Local Time Scale Research Articles

Bouncing Skew Brownian Motions

We consider two skew Brownian motions, driven by the same Brownian motion, with different starting points and different skewness coefficients. In Gloter and Martinez (Ann Probab 41(3A):1628–1655, 2013), the evolution of the distance between the two processes, in local timescale and up to their first hitting time, is shown to satisfy a stochastic differential equation with jumps driven by the excursion process of one of the two skew Brownian motions. In this article, we show that the distance between the two processes in local timescale may be viewed as the unique continuous Markovian self-similar extension of the process described in Gloter and Martinez (2013). This permits us to compute the law of the distance of the two skew Brownian motions at any time in the local timescale, when both original skew Brownian motions start from zero. As a consequence, we give an explicit formula for the entrance law of the associated excursion process and study the Markovian dependence on the skewness parameter. The results are related to an open question formulated initially by Burdzy and Chen (Ann Probab 29(4):1693–1715, 2001).

Relativistic time transfer for a Mars lander: from proper time to Areocentric Coordinate Time

As the first step in relativistic time transfer for a Mars lander from its proper time to the time scale at the ground station, we investigate the transformation between proper time and Areocentric Coordinate Time (TCA) in the framework of IAU Resolutions. TCA is a local time scale for Mars, which is analogous to the Geocentric Coordinate Time (TCG) for Earth. This transformation contains two contributions: internal and external. The internal contribution comes from the gravitational potential and the rotation of Mars. The external contribution is due to the gravitational fields of other bodies (except Mars) in the Solar System. When the (in)stability of an onboard clock is assumed to be at the level of 10−13, we find that the internal contribution is dominated by the gravitational potential of spherical Mars with necessary corrections associated with the height of the lander on the areoid, the dynamic form factor of Mars, the flattening of the areoid and the spin rate of Mars. For the external contribution, we find the gravitational effects from other bodies in the Solar System can be safely neglected in this case after calculating their maximum values.

Air–water flow characteristics in high-velocity free-surface flows with 50% void fraction

High-velocity free-surface flows are complex two-phase flows and limited information is available about the interactions between air and water for void fractions of about 50%. Herein a detailed experimental study was conducted in the intermediate flow region (C ∼ 50%) on a stepped spillway and the microscopic air–water flow characteristics were investigated. The results showed differences in water and droplet chord times with comparatively larger number of air chord times (0–2ms), and larger number of water chord times (2–6ms). A monotonic decrease of particle chord modes was observed with increasing bubble count rates. Several characteristic time scales were identified based upon inter-particle arrival time analyses of characteristic chord time classes as well as spectral analyses of the instantaneous void fraction signal. Chord times of 3–5ms appeared to be characteristic time scales of the intermediate flow region having similar time scales compared to the local correlation and integral turbulent time scales and to time scales associated with bubble break-up and turbulent velocity fluctuations. A further characteristic time scale of 100ms was identified in a frequency analysis of instantaneous void fraction. This time scale was of the same order of magnitude as free-surface auto-correlation time scales suggesting that the air–water flow structure was affected by the free-surface fluctuations.

A direct comparison between two independently calibrated time transfer techniques: T2L2 and GPS Common-Views

We present a direct comparison between two satellite time transfer techniques on independently calibrated links: Time Transfer by Laser Link (T2L2) and Common-Views (CV) of satellites from the Global Positioning System (GPS) constellation. The GPS CV and T2L2 links between three European laboratories where independently calibrated against the same reference point of the local timescales. For all the links the mean values of the differences between GPS CV and T2L2 are equal or below 240 ps, with standard deviations below 500 ps, mostly due to GPS CV. Almost all deviations from 0 ns are within the combined uncertainty estimates. Despite the weak number of common points obtained, due to the fact that T2L2 is weather dependent, these results are providing an unprecedented sub-ns consistency between two independently calibrated microwave and optical satellite time transfer techniques.

Effect of intermittent hypoxic training on hypoxia tolerance based on single-channel EEG

A single-channel algorithm was proposed in order to study effect of intermittent hypoxic training on hypoxia tolerance based on EEG pattern. EEG was decomposed by ensemble empirical mode decomposition into a finite number of intrinsic mode functions (IMFs) based on the intrinsic local characteristic time scale. Analytic amplitude, analytic frequency, and recurrence property quantified by recurrence quantification analysis were explored on IMFs, and the first two scales revealed difference between normal EEG and hypoxia EEG. Classification accuracy of hypoxia EEG and normal EEG could reach 67.8% before decline of neurobehavioral ability, which represented that hypoxia EEG pattern could be detected at an early stage. Classification accuracy of hypoxia EEG and normal EEG increased with time and deepened intensity of hypoxia was observed by regular shift of hypoxia EEG pattern with time in a three dimensional subspace. The reduced shift and classification accuracy after intermittent hypoxic training represented that hypoxia tolerance enhanced.

Influence of musical groove on postural sway.

Timescales of postural fluctuation reflect underlying neuromuscular processes in balance control that are influenced by sensory information and the performance of concurrent cognitive and motor tasks. An open question is how postural fluctuations entrain to complex environmental rhythms, such as in music, which also vary on multiple timescales. Musical groove describes the property of music that encourages auditory-motor synchronization and is used to study voluntary motor entrainment to rhythmic sounds. The influence of groove on balance control mechanisms remains unexplored. We recorded fluctuations in center of pressure (CoP) of standing participants (N = 40) listening to low and high groove music and during quiet stance. We found an effect of musical groove on radial sway variability, with the least amount of variability in the high groove condition. In addition, we observed that groove influenced postural sway entrainment at various temporal scales. For example, with increasing levels of groove, we observed more entrainment to shorter, local timescale rhythmic musical occurrences. In contrast, we observed more entrainment to longer, global timescale features of the music, such as periodicity, with decreasing levels of groove. Finally, musical experience influenced the amount of postural variability and entrainment at local and global timescales. We conclude that groove in music and musical experience can influence the neural mechanisms that govern balance control, and discuss implications of our findings in terms of multiscale sensorimotor coupling. (PsycINFO Database Record

Ignition by Hot Transient Jets in Confined Mixtures of Gaseous Fuels and Air

Ignition of a combustible mixture by a transient jet of hot reactive gas is important for safety of mines, prechamber ignition in IC engines, detonation initiation, and novel constant-volume combustors. The present work is a numerical study of the hot jet ignition process in a long constant-volume combustor (CVC) that represents a wave rotor channel. The hot jet of combustion products from a prechamber is injected through a converging nozzle into the main CVC chamber containing a premixed fuel-air mixture. Combustion in a two-dimensional analogue of the CVC chamber is modeled using a global reaction mechanism, a skeletal mechanism, or a detailed reaction mechanism for three hydrocarbon fuels: methane, propane, and ethylene. Turbulence is modeled using the two-equation SSTk-ωmodel, and each reaction rate is limited by the local turbulent mixing timescale. Hybrid turbulent-kinetic schemes using some skeletal reaction mechanisms and detailed mechanisms are good predictors of the experimental data. Shock wave traverse of the reaction zone is seen to significantly increase the overall reaction rate, likely due to compression heating, as well as baroclinic vorticity generation that stirs and mixes reactants and increases flame area. Less easily ignitable methane mixture is found to show slower initial reaction and greater dependence on shock interaction than propane and ethylene.

Water age, exposure time, and local flushing time in semi-enclosed, tidal basins with negligible freshwater inflow

Within the framework of tidally flushed, semi-enclosed basins with negligible freshwater inflow, and under steady periodic flow conditions, three frequently used local transport time scales to quantify the efficiency of water renewal, namely water age, exposure time, and local flushing time are studied and compared to each other. In these environments, water renewal is strongly controlled by diffusion, and it is significantly affected by the return flow (i.e., the fraction of effluent water that returns into the basin on each flood tide). The definition of water age is here modified to account for the return flow, in analogy with exposure time and local flushing time. We consider approximate time scales, whose accuracy is analyzed, in order to overcome problems related to the size of the computational domain and to reduce the computational effort. A new approximate procedure is introduced to estimate water age, which is based on the water aging rate. Also, the concept of local flushing time as a relevant time scale is introduced. Under steady periodic conditions, we demonstrate that the local flushing time quantitatively corresponds to water age, and well approximates exposure time when the flow is dominated by diffusion. Since the effort required to compute water age and exposure time is greater than that required to compute the local flushing time, the present results can also have a practical interest in the assessment of water renewal efficiency of semi-enclosed water basins. The results of a modeling study, in which the lagoon of Venice is used as a benchmark, confirm the substantial quantitative equivalence between these three transport time scales in highly diffusive environments.

THE ROLE OF THE COOLING PRESCRIPTION FOR DISK FRAGMENTATION: NUMERICAL CONVERGENCE AND CRITICAL COOLING PARAMETER IN SELF-GRAVITATING DISKS

Protoplanetary disks fragment due to gravitational instability when there is enough mass for self-gravitation, described by the Toomre parameter, and when heat can be lost at a rate comparable to the local dynamical timescale, described by t_c=beta Omega^-1. Simulations of self-gravitating disks show that the cooling parameter has a rough critical value at beta_crit=3. When below beta_crit, gas overdensities will contract under their own gravity and fragment into bound objects while otherwise maintaining a steady state of gravitoturbulence. However, previous studies of the critical cooling parameter have found dependence on simulation resolution, indicating that the simulation of self-gravitating protoplanetary disks is not so straightforward. In particular, the simplicity of the cooling timescale t_c prevents fragments from being disrupted by pressure support as temperatures rise. We alter the cooling law so that the cooling timescale is dependent on local surface density fluctuations, a means of incorporating optical depth effects into the local cooling of an object. For lower resolution simulations, this results in a lower critical cooling parameter and a disk more stable to gravitational stresses suggesting the formation of large gas giants planets in large, cool disks is generally suppressed by more realistic cooling. At our highest resolution however, the model becomes unstable to fragmentation for cooling timescales up to beta = 10.

RESISTIVE MAGNETOHYDRODYNAMICS SIMULATIONS OF THE IDEAL TEARING MODE

We study the linear and nonlinear evolution of the tearing instability on thin current sheets by means of two-dimensional numerical simulations, within the framework of compressible, resistive magnetohydrodynamics. In particular we analyze the behavior of current sheets whose inverse aspect ratio scales with the Lundquist number S as S 1=3 . This scaling has been recently recognized to yield the threshold separating fast, ideal reconnection, with an evolution and growth which are independent of S provided this is high enough, as it should be natural having the ideal case as a limit for S! 1. Our simulations conrm that the tearing instability growth rate can be as fast as 0:6 A 1 , where A is the ideal Alfv enic time set by the macroscopic scales, for our least diusive case with S = 10 7 . The expected instability dispersion relation and eigenmodes are also retrieved in the linear regime, for the values of S explored here. Moreover, in the nonlinear stage of the simulations we observe secondary events obeying the same critical scaling with S, here calculated on the local, much smaller lengths, leading to increasingly faster reconnection. These ndings strongly support the idea that in a fully dynamic regime, as soon as current sheets develop, thin and reach this critical threshold in their aspect ratio, the tearing mode is able to trigger plasmoid formation and reconnection on the local (ideal) Alfv enic timescales, as required to explain the explosive aring activity often observed in solar and astrophysical plasmas. Subject headings: plasmas { MHD { methods: numerical.

THE DEUTERIUM FRACTIONATION TIMESCALE IN DENSE CLOUD CORES: A PARAMETER SPACE EXPLORATION

The deuterium fraction [N$_2$D$^+$]/[N$_2$H$^+$], may provide information about the ages of dense, cold gas structures, important to compare with dynamical models of cloud core formation and evolution. Here we introduce a complete chemical network with species containing up to three atoms, with the exception of the Oxygen chemistry, where reactions involving H$_3$O$^+$ and its deuterated forms have been added, significantly improving the consistency with comprehensive chemical networks. Deuterium chemistry and spin states of H$_2$ and H$_3^+$ isotopologues are included in this primarily gas-phase chemical model. We investigate dependence of deuterium chemistry on model parameters: density ($n_{\rm H}$), temperature, cosmic ray ionization rate, and gas-phase depletion factor of heavy elements ($f_{\rm D}$). We also explore the effects of time-dependent freeze-out of gas-phase species and dynamical evolution of density at various rates relative to free-fall collapse. For a broad range of model parameters, the timescales to reach large values of $D_{\rm frac}^{\rm N_2H^+} \gtrsim 0.1$, observed in some low- and high-mass starless cores, are relatively long compared to the local free-fall timescale. These conclusions are unaffected by introducing time-dependent freeze-out and considering models with evolving density, unless the initial $f_{\rm D} \gtrsim$ 10. For fiducial model parameters, achieving $D_{\rm frac}^{\rm N_2H^+} \gtrsim 0.1$ requires collapse to be proceeding at rates at least several times slower than that of free-fall collapse, perhaps indicating a dynamically important role for magnetic fields in the support of starless cores and thus the regulation of star formation.

Hilbert marginal spectrum analysis for automatic seizure detection in EEG signals

In this paper, we present a new technique for automatic seizure detection in electroencephalogram (EEG) signals by using Hilbert marginal spectrum (HMS) analysis. As the EEG signal is highly nonlinear and nonstationary, the traditional Fourier analysis which expands signals in terms of sinusoids cannot appropriately represent the amplitude contribution from each frequency value. The HMS is derived from the empirical mode decomposition (EMD) which decomposes signal into a collection of intrinsic mode functions (IMFs). Since this decomposition is based on the local characteristic time scale of the signal, it can be well applied to nonlinear and nonstationary processes. In this work, the spectral entropies and energy features of frequency-bands of the rhythms using HMS analysis are extracted and fed into the support vector machine (SVM) for seizure detection of EEG signals. A final comparison between the results obtained with the developed technique and results adopted by Polat and coworkers using Fourier analysis with the same database is given to show the effectiveness of this technique for seizure detection.

THE STRUCTURAL EVOLUTION OF FORMING AND EARLY STAGE STAR CLUSTERS

We study the degree of angular substructure in the stellar position distribution of young members of Galactic star-forming regions, looking for correlations with distance from cluster center, surface number density of stars, and local dynamical age. To this end we adopt the catalog of members in 18 young ($\sim$1-3 Myr) clusters from the Massive Young Star-Forming Complex Study in Infrared and X-ray (MYStIX) Survey and the statistical analysis of the Angular Dispersion Parameter, $\delta_{\rm ADP}$. We find statistically significant correlation between $\delta_{\rm ADP}$ and physical projected distance from the center of the clusters, with the centers appearing smoother than the outskirts, consistent with more rapid dynamical processing on local dynamical, free-fall or orbital timescales. Similarly, smoother distributions are seen in regions of higher surface density, or older dynamical ages. These results indicate that dynamical processing that erases substructure is already well-advanced in young, sometimes still-forming, clusters. Such observations of the dissipation of substructure have the potential to constrain theoretical models of the dynamical evolution of young and forming clusters.

Analysis of Wave Groups in Crossing Seas Using Hilbert Huang Transformation

The random ocean waves have a natural tendencyto form groups of waves that produced due to the interaction of lower and higher frequency wave components. In this paper Hilbert Huang Transformationis considered, which is the result of the empirical mode decomposition (EMD) and the Hilbert spectral analysis (HSA). HHT uses the EMD method to decompose a signal into so-called intrinsic mode functions, and uses the HSA method to obtain instantaneous frequency data. Using EMD method, any non-stationary data set can be decomposed into a finite and often small number of components, which are intrinsic mode functions(IMF). This decomposition method operating in the time domain is adaptive and highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it can be applied to nonlinear and nonstationaryprocesses. This method is applied to the field data collected in the Natural Ocean Engineering Laboratory (NOEL, Reggio Calabria, Italy) and results on the wave groups in crossing sea are discussed.

A LAMMPS implementation of volume–temperature replica exchange molecular dynamics

A driver module for executing volume–temperature replica exchange molecular dynamics (VTREMD) was developed for the LAMMPS package. As a patch code, the VTREMD module performs classical molecular dynamics (MD) with Monte Carlo (MC) decisions between MD runs. The goal of inserting the MC step was to increase the breadth of sampled configurational space. In this method, states receive better sampling by making temperature or density swaps with their neighboring states. As an accelerated sampling method, VTREMD is particularly useful to explore states at low temperatures, where systems are easily trapped in local potential wells. As functional examples, TIP4P/Ew and TIP4P/2005 water models were analyzed using VTREMD. The phase diagram in this study covered the deeply supercooled regime, and this test served as a suitable demonstration of the usefulness of VTREMD in overcoming the slow dynamics problem. To facilitate using the current code, attention was also paid on how to optimize the exchange efficiency by using grid allocation. VTREMD was useful for studying systems with rough energy landscapes, such as those with numerous local minima or multiple characteristic time scales. Program summaryProgram title: vttemperCatalogue identifier: AEVB_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEVB_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 49706No. of bytes in distributed program, including test data, etc.: 1249424Distribution format: tar.gzProgramming language: C++/MPI.Computer: Tested on Intel X86 and AMD64 architectures. Should be operational on any computer with a C++ compiler.Operating system: Tested on Linux. Should run on any platform with C++ and MPI library.Has the code been vectorized or parallelized?: Yes. 1 to N processors may be used.RAM: Depends on the system size and how the program is partitioned.Classification: 16.13.External routines: LAMMPS (http://lammps.sandia.gov)Nature of problem: The code implements volume–temperature replica exchange molecular dynamics for LAMMPS. Each replica has its own temperature and density. A two-dimensional temperature–density grid is constructed.Solution method: Extending the ability of the existing temper command in LAMMPS to handle replicas of two state variables.Restrictions: The code is based on LAMMPS. A well-designed grid on temperature and density is required.Running time: Running time depends on the system size and the complexity of the problem. Using 8 processors the test run takes approximately 1 minute.

Method of Common View Based on Digital Satellite Television

This paper apply satellite digital television signal for common view based on the DVB-S standard. By choosing some information from the signal as timing signal, we can get the arriving time of timing signal on local time scale. At last, we use the arriving time and some necessary correct massage to get the time difference between two locations.

Local fault detection in helical gears via vibration and acoustic signals using EMD based statistical parameter analysis

Gear is a vital transmission element, finding numerous applications in small, medium and large machinery. Excessive loads, speeds and improper operating conditions may cause defects on their bearing surfaces, thereby triggering abnormal vibrations in whole machine structures. This paper describes the implementation of empirical mode decomposition (EMD) method for monitoring simulated faults using vibration and acoustic signals in a two stage helical gearbox. By using EMD method, a complicated signal can be decomposed into a number of intrinsic mode functions (IMF) based on the local characteristic time scale of the signal. Vibration and acoustic signals are decomposed to extract higher order statistical parameters. Results demonstrate the effectiveness of EMD based statistical parameters to diagnose severity of local faults on helical gear tooth. Kurtosis values from EMD and that obtained from vibration and acoustic signals are compared to demonstrate the superiority of EMD based technique.

Toward enhanced understanding and projections of climate extremes using physics-guided data mining techniques

Abstract. Extreme events such as heat waves, cold spells, floods, droughts, tropical cyclones, and tornadoes have potentially devastating impacts on natural and engineered systems and human communities worldwide. Stakeholder decisions about critical infrastructures, natural resources, emergency preparedness and humanitarian aid typically need to be made at local to regional scales over seasonal to decadal planning horizons. However, credible climate change attribution and reliable projections at more localized and shorter time scales remain grand challenges. Long-standing gaps include inadequate understanding of processes such as cloud physics and ocean–land–atmosphere interactions, limitations of physics-based computer models, and the importance of intrinsic climate system variability at decadal horizons. Meanwhile, the growing size and complexity of climate data from model simulations and remote sensors increases opportunities to address these scientific gaps. This perspectives article explores the possibility that physically cognizant mining of massive climate data may lead to significant advances in generating credible predictive insights about climate extremes and in turn translating them to actionable metrics and information for adaptation and policy. Specifically, we propose that data mining techniques geared towards extremes can help tackle the grand challenges in the development of interpretable climate projections, predictability, and uncertainty assessments. To be successful, scalable methods will need to handle what has been called "big data" to tease out elusive but robust statistics of extremes and change from what is ultimately small data. Physically based relationships (where available) and conceptual understanding (where appropriate) are needed to guide methods development and interpretation of results. Such approaches may be especially relevant in situations where computer models may not be able to fully encapsulate current process understanding, yet the wealth of data may offer additional insights. Large-scale interdisciplinary team efforts, involving domain experts and individual researchers who span disciplines, will be necessary to address the challenge.

Bi-spectrum based-EMD applied to the non-stationary vibration signals for bearing faults diagnosis

Empirical mode decomposition (EMD) has been widely applied to analyze vibration signals behavior for bearing failures detection. Vibration signals are almost always non-stationary since bearings are inherently dynamic (e.g., speed and load condition change over time). By using EMD, the complicated non-stationary vibration signal is decomposed into a number of stationary intrinsic mode functions (IMFs) based on the local characteristic time scale of the signal. Bi-spectrum, a third-order statistic, helps to identify phase coupling effects, the bi-spectrum is theoretically zero for Gaussian noise and it is flat for non-Gaussian white noise, consequently the bi-spectrum analysis is insensitive to random noise, which are useful for detecting faults in induction machines. Utilizing the advantages of EMD and bi-spectrum, this article proposes a joint method for detecting such faults, called bi-spectrum based EMD (BSEMD). First, original vibration signals collected from accelerometers are decomposed by EMD and a set of IMFs is produced. Then, the IMF signals are analyzed via bi-spectrum to detect outer race bearing defects. The procedure is illustrated with the experimental bearing vibration data. The experimental results show that BSEMD techniques can effectively diagnosis bearing failures.

Stiffness 1952–2012: Sixty years in search of a definition

Although stiff differential equations is a mature area of research in scientific computing, a rigorous and computationally relevant characterization of stiffness is still missing. In this paper, we present a critical review of the historical development of the notion of stiffness, before introducing a new approach. A functional, called the stiffness indicator, is defined terms of the logarithmic norms of the differential equation’s vector field. Readily computable along a solution to the problem, the stiffness indicator is independent of numerical integration methods, as well as of operational criteria such as accuracy requirements. The stiffness indicator defines a local reference time scale $$\Delta t$$ , which may vary with time and state along the solution. By comparing $$\Delta t$$ to the range of integration $$T$$ , a large stiffness factor $$T/\Delta t$$ is a necessary condition for stiffness. In numerical computations, $$\Delta t$$ can be compared to the actual step size $$h$$ , whose stiffness factor $$h/\Delta t$$ depends on the choice of integration method. Thus $$\Delta t$$ embodies the mathematical aspects of stiffness, while $$h$$ accounts for its numerical and operational aspects.To demonstrate the theory, a number of highly nonlinear test problems are solved. We show, inter alia, that the stiffness indicator is able to distinguish the complex and rapidly changing behavior at (locally unstable) turning points, such as those observed in the van der Pol and Oregonator equations. The new characterization is mathematically rigorous, and in full agreement with observations in practical computations.