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At least 1,171 records · Page 65
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DOE OSTI2015

On Volterra quadratic stochastic operators with continual state space

Let (X,F) be a measurable space, and S(X,F) be the set of all probability measures on (X,F) where X is a state space and F is σ - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (Vλ)(A) = ∫{sub X}∫{sub X}P(x,y,A)dλ(x)dλ(y), where P(x, y, A) is regarded as a function of two variables x and y with fixed A ∈ F . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim{sub n→∞} V{sup n }(λ) is exists. In this paper, we construct a family of quadratic stochastic operators defined on the segment X = [0,1] with Borel σ - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Recurrent dynamics in an epidemic model due to stimulated bifurcation crossovers

Epidemics are known to persist in the form of recurrence cycles. Despite intervention efforts through vaccination and targeted social distancing, peaks of activity for infectious diseases like influenza reappear over time. Analysis of a stochastic model is here undertaken to explore a proposed cycle-generating mechanism – the bifurcation crossover. Time series from simulations of the model exhibit oscillations similar to the temporal signature of influenza activity. Power-spectral density indicates a resonant frequency, which corresponds to the annual seasonality of influenza in temperate zones. The study finds that intervention actions influence the extinguishability of epidemic activity. Asymptotic solution to a backward Kolmogorov equation corresponds to a mean extinction time that is a function of both intervention efficacy and population size. Intervention efficacy must be greater than a certain threshold to increase the chances of extinguishing the epidemic. Agreement of the model with several phenomenological features of epidemic cycles lends to it a tractability that may serve as early warning of imminent outbreaks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

On orthogonality preserving quadratic stochastic operators

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Tuning structure and mobility of solvation shells surrounding tracer additives

Molecular dynamics simulations and a stochastic Fokker-Planck equation based approach are used to illuminate how position-dependent solvent mobility near one or more tracer particle(s) is affected when tracer-solvent interactions are rationally modified to affect corresponding solvation structure. For tracers in a dense hard-sphere fluid, we compare two types of tracer-solvent interactions: (1) a hard-sphere-like interaction, and (2) a soft repulsion extending beyond the hard core designed via statistical mechanical theory to enhance tracer mobility at infinite dilution by suppressing coordination-shell structure [Carmer et al., Soft Matter 8, 4083–4089 (2012)]. For the latter case, we show that the mobility of surrounding solvent particles is also increased by addition of the soft repulsive interaction, which helps to rationalize the mechanism underlying the tracer’s enhanced diffusivity. However, if multiple tracer surfaces are in closer proximity (as at higher tracer concentrations), similar interactions that disrupt local solvation structure instead suppress the position-dependent solvent dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Problem-free time-dependent variational principle for open quantum systems

Methods of quantum nuclear wave-function dynamics have become very efficient in simulating large isolated systems using the time-dependent variational principle (TDVP). However, a straightforward extension of the TDVP to the density matrix framework gives rise to methods that do not conserve the energy in the isolated system limit and the total system population for open systems where only energy exchange with environment is allowed. These problems arise when the system density is in a mixed state and is simulated using an incomplete basis. Thus, the basis set incompleteness, which is inevitable in practical calculations, creates artificial channels for energy and population dissipation. To overcome this unphysical behavior, we have introduced a constrained Lagrangian formulation of TDVP applied to a non-stochastic open system Schrödinger equation [L. Joubert-Doriol, I. G. Ryabinkin, and A. F. Izmaylov, J. Chem. Phys. 141, 234112 (2014)]. While our formulation can be applied to any variational ansatz for the system density matrix, derivation of working equations and numerical assessment is done within the variational multiconfiguration Gaussian approach for a two-dimensional linear vibronic coupling model system interacting with a harmonic bath.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Damping constant estimation in magnetoresistive readers

The damping constant is a key design parameter in magnetic reader design. Its value can be derived from bulk or sheet film ferromagnetic resonance (FMR) line width. However, dynamics of nanodevices is usually defined by presence of non-uniform modes. It triggers new damping mechanisms and produces stronger damping than expected from traditional FMR. This work proposes a device-level technique for damping evaluation, based on time-domain analysis of thermally excited stochastic oscillations. The signal is collected using a high bandwidth oscilloscope, by direct probing of a biased reader. Recorded waveforms may contain different noise signals, but free layer FMR is usually a dominating one. The autocorrelation function is a reflection of the damped oscillation curve, averaging out stochastic contributions. The damped oscillator formula is fitted to autocorrelation data, producing resonance frequency and damping constant values. Restricting lag range allows for mitigation of the impact of other phenomena (e.g., reader instability) on the damping constant. For a micromagnetically modeled reader, the technique proves to be much more accurate than the stochastic FMR line width approach. Application to actual reader waveforms yields a damping constant of ∼0.03.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Recovering network topologies via Taylor expansion and compressive sensing

Gaining knowledge of the intrinsic topology of a complex dynamical network is the precondition to understand its evolutionary mechanisms and to control its dynamical and functional behaviors. In this article, a general framework is developed to recover topologies of complex networks with completely unknown node dynamics based on Taylor expansion and compressive sensing. Numerical simulations illustrate the feasibility and effectiveness of the proposed method. Moreover, this method is found to have good robustness to weak stochastic perturbations. Finally, the impact of two major factors on the topology identification performance is evaluated. This method provides a natural and direct point to reconstruct network topologies from measurable data, which is likely to have potential applicability in a wide range of fields.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Reliability of unstable periodic orbit based control strategies in biological systems

Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems is now routinely used as evidence for low dimensional chaos. Extracting accurate dynamical information from the detected UPO trajectories is vital for successful control strategies that either aim to stabilize the system near the fixed point or steer the system away from the periodic orbits. A hybrid UPO detection method from return maps that combines topological recurrence criterion, matrix fit algorithm, and stringent criterion for fixed point location gives accurate and statistically significant UPOs even in the presence of significant noise. Geometry of the return map, frequency of UPOs visiting the same trajectory, length of the data set, strength of the noise, and degree of nonstationarity affect the efficacy of the proposed method. Results suggest that establishing determinism from unambiguous UPO detection is often possible in short data sets with significant noise, but derived dynamical properties are rarely accurate and adequate for controlling the dynamics around these UPOs. A repeat chaos control experiment on epileptic hippocampal slices through more stringent control strategy and adaptive UPO tracking is reinterpreted in this context through simulation of similar control experiments on an analogous but stochastic computer model of epileptic brain slices. Reproduction of equivalent results suggests that far more stringent criteria are needed for linking apparent success of control in such experiments with possible determinism in the underlying dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Numerical analysis of thermally assisted spin-transfer torque magnetization reversal in synthetic ferrimagnetic free layers

The spin transfer torque magnetization reversal of synthetic ferrimagnetic free layers under pulsed temperature rise was numerically studied by solving the Landau–Lifshitz–Gilbert equation, taking into account the stochastic random fields, the temperature dependence of magnetic parameters, and the spin torque terms. The anti-parallel magnetization configuration was retained at the elevated temperature, due to interlayer dipole coupling. A significant thermal assistance effect, resulting in a 40% reduction in the switching current, was demonstrated during a nanosecond pulsed temperature rise up to 77% of the Curie temperature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Computation of shear viscosity of colloidal suspensions by SRD-MD

The behaviour of sheared colloidal suspensions with full hydrodynamic interactions (HIs) is numerically studied. To this end, we use the hybrid stochastic rotation dynamics-molecular dynamics (SRD-MD) method. The shear viscosity of colloidal suspensions is computed for different volume fractions, both for dilute and concentrated cases. We verify that HIs help in the collisions and the streaming of colloidal particles, thereby increasing the overall shear viscosity of the suspension. Our results show a good agreement with known experimental, theoretical, and numerical studies. This work demonstrates the ability of SRD-MD to successfully simulate transport coefficients that require correct modelling of HIs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Ultrafast vibrational spectroscopy (2D-IR) of CO{sub 2} in ionic liquids: Carbon capture from carbon dioxide’s point of view

The CO{sub 2}ν{sub 3} asymmetric stretching mode is established as a vibrational chromophore for ultrafast two-dimensional infrared (2D-IR) spectroscopic studies of local structure and dynamics in ionic liquids, which are of interest for carbon capture applications. CO{sub 2} is dissolved in a series of 1-butyl-3-methylimidazolium-based ionic liquids ([C{sub 4}C{sub 1}im][X], where [X]{sup −} is the anion from the series hexafluorophosphate (PF{sub 6}{sup −}), tetrafluoroborate (BF{sub 4}{sup −}), bis-(trifluoromethyl)sulfonylimide (Tf{sub 2}N{sup −}), triflate (TfO{sup −}), trifluoroacetate (TFA{sup −}), dicyanamide (DCA{sup −}), and thiocyanate (SCN{sup −})). In the ionic liquids studied, the ν{sub 3} center frequency is sensitive to the local solvation environment and reports on the timescales for local structural relaxation. Density functional theory calculations predict charge transfer from the anion to the CO{sub 2} and from CO{sub 2} to the cation. The charge transfer drives geometrical distortion of CO{sub 2}, which in turn changes the ν{sub 3} frequency. The observed structural relaxation timescales vary by up to an order of magnitude between ionic liquids. Shoulders in the 2D-IR spectra arise from anharmonic coupling of the ν{sub 2} and ν{sub 3} normal modes of CO{sub 2}. Thermal fluctuations in the ν{sub 2} population stochastically modulate the ν{sub 3} frequency and generate dynamic cross-peaks. These timescales are attributed to the breakup of ion cages that create a well-defined local environment for CO{sub 2}. The results suggest that the picosecond dynamics of CO{sub 2} are gated by local diffusion of anions and cations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Jump rates for surface diffusion of large molecules from first principles

We apply a recently developed stochastic model for the surface diffusion of large molecules to calculate jump rates for 9,10-dithioanthracene on a Cu(111) surface. The necessary input parameters for the stochastic model are calculated from first principles using density functional theory (DFT). We find that the inclusion of van der Waals corrections to the DFT energies is critical to obtain good agreement with experimental results for the adsorption geometry and energy barrier for diffusion. The predictions for jump rates in our model are in excellent agreement with measured values and show a marked improvement over transition state theory (TST). We find that the jump rate prefactor is reduced by an order of magnitude from the TST estimate due to frictional damping resulting from energy exchange with surface phonons, as well as a rotational mode of the diffusing molecule.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

The Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy and Fokker-Planck equation for many-body dissipative randomly driven systems

By generalizing Bogolyubov’s reduced description method, we suggest a formalism to derive kinetic equations for many-body dissipative systems in external stochastic field. As a starting point, we use a stochastic Liouville equation obtained from Hamilton’s equations taking dissipation and stochastic perturbations into account. The Liouville equation is then averaged over realizations of the stochastic field by an extension of the Furutsu-Novikov formula to the case of a non-Gaussian field. As the result, a generalization of the classical Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy is derived. In order to get a kinetic equation for the single-particle distribution function, we use a regular cutoff procedure of the BBGKY hierarchy by assuming weak interaction between the particles and weak intensity of the field. Within this approximation, we get the corresponding Fokker-Planck equation for the system in a non-Gaussian stochastic field. Two particular cases are discussed by assuming either Gaussian statistics of external perturbation or homogeneity of the system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Decay of transverse correlations in quantum Heisenberg models

We study a class of quantum spin systems that include the S=1/2 Heisenberg and XY-models and prove that two-point correlations exhibit exponential decay in the presence of a transverse magnetic field. The field is not necessarily constant, it may be random, and it points in the same direction. Our proof is entirely probabilistic and it relies on a random loop representations of the correlation functions, on stochastic domination and on first-passage percolation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Stochastic rotation dynamics for nematic liquid crystals

We introduce a new mesoscopic model for nematic liquid crystals (LCs). We extend the particle-based stochastic rotation dynamics method, which reproduces the Navier-Stokes equation, to anisotropic fluids by including a simplified Ericksen-Leslie formulation of nematodynamics. We verify the applicability of this hybrid model by studying the equilibrium isotropic-nematic phase transition and nonequilibrium problems, such as the dynamics of topological defects and the rheology of sheared LCs. Our simulation results show that this hybrid model captures many essential aspects of LC physics at the mesoscopic scale, while preserving microscopic thermal fluctuations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

On a theory of stability for nonlinear stochastic chemical reaction networks

We present elements of a stability theory for small, stochastic, nonlinear chemical reaction networks. Steady state probability distributions are computed with zero-information (ZI) closure, a closure algorithm that solves chemical master equations of small arbitrary nonlinear reactions. Stochastic models can be linearized around the steady state with ZI-closure, and the eigenvalues of the Jacobian matrix can be readily computed. Eigenvalues govern the relaxation of fluctuation autocorrelation functions at steady state. Autocorrelation functions reveal the time scales of phenomena underlying the dynamics of nonlinear reaction networks. In accord with the fluctuation-dissipation theorem, these functions are found to be congruent to response functions to small perturbations. Significant differences are observed in the stability of nonlinear reacting systems between deterministic and stochastic modeling formalisms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Temperature effect on vortex-core reversals in magnetic nanodots

We studied the temperature effect on vortex-core reversals in soft magnetic nanodots by micromagnetic numerical calculations within a framework of the stochastic Landau-Lifshitz-Gilbert scheme. It was determined that vortex-core-switching events at non-zero temperatures occur stochastically, and that the threshold field strength increases with temperature for a given field frequency. The mechanism of core reversals at elevated temperatures is the same as that of vortex-antivortex-pair-mediated core reversals found at the zero temperature. The reversal criterion is also the out-of-plane component of a magnetization dip that should reach −p, which is to say, m{sub z,dip} = −p, where p is the original polarization, p = +1 (−1), for the upward (downward) core. By this criterion, the creation of a vortex-antivortex pair accompanies complete vortex-antivortex-annihilation-mediated core reversals, resulting in the maximum excess of the exchange energy density, ΔE{sub ex}{sup cri} ≈ 15.4 ± 0.2 mJ/cm{sup 3}. This work provides the underlying physics of vortex-core reversals at non-zero temperatures, and potentiates the real application of vortex random access memory operating at elevated temperatures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Extended quantum jump description of vibronic two-dimensional spectroscopy

We calculate two-dimensional (2D) vibronic spectra for a model system involving two electronic molecular states. The influence of a bath is simulated using a quantum-jump approach. We use a method introduced by Makarov and Metiu [J. Chem. Phys. 111, 10126 (1999)] which includes an explicit treatment of dephasing. In this way it is possible to characterize the influence of dissipation and dephasing on the 2D-spectra, using a wave function based method. The latter scales with the number of stochastic runs and the number of system eigenstates included in the expansion of the wave-packets to be propagated with the stochastic method and provides an efficient method for the calculation of the 2D-spectra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗