Natural Time Scale Research Articles

Inconsistencies between observed, reconstructed, and simulated precipitation indices for England since the year 1650 CE

Abstract. The scarcity of long instrumental records, uncertainty in reconstructions, and insufficient skill in model simulations hamper assessing how regional precipitation changed over past centuries. Here, we use standardized precipitation data to compare a regional climate simulation, reconstructions, and long observational records of seasonal (March to July) mean precipitation in England and Wales over the past 350 years. The Standardized Precipitation Index is a valuable tool for assessing agreement between the different sources of information, as it allows for a comparison of the temporal evolution of percentiles of the precipitation distributions. These evolutions are not consistent among reconstructions, a regional simulation, and instrumental observations for severe and extreme dry and wet conditions. The lack of consistency between the different data sets may be due to the dominance of internal climate variability over the impact of natural exogenous forcing conditions on multi-decadal timescales. The disagreement between sources of information reduces our confidence in inferences about the origins of hydroclimate variability for small regions. However, it is encouraging that there is still some agreement between a regional simulation and observations. Our results emphasize the complexity of hydroclimate changes during the recent centuries and stress the necessity of a thorough understanding of the processes affecting forced and unforced precipitation variability.

Quasi-static large deviations

Nous considérons l’exclusion simple symétrique avec des frontières ouvertes en contact avec des réservoirs de particules à différentes densités. Les densités des réservoirs changent plus lentement par rapport à l’échelle de temps naturelle où le système atteint l’état stationnaire. Cela donne lieu à la limite hydrodynamique quasi-statique. Nous étudions ici les grandes déviations par rapport à cette limite pour le champ de densité de particules et le courant total. Nous identifions explicitement le fonctionnelle de grandes déviations et nous prouvons qu’il satisfait une relation de fluctuation.

Eliciting features of 2D greenwater overtopping of a fixed box using modified dam break models

Greenwater overtopping of a 2D fixed rectangular box due to focused wave groups is investigated using Computational Fluid Dynamics (CFD). Simulations span a wide parameter space, such that a range of overtopping types previously observed in experiments - including dam-break, plunging plus dam-break and hammer fist events - are observed. For each greenwater event the horizontal momentum flux and overtopping volume are computed, as these represent integrated quantities linked to damage potential on offshore facilities. These values are compared to simplified predictions based on the classical dam-break model with the dam height based on a run-up calculation on the box. It is found that these predictions deviate from measurements made in the CFD simulations because the classical model omits physics evident during overtopping events. Modifications to the classical dam-break model are presented to account for (i) the finite duration of an overtopping event; (ii) the finite quantity of water in the crest of a wave which exceeds the freeboard; (iii) the local geometry at the edge of the box; and (iv) the horizontal momentum in the crest of a wave which exceeds the freeboard. Insight gained from the first of these corrections leads to a new parameter- the relative overtopping duration T', defined as the ratio of the duration for which fluid exceeds the freeboard to the natural time scale for runout of a dam with height equal to maximum run-up above freeboard. It is found that this new parameter dramatically reduces scatter in the integrated quantities. The results suggest that this new parameter, which combines freeboard exceedance and overtopping duration, may be an efficient indicator for screening metocean conditions to identify design sea states.

The evolution of resonance: a multiscale approach to the effect of nonlinearity, frequency dispersion and geometry

Nonlinear resonant oscillations in continuous media contain two natural time scales: the travel time in the medium and the ‘slow’ time defined by the small nonlinearity. A multiscale approach is used to describe the evolution to a periodic state. We focus on three basic experiments that define nonlinear resonant oscillations in continuous media: a gas in both a straight tube and a tube of variable cross-section, and shallow water in a tank. The outcomes of these experiments are described and the mathematical techniques that show the evolution to the final periodic states are given in some detail.

Auger-induced charge migration

Novel perspectives of controlling molecular systems have recently arisen from the possibility of generating attosecond pulses in the ultraviolet regime and tailoring electron dynamics in its natural time scale. The cornerstone mechanism is the so-called charge migration, he production of a coherent charge transfer with subfemtosecond oscillations across a molecule. Typically, charge migration is induced by the ionization of valence molecular orbitals. However, recent technological developments allow the generation of attosecond pulses in the x-ray regime. In this case, the absorption of photons creates core-hole states. In light elements, core-hole states mainly decay by Auger processes that, driven by electron correlations, involve valence orbitals. We theoretically demonstrate in a fluoroacetylene molecule a double-hole charge migration triggered by attosecond core-electron photoionization, followed by Auger electron relaxations. This opens a new route for inducing with x rays charge transfer processes in the subfemtosecond time scale.

Transient mixed convection in a channel with two facing discretely heated semicircular cavities: Buoyancy, inclination angle, and channel aspect ratio effects

ABSTRACTSpace-averaged surface temperature distributions and overall Nusselt number measurements have been carried out to study the transient mixed convection heat transfer in a channel with two facing and symmetrically heated semicircular cavities. Effects of buoyancy, channel orientation, and channel aspect ratio on thermal behavior have been investigated from Re 500 to 1,500. Depending on the parametric set, steady, oscillatory, and irregular thermal regimes have been identified. The natural frequencies and time scales of the oscillatory regimes have been obtained using spectral analysis. Results show that with increase in channel aspect ratio, the heat transfer performance reduces for all inclination angles.

The Korteweg–de Vries, Burgers and Whitham limits for a spatially periodic Boussinesq model

We are interested in the Korteweg–de Vries (KdV), Burgers and Whitham limits for a spatially periodic Boussinesq model with non-small contrast. We prove estimates of the relations between the KdV, Burgers and Whitham approximations and the true solutions of the original system that guarantee these amplitude equations make correct predictions about the dynamics of the spatially periodic Boussinesq model over their natural timescales. The proof is based on Bloch wave analysis and energy estimates and is the first justification result of the KdV, Burgers and Whitham approximations for a dispersive partial differential equation posed in a spatially periodic medium of non-small contrast.

Real‐Time Imaging of Ultrafast Charge Dynamics in Tetrafluoromethane from Attosecond Pump‐Probe Photoelectron Spectroscopy

A pump-probe experiment in the tetrafluoro-methane (CF4 ) molecule has been theoretically simulated, allowing one to access electron dynamics in its natural time scale: the attosecond. The chosen pump and probe pulses can be currently produced in most attosecond laboratories. In this scheme, CF4 is first ionized by an extreme UV (XUV) attosecond pulse and the charge dynamics induced in the corresponding cation is probed with a few-femtosecond visible light (VIS) pulse. We demonstrate that modulations in the calculated photoelectron spectra with the pump-probe delay reflect the dynamics of the XUV-induced electronic wave packet. In particular, from the analysis of these modulations in the interval of time delays where the pump and probe pulses do not overlap any more, one has access to the amplitudes and phases of the different components of the electronic wave packet generated by the attosecond pulse. These reflect a complex dynamics that basically consists of very fast charge fluctuations occurring all over the molecule without any preference for a particular molecular site.

Attosecond Pump-Probe Spectroscopy of Charge Dynamics in Tryptophan.

Attosecond pump-probe experiments performed in small molecules have allowed tracking charge dynamics in the natural time scale of electron motion. That this is also possible in biologically relevant molecules is still a matter of debate, because the large number of available nuclear degrees of freedom might destroy the coherent charge dynamics induced by the attosecond pulse. Here we investigate extreme ultraviolet-induced charge dynamics in the amino acid tryptophan. We find that, although nuclear motion and nonadiabatic effects introduce some decoherence in the moving electron wave packet, these do not significantly modify the coherence induced by the attosecond pulse during the early stages of the dynamics, at least for molecules in their equilibrium geometry. Our conclusions are based on elaborate theoretical calculations and the experimental observation of sub-4 fs dynamics, which can only be reasonably assigned to electronic motion. Hence, attosecond pump-probe spectroscopy appears as a promising approach to induce and image charge dynamics in complex molecules.

A Study on the France Climate and Natural Disasters France Monsoon Time Scale, France National Geoscope Project Irlapatism-A New Hypothetical Model of Cosmology

A Study on the France Climate and Natural Disasters France Monsoon Time Scale, France National Geoscope Project Irlapatism-A New Hypothetical Model of Cosmology

Hyperelastic modeling of the combined effects of tissue swelling and deformation-related collagen renewal in fibrous soft tissue.

A continuum mechanics constitutive model is presented for the interaction between swelling and collagen remodeling in biological soft tissue. The model is inherently two-way: swelling stretches the collagen fibers which affects their rate of degradation-the remodeled fibrous microarchitecture provides selective directional stiffening that causes the swollen tissue to expand more in the unreinforced directions. The constitutive model specifically treats stretch-stabilization wherein the rate of enzymatic-induced degradation of collagen is a decreasing function of fiber stretch. New collagen replacement takes place in a generally swollen environment, and this synthesis is tracked as a function of time by means of a time integration scheme that accounts for the historical sequence of collagen recreation. The model allows for the specification of the collagen pre-stretch at the time of first synthesis, thus allowing for the consideration of either initially limp replacement fiber or initially pre-tensioned replacement fiber. Loading and swelling that occurs on time scales that are commensurate with the natural time scales for fiber degradation and replacement lead to the consideration of time-integral constitutive equations. Loading and swelling that take place on time scales that are very different from that of the remodeling time scales provide a simplified treatment in which there are definite notions of a short-time instantaneous response and also a large-time approach to a steady-state condition of homeostasis.

Evidence for extremely rapid magma ocean crystallization and crust formation on Mars

The formation of a primordial crust is a critical step in the evolution of terrestrial planets but the timing of this process is poorly understood. The mineral zircon is a powerful tool for constraining crust formation as it can be accurately dated with the U-Pb system and is resistant to subsequent alteration. Moreover, the high concentration of Hf in zircon allow for the utilization of the 176Lu-176Hf decay system to determine the nature and formation timescale of its source reservoir1–3. Ancient igneous zircons with ages of ~4430 Ma have been reported in martian meteorites believed to represent regolith breccias from the southern highlands of Mars4,5. These zircons are present in evolved lithologies interpreted to reflect re-melted primary martian crust4 thereby potentially providing unique insights into early crustal evolution on Mars. Here, we report concomitant high-precision U-Pb ages and Hf-isotope compositions of ancient zircons from the NWA 7034 martian regolith breccia. Seven zircons with mostly concordant U-Pb ages define 207Pb/206Pb dates ranging from 4476.3±0.9 Ma to 4429.7±1.0 Ma, including the oldest directly dated material from Mars. All zircons record unradiogenic initial Hf-isotope compositions inherited from an enriched, andesitic-like crust extracted from a primitive mantle no later than 4547 Ma. Thus, a primordial crust existed on Mars by this time and survived for ~100 Myr before it was reworked, possibly by impacts4,5, to produce magmas from which the zircons crystallized. Given that formation of a stable primordial crust is the end product of planetary differentiation, our data require that the accretion, core formation and magma ocean crystallization on Mars was completed <20 Myr after Solar System formation. These timescales support models suggesting rapid magma ocean crystallization leading to a gravitationally unstable stratified mantle, which subsequently overturns resulting in decompression melting of rising cumulates and extraction of a primordial basaltic to andesitic crust6,7.

Role of Grain Boundaries under Long-Time Radiation.

Materials containing a high proportion of grain boundaries offer significant potential for the development of radiation-resistant structural materials. However, a proper understanding of the connection between the radiation-induced microstructural behavior of a grain boundary and its impact at long natural time scales is still missing. In this Letter, point defect absorption at interfaces is summarized by a jump Robin-type condition at a coarse-grained level, wherein the role of interface microstructure is effectively taken into account. Then a concise formula linking the sink strength of a polycrystalline aggregate with its grain size is introduced and is well compared with experimental observation. Based on the derived model, a coarse-grained formulation incorporating the coupled evolution of grain boundaries and point defects is proposed, so as to underpin the study of long-time morphological evolution of grains induced by irradiation. Our simulation results suggest that the presence of point defect sources within a grain further accelerates its shrinking process, and radiation tends to trigger the extension of twin boundary sections.

A mathematical model for malaria transmission with asymptomatic carriers and two age groups in the human population

In this paper a conceptual mathematical model of malaria transmission proposed in a previous paper has been analyzed in a deeper detail. Among its key epidemiological features of this model, two-age-classes (child and adult) and asymptomatic carriers have been included. The extra mortality of mosquitoes due to the use of long-lasting treated mosquito nets (LLINs) and Indoor Residual Spraying (IRS) has been included too. By taking advantage of the natural double time scale of the parasite and the human populations, it has been possible to provide interesting threshold results. In particular it has been shown that key parameters can be identified such that below a threshold level, built on these parameters, the epidemic tends to extinction, while above another threshold level it tends to a nontrivial endemic state, for which an interval estimate has been provided. Numerical simulations confirm the analytical results.

Introduction to Time-Resolved Spectroscopy: Nanosecond Transient Absorption and Time-Resolved Fluorescence of Eosin B

Here we present a new undergraduate laboratory that will introduce the concepts of time-resolved spectroscopy and provide insight into the natural time scales on which chemical dynamics occur through direct measurement. A quantitative treatment of the acquired data will provide a deeper understanding of the role of quantum mechanics and various phenomenological expressions in predicting kinetic rates for fluorescence, phosphorescence, and nonradiative decay mechanisms. This laboratory framework focuses specifically on spectroscopy in the nanosecond regime—assisted by various steady-state spectroscopic techniques—in order to fully characterize the electronic structure and the picosecond-to-microsecond dynamics of the dye eosin B. There is great flexibility in both the recommended lab duration (1 week to several months) and course level (upper-division to graduate) due to the numerous additional experiments that may be performed at varying levels of difficulty. The necessary components include pump and probe light sources, photodiode detectors, a programmable signal delay generator, and an oscilloscope for measurements with requisite resolution. The cost of building this experiment from scratch is less than $20,000 at the time of publication, but costs are expected to decrease over time and alternate excitation sources are available. Although this lab requires some expertise with optical spectroscopy to initially build and troubleshoot, use by students has been a straightforward and valuable experience.

How can attosecond pulse train interferometry interrogate electron dynamics?

Light pulses of sub-100 as (1 as=10-18 s) duration, with photon energies in the extreme-ultraviolet (XUV) spectral domain, represent the shortest event in time ever made and controlled by human beings. Their first experimental observation in 2001 has opened the door to investigating the fundamental dynamics of the quantum world on the natural time scale for electrons in atoms, molecules and solids and marks the beginning of the scientific field now called attosecond science.

Attosecond recorder of the polarization state of light

High harmonic generation in multi-color laser fields opens the opportunity of generating isolated attosecond pulses with high ellipticity. Such pulses hold the potential for time-resolving chiral electronic, magnetization, and spin dynamics at their natural timescale. However, this potential cannot be realized without characterizing the exact polarization state of light on the attosecond timescale. Here we propose and numerically demonstrate a complete solution of this problem. Our solution exploits the extrinsic two-dimensional chirality induced in an atom interacting with the chiral attosecond pulse and a linearly polarized infrared probe. The resulting asymmetry in the photoelectron spectra allows to reconstruct the complete polarization state of the attosecond pulse, including its possible time dependence. The challenging problem of distinguishing circularly polarized, partially polarized, or unpolarized pulses in the extreme ultraviolet range is also resolved. We expect this approach to become the core ingredient for attosecond measurements of chiral-sensitive processes in gas and condensed phase.

High-performance torque controller design for AC driving 4WD electric vehicle in two time scales

In this paper, a novel torque control method of AC induction motor in two time scales is proposed for 4WD electric vehicles. A two-time-scale sliding-mode control (SMC) observer and a SMC controller are synthesised to ensure high-performance torque control. Two time scales are considered based on the natural time scale separation existed in the AC induction motor driving system, i.e., rotor flux and speed corresponding to the slow dynamics and the stator current corresponding to the fast dynamics. The convergence property of the controller is considered when performing the observer design rather than the conventional control method where the controller and observer are designed separately. Moreover, the more advanced space vector modulation (SVM) technology instead of the sinusoidal pulse width modulation (SPWM) method used in the conventional SMC is also introduced in the proposed method to achieve minimum torque ripple. The effectiveness of the proposed torque control method is illustrated through simulations on a 4WD electric vehicle. Simulation results illustrate the improved performance compared with the conventional SMC method.

Single-shot structural analysis by high-energy X-ray diffraction using an ultrashort all-optical source

High-energy X-rays (HEX-rays) with photon energies on order of 100 keV have attractive characteristics, such as comparably low absorption, high spatial resolution and the ability to access inner-shell states of heavy atoms. These properties are advantageous for many applications ranging from studies of bulk materials to the investigation of materials in extreme conditions. Ultrafast X-ray diffraction allows the direct imaging of atomic dynamics simultaneously on its natural time and length scale. However, using HEX-rays for ultrafast studies has been limited due to the lack of sources that can generate pulses of sufficiently short (femtosecond) duration in this wavelength range. Here we show single-crystal diffraction using ultrashort ~90 keV HEX-ray pulses generated by an all-optical source based on inverse Compton scattering. We also demonstrate a method for measuring the crystal lattice spacing in a single shot that contains only ~105 photons in a spectral bandwidth of ~50% full width at half maximum (FWHM). Our approach allows us to obtain structural information from the full X-ray spectrum. As target we use a cylindrically bent Ge crystal in Laue transmission geometry. This experiment constitutes a first step towards measurements of ultrafast atomic dynamics using femtosecond HEX-ray pulses.

The impact of technological innovation on critical materials risk dynamics

As the technologies we use as a society have advanced, so have the materials used in these technologies. Some of these materials are exotic and highly specialized, making them particularly vulnerable to supply disruptions and supply disruptions particularly impactful. Such materials are designated as “critical” materials. Their level of criticality can be identified by accounting for a number of factors related to their supply risk and the extent to which a supply disruption would impact business operations or society at large. We highlight current methodologies used to assess materials criticality, how these assessments are used to reduce materials-related risk and to what extent there is room for improvement. Particularly, this paper reviews critical materials designations from the United States Department of Energy, the European Union, and the General Electric Company, and how they have changed over the period from 2008 to 2014. The changes suggest that the factors considered in criticality ratings have different natural time scales, and that criticality changes occur both due to supply-side risk mitigation as well as demand-side responses. Response options, whether on the supply or demand side, also span a range of time scales and the interaction between factors with different time scales can play a significant role in the dynamics. To date, many published analyses are snapshots in time. A detailed understanding of how risk profiles evolve remains an open question. The importance and impact of demand-side responses such as recycling, substitution and new technological development are discussed.