Crossover Time Scale Research Articles

Intersystem Crossing of 2-Methlypyrazine Studied by Femtosecond Photoelectron Imaging.

2-methylpyrazine was excited to the high vibrational dynamics of the S1 state with 260 nm femtosecond laser light, and the evolution of the excited state was probed with 400 nm light. Because it was unstable, the S1 state decayed via intersystem crossing to the triplet state T1, and it may have decayed to the ground state S0 via internal conversion. S1-to-T1 intersystem crossing was observed by combining time-resolved mass spectrometry and time-resolved photoelectron spectroscopy. The crossover time scale was 23 ps. Rydberg states were identified, and the photoelectron spectral and angular distributions indicated accidental resonances of the S1 and T1 states with the 3s and 3p Rydberg states, respectively, during ionization.

Dynamics of transient cages in a model 2D supercooled liquid

Supercooled state of a liquid is characterized by extremely slow and spatially heterogeneous dynamics attributed to caging of particles by their neighbors. The dynamics of cages in a model 2D supercooled liquid is studied by analyzing single particle trajectories. The temperature dependence of cage times and cage sizes is discussed. The average cage time is found to show power-law divergence as the critical temperature is approached. A correlation between cage sizes and cage survival time is identified. At higher temperatures, bigger cages survive for longer. However, this behavior changes at low enough temperatures, where a crossover timescale is observed beyond which the smallest cages are more likely to survive. This crossover time originates mainly due to different initial dynamics of the bigger and the smaller cages, which shows strong temperature dependence for smaller cages.

Dynamical relaxation of correlators in periodically driven integrable quantum systems

We show that the correlation functions of a class of periodically driven integrable closed quantum systems approach their steady-state value as ${n}^{\ensuremath{-}(\ensuremath{\alpha}+1)/\ensuremath{\beta}}$, where $n$ is the number of drive cycles and $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ denote positive integers. We find that, generically, $\ensuremath{\beta}=2$ within a dynamical phase characterized by a fixed $\ensuremath{\alpha}$; however, its value can change to $\ensuremath{\beta}=3$ or $\ensuremath{\beta}=4$ either at critical drive frequencies separating two dynamical phases or at special points within a phase. We show that such decays are realized in both driven Su-Schrieffer-Heeger (SSH) and one-dimensional (1D) transverse field Ising models, discuss the role of symmetries of the Floquet spectrum in determining $\ensuremath{\beta}$, and chart out the values of $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ realized in these models. We analyze the SSH model for a continuous drive protocol using a Floquet perturbation theory which provides analytical insight into the behavior of the correlation functions in terms of its Floquet Hamiltonian. This is supplemented by an exact numerical study of a similar behavior for the 1D Ising model driven by a square pulse protocol. For both models, we find a crossover timescale ${n}_{c}$ which diverges at the transition. We also unravel a long-time oscillatory behavior of the correlators when the critical drive frequency, ${\ensuremath{\omega}}_{c}$, is approached from below $(\ensuremath{\omega}<{\ensuremath{\omega}}_{c})$. We tie such behavior to the presence of multiple stationary points in the Floquet spectrum of these models and provide an analytic expression for the time period of these oscillations.

Practical Basis of the Geometric Mean Fitness and its Application to Risk-Spreading Behavior.

Temporal variations in population size under unpredictable environments are of primary concern in evolutionary ecology, where time scale enters as an important factor while setting up an optimization problem. Thus, short-term optimization with traditional (arithmetic) mean fitness may give a different result from long-term optimization. In the long-term optimization, the concept of geometric mean fitness has been received well by researchers and applied to various problems in ecology and evolution. However, the limit of applicability of geometric mean has not been addressed so far. Here we investigate this problem by analyzing numerically the probability distribution of a random variable obeying stochastic multiplicative growth. According to the law of large number, the expected value (i.e., arithmetic mean) manifests itself as a proper measure of optimization as the number of random processes increases to infinity. We show that the finiteness of this number plays a crucial role in arguing for the relevance of geometric mean. The geometric mean provides a satisfactory picture of the random variation in a long term above a crossover time scale that is determined by this number and the standard deviation of the randomly varying growth rates. We thus derive the applicability condition under which the geometric mean fitness is valid. We explore this condition in some examples of risk-spreading behavior.

Transition from shear-dominated to Rayleigh–Taylor turbulence

Turbulent mixing layers in nature are often characterised by the presence of a mean shear and an unstable buoyancy gradient between two streams of different velocities. Depending on the relative strength of shear versus buoyancy, either the former or the latter may dominate the turbulence and mixing between the two streams. In this paper, we present a phenomenological theory that leads to the identification of two distinct turbulent regimes: an early regime, dominated by mean shear, and a later regime dominated by buoyancy. The main theoretical result consists of the identification of a cross-over timescale that distinguishes between the shear- and the buoyancy-dominated turbulence. This cross-over time depends on three large-scale constants of the flow, namely, the buoyancy difference, the velocity difference between the two streams and the gravitational acceleration. We validate our theory against direct numerical simulations of a temporal turbulent mixing layer compounded with an unstable stratification. We observe that the cross-over time correctly predicts the transition from shear- to buoyancy-driven turbulence, in terms of turbulent kinetic energy production, energy spectra scaling and mixing layer thickness.

Intrusion into Granular Media Beyond the Quasistatic Regime.

The drag force exerted on an object intruding into granular media is typically assumed to arise from additive velocity and depth dependent contributions. We test this with intrusion experiments and molecular dynamics simulations at constant speed over four orders of magnitude, well beyond the quasistatic regime. For a vertical cylindrical rod we find velocity dependence only right after impact, followed by a crossover to a common, purely depth-dependent behavior for all intrusion speeds. The crossover is set by the timescale for material, forced to well up at impact, to subsequently settle under gravity. These results challenge current models of granular drag.

The Value of Initialization on Decadal Timescales: State-Dependent Predictability in the CESM Decadal Prediction Large Ensemble

AbstractInformation in decadal climate prediction arises from a well-initialized ocean state and from the predicted response to an external forcing. The length of time over which the initial conditions benefit the decadal forecast depends on the start date of the forecast. We characterize this state-dependent predictability for decadal forecasts of upper ocean heat content in the Community Earth System Model. We find regionally dependent initial condition predictability, with extended predictability generally observed in the extratropics. We also detect state-dependent predictability, with the year of loss of information from the initialization varying between start dates. The decadal forecasts in the North Atlantic show substantial information from the initial conditions beyond the 10-yr forecast window, and a high degree of state-dependent predictability. We find some evidence for state-dependent predictability in the ensemble spread in this region, similar to that seen in weather and subseasonal-to-seasonal forecasts. For some start dates, an increase of information with lead time is observed, for which the initialized forecasts predict a growing phase of the Atlantic multidecadal oscillation. Finally we consider the information in the forecast from the initial conditions relative to the forced response, and quantify the crossover time scale after which the forcing provides more information. We demonstrate that the climate change signal projects onto different patterns than the signal from the initial conditions. This means that even after the crossover time scale has been reached in a basin-averaged sense, the benefits of initialization can be felt locally on longer time scales.

Double power-law viscoelastic relaxation of living cells encodes motility trends

Living cells are constantly exchanging momentum with their surroundings. So far, there is no consensus regarding how cells respond to such external stimuli, although it reveals much about their internal structures, motility as well as the emergence of disorders. Here, we report that twelve cell lines, ranging from healthy fibroblasts to cancer cells, hold a ubiquitous double power-law viscoelastic relaxation compatible with the fractional Kelvin-Voigt viscoelastic model. Atomic Force Microscopy measurements in time domain were employed to determine the mechanical parameters, namely, the fast and slow relaxation exponents, the crossover timescale between power law regimes, and the cell stiffness. These cell-dependent quantities show strong correlation with their collective migration and invasiveness properties. Beyond that, the crossover timescale sets the fastest timescale for cells to perform their biological functions.

Power-law tails and non-Markovian dynamics in open quantum systems: An exact solution from Keldysh field theory

The Born-Markov approximation is widely used to study dynamics of open quantum systems coupled to external baths. Using Keldysh formalism, we show that the dynamics of a system of bosons (fermions) linearly coupled to non-interacting bosonic (fermionic) bath falls outside this paradigm if the bath spectral function has non-analyticities as a function of frequency. In this case, we show that the dissipative and noise kernels governing the dynamics have distinct power law tails. The Green's functions show a short time "quasi" Markovian exponential decay before crossing over to a power law tail governed by the non-analyticity of the spectral function. We study a system of bosons (fermions) hopping on a one dimensional lattice, where each site is coupled linearly to an independent bath of non-interacting bosons (fermions). We obtain exact expressions for the Green's functions of this system which show power law decay $\sim |t-t'|^{-3/2}$. We use these to calculate density and current profile, as well as unequal time current-current correlators. While the density and current profiles show interesting quantitative deviations from Markovian results, the current-current correlators show qualitatively distinct long time power law tails $|t-t'|^{-3}$ characteristic of non-Markovian dynamics. We show that the power law decays survive in presence of inter-particle interaction in the system, but the cross-over time scale is shifted to larger values with increasing interaction strength.

Time Correlations of Lightning Flash Sequences in Thunderstorms Revealed by Fractal Analysis

AbstractBy using the data of lightning detection and ranging system at the Kennedy Space Center, the temporal fractal and correlation of interevent time series of lightning flash sequences in thunderstorms have been investigated with Allan factor (AF), Fano factor (FF), and detrended fluctuation analysis (DFA) methods. AF, FF, and DFA methods are powerful tools to detect the time‐scaling structures and correlations in point processes. Totally 40 thunderstorms with distinguishing features of a single‐cell storm and apparent increase and decrease in the total flash rate were selected for the analysis. It is found that the time‐scaling exponents for AF (αAF) and FF (αFF) analyses are 1.62 and 0.95 in average, respectively, indicating a strong time correlation of the lightning flash sequences. DFA analysis shows that there is a crossover phenomenon—a crossover timescale (τc) ranging from 54 to 195 s with an average of 114 s. The occurrence of a lightning flash in a thunderstorm behaves randomly at timescales <τc but shows strong time correlation at scales >τc. Physically, these may imply that the establishment of an extensive strong electric field necessary for the occurrence of a lightning flash needs a timescale >τc, which behaves strongly time correlated. But the initiation of a lightning flash within a well‐established extensive strong electric field may involve the heterogeneities of the electric field at a timescale <τc, which behave randomly.

Addressing time-scale–dependent erosion rates from measurement methods with censorship

Research Article| September 12, 2017 Addressing time-scale–dependent erosion rates from measurement methods with censorship Brandon McElroy; Brandon McElroy † 1Department of Geology & Geophysics, University of Wyoming, 1000 E. University Avenue, Laramie, Wyoming 82071, USA †bmcelroy@uwyo.edu Search for other works by this author on: GSW Google Scholar Jane Willenbring; Jane Willenbring 2Scripps Institution of Oceanography–Earth Division, University of California–San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA Search for other works by this author on: GSW Google Scholar David Mohrig David Mohrig 3Department of Geological Sciences, University of Texas, 1 University Station C9000, Austin, Texas 78712, USA Search for other works by this author on: GSW Google Scholar GSA Bulletin (2018) 130 (3-4): 381–395. https://doi.org/10.1130/B31644.1 Article history received: 29 Aug 2016 rev-recd: 05 Mar 2017 accepted: 28 Jun 2017 first online: 12 Sep 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation Brandon McElroy, Jane Willenbring, David Mohrig; Addressing time-scale–dependent erosion rates from measurement methods with censorship. GSA Bulletin 2017;; 130 (3-4): 381–395. doi: https://doi.org/10.1130/B31644.1 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGSA Bulletin Search Advanced Search Abstract In a degrading landscape, does the episodic nature of erosion affect observed erosion rates in a systematic way, and can one account for the effects? We present a null hypothesis for surface change rate variations based on minimal assumptions about the processes of topographic evolution. Variance in erosion along with censorship of topographic change distributions combine to act as a first-order control on time-scale dependence of erosion rates. In general, censorship is ubiquitous, and as a result, time-scale dependence of rates is likely to apply to almost every system. In detail, this occurs because at short time scales, surface changes can be censored from field measurements that become inherently incorporated by natural surface evolution at longer time scales. Additionally, the granularity of systems implies minimum time scales below which specific rate measurements have no physical interpretation. Finally, we show the existence of a crossover time scale at which the short-term rate dependence of a process gives way to the long-term rate that is no longer subject to censoring.We demonstrate these points by applying the proposed framework to a growing seepage channel network in Florida, United States. Using a dendrogeomorphic approach in concert with cosmogenic radionuclide methods, we estimate denudation rates averaged over annual to multimillennial time scales. Exposure of hundreds of tree roots combined with tree ages supplies surface change rates along approximately one third of the valley bottom within the studied area. Erosion rates are distributed approximately between 1 mm/yr and 10 mm/yr. This erosion exhibits variance that depends linearly on time scale and is interpreted to represent a process well modeled as normal diffusion. As a result, the erosion rates show an inverse-square dependence on time scale. We used the 10Be contents from nine quartz sand samples to estimate long-term erosion rates and then coupled them with existing estimates of long-term erosion. These estimates of erosion are of the order of 0.01 mm/yr to 0.1 mm/yr and correspond to time scales of roughly 105 yr. Based on theory derived from censored measurements of rate distributions, the short-term rates can be used to infer expected long-term rates. In this case, distributions of measured and expected long-term rates do not overlap, and an explicit test of a null hypothesis is not necessary. We interpret the large-magnitude, short-time-scale rates as a product of recent influences on the ravines, and we discuss how this framework could be applied in other settings. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

On the relationship between the meridional overturning circulation, alongshore wind stress, and United States East Coast sea level in the Community Earth System Model Large Ensemble

AbstractBy the late twenty‐first century, climate models project enhanced dynamic sea level (DSL) rise along the western boundary of the North Atlantic associated with a decline in the Atlantic meridional overturning circulation (AMOC). In contrast, coastal DSL variability over the last few decades has been driven largely by local winds, with limited evidence for coupling to AMOC strength. The unclear forcing‐dependence and timescale‐dependence of relationships between local winds, AMOC strength, and DSL obscures: (1) the validity of tide gauge‐derived DSL gradients as a proxy of AMOC strength and (2) the assessment of climate model reliability. Here we analyze these relationships in the Community Earth System Model Large Ensemble (CESM‐LE) over the 1920–2100 period. In CESM‐LE, the amplitude of interannual to multidecadal DSL variability and its along‐coast correlation are comparable to detrended annual mean tide gauge records. A “crossover timescale” of approximately 5–15 years partitions a local wind‐driven coastal DSL regime from an overturning‐related regime. Processes unrelated to either AMOC strength or local winds are important at interannual to decadal timescales. As external forcing increases in strength over the twenty‐first century, DSL variability associated with the overturning circulation becomes dominant. While the largely externally forced, AMOC‐associated, component explains only 29 ± 12% of DSL variance over the 1920–2010 period, it explains 89 ± 3% of the variance in the 2011–2100 period. We discuss the implications of these results on the reliability of climate model projections of regional DSL, the use of coastal DSL as a proxy for AMOC, and the origins of multidecadal DSL variability.

Time-Delay Induced Dimensional Crossover in the Voter Model.

We investigate the ordering dynamics of the voter model with time-delayed interactions. The dynamical process in the d-dimensional lattice is shown to be equivalent to the first passage problem of a random walker in the (d+1)-dimensional strip of a finite width determined by the delay time. The equivalence reveals that the time delay leads to the dimensional crossover from the (d+1)-dimensional scaling behavior at a short time to the d-dimensional scaling behavior at a long time. The scaling property in both regimes and the crossover time scale are obtained analytically, which are confirmed with the numerical simulation results.

Time Scales of Southern Ocean Eddy Equilibration

AbstractStratification in the Southern Ocean is determined primarily by a competition between westerly wind-driven upwelling and baroclinic eddy transport. This study investigates the time scales of equilibration of the Southern Ocean in response to changing winds through an idealized channel model. An analytical framework describing the energetic pathways between wind input, available potential energy (APE), eddy kinetic energy (EKE), and dissipation provides a simple theory of the phase and amplitude response to oscillating wind stress. The transient ocean response to variable winds lies between the two limits of Ekman response (high frequency), characterized by the isopycnal slope responding directly to wind stress, and “eddy saturation” (low frequency), wherein a large fraction of the anomalous wind work goes into mesoscale eddies. The crossover time scale is the time scale of meridional eddy diffusive transport across the Antarctic Circumpolar Current (ACC) front. For wind variability with a period of 3 months (high-frequency forcing), the relative conversion of wind work to APE/EKE is 11, while for a period of 16 years (low-frequency forcing), the relative conversion to APE/EKE reduces to 3. The system’s frequency response is characterized by a complex transfer function. Both the phase and amplitude response of EKE and APE predicted by the linear analytic framework are verified using multiple ensemble experiments in an eddy-resolving (4-km horizontal resolution) isopycnal coordinate model. The results from the numerical experiments show agreement with the linear theory and can be used to explain certain features observed in previous modeling studies and observations.

Maximizing the purity of a qubit evolving in an anisotropic environment

We provide a general method to calculate and maximize the purity of a qubit interacting with an anisotropic non-Markovian environment. Counter to intuition, we find that the purity is often maximized by preparing and storing the qubit in a superposition of non-interacting eigenstates. For a model relevant to decoherence of a heavy-hole spin qubit in a quantum dot or for a singlet-triplet qubit for two electrons in a double quantum dot, we show that preparation of the qubit in its non-interacting ground state can actually be the worst choice to maximize purity. We further give analytical results for spin-echo envelope modulations of arbitrary spin components of a hole spin in a quantum dot, going beyond a standard secular approximation. We account for general dynamics in the presence of a pure-dephasing process and identify a crossover timescale at which it is again advantageous to initialize the qubit in the non-interacting ground state. Finally, we consider a general two-axis dynamical decoupling sequence and determine initial conditions that maximize purity, minimizing leakage to the environment.

Scaling Behaviors of Global Sea Surface Temperature

AbstractTemporal scaling properties of the monthly sea surface temperature anomaly (SSTA) in global ocean basins are examined by the power spectrum and detrended fluctuation analysis methods. Analysis results show that scaling behaviors of the SSTA in most ocean basins (e.g., global average, South Pacific, eastern and western tropical Pacific, tropical Indian Ocean, and tropical Atlantic) are separated into two distinct regimes by a common crossover time scale of 52 months (i.e., 4.3 yr). It is suggested that this crossover is modulated by the El Niño/La Niña–Southern Oscillation (ENSO), indicating different scaling properties at different time scales. The SSTA time series is nonstationary and antipersistent at the small scale (i.e., crossover). It is, however, stationary and long range correlated at the large scale (i.e., crossover). For both time scales, scaling behaviors of SSTA are heterogeneously distributed over the ocean, and the fluctuation of SSTA intensifies with decreasing latitude. Stronger fluctuation appears over the tropical regions (e.g., central-eastern tropical Pacific, tropical Atlantic, tropical Indian Ocean, and South China Sea), which are directly or indirectly linked to ENSO. Weaker fluctuation and stronger persistence are found in mid- and high-latitude areas, coinciding with the “reemergence” areas.

On correlation decay in low-dimensional systems

While the decay of correlations in dynamical systems has been discussed in the physics and mathematics literature for several decades, there exists virtually no nontrivial example where the actual decay rates can be computed explicitly. We construct a class of simple dynamical systems for which all correlation properties, in particular, the entire spectrum of the Perron-Frobenius operator, are accessible by analytical means. As an application we discuss an example of an interval map with a small number of branches where the decay of correlations can be made arbitrarily fast. The example can be viewed as the simplest toy model which gives rise to a crossover from transient to asymptotic behaviour with predictable crossover time scale. The model class introduced here points towards relations between correlation decay and Lyapunov spectra.

The effects of molecular weight, evaporation rate and polymer concentration on pillar formation in drying poly(ethylene oxide) droplets

Typically, when droplets of dilute suspensions are left to evaporate the final dry deposit is the familiar coffee-ring stain, with nearly all the solute deposited at the initial contact line. Contrastingly, in previous work we have shown that sessile droplets of poly(ethylene oxide) (PEO) solutions form tall central pillars (or monoliths) during a 4-stage drying process. We show that a dimensionless Péclet-type number Pe, a ratio of the competing advective and diffusive motion of the dissolved polymer, which incorporates the effects of evaporation rate, initial concentration c0 and the polymer diffusion coefficient, to determine whether the droplet will form a pillar or a flat deposit. In this work we vary concentration up to c0=0.5 and molecular weight Mw between 3.35kg/mol and 600kg/mol and find that in ambient conditions with c0=0.1 pillars only form for a limited range, 35≤Mw≤200 kg/mol. This observation is in contrast to the the Péclet argument in which high molecular weight polymers with a slow self-diffusion should still form pillars. We present various experimental measurements attempting to resolve this discrepancy: crossover time-scale for viscoelastic behaviour; fast diffusion of an entangled network; and droplet viscosity or contact line friction.

Detection of crossover time scales in multifractal detrended fluctuation analysis

Fractal is employed in this paper as a scale-based method for the identification of the scaling behavior of time series. Many spatial and temporal processes exhibiting complex multi(mono)-scaling behaviors are fractals. One of the important concepts in fractals is crossover time scale(s) that separates distinct regimes having different fractal scaling behaviors. A common method is multifractal detrended fluctuation analysis (MF-DFA). The detection of crossover time scale(s) is, however, relatively subjective since it has been made without rigorous statistical procedures and has generally been determined by eye balling or subjective observation. Crossover time scales such determined may be spurious and problematic. It may not reflect the genuine underlying scaling behavior of a time series. The purpose of this paper is to propose a statistical procedure to model complex fractal scaling behaviors and reliably identify the crossover time scales under MF-DFA. The scaling-identification regression model, grounded on a solid statistical foundation, is first proposed to describe multi-scaling behaviors of fractals. Through the regression analysis and statistical inference, we can (1) identify the crossover time scales that cannot be detected by eye-balling observation, (2) determine the number and locations of the genuine crossover time scales, (3) give confidence intervals for the crossover time scales, and (4) establish the statistically significant regression model depicting the underlying scaling behavior of a time series. To substantive our argument, the regression model is applied to analyze the multi-scaling behaviors of avian-influenza outbreaks, water consumption, daily mean temperature, and rainfall of Hong Kong. Through the proposed model, we can have a deeper understanding of fractals in general and a statistical approach to identify multi-scaling behavior under MF-DFA in particular.

The localization transition of the two-dimensional Lorentz model

We investigate the dynamics of a single tracer particle performing Brownian motion in a two-dimensional course of randomly distributed hard obstacles. At a certain critical obstacle density, the motion of the tracer becomes anomalous over many decades in time, which is rationalized in terms of an underlying percolation transition of the void space. In the vicinity of this critical density the dynamics follows the anomalous one up to a crossover time scale where the motion becomes either diffusive or localized. We analyze the scaling behavior of the time-dependent diffusion coefficient D(t) including corrections to scaling. Away from the critical density, D(t) exhibits universal hydrodynamic long-time tails both in the diffusive as well as in the localized phase.