Intrinsic Time Dependence Research Articles

Edge-dependent anomalous topology in synthetic photonic lattices subject to discrete step walks

Anomalous topological phases, where edge states coexist with topologically trivial Chern bands, can only appear in periodically driven lattices. When the driving is smooth and continuous, the bulk-edge correspondence is guaranteed by the existence of a bulk invariant known as the winding number. However, in lattices subject to periodic discrete step walks the existence of edge states does not only depend on bulk invariants but also on the boundary. This is a consequence of the absence of an intrinsic time dependence or micromotion in discrete step walks. We report the observation of edge states and a simultaneous measurement of the bulk invariants in anomalous topological phases in a two-dimensional synthetic photonic lattice subject to discrete step walks. The lattice is implemented using time multiplexing of light pulses in two coupled fibre rings, in which one of the dimensions displays real-space dynamics and the other one is parametric. The presence of edge states is inherent to the periodic driving and depends on the properties of the boundary in the implemented two-band model with zero Chern number. We provide a suitable expression for the topological invariants whose calculation does not rely on micromotion dynamics. Published by the American Physical Society 2024

Scratch hardness as a quasi-intrinsic parameter to measure the scratch resistance of polymers

In this work four different polymers (acrylonitrile-butadiene-styrene, high-impact polystyrene, rubber-toughened polybutylene terephthalate, linear low-density polyethylene) were characterized in terms of their bulk (modulus and yield stress) and surface (scratch hardness) mechanical properties. The intrinsic time-dependence of the materials was addressed by performing DMA and compression tests at varying testing speed/frequency, exploiting time-temperature superposition and Eyring's model to obtain data at strain rates compatible with scratch experiments. The latter were performed by applying different loading histories (constant depth or load) and indenters. Scratch hardness was determined using Pelletier's model; it was demonstrated that such a parameter provides a reliable and almost intrinsic (i.e. loading history independent) evaluation of scratch resistance, seen as the resistance the material opposes to indenter penetration. The material compressive yield stress (evaluated at the strain rate relevant to scratch phenomena) was found to be the key controlling factor in determining scratch hardness. It can therefore be taken as a measure of the mechanical scratch resistance when evaluating the possible effects of variables such as material composition, crystallinity, physical ageing … Its relation with other aspects of the scratch phenomenon (in particular deformation recovery) was also explored, accounting for the specific deformation regime imposed by the indenter (transitioning from elastic to predominantly plastic).

Time‐Dependent Hydraulic Fracture Initiation

AbstractRocks are known to fail in a time‐dependent manner similar to many brittle and quasi‐brittle materials. However, observed time dependence of hydraulic fracture initiation has ubiquitously been attributed to fluid flow‐related mechanisms without consideration of the intrinsic time dependence of rock failure. Laboratory delayed hydraulic fracturing breakdown experiments on three rocks (granite, sandstone, and limestone) show sensitivity to rock properties associated with subcritical crack growth as well as fluid viscosity and ambient confining pressure applied to the specimens. A new hydraulic fracture initiation model accounting for subcritical crack growth and fluid flow in a poroelastic medium, as well as the additional energy dissipation required for fluid flow in the rough fracture tip, is then used to estimate the value of the subcritical index n based on characterization experiments. Given this characterization data, the model is shown to be capable of predicting time‐dependent hydraulic fracture initiation with variation of fluid viscosity and confining stress.

On the inflationary massive field with a curved field manifold

Massive fields during inflation provide an interesting opportunity to test new physics at very high energy scales. Meanwhile in fundamental realizations, the inflationary field space typically has a curved geometry, which may leave detectable imprints in primordial observables. In this paper we study an extension of quasi-single field inflation where the inflaton and the massive field belong to a curved field manifold. Because of the nontrivial field space curvature, the massive field here can get significant mass corrections of order the Hubble scale, thus the quasi-single field predictions on primordial non-Gaussianity are affected. We derive the same result in an equivalent approach by using the background effective field theory of inflation, where a dimension-6 operator is identified to play an important role and its cutoff scale is associated with the curvature scale of the field space. In addition, due to the slow-roll evolution of the inflaton, this type of mass correction has intrinsic time-dependence. Consequently, the running mass modifies the scaling behaviour in the squeezed limit of the scalar bispectrum, while the resulting running index measures the curvature of the internal field space. Therefore the minimal setup of a massive field within curved field space during inflation may naturally lead to new observational signatures of the field space geometry.

Current‐driven flare and CME models

AbstractRoles played by the currents in the impulsive phase of a solar flare and in a coronal mass ejection (CME) are reviewed. Solar flares are magnetic explosions: magnetic energy stored in unneutralized currents in coronal loops is released into energetic electrons in the impulsive phase and into mass motion in a CME. The energy release is due to a change in current configuration effectively reducing the net current path. A flare is driven by the electromotive force (EMF) due to the changing magnetic flux. The EMF drives a flare‐associated current whose cross‐field closure is achieved by redirection along field lines to the chromosphere and back. The essential roles that currents play are obscured in the “standard” model and are described incorrectly in circuit models. A semiquantitative treatment of the energy and the EMF is provided by a multicurrent model, in which the currents are constant and the change in the current paths is described by time‐dependent inductances. There is no self‐consistent model that includes the intrinsic time dependence, the EMF, the flare‐associated current, and the internal energy transport during a flare. The current, through magnetic helicity, plays an important role in a CME, with twist converted into writhe allowing the kink instability plus reconnection to lead to a new closed loop and with the current‐current force accelerating the CME through the torus instability.

Intrinsic time dependence in the diversity–invasibility relationship

Contrasting patterns in the diversity-invasibility relationship have intrigued ecologists for many years, and are now known as the "invasion paradox." Experiments usually detect negative relationships, while field surveys find them to be positive. It is widely believed that the paradox is driven by differences in spatial scale, but this is challenged by field surveys that find positive relationships at all spatial scales. If factors that determine invasion dynamics change during the invasion process, the paradox may be partially driven by differences in temporal scale. Here we used simulation (cellular automata) models to explore the generality of temporal change in the diversity-invasibility relationship. The probability of invaders colonizing an area was inversely related to the density of natives, creating a negative native-exotic correlation when invaders first arrived. Over time, native and exotic populations were both shaped by the same post-introduction processes (disturbance, dispersal, and recolonization), shifting their correlation to positive. The rate of temporal change in the diversity-invasibility relationship was mainly dependent upon the fecundity of invaders. Greater fecundity meant that invaders spread through the landscape faster and were subject to post-introduction processes sooner. We propose a unified conceptual model where the diversity-invasiblity relationship is a function of both spatial and temporal scales.

Repolarization of the mammalian heart action potential is modulated by changes in osmotic strength

This editorial refers to ‘Osmotic modulation of slowly activating I Ks in guinea-pig ventricular myocytes’ by S. Missan et al ., pp. 429–436, this issue. Repolarization of the mammalian heart action potential is a very important physiological variable. It sets action-potential duration and thus strongly modulates contractility and refractoriness in both the atria and the ventricles. Repolarization is initiated and controlled by the time- and voltage-dependent onset of a variety of different outward potassium (K+) currents, some of which are highly non-linear.1 One of these currents, the so-called slow outward delayed rectifier, or I Ks, is expressed in the human ventricle. Its activation adds to the safety factor for repolarization (the so-called repolarization reserve) through its intrinsic time and voltage dependence. This is prominent following augmentation of I Ks by sympathetic nerve stimulation.2 A paper in this issue from the McDonald laboratory3 confirms and extends what is known about the modulation of I Ks in response to changes in osmotic strength of the external medium. A significant change in osmotic strength (±20–30%) may take place in the setting of ischaemia–reperfusion of the heart. This paper demonstrates relatively rapid (3–5 min to steady state) changes in I Ks in single ventricular myocytes obtained from the hearts of adult guinea pigs in response to alterations in osmotic strength: reductions result in reversible increases in I Ks and vice versa. These changes appear to be quite selective as judged by the reported lack of effect on a selected K+ current denoted HERG. The context for these findings and some aspects of their interpretation is aided …

NMR signal averaging in 62 T pulsed fields

Nuclear Magnetic Resonance (NMR) experiments in pulsed high magnetic fields up to 62 T at the Dresden High Magnetic Field Laboratory ( Hochfeld-Magnetlabor Dresden) are reported. The time dependence of the magnetic field is investigated by observing various free induction decays (FIDs) in the vicinity of the maximum of the field pulse. By analyzing each FID’s phase and its evolution with time the magnetic field’s time dependence can be determined with high precision. Assuming a quadratic or cubic dependence on time near the field maximum its confidence is found to be better than ±0.03 ppm at low fields and ±0.8 ppm near 62 T. In turn, the thus obtained time dependence of the field can be used to demodulate and phase-correct all FIDs so that they appear phase-locked to each other. As a consequence signal averaging is possible. The increase in signal-to-noise ratio is found to be close to that expected theoretically. This shows that the intrinsic time dependence of the pulsed fields can be removed so that the NMR signals appear to be taken at rather stable static field. This opens up the possibility of performing precise shift measurements and signal averaging also of unknown, weak signals if a reference signal is measured during the same field pulse with a double-resonance probe.

An Improved Method for Estimating Source Densities Using the Temporal Distribution of Cosmological Transients

It has been shown that the observed temporal distribution of transient events in the cosmos can be used to constrain their rate density. Here we show that the peak flux--observation time relation takes the form of a power law that is invariant to the luminosity distribution of the sources, and that the method can be greatly improved by invoking time reversal invariance and the temporal cosmological principle. We demonstrate how the method can be used to constrain distributions of transient events, by applying it to Swift gamma-ray burst data and show that the peak flux--observation time relation is in good agreement with recent estimates of source parameters. We additionally show that the intrinsic time dependence allows the method to be used as a predictive tool. Within the next year of Swift observation, we find a 50% chance of obtaining a peak flux greater than that of GRB 060017 -- the highest Swift peak flux to date -- and the same probability of detecting a burst with peak flux > 100 photons s^{-1} cm^{-2} within 6 years.

Exciton annihilation in a polyfluorene: Low threshold for singlet-singlet annihilation and the absence of singlet-triplet annihilation

Ultrafast photoinduced absorption measurements have been used to directly investigate singlet-singlet annihilation in polyfluorene. The pump fluence threshold for annihilation to dominate the decay was measured to be $\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{J}\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$ corresponding to an excitation density of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{17}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. The annihilation rate was found to be faster than that expected from a simple dipole-dipole interaction. This is ascribed to the additional influence of diffusion which, because of the dispersive nature of the exciton migration, has strong time dependence as the singlet excitons thermalize in the density of states as well as the expected intrinsic time dependence from a diffusion controlled process. Also, a comparable background level of triplets was created in the film to study the effect of singlet-triplet annihilation, which surprisingly, given the low threshold for singlet-singlet annihilation, was found to be negligible.

Precession of neutrino-cooled accretion disks in gamma-ray burst engines

We study the precession of accretion disks in the context of gamma-ray burst inner engines. With an accretion disk model that allows for neutrino cooling, we evaluate the possible periods of disk precession and nutation due to the Lense-Thirring effect. Assuming jet ejection perpendicular to the disk midplane and a typical intrinsic time dependence for the burst, we find possible gamma-ray light curves with temporal microstructure similar to what is observed in some subsamples. We conclude that the precession and nutation of a neutrino-cooled accretion disk in the burst engine might be responsible for some events, especially those with a slow rise and a fast decay.

Analytic controllability of time-dependent quantum control systems

The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation in which the state moves in an infinite-dimensional Hilbert space, a drift term is present, and the operators driving the state evolution may be unbounded. However, considerations are restricted by the assumption that there exists an analytic domain, dense in the state space, on which solutions of the controlled Schrödinger equation may be expressed globally in exponential form. The issue of controllability then naturally focuses on the ability to steer the quantum state on a finite-dimensional submanifold of the unit sphere in Hilbert space—and thus on analytic controllability. A relatively straightforward strategy allows the extension of Lie-algebraic conditions for strong analytic controllability derived earlier for the simpler, time-independent system in which the drift Hamiltonian and the interaction Hamiltonian have no intrinsic time dependence. Enlarging the state space by one dimension corresponding to the time variable, we construct an augmented control system that can be treated as time independent. Methods developed by Kunita can then be implemented to establish controllability conditions for the one-dimension-reduced system defined by the original time-dependent Schrödinger control problem. The applicability of the resulting theorem is illustrated with selected examples.

SOLVING TIME-DEPENDENT EQUATIONS OF SCHRÖDINGER-TYPE USING MAPPED INFINITE ELEMENTS

We present a general technique to solve one-dimensional time-dependent Schrödinger-type equations. A mapped infinite elements approach is used to eliminate spurious reflections of outgoing wave packets from the boundaries of the interval of interest. This procedure leads to more precise solutions because the space coordinates are discretized to approximate the solution in the entire physical domain. We show its utility giving numerical results on three typical examples: a bounded short-range potential; the unbounded potential of a particle in a dc field; and a Hamiltonian with an intrinsic time dependence like the Hamiltonian of a charged particle in an ac electromagnetic field.

Total time derivatives of operators in elementary quantum mechanics

The use of a total time derivative of operators, that depends on the time evolution of the wave function as well as on any intrinsic time dependence in the operators, simplifies the formal development of quantum mechanics and allows its development to more closely follow the corresponding development of classical mechanics. We illustrate the use of the total time derivative for a free particle, the linear potential, the harmonic oscillator, and the repulsive inverse square potential. In these cases, operators whose total time derivative is zero can be found and yield general properties of wave packets and several useful time-dependent solutions of Schrödinger’s equation, including the propagator.

Mixing in a 3D spherical model of present-day mantle convection

We present the first study of present-day mixing efficiency of the Earth that is based on a 3D spherical model of convection in the Earth's mantle. The stationary model we employ is derived from the present-day slab buoyancy forces using an approximate plate rheology, a weak upper mantle above the transition zone and an increase of viscosity into the lower mantle. The model is quite successful in predicting surface plate velocities and the geoid. We consider this model an appropriate approximation of the present-day internal velocity structure in the Earth's mantle. The mixing efficiency is studied by studying particle traces, evaluating Poincaré sections, and quantifying stretching efficiency. This allows for determining regions in the present-day mantle that are characterized by laminar or chaotic mixing and indicate the connection between different mantle regions. The modeling indicates that a variety of mixing scales exist in the present mantle velocity field. Only certain regions exhibit laminar single cell mixing. Convection in most other regions is characterized by corkscrew-like particle tracks that allow for transport of particles far from their source and possibly for chaotic mixing. The key components governing the efficiency of mixing of the present-day mantle are the driving forces of the slabs, in particular those along the Pacific rim, and the vorticity (or toroidal motion) induced by the rotation and resulting strike-slip motion of surface plates. Our approach is a conservative one, as the intrinsic time-dependence of plate tectonics and more vigorous convection in a younger and hotter Earth would cause stronger mixing. Based on this simple model approach, we conclude that the mixing in the present-day Earth is relatively efficient, and that it is not possible for large portions of the Earth mantle to remain isolated over the life time of the Earth.

Time-dependent low field microwave absorption in the high temperature superconductors

Abstract It is observed that the hysteresis in the applied magnetic field position and the intensity at the peak of the low field non-resonant microwave absorption (recorded in an EPR experiment with a modulation amplitude of ∼ 10 G) in the superconducting state of the cuprate superconductors, is time-dependent after the removal of a DC magnetic field sizably greater than the lower critical field. This intrinsic time-dependence, which we attribute to flux creep, is reported here for two copper oxide-based high temperature superconductors.

Heavy-ion induced adhesion of thin gold films to oxidized substrates of tantalum and silicon

Energetic heavy ion beams are capable of enhancing the adhesion of metallic films to a variety of substrates. Gold films (200–600 Å) evaporated onto substrates of tantalum and silicon (with native oxides) were bombarded with ions of 12C, 16O, 28Si, 35Cl and 58Ni at 2.85 MeV/nucleon. The threshold dose required to produce a peel strength greater than the Scotch-tape peel strength for a gold surface was measured as a function of ion species and angle of incidence. We observed the threshold dose to vary as the cosine of the angle with respect to normal incidence. The dependence on particle type for the AuTa system (with approximately 40 Å native oxide) was found tobe D th(cm −2) = 10 17( dE dx ) Au −3.0±0.2 for all particle beams where ( dE dx ) Au is the (MeV cm 2/mg) of the ion in gold. A substrate of 6000 Å of tantalum oxide gave identical results. The value of the exponent, −3.0±0.2, differs significantly from the value −1.6±0.2 reported earlier by Tombrello et al. for AuTa. The AuSi system is described by D th = 6 × 10 18( dE dx ) Au −4.1±0.3 . Auger analysis of the AuTa interface suggests a migration of the nativ result of ion bombardment. For the AuTa system, some irradiated regions that passed the Scotch-tape test just after bombardment were observed to fail when the test was repeated a few days later. Thicker gold films and higher doses resulted in longer adhesion times. These and other observations suggest that the post-irradiation decline of adhesion for AuTa is caused by diffusion of ambient atoms through the gold film rather than by an intrinsic time dependence of the adhesive forces.

Are vibrational relaxation times really constant? II. The vibrational relaxation of C 2H 2

Vibrational relaxation times of pure acetylene in the gas phase were measured behind incident shock waves in the temperature range 613–1184 K using a laser-schlieren technique. Overall, the results are in excellent agreement with those of acoustic and laser excitations. However, we find a marked intrinsic time dependence of the phenomenological time, which varies by factors of two to three over a wide dynamic time scale of at least six natural lifetimes. In other words, the Bethe—Teller law fails. This is confirmed by numerical solution of the master equation for a wide choice of intermode collisional coupling parameters. The density of states involved in the energy transfer process determines whether the relaxation time increases or decreases with time, and the effect is amplified by the importance of intermolecular VV processes relative to intramolecular processes.

Rayleigh-Bénard convection in an intermediate-aspect-ratio rectangular container

We report a study of the flow patterns associated with Rayleigh—Bénard convection in rectangular containers of approximate proportions 10 × 5 × 1 at Prandtl numbers σ between 2 and 20. The flow is studied at Rayleigh numbers ranging from the onset of convective flow to the onset of time dependence; Nusselt-number measurements are also presented. The results are discussed in the content of the theory for the stability of a laterally infinite system of parallel rolls. We observed transitions between time-independent flow patterns which depend on roll wavenumber, Rayleigh number and Prandtl number in a manner that is reasonably well described by this theory. For σ [lsim ] 10, the skewed-varicose instability (which leads directly to time dependence in much larger containers) is found to initiate transitions between time-independent patterns. We are then able to study the approach to time dependence in a regime of larger Rayleigh number where the instabilities in the flow are found to have an intrinsic time dependence. In this regime, the onset of time dependence appears to be explained by the recent predictions of Bolton, Busse & Clever for a new set of time-dependent instabilities.