arbitrary time-dependent protocols. Our analytical results and stochastic simulations confirm that the transcriptional machinery primarily act as a low-pass filter. We also show that depending on the system parameters, the mRNA levels in a cell population can show synchronous/asynchronous fluctuations and can deviate from Poisson statistics.

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

Sinitsyn, N. A.

We consider nonadiabatic transitions in explicitly time-dependent systems with Hamiltonians of the form Hˆ(t)=Aˆ+Bˆt+Cˆ/t, where t is time and Aˆ,Bˆ,Cˆ are Hermitian N × N matrices. We show that in any model of this type, scattering matrix elements satisfy nontrivial exact constraints that follow from the absence of the Stokes phenomenon for solutions with specific conditions at t→–∞. This allows one to continue such solutions analytically to t→+∞, and connect their asymptotic behavior at t→–∞ and t→+∞. This property becomes particularly useful when a model shows additional discrete symmetries. Specifically, we derive a number of simple exact constraints and explicitmore » expressions for scattering probabilities in such systems.« less

Exact solution of a model DNA-inversion genetic switch with orientational control.

PubMed

Visco, Paolo; Allen, Rosalind J; Evans, Martin R

2008-09-12

DNA inversion is an important mechanism by which bacteria and bacteriophage switch reversibly between phenotypic states. In such switches, the orientation of a short DNA element is flipped by a site-specific recombinase enzyme. We propose a simple model for a DNA-inversion switch in which recombinase production is dependent on the switch state (orientational control). Our model is inspired by the fim switch in E. coli. We present an exact analytical solution of the chemical master equation for the model switch, as well as stochastic simulations. Orientational control causes the switch to deviate from Poissonian behavior: the distribution of times in the on state shows a peak and successive flip times are correlated.

Random function theory revisited - Exact solutions versus the first order smoothing conjecture

NASA Technical Reports Server (NTRS)

Lerche, I.; Parker, E. N.

1975-01-01

We remark again that the mathematical conjecture known as first order smoothing or the quasi-linear approximation does not give the correct dependence on correlation length (time) in many cases, although it gives the correct limit as the correlation length (time) goes to zero. In this sense, then, the method is unreliable.

The Quench Action

NASA Astrophysics Data System (ADS)

Caux, Jean-Sébastien

2016-06-01

We give a pedagogical introduction to the methodology of the Quench Action, which is an effective representation for the calculation of time-dependent expectation values of physical operators following a generic out-of-equilibrium state preparation protocol (for example a quantum quench). The representation, originally introduced in Caux and Essler (2013 Phys. Rev. Lett. 110 257203), is founded on a mixture of exact data for overlaps together with variational reasonings. It is argued to be quite generally valid and thermodynamically exact for arbitrary times after the quench (from short times all the way up to the steady state), and applicable to a wide class of physically relevant observables. Here, we introduce the method and its language, give an overview of some recent results, suggest a roadmap and offer some perspectives on possible future research directions.

Stokes' theorem, gauge symmetry and the time-dependent Aharonov-Bohm effect

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

Macdougall, James, E-mail: jbm34@mail.fresnostate.edu; Singleton, Douglas, E-mail: dougs@csufresno.edu

2014-04-15

Stokes' theorem is investigated in the context of the time-dependent Aharonov-Bohm effect—the two-slit quantum interference experiment with a time varying solenoid between the slits. The time varying solenoid produces an electric field which leads to an additional phase shift which is found to exactly cancel the time-dependent part of the usual magnetic Aharonov-Bohm phase shift. This electric field arises from a combination of a non-single valued scalar potential and/or a 3-vector potential. The gauge transformation which leads to the scalar and 3-vector potentials for the electric field is non-single valued. This feature is connected with the non-simply connected topology ofmore » the Aharonov-Bohm set-up. The non-single valued nature of the gauge transformation function has interesting consequences for the 4-dimensional Stokes' theorem for the time-dependent Aharonov-Bohm effect. An experimental test of these conclusions is proposed.« less

Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

PubMed

Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

2002-04-01

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.

Propagators for the Time-Dependent Kohn-Sham Equations: Multistep, Runge-Kutta, Exponential Runge-Kutta, and Commutator Free Magnus Methods.

PubMed

Gómez Pueyo, Adrián; Marques, Miguel A L; Rubio, Angel; Castro, Alberto

2018-05-09

We examine various integration schemes for the time-dependent Kohn-Sham equations. Contrary to the time-dependent Schrödinger's equation, this set of equations is nonlinear, due to the dependence of the Hamiltonian on the electronic density. We discuss some of their exact properties, and in particular their symplectic structure. Four different families of propagators are considered, specifically the linear multistep, Runge-Kutta, exponential Runge-Kutta, and the commutator-free Magnus schemes. These have been chosen because they have been largely ignored in the past for time-dependent electronic structure calculations. The performance is analyzed in terms of cost-versus-accuracy. The clear winner, in terms of robustness, simplicity, and efficiency is a simplified version of a fourth-order commutator-free Magnus integrator. However, in some specific cases, other propagators, such as some implicit versions of the multistep methods, may be useful.

U(1)-invariant membranes: The geometric formulation, Abel, and pendulum differential equations

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

Zheltukhin, A. A.; Fysikum, AlbaNova, Stockholm University, 106 91 Stockholm; NORDITA, Roslagstullsbacken 23, 106 91 Stockholm

The geometric approach to study the dynamics of U(1)-invariant membranes is developed. The approach reveals an important role of the Abel nonlinear differential equation of the first type with variable coefficients depending on time and one of the membrane extendedness parameters. The general solution of the Abel equation is constructed. Exact solutions of the whole system of membrane equations in the D=5 Minkowski space-time are found and classified. It is shown that if the radial component of the membrane world vector is only time dependent, then the dynamics is described by the pendulum equation.

Exact event-driven implementation for recurrent networks of stochastic perfect integrate-and-fire neurons.

PubMed

Taillefumier, Thibaud; Touboul, Jonathan; Magnasco, Marcelo

2012-12-01

In vivo cortical recording reveals that indirectly driven neural assemblies can produce reliable and temporally precise spiking patterns in response to stereotyped stimulation. This suggests that despite being fundamentally noisy, the collective activity of neurons conveys information through temporal coding. Stochastic integrate-and-fire models delineate a natural theoretical framework to study the interplay of intrinsic neural noise and spike timing precision. However, there are inherent difficulties in simulating their networks' dynamics in silico with standard numerical discretization schemes. Indeed, the well-posedness of the evolution of such networks requires temporally ordering every neuronal interaction, whereas the order of interactions is highly sensitive to the random variability of spiking times. Here, we answer these issues for perfect stochastic integrate-and-fire neurons by designing an exact event-driven algorithm for the simulation of recurrent networks, with delayed Dirac-like interactions. In addition to being exact from the mathematical standpoint, our proposed method is highly efficient numerically. We envision that our algorithm is especially indicated for studying the emergence of polychronized motifs in networks evolving under spike-timing-dependent plasticity with intrinsic noise.

Analytical results for a stochastic model of gene expression with arbitrary partitioning of proteins

NASA Astrophysics Data System (ADS)

Tschirhart, Hugo; Platini, Thierry

2018-05-01

In biophysics, the search for analytical solutions of stochastic models of cellular processes is often a challenging task. In recent work on models of gene expression, it was shown that a mapping based on partitioning of Poisson arrivals (PPA-mapping) can lead to exact solutions for previously unsolved problems. While the approach can be used in general when the model involves Poisson processes corresponding to creation or degradation, current applications of the method and new results derived using it have been limited to date. In this paper, we present the exact solution of a variation of the two-stage model of gene expression (with time dependent transition rates) describing the arbitrary partitioning of proteins. The methodology proposed makes full use of the PPA-mapping by transforming the original problem into a new process describing the evolution of three biological switches. Based on a succession of transformations, the method leads to a hierarchy of reduced models. We give an integral expression of the time dependent generating function as well as explicit results for the mean, variance, and correlation function. Finally, we discuss how results for time dependent parameters can be extended to the three-stage model and used to make inferences about models with parameter fluctuations induced by hidden stochastic variables.

Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes.

PubMed

Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V

2013-04-01

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes

NASA Astrophysics Data System (ADS)

Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V.

2013-04-01

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

Solving Integer Programs from Dependence and Synchronization Problems

DTIC Science & Technology

1993-03-01

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

Timed and Untimed Grammaticality Judgments Measure Distinct Types of Knowledge: Evidence from Eye-Movement Patterns

ERIC Educational Resources Information Center

Godfroid, Aline; Loewen, Shawn; Jung, Sehoon; Park, Ji-Hyun; Gass, Susan; Ellis, Rod

2015-01-01

Grammaticality judgment tests (GJTs) have been used to elicit data reflecting second language (L2) speakers' knowledge of L2 grammar. However, the exact constructs measured by GJTs, whether primarily implicit or explicit knowledge, are disputed and have been argued to differ depending on test-related variables (i.e., time pressure and item…

Second-order numerical solution of time-dependent, first-order hyperbolic equations

NASA Technical Reports Server (NTRS)

Shah, Patricia L.; Hardin, Jay

1995-01-01

A finite difference scheme is developed to find an approximate solution of two similar hyperbolic equations, namely a first-order plane wave and spherical wave problem. Finite difference approximations are made for both the space and time derivatives. The result is a conditionally stable equation yielding an exact solution when the Courant number is set to one.

Radiation and polarization signatures of the 3D multizone time-dependent hadronic blazar model

DOE PAGES

Zhang, Haocheng; Diltz, Chris; Bottcher, Markus

2016-09-23

We present a newly developed time-dependent three-dimensional multizone hadronic blazar emission model. By coupling a Fokker–Planck-based lepto-hadronic particle evolution code, 3DHad, with a polarization-dependent radiation transfer code, 3DPol, we are able to study the time-dependent radiation and polarization signatures of a hadronic blazar model for the first time. Our current code is limited to parameter regimes in which the hadronic γ-ray output is dominated by proton synchrotron emission, neglecting pion production. Our results demonstrate that the time-dependent flux and polarization signatures are generally dominated by the relation between the synchrotron cooling and the light-crossing timescale, which is largely independent ofmore » the exact model parameters. We find that unlike the low-energy polarization signatures, which can vary rapidly in time, the high-energy polarization signatures appear stable. Lastly, future high-energy polarimeters may be able to distinguish such signatures from the lower and more rapidly variable polarization signatures expected in leptonic models.« less

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

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

Ibarra-Sierra, V.G.; Sandoval-Santana, J.C.; Cardoso, J.L.

We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra ismore » later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a rotating quadrupole field ion trap are presented. •Exact solutions for magneto-transport in variable electromagnetic fields are shown.« less

Reaction Event Counting Statistics of Biopolymer Reaction Systems with Dynamic Heterogeneity.

PubMed

Lim, Yu Rim; Park, Seong Jun; Park, Bo Jung; Cao, Jianshu; Silbey, Robert J; Sung, Jaeyoung

2012-04-10

We investigate the reaction event counting statistics (RECS) of an elementary biopolymer reaction in which the rate coefficient is dependent on states of the biopolymer and the surrounding environment and discover a universal kinetic phase transition in the RECS of the reaction system with dynamic heterogeneity. From an exact analysis for a general model of elementary biopolymer reactions, we find that the variance in the number of reaction events is dependent on the square of the mean number of the reaction events when the size of measurement time is small on the relaxation time scale of rate coefficient fluctuations, which does not conform to renewal statistics. On the other hand, when the size of the measurement time interval is much greater than the relaxation time of rate coefficient fluctuations, the variance becomes linearly proportional to the mean reaction number in accordance with renewal statistics. Gillespie's stochastic simulation method is generalized for the reaction system with a rate coefficient fluctuation. The simulation results confirm the correctness of the analytic results for the time dependent mean and variance of the reaction event number distribution. On the basis of the obtained results, we propose a method of quantitative analysis for the reaction event counting statistics of reaction systems with rate coefficient fluctuations, which enables one to extract information about the magnitude and the relaxation times of the fluctuating reaction rate coefficient, without a bias that can be introduced by assuming a particular kinetic model of conformational dynamics and the conformation dependent reactivity. An exact relationship is established between a higher moment of the reaction event number distribution and the multitime correlation of the reaction rate for the reaction system with a nonequilibrium initial state distribution as well as for the system with the equilibrium initial state distribution.

Time dependency of temperature of a laser-irradiated infrared target pixel as a low-pass filter

NASA Technical Reports Server (NTRS)

Scholl, Marija S.; Scholl, James W.

1990-01-01

The thermal response of a surface layer of a pixel on an infrared target simulator is discussed. This pixel is maintained at a constant temperature by a rapidly scanning laser beam. An analytical model has been developed to describe the exact temperature dependence of a pixel as a function of time for different pixel refresh rates. The top layer of the pixel surface that generates the gray-body radiation shows the temperature dependence on time that is characteristic of a low-pass filter. The experimental results agree with the analytical predictions. The application of a pulsed laser beam to a noncontact, nondestructive diagnostic technique of surface characterization for the presence of microdefects is discussed.

Nonlinear stability of Taylor's vortex array

NASA Technical Reports Server (NTRS)

Lin, S. P.; Tobak, M.

1987-01-01

It is proved that the two-dimensional Taylor vortex array, which is an exact unsteady solution of the Navier-Stokes equation, is globally and asymptotically stable in the mean with respect to three-dimensional periodic disturbances. A time-dependent bound on the decay rate of the kinetic energy of disturbances is obtained.

Reflection and Non-Reflection of Particle Wavepackets

ERIC Educational Resources Information Center

Cox, Timothy; Lekner, John

2008-01-01

Exact closed-form solutions of the time-dependent Schrodinger equation are obtained, describing the propagation of wavepackets in the neighbourhood of a potential. Examples given include zero reflection, total reflection and partial reflection of the wavepacket, for the sech[superscript 2]x/a, 1/x[superscript 2] and delta(x) potentials,…

IDENTIFYING COMPOUNDS USING SOURCE CID ON AN ORTHOGONAL ACCELERATION TIME-OF-FLIGHT MASS SPECTROMETER

EPA Science Inventory

Exact mass libraries of ESI and APCI mass spectra are not commercially available In-house libraries are dependent on CID parameters and are instrument specific. The ability to identify compounds without reliance on mass spectral libraries is therefore more crucial for liquid sam...

Modeling of matter-wave solitons in a nonlinear inductor-capacitor network through a Gross-Pitaevskii equation with time-dependent linear potential

NASA Astrophysics Data System (ADS)

Kengne, E.; Lakhssassi, A.; Liu, W. M.

2017-08-01

A lossless nonlinear L C transmission network is considered. With the use of the reductive perturbation method in the semidiscrete limit, we show that the dynamics of matter-wave solitons in the network can be modeled by a one-dimensional Gross-Pitaevskii (GP) equation with a time-dependent linear potential in the presence of a chemical potential. An explicit expression for the growth rate of a purely growing modulational instability (MI) is presented and analyzed. We find that the potential parameter of the GP equation of the system does not affect the different regions of the MI. Neglecting the chemical potential in the GP equation, we derive exact analytical solutions which describe the propagation of both bright and dark solitary waves on continuous-wave (cw) backgrounds. Using the found exact analytical solutions of the GP equation, we investigate numerically the transmission of both bright and dark solitary voltage signals in the network. Our numerical studies show that the amplitude of a bright solitary voltage signal and the depth of a dark solitary voltage signal as well as their width, their motion, and their behavior depend on (i) the propagation frequencies, (ii) the potential parameter, and (iii) the amplitude of the cw background. The GP equation derived in this paper with a time-dependent linear potential opens up different ideas that may be of considerable theoretical interest for the management of matter-wave solitons in nonlinear L C transmission networks.

Criteria for Handling Qualities of Military Aircraft.

DTIC Science & Technology

1982-06-01

loop precognitive manner. The pilot is able to apply discrete, step-like inputs which more or less exactly produce the desired aircraft response. Some...While closed loop operation depends upon the frequency domain response characteristics, successful precognitive control requires the time domain...represents the other extreme of the pilot task from the precognitive time response situation. Mich work was done in attempting to predict pilot opinion from

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

NASA Astrophysics Data System (ADS)

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

2004-01-01

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

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

PubMed

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

2018-06-08

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

Time-dependent perpendicular fluctuations in the driven lattice Lorentz gas

NASA Astrophysics Data System (ADS)

Leitmann, Sebastian; Schwab, Thomas; Franosch, Thomas

2018-02-01

We present results for the fluctuations of the displacement of a tracer particle on a planar lattice pulled by a step force in the presence of impenetrable, immobile obstacles. The fluctuations perpendicular to the applied force are evaluated exactly in first order of the obstacle density for arbitrarily strong pulling and all times. The complex time-dependent behavior is analyzed in terms of the diffusion coefficient, local exponent, and the non-Skellam parameter, which quantifies deviations from the dynamics on the lattice in the absence of obstacles. The non-Skellam parameter along the force is analyzed in terms of an asymptotic model and reveals a power-law growth for intermediate times.

Many-Body Perturbation Theory (MBPT) and Time-Dependent Density-Functional Theory (TD-DFT): MBPT Insights About What Is Missing In, and Corrections To, the TD-DFT Adiabatic Approximation.

PubMed

Casida, Mark E; Huix-Rotllant, Miquel

2016-01-01

In their famous paper, Kohn and Sham formulated a formally exact density-functional theory (DFT) for the ground-state energy and density of a system of N interacting electrons, albeit limited at the time by certain troubling representability questions. As no practical exact form of the exchange-correlation (xc) energy functional was known, the xc-functional had to be approximated, ideally by a local or semilocal functional. Nowadays, however, the realization that Nature is not always so nearsighted has driven us up Perdew's Jacob's ladder to find increasingly nonlocal density/wavefunction hybrid functionals. Time-dependent (TD-) DFT is a younger development which allows DFT concepts to be used to describe the temporal evolution of the density in the presence of a perturbing field. Linear response (LR) theory then allows spectra and other information about excited states to be extracted from TD-DFT. Once again the exact TD-DFT xc-functional must be approximated in practical calculations and this has historically been done using the TD-DFT adiabatic approximation (AA) which is to TD-DFT very similar to what the local density approximation (LDA) is to conventional ground-state DFT. Although some of the recent advances in TD-DFT focus on what can be done within the AA, others explore ways around the AA. After giving an overview of DFT, TD-DFT, and LR-TD-DFT, this chapter focuses on many-body corrections to LR-TD-DFT as one way to build hybrid density-functional/wavefunction methodology for incorporating aspects of nonlocality in time not present in the AA.

Bell-Plesset effects in Rayleigh-Taylor instability of finite-thickness spherical and cylindrical shells

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

Velikovich, A. L.; Schmit, P. F.

Bell-Plesset (BP) effects account for the influence of global convergence or divergence of the fluid flow on the evolution of the interfacial perturbations embedded in the flow. The development of the Rayleigh-Taylor instability in radiation-driven spherical capsules and magnetically-driven cylindrical liners necessarily includes a significant contribution from BP effects due to the time dependence of the radius, velocity, and acceleration of the unstable surfaces or interfaces. An analytical model is presented that, for an ideal incompressible fluid and small perturbation amplitudes, exactly evaluates the BP effects in finite-thickness shells through acceleration and deceleration phases. The time-dependent dispersion equations determining themore » “instantaneous growth rate” are derived. It is demonstrated that by integrating this approximate growth rate over time, one can accurately evaluate the number of perturbation e-foldings during the inward acceleration phase of the implosion. In the limit of small shell thickness, exact thin-shell perturbation equations and approximate thin-shell dispersion equations are obtained, generalizing the earlier results [E. G. Harris, Phys. Fluids 5, 1057 (1962); E. Ott, Phys. Rev. Lett. 29, 1429 (1972); A. B. Bud'ko et al., Phys. Fluids B 2, 1159 (1990)].« less

Bell-Plesset effects in Rayleigh-Taylor instability of finite-thickness spherical and cylindrical shells

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

Velikovich, A. L.; Schmit, P. F.

Bell-Plesset (BP) effects account for the influence of global convergence or divergence of the fluid flow on the evolution of the interfacial perturbations embedded in the flow. The development of the Rayleigh-Taylor instability in radiation-driven spherical capsules and magnetically-driven cylindrical liners necessarily includes a significant contribution from BP effects due to the time dependence of the radius, velocity, and acceleration of the unstable surfaces or interfaces. An analytical model is presented that, for an ideal incompressible fluid and small perturbation amplitudes, exactly evaluates the BP effects in finite-thickness shells through acceleration and deceleration phases. The time-dependent dispersion equations determining themore » “instantaneous growth rate” are derived. It is demonstrated that by integrating this approximate growth rate over time, one can accurately evaluate the number of perturbation e-foldings during the inward acceleration phase of the implosion. As a result, in the limit of small shell thickness, exact thin-shell perturbationequations and approximate thin-shell dispersion equations are obtained, generalizing the earlier results [E. G. Harris, Phys. Fluids 5, 1057 (1962); E. Ott, Phys. Rev. Lett. 29, 1429 (1972); A. B. Bud'ko et al., Phys. Fluids B 2, 1159 (1990)].« less

Bell-Plesset effects in Rayleigh-Taylor instability of finite-thickness spherical and cylindrical shells

DOE PAGES

Velikovich, A. L.; Schmit, P. F.

2015-12-28

Bell-Plesset (BP) effects account for the influence of global convergence or divergence of the fluid flow on the evolution of the interfacial perturbations embedded in the flow. The development of the Rayleigh-Taylor instability in radiation-driven spherical capsules and magnetically-driven cylindrical liners necessarily includes a significant contribution from BP effects due to the time dependence of the radius, velocity, and acceleration of the unstable surfaces or interfaces. An analytical model is presented that, for an ideal incompressible fluid and small perturbation amplitudes, exactly evaluates the BP effects in finite-thickness shells through acceleration and deceleration phases. The time-dependent dispersion equations determining themore » “instantaneous growth rate” are derived. It is demonstrated that by integrating this approximate growth rate over time, one can accurately evaluate the number of perturbation e-foldings during the inward acceleration phase of the implosion. As a result, in the limit of small shell thickness, exact thin-shell perturbationequations and approximate thin-shell dispersion equations are obtained, generalizing the earlier results [E. G. Harris, Phys. Fluids 5, 1057 (1962); E. Ott, Phys. Rev. Lett. 29, 1429 (1972); A. B. Bud'ko et al., Phys. Fluids B 2, 1159 (1990)].« less

Bell-Plesset effects in Rayleigh-Taylor instability of finite-thickness spherical and cylindrical shells

NASA Astrophysics Data System (ADS)

Velikovich, A. L.; Schmit, P. F.

2015-12-01

Bell-Plesset (BP) effects account for the influence of global convergence or divergence of the fluid flow on the evolution of the interfacial perturbations embedded in the flow. The development of the Rayleigh-Taylor instability in radiation-driven spherical capsules and magnetically-driven cylindrical liners necessarily includes a significant contribution from BP effects due to the time dependence of the radius, velocity, and acceleration of the unstable surfaces or interfaces. An analytical model is presented that, for an ideal incompressible fluid and small perturbation amplitudes, exactly evaluates the BP effects in finite-thickness shells through acceleration and deceleration phases. The time-dependent dispersion equations determining the "instantaneous growth rate" are derived. It is demonstrated that by integrating this approximate growth rate over time, one can accurately evaluate the number of perturbation e-foldings during the inward acceleration phase of the implosion. In the limit of small shell thickness, exact thin-shell perturbation equations and approximate thin-shell dispersion equations are obtained, generalizing the earlier results [E. G. Harris, Phys. Fluids 5, 1057 (1962); E. Ott, Phys. Rev. Lett. 29, 1429 (1972); A. B. Bud'ko et al., Phys. Fluids B 2, 1159 (1990)].

Exact and approximate stochastic simulation of intracellular calcium dynamics.

PubMed

Wieder, Nicolas; Fink, Rainer H A; Wegner, Frederic von

2011-01-01

In simulations of chemical systems, the main task is to find an exact or approximate solution of the chemical master equation (CME) that satisfies certain constraints with respect to computation time and accuracy. While Brownian motion simulations of single molecules are often too time consuming to represent the mesoscopic level, the classical Gillespie algorithm is a stochastically exact algorithm that provides satisfying results in the representation of calcium microdomains. Gillespie's algorithm can be approximated via the tau-leap method and the chemical Langevin equation (CLE). Both methods lead to a substantial acceleration in computation time and a relatively small decrease in accuracy. Elimination of the noise terms leads to the classical, deterministic reaction rate equations (RRE). For complex multiscale systems, hybrid simulations are increasingly proposed to combine the advantages of stochastic and deterministic algorithms. An often used exemplary cell type in this context are striated muscle cells (e.g., cardiac and skeletal muscle cells). The properties of these cells are well described and they express many common calcium-dependent signaling pathways. The purpose of the present paper is to provide an overview of the aforementioned simulation approaches and their mutual relationships in the spectrum ranging from stochastic to deterministic algorithms.

A Gaussian theory for fluctuations in simple liquids.

PubMed

Krüger, Matthias; Dean, David S

2017-04-07

Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point correlation functions (such as the intermediate scattering function) are derived. We show that this correlation function is exact at short times, for any interaction and, in particular, for arbitrary external potentials so that it applies to confined systems. Furthermore, we discuss the relation of this approach to previous ones, such as dynamical density functional theory as well as the formally exact treatment. This approach, inspired by the well known Landau-Ginzburg Hamiltonians, and the corresponding "Model B" equation of motion, may be seen as its microscopic version, containing information about the details on the particle level.

A Gaussian theory for fluctuations in simple liquids

NASA Astrophysics Data System (ADS)

Krüger, Matthias; Dean, David S.

2017-04-01

Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point correlation functions (such as the intermediate scattering function) are derived. We show that this correlation function is exact at short times, for any interaction and, in particular, for arbitrary external potentials so that it applies to confined systems. Furthermore, we discuss the relation of this approach to previous ones, such as dynamical density functional theory as well as the formally exact treatment. This approach, inspired by the well known Landau-Ginzburg Hamiltonians, and the corresponding "Model B" equation of motion, may be seen as its microscopic version, containing information about the details on the particle level.

Random walk in degree space and the time-dependent Watts-Strogatz model

NASA Astrophysics Data System (ADS)

Casa Grande, H. L.; Cotacallapa, M.; Hase, M. O.

2017-01-01

In this work, we propose a scheme that provides an analytical estimate for the time-dependent degree distribution of some networks. This scheme maps the problem into a random walk in degree space, and then we choose the paths that are responsible for the dominant contributions. The method is illustrated on the dynamical versions of the Erdős-Rényi and Watts-Strogatz graphs, which were introduced as static models in the original formulation. We have succeeded in obtaining an analytical form for the dynamics Watts-Strogatz model, which is asymptotically exact for some regimes.

Random walk in degree space and the time-dependent Watts-Strogatz model.

PubMed

Casa Grande, H L; Cotacallapa, M; Hase, M O

2017-01-01

In this work, we propose a scheme that provides an analytical estimate for the time-dependent degree distribution of some networks. This scheme maps the problem into a random walk in degree space, and then we choose the paths that are responsible for the dominant contributions. The method is illustrated on the dynamical versions of the Erdős-Rényi and Watts-Strogatz graphs, which were introduced as static models in the original formulation. We have succeeded in obtaining an analytical form for the dynamics Watts-Strogatz model, which is asymptotically exact for some regimes.

Quantum work statistics of charged Dirac particles in time-dependent fields

DOE PAGES

Deffner, Sebastian; Saxena, Avadh

2015-09-28

The quantum Jarzynski equality is an important theorem of modern quantum thermodynamics. We show that the Jarzynski equality readily generalizes to relativistic quantum mechanics described by the Dirac equation. After establishing the conceptual framework we solve a pedagogical, yet experimentally relevant, system analytically. As a main result we obtain the exact quantum work distributions for charged particles traveling through a time-dependent vector potential evolving under Schrödinger as well as under Dirac dynamics, and for which the Jarzynski equality is verified. Thus, special emphasis is put on the conceptual and technical subtleties arising from relativistic quantum mechanics.

Wave packet and statistical quantum calculations for the He + NeH⁺ → HeH⁺ + Ne reaction on the ground electronic state.

PubMed

Koner, Debasish; Barrios, Lizandra; González-Lezana, Tomás; Panda, Aditya N

2014-09-21

A real wave packet based time-dependent method and a statistical quantum method have been used to study the He + NeH(+) (v, j) reaction with the reactant in various ro-vibrational states, on a recently calculated ab initio ground state potential energy surface. Both the wave packet and statistical quantum calculations were carried out within the centrifugal sudden approximation as well as using the exact Hamiltonian. Quantum reaction probabilities exhibit dense oscillatory pattern for smaller total angular momentum values, which is a signature of resonances in a complex forming mechanism for the title reaction. Significant differences, found between exact and approximate quantum reaction cross sections, highlight the importance of inclusion of Coriolis coupling in the calculations. Statistical results are in fairly good agreement with the exact quantum results, for ground ro-vibrational states of the reactant. Vibrational excitation greatly enhances the reaction cross sections, whereas rotational excitation has relatively small effect on the reaction. The nature of the reaction cross section curves is dependent on the initial vibrational state of the reactant and is typical of a late barrier type potential energy profile.

Measuring the Speed of Sound through Gases Using Nitrocellulose

ERIC Educational Resources Information Center

Molek, Karen Sinclair; Reyes, Karl A.; Burnette, Brandon A.; Stepherson, Jacob R.

2015-01-01

Measuring the heat capacity ratios, ?, of gases either through adiabatic expansion or sound velocity is a well established physical chemistry experiment. The most accurate experiments depend on an exact determination of sound origin, which necessitates the use of lasers or a wave generator, where time zero is based on an electrical trigger. Other…

Tunnel ionization of atoms and molecules: How accurate are the weak-field asymptotic formulas?

NASA Astrophysics Data System (ADS)

Labeye, Marie; Risoud, François; Maquet, Alfred; Caillat, Jérémie; Taïeb, Richard

2018-05-01

Weak-field asymptotic formulas for the tunnel ionization rate of atoms and molecules in strong laser fields are often used for the analysis of strong field recollision experiments. We investigate their accuracy and domain of validity for different model systems by confronting them to exact numerical results, obtained by solving the time dependent Schrödinger equation. We find that corrections that take the dc-Stark shift into account are a simple and efficient way to improve the formula. Furthermore, analyzing the different approximations used, we show that error compensation plays a crucial role in the fair agreement between exact and analytical results.

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

Cartarius, Holger; Moiseyev, Nimrod; Department of Physics and Minerva Center for Nonlinear Physics of Complex Systems, Technion-Israel Institute of Technology, Haifa, 32000

The unique time signature of the survival probability exactly at the exceptional point parameters is studied here for the hydrogen atom in strong static magnetic and electric fields. We show that indeed the survival probability S(t)=|<{psi}(0)|{psi}(t)>|{sup 2} decays exactly as |1-at|{sup 2}e{sup -{Gamma}{sub E}{sub P}t/({Dirac_h}/2{pi})}, where {Gamma}{sub EP} is associated with the decay rate at the exceptional point and a is a complex constant depending solely on the initial wave packet that populates exclusively the two almost degenerate states of the non-Hermitian Hamiltonian. This may open the possibility for a first experimental detection of exceptional points in a quantum system.

Time-dependent variational principle in matrix-product state manifolds: Pitfalls and potential

NASA Astrophysics Data System (ADS)

Kloss, Benedikt; Lev, Yevgeny Bar; Reichman, David

2018-01-01

We study the applicability of the time-dependent variational principle in matrix-product state manifolds for the long time description of quantum interacting systems. By studying integrable and nonintegrable systems for which the long time dynamics are known we demonstrate that convergence of long time observables is subtle and needs to be examined carefully. Remarkably, for the disordered nonintegrable system we consider the long time dynamics are in good agreement with the rigorously obtained short time behavior and with previous obtained numerically exact results, suggesting that at least in this case, the apparent convergence of this approach is reliable. Our study indicates that, while great care must be exercised in establishing the convergence of the method, it may still be asymptotically accurate for a class of disordered nonintegrable quantum systems.

Exact treatment of the Jaynes-Cummings model under the action of an external classical field

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

Abdalla, M. Sebawe, E-mail: m.sebaweh@physics.org; Khalil, E.M.; Mathematics Department, College of Science, Taibah University, Al-MaDinah

2011-09-15

We consider the usual Jaynes-Cummings model (JCM), in the presence of an external classical field. Under a certain canonical transformation for the Pauli operators, the system is transformed into the usual JCM. Using the equations of motion in the Heisenberg picture, exact solutions for the time-dependent dynamical operators are obtained. In order to calculate the expectation values of these operators, the wave function has been constructed. It has been shown that the classical field augments the atomic frequency {omega}{sub 0} and mixes the original atomic states. Changes of squeezing from one quadrature to another is also observed for a strongmore » value of the coupling parameter of the classical field. Furthermore, the system in this case displays partial entanglement and the state of the field losses its purity. - Highlights: > The time-dependent JCM, in the presence of the classical field, is still one of the essential problems in the quantum optics. > A new approach is applied through a certain canonical transformation. > The classical field augments the atomic frequency {omega}{sub 0} and mixes the original atomic states.« less

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.

Tool use and the effect of action on the imagination.

PubMed

Schwartz, D L; Holton, D L

2000-11-01

Three studies examined the claim that hand movements can facilitate imagery for object rotations but that this facilitation depends on people's model of the situation. In Experiment 1, physically turning a block without vision reduced mental rotation times compared with imagining the same rotation without bodily movement. In Experiment 2, pulling a string from a spool facilitated participants' mental rotation of an object sitting on the spool. In Experiment 3, depending on participants' model of the spool, the exact same pulling movement facilitated or interfered with the exact same imagery transformation. Results of Experiments 2 and 3 indicate that the geometric characteristics of an action do not specify the trajectory of an imagery transformation. Instead, they point to people's ability to model the tools that mediate between motor activity and its environmental consequences and to transfer tool knowledge to a new situation.

Time-dependent generalized Gibbs ensembles in open quantum systems

NASA Astrophysics Data System (ADS)

Lange, Florian; Lenarčič, Zala; Rosch, Achim

2018-04-01

Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here, we demonstrate numerically that they can be used for a much broader class of problems. We consider integrable systems in the presence of weak perturbations which break both integrability and drive the system to a state far from equilibrium. Under these conditions, we show that the steady state and the time evolution on long timescales can be accurately described by a (truncated) generalized Gibbs ensemble with time-dependent Lagrange parameters, determined from simple rate equations. We compare the numerically exact time evolutions of density matrices for small systems with a theory based on block-diagonal density matrices (diagonal ensemble) and a time-dependent generalized Gibbs ensemble containing only a small number of approximately conserved quantities, using the one-dimensional Heisenberg model with perturbations described by Lindblad operators as an example.

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

PubMed

Das, Shankar P; Yoshimori, Akira

2013-10-01

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

Exact relativistic expressions for wave refraction in a generally moving fluid.

PubMed

Cavalleri, G; Tonni, E; Barbero, F

2013-04-01

The law for the refraction of a wave when the two fluids and the interface are moving with relativistic velocities is given in an exact form, at the same time correcting a first order error in a previous paper [Cavalleri and Tonni, Phys. Rev. E 57, 3478 (1998)]. The treatment is then extended to a generally moving fluid with variable refractive index, ready to be applied to the refraction of acoustic, electromagnetic, or magnetohydrodynamic waves in the atmosphere of rapidly rotating stars. In the particular case of a gas cloud receding because of the universe expansion, our result can be applied to predict observable micro- and mesolensings. The first order approximation of our exact result for the deviation due to refraction of the light coming from a further quasar has a relativistic dependence equal to the one obtained by Einsteins' linearized theory of gravitation.

Dynamic symmetries and quantum nonadiabatic transitions

DOE PAGES

Li, Fuxiang; Sinitsyn, Nikolai A.

2016-05-30

Kramers degeneracy theorem is one of the basic results in quantum mechanics. According to it, the time-reversal symmetry makes each energy level of a half-integer spin system at least doubly degenerate, meaning the absence of transitions or scatterings between degenerate states if the Hamiltonian does not depend on time explicitly. Here we generalize this result to the case of explicitly time-dependent spin Hamiltonians. We prove that for a spin system with the total spin being a half integer, if its Hamiltonian and the evolution time interval are symmetric under a specifically defined time reversal operation, the scattering amplitude between anmore » arbitrary initial state and its time reversed counterpart is exactly zero. Lastly, we also discuss applications of this result to the multistate Landau–Zener (LZ) theory.« less

Principles of VCSEL designing

NASA Astrophysics Data System (ADS)

Nakwaski, W.

2008-03-01

Comprehensive computer simulations are currently the most efficient and cheap methods in designing and optimisation of semiconductor device structures. Seemingly they should be as exact as possible, but in practice it is well known that the most exact approaches are also the most involved and the most time-consuming ones and need powerful computers. In some cases, cheaper somewhat simplified modelling simulations are sufficiently accurate. Therefore, an appropriate modelling approach should be chosen taking into account a compromise between our needs and our possibilities. Modelling of operation and designing of structures of vertical-cavity surface-emitting diode lasers (VCSELs) requires appropriate mathematical description of physical processes crucial for devices operation, i.e., various optical, electrical, thermal, recombination and sometimes also mechanical phenomena taking place within their volumes. Equally important are mutual interactions between above individual processes, usually strongly non-linear and creating a real network of various inter-relations. Chain is as strong as its weakest link. Analogously, model is as exact as its less exact part. Therefore it is useless to improve exactness of its more accurate parts and not to care about less exact ones. All model parts should exhibit similar accuracy. In any individual case, a reasonable compromise should be reached between high modelling fidelity and its practical convenience depending on a main modelling goal, importance and urgency of expected results, available equipment and also financial possibilities. In the present paper, some simplifications used in VCSEL modelling are discussed and their impact on exactness of VCSEL designing is analysed.

The Time Dependent Propensity Function for Acceleration of Spatial Stochastic Simulation of Reaction-Diffusion Systems

PubMed Central

Wu, Sheng; Li, Hong; Petzold, Linda R.

2015-01-01

The inhomogeneous stochastic simulation algorithm (ISSA) is a fundamental method for spatial stochastic simulation. However, when diffusion events occur more frequently than reaction events, simulating the diffusion events by ISSA is quite costly. To reduce this cost, we propose to use the time dependent propensity function in each step. In this way we can avoid simulating individual diffusion events, and use the time interval between two adjacent reaction events as the simulation stepsize. We demonstrate that the new algorithm can achieve orders of magnitude efficiency gains over widely-used exact algorithms, scales well with increasing grid resolution, and maintains a high level of accuracy. PMID:26609185

Two-dimensional model of resonant electron collisions with diatomic molecules and molecular cations

NASA Astrophysics Data System (ADS)

Vana, Martin; Hvizdos, David; Houfek, Karel; Curik, Roman; Greene, Chris H.; Rescigno, Thomas N.; McCurdy, C. William

2016-05-01

A simple model for resonant collisions of electrons with diatomic molecules with one electronic and one nuclear degree of freedom (2D model) which was solved numerically exactly within the time-independent approach was used to probe the local complex potential approximation and nonlocal approximation to nuclear dynamics of these collisions. This model was reformulated in the time-dependent picture and extended to model also electron collisions with molecular cations, especially with H2+.This model enables an assessment of approximate methods, such as the boomerang model or the frame transformation theory. We will present both time-dependent and time-independent results and show how we can use the model to extract deeper insight into the dynamics of the resonant collisions.

Programmable logic construction kits for hyper-real-time neuronal modeling.

PubMed

Guerrero-Rivera, Ruben; Morrison, Abigail; Diesmann, Markus; Pearce, Tim C

2006-11-01

Programmable logic designs are presented that achieve exact integration of leaky integrate-and-fire soma and dynamical synapse neuronal models and incorporate spike-time dependent plasticity and axonal delays. Highly accurate numerical performance has been achieved by modifying simpler forward-Euler-based circuitry requiring minimal circuit allocation, which, as we show, behaves equivalently to exact integration. These designs have been implemented and simulated at the behavioral and physical device levels, demonstrating close agreement with both numerical and analytical results. By exploiting finely grained parallelism and single clock cycle numerical iteration, these designs achieve simulation speeds at least five orders of magnitude faster than the nervous system, termed here hyper-real-time operation, when deployed on commercially available field-programmable gate array (FPGA) devices. Taken together, our designs form a programmable logic construction kit of commonly used neuronal model elements that supports the building of large and complex architectures of spiking neuron networks for real-time neuromorphic implementation, neurophysiological interfacing, or efficient parameter space investigations.

On the mixing time in the Wang-Landau algorithm

NASA Astrophysics Data System (ADS)

Fadeeva, Marina; Shchur, Lev

2018-01-01

We present preliminary results of the investigation of the properties of the Markov random walk in the energy space generated by the Wang-Landau probability. We build transition matrix in the energy space (TMES) using the exact density of states for one-dimensional and two-dimensional Ising models. The spectral gap of TMES is inversely proportional to the mixing time of the Markov chain. We estimate numerically the dependence of the mixing time on the lattice size, and extract the mixing exponent.

Causal properties of nonlinear gravitational waves in modified gravity

NASA Astrophysics Data System (ADS)

Suvorov, Arthur George; Melatos, Andrew

2017-09-01

Some exact, nonlinear, vacuum gravitational wave solutions are derived for certain polynomial f (R ) gravities. We show that the boundaries of the gravitational domain of dependence, associated with events in polynomial f (R ) gravity, are not null as they are in general relativity. The implication is that electromagnetic and gravitational causality separate into distinct notions in modified gravity, which may have observable astrophysical consequences. The linear theory predicts that tachyonic instabilities occur, when the quadratic coefficient a2 of the Taylor expansion of f (R ) is negative, while the exact, nonlinear, cylindrical wave solutions presented here can be superluminal for all values of a2. Anisotropic solutions are found, whose wave fronts trace out time- or spacelike hypersurfaces with complicated geometric properties. We show that the solutions exist in f (R ) theories that are consistent with Solar System and pulsar timing experiments.

An exact noniterative linear method for locating sources based on measuring receiver arrival times.

PubMed

Militello, C; Buenafuente, S R

2007-06-01

In this paper an exact, linear solution to the source localization problem based on the time of arrival at the receivers is presented. The method is unique in that the source's position can be obtained by solving a system of linear equations, three for a plane and four for a volume. This simplification means adding an additional receiver to the minimum mathematically required (3+1 in two dimensions and 4+1 in three dimensions). The equations are easily worked out for any receiver configuration and their geometrical interpretation is straightforward. Unlike other methods, the system of reference used to describe the receivers' positions is completely arbitrary. The relationship between this method and previously published ones is discussed, showing how the present, more general, method overcomes nonlinearity and unknown dependency issues.

Cued Speech Transliteration: Effects of Speaking Rate and Lag Time on Production Accuracy

ERIC Educational Resources Information Center

Krause, Jean C.; Tessler, Morgan P.

2016-01-01

Many deaf and hard-of-hearing children rely on interpreters to access classroom communication. Although the exact level of access provided by interpreters in these settings is unknown, it is likely to depend heavily on interpreter accuracy (portion of message correctly produced by the interpreter) and the factors that govern interpreter accuracy.…

Block Constraints in Age-Period-Cohort Models with Unequal-Width Intervals

ERIC Educational Resources Information Center

Luo, Liying; Hodges, James S.

2016-01-01

Age-period-cohort (APC) models are designed to estimate the independent effects of age, time periods, and cohort membership. However, APC models suffer from an identification problem: There are no unique estimates of the independent effects that fit the data best because of the exact linear dependency among age, period, and cohort. Among methods…

Quantum field between moving mirrors: A three dimensional example

NASA Technical Reports Server (NTRS)

Hacyan, S.; Jauregui, Roco; Villarreal, Carlos

1995-01-01

The scalar quantum field uniformly moving plates in three dimensional space is studied. Field equations for Dirichlet boundary conditions are solved exactly. Comparison of the resulting wavefunctions with their instantaneous static counterpart is performed via Bogolubov coefficients. Unlike the one dimensional problem, 'particle' creation as well as squeezing may occur. The time dependent Casimir energy is also evaluated.

Analytical Theory of the Destruction Terms in Dissipation Rate Transport Equations

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Zhou, Ye

1996-01-01

Modeled dissipation rate transport equations are often derived by invoking various hypotheses to close correlations in the corresponding exact equations. D. C. Leslie suggested that these models might be derived instead from Kraichnan's wavenumber space integrals for inertial range transport power. This suggestion is applied to the destruction terms in the dissipation rate equations for incompressible turbulence, buoyant turbulence, rotating incompressible turbulence, and rotating buoyant turbulence. Model constants like C(epsilon 2) are expressed as integrals; convergence of these integrals implies the absence of Reynolds number dependence in the corresponding destruction term. The dependence of C(epsilon 2) on rotation rate emerges naturally; sensitization of the modeled dissipation rate equation to rotation is not required. A buoyancy related effect which is absent in the exact transport equation for temperature variance dissipation, but which sometimes improves computational predictions, also arises naturally. Both the presence of this effect and the appropriate time scale in the modeled transport equation depend on whether Bolgiano or Kolmogorov inertial range scaling applies. A simple application of these methods leads to a preliminary, dissipation rate equation for rotating buoyant turbulence.

Comparison of exact pupil astigmatism conditions with Seidel approximations

NASA Astrophysics Data System (ADS)

Zhao, Chunyu; Burge, James H.

2002-12-01

The aberrations of axisymmetric imaging systems can be calculated to third order by use of the Seidel formulas. The Coddington equations give aberrations that have quadratic dependence on the pupil, for all field points. The pupil astigmatism conditions were recently developed to predict and control aberrations that have quadratic field dependence and arbitrary pupil dependence. We investigate the relationship between the exact pupil astigmatism conditions and the classical Seidel treatment of pupil aberrations.

Solvable two-dimensional time-dependent non-Hermitian quantum systems with infinite dimensional Hilbert space in the broken PT-regime

NASA Astrophysics Data System (ADS)

Fring, Andreas; Frith, Thomas

2018-06-01

We provide exact analytical solutions for a two-dimensional explicitly time-dependent non-Hermitian quantum system. While the time-independent variant of the model studied is in the broken PT-symmetric phase for the entire range of the model parameters, and has therefore a partially complex energy eigenspectrum, its time-dependent version has real energy expectation values at all times. In our solution procedure we compare the two equivalent approaches of directly solving the time-dependent Dyson equation with one employing the Lewis–Riesenfeld method of invariants. We conclude that the latter approach simplifies the solution procedure due to the fact that the invariants of the non-Hermitian and Hermitian system are related to each other in a pseudo-Hermitian fashion, which in turn does not hold for their corresponding time-dependent Hamiltonians. Thus constructing invariants and subsequently using the pseudo-Hermiticity relation between them allows to compute the Dyson map and to solve the Dyson equation indirectly. In this way one can bypass to solve nonlinear differential equations, such as the dissipative Ermakov–Pinney equation emerging in our and many other systems.

Out-of-equilibrium dynamics driven by localized time-dependent perturbations at quantum phase transitions

NASA Astrophysics Data System (ADS)

Pelissetto, Andrea; Rossini, Davide; Vicari, Ettore

2018-03-01

We investigate the quantum dynamics of many-body systems subject to local (i.e., restricted to a limited space region) time-dependent perturbations. If the system crosses a quantum phase transition, an off-equilibrium behavior is observed, even for a very slow driving. We show that, close to the transition, time-dependent quantities obey scaling laws. In first-order transitions, the scaling behavior is universal, and some scaling functions can be computed exactly. For continuous transitions, the scaling laws are controlled by the standard critical exponents and by the renormalization-group dimension of the perturbation at the transition. Our protocol can be implemented in existing relatively small quantum simulators, paving the way for a quantitative probe of the universal off-equilibrium scaling behavior, without the need to manipulate systems close to the thermodynamic limit.

Scalar and vector Keldysh models in the time domain

NASA Astrophysics Data System (ADS)

Kiselev, M. N.; Kikoin, K. A.

2009-04-01

The exactly solvable Keldysh model of disordered electron system in a random scattering field with extremely long correlation length is converted to the time-dependent model with extremely long relaxation. The dynamical problem is solved for the ensemble of two-level systems (TLS) with fluctuating well depths having the discrete Z 2 symmetry. It is shown also that the symmetric TLS with fluctuating barrier transparency may be described in terms of the vector Keldysh model with dime-dependent random planar rotations in xy plane having continuous SO(2) symmetry. Application of this model to description of dynamic fluctuations in quantum dots and optical lattices is discussed.

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

NASA Astrophysics Data System (ADS)

Boström, Emil; Mikkelsen, Anders; Verdozzi, Claudio

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

Space-Time Error Representation and Estimation in Navier-Stokes Calculations

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

2006-01-01

The mathematical framework for a-posteriori error estimation of functionals elucidated by Eriksson et al. [7] and Becker and Rannacher [3] is revisited in a space-time context. Using these theories, a hierarchy of exact and approximate error representation formulas are presented for use in error estimation and mesh adaptivity. Numerical space-time results for simple model problems as well as compressible Navier-Stokes flow at Re = 300 over a 2D circular cylinder are then presented to demonstrate elements of the error representation theory for time-dependent problems.

Fingerprints of exceptional points in the survival probability of resonances in atomic spectra

NASA Astrophysics Data System (ADS)

Cartarius, Holger; Moiseyev, Nimrod

2011-07-01

The unique time signature of the survival probability exactly at the exceptional point parameters is studied here for the hydrogen atom in strong static magnetic and electric fields. We show that indeed the survival probability S(t)=|<ψ(0)|ψ(t)>|2 decays exactly as |1-at|2e-ΓEPt/ℏ, where ΓEP is associated with the decay rate at the exceptional point and a is a complex constant depending solely on the initial wave packet that populates exclusively the two almost degenerate states of the non-Hermitian Hamiltonian. This may open the possibility for a first experimental detection of exceptional points in a quantum system.

Numerical solution of the exact cavity equations of motion for an unstable optical resonator.

PubMed

Bowers, M S; Moody, S E

1990-09-20

We solve numerically, we believe for the first time, the exact cavity equations of motion for a realistic unstable resonator with a simple gain saturation model. The cavity equations of motion, first formulated by Siegman ["Exact Cavity Equations for Lasers with Large Output Coupling," Appl. Phys. Lett. 36, 412-414 (1980)], and which we term the dynamic coupled modes (DCM) method of solution, solve for the full 3-D time dependent electric field inside the optical cavity by expanding the field in terms of the actual diffractive transverse eigenmodes of the bare (gain free) cavity with time varying coefficients. The spatially varying gain serves to couple the bare cavity transverse modes and to scatter power from mode to mode. We show that the DCM method numerically converges with respect to the number of eigenmodes in the basis set. The intracavity intensity in the numerical example shown reaches a steady state, and this steady state distribution is compared with that computed from the traditional Fox and Li approach using a fast Fourier transform propagation algorithm. The output wavefronts from both methods are quite similar, and the computed output powers agree to within 10%. The usefulness and advantages of using this method for predicting the output of a laser, especially pulsed lasers used for coherent detection, are discussed.

Timing and Spacing Crime in the Urban Environment: Lexington-Fayette County, Kentucky - 1985.

DTIC Science & Technology

1986-05-01

and several tracts along the northeastern segment of New Circle Road where a number of automobile dealers and shopping centers are located. The...exact time when an automobile was stolen, it seems reasonable to assume that, in actuality, the curve is flatter and shifted to the right. Figure 3...depending upon the value of the property stolen, thefts of bicycles, automobile accessories, shop- lifting, pocket-picking, or any stealing of property

Modeling L2,3-Edge X-ray Absorption Spectroscopy with Real-Time Exact Two-Component Relativistic Time-Dependent Density Functional Theory.

PubMed

Kasper, Joseph M; Lestrange, Patrick J; Stetina, Torin F; Li, Xiaosong

2018-04-10

X-ray absorption spectroscopy is a powerful technique to probe local electronic and nuclear structure. There has been extensive theoretical work modeling K-edge spectra from first principles. However, modeling L-edge spectra directly with density functional theory poses a unique challenge requiring further study. Spin-orbit coupling must be included in the model, and a noncollinear density functional theory is required. Using the real-time exact two-component method, we are able to variationally include one-electron spin-orbit coupling terms when calculating the absorption spectrum. The abilities of different basis sets and density functionals to model spectra for both closed- and open-shell systems are investigated using SiCl 4 and three transition metal complexes, TiCl 4 , CrO 2 Cl 2 , and [FeCl 6 ] 3- . Although we are working in the real-time framework, individual molecular orbital transitions can still be recovered by projecting the density onto the ground state molecular orbital space and separating contributions to the time evolving dipole moment.

Application of time dependent Green's function method to scattering of elastic waves in anisotropic solids

NASA Astrophysics Data System (ADS)

Tewary, Vinod K.; Fortunko, Christopher M.

The present, time-dependent 3D Green's function method resembles that used to study the propagation of elastic waves in a general, anisotropic half-space in the lattice dynamics of crystals. The method is used to calculate the scattering amplitude of elastic waves from a discontinuity in the half-space; exact results are obtained for 3D pulse propagation in a general, anisotropic half-space that contains either an interior point or a planar scatterer. The results thus obtained are applicable in the design of ultrasonic scattering experiments, especially as an aid in the definition of the spatial and time-domain transducer responses that can maximize detection reliability for specific categories of flaws in highly anisotropic materials.

Monolayer phosphorene under time-dependent magnetic field

NASA Astrophysics Data System (ADS)

Nascimento, J. P. G.; Aguiar, V.; Guedes, I.

2018-02-01

We obtain the exact wave function of a monolayer phosphorene under a low-intensity time-dependent magnetic field using the dynamical invariant method. We calculate the quantum-mechanical energy expectation value and the transition probability for a constant and an oscillatory magnetic field. For the former we observe that the Landau level energy varies linearly with the quantum numbers n and m and the magnetic field intensity B0. No transition takes place. For the latter, we observe that the energy oscillates in time, increasing linearly with the Landau level n and m and nonlinearly with the magnetic field. The (k , l) →(n , m) transitions take place only for l = m. We investigate the (0,0) →(n , 0) and (1 , l) and (2 , l) probability transitions.

Unimolecular diffusion-mediated reactions with a nonrandom time-modulated absorbing barrier

NASA Technical Reports Server (NTRS)

Bashford, D.; Weaver, D. L.

1986-01-01

A diffusion-reaction model with time-dependent reactivity is formulated and applied to unimolecular reactions. The model is solved exactly numerically and approximately analytically for the unreacted fraction as a function of time. It is shown that the approximate analytical solution is valid even when the system is far from equilibrium, and when the reactivity probability is more complicated than a square-wave function of time. A discussion is also given of an approach to problems of this type using a stochastically fluctuating reactivity, and the first-passage time for a particular example is derived.

BPS equations and non-trivial compactifications

NASA Astrophysics Data System (ADS)

Tyukov, Alexander; Warner, Nicholas P.

2018-05-01

We consider the problem of finding exact, eleven-dimensional, BPS supergravity solutions in which the compactification involves a non-trivial Calabi-Yau manifold, Y , as opposed to simply a T 6. Since there are no explicitly-known metrics on non-trivial, compact Calabi-Yau manifolds, we use a non-compact "local model" and take the compactification manifold to be Y={M}_{GH}× {T}^2 , where ℳGH is a hyper-Kähler, Gibbons-Hawking ALE space. We focus on backgrounds with three electric charges in five dimensions and find exact families of solutions to the BPS equations that have the same four supersymmetries as the three-charge black hole. Our exact solution to the BPS system requires that the Calabi-Yau manifold be fibered over the space-time using compensators on Y . The role of the compensators is to ensure smoothness of the eleven-dimensional metric when the moduli of Y depend on the space-time. The Maxwell field Ansatz also implicitly involves the compensators through the frames of the fibration. We examine the equations of motion and discuss the brane distributions on generic internal manifolds that do not have enough symmetry to allow smearing.

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.

Kinetic Monte Carlo modeling of chemical reactions coupled with heat transfer.

PubMed

Castonguay, Thomas C; Wang, Feng

2008-03-28

In this paper, we describe two types of effective events for describing heat transfer in a kinetic Monte Carlo (KMC) simulation that may involve stochastic chemical reactions. Simulations employing these events are referred to as KMC-TBT and KMC-PHE. In KMC-TBT, heat transfer is modeled as the stochastic transfer of "thermal bits" between adjacent grid points. In KMC-PHE, heat transfer is modeled by integrating the Poisson heat equation for a short time. Either approach is capable of capturing the time dependent system behavior exactly. Both KMC-PHE and KMC-TBT are validated by simulating pure heat transfer in a rod and a square and modeling a heated desorption problem where exact numerical results are available. KMC-PHE is much faster than KMC-TBT and is used to study the endothermic desorption of a lattice gas. Interesting findings from this study are reported.

Kinetic Monte Carlo modeling of chemical reactions coupled with heat transfer

NASA Astrophysics Data System (ADS)

Castonguay, Thomas C.; Wang, Feng

2008-03-01

In this paper, we describe two types of effective events for describing heat transfer in a kinetic Monte Carlo (KMC) simulation that may involve stochastic chemical reactions. Simulations employing these events are referred to as KMC-TBT and KMC-PHE. In KMC-TBT, heat transfer is modeled as the stochastic transfer of "thermal bits" between adjacent grid points. In KMC-PHE, heat transfer is modeled by integrating the Poisson heat equation for a short time. Either approach is capable of capturing the time dependent system behavior exactly. Both KMC-PHE and KMC-TBT are validated by simulating pure heat transfer in a rod and a square and modeling a heated desorption problem where exact numerical results are available. KMC-PHE is much faster than KMC-TBT and is used to study the endothermic desorption of a lattice gas. Interesting findings from this study are reported.

Late time behaviors of an inhomogeneous rolling tachyon

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

Kwon, O-Kab; Lee, Chong Oh; Basic Science Research Institute, Chonbuk National University, Chonju 561-756

2006-06-15

We study an inhomogeneous decay of an unstable D-brane in the context of Dirac-Born-Infeld (DBI)-type effective action. We consider tachyon and electromagnetic fields with dependence of time and one spatial coordinate, and an exact solution is found under an exponentially decreasing tachyon potential, e{sup -|T|/{radical}}{sup (2)}, which is valid for the description of the late time behavior of an unstable D-brane. Though the obtained solution contains both time and spatial dependence, the corresponding momentum density vanishes over the entire spacetime region. The solution is governed by two parameters. One adjusts the distribution of energy density in the inhomogeneous direction, andmore » the other interpolates between the homogeneous rolling tachyon and static configuration. As time evolves, the energy of the unstable D-brane is converted into the electric flux and tachyon matter.« less

Trafficking of excitatory amino acid transporter 2- laden vesiclesin cultured astrocytes: a comparison between approximate and exact determination of trajectory angles

PubMed Central

Cavender, Chapin E.; Gottipati, Manoj K.; Parpura, Vladimir

2014-01-01

A clear consensus concerning the mechanisms of intracellular secretory vesicle trafficking in astrocytes is lacking in the physiological literature. A good characterization of vesicle trafficking that may assist researchers in achieving that goal is the trajectory angle, defined as the angle between the trajectory of a vesicle and a line radial to the cell’s nucleus. In this study, we provide a precise definition of the trajectory angle, describe and compare two methods for its calculation in terms of measureable trafficking parameters, and give recommendations for the appropriate use of each method. We investigated the trafficking of excitatory amino acid transporter 2 (EAAT2) fluorescently tagged with enhanced green fluorescent protein (EGFP) to quantify and validate the usefulness of each method. The motion of fluorescent puncta—taken to represent vesicles containing EAAT2-EGFP—was found to be typical of secretory vesicle trafficking. An exact method for calculating the trajectory angle of these puncta produced no error but required large computation time. An approximate method reduced the requisite computation time but produced an error that depended on the inverse of the ratio of the punctum’s initial distance from the nucleus centroid to its maximal displacement. Fitting this dependence to a power function allowed us to establish an exclusion distance from the centroid, beyond which the approximate method is much less likely to produce an error above acceptable 5 %. We recommend that the exact method be used to calculate the trajectory angle for puncta closer to the nucleus centroid than this exclusion distance. PMID:25408463

Applications of automatic differentiation in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Green, Lawrence L.; Carle, A.; Bischof, C.; Haigler, Kara J.; Newman, Perry A.

1994-01-01

Automatic differentiation (AD) is a powerful computational method that provides for computing exact sensitivity derivatives (SD) from existing computer programs for multidisciplinary design optimization (MDO) or in sensitivity analysis. A pre-compiler AD tool for FORTRAN programs called ADIFOR has been developed. The ADIFOR tool has been easily and quickly applied by NASA Langley researchers to assess the feasibility and computational impact of AD in MDO with several different FORTRAN programs. These include a state-of-the-art three dimensional multigrid Navier-Stokes flow solver for wings or aircraft configurations in transonic turbulent flow. With ADIFOR the user specifies sets of independent and dependent variables with an existing computer code. ADIFOR then traces the dependency path throughout the code, applies the chain rule to formulate derivative expressions, and generates new code to compute the required SD matrix. The resulting codes have been verified to compute exact non-geometric and geometric SD for a variety of cases. in less time than is required to compute the SD matrix using centered divided differences.

Measures for the Dynamics in a Few-Body Quantum System with Harmonic Interactions

NASA Astrophysics Data System (ADS)

Nagy, I.; Pipek, J.; Glasser, M. L.

2018-01-01

We determine the exact time-dependent non-idempotent one-particle reduced density matrix and its spectral decomposition for a harmonically confined two-particle correlated one-dimensional system when the interaction terms in the Schrödinger Hamiltonian are changed abruptly. Based on this matrix in coordinate space we derive a precise condition for the equivalence of the purity and the overlap-square of the correlated and non-correlated wave functions as the model system with harmonic interactions evolves in time. This equivalence holds only if the interparticle interactions are affected, while the confinement terms are unaffected within the stability range of the system. Under this condition we analyze various time-dependent measures of entanglement and demonstrate that, depending on the magnitude of the changes made in the Hamiltonian, periodic, logarithmically increasing or constant value behavior of the von Neumann entropy can occur.

Nonequilibrium Steady State Generated by a Moving Defect: The Supersonic Threshold

NASA Astrophysics Data System (ADS)

Bastianello, Alvise; De Luca, Andrea

2018-02-01

We consider the dynamics of a system of free fermions on a 1D lattice in the presence of a defect moving at constant velocity. The defect has the form of a localized time-dependent variation of the chemical potential and induces at long times a nonequilibrium steady state (NESS), which spreads around the defect. We present a general formulation that allows recasting the time-dependent protocol in a scattering problem on a static potential. We obtain a complete characterization of the NESS. In particular, we show a strong dependence on the defect velocity and the existence of a sharp threshold when such velocity exceeds the speed of sound. Beyond this value, the NESS is not produced and, remarkably, the defect travels without significantly perturbing the system. We present an exact solution for a δ -like defect traveling with an arbitrary velocity and we develop a semiclassical approximation that provides accurate results for smooth defects.

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

NASA Astrophysics Data System (ADS)

Park, DaeKil

2018-06-01

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

Monopole excitations of a harmonically trapped one-dimensional Bose gas from the ideal gas to the Tonks-Girardeau regime.

PubMed

Choi, S; Dunjko, V; Zhang, Z D; Olshanii, M

2015-09-11

Using a time-dependent modified nonlinear Schrödinger equation (MNLSE)-where the conventional chemical potential proportional to the density is replaced by the one inferred from Lieb-Liniger's exact solution-we study frequencies of the collective monopole excitations of a one-dimensional Bose gas. We find that our method accurately reproduces the results of a recent experimental study [E. Haller et al., Science 325, 1224 (2009)] in the full spectrum of interaction regimes from the ideal gas, through the mean-field regime, through the mean-field Thomas-Fermi regime, all the way to the Tonks-Giradeau gas. While the former two are accessible by the standard time-dependent NLSE and inaccessible by the time-dependent local density approximation, the situation reverses in the latter case. However, the MNLSE is shown to treat all these regimes within a single numerical method.

Time's arrow: A numerical experiment

NASA Astrophysics Data System (ADS)

Fowles, G. Richard

1994-04-01

The dependence of time's arrow on initial conditions is illustrated by a numerical example in which plane waves produced by an initial pressure pulse are followed as they are multiply reflected at internal interfaces of a layered medium. Wave interactions at interfaces are shown to be analogous to the retarded and advanced waves of point sources. The model is linear and the calculation is exact and demonstrably time reversible; nevertheless the results show most of the features expected of a macroscopically irreversible system, including the approach to the Maxwell-Boltzmann distribution, ergodicity, and concomitant entropy increase.

Time Delay in the Kuramoto Model of Coupled Oscillators

NASA Astrophysics Data System (ADS)

Yeung, M. K. Stephen; Strogatz, Steven H.

1999-01-01

We generalize the Kuramoto model of coupled oscillators to allow time-delayed interactions. New phenomena include bistability between synchronized and incoherent states, and unsteady solutions with time-dependent order parameters. We derive exact formulas for the stability boundaries of the incoherent and synchronized states, as a function of the delay, in the special case where the oscillators are identical. The experimental implications of the model are discussed for populations of chirping crickets, where the finite speed of sound causes communication delays, and for physical systems such as coupled phase-locked loops or lasers.

He3 Spin-Dependent Cross Sections and Sum Rules

NASA Astrophysics Data System (ADS)

Slifer, K.; Amarian, M.; Auerbach, L.; Averett, T.; Berthot, J.; Bertin, P.; Bertozzi, B.; Black, T.; Brash, E.; Brown, D.; Burtin, E.; Calarco, J.; Cates, G.; Chai, Z.; Chen, J.-P.; Choi, Seonho; Chudakov, E.; Ciofi Degli Atti, C.; Cisbani, E.; de Jager, C. W.; Deur, A.; Disalvo, R.; Dieterich, S.; Djawotho, P.; Finn, M.; Fissum, K.; Fonvieille, H.; Frullani, S.; Gao, H.; Gao, J.; Garibaldi, F.; Gasparian, A.; Gilad, S.; Gilman, R.; Glamazdin, A.; Glashausser, C.; Glöckle, W.; Golak, J.; Goldberg, E.; Gomez, J.; Gorbenko, V.; Hansen, J.-O.; Hersman, B.; Holmes, R.; Huber, G. M.; Hughes, E.; Humensky, B.; Incerti, S.; Iodice, M.; Jensen, S.; Jiang, X.; Jones, C.; Jones, G.; Jones, M.; Jutier, C.; Kamada, H.; Ketikyan, A.; Kominis, I.; Korsch, W.; Kramer, K.; Kumar, K.; Kumbartzki, G.; Kuss, M.; Lakuriqi, E.; Laveissiere, G.; Lerose, J. J.; Liang, M.; Liyanage, N.; Lolos, G.; Malov, S.; Marroncle, J.; McCormick, K.; McKeown, R. D.; Meziani, Z.-E.; Michaels, R.; Mitchell, J.; Nogga, A.; Pace, E.; Papandreou, Z.; Pavlin, T.; Petratos, G. G.; Pripstein, D.; Prout, D.; Ransome, R.; Roblin, Y.; Rowntree, D.; Rvachev, M.; Sabatié, F.; Saha, A.; Salmè, G.; Scopetta, S.; Skibiński, R.; Souder, P.; Saito, T.; Strauch, S.; Suleiman, R.; Takahashi, K.; Teijiro, S.; Todor, L.; Tsubota, H.; Ueno, H.; Urciuoli, G.; van der Meer, R.; Vernin, P.; Voskanian, H.; Witała, H.; Wojtsekhowski, B.; Xiong, F.; Xu, W.; Yang, J.-C.; Zhang, B.; Zolnierczuk, P.

2008-07-01

We present a measurement of the spin-dependent cross sections for the He→3(e→,e')X reaction in the quasielastic and resonance regions at a four-momentum transfer 0.1≤Q2≤0.9GeV2. The spin-structure functions have been extracted and used to evaluate the nuclear Burkhardt-Cottingham and extended Gerasimov-Drell-Hearn sum rules for the first time. The data are also compared to an impulse approximation calculation and an exact three-body Faddeev calculation in the quasielastic region.

New Quantum Diffusion Monte Carlo Method for strong field time dependent problems

NASA Astrophysics Data System (ADS)

Kalinski, Matt

2017-04-01

We have recently formulated the Quantum Diffusion Quantum Monte Carlo (QDMC) method for the solution of the time-dependent Schrödinger equation when it is equivalent to the reaction-diffusion system coupled by the highly nonlinear potentials of the type of Shay. Here we formulate a new Time Dependent QDMC method free of the nonlinearities described by the constant stochastic process of the coupled diffusion with transmutation. As before two kinds of diffusing particles (color walkers) are considered but which can further also transmute one into the other. Each of the species undergoes the hypothetical Einstein random walk progression with transmutation. The progressed particles transmute into the particles of the other kind before contributing to or annihilating the other particles density. This fully emulates the Time Dependent Schrödinger equation for any number of quantum particles. The negative sign of the real and the imaginary parts of the wave function is handled by the ``spinor'' densities carrying the sign as the degree of freedom. We apply the method for the exact time-dependent observation of our discovered two-electron Langmuir configurations in the magnetic and circularly polarized fields.

Exact mapping between different dynamics of isotropically trapped quantum gases

NASA Astrophysics Data System (ADS)

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

2016-05-01

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

DFT treatment of transport through Anderson junction: exact results and approximations

NASA Astrophysics Data System (ADS)

Burke, Kieron

2012-02-01

Since the pioneering break-junction experiments of Reed and Tour measuring the conductance of dithiolated benzene between gold leads, many researchers in physics and chemistry have been calculating conductance for such systems using density functional theory (DFT). Off resonance, the predicted current is often 10-100 times larger than that measured. This error is often ascribed to the application of ground-state DFT to a non-equilibrium problem. I will argue that, in fact, this is largely due to errors in the density functional approximations in popular use, rather than necessarily errors in the methodology. A stark illustration of this principle is the ability of DFT to reproduce the exact transmission through an Anderson junction at zero-temperature and weak bias, including the Kondo plateau, but only if the exact ground-state density functional is used. In fact, this case can be used to reverse-engineer the exact functional for this problem. Popular approximations can also be tested, including both smooth and discontinuous functionals of the density, as well as symmetry-broken approaches. [4pt] [1] Kondo effect given exactly by density functional theory, J. P. Bergfield, Z. Liu, K. Burke, and C. A. Stafford, arXiv:1106.3104; [0pt] [2] Broadening of the Derivative Discontinuity in Density Functional Theory, F. Evers, and P. Schmitteckert, arXiv:1106.3658; [0pt] [3] DFT-based transport calculations, Friedel's sum rule and the Kondo effect, P. Tr"oster, P. Schmitteckert, and F. Evers, arXiv:1106.3669; [0pt] [4] Towards a description of the Kondo effect using time-dependent density functional theory, G. Stefanucci, and S. Kurth, arXiv:1106.3728.

Voltage Quench Dynamics of a Kondo System.

PubMed

Antipov, Andrey E; Dong, Qiaoyuan; Gull, Emanuel

2016-01-22

We examine the dynamics of a correlated quantum dot in the mixed valence regime. We perform numerically exact calculations of the current after a quantum quench from equilibrium by rapidly applying a bias voltage in a wide range of initial temperatures. The current exhibits short equilibration times and saturates upon the decrease of temperature at all times, indicating Kondo behavior both in the transient regime and in the steady state. The time-dependent current saturation temperature connects the equilibrium Kondo temperature to a substantially increased value at voltages outside of the linear response. These signatures are directly observable by experiments in the time domain.

Fast inference of interactions in assemblies of stochastic integrate-and-fire neurons from spike recordings.

PubMed

Monasson, Remi; Cocco, Simona

2011-10-01

We present two Bayesian procedures to infer the interactions and external currents in an assembly of stochastic integrate-and-fire neurons from the recording of their spiking activity. The first procedure is based on the exact calculation of the most likely time courses of the neuron membrane potentials conditioned by the recorded spikes, and is exact for a vanishing noise variance and for an instantaneous synaptic integration. The second procedure takes into account the presence of fluctuations around the most likely time courses of the potentials, and can deal with moderate noise levels. The running time of both procedures is proportional to the number S of spikes multiplied by the squared number N of neurons. The algorithms are validated on synthetic data generated by networks with known couplings and currents. We also reanalyze previously published recordings of the activity of the salamander retina (including from 32 to 40 neurons, and from 65,000 to 170,000 spikes). We study the dependence of the inferred interactions on the membrane leaking time; the differences and similarities with the classical cross-correlation analysis are discussed.

Deposition and growth of domains in one dimension

NASA Astrophysics Data System (ADS)

Rodgers, G. J.; Tavassoli, Z.

1998-09-01

A model of deposition and growth in one dimension is studied in which finite sized domains are deposited by the random sequential adsorption process. The domains then grow with a time dependent growth rate. When the initial deposited domains are monomers and dimers the coverage is found exactly for a number of different growth rates. A continuum version of this model is also considered.

(U) An Analytic Study of Piezoelectric Ejecta Mass Measurements

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

Tregillis, Ian Lee

2017-02-16

We consider the piezoelectric measurement of the areal mass of an ejecta cloud, for the specific case where ejecta are created by a single shock at the free surface and fly ballistically through vacuum to the sensor. To do so, we define time- and velocity-dependent ejecta “areal mass functions” at the source and sensor in terms of typically unknown distribution functions for the ejecta particles. Next, we derive an equation governing the relationship between the areal mass function at the source (which resides in the rest frame of the free surface) and at the sensor (which resides in the laboratorymore » frame). We also derive expressions for the analytic (“true”) accumulated ejecta mass at the sensor and the measured (“inferred”) value obtained via the standard method for analyzing piezoelectric voltage traces. This approach enables us to derive an exact expression for the error imposed upon a piezoelectric ejecta mass measurement (in a perfect system) by the assumption of instantaneous creation. We verify that when the ejecta are created instantaneously (i.e., when the time dependence is a delta function), the piezoelectric inference method exactly reproduces the correct result. When creation is not instantaneous, the standard piezo analysis will always overestimate the true mass. However, the error is generally quite small (less than several percent) for most reasonable velocity and time dependences. In some cases, errors exceeding 10-15% may require velocity distributions or ejecta production timescales inconsistent with experimental observations. These results are demonstrated rigorously with numerous analytic test problems.« less

Two-stage unified stretched-exponential model for time-dependence of threshold voltage shift under positive-bias-stresses in amorphous indium-gallium-zinc oxide thin-film transistors

NASA Astrophysics Data System (ADS)

Jeong, Chan-Yong; Kim, Hee-Joong; Hong, Sae-Young; Song, Sang-Hun; Kwon, Hyuck-In

2017-08-01

In this study, we show that the two-stage unified stretched-exponential model can more exactly describe the time-dependence of threshold voltage shift (ΔV TH) under long-term positive-bias-stresses compared to the traditional stretched-exponential model in amorphous indium-gallium-zinc oxide (a-IGZO) thin-film transistors (TFTs). ΔV TH is mainly dominated by electron trapping at short stress times, and the contribution of trap state generation becomes significant with an increase in the stress time. The two-stage unified stretched-exponential model can provide useful information not only for evaluating the long-term electrical stability and lifetime of the a-IGZO TFT but also for understanding the stress-induced degradation mechanism in a-IGZO TFTs.

Bell-Plesset effects in Rayleigh-Taylor instability of finite-thickness spherical and cylindrical shells

NASA Astrophysics Data System (ADS)

Velikovich, A. L.; Schmit, P. F.

2015-11-01

Bell-Plesset effects accounting for the time dependence of the radius, velocity and acceleration of the Rayleigh-Taylor-unstable surface are ubiquitous in the instability of spherical laser targets and magnetically driven cylindrical liners. We present an analytical model that, for an ideal incompressible fluid and small perturbation amplitudes, exactly accounts for the Bell-Plesset effects in finite-thickness targets and liners through acceleration and deceleration phases. We derive the time-dependent dispersion equations determining the ``instantaneous growth rate'' and demonstrate that by integrating this growth rate over time (the WKB approximation) we accurately evaluate the number of perturbation e-foldings during the acceleration phase. In the limit of the small target/liner thickness, we obtain the exact thin-shell perturbation equations and approximate thin-shell dispersion relations, generalizing the earlier results of Harris (1962), Ott (1972) and Bud'ko et al. (1989). This research was supported by the US DOE/NNSA (A.L.V.), and in part by appointment to the Sandia National Laboratories Truman Fellowship in National Security Science and Engineering (P.F.S.), which is part of the Laboratory Directed Research and Development (LDRD) Program, Project No. 165746, and sponsored by Sandia Corporation (a wholly owned subsidiary of Lockheed Martin Corporation) as Operator of Sandia National Laboratories under its U.S. Department of Energy Contract No. DE-AC04-94AL85000.

Continuous-Time Random Walk with multi-step memory: an application to market dynamics

NASA Astrophysics Data System (ADS)

Gubiec, Tomasz; Kutner, Ryszard

2017-11-01

An extended version of the Continuous-Time Random Walk (CTRW) model with memory is herein developed. This memory involves the dependence between arbitrary number of successive jumps of the process while waiting times between jumps are considered as i.i.d. random variables. This dependence was established analyzing empirical histograms for the stochastic process of a single share price on a market within the high frequency time scale. Then, it was justified theoretically by considering bid-ask bounce mechanism containing some delay characteristic for any double-auction market. Our model appeared exactly analytically solvable. Therefore, it enables a direct comparison of its predictions with their empirical counterparts, for instance, with empirical velocity autocorrelation function. Thus, the present research significantly extends capabilities of the CTRW formalism. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

Approximate bilateral symmetry in evaporation-induced polycrystalline structures from droplets of wheat grain leakages and fluctuating asymmetry as quality indicator

NASA Astrophysics Data System (ADS)

Kokornaczyk, Maria Olga; Dinelli, Giovanni; Betti, Lucietta

2013-01-01

The present paper reports on an observation that dendrite-like polycrystalline structures from evaporating droplets of wheat grain leakages exhibit bilateral symmetry. The exactness of this symmetry, measured by means of fluctuating asymmetry, varies depending on the cultivar and stress factor influence, and seems to correspond to the seed germination rate. In the bodies of plants, animals, and humans, the exactness of bilateral symmetry is known to reflect the environmental conditions of an organism's growth, its health, and its success in sexual selection. In polycrystalline structures, formed under the same conditions, the symmetry exactness depends on the properties of the crystallizing solution such as the composition and viscosity; however, it has never been associated with sample quality. We hypothesize here that, as in living nature, the exactness of approximate bilateral symmetry might be considered a quality indicator also in crystallographic methods applied to food quality analysis.

Non-equilibrium steady states in the Klein-Gordon theory

NASA Astrophysics Data System (ADS)

Doyon, Benjamin; Lucas, Andrew; Schalm, Koenraad; Bhaseen, M. J.

2015-03-01

We construct non-equilibrium steady states in the Klein-Gordon theory in arbitrary space dimension d following a local quench. We consider the approach where two independently thermalized semi-infinite systems, with temperatures {{T}L} and {{T}R}, are connected along a d-1-dimensional hypersurface. A current-carrying steady state, described by thermally distributed modes with temperatures {{T}L} and {{T}R} for left and right-moving modes, respectively, emerges at late times. The non-equilibrium density matrix is the exponential of a non-local conserved charge. We obtain exact results for the average energy current and the complete distribution of energy current fluctuations. The latter shows that the long-time energy transfer can be described by a continuum of independent Poisson processes, for which we provide the exact weights. We further describe the full time evolution of local observables following the quench. Averages of generic local observables, including the stress-energy tensor, approach the steady state with a power-law in time, where the exponent depends on the initial conditions at the connection hypersurface. We describe boundary conditions and special operators for which the steady state is reached instantaneously on the connection hypersurface. A semiclassical analysis of freely propagating modes yields the average energy current at large distances and late times. We conclude by comparing and contrasting our findings with results for interacting theories and provide an estimate for the timescale governing the crossover to hydrodynamics. As a modification of our Klein-Gordon analysis we also include exact results for free Dirac fermions.

A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. I. General formalism and application to open-shell states.

PubMed

Miranda, R P; Fisher, A J; Stella, L; Horsfield, A P

2011-06-28

The solution of the time-dependent Schrödinger equation for systems of interacting electrons is generally a prohibitive task, for which approximate methods are necessary. Popular approaches, such as the time-dependent Hartree-Fock (TDHF) approximation and time-dependent density functional theory (TDDFT), are essentially single-configurational schemes. TDHF is by construction incapable of fully accounting for the excited character of the electronic states involved in many physical processes of interest; TDDFT, although exact in principle, is limited by the currently available exchange-correlation functionals. On the other hand, multiconfigurational methods, such as the multiconfigurational time-dependent Hartree-Fock (MCTDHF) approach, provide an accurate description of the excited states and can be systematically improved. However, the computational cost becomes prohibitive as the number of degrees of freedom increases, and thus, at present, the MCTDHF method is only practical for few-electron systems. In this work, we propose an alternative approach which effectively establishes a compromise between efficiency and accuracy, by retaining the smallest possible number of configurations that catches the essential features of the electronic wavefunction. Based on a time-dependent variational principle, we derive the MCTDHF working equation for a multiconfigurational expansion with fixed coefficients and specialise to the case of general open-shell states, which are relevant for many physical processes of interest.

A position-dependent mass model for the Thomas–Fermi potential: Exact solvability and relation to δ-doped semiconductors

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

Schulze-Halberg, Axel, E-mail: xbataxel@gmail.com; García-Ravelo, Jesús; Pacheco-García, Christian

We consider the Schrödinger equation in the Thomas–Fermi field, a model that has been used for describing electron systems in δ-doped semiconductors. It is shown that the problem becomes exactly-solvable if a particular effective (position-dependent) mass distribution is incorporated. Orthogonal sets of normalizable bound state solutions are constructed in explicit form, and the associated energies are determined. We compare our results with the corresponding findings on the constant-mass problem discussed by Ioriatti (1990) [13]. -- Highlights: ► We introduce an exactly solvable, position-dependent mass model for the Thomas–Fermi potential. ► Orthogonal sets of solutions to our model are constructed inmore » closed form. ► Relation to delta-doped semiconductors is discussed. ► Explicit subband bottom energies are calculated and compared to results obtained in a previous study.« less

Synchronization as Aggregation: Cluster Kinetics of Pulse-Coupled Oscillators.

PubMed

O'Keeffe, Kevin P; Krapivsky, P L; Strogatz, Steven H

2015-08-07

We consider models of identical pulse-coupled oscillators with global interactions. Previous work showed that under certain conditions such systems always end up in sync, but did not quantify how small clusters of synchronized oscillators progressively coalesce into larger ones. Using tools from the study of aggregation phenomena, we obtain exact results for the time-dependent distribution of cluster sizes as the system evolves from disorder to synchrony.

Molecular wave function and effective adiabatic potentials calculated by extended multi-configuration time-dependent Hartree-Fock method

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

Kato, Tsuyoshi; Ide, Yoshihiro; Yamanouchi, Kaoru

We first calculate the ground-state molecular wave function of 1D model H{sub 2} molecule by solving the coupled equations of motion formulated in the extended multi-configuration time-dependent Hartree-Fock (MCTDHF) method by the imaginary time propagation. From the comparisons with the results obtained by the Born-Huang (BH) expansion method as well as with the exact wave function, we observe that the memory size required in the extended MCTDHF method is about two orders of magnitude smaller than in the BH expansion method to achieve the same accuracy for the total energy. Second, in order to provide a theoretical means to understandmore » dynamical behavior of the wave function, we propose to define effective adiabatic potential functions and compare them with the conventional adiabatic electronic potentials, although the notion of the adiabatic potentials is not used in the extended MCTDHF approach. From the comparison, we conclude that by calculating the effective potentials we may be able to predict the energy differences among electronic states even for a time-dependent system, e.g., time-dependent excitation energies, which would be difficult to be estimated within the BH expansion approach.« less

Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces.

PubMed

Bardhan, Jaydeep P; Altman, Michael D; Willis, David J; Lippow, Shaun M; Tidor, Bruce; White, Jacob K

2007-07-07

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, here methods were developed to model several important surface formulations using exact surface discretizations. Following and refining Zauhar's work [J. Comput.-Aided Mol. Des. 9, 149 (1995)], two classes of curved elements were defined that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. Numerical integration techniques are presented that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, a set of calculations are presented that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planar-triangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute-solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that the methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online as supplemental material.

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.

On a two-phase Hele-Shaw problem with a time-dependent gap and distributions of sinks and sources

NASA Astrophysics Data System (ADS)

Savina, Tatiana; Akinyemi, Lanre; Savin, Avital

2018-01-01

A two-phase Hele-Shaw problem with a time-dependent gap describes the evolution of the interface, which separates two fluids sandwiched between two plates. The fluids have different viscosities. In addition to the change in the gap width of the Hele-Shaw cell, the interface is driven by the presence of some special distributions of sinks and sources located in both the interior and exterior domains. The effect of surface tension is neglected. Using the Schwarz function approach, we give examples of exact solutions when the interface belongs to a certain family of algebraic curves and the curves do not form cusps. The family of curves are defined by the initial shape of the free boundary.

Generic short-time propagation of sharp-boundaries wave packets

NASA Astrophysics Data System (ADS)

Granot, E.; Marchewka, A.

2005-11-01

A general solution to the "shutter" problem is presented. The propagation of an arbitrary initially bounded wave function is investigated, and the general solution for any such function is formulated. It is shown that the exact solution can be written as an expression that depends only on the values of the function (and its derivatives) at the boundaries. In particular, it is shown that at short times (t << 2mx2/hbar, where x is the distance to the boundaries) the wave function propagation depends only on the wave function's values (or its derivatives) at the boundaries of the region. Finally, we generalize these findings to a non-singular wave function (i.e., for wave packets with finite-width boundaries) and suggest an experimental verification.

A memory-efficient data structure representing exact-match overlap graphs with application for next-generation DNA assembly.

PubMed

Dinh, Hieu; Rajasekaran, Sanguthevar

2011-07-15

Exact-match overlap graphs have been broadly used in the context of DNA assembly and the shortest super string problem where the number of strings n ranges from thousands to billions. The length ℓ of the strings is from 25 to 1000, depending on the DNA sequencing technologies. However, many DNA assemblers using overlap graphs suffer from the need for too much time and space in constructing the graphs. It is nearly impossible for these DNA assemblers to handle the huge amount of data produced by the next-generation sequencing technologies where the number n of strings could be several billions. If the overlap graph is explicitly stored, it would require Ω(n(2)) memory, which could be prohibitive in practice when n is greater than a hundred million. In this article, we propose a novel data structure using which the overlap graph can be compactly stored. This data structure requires only linear time to construct and and linear memory to store. For a given set of input strings (also called reads), we can informally define an exact-match overlap graph as follows. Each read is represented as a node in the graph and there is an edge between two nodes if the corresponding reads overlap sufficiently. A formal description follows. The maximal exact-match overlap of two strings x and y, denoted by ov(max)(x, y), is the longest string which is a suffix of x and a prefix of y. The exact-match overlap graph of n given strings of length ℓ is an edge-weighted graph in which each vertex is associated with a string and there is an edge (x, y) of weight ω=ℓ-|ov(max)(x, y)| if and only if ω ≤ λ, where |ov(max)(x, y)| is the length of ov(max)(x, y) and λ is a given threshold. In this article, we show that the exact-match overlap graphs can be represented by a compact data structure that can be stored using at most (2λ-1)(2⌈logn⌉+⌈logλ⌉)n bits with a guarantee that the basic operation of accessing an edge takes O(log λ) time. We also propose two algorithms for constructing the data structure for the exact-match overlap graph. The first algorithm runs in O(λℓnlogn) worse-case time and requires O(λ) extra memory. The second one runs in O(λℓn) time and requires O(n) extra memory. Our experimental results on a huge amount of simulated data from sequence assembly show that the data structure can be constructed efficiently in time and memory. Our DNA sequence assembler that incorporates the data structure is freely available on the web at http://www.engr.uconn.edu/~htd06001/assembler/leap.zip

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

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

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

1998-07-01

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

A first-principles study of the influence of helium atoms on the optical response of small silver clusters.

PubMed

Pereiro, M; Baldomir, D; Arias, J E

2011-02-28

Optical excitation spectra of Ag(n) and Ag(n)@He(60) (n = 2, 8) clusters are investigated in the framework of the time-dependent density functional theory (TDDFT) within the linear response regime. We have performed the ab initio calculations for two different exact exchange functionals (GGA-exact and LDA-exact). The computed spectra of Ag(n)@He(60) clusters with the GGA-exact functional accounting for exchange-correlation effects are found to be generally in a relatively good agreement with the experiment. A strategy is proposed to obtain the ground-state structures of the Ag(n)@He(60) clusters and in the initial process of the geometry optimization, the He environment is simulated with buckyballs. A redshift of the silver clusters spectra is observed in the He environment with respect to the ones of bare silver clusters. This observation is discussed and explained in terms of a contraction of the Ag-He bonding length and a consequent confinement of the s valence electrons in silver clusters. Likewise, the Mie-Gans predictions combined with our TDDFT calculations also show that the dielectric effect produced by the He matrix is considerably less important in explaining the redshifting observed in the optical spectra of Ag(n)@He(60) clusters.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Evolution model with a cumulative feedback coupling

NASA Astrophysics Data System (ADS)

Trimper, Steffen; Zabrocki, Knud; Schulz, Michael

2002-05-01

The paper is concerned with a toy model that generalizes the standard Lotka-Volterra equation for a certain population by introducing a competition between instantaneous and accumulative, history-dependent nonlinear feedback the origin of which could be a contribution from any kind of mismanagement in the past. The results depend on the sign of that additional cumulative loss or gain term of strength λ. In case of a positive coupling the system offers a maximum gain achieved after a finite time but the population will die out in the long time limit. In this case the instantaneous loss term of strength u is irrelevant and the model exhibits an exact solution. In the opposite case λ<0 the time evolution of the system is terminated in a crash after ts provided u=0. This singularity after a finite time can be avoided if u≠0. The approach may well be of relevance for the qualitative understanding of more realistic descriptions.

Electronic field emission models beyond the Fowler-Nordheim one

NASA Astrophysics Data System (ADS)

Lepetit, Bruno

2017-12-01

We propose several quantum mechanical models to describe electronic field emission from first principles. These models allow us to correlate quantitatively the electronic emission current with the electrode surface details at the atomic scale. They all rely on electronic potential energy surfaces obtained from three dimensional density functional theory calculations. They differ by the various quantum mechanical methods (exact or perturbative, time dependent or time independent), which are used to describe tunneling through the electronic potential energy barrier. Comparison of these models between them and with the standard Fowler-Nordheim one in the context of one dimensional tunneling allows us to assess the impact on the accuracy of the computed current of the approximations made in each model. Among these methods, the time dependent perturbative one provides a well-balanced trade-off between accuracy and computational cost.

Tunable inertia of chiral magnetic domain walls

PubMed Central

Torrejon, Jacob; Martinez, Eduardo; Hayashi, Masamitsu

2016-01-01

The time it takes to accelerate an object from zero to a given velocity depends on the applied force and the environment. If the force ceases, it takes exactly the same time to completely decelerate. A magnetic domain wall is a topological object that has been observed to follow this behaviour. Here we show that acceleration and deceleration times of chiral Neel walls driven by current are different in a system with low damping and moderate Dzyaloshinskii–Moriya exchange constant. The time needed to accelerate a domain wall with current via the spin Hall torque is much faster than the time it needs to decelerate once the current is turned off. The deceleration time is defined by the Dzyaloshinskii–Moriya exchange constant whereas the acceleration time depends on the spin Hall torque, enabling tunable inertia of chiral domain walls. Such unique feature of chiral domain walls can be utilized to move and position domain walls with lower current, key to the development of storage class memory devices. PMID:27882932

Kinetic Description of Ionospheric Outflows Based on the Exact Form of Fokker-Planck Collision Operator: Electrons

NASA Technical Reports Server (NTRS)

Khazanov, George V.; Khabibrakhmanov, Ildar K.; Glocer, Alex

2012-01-01

We present the results of a finite difference implementation of the kinetic Fokker-Planck model with an exact form of the nonlinear collisional operator, The model is time dependent and three-dimensional; one spatial dimension and two in velocity space. The spatial dimension is aligned with the local magnetic field, and the velocity space is defined by the magnitude of the velocity and the cosine of pitch angle. An important new feature of model, the concept of integration along the particle trajectories, is discussed in detail. Integration along the trajectories combined with the operator time splitting technique results in a solution scheme which accurately accounts for both the fast convection of the particles along the magnetic field lines and relatively slow collisional process. We present several tests of the model's performance and also discuss simulation results of the evolution of the plasma distribution for realistic conditions in Earth's plasmasphere under different scenarios.

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Development of analytical methods of predicting the pressure distribution about a nacelle at transonic speeds: Exact solution

NASA Technical Reports Server (NTRS)

Grossman, B.; Moretti, G.

1973-01-01

A computer program to predict the inviscid, transonic flow field about isolated nacelles was developed. The problem was to be formulated to solve Euler's equations without any approximation (such as small disturbances) and hence the terminology exact solution. The flow field was complicated by the presence of imbedded shock waves, an engine-inlet interface, and exhaust plumes. Furthermore, the transonic nacelles of interest had a very slender but blunt cowl lip. This created two distinct length scales, the length of the nacelle and the cowl lip radius that can differ by several orders of magnitude. These aspects of the flow field presented many numerical difficulties. The approach to the problem was to calculate the nacelle flow field using the method of time-dependent computations (TDC). Although at the time of the issuance of this contract, other approaches to transonic flow calculations existed, it was felt that TDC offered the most effective means of meeting the goals of the contract.

Discrete conservation properties for shallow water flows using mixed mimetic spectral elements

NASA Astrophysics Data System (ADS)

Lee, D.; Palha, A.; Gerritsma, M.

2018-03-01

A mixed mimetic spectral element method is applied to solve the rotating shallow water equations. The mixed method uses the recently developed spectral element histopolation functions, which exactly satisfy the fundamental theorem of calculus with respect to the standard Lagrange basis functions in one dimension. These are used to construct tensor product solution spaces which satisfy the generalized Stokes theorem, as well as the annihilation of the gradient operator by the curl and the curl by the divergence. This allows for the exact conservation of first order moments (mass, vorticity), as well as higher moments (energy, potential enstrophy), subject to the truncation error of the time stepping scheme. The continuity equation is solved in the strong form, such that mass conservation holds point wise, while the momentum equation is solved in the weak form such that vorticity is globally conserved. While mass, vorticity and energy conservation hold for any quadrature rule, potential enstrophy conservation is dependent on exact spatial integration. The method possesses a weak form statement of geostrophic balance due to the compatible nature of the solution spaces and arbitrarily high order spatial error convergence.

Validated multiclass targeted determination of antibiotics in fish with high performance liquid chromatography-benchtop quadrupole orbitrap hybrid mass spectrometry.

PubMed

Chiesa, Luca; Panseri, Sara; Pasquale, Elisa; Malandra, Renato; Pavlovic, Radmila; Arioli, Francesco

2018-08-30

High performance liquid chromatography, coupled with a benchtop Q-Exactive Orbitrap high-resolution mass spectrometer, was successfully applied for the determination of 24 target antibiotics (selected beta-lactams, tetracyclines, fluoroquinolones, sulfonamids, phenicols, macrolides, cephalosporins, lincosamides, diaminopyrimidine) in fish matrices. The Q-Exactive parameters were carefully studied to accomplish the best compromise between a suitable scan speed and selectivity, considering the restrictions associated with generic sample preparation methodology. Retention time, an exact mass with tolerance of 2 ppm and data-dependent MS 2 spectra were the main identifiers. The method was validated through specificity, linearity, recovery, intra- and inter-day repeatability, decision limit (CCα) and detection capability (CCβ), according to 2002/657/EC. The values of CCα and CCβ ranged from 29.2 to 36.8 and 32.5 to 48.9, respectively, while overall recovery ranged from 91.1 to 105.6%. Fifty fish samples were analysed, showing the sporadic incidence of enrofloxacin, chlortetracycline, oxytetracycline, amoxicillin and trimethoprim, albeit below the maximum residual levels. Copyright © 2018 Elsevier Ltd. All rights reserved.

Accurate physical laws can permit new standard units: The two laws F→=ma→ and the proportionality of weight to mass

NASA Astrophysics Data System (ADS)

Saslow, Wayne M.

2014-04-01

Three common approaches to F→=ma→ are: (1) as an exactly true definition of force F→ in terms of measured inertial mass m and measured acceleration a→; (2) as an exactly true axiom relating measured values of a→, F→ and m; and (3) as an imperfect but accurately true physical law relating measured a→ to measured F→, with m an experimentally determined, matter-dependent constant, in the spirit of the resistance R in Ohm's law. In the third case, the natural units are those of a→ and F→, where a→ is normally specified using distance and time as standard units, and F→ from a spring scale as a standard unit; thus mass units are derived from force, distance, and time units such as newtons, meters, and seconds. The present work develops the third approach when one includes a second physical law (again, imperfect but accurate)—that balance-scale weight W is proportional to m—and the fact that balance-scale measurements of relative weight are more accurate than those of absolute force. When distance and time also are more accurately measurable than absolute force, this second physical law permits a shift to standards of mass, distance, and time units, such as kilograms, meters, and seconds, with the unit of force—the newton—a derived unit. However, were force and distance more accurately measurable than time (e.g., time measured with an hourglass), this second physical law would permit a shift to standards of force, mass, and distance units such as newtons, kilograms, and meters, with the unit of time—the second—a derived unit. Therefore, the choice of the most accurate standard units depends both on what is most accurately measurable and on the accuracy of physical law.

Exact analytic solution of position-dependent mass Schrödinger equation

NASA Astrophysics Data System (ADS)

Rajbongshi, Hangshadhar

2018-03-01

Exact analytic solution of position-dependent mass Schrödinger equation is generated by using extended transformation, a method of mapping a known system into a new system equipped with energy eigenvalues and corresponding wave functions. First order transformation is performed on D-dimensional radial Schrödinger equation with constant mass by taking trigonometric Pöschl-Teller potential as known system. The exactly solvable potentials with position-dependent mass generated for different choices of mass functions through first order transformation are also taken as known systems in the second order transformation performed on D-dimensional radial position-dependent mass Schrödinger equation. The solutions are fitted for "Zhu and Kroemer" ordering of ambiguity. All the wave functions corresponding to nonzero energy eigenvalues are normalizable. The new findings are that the normalizability condition of the wave functions remains independent of mass functions, and some of the generated potentials show a family relationship among themselves where power law potentials also get related to non-power law potentials and vice versa through the transformation.

Exact solutions, finite time singularities and non-singular universe models from a variety of Λ(t) cosmologies

NASA Astrophysics Data System (ADS)

Pan, Supriya

2018-01-01

Cosmological models with time-dependent Λ (read as Λ(t)) have been investigated widely in the literature. Models that solve background dynamics analytically are of special interest. Additionally, the allowance of past or future singularities at finite cosmic time in a specific model signals for a generic test on its viabilities with the current observations. Following these, in this work we consider a variety of Λ(t) models focusing on their evolutions and singular behavior. We found that a series of models in this class can be exactly solved when the background universe is described by a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) line element. The solutions in terms of the scale factor of the FLRW universe offer different universe models, such as power-law expansion, oscillating, and the singularity free universe. However, we also noticed that a large number of the models in this series permit past or future cosmological singularities at finite cosmic time. At last we close the work with a note that the avoidance of future singularities is possible for certain models under some specific restrictions.

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.

Distributed Continuous Event-Based Data Acquisition Using the IEEE 1588 Synchronization and FlexRIO FPGA

NASA Astrophysics Data System (ADS)

Taliercio, C.; Luchetta, A.; Manduchi, G.; Rigoni, A.

2017-07-01

High-speed event driven acquisition is normally performed by analog-to-digital converter (ADC) boards with a given number of pretrigger sample and posttrigger sample that are recorded upon the occurrence of a hardware trigger. A direct physical connection is, therefore, required between the source of event (trigger) and the ADC, because any other software-based communication method would introduce a delay in triggering that would turn out to be not acceptable in many cases. This paper proposes a solution for the relaxation of the event communication time that can be, in this case, carried out by software messaging (e.g., via an LAN), provided that the system components are synchronized in time using the IEEE 1588 synchronization mechanism. The information about the exact event occurrence time is contained in the software packet that is sent to communicate the event and is used by the ADC FPGA to identify the exact sample in the ADC sample queue. The length of the ADC sample queue will depend on the maximum delay in software event message communication time. A prototype implementation using a National FlexRIO FPGA board connected with an ADC device is presented as the proof of concept.

Exact-Differential Large-Scale Traffic Simulation

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

Hanai, Masatoshi; Suzumura, Toyotaro; Theodoropoulos, Georgios

2015-01-01

Analyzing large-scale traffics by simulation needs repeating execution many times with various patterns of scenarios or parameters. Such repeating execution brings about big redundancy because the change from a prior scenario to a later scenario is very minor in most cases, for example, blocking only one of roads or changing the speed limit of several roads. In this paper, we propose a new redundancy reduction technique, called exact-differential simulation, which enables to simulate only changing scenarios in later execution while keeping exactly same results as in the case of whole simulation. The paper consists of two main efforts: (i) amore » key idea and algorithm of the exact-differential simulation, (ii) a method to build large-scale traffic simulation on the top of the exact-differential simulation. In experiments of Tokyo traffic simulation, the exact-differential simulation shows 7.26 times as much elapsed time improvement in average and 2.26 times improvement even in the worst case as the whole simulation.« less

Gravity Gradient Tensor of Arbitrary 3D Polyhedral Bodies with up to Third-Order Polynomial Horizontal and Vertical Mass Contrasts

NASA Astrophysics Data System (ADS)

Ren, Zhengyong; Zhong, Yiyuan; Chen, Chaojian; Tang, Jingtian; Kalscheuer, Thomas; Maurer, Hansruedi; Li, Yang

2018-03-01

During the last 20 years, geophysicists have developed great interest in using gravity gradient tensor signals to study bodies of anomalous density in the Earth. Deriving exact solutions of the gravity gradient tensor signals has become a dominating task in exploration geophysics or geodetic fields. In this study, we developed a compact and simple framework to derive exact solutions of gravity gradient tensor measurements for polyhedral bodies, in which the density contrast is represented by a general polynomial function. The polynomial mass contrast can continuously vary in both horizontal and vertical directions. In our framework, the original three-dimensional volume integral of gravity gradient tensor signals is transformed into a set of one-dimensional line integrals along edges of the polyhedral body by sequentially invoking the volume and surface gradient (divergence) theorems. In terms of an orthogonal local coordinate system defined on these edges, exact solutions are derived for these line integrals. We successfully derived a set of unified exact solutions of gravity gradient tensors for constant, linear, quadratic and cubic polynomial orders. The exact solutions for constant and linear cases cover all previously published vertex-type exact solutions of the gravity gradient tensor for a polygonal body, though the associated algorithms may differ in numerical stability. In addition, to our best knowledge, it is the first time that exact solutions of gravity gradient tensor signals are derived for a polyhedral body with a polynomial mass contrast of order higher than one (that is quadratic and cubic orders). Three synthetic models (a prismatic body with depth-dependent density contrasts, an irregular polyhedron with linear density contrast and a tetrahedral body with horizontally and vertically varying density contrasts) are used to verify the correctness and the efficiency of our newly developed closed-form solutions. Excellent agreements are obtained between our solutions and other published exact solutions. In addition, stability tests are performed to demonstrate that our exact solutions can safely be used to detect shallow subsurface targets.

Structure-specific magnetic field inhomogeneities and its effect on the correlation time.

PubMed

Ziener, Christian H; Bauer, Wolfgang R; Melkus, Gerd; Weber, Thomas; Herold, Volker; Jakob, Peter M

2006-12-01

We describe the relationship between the correlation time and microscopic spatial inhomogeneities in the static magnetic field. The theory takes into account diffusion of nuclear spins in the inhomogeneous field created by magnetized objects. A simple general expression for the correlation time is obtained. It is shown that the correlation time is dependent on a characteristic length, the diffusion coefficient of surrounding medium, the permeability of the surface and the volume fraction of the magnetized objects. For specific geometries (spheres and cylinders), exact analytical expressions for the correlation time are given. The theory can be applied to contrast agents (magnetically labeled cells), capillary network, BOLD effect and so forth.

Brownian motion in time-dependent logarithmic potential: Exact results for dynamics and first-passage properties.

PubMed

Ryabov, Artem; Berestneva, Ekaterina; Holubec, Viktor

2015-09-21

The paper addresses Brownian motion in the logarithmic potential with time-dependent strength, U(x, t) = g(t)log(x), subject to the absorbing boundary at the origin of coordinates. Such model can represent kinetics of diffusion-controlled reactions of charged molecules or escape of Brownian particles over a time-dependent entropic barrier at the end of a biological pore. We present a simple asymptotic theory which yields the long-time behavior of both the survival probability (first-passage properties) and the moments of the particle position (dynamics). The asymptotic survival probability, i.e., the probability that the particle will not hit the origin before a given time, is a functional of the potential strength. As such, it exhibits a rather varied behavior for different functions g(t). The latter can be grouped into three classes according to the regime of the asymptotic decay of the survival probability. We distinguish 1. the regular (power-law decay), 2. the marginal (power law times a slow function of time), and 3. the regime of enhanced absorption (decay faster than the power law, e.g., exponential). Results of the asymptotic theory show good agreement with numerical simulations.

Geometric Implications of Maxwell's Equations

NASA Astrophysics Data System (ADS)

Smith, Felix T.

2015-03-01

Maxwell's synthesis of the varied results of the accumulated knowledge of electricity and magnetism, based largely on the searching insights of Faraday, still provide new issues to explore. A case in point is a well recognized anomaly in the Maxwell equations: The laws of electricity and magnetism require two 3-vector and two scalar equations, but only six dependent variables are available to be their solutions, the 3-vectors E and B. This leaves an apparent redundancy of two degrees of freedom (J. Rosen, AJP 48, 1071 (1980); Jiang, Wu, Povinelli, J. Comp. Phys. 125, 104 (1996)). The observed self-consistency of the eight equations suggests that they contain additional information. This can be sought as a previously unnoticed constraint connecting the space and time variables, r and t. This constraint can be identified. It distorts the otherwise Euclidean 3-space of r with the extremely slight, time dependent curvature k (t) =Rcurv-2 (t) of the 3-space of a hypersphere whose radius has the time dependence dRcurv / dt = +/- c nonrelativistically, or dRcurvLor / dt = +/- ic relativistically. The time dependence is exactly that of the Hubble expansion. Implications of this identification will be explored.

Exact simulation of polarized light reflectance by particle deposits

NASA Astrophysics Data System (ADS)

Ramezan Pour, B.; Mackowski, D. W.

2015-12-01

The use of polarimetric light reflection measurements as a means of identifying the physical and chemical characteristics of particulate materials obviously relies on an accurate model of predicting the effects of particle size, shape, concentration, and refractive index on polarized reflection. The research examines two methods for prediction of reflection from plane parallel layers of wavelength—sized particles. The first method is based on an exact superposition solution to Maxwell's time harmonic wave equations for a deposit of spherical particles that are exposed to a plane incident wave. We use a FORTRAN-90 implementation of this solution (the Multiple Sphere T Matrix (MSTM) code), coupled with parallel computational platforms, to directly simulate the reflection from particle layers. The second method examined is based upon the vector radiative transport equation (RTE). Mie theory is used in our RTE model to predict the extinction coefficient, albedo, and scattering phase function of the particles, and the solution of the RTE is obtained from adding—doubling method applied to a plane—parallel configuration. Our results show that the MSTM and RTE predictions of the Mueller matrix elements converge when particle volume fraction in the particle layer decreases below around five percent. At higher volume fractions the RTE can yield results that, depending on the particle size and refractive index, significantly depart from the exact predictions. The particle regimes which lead to dependent scattering effects, and the application of methods to correct the vector RTE for particle interaction, will be discussed.

Exact Solutions for Stokes' Flow of a Non-Newtonian Nanofluid Model: A Lie Similarity Approach

NASA Astrophysics Data System (ADS)

Aziz, Taha; Aziz, A.; Khalique, C. M.

2016-07-01

The fully developed time-dependent flow of an incompressible, thermodynamically compatible non-Newtonian third-grade nanofluid is investigated. The classical Stokes model is considered in which the flow is generated due to the motion of the plate in its own plane with an impulsive velocity. The Lie symmetry approach is utilised to convert the governing nonlinear partial differential equation into different linear and nonlinear ordinary differential equations. The reduced ordinary differential equations are then solved by using the compatibility and generalised group method. Exact solutions for the model equation are deduced in the form of closed-form exponential functions which are not available in the literature before. In addition, we also derived the conservation laws associated with the governing model. Finally, the physical features of the pertinent parameters are discussed in detail through several graphs.

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

PubMed

Martirosyan, A; Saakian, David B

2011-08-01

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

Memory effects on a resonate-and-fire neuron model subjected to Ornstein-Uhlenbeck noise

NASA Astrophysics Data System (ADS)

Paekivi, S.; Mankin, R.; Rekker, A.

2017-10-01

We consider a generalized Langevin equation with an exponentially decaying memory kernel as a model for the firing process of a resonate-and-fire neuron. The effect of temporally correlated random neuronal input is modeled as Ornstein-Uhlenbeck noise. In the noise-induced spiking regime of the neuron, we derive exact analytical formulas for the dependence of some statistical characteristics of the output spike train, such as the probability distribution of the interspike intervals (ISIs) and the survival probability, on the parameters of the input stimulus. Particularly, on the basis of these exact expressions, we have established sufficient conditions for the occurrence of memory-time-induced transitions between unimodal and multimodal structures of the ISI density and a critical damping coefficient which marks a dynamical transition in the behavior of the system.

Time-dependent quantum wave packet calculation for nonadiabatic F(2P3/2,2P1/2)+H2 reaction

NASA Astrophysics Data System (ADS)

Zhang, Yan; Xie, Ting-Xian; Han, Ke-Li; Zhang, John Z. H.

2003-12-01

In this paper we present a time-dependent quantum wave packet calculation for the reaction of F(2P3/2,2P1/2)+H2 on the Alexander-Stark-Werner potential energy surface. The reaction probabilities and the integral cross sections for the reaction of F(2P3/2,2P1/2)+H2 (v=j=0) are computed using time-dependent quantum methods with the centrifugal sudden approximate. The results are compared with recent time-independent quantum calculations. The two-surface reaction probability for the initial ground spin-orbit state of J=0.5 is similar to the time-independent result obtained by Alexander et al. [J. Chem. Phys. 113, 11084 (2000)]. Our calculation also shows that electronic coupling has a relatively minor effect on the reactivity from the 2P3/2 state but a non-negligible one from the 2P1/2 state. By comparison with exact time-independent calculations, it is found that the Coriolis coupling plays a relatively minor role. In addition, most of the reactivity of the excited state of fluorine atom results from the spin-orbit coupling.

Green's Functions from Real-Time Bold-Line Monte Carlo Calculations: Spectral Properties of the Nonequilibrium Anderson Impurity Model

NASA Astrophysics Data System (ADS)

Cohen, Guy; Gull, Emanuel; Reichman, David R.; Millis, Andrew J.

2014-04-01

The nonequilibrium spectral properties of the Anderson impurity model with a chemical potential bias are investigated within a numerically exact real-time quantum Monte Carlo formalism. The two-time correlation function is computed in a form suitable for nonequilibrium dynamical mean field calculations. Additionally, the evolution of the model's spectral properties are simulated in an alternative representation, defined by a hypothetical but experimentally realizable weakly coupled auxiliary lead. The voltage splitting of the Kondo peak is confirmed and the dynamics of its formation after a coupling or gate quench are studied. This representation is shown to contain additional information about the dot's population dynamics. Further, we show that the voltage-dependent differential conductance gives a reasonable qualitative estimate of the equilibrium spectral function, but significant qualitative differences are found including incorrect trends and spurious temperature dependent effects.

Modeling high-order synchronization epochs and transitions in the cardiovascular system

NASA Astrophysics Data System (ADS)

García-Álvarez, David; Bahraminasab, Alireza; Stefanovska, Aneta; McClintock, Peter V. E.

2007-12-01

We study a system consisting of two coupled phase oscillators in the presence of noise. This system is used as a model for the cardiorespiratory interaction in wakefulness and anaesthesia. We show that longrange correlated noise produces transitions between epochs with different n:m synchronisation ratios, as observed in the cardiovascular system. Also, we see that, the smaller the noise (specially the one acting on the slower oscillator), the bigger the synchronisation time, exactly as happens in anaesthesia compared with wakefulness. The dependence of the synchronisation time on the couplings, in the presence of noise, is studied; such dependence is softened by low-frequency noise. We show that the coupling from the slow oscillator to the fast one (respiration to heart) plays a more important role in synchronisation. Finally, we see that the isolines with same synchronisation time seem to be a linear combination of the two couplings.

Quantum non-Abelian hydrodynamics: Anyonic or spin-orbital entangled liquids, nonunitarity of scattering matrix and charge fractionalization

NASA Astrophysics Data System (ADS)

Pareek, Tribhuvan Prasad

2015-09-01

In this article, we develop an exact (nonadiabatic, nonperturbative) density matrix scattering theory for a two component quantum liquid which interacts or scatters off from a generic spin-dependent quantum potential. The generic spin dependent quantum potential [Eq. (1)] is a matrix potential, hence, adiabaticity criterion is ill-defined. Therefore the full matrix potential should be treated nonadiabatically. We succeed in doing so using the notion of vectorial matrices which allows us to obtain an exact analytical expression for the scattered density matrix (SDM), ϱsc [Eq. (30)]. We find that the number or charge density in scattered fluid, Tr(ϱsc), expressions in Eqs. (32) depends on nontrivial quantum interference coefficients, Qα β 0ijk, which arises due to quantum interference between spin-independent and spin-dependent scattering amplitudes and among spin-dependent scattering amplitudes. Further it is shown that Tr(ϱsc) can be expressed in a compact form [Eq. (39)] where the effect of quantum interference coefficients can be included using a vector Qαβ, which allows us to define a vector order parameterQ. Since the number density is obtained using an exact scattered density matrix, therefore, we do not need to prove that Q is non-zero. However, for sake of completeness, we make detailed mathematical analysis for the conditions under which the vector order parameterQ would be zero or nonzero. We find that in presence of spin-dependent interaction the vector order parameterQ is necessarily nonzero and is related to the commutator and anti-commutator of scattering matrix S with its dagger S† [Eq. (78)]. It is further shown that Q≠0, implies four physically equivalent conditions,i.e., spin-orbital entanglement is nonzero, non-Abelian scattering phase, i.e., matrices, scattering matrix is nonunitary and the broken time reversal symmetry for SDM. This also implies that quasi particle excitation are anyonic in nature, hence, charge fractionalization is a natural consequence. This aspect has also been discussed from the perspective of number or charge density conservation, which implies i.e., Tr(ϱ} sc) = Tr(ϱin). On the other hand Q = 0 turns out to be a mathematically forced unphysical solution in presence of spin-dependent potential or scattering which is equivalent to Abelian hydrodynamics, unitary scattering matrix, absence of spin-space entanglement and preserved time reversal symmetry. We have formulated the theory using mesoscopic language, specifically, we have considered two terminal systems connected to spin-dependent scattering region, which is equivalent to having two potential wells separated by a generic spin-dependent potential barrier. The formulation using mesoscopic language is practically useful because it leads directly to the measured quantities such as conductance and spin-polarization density in the leads, however, the presented formulation is not limited to the mesoscopic system only, its generality has been stressed at various places in this article.

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

NASA Astrophysics Data System (ADS)

Saakian, David B.

2017-08-01

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

Collision Dynamics of Rydberg Atoms and Molecules at Ultralow Energies

DTIC Science & Technology

2005-12-31

body recombination between electrons, ions and neural gas atoms. We wish to study the interaction and collisions between two Rydberg atoms in the...transitions, Exact solutions of Stark mixing in atomic hydro- where Ekjn is the Levi - Civita antisymmetric symbol gen induced by the time-dependent...L and U do not close under commutation to form a Lie algebra because [Ui, Uj] = (-2g)iCijkLk, where cijk is the Levi - Civita antisymmetric symbol for

Stratified Shear Flows In Pipe Geometries

NASA Astrophysics Data System (ADS)

Harabin, George; Camassa, Roberto; McLaughlin, Richard; UNC Joint Fluids Lab Team Team

2015-11-01

Exact and series solutions to the full Navier-Stokes equations coupled to the advection diffusion equation are investigated in tilted three-dimensional pipe geometries. Analytic techniques for studying the three-dimensional problem provide a means for tackling interesting questions such as the optimal domain for mass transport, and provide new avenues for experimental investigation of diffusion driven flows. Both static and time dependent solutions will be discussed. NSF RTG DMS-0943851, NSF RTG ARC-1025523, NSF DMS-1009750.

Heisenberg operator approach for spin squeezing dynamics

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Summer Research Program (1992). Graduate Student Research Programs Reports. Armstrong Laboratory. Volume 7

DTIC Science & Technology

1992-12-28

vehicle rolled over a switch which caused hydraulic cylinders to actuate. These cylinders pushed the truck from the cart, and the cart decelerated. The... hydraulic cylinders on the cart began to push the vehicle. So, to determine the exact time that the 30 cylinders began to move, plots were 25 - studied...attempts because of its dependence on well understood hydraulic principles and because of the wealth of understanding about the various constituent

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

PubMed

Chen, Lipeng; Borrelli, Raffaele; Zhao, Yang

2017-11-22

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

Calculating pH-dependent free energy of proteins by using Monte Carlo protonation probabilities of ionizable residues.

PubMed

Huang, Qiang; Herrmann, Andreas

2012-03-01

Protein folding, stability, and function are usually influenced by pH. And free energy plays a fundamental role in analysis of such pH-dependent properties. Electrostatics-based theoretical framework using dielectric solvent continuum model and solving Poisson-Boltzmann equation numerically has been shown to be very successful in understanding the pH-dependent properties. However, in this approach the exact computation of pH-dependent free energy becomes impractical for proteins possessing more than several tens of ionizable sites (e.g. > 30), because exact evaluation of the partition function requires a summation over a vast number of possible protonation microstates. Here we present a method which computes the free energy using the average energy and the protonation probabilities of ionizable sites obtained by the well-established Monte Carlo sampling procedure. The key feature is to calculate the entropy by using the protonation probabilities. We used this method to examine a well-studied protein (lysozyme) and produced results which agree very well with the exact calculations. Applications to the optimum pH of maximal stability of proteins and protein-DNA interactions have also resulted in good agreement with experimental data. These examples recommend our method for application to the elucidation of the pH-dependent properties of proteins.

Numerical Integration Techniques for Curved-Element Discretizations of Molecule–Solvent Interfaces

PubMed Central

Bardhan, Jaydeep P.; Altman, Michael D.; Willis, David J.; Lippow, Shaun M.; Tidor, Bruce; White, Jacob K.

2012-01-01

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, we have developed methods to model several important surface formulations using exact surface discretizations. Following and refining Zauhar’s work (J. Comp.-Aid. Mol. Des. 9:149-159, 1995), we define two classes of curved elements that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. We then present numerical integration techniques that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, we present a set of calculations that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planartriangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute–solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that our methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online at http://web.mit.edu/tidor. PMID:17627358

A new class of accelerated kinetic Monte Carlo algorithms

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

Bulatov, V V; Oppelstrup, T; Athenes, M

2011-11-30

Kinetic (aka dynamic) Monte Carlo (KMC) is a powerful method for numerical simulations of time dependent evolution applied in a wide range of contexts including biology, chemistry, physics, nuclear sciences, financial engineering, etc. Generally, in a KMC the time evolution takes place one event at a time, where the sequence of events and the time intervals between them are selected (or sampled) using random numbers. While details of the method implementation vary depending on the model and context, there exist certain common issues that limit KMC applicability in almost all applications. Among such is the notorious 'flicker problem' where themore » same states of the systems are repeatedly visited but otherwise no essential evolution is observed. In its simplest form the flicker problem arises when two states are connected to each other by transitions whose rates far exceed the rates of all other transitions out of the same two states. In such cases, the model will endlessly hop between the two states otherwise producing no meaningful evolution. In most situation of practical interest, the trapping cluster includes more than two states making the flicker somewhat more difficult to detect and to deal with. Several methods have been proposed to overcome or mitigate the flicker problem, exactly [1-3] or approximately [4,5]. Of the exact methods, the one proposed by Novotny [1] is perhaps most relevant to our research. Novotny formulates the problem of escaping from a trapping cluster as a Markov system with absorbing states. Given an initial state inside the cluster, it is in principle possible to solve the Master Equation for the time dependent probabilities to find the walker in a given state (transient or absorbing) of the cluster at any time in the future. Novotny then proceeds to demonstrate implementation of his general method to trapping clusters containing the initial state plus one or two transient states and all of their absorbing states. Similar methods have been subsequently proposed in [refs] but applied in a different context. The most serious deficiency of the earlier methods is that size of the trapping cluster size is fixed and often too small to bring substantial simulation speedup. Furthermore, the overhead associated with solving for the probability distribution on the trapping cluster sometimes makes such simulations less efficient than the standard KMC. Here we report on a general and exact accelerated kinetic Monte Carlo algorithm generally applicable to arbitrary Markov models1. Two different implementations are attempted both based on incremental expansion of trapping sub-set of Markov states: (1) numerical solution of the Master Equation with absorbing states and (2) incremental graph reduction followed by randomization. Of the two implementations, the 2nd one performs better allowing, for the first time, to overcome trapping basins spanning several million Markov states. The new method is used for simulations of anomalous diffusion on a 2D substrate and of the kinetics of diffusive 1st order phase transformations in binary alloys. Depending on temperature and (alloy) super-saturation conditions, speedups of 3 to 7 orders of magnitude are demonstrated, with no compromise of simulation accuracy.« less

An Algorithm for the Calculation of Exact Term Discrimination Values.

ERIC Educational Resources Information Center

Willett, Peter

1985-01-01

Reports algorithm for calculation of term discrimination values that is sufficiently fast in operation to permit use of exact values. Evidence is presented to show that relationship between term discrimination and term frequency is crucially dependent upon type of inter-document similarity measure used for calculation of discrimination values. (13…

Chemical dynamics between wells across a time-dependent barrier: Self-similarity in the Lagrangian descriptor and reactive basins.

PubMed

Junginger, Andrej; Duvenbeck, Lennart; Feldmaier, Matthias; Main, Jörg; Wunner, Günter; Hernandez, Rigoberto

2017-08-14

In chemical or physical reaction dynamics, it is essential to distinguish precisely between reactants and products for all times. This task is especially demanding in time-dependent or driven systems because therein the dividing surface (DS) between these states often exhibits a nontrivial time-dependence. The so-called transition state (TS) trajectory has been seen to define a DS which is free of recrossings in a large number of one-dimensional reactions across time-dependent barriers and thus, allows one to determine exact reaction rates. A fundamental challenge to applying this method is the construction of the TS trajectory itself. The minimization of Lagrangian descriptors (LDs) provides a general and powerful scheme to obtain that trajectory even when perturbation theory fails. Both approaches encounter possible breakdowns when the overall potential is bounded, admitting the possibility of returns to the barrier long after the trajectories have reached the product or reactant wells. Such global dynamics cannot be captured by perturbation theory. Meanwhile, in the LD-DS approach, it leads to the emergence of additional local minima which make it difficult to extract the optimal branch associated with the desired TS trajectory. In this work, we illustrate this behavior for a time-dependent double-well potential revealing a self-similar structure of the LD, and we demonstrate how the reflections and side-minima can be addressed by an appropriate modification of the LD associated with the direct rate across the barrier.

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

PubMed

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

1991-07-01

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

Correlated Light-Matter Interactions in Cavity QED

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

Quantum Chemistry on Quantum Computers: A Polynomial-Time Quantum Algorithm for Constructing the Wave Functions of Open-Shell Molecules.

PubMed

Sugisaki, Kenji; Yamamoto, Satoru; Nakazawa, Shigeaki; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Takui, Takeji

2016-08-18

Quantum computers are capable to efficiently perform full configuration interaction (FCI) calculations of atoms and molecules by using the quantum phase estimation (QPE) algorithm. Because the success probability of the QPE depends on the overlap between approximate and exact wave functions, efficient methods to prepare accurate initial guess wave functions enough to have sufficiently large overlap with the exact ones are highly desired. Here, we propose a quantum algorithm to construct the wave function consisting of one configuration state function, which is suitable for the initial guess wave function in QPE-based FCI calculations of open-shell molecules, based on the addition theorem of angular momentum. The proposed quantum algorithm enables us to prepare the wave function consisting of an exponential number of Slater determinants only by a polynomial number of quantum operations.

Determining the Binding Sites of β-Cyclodextrin and Peptides by Electron-Capture Dissociation High Resolution Tandem Mass Spectrometry

NASA Astrophysics Data System (ADS)

Qi, Yulin; Geib, Timon; Volmer, Dietrich A.

2015-07-01

Cyclodextrins (CDs) are a group of cyclic oligosaccharides, which readily form inclusion complexes with hydrophobic compounds to increase bioavailability, thus making CDs ideal drug excipients. Recent studies have also shown that CDs exhibit a wide range of protective effects, preventing proteins from aggregation, degradation, and folding. These effects strongly depend on the binding sites on the protein surface. CDs only exhibit weak interactions with amino acids, however; conventional analytical techniques therefore usually fail to reveal the exact location of the binding sites. Moreover, some studies even suggest that CD inclusion complexes are merely electrostatic adducts. Here, electron capture dissociation (ECD) was applied in this proof-of-concept study to examine the exact nature of the CD/peptide complexes, and CD binding sites were unambiguously located for the first time via Fourier-transform ion cyclotron resonance (FTICR) tandem mass spectrometry.

Correlation functions in first-order phase transitions

NASA Astrophysics Data System (ADS)

Garrido, V.; Crespo, D.

1997-09-01

Most of the physical properties of systems underlying first-order phase transitions can be obtained from the spatial correlation functions. In this paper, we obtain expressions that allow us to calculate all the correlation functions from the droplet size distribution. Nucleation and growth kinetics is considered, and exact solutions are obtained for the case of isotropic growth by using self-similarity properties. The calculation is performed by using the particle size distribution obtained by a recently developed model (populational Kolmogorov-Johnson-Mehl-Avrami model). Since this model is less restrictive than that used in previously existing theories, the result is that the correlation functions can be obtained for any dependence of the kinetic parameters. The validity of the method is tested by comparison with the exact correlation functions, which had been obtained in the available cases by the time-cone method. Finally, the correlation functions corresponding to the microstructure developed in partitioning transformations are obtained.

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

Sinitsyn, Nikolai A.

In this paper, I identify a nontrivial four-state Landau-Zener model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. The model describes an experimentally accessible system of two interacting qubits, such as a localized state in a Dirac material with both valley and spin degrees of freedom or a singly charged quantum dot (QD) molecule with spin orbit coupling. Application of the linearly time-dependent magnetic field induces a sequence of quantum level crossings with possibility of interference of different trajectories in a semiclassical picture. I argue that this system satisfies the criteria ofmore » integrability in the multistate Landau-Zener theory, which allows one to derive explicit exact analytical expressions for the transition probability matrix. Finally, I also argue that this model is likely a special case of a larger class of solvable systems, and present a six-state generalization as an example.« less

Exact transition probabilities for a linear sweep through a Kramers-Kronig resonance

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

Sun, Chen; Sinitsyn, Nikolai A.

2015-11-19

We consider a localized electronic spin controlled by a circularly polarized optical beam and an external magnetic field. When the frequency of the beam is tuned near an optical resonance with a continuum of higher energy states, effective magnetic fields are induced on the two-level system via the inverse Faraday effect. We explore the process in which the frequency of the beam is made linearly time-dependent so that it sweeps through the optical resonance, starting and ending at the values far away from it. In addition to changes of spin states, Kramers-Kronig relations guarantee that a localized electron can alsomore » escape into a continuum of states. We argue that probabilities of transitions between different possible electronic states after such a sweep of the optical frequency can be found exactly, regardless the shape of the resonance. In conclusion, we also discuss extension of our results to multistate systems.« less

MP Resulting in Autophagic Cell Death of Microglia through Zinc Changes against Spinal Cord Injury

PubMed Central

Li, Dingding; Wang, Guannan; Han, Donghe; Bi, Jing; Li, Chenyuan; Wang, Hongyu; Liu, Zhiyuan; Gao, Wei; Gao, Kai; Yao, Tianchen; Wan, Zhanghui; Li, Haihong; Mei, Xifan

2016-01-01

Methylprednisolone pulse therapy (MPPT), as a public recognized therapy of spinal cord injury (SCI), is doubted recently, and the exact mechanism of MP on SCI is unclear. This study sought to investigate the exact effect of MP on SCI. We examined the effect of MP in a model of SCI in vivo and an LPS induced model in vitro. We found that administration of MP produced an increase in the Basso, Beattie, and Bresnahan scores and motor neurons counts of injured rats. Besides the number of activated microglia was apparently reduced by MP in vivo, and Beclin-1 dependent autophagic cell death of microglia was induced by MP in LPS induced model. At the same time, MP increases cellular zinc concentration and level of ZIP8, and TPEN could revert effect of MP on autophagic cell death of microglia. Finally, we have found that MP could inhibit NF-κβ in LPS induced model. These results show that the MP could result in autophagic cell death of microglia, which mainly depends on increasing cellular labile zinc, and may be associated with inhibition of NF-κβ, and that MP can produce neuroprotective effect in SCI. PMID:27057544

Weakly collisional Landau damping and three-dimensional Bernstein-Greene-Kruskal modes: New results on old problems

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

Ng, C.; Bhattacharjee, A.; Skiff, F.

2006-05-15

Landau damping and Bernstein-Greene-Kruskal (BGK) modes are among the most fundamental concepts in plasma physics. While the former describes the surprising damping of linear plasma waves in a collisionless plasma, the latter describes exact undamped nonlinear solutions of the Vlasov equation. There does exist a relationship between the two: Landau damping can be described as the phase mixing of undamped eigenmodes, the so-called Case-Van Kampen modes, which can be viewed as BGK modes in the linear limit. While these concepts have been around for a long time, unexpected new results are still being discovered. For Landau damping, we show thatmore » the textbook picture of phase mixing is altered profoundly in the presence of collision. In particular, the continuous spectrum of Case-Van Kampen modes is eliminated and replaced by a discrete spectrum, even in the limit of zero collision. Furthermore, we show that these discrete eigenmodes form a complete set of solutions. Landau-damped solutions are then recovered as true eigenmodes (which they are not in the collisionless theory). For BGK modes, our interest is motivated by recent discoveries of electrostatic solitary waves in magnetospheric plasmas. While one-dimensional BGK theory is quite mature, there appear to be no exact three-dimensional solutions in the literature (except for the limiting case when the magnetic field is sufficiently strong so that one can apply the guiding-center approximation). We show, in fact, that two- and three-dimensional solutions that depend only on energy do not exist. However, if solutions depend on both energy and angular momentum, we can construct exact three-dimensional solutions for the unmagnetized case, and two-dimensional solutions for the case with a finite magnetic field. The latter are shown to be exact, fully electromagnetic solutions of the steady-state Vlasov-Poisson-Ampere system.« less

Kohn-Sham approach to quantum electrodynamical density-functional theory: Exact time-dependent effective potentials in real space.

PubMed

Flick, Johannes; Ruggenthaler, Michael; Appel, Heiko; Rubio, Angel

2015-12-15

The density-functional approach to quantum electrodynamics extends traditional density-functional theory and opens the possibility to describe electron-photon interactions in terms of effective Kohn-Sham potentials. In this work, we numerically construct the exact electron-photon Kohn-Sham potentials for a prototype system that consists of a trapped electron coupled to a quantized electromagnetic mode in an optical high-Q cavity. Although the effective current that acts on the photons is known explicitly, the exact effective potential that describes the forces exerted by the photons on the electrons is obtained from a fixed-point inversion scheme. This procedure allows us to uncover important beyond-mean-field features of the effective potential that mark the breakdown of classical light-matter interactions. We observe peak and step structures in the effective potentials, which can be attributed solely to the quantum nature of light; i.e., they are real-space signatures of the photons. Our findings show how the ubiquitous dipole interaction with a classical electromagnetic field has to be modified in real space to take the quantum nature of the electromagnetic field fully into account.

Nonstationary stochastic charge fluctuations of a dust particle in plasmas.

PubMed

Shotorban, B

2011-06-01

Stochastic charge fluctuations of a dust particle that are due to discreteness of electrons and ions in plasmas can be described by a one-step process master equation [T. Matsoukas and M. Russell, J. Appl. Phys. 77, 4285 (1995)] with no exact solution. In the present work, using the system size expansion method of Van Kampen along with the linear noise approximation, a Fokker-Planck equation with an exact Gaussian solution is developed by expanding the master equation. The Gaussian solution has time-dependent mean and variance governed by two ordinary differential equations modeling the nonstationary process of dust particle charging. The model is tested via the comparison of its results to the results obtained by solving the master equation numerically. The electron and ion currents are calculated through the orbital motion limited theory. At various times of the nonstationary process of charging, the model results are in a very good agreement with the master equation results. The deviation is more significant when the standard deviation of the charge is comparable to the mean charge in magnitude.

Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit

NASA Astrophysics Data System (ADS)

Heidrich-Meisner, Fabian; Pollet, Lode; Sorg, Stefan; Vidmar, Lev

2015-03-01

We study the relaxation dynamics and thermalization in the one-dimensional Bose-Hubbard model induced by a global interaction quench. Specifically, we start from an initial state that has exactly one boson per site and is the ground state of a system with infinitely strong repulsive interactions at unit filling. The same interaction quench was realized in a recent experiment. Using exact diagonalization and the density-matrix renormalization-group method, we compute the time dependence of such observables as the multiple occupancy and the momentum distribution function. We discuss our numerical results in the framework of the eigenstate thermalization hypothesis and we observe that the microcanonical ensemble describes the time averages of many observables reasonably well for small and intermediate interaction strength. Moreover, the diagonal and the canonical ensembles are practically identical for our initial conditions already on the level of their respective energy distributions for small interaction strengths. Supported by the DFG through FOR 801 and the Alexander von Humboldt foundation.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Wave-packet continuum-discretization approach to ion-atom collisions including rearrangement: Application to differential ionization in proton-hydrogen scattering

NASA Astrophysics Data System (ADS)

Abdurakhmanov, I. B.; Bailey, J. J.; Kadyrov, A. S.; Bray, I.

2018-03-01

In this work, we develop a wave-packet continuum-discretization approach to ion-atom collisions that includes rearrangement processes. The total scattering wave function is expanded using a two-center basis built from wave-packet pseudostates. The exact three-body Schrödinger equation is converted into coupled-channel differential equations for time-dependent expansion coefficients. In the asymptotic region these time-dependent coefficients represent transition amplitudes for all processes including elastic scattering, excitation, ionization, and electron capture. The wave-packet continuum-discretization approach is ideal for differential ionization studies as it allows one to generate pseudostates with arbitrary energies and distribution. The approach is used to calculate the double differential cross section for ionization in proton collisions with atomic hydrogen. Overall good agreement with experiment is obtained for all considered cases.

Chiral dynamics in the low-temperature phase of QCD

NASA Astrophysics Data System (ADS)

Brandt, Bastian B.; Francis, Anthony; Meyer, Harvey B.; Robaina, Daniel

2014-09-01

We investigate the low-temperature phase of QCD and the crossover region with two light flavors of quarks. The chiral expansion around the point (T,m=0) in the temperature vs quark-mass plane indicates that a sharp real-time excitation exists with the quantum numbers of the pion. An exact sum rule is derived for the thermal modification of the spectral function associated with the axial charge density; the (dominant) pion pole contribution obeys the sum rule. We determine the two parameters of the pion dispersion relation using lattice QCD simulations and test the applicability of the chiral expansion. The time-dependent correlators are also analyzed using the maximum entropy method, yielding consistent results. Finally, we test the predictions of the chiral expansion around the point (T=0,m=0) for the temperature dependence of static observables.

Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1 dimensions

NASA Astrophysics Data System (ADS)

Wen, Xiao-Gang

2017-05-01

We propose a generic construction of exactly soluble local bosonic models that realize various topological orders with gappable boundaries. In particular, we construct an exactly soluble bosonic model that realizes a (3+1)-dimensional [(3+1)D] Z2-gauge theory with emergent fermionic Kramers doublet. We show that the emergence of such a fermion will cause the nucleation of certain topological excitations in space-time without pin+ structure. The exactly soluble model also leads to a statistical transmutation in (3+1)D. In addition, we construct exactly soluble bosonic models that realize 2 types of time-reversal symmetry-enriched Z2 topological orders in 2+1 dimensions, and 20 types of simplest time-reversal symmetry-enriched topological (SET) orders which have only one nontrivial pointlike and stringlike topological excitation. Many physical properties of those topological states are calculated using the exactly soluble models. We find that some time-reversal SET orders have pointlike excitations that carry Kramers doublet, a fractionalized time-reversal symmetry. We also find that some Z2 SET orders have stringlike excitations that carry anomalous (nononsite) Z2 symmetry, which can be viewed as a fractionalization of Z2 symmetry on strings. Our construction is based on cochains and cocycles in algebraic topology, which is very versatile. In principle, it can also realize emergent topological field theory beyond the twisted gauge theory.

Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement

NASA Astrophysics Data System (ADS)

Roldán, Édgar; Gupta, Shamik

2017-08-01

We study the dynamics of overdamped Brownian particles diffusing in conservative force fields and undergoing stochastic resetting to a given location at a generic space-dependent rate of resetting. We present a systematic approach involving path integrals and elements of renewal theory that allows us to derive analytical expressions for a variety of statistics of the dynamics such as (i) the propagator prior to first reset, (ii) the distribution of the first-reset time, and (iii) the spatial distribution of the particle at long times. We apply our approach to several representative and hitherto unexplored examples of resetting dynamics. A particularly interesting example for which we find analytical expressions for the statistics of resetting is that of a Brownian particle trapped in a harmonic potential with a rate of resetting that depends on the instantaneous energy of the particle. We find that using energy-dependent resetting processes is more effective in achieving spatial confinement of Brownian particles on a faster time scale than performing quenches of parameters of the harmonic potential.

Passive advection of a vector field: Anisotropy, finite correlation time, exact solution, and logarithmic corrections to ordinary scaling

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.

2015-10-01

In this work we study the generalization of the problem considered in [Phys. Rev. E 91, 013002 (2015), 10.1103/PhysRevE.91.013002] to the case of finite correlation time of the environment (velocity) field. The model describes a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow. Inertial-range asymptotic behavior is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, with finite correlation time and preassigned pair correlation function. Due to the presence of distinguished direction n , all the multiloop diagrams in this model vanish, so that the results obtained are exact. The inertial-range behavior of the model is described by two regimes (the limits of vanishing or infinite correlation time) that correspond to the two nontrivial fixed points of the RG equations. Their stability depends on the relation between the exponents in the energy spectrum E ∝k⊥1 -ξ and the dispersion law ω ∝k⊥2 -η . In contrast to the well-known isotropic Kraichnan's model, where various correlation functions exhibit anomalous scaling behavior with infinite sets of anomalous exponents, here the corrections to ordinary scaling are polynomials of logarithms of the integral turbulence scale L .

Numerically Exact Long Time Magnetization Dynamics Near the Nonequilibrium Kondo Regime

NASA Astrophysics Data System (ADS)

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

2013-03-01

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

Semiclassical Dynamicswith Exponentially Small Error Estimates

NASA Astrophysics Data System (ADS)

Hagedorn, George A.; Joye, Alain

We construct approximate solutions to the time-dependent Schrödingerequation for small values of ħ. If V satisfies appropriate analyticity and growth hypotheses and , these solutions agree with exact solutions up to errors whose norms are bounded by for some C and γ>0. Under more restrictive hypotheses, we prove that for sufficiently small T', implies the norms of the errors are bounded by for some C', γ'>0, and σ > 0.

Solvable multistate model of Landau-Zener transitions in cavity QED

DOE PAGES

Sinitsyn, Nikolai; Li, Fuxiang

2016-06-29

We consider the model of a single optical cavity mode interacting with two-level systems (spins) driven by a linearly time-dependent field. When this field passes through values at which spin energy level splittings become comparable to spin coupling to the optical mode, a cascade of Landau-Zener (LZ) transitions leads to co-flips of spins in exchange for photons of the cavity. We derive exact transition probabilities between different diabatic states induced by such a sweep of the field.

An exact solution for the solidification of a liquid slab of binary mixture

NASA Technical Reports Server (NTRS)

Antar, B. N.; Collins, F. G.; Aumalia, A. E.

1986-01-01

The time dependent temperature and concentration profiles of a one dimensional finite slab of a binary liquid alloy is investigated during solidification. The governing equations are reduced to a set of coupled, nonlinear initial value problems using the method outlined by Meyer. Two methods will be used to solve these equations. The first method uses a Runge-Kutta-Fehlberg integrator to solve the equations numerically. The second method comprises of finding closed form solutions of the equations.

Nonlinear response of a harmonic diatomic molecule: Algebraic nonperturbative calculation

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

Recamier, Jose; Mochan, W. Luis; Maytorena, Jesus A.

2005-08-15

Even harmonic molecules display a nonlinear behavior when driven by an inhomogeneous field. We calculate the response of single harmonic molecules to a monochromatic time and space dependent electric field E(r,t) of frequency {omega} employing exact algebraic methods. We evaluate the responses at the fundamental frequency {omega} and at successive harmonics 2{omega}, 3{omega}, etc., as a function of the intensity and of the frequency of the field and compare the results with those of first and second order perturbation theory.

Dynamics of atom-field entanglement for Tavis-Cummings models

NASA Astrophysics Data System (ADS)

Bashkirov, Eugene K.

2018-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Gaussian and Airy wave packets of massive particles with orbital angular momentum

NASA Astrophysics Data System (ADS)

Karlovets, Dmitry V.

2015-01-01

While wave-packet solutions for relativistic wave equations are oftentimes thought to be approximate (paraxial), we demonstrate, by employing a null-plane- (light-cone-) variable formalism, that there is a family of such solutions that are exact. A scalar Gaussian wave packet in the transverse plane is generalized so that it acquires a well-defined z component of the orbital angular momentum (OAM), while it may not acquire a typical "doughnut" spatial profile. Such quantum states and beams, in contrast to the Bessel states, may have an azimuthal-angle-dependent probability density and finite uncertainty of the OAM, which is determined by the packet's width. We construct a well-normalized Airy wave packet, which can be interpreted as a one-particle state for a relativistic massive boson, show that its center moves along the same quasiclassical straight path, and, which is more important, spreads with time and distance exactly as a Gaussian wave packet does, in accordance with the uncertainty principle. It is explained that this fact does not contradict the well-known "nonspreading" feature of the Airy beams. While the effective OAM for such states is zero, its uncertainty (or the beam's OAM bandwidth) is found to be finite, and it depends on the packet's parameters. A link between exact solutions for the Klein-Gordon equation in the null-plane-variable formalism and the approximate ones in the usual approach is indicated; generalizations of these states for a boson in the external field of a plane electromagnetic wave are also presented.

New exact periodic solitary-wave solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in multi-temperature electron plasmas

NASA Astrophysics Data System (ADS)

Liu, Jian-Guo; Tian, Yu; Zeng, Zhi-Fang

2017-10-01

In this paper, we aim to introduce a new form of the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation for the long waves of small amplitude with slow dependence on the transverse coordinate. By using the Hirota's bilinear form and the extended homoclinic test approach, new exact periodic solitary-wave solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation are presented. Moreover, the properties and characteristics for these new exact periodic solitary-wave solutions are discussed with some figures.

A contribution to calculation of the mathematical pendulum

NASA Astrophysics Data System (ADS)

Anakhaev, K. N.

2014-11-01

In this work, as a continuation of rigorous solutions of the mathematical pendulum theory, calculated dependences were obtained in elementary functions (with construction of plots) for a complete description of the oscillatory motion of the pendulum with determination of its parameters, such as the oscillation period, deviation angles, time of motion, angular velocity and acceleration, and strains in the pendulum rod (maximum, minimum, zero, and gravitational). The results of calculations according to the proposed dependences closely (≪1%) coincide with the exact tabulated data for individual points. The conditions of ascending at which the angular velocity, angular acceleration, and strains in the pendulum rod reach their limiting values equal to and 5 m 1 g, respectively, are shown. It was revealed that the angular acceleration does not depend on the pendulum oscillation amplitude; the pendulum rod strain equal to the gravitation force of the pendulum R s = m 1 g at the time instant is also independent on the amplitude. The dependences presented in this work can also be invoked for describing oscillations of a physical pendulum, mass on a spring, electric circuit, etc.

Robust pre-specified time synchronization of chaotic systems by employing time-varying switching surfaces in the sliding mode control scheme

NASA Astrophysics Data System (ADS)

Khanzadeh, Alireza; Pourgholi, Mahdi

2016-08-01

In the conventional chaos synchronization methods, the time at which two chaotic systems are synchronized, is usually unknown and depends on initial conditions. In this work based on Lyapunov stability theory a sliding mode controller with time-varying switching surfaces is proposed to achieve chaos synchronization at a pre-specified time for the first time. The proposed controller is able to synchronize chaotic systems precisely at any time when we want. Moreover, by choosing the time-varying switching surfaces in a way that the reaching phase is eliminated, the synchronization becomes robust to uncertainties and exogenous disturbances. Simulation results are presented to show the effectiveness of the proposed method of stabilizing and synchronizing chaotic systems with complete robustness to uncertainty and disturbances exactly at a pre-specified time.

Mathematical analysis of thermal diffusion shock waves

NASA Astrophysics Data System (ADS)

Gusev, Vitalyi; Craig, Walter; Livoti, Roberto; Danworaphong, Sorasak; Diebold, Gerald J.

2005-10-01

Thermal diffusion, also known as the Ludwig-Soret effect, refers to the separation of mixtures in a temperature gradient. For a binary mixture the time dependence of the change in concentration of each species is governed by a nonlinear partial differential equation in space and time. Here, an exact solution of the Ludwig-Soret equation without mass diffusion for a sinusoidal temperature field is given. The solution shows that counterpropagating shock waves are produced which slow and eventually come to a halt. Expressions are found for the shock time for two limiting values of the starting density fraction. The effects of diffusion on the development of the concentration profile in time and space are found by numerical integration of the nonlinear differential equation.

Homotopy decomposition method for solving one-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Abuasad, Salah; Hashim, Ishak

2018-04-01

In this paper, we present the homotopy decomposition method with a modified definition of beta fractional derivative for the first time to find exact solution of one-dimensional time-fractional diffusion equation. In this method, the solution takes the form of a convergent series with easily computable terms. The exact solution obtained by the proposed method is compared with the exact solution obtained by using fractional variational homotopy perturbation iteration method via a modified Riemann-Liouville derivative.

Carrier-envelope phase-dependent field-free molecular orientation

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

Shu Chuancun; Yuan Kaijun; Hu Wenhui

2009-07-15

We present a strategy to achieve carrier-envelope phase-dependent field-free molecular orientation with the use of carrier-envelope phase (CEP) stabilization and asymmetric few-cycle terahertz (THz) laser pulses. The calculations are performed on the LiH molecule by an exact solution of the full time-dependent Schroedinger equation including both the vibrational and the rotational degrees of freedom. Our calculations show that an efficient field-free molecular orientation can be obtained even at considerable temperatures. Moreover, we find a simple dependence of the field-free orientation on the CEP, which implies that the CEP becomes an important parameter for control of molecular orientation. More importantly, themore » realization of this scenario is appealing based on the fact that the intense few-cycle THz pulse with duration as short as a few optical cycles is available as a research tool.« less

Time dependent semiclassical tunneling through one dimensional barriers using only real valued trajectories

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

Herman, Michael F.

2015-10-28

The time independent semiclassical treatment of barrier tunneling has been understood for a very long time. Several semiclassical approaches to time dependent tunneling through barriers have also been presented. These typically involve trajectories for which the position variable is a complex function of time. In this paper, a method is presented that uses only real valued trajectories, thus avoiding the complications that can arise when complex trajectories are employed. This is accomplished by expressing the time dependent wave packet as an integration over momentum. The action function in the exponent in this expression is expanded to second order in themore » momentum. The expansion is around the momentum, p{sub 0{sup *}}, at which the derivative of the real part of the action is zero. The resulting Gaussian integral is then taken. The stationary phase approximation requires that the derivative of the full action is zero at the expansion point, and this leads to a complex initial momentum and complex tunneling trajectories. The “pseudo-stationary phase” approximation employed in this work results in real values for the initial momentum and real valued trajectories. The transmission probabilities obtained are found to be in good agreement with exact quantum results.« less

The mean and variance of phylogenetic diversity under rarefaction

PubMed Central

Matsen, Frederick A.

2013-01-01

Summary Phylogenetic diversity (PD) depends on sampling depth, which complicates the comparison of PD between samples of different depth. One approach to dealing with differing sample depth for a given diversity statistic is to rarefy, which means to take a random subset of a given size of the original sample. Exact analytical formulae for the mean and variance of species richness under rarefaction have existed for some time but no such solution exists for PD.We have derived exact formulae for the mean and variance of PD under rarefaction. We confirm that these formulae are correct by comparing exact solution mean and variance to that calculated by repeated random (Monte Carlo) subsampling of a dataset of stem counts of woody shrubs of Toohey Forest, Queensland, Australia. We also demonstrate the application of the method using two examples: identifying hotspots of mammalian diversity in Australasian ecoregions, and characterising the human vaginal microbiome.There is a very high degree of correspondence between the analytical and random subsampling methods for calculating mean and variance of PD under rarefaction, although the Monte Carlo method requires a large number of random draws to converge on the exact solution for the variance.Rarefaction of mammalian PD of ecoregions in Australasia to a common standard of 25 species reveals very different rank orderings of ecoregions, indicating quite different hotspots of diversity than those obtained for unrarefied PD. The application of these methods to the vaginal microbiome shows that a classical score used to quantify bacterial vaginosis is correlated with the shape of the rarefaction curve.The analytical formulae for the mean and variance of PD under rarefaction are both exact and more efficient than repeated subsampling. Rarefaction of PD allows for many applications where comparisons of samples of different depth is required. PMID:23833701

The mean and variance of phylogenetic diversity under rarefaction.

PubMed

Nipperess, David A; Matsen, Frederick A

2013-06-01

Phylogenetic diversity (PD) depends on sampling depth, which complicates the comparison of PD between samples of different depth. One approach to dealing with differing sample depth for a given diversity statistic is to rarefy, which means to take a random subset of a given size of the original sample. Exact analytical formulae for the mean and variance of species richness under rarefaction have existed for some time but no such solution exists for PD.We have derived exact formulae for the mean and variance of PD under rarefaction. We confirm that these formulae are correct by comparing exact solution mean and variance to that calculated by repeated random (Monte Carlo) subsampling of a dataset of stem counts of woody shrubs of Toohey Forest, Queensland, Australia. We also demonstrate the application of the method using two examples: identifying hotspots of mammalian diversity in Australasian ecoregions, and characterising the human vaginal microbiome.There is a very high degree of correspondence between the analytical and random subsampling methods for calculating mean and variance of PD under rarefaction, although the Monte Carlo method requires a large number of random draws to converge on the exact solution for the variance.Rarefaction of mammalian PD of ecoregions in Australasia to a common standard of 25 species reveals very different rank orderings of ecoregions, indicating quite different hotspots of diversity than those obtained for unrarefied PD. The application of these methods to the vaginal microbiome shows that a classical score used to quantify bacterial vaginosis is correlated with the shape of the rarefaction curve.The analytical formulae for the mean and variance of PD under rarefaction are both exact and more efficient than repeated subsampling. Rarefaction of PD allows for many applications where comparisons of samples of different depth is required.

Heisenberg-Langevin versus quantum master equation

NASA Astrophysics Data System (ADS)

Boyanovsky, Daniel; Jasnow, David

2017-12-01

The quantum master equation is an important tool in the study of quantum open systems. It is often derived under a set of approximations, chief among them the Born (factorization) and Markov (neglect of memory effects) approximations. In this article we study the paradigmatic model of quantum Brownian motion of a harmonic oscillator coupled to a bath of oscillators with a Drude-Ohmic spectral density. We obtain analytically the exact solution of the Heisenberg-Langevin equations, with which we study correlation functions in the asymptotic stationary state. We compare the exact correlation functions to those obtained in the asymptotic long time limit with the quantum master equation in the Born approximation with and without the Markov approximation. In the latter case we implement a systematic derivative expansion that yields the exact asymptotic limit under the factorization approximation only. We find discrepancies that could be significant when the bandwidth of the bath Λ is much larger than the typical scales of the system. We study the exact interaction energy as a proxy for the correlations missed by the Born approximation and find that its dependence on Λ is similar to the discrepancy between the exact solution and that of the quantum master equation in the Born approximation. We quantify the regime of validity of the quantum master equation in the Born approximation with or without the Markov approximation in terms of the system's relaxation rate γ , its unrenormalized natural frequency Ω and Λ : γ /Ω ≪1 and also γ Λ /Ω2≪1 . The reliability of the Born approximation is discussed within the context of recent experimental settings and more general environments.

A real-time extension of density matrix embedding theory for non-equilibrium electron dynamics

NASA Astrophysics Data System (ADS)

Kretchmer, Joshua S.; Chan, Garnet Kin-Lic

2018-02-01

We introduce real-time density matrix embedding theory (DMET), a dynamical quantum embedding theory for computing non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static DMET, real-time DMET partitions the system into an impurity corresponding to the region of interest coupled to the surrounding environment, which is efficiently represented by a quantum bath of the same size as the impurity. In this work, we focus on a simplified single-impurity time-dependent formulation as a first step toward a multi-impurity theory. The equations of motion of the coupled impurity and bath embedding problem are derived using the time-dependent variational principle. The accuracy of real-time DMET is compared to that of time-dependent complete active space self-consistent field (TD-CASSCF) theory and time-dependent Hartree-Fock (TDHF) theory for a variety of quantum quenches in the single impurity Anderson model (SIAM), in which the Hamiltonian is suddenly changed (quenched) to induce a non-equilibrium state. Real-time DMET shows a marked improvement over the mean-field TDHF, converging to the exact answer even in the non-trivial Kondo regime of the SIAM. However, as expected from analogous behavior in static DMET, the constrained structure of the real-time DMET wavefunction leads to a slower convergence with respect to active space size, in the single-impurity formulation, relative to TD-CASSCF. Our initial results suggest that real-time DMET provides a promising framework to simulate non-equilibrium electron dynamics in which strong electron correlation plays an important role, and lays the groundwork for future multi-impurity formulations.

A real-time extension of density matrix embedding theory for non-equilibrium electron dynamics.

PubMed

Kretchmer, Joshua S; Chan, Garnet Kin-Lic

2018-02-07

We introduce real-time density matrix embedding theory (DMET), a dynamical quantum embedding theory for computing non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static DMET, real-time DMET partitions the system into an impurity corresponding to the region of interest coupled to the surrounding environment, which is efficiently represented by a quantum bath of the same size as the impurity. In this work, we focus on a simplified single-impurity time-dependent formulation as a first step toward a multi-impurity theory. The equations of motion of the coupled impurity and bath embedding problem are derived using the time-dependent variational principle. The accuracy of real-time DMET is compared to that of time-dependent complete active space self-consistent field (TD-CASSCF) theory and time-dependent Hartree-Fock (TDHF) theory for a variety of quantum quenches in the single impurity Anderson model (SIAM), in which the Hamiltonian is suddenly changed (quenched) to induce a non-equilibrium state. Real-time DMET shows a marked improvement over the mean-field TDHF, converging to the exact answer even in the non-trivial Kondo regime of the SIAM. However, as expected from analogous behavior in static DMET, the constrained structure of the real-time DMET wavefunction leads to a slower convergence with respect to active space size, in the single-impurity formulation, relative to TD-CASSCF. Our initial results suggest that real-time DMET provides a promising framework to simulate non-equilibrium electron dynamics in which strong electron correlation plays an important role, and lays the groundwork for future multi-impurity formulations.

Exact solutions to the time-fractional differential equations via local fractional derivatives

NASA Astrophysics Data System (ADS)

Guner, Ozkan; Bekir, Ahmet

2018-01-01

This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.

Integrable equations of the infinite nonlinear Schrödinger equation hierarchy with time variable coefficients.

PubMed

Kedziora, D J; Ankiewicz, A; Chowdury, A; Akhmediev, N

2015-10-01

We present an infinite nonlinear Schrödinger equation hierarchy of integrable equations, together with the recurrence relations defining it. To demonstrate integrability, we present the Lax pairs for the whole hierarchy, specify its Darboux transformations and provide several examples of solutions. These resulting wavefunctions are given in exact analytical form. We then show that the Lax pair and Darboux transformation formalisms still apply in this scheme when the coefficients in the hierarchy depend on the propagation variable (e.g., time). This extension thus allows for the construction of complicated solutions within a greatly diversified domain of generalised nonlinear systems.

Continuous-time quantum walks on multilayer dendrimer networks

NASA Astrophysics Data System (ADS)

Galiceanu, Mircea; Strunz, Walter T.

2016-08-01

We consider continuous-time quantum walks (CTQWs) on multilayer dendrimer networks (MDs) and their application to quantum transport. A detailed study of properties of CTQWs is presented and transport efficiency is determined in terms of the exact and average return probabilities. The latter depends only on the eigenvalues of the connectivity matrix, which even for very large structures allows a complete analytical solution for this particular choice of network. In the case of MDs we observe an interplay between strong localization effects, due to the dendrimer topology, and good efficiency from the linear segments. We show that quantum transport is enhanced by interconnecting more layers of dendrimers.

Calculation of precise firing statistics in a neural network model

NASA Astrophysics Data System (ADS)

Cho, Myoung Won

2017-08-01

A precise prediction of neural firing dynamics is requisite to understand the function of and the learning process in a biological neural network which works depending on exact spike timings. Basically, the prediction of firing statistics is a delicate manybody problem because the firing probability of a neuron at a time is determined by the summation over all effects from past firing states. A neural network model with the Feynman path integral formulation is recently introduced. In this paper, we present several methods to calculate firing statistics in the model. We apply the methods to some cases and compare the theoretical predictions with simulation results.

Persistent-random-walk approach to anomalous transport of self-propelled particles

NASA Astrophysics Data System (ADS)

Sadjadi, Zeinab; Shaebani, M. Reza; Rieger, Heiko; Santen, Ludger

2015-06-01

The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's displacement. It is shown that the interplay of step length and turning angle distributions and self-propulsion produces various signs of anomalous diffusion at short time scales and asymptotically a normal diffusion behavior with a broad range of diffusion coefficients. The crossover from the anomalous short-time behavior to the asymptotic diffusion regime is studied and the parameter dependencies of the crossover time are discussed. Higher moments of the displacement distribution are calculated and analytical expressions for the time evolution of the skewness and the kurtosis of the distribution are presented.

New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods

NASA Astrophysics Data System (ADS)

S Saha, Ray

2016-04-01

In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov (KdV-KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann-Liouville derivative is used to convert the nonlinear time fractional KdV-KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV-KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV-KZK equation.

Cluster Analysis of Time-Dependent Crystallographic Data: Direct Identification of Time-Independent Structural Intermediates

PubMed Central

Kostov, Konstantin S.; Moffat, Keith

2011-01-01

The initial output of a time-resolved macromolecular crystallography experiment is a time-dependent series of difference electron density maps that displays the time-dependent changes in underlying structure as a reaction progresses. The goal is to interpret such data in terms of a small number of crystallographically refinable, time-independent structures, each associated with a reaction intermediate; to establish the pathways and rate coefficients by which these intermediates interconvert; and thereby to elucidate a chemical kinetic mechanism. One strategy toward achieving this goal is to use cluster analysis, a statistical method that groups objects based on their similarity. If the difference electron density at a particular voxel in the time-dependent difference electron density (TDED) maps is sensitive to the presence of one and only one intermediate, then its temporal evolution will exactly parallel the concentration profile of that intermediate with time. The rationale is therefore to cluster voxels with respect to the shapes of their TDEDs, so that each group or cluster of voxels corresponds to one structural intermediate. Clusters of voxels whose TDEDs reflect the presence of two or more specific intermediates can also be identified. From such groupings one can then infer the number of intermediates, obtain their time-independent difference density characteristics, and refine the structure of each intermediate. We review the principles of cluster analysis and clustering algorithms in a crystallographic context, and describe the application of the method to simulated and experimental time-resolved crystallographic data for the photocycle of photoactive yellow protein. PMID:21244840

When can time-dependent currents be reproduced by the Landauer steady-state approximation?

NASA Astrophysics Data System (ADS)

Carey, Rachel; Chen, Liping; Gu, Bing; Franco, Ignacio

2017-05-01

We establish well-defined limits in which the time-dependent electronic currents across a molecular junction subject to a fluctuating environment can be quantitatively captured via the Landauer steady-state approximation. For this, we calculate the exact time-dependent non-equilibrium Green's function (TD-NEGF) current along a model two-site molecular junction, in which the site energies are subject to correlated noise, and contrast it with that obtained from the Landauer approach. The ability of the steady-state approximation to capture the TD-NEGF behavior at each instant of time is quantified via the same-time correlation function of the currents obtained from the two methods, while their global agreement is quantified by examining differences in the average currents. The Landauer steady-state approach is found to be a useful approximation when (i) the fluctuations do not disrupt the degree of delocalization of the molecular eigenstates responsible for transport and (ii) the characteristic time for charge exchange between the molecule and leads is fast with respect to the molecular correlation time. For resonant transport, when these conditions are satisfied, the Landauer approach is found to accurately describe the current, both on average and at each instant of time. For non-resonant transport, we find that while the steady-state approach fails to capture the time-dependent transport at each instant of time, it still provides a good approximation to the average currents. These criteria can be employed to adopt effective modeling strategies for transport through molecular junctions in interaction with a fluctuating environment, as is necessary to describe experiments.

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

PubMed

Berry, K J; Mielke, P W

2000-12-01

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

Exact exchange potential for slabs: Asymptotic behavior of the Krieger-Li-Iafrate approximation

NASA Astrophysics Data System (ADS)

Engel, Eberhard

2018-02-01

The Krieger-Li-Iafrate (KLI) approximation for the exact exchange (EXX) potential of density functional theory is investigated far outside the surface of slabs. For large z the Slater component of the EXX/KLI potential falls off as -1 /z , where z is the distance to the surface of a slab parallel to the x y plane. The Slater potential thus reproduces the behavior of the exact EXX potential. Here it is demonstrated that the second component of the EXX/KLI potential, often called the orbital-shift term, is also proportional to 1 /z for large z , at least in general. This result is obtained by an analytical evaluation of the Brillouin zone integrals involved, relying on the exponential decay of the states into the vacuum. Several situations need to be distinguished in the Brillouin zone integration, depending on the band structure of the slab. In all standard situations, including such prominent cases as graphene and Si(111) slabs, however, a 1 /z dependence of the orbital-shift potential is obtained to leading order. The complete EXX/KLI potential therefore does not reproduce the asymptotic behavior of the exact EXX potential.

On the similarity of theories of anelastic and scattering attenuation

USGS Publications Warehouse

Wennerberg, Leif; Frankel, Arthur D.

1989-01-01

We point out basic parallels between theories of anelastic and scattering attenuation. We consider approximations to scattering effects presented by O'Doherty and Anstey (1971), Sato (1982), and Wu (1982). We use the linear theory of anelasticity. We note that the frequency dependence of Q can be related to a distribution of scales of physical properties of the medium. The frequency dependence of anelastic Q is related to the distribution of relaxation times in exactly the same manner as the frequency dependence of scattering Q is related to the distribution of scatterer sizes. Thus, the well-known difficulty of separating scattering from intrinsic attenuation is seen from this point of view as a consequence of the fact that certain observables can be interpreted by identical equations resulting from either of two credible physical theories describing fundamentally different processes. -from Authors

Time-dependent broken-symmetry density functional theory simulation of the optical response of entangled paramagnetic defects: Color centers in lithium fluoride

NASA Astrophysics Data System (ADS)

Janesko, Benjamin G.

2018-02-01

Parameter-free atomistic simulations of entangled solid-state paramagnetic defects may aid in the rational design of devices for quantum information science. This work applies time-dependent density functional theory (TDDFT) embedded-cluster simulations to a prototype entangled-defect system, namely two adjacent singlet-coupled F color centers in lithium fluoride. TDDFT calculations accurately reproduce the experimental visible absorption of both isolated and coupled F centers. The most accurate results are obtained by combining spin symmetry breaking to simulate strong correlation, a large fraction of exact (Hartree-Fock-like) exchange to minimize the defect electrons' self-interaction error, and a standard semilocal approximation for dynamical correlations between the defect electrons and the surrounding ionic lattice. These results motivate application of two-reference correlated ab initio approximations to the M-center, and application of TDDFT in parameter-free simulations of more complex entangled paramagnetic defect architectures.

Doppler tracking in time-dependent cosmological spacetimes

NASA Astrophysics Data System (ADS)

Giulini, Domenico; Carrera, Matteo

I will discuss the theoretical problems associated with Doppler tracking in time dependent background geometries, where ordinary Newtonian kinematics fails. A derivation of an exact general-relativistic formula for the two-way Doppler tracking of a spacecraft in homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetimes is presented, as well as a controlled approximation in McVittie spacetimes representing an FLRW background with a single spherically-symmetric inhomogeneity (e.g. a single star or black hole). The leading-order corrections of the acceleration as compared to the Newtonian expression are calculated, which are due to retardation and cosmological expansion and which in the Solar System turn out to be significantly below the scale (nanometer per square-second) set by the Pioneer Anomaly. Last, but not least, I discuss kinematical ambiguities connected with notions of "simultaneity" and "spatial distance", which, in principle, also lead to tracking corrections.

Dissociation between exact and approximate addition in developmental dyslexia.

PubMed

Yang, Xiujie; Meng, Xiangzhi

2016-09-01

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

Time-dependent entropy evolution in microscopic and macroscopic electromagnetic relaxation

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

Baker-Jarvis, James

This paper is a study of entropy and its evolution in the time and frequency domains upon application of electromagnetic fields to materials. An understanding of entropy and its evolution in electromagnetic interactions bridges the boundaries between electromagnetism and thermodynamics. The approach used here is a Liouville-based statistical-mechanical theory. I show that the microscopic entropy is reversible and the macroscopic entropy satisfies an H theorem. The spectral entropy development can be very useful for studying the frequency response of materials. Using a projection-operator based nonequilibrium entropy, different equations are derived for the entropy and entropy production and are applied tomore » the polarization, magnetization, and macroscopic fields. I begin by proving an exact H theorem for the entropy, progress to application of time-dependent entropy in electromagnetics, and then apply the theory to relevant applications in electromagnetics. The paper concludes with a discussion of the relationship of the frequency-domain form of the entropy to the permittivity, permeability, and impedance.« less

Symplectic evolution of Wigner functions in Markovian open systems.

PubMed

Brodier, O; Almeida, A M Ozorio de

2004-01-01

The Wigner function is known to evolve classically under the exclusive action of a quadratic Hamiltonian. If the system also interacts with the environment through Lindblad operators that are complex linear functions of position and momentum, then the general evolution is the convolution of a non-Hamiltonian classical propagation of the Wigner function with a phase space Gaussian that broadens in time. We analyze the consequences of this in the three generic cases of elliptic, hyperbolic, and parabolic Hamiltonians. The Wigner function always becomes positive in a definite time, which does not depend on the initial pure state. We observe the influence of classical dynamics and dissipation upon this threshold. We also derive an exact formula for the evolving linear entropy as the average of a narrowing Gaussian taken over a probability distribution that depends only on the initial state. This leads to a long time asymptotic formula for the growth of linear entropy. We finally discuss the possibility of recovering the initial state.

Asymptotically exact parabolic solutions of the generalized nonlinear Schrödinger equation with varying parameters

NASA Astrophysics Data System (ADS)

Kruglov, Vladimir I.; Harvey, John D.

2006-12-01

We present exact asymptotic similariton solutions of the generalized nonlinear Schrödinger equation (NLSE) with gain or loss terms for a normal-dispersion fiber amplifier with dispersion, nonlinearity, and gain profiles that depend on the propagation distance. Our treatment is based on the mapping of the NLSE with varying parameters to the NLSE with constant dispersion and nonlinearity coefficients and an arbitrary varying gain function. We formulate an effective procedure that leads directly, under appropriate conditions, to a wide range of exact asymptotic similariton solutions of NLSE demonstrating self-similar propagating regimes with linear chirp.

Importance of Context Dependence in the Measurement of Reading Skills.

ERIC Educational Resources Information Center

Oaster, T. R. F.; Thomas, Rick D.

Past reading research suggests that measures of reading comprehension should be made context dependent. Reading comprehension test questions that are context dependent are best answered by examinees only after the accompanying passages have been read. Recently, there has been some disagreement concerning the exact importance of context dependence…

32 CFR 199.18 - Uniform HMO Benefit.

Code of Federal Regulations, 2010 CFR

2010-07-01

... (x) Appropriate education and counseling services. The exact services offered shall be established... groups: dependents of active duty members in pay grades of E-4 and below; active duty dependents of... visits. For group visits, there is a lower per visit fee for retirees and their dependents. (iii) There...

An exact formulation of the time-ordered exponential using path-sums

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

Giscard, P.-L., E-mail: p.giscard1@physics.ox.ac.uk; Lui, K.; Thwaite, S. J.

2015-05-15

We present the path-sum formulation for the time-ordered exponential of a time-dependent matrix. The path-sum formulation gives the time-ordered exponential as a branched continued fraction of finite depth and breadth. The terms of the path-sum have an elementary interpretation as self-avoiding walks and self-avoiding polygons on a graph. Our result is based on a representation of the time-ordered exponential as the inverse of an operator, the mapping of this inverse to sums of walks on a graphs, and the algebraic structure of sets of walks. We give examples demonstrating our approach. We establish a super-exponential decay bound for the magnitudemore » of the entries of the time-ordered exponential of sparse matrices. We give explicit results for matrices with commonly encountered sparse structures.« less

Real-time dynamic simulation of the Cassini spacecraft using DARTS. Part 2: Parallel/vectorized real-time implementation

NASA Technical Reports Server (NTRS)

Fijany, A.; Roberts, J. A.; Jain, A.; Man, G. K.

1993-01-01

Part 1 of this paper presented the requirements for the real-time simulation of Cassini spacecraft along with some discussion of the DARTS algorithm. Here, in Part 2 we discuss the development and implementation of parallel/vectorized DARTS algorithm and architecture for real-time simulation. Development of the fast algorithms and architecture for real-time hardware-in-the-loop simulation of spacecraft dynamics is motivated by the fact that it represents a hard real-time problem, in the sense that the correctness of the simulation depends on both the numerical accuracy and the exact timing of the computation. For a given model fidelity, the computation should be computed within a predefined time period. Further reduction in computation time allows increasing the fidelity of the model (i.e., inclusion of more flexible modes) and the integration routine.

Exact Dynamics via Poisson Process: a unifying Monte Carlo paradigm

NASA Astrophysics Data System (ADS)

Gubernatis, James

2014-03-01

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

Calculation of Thermal Conductivity Coefficients of Electrons in Magnetized Dense Matter

NASA Astrophysics Data System (ADS)

Bisnovatyi-Kogan, G. S.; Glushikhina, M. V.

2018-04-01

The solution of Boltzmann equation for plasma in magnetic field with arbitrarily degenerate electrons and nondegenerate nuclei is obtained by Chapman-Enskog method. Functions generalizing Sonine polynomials are used for obtaining an approximate solution. Fully ionized plasma is considered. The tensor of the heat conductivity coefficients in nonquantized magnetic field is calculated. For nondegenerate and strongly degenerate plasma the asymptotic analytic formulas are obtained and compared with results of previous authors. The Lorentz approximation with neglecting of electron-electron encounters is asymptotically exact for strongly degenerate plasma. For the first time, analytical expressions for the heat conductivity tensor for nondegenerate electrons in the presence of a magnetic field are obtained in the three-polynomial approximation with account of electron-electron collisions. Account of the third polynomial improved substantially the precision of results. In the two-polynomial approximation, the obtained solution coincides with the published results. For strongly degenerate electrons, an asymptotically exact analytical solution for the heat conductivity tensor in the presence of a magnetic field is obtained for the first time. This solution has a considerably more complicated dependence on the magnetic field than those in previous publications and gives a several times smaller relative value of the thermal conductivity across the magnetic field at ωτ * 0.8.

Generalized Langevin equation with tempered memory kernel

NASA Astrophysics Data System (ADS)

Liemert, André; Sandev, Trifce; Kantz, Holger

2017-01-01

We study a generalized Langevin equation for a free particle in presence of a truncated power-law and Mittag-Leffler memory kernel. It is shown that in presence of truncation, the particle from subdiffusive behavior in the short time limit, turns to normal diffusion in the long time limit. The case of harmonic oscillator is considered as well, and the relaxation functions and the normalized displacement correlation function are represented in an exact form. By considering external time-dependent periodic force we obtain resonant behavior even in case of a free particle due to the influence of the environment on the particle movement. Additionally, the double-peak phenomenon in the imaginary part of the complex susceptibility is observed. It is obtained that the truncation parameter has a huge influence on the behavior of these quantities, and it is shown how the truncation parameter changes the critical frequencies. The normalized displacement correlation function for a fractional generalized Langevin equation is investigated as well. All the results are exact and given in terms of the three parameter Mittag-Leffler function and the Prabhakar generalized integral operator, which in the kernel contains a three parameter Mittag-Leffler function. Such kind of truncated Langevin equation motion can be of high relevance for the description of lateral diffusion of lipids and proteins in cell membranes.

A Numerical Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear Coefficients Based on the State Transition Matrix

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2002-01-01

A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.

Target annihilation by diffusing particles in inhomogeneous geometries

NASA Astrophysics Data System (ADS)

Cassi, Davide

2009-09-01

The survival probability of immobile targets annihilated by a population of random walkers on inhomogeneous discrete structures, such as disordered solids, glasses, fractals, polymer networks, and gels, is analytically investigated. It is shown that, while it cannot in general be related to the number of distinct visited points as in the case of homogeneous lattices, in the case of bounded coordination numbers its asymptotic behavior at large times can still be expressed in terms of the spectral dimension d˜ and its exact analytical expression is given. The results show that the asymptotic survival probability is site-independent of recurrent structures (d˜≤2) , while on transient structures (d˜>2) it can strongly depend on the target position, and such dependence is explicitly calculated.

Communication: Coordinate-dependent diffusivity from single molecule trajectories

NASA Astrophysics Data System (ADS)

Berezhkovskii, Alexander M.; Makarov, Dmitrii E.

2017-11-01

Single-molecule observations of biomolecular folding are commonly interpreted using the model of one-dimensional diffusion along a reaction coordinate, with a coordinate-independent diffusion coefficient. Recent analysis, however, suggests that more general models are required to account for single-molecule measurements performed with high temporal resolution. Here, we consider one such generalization: a model where the diffusion coefficient can be an arbitrary function of the reaction coordinate. Assuming Brownian dynamics along this coordinate, we derive an exact expression for the coordinate-dependent diffusivity in terms of the splitting probability within an arbitrarily chosen interval and the mean transition path time between the interval boundaries. This formula can be used to estimate the effective diffusion coefficient along a reaction coordinate directly from single-molecule trajectories.

Time-dependent importance sampling in semiclassical initial value representation calculations for time correlation functions. II. A simplified implementation.

PubMed

Tao, Guohua; Miller, William H

2012-09-28

An efficient time-dependent (TD) Monte Carlo (MC) importance sampling method has recently been developed [G. Tao and W. H. Miller, J. Chem. Phys. 135, 024104 (2011)] for the evaluation of time correlation functions using the semiclassical (SC) initial value representation (IVR) methodology. In this TD-SC-IVR method, the MC sampling uses information from both time-evolved phase points as well as their initial values, and only the "important" trajectories are sampled frequently. Even though the TD-SC-IVR was shown in some benchmark examples to be much more efficient than the traditional time-independent sampling method (which uses only initial conditions), the calculation of the SC prefactor-which is computationally expensive, especially for large systems-is still required for accepted trajectories. In the present work, we present an approximate implementation of the TD-SC-IVR method that is completely prefactor-free; it gives the time correlation function as a classical-like magnitude function multiplied by a phase function. Application of this approach to flux-flux correlation functions (which yield reaction rate constants) for the benchmark H + H(2) system shows very good agreement with exact quantum results. Limitations of the approximate approach are also discussed.

Exact periodic solutions of the sixth-order generalized Boussinesq equation

NASA Astrophysics Data System (ADS)

Kamenov, O. Y.

2009-09-01

This paper examines a class of nonlinear sixth-order generalized Boussinesq-like equations (SGBE): utt = uxx + 3(u2)xx + uxxxx + αuxxxxxx, α in R, depending on the positive parameter α. Hirota's bilinear transformation method is applied to the above class of non-integrable equations and exact periodic solutions have been obtained. The results confirmed the well-known nonlinear superposition principle.

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

NASA Astrophysics Data System (ADS)

Montes, Sebastián; Hamma, Alioscia

2012-08-01

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

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

PubMed

Montes, Sebastián; Hamma, Alioscia

2012-08-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

Microwave-induced resistance oscillations on a high-mobility two-dimensional electron gas: Exact waveform, absorption/reflection and temperature damping

NASA Astrophysics Data System (ADS)

Studenikin, S. A.; Potemski, M.; Sachrajda, A.; Hilke, M.; Pfeiffer, L. N.; West, K. W.

2005-06-01

In this work we address experimentally a number of unresolved issues related to microwave induced resistance oscillations (MIROs) leading to the zero-resistance states observed recently on 2D electron gases in GaAs/AlGaAs heterostructures. We stress the importance of the electrodynamic effects detected in both reflection and absorption experiments, although they are not revealed in transport experiments on very high mobility samples. We also study the exact waveform of MIROs and their damping due to temperature. A simple equation is given, which can be considered as phenomenological, which describes precisely the experimental MIROs waveform. The waveform depends only on a single parameter—the width of the Landau levels, which is related to the quantum lifetime. A very good correlation was found between the temperature dependencies of the quantum lifetime from MIROs and the transport scattering time from the electron mobility with a ratio τtr/τq≃20 . It is found that the prefactor in the equation for MIROs decays as 1/T2 with the temperature which can be explained within the distribution function model suggested by Dmitriev . The results are compared with measurements of the Shubnikov-de Haas oscillations down to 30mK on the same sample.

Role of Helicobacter pylori infection in gastric carcinogenesis: Current knowledge and future directions

PubMed Central

Sokic-Milutinovic, Aleksandra; Alempijevic, Tamara; Milosavljevic, Tomica

2015-01-01

Helicobacter pylori (H. pylori) plays a role in the pathogenesis of gastric cancer. The outcome of the infection depends on environmental factors and bacterial and host characteristics. Gastric carcinogenesis is a multistep process that is reversible in the early phase of mucosal damage, but the exact point of no return has not been identified. Therefore, two main therapeutic strategies could reduce gastric cancer incidence: (1) eradication of the already present infection; and (2) immunization (prior to or during the course of the infection). The success of a gastric cancer prevention strategy depends on timing because the prevention strategy must be introduced before the point of no return in gastric carcinogenesis. Although the exact point of no return has not been identified, infection should be eradicated before severe atrophy of the gastric mucosa develops. Eradication therapy rates remain suboptimal due to increasing H. pylori resistance to antibiotics and patient noncompliance. Vaccination against H. pylori would reduce the cost of eradication therapies and lower gastric cancer incidence. A vaccine against H. pylori is still a research challenge. An effective vaccine should have an adequate route of delivery, appropriate bacterial antigens and effective and safe adjuvants. Future research should focus on the development of rescue eradication therapy protocols until an efficacious vaccine against the bacterium becomes available. PMID:26556993

Resummed tree heptagon

NASA Astrophysics Data System (ADS)

Belitsky, A. V.

2018-04-01

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

Time-dependent Gutzwiller theory of magnetic excitations in the Hubbard model

NASA Astrophysics Data System (ADS)

Seibold, G.; Becca, F.; Rubin, P.; Lorenzana, J.

2004-04-01

We use a spin-rotational invariant Gutzwiller energy functional to compute random-phase-approximation-like (RPA) fluctuations on top of the Gutzwiller approximation (GA). The method can be viewed as an extension of the previously developed GA+RPA approach for the charge sector [G. Seibold and J. Lorenzana, Phys. Rev. Lett. 86, 2605 (2001)] with respect to the inclusion of the magnetic excitations. Unlike the charge case, no assumptions about the time evolution of the double occupancy are needed in this case. Interestingly, in a spin-rotational invariant system, we find the correct degeneracy between triplet excitations, showing the consistency of both computations. Since no restrictions are imposed on the symmetry of the underlying saddle-point solution, our approach is suitable for the evaluation of the magnetic susceptibility and dynamical structure factor in strongly correlated inhomogeneous systems. We present a detailed study of the quality of our approach by comparing with exact diagonalization results and show its much higher accuracy compared to the conventional Hartree-Fock+RPA theory. In infinite dimensions, where the GA becomes exact for the Gutzwiller variational energy, we evaluate ferromagnetic and antiferromagnetic instabilities from the transverse magnetic susceptibility. The resulting phase diagram is in complete agreement with previous variational computations.

33 CFR 165.1191 - Northern California and Lake Tahoe Area Annual Fireworks Events.

Code of Federal Regulations, 2012 CFR

2012-07-01

... exact dates, times, and other details concerning the exact geographical description of the areas are... zone during all applicable effective dates and times unless cleared to do so by or through an official... a safety zone during all applicable effective dates and times shall come to an immediate stop. (3...

33 CFR 165.1191 - Northern California and Lake Tahoe Area Annual Fireworks Events.

Code of Federal Regulations, 2014 CFR

2014-07-01

... exact dates, times, and other details concerning the exact geographical description of the areas are... zone during all applicable effective dates and times unless cleared to do so by or through an official... a safety zone during all applicable effective dates and times shall come to an immediate stop. (3...

33 CFR 165.1191 - Northern California and Lake Tahoe Area Annual Fireworks Events.

Code of Federal Regulations, 2013 CFR

2013-07-01

... exact dates, times, and other details concerning the exact geographical description of the areas are... zone during all applicable effective dates and times unless cleared to do so by or through an official... a safety zone during all applicable effective dates and times shall come to an immediate stop. (3...

Exact collisional moments for plasma fluid theories

NASA Astrophysics Data System (ADS)

Pfefferlé, D.; Hirvijoki, E.; Lingam, M.

2017-04-01

The velocity-space moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multi-index Hermite-polynomial moments of distribution functions. The collisional moments are shown to be generated by derivatives of two well-known functions, namely, the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the root-mean-square of the corresponding thermal velocities and a bilinear dependency on densities and higher-order velocity moments of the distribution functions, with no restriction on temperature, flow, or mass ratio of the species. The result can be applied to both the classic transport theory of plasmas that relies on the Chapman-Enskog method, as well as to derive collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional ten-moment equations with exact conservation laws for momentum- and energy-transfer rates.

Exact collisional moments for plasma fluid theories

NASA Astrophysics Data System (ADS)

Pfefferle, David; Hirvijoki, Eero; Lingam, Manasvi

2017-10-01

The velocity-space moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multi-index Hermite-polynomial moments of the distribution functions. The collisional moments are shown to be generated by derivatives of two well-known functions, namely the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the root-mean-square of the corresponding thermal velocities, and a bilinear dependency on densities and higher-order velocity moments of the distribution functions, with no restriction on temperature, flow or mass ratio of the species. The result can be applied to both the classic transport theory of plasmas, that relies on the Chapman-Enskog method, as well as to deriving collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional ten-moment equations with exact conservation laws for momentum- and energy-transfer rate.

Exact collisional moments for plasma fluid theories

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

Pfefferlé, D.; Hirvijoki, E.; Lingam, M.

The velocity-space moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multi-index Hermite-polynomial moments of distribution functions. The collisional moments are shown to be generated by derivatives of two well-known functions, namely, the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the root-mean-square of the corresponding thermal velocities and a bilinear dependency on densities and higher-order velocity moments of the distribution functions, with no restriction on temperature, flow, or mass ratio of the species. The result can bemore » applied to both the classic transport theory of plasmas that relies on the Chapman-Enskog method, as well as to derive collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional ten-moment equations with exact conservation laws for momentum-and energy-transfer rates.« less

Exact collisional moments for plasma fluid theories

DOE PAGES

Pfefferlé, D.; Hirvijoki, E.; Lingam, M.

2017-04-01

The velocity-space moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multi-index Hermite-polynomial moments of distribution functions. The collisional moments are shown to be generated by derivatives of two well-known functions, namely, the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the root-mean-square of the corresponding thermal velocities and a bilinear dependency on densities and higher-order velocity moments of the distribution functions, with no restriction on temperature, flow, or mass ratio of the species. The result can bemore » applied to both the classic transport theory of plasmas that relies on the Chapman-Enskog method, as well as to derive collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional ten-moment equations with exact conservation laws for momentum-and energy-transfer rates.« less

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

Treesearch

James R. Reilly; Ann E. Hajek

2007-01-01

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

The coalescent of a sample from a binary branching process.

PubMed

Lambert, Amaury

2018-04-25

At time 0, start a time-continuous binary branching process, where particles give birth to a single particle independently (at a possibly time-dependent rate) and die independently (at a possibly time-dependent and age-dependent rate). A particular case is the classical birth-death process. Stop this process at time T>0. It is known that the tree spanned by the N tips alive at time T of the tree thus obtained (called a reduced tree or coalescent tree) is a coalescent point process (CPP), which basically means that the depths of interior nodes are independent and identically distributed (iid). Now select each of the N tips independently with probability y (Bernoulli sample). It is known that the tree generated by the selected tips, which we will call the Bernoulli sampled CPP, is again a CPP. Now instead, select exactly k tips uniformly at random among the N tips (a k-sample). We show that the tree generated by the selected tips is a mixture of Bernoulli sampled CPPs with the same parent CPP, over some explicit distribution of the sampling probability y. An immediate consequence is that the genealogy of a k-sample can be obtained by the realization of k random variables, first the random sampling probability Y and then the k-1 node depths which are iid conditional on Y=y. Copyright © 2018. Published by Elsevier Inc.

Monitoring automotive oil degradation: analytical tools and onboard sensing technologies.

PubMed

Mujahid, Adnan; Dickert, Franz L

2012-09-01

Engine oil experiences a number of thermal and oxidative phases that yield acidic products in the matrix consequently leading to degradation of the base oil. Generally, oil oxidation is a complex process and difficult to elucidate; however, the degradation pathways can be defined for almost every type of oil because they mainly depend on the mechanical status and operating conditions. The exact time of oil change is nonetheless difficult to predict, but it is of great interest from an economic and ecological point of view. In order to make a quick and accurate decision about oil changes, onboard assessment of oil quality is highly desirable. For this purpose, a variety of physical and chemical sensors have been proposed along with spectroscopic strategies. We present a critical review of all these approaches and of recent developments to analyze the exact lifetime of automotive engine oil. Apart from their potential for degradation monitoring, their limitations and future perspectives have also been investigated.

The marriage problem and the fate of bachelors

NASA Astrophysics Data System (ADS)

Nieuwenhuizen, Th. M.

In the marriage problem, a variant of the bi-parted matching problem, each member has a “wish-list” expressing his/her preference for all possible partners; this list consists of random, positive real numbers drawn from a certain distribution. One searches the lowest cost for the society, at the risk of breaking up pairs in the course of time. Minimization of a global cost function (Hamiltonian) is performed with statistical mechanics techniques at a finite fictitious temperature. The problem is generalized to include bachelors, needed in particular when the groups have different size, and polygamy. Exact solutions are found for the optimal solution ( T=0). The entropy is found to vanish quadratically in T. Also, other evidence is found that the replica symmetric solution is exact, implying at most a polynomial degeneracy of the optimal solution. Whether bachelors occur or not, depends not only on their intrinsic qualities, or lack thereof, but also on global aspects of the chance for pair formation in society.

Harmonic generation beyond the Strong-Field Approximation: the physics behind the short-wave-infrared scaling laws.

PubMed

Pérez-Hernández, J A; Roso, L; Plaja, L

2009-06-08

The physics of laser-mater interactions beyond the perturbative limit configures the field of extreme non-linear optics. Although most experiments have been done in the near infrared ( lambda

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

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

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

2015-07-07

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

Solvable four-state Landau-Zener model of two interacting qubits with path interference

DOE PAGES

Sinitsyn, Nikolai A.

2015-11-30

In this paper, I identify a nontrivial four-state Landau-Zener model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. The model describes an experimentally accessible system of two interacting qubits, such as a localized state in a Dirac material with both valley and spin degrees of freedom or a singly charged quantum dot (QD) molecule with spin orbit coupling. Application of the linearly time-dependent magnetic field induces a sequence of quantum level crossings with possibility of interference of different trajectories in a semiclassical picture. I argue that this system satisfies the criteria ofmore » integrability in the multistate Landau-Zener theory, which allows one to derive explicit exact analytical expressions for the transition probability matrix. Finally, I also argue that this model is likely a special case of a larger class of solvable systems, and present a six-state generalization as an example.« less

Exact analytic solutions for a global equation of plant cell growth.

PubMed

Pietruszka, Mariusz

2010-05-21

A generalization of the Lockhart equation for plant cell expansion in isotropic case is presented. The goal is to account for the temporal variation in the wall mechanical properties--in this case by making the wall extensibility a time dependent parameter. We introduce a time-differential equation describing the plant growth process with some key biophysical aspects considered. The aim of this work was to improve prior modeling efforts by taking into account the dynamic character of the plant cell wall with characteristics reminiscent of damped (aperiodic) motion. The equations selected to encapsulate the time evolution of the wall extensibility offer a new insight into the control of cell wall expansion. We find that the solutions to the time dependent second order differential equation reproduce much of the known experimental data for long- and short-time scales. Additionally, in order to support the biomechanical approach, a new growth equation based on the action of expansin proteins is proposed. Remarkably, both methods independently converge to the same kind, sigmoid-shaped, growth description functional V(t) proportional, exp(-exp(-t)), properly describing the volumetric growth and, consequently, growth rate as its time derivative. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

Time-sliced perturbation theory for large scale structure I: general formalism

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

Blas, Diego; Garny, Mathias; Sibiryakov, Sergey

2016-07-01

We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein-de Sitter universe, the time evolution ofmore » the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This paves the way towards the systematic resummation of infrared effects in large scale structure formation. We also argue that the approach proposed here provides a natural framework to account for the influence of short-scale dynamics on larger scales along the lines of effective field theory.« less

Adiabatic state preparation of stripe phases with strongly magnetic atoms

NASA Astrophysics Data System (ADS)

Mazloom, Azadeh; Vermersch, Benoît; Baranov, Mikhail A.; Dalmonte, Marcello

2017-09-01

We propose a protocol for realizing the stripe phase in two spin models on a two-dimensional square lattice, which can be implemented with strongly magnetic atoms (Cr, Dy, Er, etc.) in optical lattices by encoding spin states into Zeeman sublevels of the ground-state manifold. The protocol is tested with cluster-mean-field time-dependent variational Ansätze, validated by comparison with exact results for small systems, which enable us to simulate the dynamics of systems with up to 64 sites during the state-preparation protocol. This allows us, in particular, to estimate the time required for preparation of the stripe phase with high fidelity under real experimental conditions.

The calculation of transport properties in quantum liquids using the maximum entropy numerical analytic continuation method: Application to liquid para-hydrogen

PubMed Central

Rabani, Eran; Reichman, David R.; Krilov, Goran; Berne, Bruce J.

2002-01-01

We present a method based on augmenting an exact relation between a frequency-dependent diffusion constant and the imaginary time velocity autocorrelation function, combined with the maximum entropy numerical analytic continuation approach to study transport properties in quantum liquids. The method is applied to the case of liquid para-hydrogen at two thermodynamic state points: a liquid near the triple point and a high-temperature liquid. Good agreement for the self-diffusion constant and for the real-time velocity autocorrelation function is obtained in comparison to experimental measurements and other theoretical predictions. Improvement of the methodology and future applications are discussed. PMID:11830656

Simple iterative construction of the optimized effective potential for orbital functionals, including exact exchange.

PubMed

Kümmel, Stephan; Perdew, John P

2003-01-31

For exchange-correlation functionals that depend explicitly on the Kohn-Sham orbitals, the potential V(xcsigma)(r) must be obtained as the solution of the optimized effective potential (OEP) integral equation. This is very demanding and has limited the use of orbital functionals. We demonstrate that instead the OEP can be obtained iteratively by solving the partial differential equations for the orbital shifts that exactify the Krieger-Li-Iafrate approximation. Unoccupied orbitals do not need to be calculated. Accuracy and efficiency of the method are shown for atoms and clusters using the exact-exchange energy. Counterintuitive asymptotic limits of the exact OEP are presented.

Signal Statistics and Maximum Likelihood Sequence Estimation in Intensity Modulated Fiber Optic Links Containing a Single Optical Pre-amplifier.

PubMed

Alić, Nikola; Papen, George; Saperstein, Robert; Milstein, Laurence; Fainman, Yeshaiahu

2005-06-13

Exact signal statistics for fiber-optic links containing a single optical pre-amplifier are calculated and applied to sequence estimation for electronic dispersion compensation. The performance is evaluated and compared with results based on the approximate chi-square statistics. We show that detection in existing systems based on exact statistics can be improved relative to using a chi-square distribution for realistic filter shapes. In contrast, for high-spectral efficiency systems the difference between the two approaches diminishes, and performance tends to be less dependent on the exact shape of the filter used.

The microscopic structure of an exactly solvable model binary solution that exhibits two closed loops in the phase diagram.

PubMed

Lungu, Radu P; Huckaby, Dale A

2008-07-21

An exactly solvable lattice model describing a binary solution is considered where rodlike molecules of types AA and BB cover the links of a honeycomb lattice, the neighboring molecular ends having three-body and orientation-dependent bonding interactions. At phase coexistence of AA-rich and BB-rich phases, the average fraction of each type of triangle of neighboring molecular ends is calculated exactly. The fractions of the different types of triangles are then used to deduce the local microscopic structure of the coexisting phases for a case of the model that contains two closed loops in the phase diagram.

Fano resonance in the nonadiabatically pumped shot noise of a time-dependent quantum well in a two-dimensional electron gas and graphene

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

Zhu, Rui, E-mail: rzhu@scut.edu.cn; Dai, Jiao-Hua; Guo, Yong

Interference between different quantum paths can generate Fano resonance. One of the examples is transport through a quasibound state driven by a time-dependent scattering potential. Previously it is found that Fano resonance occurs as a result of energy matching in one-dimensional systems. In this work, we demonstrate that when transverse motion is present, Fano resonance occurs precisely at the wavevector matching situation. Using the Floquet scattering theory, we considered the transport properties of a nonadiabatic time-dependent well both in a two-dimensional electron gas and monolayer graphene structure. Dispersion of the quasibound state of a static quantum well is obtained withmore » transverse motion present. We found that Fano resonance occurs when the wavevector in the transport direction of one of the Floquet sidebands is exactly identical to that of the quasibound state in the well at equilibrium and follows the dispersion pattern of the latter. To observe the Fano resonance phenomenon in the transmission spectrum, we also considered the pumped shot noise properties when time and spatial symmetry secures vanishing current in the considered configuration. Prominent Fano resonance is found in the differential pumped shot noise with respect to the reservoir Fermi energy.« less

Applying Boundary Conditions Using a Time-Dependent Lagrangian for Modeling Laser-Plasma Interactions

NASA Astrophysics Data System (ADS)

Reyes, Jonathan; Shadwick, B. A.

2016-10-01

Modeling the evolution of a short, intense laser pulse propagating through an underdense plasma is of particular interest in the physics of laser-plasma interactions. Numerical models are typically created by first discretizing the equations of motion and then imposing boundary conditions. Using the variational principle of Chen and Sudan, we spatially discretize the Lagrangian density to obtain discrete equations of motion and a discrete energy conservation law which is exactly satisfied regardless of the spatial grid resolution. Modifying the derived equations of motion (e.g., enforcing boundary conditions) generally ruins energy conservation. However, time-dependent terms can be added to the Lagrangian which force the equations of motion to have the desired boundary conditions. Although some foresight is needed to choose these time-dependent terms, this approach provides a mechanism for energy to exit the closed system while allowing the conservation law to account for the loss. An appropriate time discretization scheme is selected based on stability analysis and resolution requirements. We present results using this variational approach in a co-moving coordinate system and compare such results to those using traditional second-order methods. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY- 1104683.

SW#db: GPU-Accelerated Exact Sequence Similarity Database Search.

PubMed

Korpar, Matija; Šošić, Martin; Blažeka, Dino; Šikić, Mile

2015-01-01

In recent years we have witnessed a growth in sequencing yield, the number of samples sequenced, and as a result-the growth of publicly maintained sequence databases. The increase of data present all around has put high requirements on protein similarity search algorithms with two ever-opposite goals: how to keep the running times acceptable while maintaining a high-enough level of sensitivity. The most time consuming step of similarity search are the local alignments between query and database sequences. This step is usually performed using exact local alignment algorithms such as Smith-Waterman. Due to its quadratic time complexity, alignments of a query to the whole database are usually too slow. Therefore, the majority of the protein similarity search methods prior to doing the exact local alignment apply heuristics to reduce the number of possible candidate sequences in the database. However, there is still a need for the alignment of a query sequence to a reduced database. In this paper we present the SW#db tool and a library for fast exact similarity search. Although its running times, as a standalone tool, are comparable to the running times of BLAST, it is primarily intended to be used for exact local alignment phase in which the database of sequences has already been reduced. It uses both GPU and CPU parallelization and was 4-5 times faster than SSEARCH, 6-25 times faster than CUDASW++ and more than 20 times faster than SSW at the time of writing, using multiple queries on Swiss-prot and Uniref90 databases.

Theoretical test of Jarzynski's equality for reversible volume-switching processes of an ideal gas system.

PubMed

Sung, Jaeyoung

2007-07-01

We present an exact theoretical test of Jarzynski's equality (JE) for reversible volume-switching processes of an ideal gas system. The exact analysis shows that the prediction of JE for the free energy difference is the same as the work done on the gas system during the reversible process that is dependent on the shape of path of the reversible volume-switching process.

Comparing exact energy solutions of quartic eigenvalue polynomials in commutative, non-commutative and non-commutative phase frameworks for boson π‑

NASA Astrophysics Data System (ADS)

Derakhshani, Z.; Ghominejad, M.

2018-04-01

In this paper, the behavior of a Duffin-Kemmer-Petiau (DKP) boson particle in the presence of a harmonic energy-dependent interaction, under the influence of an external magnetic field is precisely studied. In order to exactly solve all equations in commutative (C), non-commutative (NC) and non-commutative phase (NCP) frameworks, the Nikiforov-Uvarov (NU) powerful exact approach is employed. All these attempts end up with solving their quartic equations, trying to find and discuss on their discriminant function Δ, in a unique way which has never been discussed for any boson in any other research, especially for the boson π‑ on which, we have been exclusively concerned. We finally succeeded to obtain the exact energy spectrums and wave functions under the effects of NC and NCP parameters and energy-dependent interaction on energy eigenvalues. In this step, we analyze the behaviors of their quartic energy eigenvalue polynomials in three sections and accurately compare all achieved physical-admissible roots one by one. This comparison surprisingly shows that the NC and NCP effects on the other hand, and the assumed harmonic energy-dependent interaction on the other hand, have almost the same order of perturbation effects for limited amounts of the magnetic field in a system of DKP bosons. Furthermore, through some calculations within this paper, we came up with a very crucial point about the NU method which was mistakenly being used in many papers by several researchers and improved it to be used safely.

Large deviations of a long-time average in the Ehrenfest urn model

NASA Astrophysics Data System (ADS)

Meerson, Baruch; Zilber, Pini

2018-05-01

Since its inception in 1907, the Ehrenfest urn model (EUM) has served as a test bed of key concepts of statistical mechanics. Here we employ this model to study large deviations of a time-additive quantity. We consider two continuous-time versions of the EUM with K urns and N balls: with and without interactions between the balls in the same urn. We evaluate the probability distribution that the average number of balls in one urn over time T, , takes any specified value aN, where . For long observation time, , a Donsker–Varadhan large deviation principle holds: , where … denote additional parameters of the model. We calculate the rate function exactly by two different methods due to Donsker and Varadhan and compare the exact results with those obtained with a variant of WKB approximation (after Wentzel, Kramers and Brillouin). In the absence of interactions the WKB prediction for is exact for any N. In the presence of interactions the WKB method gives asymptotically exact results for . The WKB method also uncovers the (very simple) time history of the system which dominates the contribution of different time histories to .

Correcting for dependent censoring in routine outcome monitoring data by applying the inverse probability censoring weighted estimator.

PubMed

Willems, Sjw; Schat, A; van Noorden, M S; Fiocco, M

2018-02-01

Censored data make survival analysis more complicated because exact event times are not observed. Statistical methodology developed to account for censored observations assumes that patients' withdrawal from a study is independent of the event of interest. However, in practice, some covariates might be associated to both lifetime and censoring mechanism, inducing dependent censoring. In this case, standard survival techniques, like Kaplan-Meier estimator, give biased results. The inverse probability censoring weighted estimator was developed to correct for bias due to dependent censoring. In this article, we explore the use of inverse probability censoring weighting methodology and describe why it is effective in removing the bias. Since implementing this method is highly time consuming and requires programming and mathematical skills, we propose a user friendly algorithm in R. Applications to a toy example and to a medical data set illustrate how the algorithm works. A simulation study was carried out to investigate the performance of the inverse probability censoring weighted estimators in situations where dependent censoring is present in the data. In the simulation process, different sample sizes, strengths of the censoring model, and percentages of censored individuals were chosen. Results show that in each scenario inverse probability censoring weighting reduces the bias induced in the traditional Kaplan-Meier approach where dependent censoring is ignored.

Advanced propeller noise prediction in the time domain

NASA Technical Reports Server (NTRS)

Farassat, F.; Dunn, M. H.; Spence, P. L.

1992-01-01

The time domain code ASSPIN gives acousticians a powerful technique of advanced propeller noise prediction. Except for nonlinear effects, the code uses exact solutions of the Ffowcs Williams-Hawkings equation with exact blade geometry and kinematics. By including nonaxial inflow, periodic loading noise, and adaptive time steps to accelerate computer execution, the development of this code becomes complete.

Resistivity scaling and electron relaxation times in metallic nanowires

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

Moors, Kristof, E-mail: kristof@itf.fys.kuleuven.be; Imec, Kapeldreef 75, B-3001 Leuven; Sorée, Bart

2014-08-14

We study the resistivity scaling in nanometer-sized metallic wires due to surface roughness and grain-boundaries, currently the main cause of electron scattering in nanoscaled interconnects. The resistivity has been obtained with the Boltzmann transport equation, adopting the relaxation time approximation of the distribution function and the effective mass approximation for the conducting electrons. The relaxation times are calculated exactly, using Fermi's golden rule, resulting in a correct relaxation time for every sub-band state contributing to the transport. In general, the relaxation time strongly depends on the sub-band state, something that remained unclear with the methods of previous work. The resistivitymore » scaling is obtained for different roughness and grain-boundary properties, showing large differences in scaling behavior and relaxation times. Our model clearly indicates that the resistivity is dominated by grain-boundary scattering, easily surpassing the surface roughness contribution by a factor of 10.« less

First-Passage Times in d -Dimensional Heterogeneous Media

NASA Astrophysics Data System (ADS)

Vaccario, G.; Antoine, C.; Talbot, J.

2015-12-01

Although there are many theoretical studies of the mean first-passage time (MFPT), most neglect the diffusive heterogeneity of real systems. We present exact analytical expressions for the MFPT and residence times of a pointlike particle diffusing in a spherically symmetric d -dimensional heterogeneous system composed of two concentric media with different diffusion coefficients with an absorbing inner boundary (target) and a reflecting outer boundary. By varying the convention, e.g., Itō, Stratonovich, or isothermal, chosen to interpret the overdamped Langevin equation with multiplicative noise describing the diffusion process, we find different predictions and counterintuitive results for the residence time in the outer region and hence for the MFPT, while the residence time in the inner region is independent of the convention. This convention dependence of residence times and the MFPT could provide insights about the heterogeneous diffusion in a cell or in a tumor, or for animal and insect searches inside their home range.

Weak ergodicity breaking, irreproducibility, and ageing in anomalous diffusion processes

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

Metzler, Ralf

2014-01-14

Single particle traces are standardly evaluated in terms of time averages of the second moment of the position time series r(t). For ergodic processes, one can interpret such results in terms of the known theories for the corresponding ensemble averaged quantities. In anomalous diffusion processes, that are widely observed in nature over many orders of magnitude, the equivalence between (long) time and ensemble averages may be broken (weak ergodicity breaking), and these time averages may no longer be interpreted in terms of ensemble theories. Here we detail some recent results on weakly non-ergodic systems with respect to the time averagedmore » mean squared displacement, the inherent irreproducibility of individual measurements, and methods to determine the exact underlying stochastic process. We also address the phenomenon of ageing, the dependence of physical observables on the time span between initial preparation of the system and the start of the measurement.« less

Physical Meaning of Virtual Kohn-Sham Orbitals and Orbital Energies: An Ideal Basis for the Description of Molecular Excitations.

PubMed

van Meer, R; Gritsenko, O V; Baerends, E J

2014-10-14

In recent years, several benchmark studies on the performance of large sets of functionals in time-dependent density functional theory (TDDFT) calculations of excitation energies have been performed. The tested functionals do not approximate exact Kohn-Sham orbitals and orbital energies closely. We highlight the advantages of (close to) exact Kohn-Sham orbitals and orbital energies for a simple description, very often as just a single orbital-to-orbital transition, of molecular excitations. Benchmark calculations are performed for the statistical average of orbital potentials (SAOP) functional for the potential [J. Chem. Phys. 2000, 112, 1344; 2001, 114, 652], which approximates the true Kohn-Sham potential much better than LDA, GGA, mGGA, and hybrid potentials do. An accurate Kohn-Sham potential does not only perform satisfactorily for calculated vertical excitation energies of both valence and Rydberg transitions but also exhibits appealing properties of the KS orbitals including occupied orbital energies close to ionization energies, virtual-occupied orbital energy gaps very close to excitation energies, realistic shapes of virtual orbitals, leading to straightforward interpretation of most excitations as single orbital transitions. We stress that such advantages are completely lost in time-dependent Hartree-Fock and partly in hybrid approaches. Many excitations and excitation energies calculated with local density, generalized gradient, and hybrid functionals are spurious. There is, with an accurate KS, or even the LDA or GGA potentials, nothing problematic about the "band gap" in molecules: the HOMO-LUMO gap is close to the first excitation energy (the optical gap).

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

Eich, F. G.; Agostini, Federica, E-mail: agostini@mpi-halle.mpg.de

We propose a procedure to analyze the relation between the exact factorization of the electron-nuclear wave function and the Born-Oppenheimer approximation. We define the adiabatic limit as the limit of infinite nuclear mass. To this end, we introduce a unit system that singles out the dependence on the electron-nuclear mass ratio of each term appearing in the equations of the exact factorization. We observe how non-adiabatic effects induced by the coupling to the nuclear motion affect electronic properties and we analyze the leading term, connecting it to the classical nuclear momentum. Its dependence on the mass ratio is tested numericallymore » on a model of proton-coupled electron transfer in different non-adiabatic regimes.« less

Exact solutions for mass-dependent irreversible aggregations.

PubMed

Son, Seung-Woo; Christensen, Claire; Bizhani, Golnoosh; Grassberger, Peter; Paczuski, Maya

2011-10-01

We consider the mass-dependent aggregation process (k+1)X→X, given a fixed number of unit mass particles in the initial state. One cluster is chosen proportional to its mass and is merged into one, either with k neighbors in one dimension, or--in the well-mixed case--with k other clusters picked randomly. We find the same combinatorial exact solutions for the probability to find any given configuration of particles on a ring or line, and in the well-mixed case. The mass distribution of a single cluster exhibits scaling laws and the finite-size scaling form is given. The relation to the classical sum kernel of irreversible aggregation is discussed.

The Laplace method for probability measures in Banach spaces

NASA Astrophysics Data System (ADS)

Piterbarg, V. I.; Fatalov, V. R.

1995-12-01

Contents §1. Introduction Chapter I. Asymptotic analysis of continual integrals in Banach space, depending on a large parameter §2. The large deviation principle and logarithmic asymptotics of continual integrals §3. Exact asymptotics of Gaussian integrals in Banach spaces: the Laplace method 3.1. The Laplace method for Gaussian integrals taken over the whole Hilbert space: isolated minimum points ([167], I) 3.2. The Laplace method for Gaussian integrals in Hilbert space: the manifold of minimum points ([167], II) 3.3. The Laplace method for Gaussian integrals in Banach space ([90], [174], [176]) 3.4. Exact asymptotics of large deviations of Gaussian norms §4. The Laplace method for distributions of sums of independent random elements with values in Banach space 4.1. The case of a non-degenerate minimum point ([137], I) 4.2. A degenerate isolated minimum point and the manifold of minimum points ([137], II) §5. Further examples 5.1. The Laplace method for the local time functional of a Markov symmetric process ([217]) 5.2. The Laplace method for diffusion processes, a finite number of non-degenerate minimum points ([116]) 5.3. Asymptotics of large deviations for Brownian motion in the Hölder norm 5.4. Non-asymptotic expansion of a strong stable law in Hilbert space ([41]) Chapter II. The double sum method - a version of the Laplace method in the space of continuous functions §6. Pickands' method of double sums 6.1. General situations 6.2. Asymptotics of the distribution of the maximum of a Gaussian stationary process 6.3. Asymptotics of the probability of a large excursion of a Gaussian non-stationary process §7. Probabilities of large deviations of trajectories of Gaussian fields 7.1. Homogeneous fields and fields with constant dispersion 7.2. Finitely many maximum points of dispersion 7.3. Manifold of maximum points of dispersion 7.4. Asymptotics of distributions of maxima of Wiener fields §8. Exact asymptotics of large deviations of the norm of Gaussian vectors and processes with values in the spaces L_k^p and l^2. Gaussian fields with the set of parameters in Hilbert space 8.1 Exact asymptotics of the distribution of the l_k^p-norm of a Gaussian finite-dimensional vector with dependent coordinates, p > 1 8.2. Exact asymptotics of probabilities of high excursions of trajectories of processes of type \\chi^2 8.3. Asymptotics of the probabilities of large deviations of Gaussian processes with a set of parameters in Hilbert space [74] 8.4. Asymptotics of distributions of maxima of the norms of l^2-valued Gaussian processes 8.5. Exact asymptotics of large deviations for the l^2-valued Ornstein-Uhlenbeck process Bibliography

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

NASA Astrophysics Data System (ADS)

Boström, Emil; Mikkelsen, Anders; Verdozzi, Claudio

2016-05-01

We introduce a model description of femtosecond laser induced desorption at surfaces. The substrate part of the system is taken into account as a (possibly semi-infinite) linear chain. Here, being especially interested in the early stages of dissociation, we consider a finite-size implementation of the model (i.e., a finite substrate), for which an exact numerical solution is possible. By time-evolving the many-body wave function, and also using results from a time-dependent density functional theory description for electron-nuclear systems, we analyze the competition between several surface-response mechanisms and electronic correlations in the transient and longer time dynamics under the influence of dipole-coupled fields. Our model allows us to explore how coherent multiple-pulse protocols can impact desorption in a variety of prototypical experiments.

On modeling animal movements using Brownian motion with measurement error.

PubMed

Pozdnyakov, Vladimir; Meyer, Thomas; Wang, Yu-Bo; Yan, Jun

2014-02-01

Modeling animal movements with Brownian motion (or more generally by a Gaussian process) has a long tradition in ecological studies. The recent Brownian bridge movement model (BBMM), which incorporates measurement errors, has been quickly adopted by ecologists because of its simplicity and tractability. We discuss some nontrivial properties of the discrete-time stochastic process that results from observing a Brownian motion with added normal noise at discrete times. In particular, we demonstrate that the observed sequence of random variables is not Markov. Consequently the expected occupation time between two successively observed locations does not depend on just those two observations; the whole path must be taken into account. Nonetheless, the exact likelihood function of the observed time series remains tractable; it requires only sparse matrix computations. The likelihood-based estimation procedure is described in detail and compared to the BBMM estimation.

Resolution Enhancement In Ultrasonic Imaging By A Time-Varying Filter

NASA Astrophysics Data System (ADS)

Ching, N. H.; Rosenfeld, D.; Braun, M.

1987-09-01

The study reported here investigates the use of a time-varying filter to compensate for the spreading of ultrasonic pulses due to the frequency dependence of attenuation by tissues. The effect of this pulse spreading is to degrade progressively the axial resolution with increasing depth. The form of compensation required to correct for this effect is impossible to realize exactly. A novel time-varying filter utilizing a bank of bandpass filters is proposed as a realizable approximation of the required compensation. The performance of this filter is evaluated by means of a computer simulation. The limits of its application are discussed. Apart from improving the axial resolution, and hence the accuracy of axial measurements, the compensating filter could be used in implementing tissue characterization algorithms based on attenuation data.

Dissolution of multicomponent bubbles. [gases in glass melts

NASA Technical Reports Server (NTRS)

Weinberg, M. C.; Subramanian, R. S.

1980-01-01

The behavior of an isolated, stationary, multicomponent gas bubble in a glassmelt containing several dissolved gases is considered. The relevant mass-transport equations are formulated and calculations are performed for the case of two diffusing gases using a quasi-stationary model and a numerical solution of the exact mass-transfer equations. The results obtained from these two approaches are compared. The factors which govern the dissolution or growth of a bubble are thermodynamic and kinetic in origin. The tendency of a bubble to grow or shrink at long times is controlled by departure from overall equilibrium, whereas the short-time bubble dynamics may be dominated by kinetic effects. As a result of the existence of these dual influences, maxima and/or minima occur in the functional dependence of the bubble radius on time.

Stochastic Resonance and First Arrival Time for Excitable Systems

NASA Astrophysics Data System (ADS)

Duki, Solomon Fekade; Taye, Mesfin Asfaw

2018-04-01

We study the noise induced thermally activated barrier crossing of Brownian particles that hop in a piecewise linear potential. Using the exact analytic solutions and via numerical simulations not only we explore the dependence for the first passage time of a single particle but also we calculate the first arrival time for one particle out of N particles. The first arrival time decreases as the number of particles increases as expected. We then explore the thermally activated barrier crossing rate of the system in the presence of time varying signal. The dependence of signal to noise ratio SNR as well as the power amplification (η ) on model parameters is explored. η and SNR depict a pronounced peak at particular noise strength. In the presence of N particles, η is considerably amplified as N steps up showing the weak periodic signal plays a vital role in controlling the noise induced dynamics of the system. Moreover, for the sake of generality, the viscous friction γ is considered to decrease exponentially when the temperature T of the medium increases (γ =Be^{-A T} ) as proposed originally by Reynolds (Philos Trans R Soc Lond 177:157, 1886).

Stochastic Resonance and First Arrival Time for Excitable Systems

NASA Astrophysics Data System (ADS)

Duki, Solomon Fekade; Taye, Mesfin Asfaw

2018-06-01

We study the noise induced thermally activated barrier crossing of Brownian particles that hop in a piecewise linear potential. Using the exact analytic solutions and via numerical simulations not only we explore the dependence for the first passage time of a single particle but also we calculate the first arrival time for one particle out of N particles. The first arrival time decreases as the number of particles increases as expected. We then explore the thermally activated barrier crossing rate of the system in the presence of time varying signal. The dependence of signal to noise ratio SNR as well as the power amplification (η ) on model parameters is explored. η and SNR depict a pronounced peak at particular noise strength. In the presence of N particles, η is considerably amplified as N steps up showing the weak periodic signal plays a vital role in controlling the noise induced dynamics of the system. Moreover, for the sake of generality, the viscous friction γ is considered to decrease exponentially when the temperature T of the medium increases (γ =Be^{-A T}) as proposed originally by Reynolds (Philos Trans R Soc Lond 177:157, 1886).

An exact solution for the history-dependent material and delamination behavior of laminated plates subjected to cylindrical bending

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

Williams, Todd O

2009-01-01

The exact solution for the history-dependent behavior of laminated plates subjected to cylindrical bending is presented. The solution represents the extension of Pagano's solution to consider arbitrary types of constitutive behaviors for the individual lamina as well as arbitrary types of cohesive zones models for delamination behavior. Examples of the possible types of material behavior are plasticity, viscoelasticity, viscoplasticity, and damaging. Examples of possible CZMs that can be considered are linear, nonlinear hardening, as well as nonlinear with softening. The resulting solution is intended as a benchmark solution for considering the predictive capabilities of different plate theories. Initial results aremore » presented for several types of history-dependent material behaviors. It is shown that the plate response in the presence of history-dependent behaviors can differ dramatically from the elastic response. These results have strong implications for what constitutes an appropriate plate theory for modeling such behaviors.« less

Identification of the population density of a species model with nonlocal diffusion and nonlinear reaction

NASA Astrophysics Data System (ADS)

Tuan, Nguyen Huy; Van Au, Vo; Khoa, Vo Anh; Lesnic, Daniel

2017-05-01

The identification of the population density of a logistic equation backwards in time associated with nonlocal diffusion and nonlinear reaction, motivated by biology and ecology fields, is investigated. The diffusion depends on an integral average of the population density whilst the reaction term is a global or local Lipschitz function of the population density. After discussing the ill-posedness of the problem, we apply the quasi-reversibility method to construct stable approximation problems. It is shown that the regularized solutions stemming from such method not only depend continuously on the final data, but also strongly converge to the exact solution in L 2-norm. New error estimates together with stability results are obtained. Furthermore, numerical examples are provided to illustrate the theoretical results.

Nonadiabatic Molecular Dynamics and Orthogonality Constrained Density Functional Theory

NASA Astrophysics Data System (ADS)

Shushkov, Philip Georgiev

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

Exact and approximate solutions to the oblique shock equations for real-time applications

NASA Technical Reports Server (NTRS)

Hartley, T. T.; Brandis, R.; Mossayebi, F.

1991-01-01

The derivation of exact solutions for determining the characteristics of an oblique shock wave in a supersonic flow is investigated. Specifically, an explicit expression for the oblique shock angle in terms of the free stream Mach number, the centerbody deflection angle, and the ratio of the specific heats, is derived. A simpler approximate solution is obtained and compared to the exact solution. The primary objectives of obtaining these solutions is to provide a fast algorithm that can run in a real time environment.

Transitionless driving on adiabatic search algorithm

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

Oh, Sangchul, E-mail: soh@qf.org.qa; Kais, Sabre, E-mail: kais@purdue.edu; Department of Chemistry, Department of Physics and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907

We study quantum dynamics of the adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolution is studied and visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the non-adiabatic transition probability from exponential decay for the short running time to inverse-square decay in asymptotic running time. The scaling of the critical running time is expressed in terms of the Lambert W function. We derive the transitionless driving Hamiltonian for the adiabatic search algorithm, which makes a quantum state follow the adiabatic path. We demonstrate that a uniform transitionless driving Hamiltonian,more » approximate to the exact time-dependent driving Hamiltonian, can alter the non-adiabatic transition probability from the inverse square decay to the inverse fourth power decay with the running time. This may open up a new but simple way of speeding up adiabatic quantum dynamics.« less

Exact semiclassical expansions for one-dimensional quantum oscillators

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

Delabaere, E.; Dillinger, H.; Pham, F.

1997-12-01

A set of rules is given for dealing with WKB expansions in the one-dimensional analytic case, whereby such expansions are not considered as approximations but as exact encodings of wave functions, thus allowing for analytic continuation with respect to whichever parameters the potential function depends on, with an exact control of small exponential effects. These rules, which include also the case when there are double turning points, are illustrated on various examples, and applied to the study of bound state or resonance spectra. In the case of simple oscillators, it is thus shown that the Rayleigh{endash}Schr{umlt o}dinger series is Borelmore » resummable, yielding the exact energy levels. In the case of the symmetrical anharmonic oscillator, one gets a simple and rigorous justification of the Zinn-Justin quantization condition, and of its solution in terms of {open_quotes}multi-instanton expansions.{close_quotes} {copyright} {ital 1997 American Institute of Physics.}« less

Correlated electron-nuclear dynamics with conditional wave functions.

PubMed

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

2014-08-22

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

Structure of weakly 2-dependent siphons

NASA Astrophysics Data System (ADS)

Chao, Daniel Yuh; Chen, Jiun-Ting

2013-09-01

Deadlocks arising from insufficiently marked siphons in flexible manufacturing systems can be controlled by adding monitors to each siphon - too many for large systems. Li and Zhou add monitors to elementary siphons only while controlling the rest of (called dependent) siphons by adjusting control depth variables of elementary siphons. Only a linear number of monitors are required. The control of weakly dependent siphons (WDSs) is rather conservative since only positive terms were considered. The structure for strongly dependent siphons (SDSs) has been studied earlier. Based on this structure, the optimal sequence of adding monitors has been discovered earlier. Better controllability has been discovered to achieve faster and more permissive control. The results have been extended earlier to S3PGR2 (systems of simple sequential processes with general resource requirements). This paper explores the structures for WDSs, which, as found in this paper, involve elementary resource circuits interconnecting at more than (for SDSs, exactly) one resource place. This saves the time to compute compound siphons, their complementary sets and T-characteristic vectors. Also it allows us (1) to improve the controllability of WDSs and control siphons and (2) to avoid the time to find independent vectors for elementary siphons. We propose a sufficient and necessary test for adjusting control depth variables in S3PR (systems of simple sequential processes with resources) to avoid the sufficient-only time-consuming linear integer programming test (LIP) (Nondeterministic Polynomial (NP) time complete problem) required previously for some cases.

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.

Topics in High-Energy Astrophysics: X-ray Time Lags and Gamma-ray Flares

NASA Astrophysics Data System (ADS)

Kroon, John J.

2016-03-01

The Universe is host to a wide variety of high-energy processes that convert gravitational potential energy or rest-mass energy into non-thermal radiation such as bremsstrahlung and synchrotron. Prevailing models of X-ray emission from accreting Black Hole Binaries (BHBs) struggle to simultaneously fit the quiescent X-ray spectrum and the transients which result in the phenomenon known as X-ray time lags. And similarly, classical models of diffusive shock acceleration in pulsar wind nebulae fail to explain the extreme particle acceleration in very short timescales as is inferred from recent gamma-ray flares from the Crab nebula. In this dissertation, I develop new exact analytic models to shed light on these intriguing processes. I take a fresh look at the formation of X-ray time lags in compact sources using a new mathematical approach in which I obtain the exact Green's function solution. The resulting Green's function allows one to explore a variety of injection scenarios, including both monochromatic and broadband (bremsstrahlung) seed photon injection. I obtain the exact solution for the dependence of the time lags on the Fourier frequency, for both homogeneous and inhomogeneous clouds. The model can successfully reproduce both the observed time lags and the quiescent X-ray spectrum using a single set of coronal parameters. I show that the implied coronal radii in the new model are significantly smaller than those obtained in the Monte Carlo simulations, hence greatly reducing the coronal heating problem. Recent bright gamma-ray flares from the Crab nebula observed by AGILE and Fermi reaching GeV energies and lasting several days challenge the contemporary model for particle acceleration in pulsar wind nebulae, specifically the diffusive shock acceleration model. Simulations indicate electron/positron pairs in the Crab nebula pulsar wind must be accelerated up to PeV energies in the presence of ambient magnetic fields with strength B ~100 microG. No comprehensive model has been presented that simultaneously and self-consistently explains the energetic and temporal properties of the observed flares. In this component of my dissertation research, I revisit the problem based on an analytical approach using a transport equation that includes terms describing electrostatic acceleration, stochastic wave-particle acceleration, synchrotron losses, and particle escape. I obtain an exact solution and use it to compute the resulting gamma-ray synchrotron spectrum. I find that the spectra of all the Fermi-LAT flares from the Crab nebula can be reproduced with this model using magnetic fields that are in agreement with multi-wavelength observations.

Cross-Dependency Inference in Multi-Layered Networks: A Collaborative Filtering Perspective.

PubMed

Chen, Chen; Tong, Hanghang; Xie, Lei; Ying, Lei; He, Qing

2017-08-01

The increasingly connected world has catalyzed the fusion of networks from different domains, which facilitates the emergence of a new network model-multi-layered networks. Examples of such kind of network systems include critical infrastructure networks, biological systems, organization-level collaborations, cross-platform e-commerce, and so forth. One crucial structure that distances multi-layered network from other network models is its cross-layer dependency, which describes the associations between the nodes from different layers. Needless to say, the cross-layer dependency in the network plays an essential role in many data mining applications like system robustness analysis and complex network control. However, it remains a daunting task to know the exact dependency relationships due to noise, limited accessibility, and so forth. In this article, we tackle the cross-layer dependency inference problem by modeling it as a collective collaborative filtering problem. Based on this idea, we propose an effective algorithm Fascinate that can reveal unobserved dependencies with linear complexity. Moreover, we derive Fascinate-ZERO, an online variant of Fascinate that can respond to a newly added node timely by checking its neighborhood dependencies. We perform extensive evaluations on real datasets to substantiate the superiority of our proposed approaches.

Finite-temperature time-dependent variation with multiple Davydov states

NASA Astrophysics Data System (ADS)

Wang, Lu; Fujihashi, Yuta; Chen, Lipeng; Zhao, Yang

2017-03-01

The Dirac-Frenkel time-dependent variational approach with Davydov Ansätze is a sophisticated, yet efficient technique to obtain an accurate solution to many-body Schrödinger equations for energy and charge transfer dynamics in molecular aggregates and light-harvesting complexes. We extend this variational approach to finite temperature dynamics of the spin-boson model by adopting a Monte Carlo importance sampling method. In order to demonstrate the applicability of this approach, we compare calculated real-time quantum dynamics of the spin-boson model with that from numerically exact iterative quasiadiabatic propagator path integral (QUAPI) technique. The comparison shows that our variational approach with the single Davydov Ansätze is in excellent agreement with the QUAPI method at high temperatures, while the two differ at low temperatures. Accuracy in dynamics calculations employing a multitude of Davydov trial states is found to improve substantially over the single Davydov Ansatz, especially at low temperatures. At a moderate computational cost, our variational approach with the multiple Davydov Ansatz is shown to provide accurate spin-boson dynamics over a wide range of temperatures and bath spectral densities.

Application of hierarchical equations of motion (HEOM) to time dependent quantum transport at zero and finite temperatures

NASA Astrophysics Data System (ADS)

Tian, Heng; Chen, GuanHua

2013-10-01

Going beyond the limitations of our earlier works [X. Zheng, F. Wang, C.Y. Yam, Y. Mo, G.H. Chen, Phys. Rev. B 75, 195127 (2007); X. Zheng, G.H. Chen, Y. Mo, S.K. Koo, H. Tian, C.Y. Yam, Y.J. Yan, J. Chem. Phys. 133, 114101 (2010)], we propose, in this manuscript, a new alternative approach to simulate time-dependent quantum transport phenomenon from first-principles. This new practical approach, still retaining the formal exactness of HEOM framework, does not rely on any intractable parametrization scheme and the pole structure of Fermi distribution function, thus, can seamlessly incorporated into first-principles simulation and treat transient response of an open electronic systems to an external bias voltage at both zero and finite temperatures on the equal footing. The salient feature of this approach is surveyed, and its time complexity is analysed. As a proof-of-principle of this approach, simulation of the transient current of one dimensional tight-binding chain, driven by some direct external voltages, is demonstrated.

Quantum return probability of a system of N non-interacting lattice fermions

NASA Astrophysics Data System (ADS)

Krapivsky, P. L.; Luck, J. M.; Mallick, K.

2018-02-01

We consider N non-interacting fermions performing continuous-time quantum walks on a one-dimensional lattice. The system is launched from a most compact configuration where the fermions occupy neighboring sites. We calculate exactly the quantum return probability (sometimes referred to as the Loschmidt echo) of observing the very same compact state at a later time t. Remarkably, this probability depends on the parity of the fermion number—it decays as a power of time for even N, while for odd N it exhibits periodic oscillations modulated by a decaying power law. The exponent also slightly depends on the parity of N, and is roughly twice smaller than what it would be in the continuum limit. We also consider the same problem, and obtain similar results, in the presence of an impenetrable wall at the origin constraining the particles to remain on the positive half-line. We derive closed-form expressions for the amplitudes of the power-law decay of the return probability in all cases. The key point in the derivation is the use of Mehta integrals, which are limiting cases of the Selberg integral.

Particle paths and phase plane for time-dependent similarity solutions of the one-dimensional Vlasov-Maxwell equations

NASA Technical Reports Server (NTRS)

Roberts, Dana Aaron; Abraham-Shrauner, Barbara

1987-01-01

The phase trajectories of particles in a plasma described by the one-dimensional Vlasov-Maxwell equations are determined qualitatively, analyzing exact general similarity solutions for the cases of temporally damped and growing (sinusoidal or localized) electric fields. The results of numerical integration in both untransformed and Lie-group point-transformed coordinates are presented in extensive graphs and characterized in detail. The implications of the present analysis for the stability of BGK equilibria are explored, and the existence of nonlinear solutions arbitrarily close to and significantly different from the BGK solutions is demonstrated.

Non-Markovian optimal sideband cooling

NASA Astrophysics Data System (ADS)

Triana, Johan F.; Pachon, Leonardo A.

2018-04-01

Optimal control theory is applied to sideband cooling of nano-mechanical resonators. The formulation described here makes use of exact results derived by means of the path-integral approach of quantum dynamics, so that no approximation is invoked. It is demonstrated that the intricate interplay between time-dependent fields and structured thermal bath may lead to improve results of the sideband cooling by an order of magnitude. Cooling is quantified by means of the mean number of phonons of the mechanical modes as well as by the von Neumann entropy. Potencial extension to non-linear systems, by means of semiclassical methods, is briefly discussed.

Landau-Zener extension of the Tavis-Cummings model: Structure of the solution

DOE PAGES

Sun, Chen; Sinitsyn, Nikolai A.

2016-09-07

We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of an arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and tractable expressions for transition probabilities in terms of the well-known special functions. In this form, our formulas are suitable for fast numerical calculations and analytical approximations. As an application, we obtain the semiclassical limit of the exact solution and compare it to prior approximations. Furthermore, we also reveal connection between DTCM and q-deformed binomial statistics.

Vortex breakdown simulation - A circumspect study of the steady, laminar, axisymmetric model

NASA Technical Reports Server (NTRS)

Salas, M. D.; Kuruvila, G.

1989-01-01

The incompressible axisymmetric steady Navier-Stokes equations are written using the streamfunction-vorticity formulation. The resulting equations are discretized using a second-order central-difference scheme. The discretized equations are linearized and then solved using an exact LU decomposition, Gaussian elimination, and Newton iteration. Solutions are presented for Reynolds numbers (based on vortex core radius) 100-1800 and swirl parameter 0.9-1.1. The effects of inflow boundary conditions, the location of farfield and outflow boundaries, and mesh refinement are examined. Finally, the stability of the steady solutions is investigated by solving the time-dependent equations.

Sample and population exponents of generalized Taylor's law.

PubMed

Giometto, Andrea; Formentin, Marco; Rinaldo, Andrea; Cohen, Joel E; Maritan, Amos

2015-06-23

Taylor's law (TL) states that the variance V of a nonnegative random variable is a power function of its mean M; i.e., V = aM(b). TL has been verified extensively in ecology, where it applies to population abundance, physics, and other natural sciences. Its ubiquitous empirical verification suggests a context-independent mechanism. Sample exponents b measured empirically via the scaling of sample mean and variance typically cluster around the value b = 2. Some theoretical models of population growth, however, predict a broad range of values for the population exponent b pertaining to the mean and variance of population density, depending on details of the growth process. Is the widely reported sample exponent b ≃ 2 the result of ecological processes or could it be a statistical artifact? Here, we apply large deviations theory and finite-sample arguments to show exactly that in a broad class of growth models the sample exponent is b ≃ 2 regardless of the underlying population exponent. We derive a generalized TL in terms of sample and population exponents b(jk) for the scaling of the kth vs. the jth cumulants. The sample exponent b(jk) depends predictably on the number of samples and for finite samples we obtain b(jk) ≃ k = j asymptotically in time, a prediction that we verify in two empirical examples. Thus, the sample exponent b ≃ 2 may indeed be a statistical artifact and not dependent on population dynamics under conditions that we specify exactly. Given the broad class of models investigated, our results apply to many fields where TL is used although inadequately understood.

MODELING TIME DISPERSION DUE TO OPTICAL PATH LENGTH DIFFERENCES IN SCINTILLATION DETECTORS*

PubMed Central

Moses, W.W.; Choong, W.-S.; Derenzo, S.E.

2015-01-01

We characterize the nature of the time dispersion in scintillation detectors caused by path length differences of the scintillation photons as they travel from their generation point to the photodetector. Using Monte Carlo simulation, we find that the initial portion of the distribution (which is the only portion that affects the timing resolution) can usually be modeled by an exponential decay. The peak amplitude and decay time depend both on the geometry of the crystal, the position within the crystal that the scintillation light originates from, and the surface finish. In a rectangular parallelpiped LSO crystal with 3 mm × 3 mm cross section and polished surfaces, the decay time ranges from 10 ps (for interactions 1 mm from the photodetector) up to 80 ps (for interactions 50 mm from the photodetector). Over that same range of distances, the peak amplitude ranges from 100% (defined as the peak amplitude for interactions 1 mm from the photodetector) down to 4% for interactions 50 mm from the photodetector. Higher values for the decay time are obtained for rough surfaces, but the exact value depends on the simulation details. Estimates for the decay time and peak amplitude can be made for different cross section sizes via simple scaling arguments. PMID:25729464

Modeling Time Dispersion Due to Optical Path Length Differences in Scintillation Detectors

DOE PAGES

Moses, W. W.; Choong, W. -S.; Derenzo, S. E.

2014-08-20

In this paper, we characterize the nature of the time dispersion in scintillation detectors caused by path length differences of the scintillation photons as they travel from their generation point to the photodetector. Using Monte Carlo simulation, we find that the initial portion of the distribution (which is the only portion that affects the timing resolution) can usually be modeled by an exponential decay. The peak amplitude and decay time depend both on the geometry of the crystal, the position within the crystal that the scintillation light originates from, and the surface finish. In a rectangular parallelpiped LSO crystal withmore » 3 mm × 3 mm cross section and polished surfaces, the decay time ranges from 10 ps (for interactions 1 mm from the photodetector) up to 80 ps (for interactions 50 mm from the photodetector). Over that same range of distances, the peak amplitude ranges from 100% (defined as the peak amplitude for interactions 1 mm from the photodetector) down to 4% for interactions 50 mm from the photodetector. Higher values for the decay time are obtained for rough surfaces, but the exact value depends on the simulation details. Finally, estimates for the decay time and peak amplitude can be made for different cross section sizes via simple scaling arguments.« less

Two-time correlation function of an open quantum system in contact with a Gaussian reservoir

NASA Astrophysics Data System (ADS)

Ban, Masashi; Kitajima, Sachiko; Shibata, Fumiaki

2018-05-01

An exact formula of a two-time correlation function is derived for an open quantum system which interacts with a Gaussian thermal reservoir. It is provided in terms of functional derivative with respect to fictitious fields. A perturbative expansion and its diagrammatic representation are developed, where the small expansion parameter is related to a correlation time of the Gaussian thermal reservoir. The two-time correlation function of the lowest order is equivalent to that calculated by means of the quantum regression theorem. The result clearly shows that the violation of the quantum regression theorem is caused by a finiteness of the reservoir correlation time. By making use of an exactly solvable model consisting of a two-level system and a set of harmonic oscillators, it is shown that the two-time correlation function up to the first order is a good approximation to the exact one.

Test of Relativistic Gravity for Propulsion at the Large Hadron Collider

NASA Astrophysics Data System (ADS)

Felber, Franklin

2010-01-01

A design is presented of a laboratory experiment that could test the suitability of relativistic gravity for propulsion of spacecraft to relativistic speeds. An exact time-dependent solution of Einstein's gravitational field equation confirms that even the weak field of a mass moving at relativistic speeds could serve as a driver to accelerate a much lighter payload from rest to a good fraction of the speed of light. The time-dependent field of ultrarelativistic particles in a collider ring is calculated. An experiment is proposed as the first test of the predictions of general relativity in the ultrarelativistic limit by measuring the repulsive gravitational field of bunches of protons in the Large Hadron Collider (LHC). The estimated `antigravity beam' signal strength at a resonant detector of each proton bunch is 3 nm/s2 for 2 ns during each revolution of the LHC. This experiment can be performed off-line, without interfering with the normal operations of the LHC.

Breathing is different in the quantum world

NASA Astrophysics Data System (ADS)

Bonitz, Michael; Bauch, Sebastian; Balzer, Karsten; Henning, Christian; Hochstuhl, David

2009-11-01

Interacting classicle particles in a harmonic trap are known to possess a radial collective oscillation -- the breathing mode (BM). In case of Coulomb interaction its frequency is universal -- it is independent of the particle number and system dimensionality [1]. Here we study strongly correlated quantum systems. We report a qualitatively different breathing behavior: a quantum system has two BMs one of which is universal whereas the frequency of the other varies with system dimensionality, the particle spin and the strength of the pair interaction. The results are based on exact solutions of the time-dependent Schr"odinger equation for two particles and on time-dependent many-body results for larger particle numbers. Finally, we discuss experimental ways to excite and measure the breathing frequencies which should give direct access to key properties of trapped particles, including their many-body effects [2]. [4pt] [1] C. Henning et al., Phys. Rev. Lett. 101, 045002 (2008) [0pt] [2] S. Bauch, K. Balzer, C. Henning, and M. Bonitz, submitted to Phys. Rev. Lett., arXiv:0903.1993

The multi-layer multi-configuration time-dependent Hartree method for bosons: theory, implementation, and applications.

PubMed

Cao, Lushuai; Krönke, Sven; Vendrell, Oriol; Schmelcher, Peter

2013-10-07

We develop the multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB), a variational numerically exact ab initio method for studying the quantum dynamics and stationary properties of general bosonic systems. ML-MCTDHB takes advantage of the permutation symmetry of identical bosons, which allows for investigations of the quantum dynamics from few to many-body systems. Moreover, the multi-layer feature enables ML-MCTDHB to describe mixed bosonic systems consisting of arbitrary many species. Multi-dimensional as well as mixed-dimensional systems can be accurately and efficiently simulated via the multi-layer expansion scheme. We provide a detailed account of the underlying theory and the corresponding implementation. We also demonstrate the superior performance by applying the method to the tunneling dynamics of bosonic ensembles in a one-dimensional double well potential, where a single-species bosonic ensemble of various correlation strengths and a weakly interacting two-species bosonic ensemble are considered.

Extended slow dynamical regime close to the many-body localization transition

NASA Astrophysics Data System (ADS)

Luitz, David J.; Laflorencie, Nicolas; Alet, Fabien

2016-02-01

Many-body localization is characterized by a slow logarithmic growth of the entanglement entropy after a global quantum quench while the local memory of an initial density imbalance remains at infinite time. We investigate how much the proximity of a many-body localized phase can influence the dynamics in the delocalized ergodic regime where thermalization is expected. Using an exact Krylov space technique, the out-of-equilibrium dynamics of the random-field Heisenberg chain is studied up to L =28 sites, starting from an initially unentangled high-energy product state. Within most of the delocalized phase, we find a sub-ballistic entanglement growth S (t ) ∝t1 /z with a disorder-dependent exponent z ≥1 , in contrast with the pure ballistic growth z =1 of clean systems. At the same time, anomalous relaxation is also observed for the spin imbalance I (t ) ∝t-ζ with a continuously varying disorder-dependent exponent ζ , vanishing at the transition. This provides a clear experimental signature for detecting this nonconventional regime.

Laser phase control of high-order harmonic generation at large internuclear distance: the H+ -H2+ system.

PubMed

Bandrauk, André D; Barmaki, Samira; Kamta, Gerard Lagmago

2007-01-05

Exact (Born-Oppenheimer) 3-D numerical solutions of the time-dependent Schrödinger equation are obtained for the one electron linear H+-H2+ atom-molecule system at large internuclear distance R in interaction with two-cycles intense (I>10(14) W cm(-2)) 800 nm laser pulses. High-order harmonic generation (HHG) spectra are obtained with an energy cutoff larger than the atomic maximum of I(p)+3U(p), where I(p) is the ionization potential and U(p) is the ponderomotive energy. At large R, this extended cutoff is shown to be related to the nature of electron transfer, whose direction is shown to depend critically on the carrier-envelope phase (CEP) of the ultrashort pulse. Constructive and destructive interferences in the HHG spectrum resulting from coherent superpositions of electronic states in the H+-H2+ system are interpreted in terms of multiple electron trajectories extracted from a time profile analysis.

The impact of reward and punishment on skill learning depends on task demands

PubMed Central

Steel, Adam; Silson, Edward H.; Stagg, Charlotte J.; Baker, Chris I.

2016-01-01

Reward and punishment motivate behavior, but it is unclear exactly how they impact skill performance and whether the effect varies across skills. The present study investigated the effect of reward and punishment in both a sequencing skill and a motor skill context. Participants trained on either a sequencing skill (serial reaction time task) or a motor skill (force-tracking task). Skill knowledge was tested immediately after training, and again 1 hour, 24–48 hours, and 30 days after training. We found a dissociation of the effects of reward and punishment on the tasks, primarily reflecting the impact of punishment. While punishment improved serial reaction time task performance, it impaired force-tracking task performance. In contrast to prior literature, neither reward nor punishment benefitted memory retention, arguing against the common assumption that reward ubiquitously benefits skill retention. Collectively, these results suggest that punishment impacts skilled behavior more than reward in a complex, task dependent fashion. PMID:27786302

The impact of reward and punishment on skill learning depends on task demands.

PubMed

Steel, Adam; Silson, Edward H; Stagg, Charlotte J; Baker, Chris I

2016-10-27

Reward and punishment motivate behavior, but it is unclear exactly how they impact skill performance and whether the effect varies across skills. The present study investigated the effect of reward and punishment in both a sequencing skill and a motor skill context. Participants trained on either a sequencing skill (serial reaction time task) or a motor skill (force-tracking task). Skill knowledge was tested immediately after training, and again 1 hour, 24-48 hours, and 30 days after training. We found a dissociation of the effects of reward and punishment on the tasks, primarily reflecting the impact of punishment. While punishment improved serial reaction time task performance, it impaired force-tracking task performance. In contrast to prior literature, neither reward nor punishment benefitted memory retention, arguing against the common assumption that reward ubiquitously benefits skill retention. Collectively, these results suggest that punishment impacts skilled behavior more than reward in a complex, task dependent fashion.

Benchmark Results Of Active Tracer Particles In The Open Souce Code ASPECT For Modelling Convection In The Earth's Mantle

NASA Astrophysics Data System (ADS)

Jiang, J.; Kaloti, A. P.; Levinson, H. R.; Nguyen, N.; Puckett, E. G.; Lokavarapu, H. V.

2016-12-01

We present the results of three standard benchmarks for the new active tracer particle algorithm in ASPECT. The three benchmarks are SolKz, SolCx, and SolVI (also known as the 'inclusion benchmark') first proposed by Duretz, May, Gerya, and Tackley (G Cubed, 2011) and in subsequent work by Theilman, May, and Kaus (Pure and Applied Geophysics, 2014). Each of the three benchmarks compares the accuracy of the numerical solution to a steady (time-independent) solution of the incompressible Stokes equations with a known exact solution. These benchmarks are specifically designed to test the accuracy and effectiveness of the numerical method when the viscosity varies up to six orders of magnitude. ASPECT has been shown to converge to the exact solution of each of these benchmarks at the correct design rate when all of the flow variables, including the density and viscosity, are discretized on the underlying finite element grid (Krobichler, Heister, and Bangerth, GJI, 2012). In our work we discretize the density and viscosity by initially placing the true values of the density and viscosity at the intial particle positions. At each time step, including the initialization step, the density and viscosity are interpolated from the particles onto the finite element grid. The resulting Stokes system is solved for the velocity and pressure, and the particle positions are advanced in time according to this new, numerical, velocity field. Note that this procedure effectively changes a steady solution of the Stokes equaton (i.e., one that is independent of time) to a solution of the Stokes equations that is time dependent. Furthermore, the accuracy of the active tracer particle algorithm now also depends on the accuracy of the interpolation algorithm and of the numerical method one uses to advance the particle positions in time. Finally, we will present new interpolation algorithms designed to increase the overall accuracy of the active tracer algorithms in ASPECT and interpolation algotithms designed to conserve properties, such as mass density, that are being carried by the particles.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Critical quench dynamics in confined systems.

PubMed

Collura, Mario; Karevski, Dragi

2010-05-21

We analyze the coherent quantum evolution of a many-particle system after slowly sweeping a power-law confining potential. The amplitude of the confining potential is varied in time along a power-law ramp such that the many-particle system finally reaches or crosses a critical point. Under this protocol we derive general scaling laws for the density of excitations created during the nonadiabatic sweep of the confining potential. It is found that the mean excitation density follows an algebraic law as a function of the sweeping rate with an exponent that depends on the space-time properties of the potential. We confirm our scaling laws by first order adiabatic calculation and exact results on the Ising quantum chain with a varying transverse field.

Estimate of blow-up and relaxation time for self-gravitating Brownian particles and bacterial populations.

PubMed

Chavanis, P-H; Sire, C

2004-08-01

We determine an exact asymptotic expression of the blow-up time t(coll) for self-gravitating Brownian particles or bacterial populations (chemotaxis) close to the critical point in d=3. We show that t(coll) = t(*) (eta- eta(c) )(-1/2) with t(*) =0.917 677 02..., where eta represents the inverse temperature (for Brownian particles) or the mass (for bacterial colonies), and eta(c) is the critical value of eta above which the system blows up. This result is in perfect agreement with the numerical solution of the Smoluchowski-Poisson system. We also determine the exact asymptotic expression of the relaxation time close to but above the critical temperature and derive a large time asymptotic expansion for the density profile exactly at the critical point.

Shape Universality Classes in the Random Sequential Adsorption of Nonspherical Particles

NASA Astrophysics Data System (ADS)

Baule, Adrian

2017-07-01

Random sequential adsorption (RSA) of particles of a particular shape is used in a large variety of contexts to model particle aggregation and jamming. A key feature of these models is the observed algebraic time dependence of the asymptotic jamming coverage ˜t-ν as t →∞ . However, the exact value of the exponent ν is not known apart from the simplest case of the RSA of monodisperse spheres adsorbed on a line (Renyi's seminal "car parking problem"), where ν =1 can be derived analytically. Empirical simulation studies have conjectured on a case-by-case basis that for general nonspherical particles, ν =1 /(d +d ˜ ), where d denotes the dimension of the domain, and d ˜ the number of orientational degrees of freedom of a particle. Here, we solve this long-standing problem analytically for the d =1 case—the "Paris car parking problem." We prove, in particular, that the scaling exponent depends on the particle shape, contrary to the original conjecture and, remarkably, falls into two universality classes: (i) ν =1 /(1 +d ˜ /2 ) for shapes with a smooth contact distance, e.g., ellipsoids, and (ii) ν =1 /(1 +d ˜ ) for shapes with a singular contact distance, e.g., spherocylinders and polyhedra. The exact solution explains, in particular, why many empirically observed scalings fall in between these two limits.

Electromagnetic fields and potentials generated by massless charged particles

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

Azzurli, Francesco, E-mail: francesco.azzurli@gmail.com; Lechner, Kurt, E-mail: lechner@pd.infn.it; INFN, Sezione di Padova, Via F. Marzolo, 8, 35131 Padova

2014-10-15

We provide for the first time the exact solution of Maxwell’s equations for a massless charged particle moving on a generic trajectory at the speed of light. In particular we furnish explicit expressions for the vector potential and the electromagnetic field, which were both previously unknown, finding that they entail different physical features for bounded and unbounded trajectories. With respect to the standard Liénard–Wiechert field the electromagnetic field acquires singular δ-like contributions whose support and dimensionality depend crucially on whether the motion is (a) linear, (b) accelerated unbounded, (c) accelerated bounded. In the first two cases the particle generates amore » planar shock-wave-like electromagnetic field traveling along a straight line. In the second and third cases the field acquires, in addition, a δ-like contribution supported on a physical singularity-string attached to the particle. For generic accelerated motions a genuine radiation field is also present, represented by a regular principal-part type distribution diverging on the same singularity-string. - Highlights: • First exact solution of Maxwell’s equations for massless charges in arbitrary motion. • Explicit expressions of electromagnetic fields and potentials. • Derivations are rigorous and based on distribution theory. • The form of the field depends heavily on whether the motion is bounded or unbounded. • The electromagnetic field contains unexpected Dirac-delta-function contributions.« less

Hierarchic models for laminated plates. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Actis, Ricardo Luis

1991-01-01

Structural plates and shells are three-dimensional bodies, one dimension of which happens to be much smaller than the other two. Thus, the quality of a plate or shell model must be judged on the basis of how well its exact solution approximates the corresponding three-dimensional problem. Of course, the exact solution depends not only on the choice of the model but also on the topology, material properties, loading and constraints. The desired degree of approximation depends on the analyst's goals in performing the analysis. For these reasons models have to be chosen adaptively. Hierarchic sequences of models make adaptive selection of the model which is best suited for the purposes of a particular analysis possible. The principles governing the formulation of hierarchic models for laminated plates are presented. The essential features of the hierarchic models described models are: (1) the exact solutions corresponding to the hierarchic sequence of models converge to the exact solution of the corresponding problem of elasticity for a fixed laminate thickness; and (2) the exact solution of each model converges to the same limit as the exact solution of the corresponding problem of elasticity with respect to the laminate thickness approaching zero. The formulation is based on one parameter (beta) which characterizes the hierarchic sequence of models, and a set of constants whose influence was assessed by a numerical sensitivity study. The recommended selection of these constants results in the number of fields increasing by three for each increment in the power of beta. Numerical examples analyzed with the proposed sequence of models are included and good correlation with the reference solutions was found. Results were obtained for laminated strips (plates in cylindrical bending) and for square and rectangular plates with uniform loading and with homogeneous boundary conditions. Cross-ply and angle-ply laminates were evaluated and the results compared with those of MSC/PROBE. Hierarchic models make the computation of any engineering data possible to an arbitrary level of precision within the framework of the theory of elasticity.

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

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

Faster and exact implementation of the continuous cellular automaton for anisotropic etching simulations

NASA Astrophysics Data System (ADS)

Ferrando, N.; Gosálvez, M. A.; Cerdá, J.; Gadea, R.; Sato, K.

2011-02-01

The current success of the continuous cellular automata for the simulation of anisotropic wet chemical etching of silicon in microengineering applications is based on a relatively fast, approximate, constant time stepping implementation (CTS), whose accuracy against the exact algorithm—a computationally slow, variable time stepping implementation (VTS)—has not been previously analyzed in detail. In this study we show that the CTS implementation can generate moderately wrong etch rates and overall etching fronts, thus justifying the presentation of a novel, exact reformulation of the VTS implementation based on a new state variable, referred to as the predicted removal time (PRT), and the use of a self-balanced binary search tree that enables storage and efficient access to the PRT values in each time step in order to quickly remove the corresponding surface atom/s. The proposed PRT method reduces the simulation cost of the exact implementation from {O}(N^{5/3}) to {O}(N^{3/2} log N) without introducing any model simplifications. This enables more precise simulations (only limited by numerical precision errors) with affordable computational times that are similar to the less precise CTS implementation and even faster for low reactivity systems.

Exact solutions of fractional mBBM equation and coupled system of fractional Boussinesq-Burgers

NASA Astrophysics Data System (ADS)

Javeed, Shumaila; Saif, Summaya; Waheed, Asif; Baleanu, Dumitru

2018-06-01

The new exact solutions of nonlinear fractional partial differential equations (FPDEs) are established by adopting first integral method (FIM). The Riemann-Liouville (R-L) derivative and the local conformable derivative definitions are used to deal with the fractional order derivatives. The proposed method is applied to get exact solutions for space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation and coupled time-fractional Boussinesq-Burgers equation. The suggested technique is easily applicable and effectual which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs.

The origin of the criticality in meme popularity distribution on complex networks.

PubMed

Kim, Yup; Park, Seokjong; Yook, Soon-Hyung

2016-03-24

Previous studies showed that the meme popularity distribution is described by a heavy-tailed distribution or a power-law, which is a characteristic feature of the criticality. Here, we study the origin of the criticality on non-growing and growing networks based on the competition induced criticality model. From the direct Mote Carlo simulations and the exact mapping into the position dependent biased random walk (PDBRW), we find that the meme popularity distribution satisfies a very robust power- law with exponent α = 3/2 if there is an innovation process. On the other hand, if there is no innovation, then we find that the meme popularity distribution is bounded and highly skewed for early transient time periods, while it satisfies a power-law with exponent α ≠ 3/2 for intermediate time periods. The exact mapping into PDBRW clearly shows that the balance between the creation of new memes by the innovation process and the extinction of old memes is the key factor for the criticality. We confirm that the balance for the criticality sustains for relatively small innovation rate. Therefore, the innovation processes with significantly influential memes should be the simple and fundamental processes which cause the critical distribution of the meme popularity in real social networks.

The origin of the criticality in meme popularity distribution on complex networks

PubMed Central

Kim, Yup; Park, Seokjong; Yook, Soon-Hyung

2016-01-01

Previous studies showed that the meme popularity distribution is described by a heavy-tailed distribution or a power-law, which is a characteristic feature of the criticality. Here, we study the origin of the criticality on non-growing and growing networks based on the competition induced criticality model. From the direct Mote Carlo simulations and the exact mapping into the position dependent biased random walk (PDBRW), we find that the meme popularity distribution satisfies a very robust power- law with exponent α = 3/2 if there is an innovation process. On the other hand, if there is no innovation, then we find that the meme popularity distribution is bounded and highly skewed for early transient time periods, while it satisfies a power-law with exponent α ≠ 3/2 for intermediate time periods. The exact mapping into PDBRW clearly shows that the balance between the creation of new memes by the innovation process and the extinction of old memes is the key factor for the criticality. We confirm that the balance for the criticality sustains for relatively small innovation rate. Therefore, the innovation processes with significantly influential memes should be the simple and fundamental processes which cause the critical distribution of the meme popularity in real social networks. PMID:27009399

The origin of the criticality in meme popularity distribution on complex networks

NASA Astrophysics Data System (ADS)

Kim, Yup; Park, Seokjong; Yook, Soon-Hyung

2016-03-01

Previous studies showed that the meme popularity distribution is described by a heavy-tailed distribution or a power-law, which is a characteristic feature of the criticality. Here, we study the origin of the criticality on non-growing and growing networks based on the competition induced criticality model. From the direct Mote Carlo simulations and the exact mapping into the position dependent biased random walk (PDBRW), we find that the meme popularity distribution satisfies a very robust power- law with exponent α = 3/2 if there is an innovation process. On the other hand, if there is no innovation, then we find that the meme popularity distribution is bounded and highly skewed for early transient time periods, while it satisfies a power-law with exponent α ≠ 3/2 for intermediate time periods. The exact mapping into PDBRW clearly shows that the balance between the creation of new memes by the innovation process and the extinction of old memes is the key factor for the criticality. We confirm that the balance for the criticality sustains for relatively small innovation rate. Therefore, the innovation processes with significantly influential memes should be the simple and fundamental processes which cause the critical distribution of the meme popularity in real social networks.

Vortex reconnection rate, and loop birth rate, for a random wavefield

NASA Astrophysics Data System (ADS)

Hannay, J. H.

2017-04-01

A time dependent, complex scalar wavefield in three dimensions contains curved zero lines, wave ‘vortices’, that move around. From time to time pairs of these lines contact each other and ‘reconnect’ in a well studied manner, and at other times tiny loops of new line appear from nowhere (births) and grow, or the reverse, existing loops shrink and disappear (deaths). These three types are known to be the only generic events. Here the average rate of their occurrences per unit volume is calculated exactly for a Gaussian random wavefield that has isotropic, stationary statistics, arising from a superposition of an infinity of plane waves in different directions. A simplifying ‘axis fixing’ technique is introduced to achieve this. The resulting formulas are proportional to the standard deviation of angular frequencies, and depend in a simple way on the second and fourth moments of the power spectrum of the plane waves. Reconnections turn out to be more common than births and deaths combined. As an expository preliminary, the case of two dimensions, where the vortices are points, is studied and the average rate of pair creation (and likewise destruction) per unit area is calculated.

Heterogeneous network epidemics: real-time growth, variance and extinction of infection.

PubMed

Ball, Frank; House, Thomas

2017-09-01

Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular choice in theoretical studies since it combines the ability to specify the distribution of the number of contacts (degree) with analytical tractability. Here we consider the early real-time behaviour of the Markovian SIR epidemic model on a configuration model network using a multitype branching process. We find closed-form analytic expressions for the mean and variance of the number of infectious individuals as a function of time and the degree of the initially infected individual(s), and write down a system of differential equations for the probability of extinction by time t that are numerically fast compared to Monte Carlo simulation. We show that these quantities are all sensitive to the degree distribution-in particular we confirm that the mean prevalence of infection depends on the first two moments of the degree distribution and the variance in prevalence depends on the first three moments of the degree distribution. In contrast to most existing analytic approaches, the accuracy of these results does not depend on having a large number of infectious individuals, meaning that in the large population limit they would be asymptotically exact even for one initial infectious individual.

Semiparametric regression analysis of failure time data with dependent interval censoring.

PubMed

Chen, Chyong-Mei; Shen, Pao-Sheng

2017-09-20

Interval-censored failure-time data arise when subjects are examined or observed periodically such that the failure time of interest is not examined exactly but only known to be bracketed between two adjacent observation times. The commonly used approaches assume that the examination times and the failure time are independent or conditionally independent given covariates. In many practical applications, patients who are already in poor health or have a weak immune system before treatment usually tend to visit physicians more often after treatment than those with better health or immune system. In this situation, the visiting rate is positively correlated with the risk of failure due to the health status, which results in dependent interval-censored data. While some measurable factors affecting health status such as age, gender, and physical symptom can be included in the covariates, some health-related latent variables cannot be observed or measured. To deal with dependent interval censoring involving unobserved latent variable, we characterize the visiting/examination process as recurrent event process and propose a joint frailty model to account for the association of the failure time and visiting process. A shared gamma frailty is incorporated into the Cox model and proportional intensity model for the failure time and visiting process, respectively, in a multiplicative way. We propose a semiparametric maximum likelihood approach for estimating model parameters and show the asymptotic properties, including consistency and weak convergence. Extensive simulation studies are conducted and a data set of bladder cancer is analyzed for illustrative purposes. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Self-diffusion in periodic porous media: a comparison of numerical simulation and eigenvalue methods.

PubMed

Schwartz, L M; Bergman, D J; Dunn, K J; Mitra, P P

1996-01-01

Random walk computer simulations are an important tool in understanding magnetic resonance measurements in porous media. In this paper we focus on the description of pulsed field gradient spin echo (PGSE) experiments that measure the probability, P(R,t), that a diffusing water molecule will travel a distance R in a time t. Because PGSE simulations are often limited by statistical considerations, we will see that valuable insight can be gained by working with simple periodic geometries and comparing simulation data to the results of exact eigenvalue expansions. In this connection, our attention will be focused on (1) the wavevector, k, and time dependent magnetization, M(k, t); and (2) the normalized probability, Ps(delta R, t), that a diffusing particle will return to within delta R of the origin after time t.

Asymptotic neutron scattering laws for anomalously diffusing quantum particles

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

Kneller, Gerald R.; Université d’Orléans, Chateau de la Source-Ave. du Parc Floral, 45067 Orléans; Synchrotron-SOLEIL, L’Orme de Merisiers, 91192 Gif-sur-Yvette

2016-07-28

The paper deals with a model-free approach to the analysis of quasielastic neutron scattering intensities from anomalously diffusing quantum particles. All quantities are inferred from the asymptotic form of their time-dependent mean square displacements which grow ∝t{sup α}, with 0 ≤ α < 2. Confined diffusion (α = 0) is here explicitly included. We discuss in particular the intermediate scattering function for long times and the Fourier spectrum of the velocity autocorrelation function for small frequencies. Quantum effects enter in both cases through the general symmetry properties of quantum time correlation functions. It is shown that the fractional diffusion constantmore » can be expressed by a Green-Kubo type relation involving the real part of the velocity autocorrelation function. The theory is exact in the diffusive regime and at moderate momentum transfers.« less

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

PubMed Central

Aniulis, Povilas; Skaudickas, Darijus

2015-01-01

Objectives The aim of the study is to compare results, effectiveness and complications of TVT exact and midurethral sling (SLING-IUFT) operations in the treatment of female stress urinary incontinence (SUI). Methods A single center nonblind, randomized study of women with SUI who were randomized to TVT-Exact and SLING-IUFT was performed by one surgeon from April 2009 to April 2011. SUI was diagnosed on coughing and Valsalva test and urodynamics (cystometry and uroflowmetry) were assessed before operation and 1 year after surgery. This was a prospective randomized study. The follow up period was 12 months. 76 patients were operated using the TVT-Exact operation and 78 patients – using the SLING-IUFT operation. There was no statistically significant differences between groups for BMI, parity, menopausal status and prolapsed stage (no patients had cystocele greater than stage II). Results Mean operative time was significantly shorter in the SLING-IUFT group (19 ± 5.6 min.) compared with the TVT-Exact group (27 ± 7.1 min.). There were statistically significant differences in the effectiveness of both procedures: TVT-Exact – at 94.5% and SLING-IUFT – at 61.2% after one year. Hospital stay was statistically significantly shorter in the SLING-IUFT group (1. 2 ± 0.5 days) compared with the TVT-Exact group (3.5 ± 1.5 days). Statistically significantly fewer complications occurred in the SLING-IUFT group. Conclusion the TVT-Exact and SLING-IUFT operations are both effective for surgical treatment of female stress urinary incontinence. The SLING-IUFT involved a shorter operation time and lower complications rate., the TVT-Exact procedure had statistically significantly more complications than the SLING-IUFT operation, but a higher effectiveness. PMID:28352711

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

PubMed

Aniuliene, Rosita; Aniulis, Povilas; Skaudickas, Darijus

2015-01-01

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

78 FR 69706 - Notice of Public Meeting for the Southeast Oregon Resource Advisory Council

Federal Register 2010, 2011, 2012, 2013, 2014

2013-11-20

... and Tuesday, January 13 and 14, 2014. The exact meeting time, agenda, and location will be announced... accommodate necessary business and all who seek to be heard regarding matters before the Southeast Oregon RAC. ADDRESSES: The exact meeting time, agenda, and location will be announced online at www.blm.gov/or/rac...

On the motion of a quantum particle in the spinning cosmic string space–time

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

Hassanabadi, H., E-mail: h.hasanabadi@shahroodut.ac.ir; Afshardoost, A.; Zarrinkamar, S.

2015-05-15

We analyze the energy spectrum and the wave function of a particle subjected to magnetic field in the spinning cosmic string space–time and investigate the influence of the spinning reference frame and topological defect on the system. To do this we solve Schrödinger equation in the spinning cosmic string background. In our work, instead of using an approximation in the calculations, we use the quasi-exact ansatz approach which gives the exact solutions for some primary levels. - Highlights: • Solving the Schrödinger equation in the spinning cosmic string space time. • Proposing a quasi-exact analytical solution to the general formmore » of the corresponding equation. • Generalizing the previous works.« less

A Legendre–Fourier spectral method with exact conservation laws for the Vlasov–Poisson system

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

Manzini, Gianmarco; Delzanno, Gian Luca; Vencels, Juris

In this study, we present the design and implementation of an L 2-stable spectral method for the discretization of the Vlasov–Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov equation are resolved through a truncated spectral expansion based on Legendre and Fourier basis functions, respectively. The Poisson equation, which is coupled to the Vlasov equation, is also resolved through a Fourier expansion. The resulting system of ordinary differential equation is discretized by the implicit second-order accurate Crank–Nicolson time discretization. The non-linear dependence between the Vlasov and Poisson equations ismore » iteratively solved at any time cycle by a Jacobian-Free Newton–Krylov method. In this work we analyze the structure of the main conservation laws of the resulting Legendre–Fourier model, e.g., mass, momentum, and energy, and prove that they are exactly satisfied in the semi-discrete and discrete setting. The L 2-stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term. The impact of the penalty term on the conservation properties is investigated theoretically and numerically. An implementation of the penalty term that does not affect the conservation of mass, momentum and energy, is also proposed and studied. A collisional term is introduced in the discrete model to control the filamentation effect, but does not affect the conservation properties of the system. Numerical results on a set of standard test problems illustrate the performance of the method.« less

A Legendre–Fourier spectral method with exact conservation laws for the Vlasov–Poisson system

DOE PAGES

Manzini, Gianmarco; Delzanno, Gian Luca; Vencels, Juris; ...

2016-04-22

In this study, we present the design and implementation of an L 2-stable spectral method for the discretization of the Vlasov–Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov equation are resolved through a truncated spectral expansion based on Legendre and Fourier basis functions, respectively. The Poisson equation, which is coupled to the Vlasov equation, is also resolved through a Fourier expansion. The resulting system of ordinary differential equation is discretized by the implicit second-order accurate Crank–Nicolson time discretization. The non-linear dependence between the Vlasov and Poisson equations ismore » iteratively solved at any time cycle by a Jacobian-Free Newton–Krylov method. In this work we analyze the structure of the main conservation laws of the resulting Legendre–Fourier model, e.g., mass, momentum, and energy, and prove that they are exactly satisfied in the semi-discrete and discrete setting. The L 2-stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term. The impact of the penalty term on the conservation properties is investigated theoretically and numerically. An implementation of the penalty term that does not affect the conservation of mass, momentum and energy, is also proposed and studied. A collisional term is introduced in the discrete model to control the filamentation effect, but does not affect the conservation properties of the system. Numerical results on a set of standard test problems illustrate the performance of the method.« less

Monte Carlo study of exact {ital S}-matrix duality in nonsimply laced affine Toda theories

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

Beccaria, M.

The ({ital g}{sub 2}{sup (1)},{ital d}{sub 4}{sup (3)}) pair of nonsimply laced affine Toda theories is studied from the point of view of nonperturbative duality. The classical spectrum of each member is composed of two massive scalar particles. The exact {ital S}-matrix prediction for the dual behavior of the coupling-dependent mass ratio is found to be in strong agreement with Monte Carlo data. {copyright} {ital 1996 The American Physical Society.}

An exact solution of the Currie-Hill equations in 1 + 1 dimensional Minkowski space

NASA Astrophysics Data System (ADS)

Balog, János

2014-11-01

We present an exact two-particle solution of the Currie-Hill equations of Predictive Relativistic Mechanics in 1 + 1 dimensional Minkowski space. The instantaneous accelerations are given in terms of elementary functions depending on the relative particle position and velocities. The general solution of the equations of motion is given and by studying the global phase space of this system it is shown that this is a subspace of the full kinematic phase space.

Crossover between collective and independent-particle excitations in quasi-2D electron gas with one filled subband

NASA Astrophysics Data System (ADS)

Nazarov, Vladimir U.

2018-05-01

While it has been recently demonstrated that, for quasi-two-dimensional electron gas (Q2DEG) with one filled subband, the dynamic exchange f x and Hartree f H kernels cancel each other in the low-density regime r s → ∞ (by half and completely, for the spin-neutral and fully spin-polarized cases, respectively), here we analytically show that the same happens at arbitrary densities at short distances. This motivates us to study the confinement dependence of the excitations in Q2DEG. Our calculations unambiguously confirm that, at strong confinements, the time-dependent exact exchange excitation energies approach the single-particle Kohn-Sham ones for the spin-polarized case, while the same, but less pronounced, tendency is observed for spin-neutral Q2DEG.

Scaling of average weighted shortest path and average receiving time on weighted expanded Koch networks

NASA Astrophysics Data System (ADS)

Wu, Zikai; Hou, Baoyu; Zhang, Hongjuan; Jin, Feng

2014-04-01

Deterministic network models have been attractive media for discussing dynamical processes' dependence on network structural features. On the other hand, the heterogeneity of weights affect dynamical processes taking place on networks. In this paper, we present a family of weighted expanded Koch networks based on Koch networks. They originate from a r-polygon, and each node of current generation produces m r-polygons including the node and whose weighted edges are scaled by factor w in subsequent evolutionary step. We derive closed-form expressions for average weighted shortest path length (AWSP). In large network, AWSP stays bounded with network order growing (0 < w < 1). Then, we focus on a special random walks and trapping issue on the networks. In more detail, we calculate exactly the average receiving time (ART). ART exhibits a sub-linear dependence on network order (0 < w < 1), which implies that nontrivial weighted expanded Koch networks are more efficient than un-weighted expanded Koch networks in receiving information. Besides, efficiency of receiving information at hub nodes is also dependent on parameters m and r. These findings may pave the way for controlling information transportation on general weighted networks.

Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.

PubMed

Li, Haifeng; Shao, Jiushu; Wang, Shikuan

2011-11-01

A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.

Analysis of bovine milk caseins on organic monolithic columns: an integrated capillary liquid chromatography-high resolution mass spectrometry approach for the study of time-dependent casein degradation.

PubMed

Pierri, Giuseppe; Kotoni, Dorina; Simone, Patrizia; Villani, Claudio; Pepe, Giacomo; Campiglia, Pietro; Dugo, Paola; Gasparrini, Francesco

2013-10-25

Casein proteins constitute approximately 80% of the proteins present in bovine milk and account for many of its nutritional and technological properties. The analysis of the casein fraction in commercially available pasteurized milk and the study of its time-dependent degradation is of considerable interest in the agro-food industry. Here we present new analytical methods for the study of caseins in fresh and expired bovine milk, based on the use of lab-made capillary organic monolithic columns. An integrated capillary high performance liquid chromatography and high-resolution mass spectrometry (Cap-LC-HRMS) approach was developed, exploiting the excellent resolution, permeability and biocompatibility of organic monoliths, which is easily adaptable to the analysis of intact proteins. The resolution obtained on the lab-made Protein-Cap-RP-Lauryl-γ-Monolithic column (270 mm × 0.250 mm length × internal diameter, L × I.D.) in the analysis of commercial standard caseins (αS-CN, β-CN and κ-CN) through Cap-HPLC-UV was compared to the one observe using two packed capillary C4 columns, the ACE C4 (3 μm, 150 mm × 0.300 mm, L × I.D.) and the Jupiter C4 column (5 μm, 150 mm × 0.300 mm, L × I.D.). Thanks to the higher resolution observed, the monolithic capillary column was chosen for the successive degradation studies of casein fractions extracted from bovine milk 1-4 weeks after expiry date. The comparison of the UV chromatographic profiles of skim, semi-skim and whole milk showed a major stability of whole milk towards time-dependent degradation of caseins, which was further sustained by high-resolution analysis on a 50-cm long monolithic column using a 120-min time gradient. Contemporarily, the exact monoisotopic and average molecular masses of intact αS-CN and β-CN protein standards were obtained through high resolution mass spectrometry and used for casein identification in Cap-LC-HRMS analysis. Finally, the proteolytic degradation of β-CN in skim milk and the contemporary formation of low-molecular-weight proteose-peptones (PP) with exact monoisotopic Mr between 9444.0989 Da and 14098.9861 Da was confirmed through the deconvolution of high resolution mass spectra and literature data. Copyright © 2013 Elsevier B.V. All rights reserved.

Moduli vacuum misalignment and precise predictions in string inflation

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

Cicoli, Michele; INFN sezione di Bologna,viale Berti Pichat 6/2, 40127 Bologna; Abdus Salam ICTP,Strada Costiera 11, Trieste 34014

2016-08-03

The predictions for all the cosmological observables of any inflationary model depend on the number of e-foldings which is sensitive to the post-inflationary history of the universe. In string models the generic presence of light moduli leads to a late-time period of matter domination which lowers the required number of e-foldings and, in turn, modifies the exact predictions of any inflationary model. In this paper we compute exactly the shift of the number of e-foldings in Kähler moduli inflation which is determined by the magnitude of the moduli initial displacement caused by vacuum misalignment and the moduli decay rates. Wemore » find that the preferred number of e-foldings gets reduced from 50 to 45, causing a modification of the spectral index at the percent level. Our results illustrate the importance of understanding the full post-inflationary evolution of the universe in order to derive precise predictions in string inflation. To perform this task it is crucial to work in a setting where there is good control over moduli stabilisation.« less

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

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

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

2012-08-07

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

Lagrangian descriptors of driven chemical reaction manifolds.

PubMed

Craven, Galen T; Junginger, Andrej; Hernandez, Rigoberto

2017-08-01

The persistence of a transition state structure in systems driven by time-dependent environments allows the application of modern reaction rate theories to solution-phase and nonequilibrium chemical reactions. However, identifying this structure is problematic in driven systems and has been limited by theories built on series expansion about a saddle point. Recently, it has been shown that to obtain formally exact rates for reactions in thermal environments, a transition state trajectory must be constructed. Here, using optimized Lagrangian descriptors [G. T. Craven and R. Hernandez, Phys. Rev. Lett. 115, 148301 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.148301], we obtain this so-called distinguished trajectory and the associated moving reaction manifolds on model energy surfaces subject to various driving and dissipative conditions. In particular, we demonstrate that this is exact for harmonic barriers in one dimension and this verification gives impetus to the application of Lagrangian descriptor-based methods in diverse classes of chemical reactions. The development of these objects is paramount in the theory of reaction dynamics as the transition state structure and its underlying network of manifolds directly dictate reactivity and selectivity.

Heterogeneous delays making parents synchronized: A coupled maps on Cayley tree model

NASA Astrophysics Data System (ADS)

Singh, Aradhana; Jalan, Sarika

2014-06-01

We study the phase synchronized clusters in the diffusively coupled maps on the Cayley tree networks for heterogeneous delay values. Cayley tree networks comprise of two parts: the inner nodes and the boundary nodes. We find that heterogeneous delays lead to various cluster states, such as; (a) cluster state consisting of inner nodes and boundary nodes, and (b) cluster state consisting of only boundary nodes. The former state may comprise of nodes from all the generations forming self-organized cluster or nodes from few generations yielding driven clusters depending upon on the parity of heterogeneous delay values. Furthermore, heterogeneity in delays leads to the lag synchronization between the siblings lying on the boundary by destroying the exact synchronization among them. The time lag being equal to the difference in the delay values. The Lyapunov function analysis sheds light on the destruction of the exact synchrony among the last generation nodes. To the end we discuss the relevance of our results with respect to their applications in the family business as well as in understanding the occurrence of genetic diseases.

Adaptive control using neural networks and approximate models.

PubMed

Narendra, K S; Mukhopadhyay, S

1997-01-01

The NARMA model is an exact representation of the input-output behavior of finite-dimensional nonlinear discrete-time dynamical systems in a neighborhood of the equilibrium state. However, it is not convenient for purposes of adaptive control using neural networks due to its nonlinear dependence on the control input. Hence, quite often, approximate methods are used for realizing the neural controllers to overcome computational complexity. In this paper, we introduce two classes of models which are approximations to the NARMA model, and which are linear in the control input. The latter fact substantially simplifies both the theoretical analysis as well as the practical implementation of the controller. Extensive simulation studies have shown that the neural controllers designed using the proposed approximate models perform very well, and in many cases even better than an approximate controller designed using the exact NARMA model. In view of their mathematical tractability as well as their success in simulation studies, a case is made in this paper that such approximate input-output models warrant a detailed study in their own right.

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

NASA Astrophysics Data System (ADS)

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

2015-04-01

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

Spin-locking of half-integer quadrupolar nuclei in NMR of solids: The far off-resonance case.

PubMed

Odedra, Smita; Wimperis, Stephen

Spin-locking of spin I=3/2 and I=5/2 nuclei in the presence of large resonance offsets has been studied using both approximate and exact theoretical approaches and, in the case of I=3/2, experimentally. We show the variety of coherences and population states produced in a far off-resonance spin-locking NMR experiment (one consisting solely of a spin-locking pulse) and how these vary with the radiofrequency field strength and offset frequency. Under magic angle spinning (MAS) conditions and in the "adiabatic limit", these spin-locked states acquire a time dependence. We discuss the rotor-driven interconversion of the spin-locked states, using an exact density matrix approach to confirm the results of the approximate model. Using conventional and multiple-quantum filtered spin-locking 23 Na (I=3/2) NMR experiments under both static and MAS conditions, we confirm the results of the theoretical calculations, demonstrating the applicability of the approximate theoretical model to the far off-resonance case. This simplified model includes only the effects of the initial rapid dephasing of coherences that occurs at the start of the spin-locking period and its success in reproducing both experimental and exact simulation data indicates that it is this dephasing that is the dominant phenomenon in NMR spin-locking of quadrupolar nuclei, as we have previously found for the on-resonance and near-resonance cases. Potentially, far off-resonance spin-locking of quadrupolar nuclei could be of interest in experiments such as cross polarisation as a consequence of the spin-locking pulse being applied to a better defined initial state (the thermal equilibrium bulk magnetisation aligned along the z-axis) than can be created in a powdered solid with a selective radiofrequency pulse, where the effect of the pulse depends on the orientation of the individual crystallites. Copyright © 2016 Elsevier Inc. All rights reserved.

Is there scale-dependent bias in single-field inflation?

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

De Putter, Roland; Doré, Olivier; Green, Daniel, E-mail: rdputter@caltech.edu, E-mail: Olivier.P.Dore@jpl.nasa.gov, E-mail: drgreen@cita.utoronto.ca

2015-10-01

Scale-dependent halo bias due to local primordial non-Gaussianity provides a strong test of single-field inflation. While it is universally understood that single-field inflation predicts negligible scale-dependent bias compared to current observational uncertainties, there is still disagreement on the exact level of scale-dependent bias at a level that could strongly impact inferences made from future surveys. In this paper, we clarify this confusion and derive in various ways that there is exactly zero scale-dependent bias in single-field inflation. Much of the current confusion follows from the fact that single-field inflation does predict a mode coupling of matter perturbations at the levelmore » of f{sub NL}{sup local}; ≈ −5/3, which naively would lead to scale-dependent bias. However, we show explicitly that this mode coupling cancels out when perturbations are evaluated at a fixed physical scale rather than fixed coordinate scale. Furthermore, we show how the absence of scale-dependent bias can be derived easily in any gauge. This result can then be incorporated into a complete description of the observed galaxy clustering, including the previously studied general relativistic terms, which are important at the same level as scale-dependent bias of order f{sub NL}{sup local} ∼ 1. This description will allow us to draw unbiased conclusions about inflation from future galaxy clustering data.« less

Time reversal for photoacoustic tomography based on the wave equation of Nachman, Smith, and Waag

NASA Astrophysics Data System (ADS)

Kowar, Richard

2014-02-01

One goal of photoacoustic tomography (PAT) is to estimate an initial pressure function φ from pressure data measured at a boundary surrounding the object of interest. This paper is concerned with a time reversal method for PAT that is based on the dissipative wave equation of Nachman, Smith, and Waag [J. Acoust. Soc. Am. 88, 1584 (1990), 10.1121/1.400317]. This equation is a correction of the thermoviscous wave equation such that its solution has a finite wave front speed and, in contrast, it can model several relaxation processes. In this sense, it is more accurate than the thermoviscous wave equation. For simplicity, we focus on the case of one relaxation process. We derive an exact formula for the time reversal image I, which depends on the relaxation time τ1 and the compressibility κ1 of the dissipative medium, and show I (τ1,κ1)→φ for κ1→0. This implies that I =φ holds in the dissipation-free case and that I is similar to φ for sufficiently small compressibility κ1. Moreover, we show for tissue similar to water that the small wave number approximation I0 of the time reversal image satisfies I0=η0*xφ with accent="true">η̂0(|k|)≈const. for |k|≪1/c0τ1, where φ denotes the initial pressure function. For such tissue, our theoretical analysis and numerical simulations show that the time reversal image I is very similar to the initial pressure function φ and that a resolution of σ ≈0.036mm is feasible (for exact measurement data).

Analytical Description of the H/D Exchange Kinetic of Macromolecule.

PubMed

Kostyukevich, Yury; Kononikhin, Alexey; Popov, Igor; Nikolaev, Eugene

2018-04-17

We present the accurate analytical solution obtained for the system of rate equations describing the isotope exchange process for molecules containing an arbitrary number of equivalent labile atoms. The exact solution was obtained using Mathematica 7.0 software, and this solution has the form of the time-dependent Gaussian distribution. For the case when forward exchange considerably overlaps the back exchange, it is possible to estimate the activation energy of the reaction by obtaining a temperature dependence of the reaction degree. Using a previously developed approach for performing H/D exchange directly in the ESI source, we have estimated the activation energies for ions with different functional groups and they were found to be in a range 0.04-0.3 eV. Since the value of the activation energy depends on the type of functional group, the developed approach can have potential analytical applications for determining types of functional groups in complex mixtures, such as petroleum, humic substances, bio-oil, and so on.

Metadynamics convergence law in a multidimensional system

NASA Astrophysics Data System (ADS)

Crespo, Yanier; Marinelli, Fabrizio; Pietrucci, Fabio; Laio, Alessandro

2010-05-01

Metadynamics is a powerful sampling technique that uses a nonequilibrium history-dependent process to reconstruct the free-energy surface as a function of the relevant collective variables s . In Bussi [Phys. Rev. Lett. 96, 090601 (2006)] it is proved that, in a Langevin process, metadynamics provides an unbiased estimate of the free energy F(s) . We here study the convergence properties of this approach in a multidimensional system, with a Hamiltonian depending on several variables. Specifically, we show that in a Monte Carlo metadynamics simulation of an Ising model the time average of the history-dependent potential converge to F(s) with the same law of an umbrella sampling performed in optimal conditions (i.e., with a bias exactly equal to the negative of the free energy). Remarkably, after a short transient, the error becomes approximately independent on the filling speed, showing that even in out-of-equilibrium conditions metadynamics allows recovering an accurate estimate of F(s) . These results have been obtained introducing a functional form of the history-dependent potential that avoids the onset of systematic errors near the boundaries of the free-energy landscape.

Metadynamics convergence law in a multidimensional system.

PubMed

Crespo, Yanier; Marinelli, Fabrizio; Pietrucci, Fabio; Laio, Alessandro

2010-05-01

Metadynamics is a powerful sampling technique that uses a nonequilibrium history-dependent process to reconstruct the free-energy surface as a function of the relevant collective variables s . In Bussi [Phys. Rev. Lett. 96, 090601 (2006)] it is proved that, in a Langevin process, metadynamics provides an unbiased estimate of the free energy F(s) . We here study the convergence properties of this approach in a multidimensional system, with a Hamiltonian depending on several variables. Specifically, we show that in a Monte Carlo metadynamics simulation of an Ising model the time average of the history-dependent potential converge to F(s) with the same law of an umbrella sampling performed in optimal conditions (i.e., with a bias exactly equal to the negative of the free energy). Remarkably, after a short transient, the error becomes approximately independent on the filling speed, showing that even in out-of-equilibrium conditions metadynamics allows recovering an accurate estimate of F(s) . These results have been obtained introducing a functional form of the history-dependent potential that avoids the onset of systematic errors near the boundaries of the free-energy landscape.

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

Zhou, Quanlin; Oldenburg, Curtis M.; Spangler, Lee H.

Analytical solutions with infinite exponential series are available to calculate the rate of diffusive transfer between low-permeability blocks and high-permeability zones in the subsurface. Truncation of these series is often employed by neglecting the early-time regime. Here in this paper, we present unified-form approximate solutions in which the early-time and the late-time solutions are continuous at a switchover time. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the first coefficient dependent only on the dimensionless area-to-volume ratio. The last two coefficients are either determined analytically for isotropic blocks (e.g., spheresmore » and slabs) or obtained by fitting the exact solutions, and they solely depend on the aspect ratios for rectangular columns and parallelepipeds. For the late-time solutions, only the leading exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic rectangular blocks. The optimal switchover time is between 0.157 and 0.229, with highest relative approximation error less than 0.2%. The solutions are used to demonstrate the storage of dissolved CO 2 in fractured reservoirs with low-permeability matrix blocks of single and multiple shapes and sizes. These approximate solutions are building blocks for development of analytical and numerical tools for hydraulic, solute, and thermal diffusion processes in low-permeability matrix blocks.« less

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

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

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

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.

Denjoy minimal sets and Birkhoff periodic orbits for non-exact monotone twist maps

NASA Astrophysics Data System (ADS)

Qin, Wen-Xin; Wang, Ya-Nan

2018-06-01

A non-exact monotone twist map φbarF is a composition of an exact monotone twist map φ bar with a generating function H and a vertical translation VF with VF ((x , y)) = (x , y - F). We show in this paper that for each ω ∈ R, there exists a critical value Fd (ω) ≥ 0 depending on H and ω such that for 0 ≤ F ≤Fd (ω), the non-exact twist map φbarF has an invariant Denjoy minimal set with irrational rotation number ω lying on a Lipschitz graph, or Birkhoff (p , q)-periodic orbits for rational ω = p / q. Like the Aubry-Mather theory, we also construct heteroclinic orbits connecting Birkhoff periodic orbits, and show that quasi-periodic orbits in these Denjoy minimal sets can be approximated by periodic orbits. In particular, we demonstrate that at the critical value F =Fd (ω), the Denjoy minimal set is not uniformly hyperbolic and can be approximated by smooth curves.

Stochastic resetting in backtrack recovery by RNA polymerases

NASA Astrophysics Data System (ADS)

Roldán, Édgar; Lisica, Ana; Sánchez-Taltavull, Daniel; Grill, Stephan W.

2016-06-01

Transcription is a key process in gene expression, in which RNA polymerases produce a complementary RNA copy from a DNA template. RNA polymerization is frequently interrupted by backtracking, a process in which polymerases perform a random walk along the DNA template. Recovery of polymerases from the transcriptionally inactive backtracked state is determined by a kinetic competition between one-dimensional diffusion and RNA cleavage. Here we describe backtrack recovery as a continuous-time random walk, where the time for a polymerase to recover from a backtrack of a given depth is described as a first-passage time of a random walker to reach an absorbing state. We represent RNA cleavage as a stochastic resetting process and derive exact expressions for the recovery time distributions and mean recovery times from a given initial backtrack depth for both continuous and discrete-lattice descriptions of the random walk. We show that recovery time statistics do not depend on the discreteness of the DNA lattice when the rate of one-dimensional diffusion is large compared to the rate of cleavage.

Heuristic Green's function of the time dependent radiative transfer equation for a semi-infinite medium.

PubMed

Martelli, Fabrizio; Sassaroli, Angelo; Pifferi, Antonio; Torricelli, Alessandro; Spinelli, Lorenzo; Zaccanti, Giovanni

2007-12-24

The Green's function of the time dependent radiative transfer equation for the semi-infinite medium is derived for the first time by a heuristic approach based on the extrapolated boundary condition and on an almost exact solution for the infinite medium. Monte Carlo simulations performed both in the simple case of isotropic scattering and of an isotropic point-like source, and in the more realistic case of anisotropic scattering and pencil beam source, are used to validate the heuristic Green's function. Except for the very early times, the proposed solution has an excellent accuracy (> 98 % for the isotropic case, and > 97 % for the anisotropic case) significantly better than the diffusion equation. The use of this solution could be extremely useful in the biomedical optics field where it can be directly employed in conditions where the use of the diffusion equation is limited, e.g. small volume samples, high absorption and/or low scattering media, short source-receiver distances and early times. Also it represents a first step to derive tools for other geometries (e.g. slab and slab with inhomogeneities inside) of practical interest for noninvasive spectroscopy and diffuse optical imaging. Moreover the proposed solution can be useful to several research fields where the study of a transport process is fundamental.

Time-dependent evolution of the near nuclear coma of cometary nuclei during their rotational motion

NASA Astrophysics Data System (ADS)

Szego, K.; Crifo, J.-F.; Fulle, M.; Rodionov, A. V.

2003-04-01

The new physical model of Rodionov et al. (Planetary and Space Sci., 50, 983, 2002) that describes the cometary activity based on a 3-d collisional gas dynamical model has been successfully applied to account for the dust features observed by the cameras flying onboard of the VEGA and Giotto probes during the encounter with comet Halley. This indicates, in particular, that these structures are dominantly controlled by the nucleus topography. An upgraded version of this model has been recently developed and is being applied to the vast body of data gathered in 1986 on comet Halley. This new version is tridimensional as previously, and, in addition, time-dependent. This allows the exact, self-consistent computation of the whole coma structure (primary and daughter molecules, dust), allowing to study its dependence upon nucleus shape, composition, and rotation. The results presented here assume that the coma is formed by solar-driven sublimation of a homogeneous dusty-ice nucleus with shape and rotational state derived for P/Halley. The results are, however, of quite general significance -- in particular they remain valid for different shapes and for inhomogeneous nucleus. This presentation focuses on the time dependence of the dust and gas features obtained around the nucleus. Movies will summarize the results of the calculations exhibiting the time development of the dust and gas coma and its relation to the surface orography for a rotating nucleus. The effect of nucleus activity on its rotational motion, and possible constraints hampering the observation of the activity will be also analyzed.

The gravitational law of social interaction

NASA Astrophysics Data System (ADS)

Levy, Moshe; Goldenberg, Jacob

2014-01-01

While a great deal is known about the topology of social networks, there is much less agreement about the geographical structure of these networks. The fundamental question in this context is: how does the probability of a social link between two individuals depend on the physical distance between them? While it is clear that the probability decreases with the distance, various studies have found different functional forms for this dependence. The exact form of the distance dependence has crucial implications for network searchability and dynamics: Kleinberg (2000) [15] shows that the small-world property holds if the probability of a social link is a power-law function of the distance with power -2, but not with any other power. We investigate the distance dependence of link probability empirically by analyzing four very different sets of data: Facebook links, data from the electronic version of the Small-World experiment, email messages, and data from detailed personal interviews. All four datasets reveal the same empirical regularity: the probability of a social link is proportional to the inverse of the square of the distance between the two individuals, analogously to the distance dependence of the gravitational force. Thus, it seems that social networks spontaneously converge to the exact unique distance dependence that ensures the Small-World property.

UV-VIS depolarization from Arizona Test Dust particles at exact backscattering angle

NASA Astrophysics Data System (ADS)

Miffre, Alain; Mehri, Tahar; Francis, Mirvatte; Rairoux, Patrick

2016-01-01

In this paper, a controlled laboratory experiment is performed to accurately evaluate the depolarization from mineral dust particles in the exact backward scattering direction (ϴ=180.0±0.2°). The experiment is carried out at two wavelengths simultaneously (λ=355 nm, λ=532 nm), on a determined size and shape distribution of Arizona Test Dust (ATD) particles, used as a proxy for mineral dust particles. After validating the set-up on spherical water droplets, two determined ATD-particle size distributions, representative of mineral dust after long-range transport, are generated to accurately retrieve the UV-VIS depolarization from ATD-particles at exact backscattering angle, which is new. The measured depolarization reaches at most 37.5% at λ=355 nm (35.5% at λ=532 nm), and depends on the particle size distribution. Moreover, these laboratory findings agree with T-matrix numerical simulations, at least for a determined particle size distribution and at a determined wavelength, showing the ability of the spheroidal model to reproduce mineral dust particles in the exact backward scattering direction. However, the spectral dependence of the measured depolarization could not be reproduced with the spheroidal model, even for not evenly distributed aspect ratios. Hence, these laboratory findings can be used to evaluate the applicability of the spheroidal model in the backward scattering direction and moreover, to invert UV-VIS polarization lidar returns, which is useful for radiative transfer and climatology, in which mineral dust particles are strongly involved.

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

PubMed

Hele, Timothy J H; Ananth, Nandini

2016-12-22

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

Exact solutions for a type of electron pairing model with spin-orbit interactions and Zeeman coupling.

PubMed

Liu, Jia; Han, Qiang; Shao, L B; Wang, Z D

2011-07-08

A type of electron pairing model with spin-orbit interactions or Zeeman coupling is solved exactly in the framework of the Richardson ansatz. Based on the exact solutions for the case with spin-orbit interactions, it is shown rigorously that the pairing symmetry is of the p + ip wave and the ground state possesses time-reversal symmetry, regardless of the strength of the pairing interaction. Intriguingly, how Majorana fermions can emerge in the system is also elaborated. Exact results are illustrated for two systems, respectively, with spin-orbit interactions and Zeeman coupling.

NEMA count-rate evaluation of the first and second generation of the Ecat Exact and Ecat Exact HR family of scanners

NASA Astrophysics Data System (ADS)

Eriksson, L.; Wienhard, K.; Eriksson, M.; Casey, M. E.; Knoess, C.; Bruckbauer, T.; Hamill, J.; Mulnix, T.; Vollmar, S.; Bendriem, B.; Heiss, W. D.; Nutt, R.

2002-06-01

The first and second generation of the Exact and Exact HR family of scanners has been evaluated in terms of noise equivalent count rate (NEC) and count-rate capabilities. The new National Electrical Manufacturers Association standard was used for the evaluation. In spite of improved electronics and improved count-rate capabilities, the peak NEC was found to be fairly constant between the generations. The results are discussed in terms of the different electronic solutions for the two generations and its implications on system dead time and NEC count-rate capability.

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

Xu, Xin-Ping, E-mail: xuxp@mail.ihep.ac.cn; Ide, Yusuke

In the literature, there are numerous studies of one-dimensional discrete-time quantum walks (DTQWs) using a moving shift operator. However, there is no exact solution for the limiting probability distributions of DTQWs on cycles using a general coin or swapping shift operator. In this paper, we derive exact solutions for the limiting probability distribution of quantum walks using a general coin and swapping shift operator on cycles for the first time. Based on the exact solutions, we show how to generate symmetric quantum walks and determine the condition under which a symmetric quantum walk appears. Our results suggest that choosing various coinmore » and initial state parameters can achieve a symmetric quantum walk. By defining a quantity to measure the variation of symmetry, deviation and mixing time of symmetric quantum walks are also investigated.« less

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

NASA Astrophysics Data System (ADS)

Rein, Hanno; Tamayo, Daniel

2018-01-01

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

Critical Frequency in Nuclear Chiral Rotation

NASA Astrophysics Data System (ADS)

Olbratowski, P.; Dobaczewski, J.; Dudek, J.; Płóciennik, W.

2004-07-01

Self-consistent solutions for the so-called planar and chiral rotational bands in 132La are obtained for the first time within the Skyrme-Hartree-Fock cranking approach. It is suggested that the chiral rotation cannot exist below a certain critical frequency which under the approximations used is estimated as ℏωcrit≈0.5 0.6 MeV. However, the exact values of ℏωcrit may vary, to an extent, depending on the microscopic model used, in particular, through the pairing correlations and/or calculated equilibrium deformations. The existence of the critical frequency is explained in terms of a simple classical model of two gyroscopes coupled to a triaxial rigid body.

Granger Causality and Transfer Entropy Are Equivalent for Gaussian Variables

NASA Astrophysics Data System (ADS)

Barnett, Lionel; Barrett, Adam B.; Seth, Anil K.

2009-12-01

Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. Developed originally in the field of econometrics, it has since found application in a broader arena, particularly in neuroscience. More recently transfer entropy, an information-theoretic measure of time-directed information transfer between jointly dependent processes, has gained traction in a similarly wide field. While it has been recognized that the two concepts must be related, the exact relationship has until now not been formally described. Here we show that for Gaussian variables, Granger causality and transfer entropy are entirely equivalent, thus bridging autoregressive and information-theoretic approaches to data-driven causal inference.

Hawking radiation of charged Dirac particles from a Kerr-Newman black hole

NASA Astrophysics Data System (ADS)

Zhou, Shiwei; Liu, Wenbiao

2008-05-01

Charged Dirac particles’ Hawking radiation from a Kerr-Newman black hole is calculated using Damour-Ruffini’s method. When energy conservation and the backreaction of particles to the space-time are considered, the emission spectrum is not purely thermal anymore. The leading term is exactly the Boltzman factor, and the deviation from the purely thermal spectrum can bring some information out, which can be treated as an explanation to the information loss paradox. The result can also be treated as a quantum-corrected radiation temperature, which is dependent on the black hole background and the radiation particle’s energy, angular momentum, and charge.

Molecular analysis of the replication program in unicellular model organisms.

PubMed

Raghuraman, M K; Brewer, Bonita J

2010-01-01

Eukaryotes have long been reported to show temporal programs of replication, different portions of the genome being replicated at different times in S phase, with the added possibility of developmentally regulated changes in this pattern depending on species and cell type. Unicellular model organisms, primarily the budding yeast Saccharomyces cerevisiae, have been central to our current understanding of the mechanisms underlying the regulation of replication origins and the temporal program of replication in particular. But what exactly is a temporal program of replication, and how might it arise? In this article, we explore this question, drawing again on the wealth of experimental information in unicellular model organisms.

Ground-state and magnetocaloric properties of a coupled spin-electron double-tetrahedral chain (exact study at the half filling)

NASA Astrophysics Data System (ADS)

Gálisová, Lucia; Jakubczyk, Dorota

2017-01-01

Ground-state and magnetocaloric properties of a double-tetrahedral chain, in which nodal lattice sites occupied by the localized Ising spins regularly alternate with triangular clusters half filled with mobile electrons, are exactly investigated by using the transfer-matrix method in combination with the construction of the Nth tensor power of the discrete Fourier transformation. It is shown that the ground state of the model is formed by two non-chiral phases with the zero residual entropy and two chiral phases with the finite residual entropy S = NkB ln 2. Depending on the character of the exchange interaction between the localized Ising spins and mobile electrons, one or three magnetization plateaus can be observed in the magnetization process. Their heights basically depend on the values of Landé g-factors of the Ising spins and mobile electrons. It is also evidenced that the system exhibits both the conventional and inverse magnetocaloric effect depending on values of the applied magnetic field and temperature.

Analytical approach for the fractional differential equations by using the extended tanh method

NASA Astrophysics Data System (ADS)

Pandir, Yusuf; Yildirim, Ayse

2018-07-01

In this study, we consider analytical solutions of space-time fractional derivative foam drainage equation, the nonlinear Korteweg-de Vries equation with time and space-fractional derivatives and time-fractional reaction-diffusion equation by using the extended tanh method. The fractional derivatives are defined in the modified Riemann-Liouville context. As a result, various exact analytical solutions consisting of trigonometric function solutions, kink-shaped soliton solutions and new exact solitary wave solutions are obtained.

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

NASA Astrophysics Data System (ADS)

Smith, Naftali R.; Meerson, Baruch

2018-05-01

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

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