Short-time Propagation Research Articles

Exploring the Temporal Patterns of Dynamic Information Flow during Attention Network Test (ANT)

The attentional processes are conceptualized as a system of anatomical brain areas involving three specialized networks of alerting, orienting and executive control, each of which has been proven to have a relation with specified time-frequency oscillations through electrophysiological techniques. Nevertheless, at present, it is still unclear how the idea of these three independent attention networks is reflected in the specific short-time topology propagation of the brain, assembled with complexity and precision. In this study, we investigated the temporal patterns of dynamic information flow in each attention network via electroencephalograph (EEG)-based analysis. A modified version of the attention network test (ANT) with an EEG recording was adopted to probe the dynamic topology propagation in the three attention networks. First, the event-related potentials (ERP) analysis was used to extract sub-stage networks corresponding to the role of each attention network. Then, the dynamic network model of each attention network was constructed by post hoc test between conditions followed by the short-time-windows fitting model and brain network construction. We found that the alerting involved long-range interaction among the prefrontal cortex and posterior cortex of brain. The orienting elicited more sparse information flow after the target onset in the frequency band 1-30 Hz, and the executive control contained complex top-down control originating from the frontal cortex of the brain. Moreover, the switch of the activated regions in the associated time courses was elicited in attention networks contributing to diverse processing stages, which further extends our knowledge of the mechanism of attention networks.

On the Numerical Solution of 1D and 2D KdV Equations Using Variational Homotopy Perturbation and Finite Difference Methods

The KdV equation has special significance as it describes various physical phenomena. In this paper, we use two methods, namely, a variational homotopy perturbation method and a classical finite-difference method, to solve 1D and 2D KdV equations with homogeneous and non-homogeneous source terms by considering five numerical experiments with initial and boundary conditions. The variational homotopy perturbation method is a semi-analytic technique for handling linear as well as non-linear problems. We derive classical finite difference methods to solve the five numerical experiments. We compare the performance of the two classes of methods for these numerical experiments by computing absolute and relative errors at some spatial nodes for short, medium and long time propagation. The logarithm of maximum error vs. time from the numerical methods is also obtained for the experiments undertaken. The stability and consistency of the finite difference scheme is obtained. To the best of our knowledge, a comparison between the variational homotopy perturbation method and the classical finite difference method to solve these five numerical experiments has not been undertaken before. The ideal extension of this work would be an application of the employed methods for fractional and stochastic KdV type equations and their variants.

Resolving the data asynchronicity in high-speed atomic force microscopy measurement via the Kalman Smoother

High-speed atomic force microscopy (HS-AFM) is a scanning probe microscopy that can capture structural dynamics of biomolecules in real time at single molecule level near physiological condition. Albeit much improvement, while scanning one frame of HS-AFM movies, biomolecules often change their conformations largely. Thus, the obtained frame images can be hampered by the time-difference, the asynchronicity, in the data acquisition. Here, to resolve this data asynchronicity in the HS-AFM movie, we developed Kalman filter and smoother methods, some of the sequential Bayesian filtering approaches. The Kalman filter/smoother methods use alternative steps of a short time-propagation by a linear dynamical system and a correction by the likelihood of AFM data acquired pixel by pixel. We first tested the method using a toy model of a diffusing cone, showing that the Kalman smoother method outperforms to reproduce the ground-truth movie. We then applied the Kalman smoother to a synthetic movie for conformational change dynamics of a motor protein, i.e., dynein, confirming the superiority of the Kalman smoother. Finally, we applied the Kalman smoother to two real HS-AFM movies, FlhAC and centralspindlin, reducing distortion and noise in the AFM movies. The method is general and can be applied to any HS-AFM movies.

Interpreting Experimental Results from Shock Impacts on Single Crystal PETN in the Context of Continuum Models

AbstractIn this paper we interpret previous experimental measurements of impacts on single crystal PETN in the context of a simple continuum model. Hugoniot calculations using the simple model framework under various limiting assumptions envelope measured Hugoniot states reasonably well and suggest that non‐negligible deviatoric elastic strains may exist in the shock compressed state for weak impacts. An accompanying simple kinematic model for lattice deformation was used to estimate the expected shifts in X‐ray diffraction peaks for the (211) plane under impacts normal to (110) planes. The results suggest that negligible relaxation of the deviatoric lattice deformation occurs on the short (10–20 ns) time and wave propagation (40–80 m) scales of laser‐driven shock experiments, and that the corresponding elastic strains may be large. Because of the potentially large deviatoric elastic strains, the specific finite deformation strain measure used within thermomechanical single crystal models is of significant consequence, which is explored numerically by the comparison of isothermal purely elastic responses under uniaxial and simple shear deformations.

Symmetric quasi-classical dynamics with quasi-diabatic propagation scheme.

We apply a recently developed quasi-diabatic (QD) scheme to the symmetric quasi-classical (SQC) approach for accurate quantum dynamics propagation. By using the adiabatic states as the QD states during a short-time quantum dynamics propagation, the QD scheme allows for directly interfacing the diabatic SQC method with commonly used adiabatic electronic structure calculations, thus alleviating any non-trivial theoretical efforts to reformulate SQC in the adiabatic representation. Furthermore, the QD scheme ensures a stable propagation of the dynamics and allows using a much larger time step compared to directly propagating SQC dynamics in the adiabatic representation. This is due to the fact that the QD scheme does not explicitly require non-adiabatic couplings that could exhibit highly peaked values during non-adiabatic dynamics propagation. We perform the QD-SQC calculations with a wide range of model non-adiabatic systems to demonstrate the accuracy of the proposed scheme. This study opens up the possibility for combining accurate diabatic quantum dynamics methods such as SQC with any adiabatic electronic structure calculations for non-adiabatic on-the-fly propagations.

Quasi-Diabatic Representation for Nonadiabatic Dynamics Propagation.

We develop a nonadiabatic dynamics propagation scheme that allows interfacing diabatic quantum dynamics methods with commonly used adiabatic electronic structure calculations. This scheme uses adiabatic states as the quasi-diabatic (QD) states during a short-time quantum dynamics propagation. At every dynamical propagation step, these QD states are updated based on a new set of adiabatic basis. Using the partial linearized density matrix (PLDM) path-integral method as one specific example for diabatic dynamics approaches, we demonstrate the accuracy of the QD scheme with a wide range of model nonadiabatic systems as well as the on-the-fly propagations with density functional tight-binding (DFTB) calculations. This study opens the possibility to combine accurate diabatic quantum dynamics methods with adiabatic electronic structure calculations for nonadiabatic dynamics propagations.

Quantum Dynamics with Short-Time Trajectories and Minimal Adaptive Basis Sets.

Methods for solving the time-dependent Schrödinger equation via basis set expansion of the wave function can generally be categorized as having either static (time-independent) or dynamic (time-dependent) basis functions. We have recently introduced an alternative simulation approach which represents a middle road between these two extremes, employing dynamic (classical-like) trajectories to create a static basis set of Gaussian wavepackets in regions of phase-space relevant to future propagation of the wave function [J. Chem. Theory Comput., 11, 8 (2015)]. Here, we propose and test a modification of our methodology which aims to reduce the size of basis sets generated in our original scheme. In particular, we employ short-time classical trajectories to continuously generate new basis functions for short-time quantum propagation of the wave function; to avoid the continued growth of the basis set describing the time-dependent wave function, we employ Matching Pursuit to periodically minimize the number of basis functions required to accurately describe the wave function. Overall, this approach generates a basis set which is adapted to evolution of the wave function while also being as small as possible. In applications to challenging benchmark problems, namely a 4-dimensional model of photoexcited pyrazine and three different double-well tunnelling problems, we find that our new scheme enables accurate wave function propagation with basis sets which are around an order-of-magnitude smaller than our original trajectory-guided basis set methodology, highlighting the benefits of adaptive strategies for wave function propagation.

Wavepacket revivals via complex trajectory propagation

Complex-valued semiclassical methods hold out the promise of treating classically allowed and classically forbidden processes on the same footing. In addition, they provide a natural way to describe optical excitation with complex fields within the trajectory framework. Despite their promise, these methods have until now been limited to short time propagation, due to the numerical difficulties introduced by the complexification. Using a new Final Value Representation of the Coherent State Propagator (FINCO), combined with an analysis of the complex classical phase space, we achieve accurate wavepacket propagation all the way to the revival time of a strongly anharmonic system.

Self-Consistent Filtering Scheme for Efficient Calculations of Observables via the Mixed Quantum-Classical Liouville Approach.

Over the past decade, several algorithms have been developed for calculating observables using mixed quantum-classical Liouville dynamics, which differ in how accurately they solve the quantum-classical Liouville equation (QCLE). One of these algorithms, known as sequential short-time propagation (SSTP), is a surface-hopping algorithm that solves the QCLE almost exactly, but obtaining converged values of observables requires very large ensembles of trajectories due to the rapidly growing statistical errors inherent to this algorithm. To reduce the ensemble sizes, two filtering schemes (viz., observable cutting and transition filtering) have been previously developed and effectively applied to both simple and complex models. However, these schemes are either ad hoc in nature or require significant trial and error for them to work as intended. In this study, we present a self-consistent scheme, which, in combination with a soundly motivated probability function used for the Monte Carlo sampling of the nonadiabatic transitions, avoids the ad hoc observable cutting and reduces the amount of trial and error required for the transition filtering to work. This scheme is tested on the spin-boson model, in the weak, intermediate, and strong coupling regimes. Our transition filtered results obtained using a newly proposed probability function, which favors the sampling of nonadiabatic transitions with small energy gaps, show a significant improvement in accuracy and efficiency for all coupling regimes over the results obtained using observable cutting and the original implementation of transition filtering and are comparable to those obtained using the combination of these two techniques. It is therefore expected that this novel scheme will substantially reduce ensemble sizes and simplify the computation of observables in more complex systems.

Laser-induced dissociation dynamics of triatomic molecule in electronic excited states: A full-dimensional quantum mechanics study.

We present a detailed theoretical approach to investigate the laser-induced dissociation dynamics of a triatomic molecule on its electronic excited state in full dimensional case. In this method, the time evolution of the time-dependent system is propagated via combined the split operator method and the expansion of Chebyshev polynomials (or short-time Chebyshev propagation) and the system wave functions are expanded in terms of molecular rotational bases. As an example of the application of this formalism, the dissociation dynamics of H3(+)→H2(+)+H induced by ultrashort UV laser pulses are investigated on new Born-Oppenheimer potential energy surfaces. Our numerical results show that the signals of dissociation products will be easier to observe as the increasing of field strength. Driving by a 266 nm laser beam, the calculated central value of kinetic-energy-release is 2.04 eV which shows excellent agreement with the experimental estimation of 2.1 eV. When the H3(+) ion is rotationally excited, the spatial distribution of product fragments will become well converged.

Insights into the evolution of the Yenkahe resurgent dome (Siwi caldera, Tanna Island, Vanuatu) inferred from aerial high-resolution photogrammetry

The Yenkahe dome (Tanna Island, Vanuatu) is one of the most spectacular examples of presently active post-caldera resurgence, exhibiting a very high uplift rate over the past 1000years (156mm/year on average). Although numerous inhabited areas are scattered around the dome, the dynamics of this structure and associated hazards remain poorly studied because of its remote location and dense vegetation cover. A high-resolution photogrammetric campaign was carried out in November 2011 over the dome. Georeferenced photographs were treated by “Structure from Motion” and “Multiple-view Stereophotogrammetry” methods to produce a 3D-digital surface model (DSM) of the area and its associated orthophotograph. This DSM is much more accurate than previously available SRTM and Aster digital elevation models (DEMs), particularly at minimal (coastline) and maximal altitudes (Yasur culmination point, ~390m). While previous mapping relied mostly on low resolution DEMs and satellite images, the high precision of the DSM allows for a detailed structural analysis of the Yenkahe dome, notably based on the quantification of fault displacements. The new structural map, inferred from the 3D reconstruction and morphological analysis of the dome, reveals a complex pattern of faults and destabilization scars reflecting a succession of constructive and destructive events. Numerous landslide scars directed toward the sea highlight the probable occurrence of a tsunami event affecting the south-eastern coast of Tanna. Simulations of landslide-triggered tsunamis show the short time propagation of such a wave (1–2min), which could affect coastal localities even following relatively small destabilized volumes (a few million cubic meters).

Analytic propagation of near-circular satellite orbits in the atmosphere of an oblate planet

In the present paper, an averaging perturbation technique leads to the determination of a time-explicit analytic approximate solution for the motion of a low-Earth-orbiting satellite . The two dominant perturbations are taken into account: the Earth oblateness and the atmospheric drag. The proposed orbit propagation algorithm comprises the Brouwer–Lyddane transformation (direct and inverse), coupled with the analytic solution of the averaged equations of motion. This solution, based on equinoctial elements, is singularity-free, and therefore it stands for low inclinations and small eccentricities as well. The simplifying assumption of a constant atmospheric density is made, which is reasonable for near-circular orbits and short-time orbit propagation. Two sets of time-explicit equations are provided, for moderate and small eccentricities ( $$\mathcal {O} ( e^{4}) =0$$ and $$\mathcal {O}( e^{2}) =0,$$ respectively), and they are obtained by performing (1) a regularization of the original averaged differential equations of motion for the vectorial orbital elements, and (2) Taylor series expansions of the aforementioned equations with respect to the eccentricity. The numerical simulations show that the errors due to the use of the proposed analytic model in the presence of drag are almost the same as the errors of the Brouwer first-order approximation in the absence of drag.

An Extension of STFT Uncertainty Propagation for GMM-Based Super-Gaussian a Priori Models

Feature compensation is a low computational cost technique to achieve robust automatic speech recognition (ASR). Short-time Fourier Transform Uncertainty Propagation (STFT-UP) provides feature compensation in domains used for ASR as, e.g., Mel-Frequency Cepstra Coefficient (MFCC), while using STFT domain distortion models. However, STFT-UP is limited to Gaussian priors when modeling speech distortion, whereas super-Gaussian priors are known to provide improved performance. In this letter, an extension of STFT-UP is presented that uses approximate super-Gaussian priors. This is achieved by extending the conventional complex Gaussian priors to complex Gaussian mixture priors. The approach can be applied to any of the STFT-UP existing solutions, thus providing super-Gaussian uncertainty propagation. The method is exemplified by a Minimum Mean Square Error (MMSE) MFCC estimator with an approximate generalized Gamma speech prior. This estimator clearly outperforms the Gaussian-based MMSE-MFCC feature compensation on the AURORA4 corpus.

Propagation in quantum walks and relativistic diffusions

Propagation in quantum walks is revisited by showing that very general 1D discrete-time quantum walks with time- and space-dependent coefficients can be described, at the continuous limit, by Dirac fermions coupled to electromagnetic fields. Short-time propagation is also established for relativistic diffusions by presenting new numerical simulations of the relativistic Ornstein–Uhlenbeck process. A geometrical generalization of Fick's law is also obtained for this process. The results suggest that relativistic diffusions may be realistic models of decohering or random quantum walks. Links with general relativity and geometrical flows are also mentioned.

Can Diffusions Propagate?

The diffusion of relativistic particle in a fluid at equilibrium is investigated through an analytical and numerical study of the Relativistic Ornstein-Uhlenbeck process (ROUP). Contrary to expectations, the ROUP exhibits short-time propagation in physical space and only displays typical diffuse behavior at asymptotic times. The short-time propagation is understood through an analytical computation and the density profile is fitted at all times by a simple Ansatz. A generalization of Fick’s law is finally obtained, in which the diffusion coefficient is replaced by a time-dependent metric. These results connect relativistic diffusion with gravitational horizons and geometrical flows.

Dynamic torsional buckling of cylindrical shells

In this paper the local buckling of cylindrical shell under torsion is discussed. The Hamiltonian system approach is employed to analyze the propagation of shear wave. In this system, critical torsional loads and buckling modes are reduced to a problem of eigenvalues and eigensolutions of increasing orders. Buckling modes are divided into two types, the local torsional buckling modes and the helical buckling modes. For short-time shear wave propagation, local torsional buckling occurs easily. On the contrary, the helical buckling modes appear when the wave propagates for a longer time and these modes correspond to the first-order eigensolution.

Properties of quantum systems via diagonalization of transition amplitudes. I. Discretization effects

We analyze the method for calculation of properties of nonrelativistic quantum systems based on exact diagonalization of space-discretized short-time evolution operators. In this paper we present a detailed analysis of the errors associated with space discretization. Approaches using direct diagonalization of real-space discretized Hamiltonians lead to polynomial errors in discretization spacing Delta . Here we show that the method based on the diagonalization of the short-time evolution operators leads to substantially smaller discretization errors, vanishing exponentially with 1/Delta(2). As a result, the presented calculation scheme is particularly well suited for numerical studies of few-body quantum systems. The analytically derived discretization errors estimates are numerically shown to hold for several models. In the follow up paper [I. Vidanović, A. Bogojević, A. Balaz, and A. Belić, Phys. Rev. E 80, 066706 (2009)] we present and analyze substantial improvements that result from the merger of this approach with the recently introduced effective-action scheme for high-precision calculation of short-time propagation.

Properties of quantum systems via diagonalization of transition amplitudes. II. Systematic improvements of short-time propagation

In this paper, building on a previous analysis [I. Vidanović, A. Bogojević, and A. Belić, preceding paper, Phys. Rev. E 80, 066705 (2009)] of exact diagonalization of the space-discretized evolution operator for the study of properties of nonrelativistic quantum systems, we present a substantial improvement to this method. We apply recently introduced effective action approach for obtaining short-time expansion of the propagator up to very high orders to calculate matrix elements of space-discretized evolution operator. This improves by many orders of magnitude previously used approximations for discretized matrix elements and allows us to numerically obtain large numbers of accurate energy eigenvalues and eigenstates using numerical diagonalization. We illustrate this approach on several one- and two-dimensional models. The quality of numerically calculated higher-order eigenstates is assessed by comparison with semiclassical cumulative density of states.

Periodic orbit basis for the quantum baker map

A set of quantum states, dynamically related to the classical periodic orbits of a chaotic map, is used as a basis in which the description of the eigenstates of its quantum version is greatly simplified. This set can be improved with the inclusion of short time propagation along the stable and unstable manifolds of the periodic orbits resulting in a construction similar to the scar functions of Vergini [J. Phys. A 33, 4709 (2000)]. The average participation ratio is used to quantify the quality of the basis.

Short-time inertial response of viscoelastic fluids measured with Brownian motion and with active probes

We have directly observed short-time stress propagation in viscoelastic fluids using two optically trapped particles and a fast interferometric particle-tracking technique. We have done this both by recording correlations in the thermal motion of the particles and by measuring the response of one particle to the actively oscillated second particle. Both methods detect the vortexlike flow patterns associated with stress propagation in fluids. This inertial vortex flow propagates diffusively for simple liquids, while for viscoelastic solutions the pattern spreads superdiffusively, depending on the shear modulus of the medium.