Time-dependent Moment Research Articles

Slow Phase Transition-Induced Scan Rate Dependence of Spin Crossover in a Two-Dimensional Supramolecular Fe(III) Complex

Slow Phase Transition-Induced Scan Rate Dependence of Spin Crossover in a Two-Dimensional Supramolecular Fe(III) Complex

Uncertainty quantification of dynamical systems by a POD–Kriging surrogate model

Uncertainty quantification (UQ) of dynamical systems with a surrogate model is difficult as the surrogate model parameters often need to be computed at each time step. For that reason, a different kind of surrogate model is presented in this article by representing the stochastic response quantity using lower number of bases. Proper orthogonal decomposition (POD) is used to project the response quantity with low number of POD bases and the uncertainty is propagated using the Kriging model. The combined POD–Kriging model is used for UQ of four dynamical systems and all the results are compared with the Monte Carlo simulation results. The first three problems are long time integration problems and the time-dependent statistical moments are predicted well by the POD–Kriging model using low number of model evaluations. For the last example (a building subjected to Gaussian white noise base acceleration), the prediction accuracy of the POD–Kriging model is also high as compared to a similar surrogate model.

Investigation of the effects of managed ice field characteristics on a dynamic positioning AHTS vessel using physical modelling techniques

This paper presents the tools, techniques and outcomes of a model testing program of a dynamically positioned (DP) Ice-1A classed Anchor Handling Tug Supply (AHTS) vessel called the “Magne Viking” in different managed ice environments with ice thickness, concentration, floe size, floe distribution, drift speed, and ice encroachment direction as test variables. A total of 168 test runs were carried out in 7 ice sheets to evaluate the vessel's thruster forces and moment on the horizontal plane and the vessel's 6-DOF motions and accelerations. The time series and probability of exceedance plots of thruster forces and yawing moments are presented, along with the vessel's positioning relative to a set-point in various managed ice conditions. In addition, investigations are carried out to evaluate the influence of various ice field parameters on the time-averaged and time-dependent thruster forces and moment. Both measurements and video recordings confirmed complex and stochastic ice-ship-basin wall interactions and different ice failure modes. Overall, the study demonstrated the capability of the DP-controlled ship to maintain the station for most head-on tests and the oblique ice tests not exceeding 15°. The dataset and video recordings acquired through the testing have improved the understanding of the dynamic ice-vessel interactions.

Theory of dipole moment reconstruction by attosecond transient absorption spectroscopy

We propose a general procedure for the reconstruction of time-dependent dipole moment via transient absorption spectrum, within the framework of linear response theory. The reconstruction method is demonstrated with two examples: the self-reconstruction of extreme-ultraviolet-light-atom interaction (analytically) and the infrared-dressed helium system (numerically). A correlation coefficient is introduced to quantify the fidelity of the reconstruction, which reaches almost 100$%$ over a wide range of laser parameters and thus indicates the robustness of our reconstruction method. Our theory provides a solid basis for understanding the recent experiment [Phys. Rev. Lett. 121, 173005 (2018)], explaining when and why the dipole moment can be well reconstructed solely from the absorption spectrum even without exact knowledge of the attosecond probe pulse.

Solving the chemical master equation for monomolecular reaction systems and beyond: a Doi-Peliti path integral view.

The chemical master equation (CME) is a fundamental description of interacting molecules commonly used to model chemical kinetics and noisy gene regulatory networks. Exact time-dependent solutions of the CME-which typically consists of infinitely many coupled differential equations-are rare, and are valuable for numerical benchmarking and getting intuition for the behavior of more complicated systems. Jahnke and Huisinga's landmark calculation of the exact time-dependent solution of the CME for monomolecular reaction systems is one of the most general analytic results known; however, it is hard to generalize, because it relies crucially on special properties of monomolecular reactions. In this paper, we rederive Jahnke and Huisinga's result on the time-dependent probability distribution and moments of monomolecular reaction systems using the Doi-Peliti path integral approach, which reduces solving the CME to evaluating many integrals. While the Doi-Peliti approach is less intuitive, it is also more mechanical, and hence easier to generalize. To illustrate how the Doi-Peliti approach can go beyond the method of Jahnke and Huisinga, we also find an explicit and exact time-dependent solution to a problem involving an autocatalytic reaction that Jahnke and Huisinga identified as not solvable using their method. Most interestingly, we are able to find a formal exact time-dependent solution for any CME whose list of reactions involves only zero and first order reactions, which may be the most general result currently known. This formal solution also yields a useful algorithm for efficiently computing numerical solutions to CMEs of this type.

First passage time properties of miRNA-mediated protein translation

An important function of microRNAs in gene regulation is to repress the protein synthesis in a multi-step process with implications in timing efficiency of the regulatory network. We propose a stochastic description of translation-initiation mechanism and solve for the steady state distribution of protein number in the linear regime. The time-dependent moments have been approximately calculated and the role of miRNAs in determining the First Passage Time (FPT) properties of protein dynamics has been established. We analytically show that the modulation of slow rates of the translation process will result in efficient and robust timing mechanism. For a general nonlinear model our numerical simulation results are in qualitative agreement with the linear model.

Preliminary design of bionic flapping wing vehicle

This paper deals with the preliminary design of bionic flapping wing vehicle. The design is driven by its requirement and objective namely the maximum weight should be less than 0.5 kg with 1.5 m wingspan. In the conceptual design, the wing planform, wing structures and system of flapping mechanism will be considered to find the initial configuration and then continued the sizing of the flapping vehicle. The analysis of designed flapping vehicle is increasingly complex due to firstly the generation of time-dependent aerodynamic forces and moments from unsteady flow around the flapping wing, secondly, flexible wing structure which generates higher thrust may cause a structure failure and thirdly, a flapping mechanism system generating differential flapping motion for the vehicle maneuver. The aerodynamic analysis for given flapping motion model is carried out using Computational Fluid Dynamics method based the solution of unsteady Reynold Averaged Navier-Stokes equations and the structure analysis is conducted with the input of aerodynamic loads using Finite Element method to find critical stresses that may cause a structure failure. As a solution of differential flapping two controlled servos are used. The architecture of electrical system is made to analysis of the distribution of data signal and power. The flight maneuver is achieved by changes in flapping frequency and sweeping angle. The selection of system components is performed by considering weight constraint. The flight maneuver is achieved by changes in flapping frequency and sweeping angle. The wing platform has elliptical shape with airfoil maximum camber of 6% chord at a quarter chord. The outer body and wing are made of foam laminated by glass fibre with the foam density of 0.045 g/cm3. The horizontal tail is made of mylar film with density of 1.38 g/cm3 and its area of 168.3 cm2. As simulated results, the amount of total lift is 4.18 Newton generated at 6 Hz flapping frequency.

Time-dependent reliability analysis for a set of RC T-beam bridges under realistic traffic considering creep and shrinkage

Reinforced concrete bridges constitute the major part of existing bridges. The purpose of this paper is to present a serviceability evaluation methodology for RC bridges under probabilistic conditions. It will be based on analytical calculations with no need to complex modeling or advanced software. For this purpose, a realistic traffic model is simulated based on existing weigh-in-motion WIM data from some European sites. The probabilistic distributions of the time-dependent load effects, moment and deflection, are then deduced after hundreds of simulations. The degradation effects are introduced in the analysis by considering the concrete creep and shrinkage. A simplified model to introduce creep effect under variable traffic load is also proposed. The time dependent reliability indices are then calculated for a set of 21 simply supported RC T-beam bridges with varying parameters such as span lengths, number of girders, girder spacing and number of design lanes. The first order reliability method FORM, is used in the reliability calculation in order to evaluate the structural performance under the considered failure scenario.

Effects of Structural Dynamics on Charge Carrier Transfer in B-DNA: A Combined MD and RT-TDDFT Study.

Hole transfer along the axis of duplex DNA has been the focus of physical chemistry research for decades, with implications in diverse fields, from nanotechnology to cell oxidative damage. Computational approaches are particularly amenable for this problem, to complement experimental data for interpretation of transfer mechanisms. To be predictive, computational results need to account for the inherent mobility of biological molecules during the time frame of experimental measurements. Here, we address the structural variability of B-DNA and its effects on hole transfer in a combined molecular dynamics (MD) and real-time time-dependent density functional theory (RT-TDDFT) study. Our results show that quantities that characterize the charge transfer process, such as the time-dependent dipole moment and hole population at a specific site, are sensitive to structural changes that occur on the nanosecond time scale. We extend the range of physical properties for which such a correlation has been observed, further establishing the fact that quantitative computational data on charge transfer properties should include statistical averages. Furthermore, we use the RT-TDDFT results to assess an efficient tight-binding method suitable for high-throughput predictions. We demonstrate that charge transfer, although affected by structural variability, on average, remains strong in AA and GG dimers.

Primordial monopolium as dark matter

The existence of monopoles is a characteristic signature of Kaluza–Klein multidimensional theories. The topology of these solutions is extremely interesting. The existence of a dipole solution, which we have associated to a monopole–anti-monopole bound state, is the leitmotiv of this investigation. The dipole in its lowest energy state, which we here call also monopolium, is electromagnetically inert in free space interacting only gravitationally. Monopolium when interacting with time dependent magnetic fields acquires a time dependent induced magnetic moment and radiates. We have analyzed the most favorable astrophysical scenario for radiative monopolium and found that the amount of radiation is so small that is not detectable by conventional equipments. These findings suggest that Kaluza–Klein monopolium, if existent, would be a candidate for a primordial dark matter constituent.

Determination of the time-dependent moment tensor using time reverse imaging

We have developed an approach to determine the time-dependent moment tensor and the origin time in addition to commonly derived locations of seismic events using time reverse imaging (TRI). It is crucial to locate and characterize the occurring microseismicity without making a priori assumptions about the sources to fully understand the subsurface processes inducing seismicity. Low signal-to-noise ratios (S/Ns) often force standard methods to make assumptions about sources or only characterize selected larger magnitude events. In TRI, microearthquakes are located by back propagating the full-recorded time-reversed wavefield through a velocity model until it ideally convergences on the source location. Therefore, it is less affected by low S/Ns and potentially locates and characterizes most of the events. After distinguishing artificial convergence locations from source locations, the quality of the source location and the moment tensors are derived by recording the stress at the determined source locations during the back propagation of the time-reversed wavefield. A robust workflow is derived using synthetic test cases in a realistic scenario with velocity models that only approximate the true velocity model and/or noisy displacement traces. The influence of a rudimentary velocity model on the source-location accuracy and characterization is significant. Our workflow handles these less-than-optimal station distributions and velocity models. Finally, the derived workflow is successfully applied to field data recorded at the geothermal field of Los Humeros, Mexico. Although only a 1D velocity model is currently available, source locations and (time-dependent) moment tensors could be determined for selected events.

Nuclear-electronic orbital Ehrenfest dynamics.

The recently developed real-time nuclear-electronic orbital (RT-NEO) approach provides an elegant framework for treating electrons and selected nuclei, typically protons, quantum mechanically in nonequilibrium dynamical processes. However, the RT-NEO approach neglects the motion of the other nuclei, preventing a complete description of the coupled nuclear-electronic dynamics and spectroscopy. In this work, the dynamical interactions between the other nuclei and the electron-proton subsystem are described with the mixed quantum-classical Ehrenfest dynamics method. The NEO-Ehrenfest approach propagates the electrons and quantum protons in a time-dependent variational framework, while the remaining nuclei move classically on the corresponding average electron-proton vibronic surface. This approach includes the non-Born-Oppenheimer effects between the electrons and the quantum protons with RT-NEO and between the classical nuclei and the electron-proton subsystem with Ehrenfest dynamics. Spectral features for vibrational modes involving both quantum and classical nuclei are resolved from the time-dependent dipole moments. This work shows that the NEO-Ehrenfest method is a powerful tool to study dynamical processes with coupled electronic and nuclear degrees of freedom.

Time-dependent spintronic anisotropy in magnetic molecules

We theoretically study the quench dynamics of induced anisotropy of a large-spin magnetic molecule coupled to spin-polarized ferromagnetic leads. The real-time evolution is calculated by means of the time-dependent density-matrix numerical renormalization group method implemented within the matrix product states framework, which takes into account all correlations in very accurate manner. We determine the system's response to a quench in the spin-dependent coupling to ferromagnetic leads. In particular, we focus on the transient dynamics associated with crossing from the weak to the strong coupling regime, where the Kondo correlations become important. The dynamics is examined by calculating the time-dependent expectation values of the spin-quadrupole moment and the associated spin operators. We identify the relevant time scales describing the quench dynamics and determine the influence of the molecule's effective exchange coupling and leads spin-polarization on the dynamical behavior of the system. Furthermore, the generalization of our predictions for large values of molecule's spin is considered. Finally, we analyze the effect of finite temperature and show that it gives rise to a reduction of magnetic anisotropy by strong suppression of the time-dependent spin-quadrupole moment due to thermal fluctuations.

Real-Time Time-Dependent Nuclear-Electronic Orbital Approach: Dynamics beyond the Born-Oppenheimer Approximation.

The quantum mechanical treatment of both electrons and nuclei is crucial in nonadiabatic dynamical processes such as proton-coupled electron transfer. The nuclear-electronic orbital (NEO) method provides an elegant framework for including nuclear quantum effects beyond the Born-Oppenheimer approximation. To enable the study of nonequilibrium properties, we derive and implement a real-time NEO (RT-NEO) approach based on time-dependent Hatree-Fock or density functional theory, in which the electronic and nuclear degrees of freedom are propagated in a time-dependent variational framework. Nuclear and electronic spectral features can be resolved from the time-dependent dipole moment computed using the RT-NEO method. The test cases show the dynamical interplay between the quantum nuclei and the electrons through vibronic coupling. Moreover, vibrational excitation in the RT-NEO approach is demonstrated by applying a resonant driving field, and electronic excitation is demonstrated by simulating excited state intramolecular proton transfer. This work shows that the RT-NEO approach is a promising tool to study nonadiabatic quantum dynamical processes within a time-dependent variational description for the coupled electronic and nuclear degrees of freedom.

Evaluation of the need for negative moment reinforcing in prestressed concrete bridges in the view of service loads

It is common practice to put additional longitudinal reinforcement (b2 bars) over intermediate supports to resist any negative moment induced by the superimposed dead loads and live loads on bridges. However, little research has been conducted on the performance of the additional negative reinforcing steel. Requirements for the termination of the additional negative moment reinforcing steel have largely been based upon the engineering judgement, previous performance, and existing practice. The main objective of the research is to evaluate the effect of different amounts of b2 bars on resisting the negative moment over the pier on a continuous prestressed concrete girder bridge when it subject to the live load generated moment and secondary moment. To achieve this objective, a live load field test was performed on a bridge designed with different amounts of b2 bars to allow for comparison of the varying levels of negative moment reinforcement present. A full-scale finite element model was developed and validated against the field-collected data to study the b2 bar performance subjected to live loads. An evaluation was performed, utilizing an analytical approach by calculating the time-dependent secondary moment using mRESTRAINT and loading the beam-line FE model with the maximum negative moment. It was found that the negative moment induced by the live load and secondary moment does appear through the service life of the bridge. The high differential shrinkage rate between the fresh deck concrete and the girder concrete is the main source of the negative moment over the supports. The magnitude of the secondary moment was found to be highly influenced by the time when the continuity established. The results also indicated that the additional longitudinal reinforcing steel provides minimal effect on resistance to the negative moment prior to the formulation of deck cracking, regardless of whether the negative moment was induced by live loads or secondary moment. The current design approach determines the b2 bars requirement for the strength level based on the live load, it may be necessary to include the secondary moment in the design.

Do portfolio investors need to consider the asymmetry of returns on the Russian stock market?

This paper, following (Ghalanos, 2012), uses the simple method of embedding skewness in asset allocation based on the Taylor expansion of the investor utility function up to the third term and maximizing it by portfolio weights. This approach also enables us to consider investor risk aversion. Time-dependent multivariate asset moments are obtained via the GO-GARCH volatility model with a normal-inverse Gaussian distribution for the error term. By means of parma package (Ghalanos & Pfaff, 2016) we explore the performance of the usual 2 moment utility and its 3 moment counterpart for a portfolio consisted of twenty assets traded on the Russian stock market. The results demonstrate that the 3 moment utility significantly outperforms the 2 moment utility by SD, MAD and CVaR for low levels of absolute risk aversion and by portfolio returns and investor utility level during the whole forecast period.

Ultrafast electron transfer through a silicon–vacuum interface induced by the action of an intense femtosecond laser pulse

A theoretical study of the influence of a quasistationary electric field formed during emission separation of charges on ultrafast electron transfer near a silicon–vacuum interface irradiated by femtosecond laser pulses was carried out. The values of the strength of the arising quasistationary field during irradiation by femtosecond pulses with fluences near and above the silicon damage thresholds were estimated. The possibility of the formation of a dynamic optically layered structure in the near-surface layers of silicon irradiated by a femtosecond pulse, resulting from a modification of its optical properties due to the depletion of electrons in the surface layer, was studied. It is suggested that the time-dependent dipole moment induced by the emission separation of charges should lead to the generation of electromagnetic radiation from the terahertz frequency range. The basic properties of this radiation were theoretically investigated.

Relativistic Real-Time Time-Dependent Equation-of-Motion Coupled-Cluster

We present a relativistic time-dependent equation-of-motion coupled-cluster with single and double excitations (TD-EOM-CCSD) formalism. Unlike other explicitly time-dependent quantum chemical methods, the present approach considers the time correlation function of the dipole operator, as opposed to the expectation value of the time-dependent dipole moment. We include both scalar relativistic effects and spin-orbit coupling variationally in this scheme via the use of the exact two-component (X2C) wave function as the reference that enters the coupled-cluster formalism. In order to evaluate the accuracy of X2C-TD-EOM-CCSD, we compare zero-field splitting in atomic absorption spectra of open-shell systems (Na, K, Mg+, and Ca+) with values obtained from experiment. In closed-shell species (Na+, K+, Mg2+, and Ca2+), we observe singlet-triplet mixing in the X2C-TD-EOM-CC calculations, which results from the use of the X2C reference. The effects of the X2C reference are evaluated by comparing spectra derived from X2C-TD-EOM-CC calculations to those from TD-EOM-CC calculations using a complex generalized Hartree-Fock ([Formula: see text]-GHF) reference.

Gravitational wave emission from quadrupole Josephson junction device

We suggest a hybrid quantum mechanical/classical set up capable of gravitational wave emission. The proposed device consists of two superconducting tunneling junctions which act as quantum voltage-to-frequency converters and produce oscillation of the charges (masses) in the superconducting condensate. The classical interpretation of the set up is associated with the particular arrangement which leads to suppression of the dipole radiation and formation of time dependent quadrupole mass moment - the gravitational wave source. The proposed device converts electrical energy/momentum into gravitational ones thus suggesting a form of propulsion. Provided the reverse effect: curvature-to-voltage conversion is possible, the device represents an emitter-receiver pair for gravitational wave based communication (favorable 1/r fall off with distance).

Langevin equation for the dipole vector of an accidental symmetric top molecule

The Langevin equation governing the time dependent dipole moment μ(t) of an accidental symmetric top (i.e., the direction of μ(t) does not coincide with the axis of symmetry) in an external electric field is directly derived from the Euler-Langevin equation. Results which have been previously obtained in J. Mol. Liquids. 1991, 49, 79 are regained as special cases. The scalar Langevin equation governing the longitudinal component of μ(t) along a space fixed axis is also derived.