Decay Regime Research Articles

The lower tail of the half-space KPZ equation

We establish the first tight bound on the lower tail probability of the half-space KPZ equation with Neumann boundary parameter A=−1/2 and narrow-wedge initial data. The lower bound demonstrates a crossover between two regimes of super-exponential decay with exponents 52 and 3; the upper bound demonstrates a crossover between regimes with exponents 32 and 3. Given a crude leading-order asymptotic in the Stokes region for the Ablowitz–Segur solution to Painlevé II (Definition 1.8), we improve the upper bound to demonstrate the same crossover as the lower bound. We also establish novel bounds on the large deviations of the GOE point process.

Magnetic resonance free induction decay in geological porous materials.

Magnetic resonance is an important noninvasive technology across life sciences and industry. Free induction decay is the simplest [Formula: see text]H magnetic resonance measurement method and an important means of probing fast-decaying signals in porous materials such as rocks, lung, and bone. It is commonly assumed that the free induction decay in geological porous materials is single-exponential. We experimentally observed two regimes of free induction decay behavior in geological porous materials: single-exponential and non-exponential decay. Numerical simulations that match experimental data highlight the effect of mass diffusion, especially in the single-exponential behavior. These two regimes of free induction decay in porous materials are associated with a bifurcation point in the solutions of the Bloch-Torrey equation for diffusion of fluids in confined domains in the presence of internal magnetic field gradients. This finding facilitates the extraction of absolute internal magnetic field gradient intensities from simple free induction decay measurements in the laboratory and field. This work also warns against common single-exponential assumptions in surface magnetic resonance methods employed in surveying underground water aquifers.

Drops on the Underside of a Slightly Inclined Wet Substrate Move Too Fast to Grow

Pendant drops suspended on the underside of a wet substrate are known to accumulate fluid from the surrounding thin liquid film, a process that often results in dripping. The growth of such drops is hastened by their ability to translate over an otherwise uniform horizontal film. Here we show that this scenario is surprisingly reversed when the substrate is slightly tilted (≈2°); drops become too fast to grow and shrink over the course of their motion. Combining experiments and numerical simulations, we rationalize the transition between the conventional growth regime and the previously unknown decay regime we report. Using an analytical treatment of the Landau-Levich meniscus that connects the drop to the film, we quantitatively predict the drop dynamics in the two flow regimes and the value of the critical inclination angle where the transition between them occurs.

Non-Markovian effects in the spin-boson model at zero temperature

We investigate memory effects in the spin-boson model using a recently proposed measure for non-Markovian behavior based on the information exchange between an open system and its environment. Employing the numerical exact multilayer multiconfguration time-dependent Hartree approach, we simulate the dynamics of the spin-boson model at zero temperature for a broad range of parameters. For a fast bath, i.e. in the scaling limit, we find non-Markovian dynamics for a coherently decaying spin at weak system-bath coupling, whereas memory effects are absent for stronger coupling in the regimes of incoherent decay and localization. If the time scales of system and bath are comparable, a complex, non-monotonic dependence of non-Markovianity on the system-bath coupling strength is observed.

Eigenoscillations in an angular domain and spectral properties of functional equations

This work studies functional difference equations of the second order with a potential belonging to a special class of meromorphic functions. The equations depend on a spectral parameter. Consideration of this type of equations is motivated by applications in diffraction theory and by construction of eigenfunctions for the Laplace operator in angular domains. In particular, such eigenfunctions describe eigenoscillations of acoustic waves in angular domains with ‘semitransparent’ boundary conditions. For negative values of the spectral parameter, we study essential and discrete spectrum of the equations and describe properties of the corresponding solutions. The study is based on the reduction of the functional difference equations to integral equations with a symmetric kernel. A sufficient condition is formulated for the potential that ensures existence of the discrete spectrum. The obtained results are applied for studying the behaviour of eigenfunctions for the Laplace operator in adjacent angular domains with the Robin-type boundary conditions on their common boundary. At infinity, the eigenfunctions vanish exponentially as was expected. However, the rate of such decay depends on the observation direction. In particular, in a vicinity of some directions, the regime of decay is switched from one to another and such asymptotic behaviour is described by a Fresnel-type integral.

Updated constraints on decaying cold dark matter

In this paper we update the constraints on the simple decaying cold dark matter (DCDM) model with dark radiation (DR) as decay product. We consider two different regimes of the lifetime, i.e. short-lived and long-lived, and use the most recent CMB data from Planck (2018) to infer new constraints on the decay parameters with which we compare the constraints inferred by the previous Planck data (2015). We hereby show that the newest CMB data constrains the fractional amount of DCDM twice as much as the previous data in the long-lived regime, leading to our current best 2σ upper bound of f dcdm < 2.44%. In the short-lived regime, we get a slightly looser 2σ upper bound of f dcdm < 13.1% compared to the previous CMB data. If we include Baryonic Acoustic Oscillations data from BOSS DR-12, the constraints in both the long-lived and the short-lived regimes relax to f dcdm < 2.62% and f dcdm < 1.49%, respectively. We also investigate how this model impacts the Hubble and σ8 tensions, and we find that each of the decay regimes can slightly relieve a different one of the tensions. The model can thus not accommodate both tensions at once, and the improvements on each are not significant. We furthermore improve on previous work by thoroughly analysing the impacts of short-lived DCDM on the radiation density and deriving a mapping between short-lived DCDM and a correction, ΔN eff, to the effective number of massless neutrino species.

Self-Diffusion in 57Fe/natFe Multilayers by In Situ Neutron Reflectometry

Time-of-flight in situ neutron reflectometry (i-NR) on Si/[57Fe(x nm)/natFe(x nm)]4/Pt with x = 4 and 8 nm multilayers during consecutive heat treatments at 423, 448, 473 and 498 K reveal an unexpected rearrangement of free volumes and an interface smoothening in the isotopic Fe multilayer below 473 K, before the regime of regular Bragg intensity decay starts. The bilayer period dependence of the diffusivities at around 500 K, however, does not follow predictions of Harrison’s theory for the C-type regime representing grain boundary diffusion.

Comparing the accuracy of the visual assessment of longitudinal wheeltimbers against decay detection drilling methods

ABSTRACT Timber has been a versatile material for centuries. During the start of the Railway Age in the nineteenth century it was in considerable demand, particularly for bridge building. Timber is still in service and widely used throughout the UK network. The resilience and favourable strength to weight ratio and its relative ease of fabrication make it an attractive material. Longitudinal wheeltimbers are used extensively to carry track in situations where it is desirable to reduce the weight of bridges and in locations where the depth of the structure prevents the use of ballasted track. Most wheeltimbers in the UK comprise creosoted Douglas fir and to a lesser extent, naturally durable tropical hardwoods. Concerns about the effects of fungal decay and non-standardised inspection regimes are problematic. Managing the network is complex and imposes high and often conflicting demands on infrastructure asset managers. Effective asset management within a safety critical sector is an essential discipline. It is the variable nature of timber that presents significant management challenges. This paper summarises a strategy to improve the examination of wheeltimbers and assesses the feasibility of extending service life. This approach may deliver more effective asset management of timber assets.

Addendum: Mapping electron dynamics in highly transient EUV photon-induced plasmas: a novel diagnostic approach using multi-mode microwave cavity resonance spectroscopy (2018 J. Phys: D. Appl. Phys. 52 034004)

A new approach for an in-line beam monitor for ionizing radiation was introduced in a recent publication (Beckers J et al 2018 J. Phys. D: Appl. Phys. 52 034004). Due to the recent detection and investigation of an additional third decay regime of the afterglow of an extreme ultraviolet photon-induced plasma described in a later article (Platier B et al 2020 Appl. Phys. Lett. 116 103703) there is an additional reason for a minimum number of photons for this approach to work. Near or below this threshold, we explain that the response time of the diagnostic method is a limiting factor. Further, a second limit for the number of photons within a pulse is formalized related to the trapping of highly energetic free electrons.

Unlocked-relative-phase states in arrays of Bose-Einstein condensates

Phase engineering techniques are used to control the dynamics of long-bosonic-Josephson-junction arrays built by linearly coupling Bose-Einstein condensates. Just at the middle point of the underlying discrete energy band of the system, unlocked-relative-phase states are shown to be stationary along with the locked-relative-phase Bloch waves. In finite, experimentally-feasible systems, such states find ranges of dynamical stability that depend on the ratio of coupling to interaction energy. The same ratio determines different decay regimes, which include the recurrence of staggered-soliton trains in the condensates around Josephson loop currents at the junctions. These transient solitons are also found in their stationary configurations, which provide striped-density states by means of either dark-soliton or bright-soliton trains. Additionally, the preparation of maximally out-of-phase (or splay) states is demonstrated to evolve into an oscillation of the uniform density of the condensates that keeps constant the total density of the system and robust against noise at low coupling.

Linear stability of plane Poiseuille flow of a Bingham fluid in a channel with the presence of wall slip

In the present paper, the effects of a channel symmetric wall slip are investigated on the stability of plane Poiseuille flow of a Bingham fluid, based on the modal and non-modal linear stability analysis approaches. Both streamwise and spanwise slip conditions are considered and their results are compared with those of the no-slip condition, in terms of the flow stability. The results are obtained for different dimensionless groups that govern the stability picture, for example the Bingham number, the Reynolds number and the streamwise/spanwise slip numbers. The linearized perturbation equations are obtained and the corresponding eigenvalue problem is solved based on the Chebyshev collocation method at the Gauss-Lobatto grid points, using the QZ algorithm. In the modal analysis, the focus is on the changes made by the channel wall slip on the eigenvalue spectra. The flow is shown to be linearly stable for no-slip and streamwise slip conditions. However, for the spanwise slip condition, an unstable eigenvalue is found for large values of the spanwise slip number. The non-modal stability analysis is based on the transient energy growth of the perturbations, which is calculated using the eigenfunctions of the eigenvalue problem representing the amplitude of the perturbations. Increasing the streamwise slip decreases the maximum energy growth, eventually leading to a flow for which the transient energy only decays in time. Thus, two distinct flows showing the energy growth and energy decay regimes can be identified, for a range of Bingham, Reynolds and streamwise slip numbers.

Transition from ambipolar to free diffusion in an EUV-induced argon plasma

Extreme Ultraviolet (EUV) optical components used in EUV lithography tools are continuously impacted by an exotic and highly transient type of plasma: EUV-induced plasma. Such an EUV-induced plasma is generated in a repetitive fashion upon sending a pulsed beam of high energy (92 eV) photons through a low-pressure background gas. Although its formation occurs on a time scale of ∼100 ns, it is the plasma's decay dynamics on longer time scales that dictates the fluxes and energy distribution of the produced ions. Therefore, the plasma decay also determines the overall impact on plasma-facing EUV optical components. Enabled by electron density measurements using Microwave Cavity Resonance Spectroscopy at a much higher sensitivity, we clearly show the breakdown of the ambipolar field in an EUV photon-induced plasma below electron densities of ∼2 × 1012 m−3 and the—until now—unidentified transition from ambipolar diffusion-driven decay into a decay regime driven by free diffusion. These results not only further improve the understanding of elementary processes in this type of plasma but also have a significant value for modeling and predicting the stability and lifetime of optical components in EUV lithography.

Magnetic Activity of F-, G-, and K-type Stars in the LAMOST–Kepler Field

Abstract Monitoring chromospheric and photospheric indexes of magnetic activity can provide valuable information, especially the interaction between different parts of the atmosphere and their response to magnetic fields. We extract chromospheric indexes, S and , for 59,816 stars from LAMOST spectra in the LAMOST–Kepler program, and photospheric index, R eff, for 5575 stars from Kepler light curves. The log R eff shows positive correlation with log . We estimate the power-law indexes between R eff and for F-, G-, and K-type stars, respectively. We also confirm the dependence of both chromospheric and photospheric activity on stellar rotation. Ca ii H and K emissions and photospheric variations generally decrease with increasing rotation periods for stars with rotation periods exceeding a few days. The power-law indexes in exponential decay regimes show different characteristics in the two activity–rotation relations. The updated largest sample including the activity proxies and reported rotation periods provides more information to understand the magnetic activity for cool stars.

Shock wave characterization of precipitate strengthening of PH 13–8 Mo stainless steel

The shear stresses required for dislocations passage of highly coherent NiAl-based precipitates, formed in commercial PH 13–8 Mo steel after homogenization, quenching and aging for different duration of time at 510 °C, were determined in a series of planar impact experiments using samples with different thickness. The experiments revealed two regimes of decay of the elastic precursor waves: a fast one, at the shear stress τ greater than some threshold τ*, associated with the interaction of moving dislocations with lattice phonons, and a slow one, at τ < τ*, corresponding to the precipitates' cutting with the help of thermal fluctuations. Consequently, the stress τ* can be regarded as the stress which permits the passage of the precipitate by a dislocation without thermal support. Precipitates' geometry and size, determined based on the activation volume at thermally-activated regime, are in a reasonable agreement with precipitates dimensions estimated from High Resolution Transmission Electron Microscopy images.

Local well-posedness of the Boltzmann equation with polynomially decaying initial data

<p style='text-indent:20px;'>We consider the Cauchy problem for the spatially inhomogeneous non-cutoff Boltzmann equation with polynomially decaying initial data in the velocity variable. We establish short-time existence for any initial data with this decay in a fifth order Sobolev space by working in a mixed <inline-formula><tex-math id="M1">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ L^\infty $\end{document}</tex-math></inline-formula> space that allows to compensate for potential moment generation and obtaining new estimates on the collision operator that are well-adapted to this space. Our results improve the range of parameters for which the Boltzmann equation is well-posed in this decay regime, as well as relax the restrictions on the initial regularity. As an application, we can combine our existence result with the recent conditional regularity estimates of Imbert-Silvestre (arXiv:1909.12729 [math.AP]) to conclude solutions can be continued for as long as the mass, energy, and entropy densities remain under control. This continuation criterion was previously only available in the restricted range of parameters of previous well-posedness results for polynomially decaying initial data.

Analysis of the Breakdown of Exponential Decays of Resonances

In the paper, a simple model of alpha decay with Dirac delta potential is studied. The model leads to breakdown of the exponential decay and to power law behavior at asymptotic times. Time dependence of the survival probability of the particle in the potential well is analyzed numerically with two methods: integration of Green's function representation and numerical solution of the time-dependent Schr\odinger equation. In particular, finite depth potential wells and behavior between the exponential and power law regimes, which are situations that could not be described in detail analytically, are studied. The numerical results confirm power law with exponent n = 3 after the turnover into the non-exponential decay regime. Moreover, the constructive and destructive interference is observed in the intermediate stage of the process. The simple alpha decay model is compared to the results of Rothe- Hintschich-Monkman experiment which was the first experimental proof of violation of the exponential law.

Axion-like-particle decay in strong electromagnetic backgrounds

The decay of a massive pseudoscalar, scalar and U(1) boson into an electron-positron pair in the presence of strong electromagnetic backgrounds is calculated. Of particular interest is the constant-crossed-field limit, relevant for experiments that aim to measure high-energy axion-like-particle conversion into electron-positron pairs in a magnetic field. The total probability depends on the quantum nonlinearity parameter — a product of field and lightfront momentum invariants. Depending on the seed particle mass, different decay regimes are identified. In the below-threshold case, we find the probability depends on a non-perturbative tunneling exponent depending on the quantum parameter and the particle mass. In the above-threshold case, we find that when the quantum parameter is varied linearly, the probability oscillates nonlinearly around the spontaneous decay probability. A strong-field limit is identified in which the threshold is found to disappear. In modelling the fall-off of a quasi-constant-crossed magnetic field, we calculate probabilities beyond the constant limit and investigate when the decay probability can be regarded as locally constant.

Scalar mixing in an urban canyon

The scalar dynamics within a unit-aspect-ratio street canyon are studied using large-eddy simulation. The key processes of ventilation and mixing are analysed with the canyon-averaged concentration, mean tracer age and variance. The results are sensitive to the source location and can be classified according to the streamline geometry. The canyon-averaged concentrations for the corner vortices, vortex sea and central vortex do not converge to the same value at large times, though the mean decay rates do. The variance measured with respect to the canyon average shows two distinct decay regimes: the early regime reflects large-scale straining and enhanced diffusion across streamlines, while the late regime is associated with escape from the canyon, i.e., ventilation. Analytical predictions for the variance-decay or mixing time scales are verified for the early regime. It is argued that the presence of an open boundary at the roof level suppresses rapid mixing of the scalar field and is responsible for differences with respect to scalar dynamics within closed domains.

Experimental Investigation of Quantum Decay at Short, Intermediate, and Long Times via Integrated Photonics.

The decay of an unstable system is usually described by an exponential law. Quantum mechanics predicts strong deviations of the survival probability from the exponential: Indeed, the decay is initially quadratic, while at very large times it follows a power law, with superimposed oscillations. The latter regime is particularly elusive and difficult to observe. Here we employ arrays of single-mode optical waveguides, fabricated by femtosecond laser direct inscription, to implement quantum systems where a discrete state is coupled and can decay into a continuum. The optical modes correspond to distinct quantum states of the photon, and the temporal evolution of the quantum system is mapped into the spatial propagation coordinate. By injecting coherent light states in the fabricated photonic structures and by measuring a small scattered fraction of such light with an unprecedented dynamic range, we are able to experimentally observe not only the exponential decay regime, but also the quadratic Zeno region and the power-law decay at long evolution times.

Characterization of time-resolved emission of N2(C) in an atmospheric pressure nanosecond pulsed air-plasma using streak spectroscopy

A new optical emission spectroscopy (OES) system using a streak camera (streak-OES) is developed to obtain highly time-resolved OES measurements of nanosecond-duration pulsed air-plasmas at atmospheric pressure. The newly developed system is used to measure the time evolution of the emission of N2(C), a critical species in the two-step mechanism of rapid heating characteristic of nanosecond pulsed discharges. Time resolution of less than 400 ps is achieved in the current system, a significant improvement over conventional OES measurements with ICCD cameras or photomultiplier tubes. In addition, as long as the driving voltage pulse lies within the streak camera sweep window, the entire plasma emission spectrum for a single discharge is acquired. This capability is in contrast to prior studies where the time-dependent emission is obtained by plotting measurements at single steps from separate discharges. The effect of pulse repetition frequency (PRF) on the N2(C) decay is investigated by recording emission spectra for single discharges at 5–100 kHz. The streak images clearly show that the decay time of the N2(C–B, 0–0) transition increases as the PRF is increased. The emission decay exhibits two distinct phases with significantly different decay rates, consistent with prior measurements. The 1/e lifetimes of the two decay regimes are found using exponential fits to the emission decay curves. In addition, joint statistics relating the decay times and energy deposited in the plasma were also obtained.