Exponential Timescale Research Articles

Falling Body Motion in Time Scale Calculus

The falling body problem for different time scales, such as ℝ, ℤ, hℤ, qℕ0, ℙc,d is the subject of this study. To deal with this problem, we use time-scale calculus. Time scale dynamic equations are used to define the falling body problem. The exponential time scale function is used for the solutions of these problems. The solutions of the falling body problem in each of these time scales are found. Moreover, we also test our mathematical results with numerical simulations.

On codimension one stability of the soliton for the 1D focusing cubic Klein-Gordon equation

We consider the codimension one asymptotic stability problem for the soliton of the focusing cubic Klein-Gordon equation on the line under even perturbations. The main obstruction to full asymptotic stability on the center-stable manifold is a small divisor in a quadratic source term of the perturbation equation. This singularity is due to the threshold resonance of the linearized operator and the absence of null structure in the nonlinearity. The threshold resonance of the linearized operator produces a one-dimensional space of slowly decaying Klein-Gordon waves, relative to local norms. In contrast, the closely related perturbation equation for the sine-Gordon kink does exhibit null structure, which makes the corresponding quadratic source term amenable to normal forms (see Lührmann and Schlag [Duke Math. J. 172 (2023), pp. 2715–2820]). The main result of this work establishes decay estimates up to exponential time scales for small “codimension one type” perturbations of the soliton of the focusing cubic Klein-Gordon equation. The proof is based upon a super-symmetric approach to the study of modified scattering for 1D nonlinear Klein-Gordon equations with Pöschl-Teller potentials from Lührmann and Schlag [Duke Math. J. 172 (2023), pp. 2715–2820], and an implementation of a version of an adapted functional framework introduced by Germain and Pusateri [Forum Math. Pi 10 (2022), p. 172].

Defining Mammalian Lifespan through Epigenetic Aging Timescales

The lifespans of mammalian species vary across orders of magnitude, with the shortest on the order of a year and the longest more than one hundred years. These lifespans are influenced by both genetic and environmental factors. Here we asked whether we can define a molecular process that can be used to define the intrinsic molecular lifespan of a species that is largely independent of environmental factors. To address this question, we have focused on ‘epigenetic clocks’ - highly accurate age-predicting biomarkers based on DNA methylation. Our previous research has demonstrated that the alterations in DNA methylation related to age are non-linear, changing rapidly early in life and slowing down with advancing age. We have proposed the use of saturating exponential functions to represent these changes, which tend to stabilize at terminal methylation levels towards the end of an organism's lifespan. Our current study expands upon this by examining the exponential aging timescales across various mammalian species. We show that the DNA methylation trajectories of a broad range of species, ranging from mice to humans, adhere to a saturating exponential function. Furthermore, we find the timescale of this exponential decay to be about one third of a species’ lifespan. This striking and novel observation implies that we can define an intrinsic molecular lifespan of a species that is largely unaffected by environmental factors. Although the exact mechanisms behind the variation in species-specific rates remain unclear, we hypothesize that they may be linked to the distinct metabolic rates found in each species.

Prethermalization and the Local Robustness of Gapped Systems.

We prove that prethermalization is a generic property of gapped local many-body quantum systems, subjected to small perturbations, in any spatial dimension. More precisely, let H_{0} be a Hamiltonian, spatially local in d spatial dimensions, with a gap Δ in the many-body spectrum; let V be a spatially local Hamiltonian consisting of a sum of local terms, each of which is bounded by ε≪Δ. Then, the approximation that quantum dynamics is restricted to the low-energy subspace of H_{0} is accurate, in the correlation functions of local operators, for stretched exponential timescale τ∼exp[(Δ/ε)^{a}] for any a<1/(2d-1). This result does not depend on whether the perturbation closes the gap. It significantly extends previous rigorous results on prethermalization in models where H_{0} was frustration-free. We infer the robustness of quantum simulation in low-energy subspaces, the existence of athermal "scarred" correlation functions in gapped systems subject to generic perturbations, the long lifetime of false vacua in symmetry broken systems, and the robustness of quantum information in non-frustration-free gapped phases with topological order.

The Rapid Onset of Stellar Bars in the Baryon-dominated Centers of Disk Galaxies

Recent observations of high-redshift galactic disks (z ≈ 1–3) show a strong negative trend in the dark-matter (DM) fraction f DM with increasing baryon surface density. For this to be true, the inner baryons must dominate over DM in early massive galaxies, as observed in the Milky Way today. If disks are dominant at early times, we show that stellar bars form promptly within these disks, leading to a high bar fraction. New James Webb Space Telescope observations provide the best evidence for mature stellar bars in this redshift range. The disk mass fraction f disk within R s = 2.2 R disk is the dominant factor determining how rapidly a bar forms. Using 3D hydro simulations of halo-bulge-disk galaxies, we confirm the “Fujii relation” for the exponential dependence of the bar formation time τ bar as a function of f disk. For f disk > 0.3, the bar formation time declines exponentially fast with increasing f disk. Instead of Fujii's arbitrary threshold for when a bar appears, for the first time, we exploit the exponential growth timescale associated with the positive feedback cycle as the bar emerges from the underlying disk. A modified, mass-dependent trend is observed for halos relevant to systems at cosmic noon (), where the bar onset is slower for higher-mass halos at a fixed f disk. If baryons dominate over DM within R ≈ R s , we predict that a high fraction of bars will be found in high-redshift disks long before z = 1.

Coexistence times in the Moran process with environmental heterogeneity

Populations evolve in spatially heterogeneous environments. While a certain trait might bring a fitness advantage in some patch of the environment, a different trait might be advantageous in another patch. Here, we study the Moran birth–death process with two types of individuals in a population stretched across two patches of size N , each patch favouring one of the two types. We show that the long-term fate of such populations crucially depends on the migration rate μ between the patches. To classify the possible fates, we use the distinction between polynomial (short) and exponential (long) timescales. We show that when μ is high then one of the two types fixates on the whole population after a number of steps that is only polynomial in N . By contrast, when μ is low then each type holds majority in the patch where it is favoured for a number of steps that is at least exponential in N . Moreover, we precisely identify the threshold migration rate μ ⋆ that separates those two scenarios, thereby exactly delineating the situations that support long-term coexistence of the two types. We also discuss the case of various cycle graphs and we present computer simulations that perfectly match our analytical results.

Probing Galaxy Evolution in Massive Clusters Using ACT and DES: Splashback as a Cosmic Clock

Abstract We measure the projected number density profiles of galaxies and the splashback feature in clusters selected by the Sunyaev–Zel’dovich effect from the Advanced Atacama Cosmology Telescope (AdvACT) survey using galaxies observed by the Dark Energy Survey (DES). The splashback radius is consistent with CDM-only simulations and is located at 2.4 − 0.4 + 0.3 Mpc h − 1 . We split the galaxies on color and find significant differences in their profile shapes. Red and green-valley galaxies show a splashback-like minimum in their slope profile consistent with theory, while the bluest galaxies show a weak feature at a smaller radius. We develop a mapping of galaxies to subhalos in simulations and assign colors based on infall time onto their hosts. We find that the shift in location of the steepest slope and different profile shapes can be mapped to the average time of infall of galaxies of different colors. The steepest slope traces a discontinuity in the phase space of dark matter halos. By relating spatial profiles to infall time, we can use splashback as a clock to understand galaxy quenching. We find that red galaxies have on average been in clusters over 3.2 Gyr, green galaxies about 2.2 Gyr, while blue galaxies have been accreted most recently and have not reached apocenter. Using the full radial profiles, we fit a simple quenching model and find that the onset of galaxy quenching occurs after a delay of about a gigayear and that galaxies quench rapidly thereafter with an exponential timescale of 0.6 Gyr.

Discovery of a strong 6.6 keV emission feature from EXO 1745−248 after the superburst in 2011 October

Abstract We discover an unidentified strong emission feature in the X-ray spectrum of EXO 1745−248 obtained by RXTE at 40 hr after the peak of a superburst. The structure was centered at 6.6 keV and significantly broadened with a large equivalent width of 4.3 keV, corresponding to a line photon flux of 4.7 × 10−3 ph cm−2 s−1. The 3–20 keV spectrum was reproduced successfully by a power-law continuum with narrow and broad (2.7 keV in full width at half maximum) Gaussian emission components. Alternatively, the feature can be described by four narrow Gaussians, centered at 5.5 keV, 6.5 keV, 7.5 keV, and 8.6 keV. Considering the strength and shape of the feature, it is unlikely to have originated from reflection of the continuum X-rays by some optically thick material, such as an accretion disk. Moreover, the intensity of the emission structure decreased significantly with an exponential time scale of 1 hr. The feature was not detected in an INTEGRAL observation performed 10 hr before the RXTE observation with a line flux upper limit of 1.5 × 10−3 ph cm−2 s−1. The observed emission structure is consistent with gravitationally redshifted charge exchange emission from Ti, Cr, Fe, and Co. We suggest that the emission results from a charge exchange interaction between a highly metal-enriched fall-back ionized burst wind and an accretion disk, at a distance of ∼60 km from the neutron star. If this interpretation is correct, the results provide new information on nuclear burning processes during thermonuclear X-ray bursts.

Evaluating and Optimizing Surface Soil Moisture Drydowns in the ORCHIDEE Land Surface Model at In Situ Locations

AbstractThe rate at which land surface soils dry following rain events is an important feature of terrestrial models. It determines, for example, the water availability for vegetation, the occurrences of droughts, and the surface heat exchanges. As such, surface soil moisture (SSM) “drydowns,” i.e., the SSM temporal dynamics following a significant rainfall event, are of particular interest when evaluating and calibrating land surface models (LSMs). By investigating drydowns, characterized by an exponential decay time scale τ, we aim to improve the representation of SSM in the ORCHIDEE global LSM. We consider τ calculated over 18 International Soil Moisture Network sites found within the footprint of FLUXNET towers, covering different vegetation types and climates. Using the ORCHIDEE LSM, we compare τ from the modeled SSM time series to values computed from in situ SSM measurements. We then assess the potential of using τ observations to constrain some water, carbon, and energy parameters of ORCHIDEE, selected using a sensitivity analysis, through a standard Bayesian optimization procedure. The impact of the SSM optimization is evaluated using FLUXNET evapotranspiration and gross primary production (GPP) data. We find that the relative drydowns of SSM can be well calibrated using observation-based τ estimates, when there is no need to match the absolute observed and modeled SSM values. When evaluated using independent data, τ-calibration parameters were able to improve drydowns for 73% of the sites. Furthermore, the fit of the model to independent fluxes was only minutely changed. We conclude by considering the potential of global satellite products to scale up the experiment to a global-scale optimization.

Approximate Normal Forms via Floquet–Bloch Theory: Nehorošev Stability for Linear Waves in Quasiperiodic Media

We study the long-time behavior of the Schr{\"o}dinger flow in a heterogeneous potential $\lambda$V with small intensity 0<$\lambda$$\ll$1 (or alternatively at high frequencies). The main new ingredient, which we introduce in the general setting of a stationary ergodic potential, is an approximate stationary Floquet--Bloch theory that is used to put the perturbed Schr{\"o}dinger operator into approximate normal form. We apply this approach to quasiperiodic potentials and establish a Nehoro{\v s}ev-type stability result. In particular, this ensures asymptotic ballistic transport up to a stretched exponential timescale exp($\lambda$--1/s) for some s>0. More precisely, the approximate normal form leads to an accurate long-time description of the Schr{\"o}dinger flow as an effective unitary correction of the free flow. The approach is robust and generically applies to linear waves. For classical waves, for instance, this allows to extend diffractive geometric optics to quasiperiodically perturbed media.

Development of a method of adaptive control of military radio network parameters

A method of adaptive control of military radio network parameters has been developed. This method allows predicting suppressed frequencies by electronic warfare devices, determining the topology of the military radio network. Also, this method allows determining rational routes of information transmission and operating mode of radio communications. Forecasting of the electronic environment is characterized by recirculation of input data for one count, resampling on a logarithmic time scale, finding a forecast for the maximum value of entropy and resampling the forecast on the exponential time scale. The developed method allows choosing a rational network topology. The choice of topology of the military radio communication system is based on the method of ant multi-colony system. The main idea of the new option of ant colony optimization is that instead of one colony of the traditional ant algorithm several colonies are used that work together in a common search space. However, this procedure additionally takes into account the type of a priori uncertainty and the evaporation coefficient of the pheromone level. The proposed method allows choosing a rational route for information transmission. The proposed procedure is based on an improved DSR algorithm. This method uses several operating modes of radio communications, namely the technology of multi-antenna systems with noise-like signals, with pseudo-random adjustment of the operating frequency and with orthogonal frequency multiplexing. The developed method provides a gain of 10‒16 % compared to conventional management approaches

Fluctuation Bounds for the Max-Weight Policy with Applications to State Space Collapse

We consider a multihop switched network operating under a max-weight scheduling policy and show that the distance between the queue length process and a fluid solution remains bounded by a constant multiple of the deviation of the cumulative arrival process from its average. We then exploit this result to prove matching upper and lower bounds for the time scale over which additive state space collapse (SSC) takes place. This implies, as two special cases, an additive SSC result in diffusion scaling under non-Markovian arrivals and, for the case of independent and identically distributed arrivals, an additive SSC result over an exponential time scale.

Research on time scale algorithm based on hydrogen masers

In order to ensure the long-term stability of the time scale, the traditional timekeeping clock ensemble is mainly composed of a cesium clock and a few hydrogen masers. Since 2014, the Bureau International des Poids et Mesures (BIPM) has changed the weighting method of atomic clocks, using the predictability of atomic clocks to weight the global atomic clocks to obtain the International Atomic Time (TAI) and Coordinated Universal Time (UTC). Because of the good predictability of hydrogen masers, less than one third of the number of atomic clocks in TAI/UTC calculation is hydrogen masers which has gained 75% weight. Effective utilization of hydrogen masers has become a research hotspot in timekeeping laboratories. In order to give full play to the advantages of hydrogen masers in timekeeping, the time scale of hydrogen masers is tested in this paper. Firstly, the frequency drift parameters of hydrogen masers are dynamically estimated by using the minimum error theory. Then the estimated parameters are applied to a real-time exponential filtering time scale algorithm. The results show that the stability of the time scale produced by this method can reach 6e-15/day, and the absolute maximum deviation from TA(NTSC) within a month can be kept within 5 ns, which is better than the time scales produced by a traditional fixed frequency drift parameters method and the classical weighted averaging algorithm ALGOS.

Pulsar Glitch Detection with a Hidden Markov Model

Abstract Pulsar timing experiments typically generate a phase-connected timing solution from a sequence of times of arrival (TOAs) by absolute pulse numbering, i.e., by fitting an integer number of pulses between TOAs in order to minimize the residuals with respect to a parameterized phase model. In this observing mode, rotational glitches are discovered, when the residuals of the no-glitch phase model diverge after some epoch, and glitch parameters are refined by Bayesian follow-up. Here, we present an alternative, complementary approach which tracks the pulse frequency f and its time derivative with a hidden Markov model (HMM), whose dynamics include stochastic spin wandering (timing noise) and impulsive jumps in f and (glitches). The HMM tracks spin wandering explicitly, as a specific realization of a discrete-time Markov chain. It discovers glitches by comparing the Bayes factor for glitch and no-glitch models. It ingests standard TOAs for convenience, and being fully automated, allows performance bounds to be calculated quickly via Monte Carlo simulations. Practical, user-oriented plots of the false-alarm probability and detection threshold (e.g., minimum resolvable glitch size) versus observational scheduling parameters (e.g., TOA uncertainty, mean delay between TOAs) and glitch parameters (e.g., transient and permanent jump sizes, exponential recovery timescale) are presented. The HMM is also applied to ∼1 yr of real data bracketing the 2016 December 12 glitch in PSR J0835−4510 as a proof of principle. It detects the known glitch and confirms that no other glitch exists in the same data with size ≳10−7 f.

Year-ahead predictability of South Asian Summer Monsoon precipitation

Since the South Asia Summer Monsoon is the main source of water for a densely cultivated and climate-sensitive region, its predictability has long been the target of research. This work estimates the predictability horizon of monsoon precipitation amount by systematically comparing statistical forecasts made using information from different lead times before the monsoon start. Linear and nonlinear prediction methods are considered that use the leading modes of the global sea surface temperature field to forecast monsoon-season (June–September) total precipitation on a 0.5° grid over South Asia, where each method is trained on data from 1901 to 1996 and evaluated on data from 1997 to 2017. Forecasts were found to outperform a climatology baseline up to at least 1 year ahead, with a nonlinear method (random forest) on average outperforming linear regression with group lasso, although with greater variability in skill across locations and years. Forecast performance measures (fractional reduction in root mean square error and information skill score) decreased with increasing lead time following exponential decay timescales of 5–12 months, depending on the performance measure and forecast method. Even at lead times of several years, there was some forecast skill compared to climatology, as a result of the impact of long-term climate change on monsoon precipitation. The results suggest that monsoon prediction is possible with longer lead times than generally attempted now.

Conditional quenching: a detailed look at the SFR−density relation at $z$ ∼ 0.9 from ORELSE

We present a study of the star-formation rate (SFR)-density relation at z ~ 0.9 using data drawn from the Observations of Redshift Evolution in Large Scale Environments (ORELSE) survey. We find that SFR does depend on environment, but only for intermediate-stellar mass galaxies (10^10.1 < M* / Msol < 10^10.8) wherein the median SFR at the highest densities is 0.2-0.3 dex less than at lower densities at a significance of 4 sigma. Interestingly, mass does not drive SFR; galaxies that are more/less massive have SFRs that vary at most by ~20% across all environments showing no statistically significant dependence. We further split galaxies into low-redshift (z ~ 0.8) and high-redshift (z ~ 1.05) subsamples and observe nearly identical behavior. We devise a simple toy model to explore possible star-formation histories (SFHs) for galaxies evolving between these redshifts. The key assumption in this model is that star-forming galaxies in a given environment-stellar mass bin can be described as a superposition of two exponential timescales (SFR ~ e^(-t/tau)): a long-tau timescale with tau = 4 Gyr to simulate "normal" star-forming galaxies, and a short-tau timescale with free tau (between 0.3 < tau/Gyr < 2) to simulate galaxies on a quenching trajectory. In general we find that galaxies residing in low/high environmental densities are more heavily weighted to the long-tau/short-tau pathways respectively, which we argue is a signature of environmental quenching. Furthermore, for intermediate-stellar mass galaxies this transition begins at intermediate-density environments suggesting that environmental quenching is relevant in group-like halos and/or cluster infall regions.

USING TIME SCALES WHILE APPROXIMATING THE LENGTH OF COMPUTER NETWORKS

The subject of the research is to predict the queue length for the communication device of a high-speed computer network with non-Gaussian traffic. The goal of this article is to examine the probabilities of the application of time scales used to study the organization of queues of modern high-speed computer networks. The following methods were used: the fractal analysis, scaling methods, methods of approximation. The following results were achieved: the results of the time scale selection for constructing adequate models of modern traffic were presented. The use of such models, in particular, enables studying the dynamics of the queues of active network devices, which is important for planning and distributing the network load. The use of statistical characteristics of traffic on a small number of time scales enables expanding theoretical concepts for critical time scales, which makes this approach applicable to any traffic process including the long-term traffic. In addition, the issues of describing the behaviour of queue tails for modern high-speed computer networks are considered and the properties of the proposed model approximations are determined. The analysis of the independent Gaussian model of a wavelet domain and the multifractal wavelet model showed the advantage of the first one for the fractal traffic and a slight discrepancy in the results for traffic close to the Gaussian one. Conclusions . Various approaches to the selection of time scales used in the study of the organization of queues of modern high-speed data networks were studied. The effect of the necessary accuracy and computational power required for calculating the maximum approximation were analyzed and it was established that exponential time scales are optimal for the fractal traffic. The impact of the tails of distributions in different time scales on the process of queue organization was also shown. It was noted that in the context of non-Gaussian traffic scenarios, the correlation structure (both short-term and long-term ones) does not describe the queues behaviour adequately enough.

Application of Electrochemical Devices to Characterize the Dynamic Actions of Helicases on DNA.

Much remains to be understood about the kinetics and thermodynamics of DNA helicase binding and activity. Here, we utilize probe-modified DNA monolayers on multiplexed gold electrodes as a sensitive recognition element and morphologically responsive transducer of helicase-DNA interactions. The electrochemical signals from these devices are highly sensitive to structural distortion of the DNA produced by the helicases. We used this DNA electrochemistry to distinguish the details of the DNA interactions of three distinct XPB helicases, which belong to the superfamily-2 of helicases. Clear changes in DNA melting temperature and duplex stability were observed upon helicase binding, shifts that could not be observed with conventional UV-visible absorption measurements. Binding dissociation constants were estimated in the range from 10 to 50 nM and correlated with observations of activity. ATP-stimulated DNA unwinding activity was also followed, revealing exponential time scales and distinct time constants associated with conventional and molecular wrench modes of operation further confirmed by crystal structures. These devices thus provide a sensitive measure of the structural thermodynamics and kinetics of helicase-DNA interactions.

The Glitches and Rotational History of the Highly Energetic Young Pulsar PSR J0537–6910

Abstract We present a timing and glitch analysis of the young X-ray pulsar PSR J0537−6910, located within the Large Magellanic Cloud, using 13 yr of data from the now-decommissioned Rossi X-ray Timing Explorer. Rotating with a spin period of 16 ms, PSR J0537−6910 is the fastest-spinning and most energetic young pulsar known. It also displays the highest glitch activity of any known pulsar. We have found 42 glitches over the data span, corresponding to a glitch rate of 3.2 yr−1, with an overall glitch activity rate of . The high glitch frequency has allowed us to study the glitch behavior in ways that are inaccessible in other pulsars. We observe a strong linear correlation between spin frequency glitch magnitude and wait time to the following glitch. We also find that the post-glitch spin-down recovery is well described by a single two-component model fit to all glitches for which we have adequate input data. This consists of an exponential amplitude , decay timescale s, and linear slope . The latter slope corresponds to a second frequency derivative , from which we find an implied braking index . We also present a maximum likelihood technique for searching for periods in event-time data, which we used to both confirm previously published values and determine rotation frequencies in later observations. We discuss the implied constraints on glitch models from the observed behavior of this system, which we argue cannot be fully explained in the context of existing theories.

On the behavior of diffusion processes with traps

We consider processes that coincide with a given diffusion process outside a finite collection of domains. In each of the domains, there is, additionally, a large drift directed towards the interior of the domain. We describe the limiting behavior of the processes as the magnitude of the drift tends to infinity, and thus the domains become trapping, with the time to exit the domains being exponentially large. In particular, in exponential time scales, metastable distributions between the trapping regions are considered.