Temporal Relaxation Research Articles

Identification of a Griffiths singularity in a geometrically frustrated antiferromagnet

We report the observation of a Griffiths Phase in the geometrically frustrated antiferromagnet DyBaCo${_4}$O${_{7+\delta}}$. Its onset is determined using measurements of the thermoremanent magnetization, which is shown to be superior to conventional in-field measurement protocols for the identification of the Griffiths Phase. Within this phase, the temporal relaxation of magnetization exhibits a functional form which is expected for Heisenberg systems, reflecting the nature of spin interactions in this class of materials. Interestingly, the effective Co${^{2+}}$/Co${^{3+}}$ ratio tailored by varying the oxygen non-stoichiometry $\delta$ is only seen to influence the antiferromagnetic ordering temperature ($T{_N}$), leaving the Griffiths Temperature ($T{_G}$) invariant.

Temporal and Dose Kinetics of Tunnel Relaxation of Non-Equilibrium Near-Interfacial Charged Defects in Insulators

This paper is devoted mainly to mathematical aspects of modeling and simulation of tunnel relaxation of nonequilibrium charged oxide traps located at/near the interface insulator - conductive channel, for instance in irradiated MOS devices. The generic form of the tunnel annealing response function was derived from the rate equation for the charged defect buildup and annealing as a linear superposition of the responses of different defects with different time constants. Using this linear response function, a number of important practical problems are analyzed and discussed. Combined tunnel and thermal or RICN annealing, power-like temporal relaxation after a single ion strike into the gate oxide, are described in context of general approach.

Effect of wall-mediated hydrodynamic fluctuations on the kinetics of a Brownian nanoparticle.

The reactive flux formalism (Chandler 1978 J. Chem. Phys.68, 2959-2970. (doi:10.1063/1.436049)) and the subsequent development of methods such as transition path sampling have laid the foundation for explicitly quantifying the rate process in terms of microscopic simulations. However, explicit methods to account for how the hydrodynamic correlations impact the transient reaction rate are missing in the colloidal literature. We show that the composite generalized Langevin equation (Yu et al. 2015 Phys. Rev. E91, 052303. (doi:10.1103/PhysRevE.91.052303)) makes a significant step towards solving the coupled processes of molecular reactions and hydrodynamic relaxation by examining how the wall-mediated hydrodynamic memory impacts the two-stage temporal relaxation of the reaction rate for a nanoparticle transition between two bound states in the bulk, near-wall and lubrication regimes.

Engineering and Scaling the Spontaneous Magnetization Reversal of Faraday Induced Magnetic Relaxation in Nano-Sized Amorphous Ni Coated on Crystalline Au.

We report on the generation of large inverse remanent magnetizations in nano-sized core/shell structure of Au/Ni by turning off the applied magnetic field. The remanent magnetization is very sensitive to the field reduction rate as well as to the thermal and field processes before the switching off of the magnetic field. Spontaneous reversal in direction and increase in magnitude of the remanent magnetization in subsequent relaxations over time were found. All of the various types of temporal relaxation curves of the remanent magnetizations are successfully scaled by a stretched exponential decay profile, characterized by two pairs of relaxation times and dynamic exponents. The relaxation time is used to describe the reduction rate, while the dynamic exponent describes the dynamical slowing down of the relaxation through time evolution. The key to these effects is to have the induced eddy current running beneath the amorphous Ni shells through Faraday induction.

Many-body delocalization transition and relaxation in a quantum dot

We revisit the problem of quantum localization of many-body states in a quantum dot and the associated problem of relaxation of an excited state in a finite correlated electron system. We determine the localization threshold for the eigenstates in Fock space. We argue that the localization-delocalization transition (which manifests itself, e.g., in the statistics of many-body energy levels) becomes sharp in the limit of a large dimensionless conductance (or, equivalently, in the limit of weak interaction). We also analyze the temporal relaxation of quantum states of various types (a "hot-electron state", a "typical" many-body state, and a single-electron excitation added to a "thermal state") with energies below, at, and above the transition.

Typical fast thermalization processes in closed many-body systems.

The lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a very successful general framework to cope with this problem. However, far from equilibrium, only very few quantitative and comparably universal results are known. Here a quantum mechanical prediction of this type is derived and verified against various experimental and numerical data from the literature. It quantitatively describes the entire temporal relaxation towards thermal equilibrium for a large class (in a mathematically precisely defined sense) of closed many-body systems, whose initial state may be arbitrarily far from equilibrium.

Analysis of the electric field development and the relaxation of electron velocity distribution function for nanosecond breakdown in air

Using theoretical and experimental methods, the electric field and the electron multiplication in direct vicinity of a sharp cathode is analysed. The development of the electric field in the pre-breakdown phase of the atmospheric pressure air negative DC corona discharge in the Trichel pulse regime is determined. During the following ultra-fast electrical breakdown, the emission of selected spectral bands of the nitrogen molecule is recorded with high spatiotemporal resolution using the time-correlated single photon counting method. The emission of a Townsend discharge is used to calibrate the setup for the quantitative determination of electric field. Therefore, the Trichel pulse corona and Townsend discharge cell are arranged in the same single-table setup. This direct calibration procedure is described step-by-step including the discussion of known limitations. Finally, the electric field development of the positive streamer passing the 160 μm distance in less than two nanoseconds is determined.Due to the high spatiotemporal gradients of the electric field strength within the streamer breakdown, the local field approximation of the electron component is analysed by investigating numerically the temporal and spatial electron relaxation by means of the solution of the electron Boltzmann equation and Monte Carlo simulation. Results of these computations are given for several reduced electric field values and prove that the electrons are in a hydrodynamic equilibrium state for experimentally given space and time scales for reduced fields above 100 Td.

Short-Time Beta Relaxation in Glass-Forming Liquids Is Cooperative in Nature.

Temporal relaxation of density fluctuations in supercooled liquids near the glass transition occurs in multiple steps. Using molecular dynamics simulations for three model glass-forming liquids, we show that the short-time β relaxation is cooperative in nature. Using finite-size scaling analysis, we extract a growing length scale associated with beta relaxation from the observed dependence of the beta relaxation time on the system size. We find, in qualitative agreement with the prediction of the inhomogeneous mode coupling theory, that the temperature dependence of this length scale is the same as that of the length scale that describes the spatial heterogeneity of local dynamics in the long-time α-relaxation regime.

T2 shuffling: Sharp, multicontrast, volumetric fast spin-echo imaging.

A new acquisition and reconstruction method called T2 Shuffling is presented for volumetric fast spin-echo (three-dimensional [3D] FSE) imaging. T2 Shuffling reduces blurring and recovers many images at multiple T2 contrasts from a single acquisition at clinically feasible scan times (6-7 min). The parallel imaging forward model is modified to account for temporal signal relaxation during the echo train. Scan efficiency is improved by acquiring data during the transient signal decay and by increasing echo train lengths without loss in signal-to-noise ratio (SNR). By (1) randomly shuffling the phase encode view ordering, (2) constraining the temporal signal evolution to a low-dimensional subspace, and (3) promoting spatio-temporal correlations through locally low rank regularization, a time series of virtual echo time images is recovered from a single scan. A convex formulation is presented that is robust to partial voluming and radiofrequency field inhomogeneity. Retrospective undersampling and in vivo scans confirm the increase in sharpness afforded by T2 Shuffling. Multiple image contrasts are recovered and used to highlight pathology in pediatric patients. A proof-of-principle method is integrated into a clinical musculoskeletal imaging workflow. The proposed T2 Shuffling method improves the diagnostic utility of 3D FSE by reducing blurring and producing multiple image contrasts from a single scan. Magn Reson Med 77:180-195, 2017. © 2016 Wiley Periodicals, Inc.

A discrete spectral analysis for determining quasi-linear viscoelastic properties of biological materials.

The viscoelastic behaviour of a biological material is central to its functioning and is an indicator of its health. The Fung quasi-linear viscoelastic (QLV) model, a standard tool for characterizing biological materials, provides excellent fits to most stress-relaxation data by imposing a simple form upon a material's temporal relaxation spectrum. However, model identification is challenging because the Fung QLV model's 'box'-shaped relaxation spectrum, predominant in biomechanics applications, can provide an excellent fit even when it is not a reasonable representation of a material's relaxation spectrum. Here, we present a robust and simple discrete approach for identifying a material's temporal relaxation spectrum from stress-relaxation data in an unbiased way. Our 'discrete QLV' (DQLV) approach identifies ranges of time constants over which the Fung QLV model's typical box spectrum provides an accurate representation of a particular material's temporal relaxation spectrum, and is effective at providing a fit to this model. The DQLV spectrum also reveals when other forms or discrete time constants are more suitable than a box spectrum. After validating the approach against idealized and noisy data, we applied the methods to analyse medial collateral ligament stress-relaxation data and identify the strengths and weaknesses of an optimal Fung QLV fit.

First-passage-time statistics of a Brownian particle driven by an arbitrary unidimensional potential with a superimposed exponential time-dependent drift

In one-dimensional systems, the dynamics of a Brownian particle are governed by the force derived from a potential as well as by diffusion properties. In this work, we obtain the first-passage-time statistics of a Brownian particle driven by an arbitrary potential with an exponential temporally decaying superimposed field up to a prescribed threshold. The general system analyzed here describes the sub-threshold signal integration of integrate-and-fire neuron models, of any kind, supplemented by an adaptation-like current, whereas the first-passage-time corresponds to the declaration of a spike. Following our previous studies, we base our analysis on the backward Fokker–Planck equation and study the survival probability and the first-passage-time density function in the space of the initial condition. By proposing a series solution we obtain a system of recurrence equations, which given the specific structure of the exponential time-dependent drift, easily admit a simpler Laplace representation. Naturally, the present general derivation agrees with the explicit solution we found previously for the Wiener process in (2012 J. Phys. A: Math. Theor. 45 185001). However, to demonstrate the generality of the approach, we further explicitly evaluate the first-passage-time statistics of the underlying Ornstein–Uhlenbeck process. To test the validity of the series solution, we extensively compare theoretical expressions with the data obtained from numerical simulations in different regimes. As shown, agreement is precise whenever the series is truncated at an appropriate order. Beyond the fact that both the Wiener and Ornstein–Uhlenbeck processes have a direct interpretation in the context of neuronal models, given their ubiquity in different fields, our present results will be of interest in other settings where an additive state-independent temporal relaxation process is being developed as the particle diffuses.

Dynamical transition in the temporal relaxation of stochastic processes under resetting.

A stochastic process, when subject to resetting to its initial condition at a constant rate, generically reaches a nonequilibrium steady state. We study analytically how the steady state is approached in time and find an unusual relaxation mechanism in these systems. We show that as time progresses an inner core region around the resetting point reaches the steady state, while the region outside the core is still transient. The boundaries of the core region grow with time as power laws at late times with new exponents. Alternatively, at a fixed spatial point, the system undergoes a dynamical transition from the transient to the steady state at a characteristic space-dependent timescale t(*)(x). We calculate analytically in several examples the large deviation function associated with this spatiotemporal fluctuation and show that, generically, it has a second-order discontinuity at a pair of critical points characterizing the edges of the inner core. These singularities act as separatrices between typical and atypical trajectories. Our results are verified in the numerical simulations of several models, such as simple diffusion and fluctuating one-dimensional interfaces.

Long term relaxation of CdHgTe n+-n–structures formed with ion milling

Experimental studies of long-term (more than 7 years) temporal relaxation at the room terms of electric parameters (concentration and mobility) of the CdHgTe n + -n structures formed by an ion milling are studied. It is shown that parameters of samples after short-term relaxation (about 200000 min), are saved during of long-term aging. Thus, the method of ion milling can be used for forming of р-n junction of CdHgTe photodiodes.

Spatial Heterogeneity of Glassy Polymer Films

By studying the morphology of polystyrene films subjected to a fast structuration method, we demonstrate the spatial heterogeneity of their surface viscoelasticity at temperatures well below the glass transition temperature, Tg. Our results point to a nonrandom arrangement of zones of different elastic modulus deep in the glassy state. The spatial distribution of viscoelastic properties of the film was temperature dependent; we observed the presence of soft zones (surrounded by areas of larger elastic modulus) spanning increasingly larger areas of the surface as T gets closer to Tg. The heterogeneity on viscoelastic properties of the film is supported by the temporal evolution and relaxation of the structured surfaces and by direct measurements of the spatial distribution of the local elastic modulus of polystyrene films.

Extended‐range high‐resolution dynamical downscaling over a continental‐scale spatial domain with atmospheric and surface nudging

AbstractExtended‐range high‐resolution mesoscale simulations with limited‐area atmospheric models when applied to downscale regional analysis fields over large spatial domains can provide valuable information for many applications including the weather‐dependent renewable energy industry. Long‐term simulations over a continental‐scale spatial domain, however, require mechanisms to control the large‐scale deviations in the high‐resolution simulated fields from the coarse‐resolution driving fields. As enforcement of the lateral boundary conditions is insufficient to restrict such deviations, large scales in the simulated high‐resolution meteorological fields are therefore spectrally nudged toward the driving fields. Different spectral nudging approaches, including the appropriate nudging length scales as well as the vertical profiles and temporal relaxations for nudging, have been investigated to propose an optimal nudging strategy. Impacts of time‐varying nudging and generation of hourly analysis estimates are explored to circumvent problems arising from the coarse temporal resolution of the regional analysis fields. Although controlling the evolution of the atmospheric large scales generally improves the outputs of high‐resolution mesoscale simulations within the surface layer, the prognostically evolving surface fields can nevertheless deviate from their expected values leading to significant inaccuracies in the predicted surface layer meteorology. A forcing strategy based on grid nudging of the different surface fields, including surface temperature, soil moisture, and snow conditions, toward their expected values obtained from a high‐resolution offline surface scheme is therefore proposed to limit any considerable deviation. Finally, wind speed and temperature at wind turbine hub height predicted by different spectrally nudged extended‐range simulations are compared against observations to demonstrate possible improvements achievable using higher spatiotemporal resolution.

Temporal linear relaxation in IBM ILOG CP Optimizer

IBM ILOG CP Optimizer is a constraint solver that implements a model-and-run paradigm. For scheduling problems, CP Optimizer provides a relatively simple but very expressive modeling language based on the notion of interval variables. This paper presents the temporal linear relaxation (TLR) used to guide the automatic search when solving scheduling problems that involve temporal and resource allocation costs. We give the rationale of the TLR, describe its integration in the automatic search of CP Optimizer, and present the relaxation of most of the constraints and expressions of the model. An experimental study on a set of classical scheduling benchmarks shows that using the TLR is essential for problems with irregular temporal costs and generally helps for problems with resource allocation costs.

Reduced lasing threshold from organic dye microcavities

We demonstrate an unexpected tenfold reduction in the lasing threshold of an organic vertical microcavity under subpicosecond optical excitation. In contrast to conventional theory of lasing, we find that the lasing threshold depends on the rate at which excitons are created rather than the total energy delivered within the exciton lifetime. The threshold reduction is discussed in the context of microcavity-enhanced super-radiant coupling between the excitons. The interpretation of super-radiance is supported by the temporal relaxation dynamics of the microcavity emission, which follows the super-radiance time rather than the cavity lifetime. This demonstration suggests that room-temperature super-radiant effects could generally lower the threshold in four-level lasing systems of similar relaxation dynamics.

Trapping ions from a fast beam in a radio-frequency ion trap: The relaxation of the ion cloud and its resulting column density

The relaxation of trapped Cl${{}_{2}}^{\ensuremath{-}}$ ions and their resulting column density in a multipole radio-frequency (RF) ion trap have been investigated after loading the trap from an initial fast-moving beam exploiting a mechanism described recently [A. Svendsen et al., Phys. Rev. A 87, 043410 (2013)] where the injection is mediated through the exchange of energy between ions and the oscillating RF field. The temporal relaxation of the energy distribution of the trapped ion cloud was probed by observing the evolution of the resulting time-of-flight distribution of ions after extraction and fragment mass analysis in a quadrupole mass filter. The ion energy distribution was found to be essentially stationary after $\ensuremath{\sim}20$ ms. The resulting column density of trapped ions after relaxation was probed by two-dimensional position-resolved photodissociation of the trapped Cl${{}_{2}}^{\ensuremath{-}}$ ions. A detailed statistical analysis of the ion column density in the ring-electrode trap is given, and by comparison to the experimental data, a value of the maximum adiabaticity parameter of ${\ensuremath{\eta}}_{\mathrm{max}}\ensuremath{\simeq}0.28$ is inferred. It is further demonstrated how the present experimental system allows for time-resolved mass spectrometry by probing explicitly the populations of both parent (Cl${{}_{2}}^{\ensuremath{-}}$) and daughter (Cl${}^{\ensuremath{-}}$) ions as a function of time after closing the trap and after laser irradiation. Finally, it is discussed how the setup can be used to obtain absolute photodissociation cross sections via a tomographic method without assumptions on the decay law for the trapped ions.

Correlation Between Hydroxide ion Dynamics and Transport Properties of Hydroxide/Chloride Melts According to Raman Spectroscopy Data

UDC 541.454;543.42;535.375.5 Using data obtained in analysis of the band contour for the totally symmetric stretching vibration of the OH - anion in Raman spectra of hydroxide/chloride ionic melts, a correlation has been established between the orientational relaxation time and effective moment of inertia of the hydroxide ion and the transport properties of the electrolyte. Study of the structure of ionic compounds and its controlling infl uence on physical and chemical properties is one of the fundamental scientifi c problems in physical chemistry. Today the appearance of new and improvement of conventional experimental methods for studying the structure of matter and also creation of high-tech device components has permitted considerable expansion of the range of systems that can be studied, including high-temperature ionic melts. Development of methodological approaches has led to a signifi cant increase in the amount of information that can be extracted and an increase in the reliability of this information. Raman spectroscopy is a physical method for investigation of matter which, based on recorded vibrational spectra of the analyte system, allows us to carry out structural analysis, to determine the vibrational frequencies, and to calculate force constants and the moment of inertia of a molecule and the rates of relaxation processes. In contrast to x-ray diffraction and neutron diffraction methods, determining the structure of materials (the symmetry type, the interatomic distances, the coordination numbers), the Raman spectroscopy method allows us to obtain a much greater amount of information: the recorded vibrational frequencies correspond to the position of the vibrational levels in the molecule, the width of the vibrational bands contain information about its rotational motion, and the intensity of the Raman spectra directly determines the bond ionicity or covalency (1, 2). Today a methodological approach has been developed that allows us, from analysis of the contour of the vibrational bands and the width of their isotropic and anisotropic components, to obtain important information about the dynamics of the particles in the picosecond time range (1-4). It has been shown (4) that information about relaxation processes can be obtained by calculating the temporal correlation functions, the vibrational and orientational relaxation times for the structural units. Unique information on estimation of the moments of inertia of particles, which is practically inaccessible by other methods for studying the condensed state of matter and which can be obtained only using high-resolution rotational spectra of gas molecules, can be extracted by analyzing the shape of the contour of vibrational bands using the spectral moments method (4). According to this method, the moment of inertia can be calculated from the equation (3): I = 6kT/4π 2 c 2 Mor(2),

Finite-Time and Finite-Size Scaling of the Kuramoto Oscillators

Phase transition in its strict sense can only be observed in an infinite system, for which equilibration takes an infinitely long time at criticality. In numerical simulations, we are often limited both by the finiteness of the system size and by the finiteness of the observation time scale. We propose that one can overcome this barrier by measuring the nonequilibrium temporal relaxation for finite systems and by applying the finite-time-finite-size scaling (FTFSS) which systematically uses two scaling variables, one temporal and the other spatial. The FTFSS method yields a smooth scaling surface, and the conventional finite-size scaling curves can be viewed as proper cross sections of the surface. The validity of our FTFSS method is tested for the synchronization transition of Kuramoto models in the globally coupled structure and in the small-world network structure. Our FTFSS method is also applied to the MonteCarlo dynamics of the globally coupled q-state clock model.