Power-law Time Dependence Research Articles

On the Rayleigh-Taylor unstable dynamics of three-dimensional interfacial coherent structures with time-dependent acceleration

Rayleigh-Taylor instability (RTI) occurs in a range of natural and industrial processes. Whereas the majority of existing studies have considered constant acceleration, RTI is in many instances driven by variable acceleration. Here we focus on RTI driven by acceleration with a power-law time-dependence, and, by applying a group theoretic method, find solutions to this classical nonlinear boundary value problem. We deduce that the dynamics is dominated by the acceleration and that the solutions depend critically on the acceleration parameters for values of the acceleration exponent greater than (-2). We find that in the early-time dynamics, the RTI growth-rate is defined by modified Bessel functions. For the late-time dynamics, we link the interface dynamics with an interfacial shear function, find a continuous family of regular asymptotic solutions and identify invariant properties of nonlinear RTI. The essentially interfacial and multi-scale character of the dynamics is also demonstrated. The velocity field is potential in the bulk, and vortical structures may appear at the interface due to interfacial shear. The multi-scale character becomes clear from the invariance properties of the dynamics. We achieve good agreement with existing observations and elaborate new benchmarks for future research.

Nanocomposite hydrogel of poly(vinyl alcohol) and biocatalytically synthesized polypyrrole as potential system for controlled release of metoprolol

The inclusion of nanostructures into cross-linked polymer networks allows obtaining nanocomposite hydrogels with suitable multifuncionalities for drug delivery applications. In this work, polypyrrole (PPy) nanoparticles, synthesized by a biocatalytic route, were encapsulated into a hydrogel matrix of poly(vinyl alcohol) (PVA) during its reticulation with glutaraldehyde. The novel composite hydrogels were characterized by infrared spectroscopy, thermogravimetric analysis, swelling kinetic measurements, scanning electron microscopy and cyclic voltammetry. The loading capabilities of PVA/PPy hydrogels were tested for metoprolol, a beta blocker used to treat angina, hypertension and to prevent heart attack. In vitro drug release profiles were obtained without and under electrical stimulations. The kinetics of drug release exhibited a power-law time dependence, typical of hydrogel-based systems. The application of electrical potentials changed the release rate of the drug, increasing or decreasing the delivery rate depending on bias voltage. Composite system of PVA and PPy combines the electrochemical redox properties of the conductive polymer with the swelling capacity and molecular diffusivity associated with PVA network; therefore, it can be considered a potential stimuli-responsive platform for biomedical applications.

Scaling and universality in extremal black hole perturbations

We show that the emergent near-horizon conformal symmetry of extremal black holes gives rise to universal behavior in perturbing fields, both near and far from the black hole horizon. The scale-invariance of the near-horizon region entails power law time-dependence with three universal features: (1) the decay off the horizon is always precisely twice as fast as the decay on the horizon; (2) the special rates of 1/t off the horizon and 1/sqrt{v} on the horizon commonly occur; and (3) sufficiently high-order transverse derivatives grow on the horizon (Aretakis instability). The results are simply understood in terms of near-horizon (AdS2) holography. We first show how the general features follow from symmetry alone and then go on to present the detailed universal behavior of scalar, electromagnetic, and gravitational perturbations of d-dimensional electrovacuum black holes.

Elucidating the Formation Mechanisms of Silver Nanoparticles from a Comprehensive Simulation Based on First-Principles Calculations

The nucleation and growth of silver nanoparticles are modeled and simulated based on first-principles calculations. The formation energy of single-crystal and multiply twinned particles is calculated to elucidate the thermodynamic properties of particles and modeled as a function of geometric parameters. On the basis of the calculated formation energy and the molecular collision theory, Kinetic Monte Carlo simulations are performed to trace the formation process of silver nanoparticles. In particular, the temporal change of size distribution and morphology are obtained and used to elucidate the governing mechanism in each stage of the formation process. It is demonstrated that the formation process is separated into four phases depending on the power-law time dependence of the particle formation and they are characterized by the size difference between coalescent particles. The temperature dependence of size distribution and morphology is also studied to elucidate the underlying mechanisms. The findings a...

Large energy storage efficiency of the dielectric layer of graphene nanocapacitors

Electric capacitors are commonly used in electronic circuits for the short-term storage of small amounts of energy. It is desirable however to use capacitors to store much larger energy amounts to replace rechargeable batteries. Unfortunately existing capacitors cannot store sufficient energy to be able to replace common electrochemical energy storage systems. Here we examine the energy storage capabilities of graphene nanocapacitors, which are tri-layer devices involving an Al film, Al2O3 dielectric layer, and a single layer of carbon atoms, i.e., graphene. This is a purely electronic capacitor and therefore it can function in a wide temperature interval. The capacitor shows a high dielectric breakdown electric field strength, of the order of 1000 kV mm−1 (i.e., 1 GV m−1), which is much larger than the table value of the Al2O3 dielectric strength. The corresponding energy density is 10–100 times larger than the energy density of a common electrolytic capacitor. Moreover, we discover that the amount of charge stored in the dielectric layer can be equal or can even exceed the amount of charge stored on the capacitor plates. The dielectric discharge current follows a power-law time dependence. We suggest a model to explain this behavior.

Detailed study of NBTI characterization in 40-nm CMOS process using comprehensive models**Project supported by the National Natural Science Foundation of China (Grant Nos. 61574056 and 61204038), the Natural Science Funds of Shanghai, China (Grant No. 14ZR1412000), the Fund from the Science and Technology Commission of Shanghai Municipality (Grant No. 14DZ2260800), and Shanghai Sailing Program (Grant No. 17YF1404700).

The impact of negative bias temperature instability (NBTI) can be ascribed to three mutually uncorrelated factors, including hole trapping by pre-existing traps ( in gate insulator, generated traps ( in bulk insulator, and interface trap generation (. In this paper, we have experimentally investigated the NBTI characteristic for a 40-nm complementary metal–oxide semiconductor (CMOS) process. The power-law time dependence, temperature activation, and field acceleration have also been explored based on the physical reaction–diffusion model. Moreover, the end-of-life of stressed device dependent on the variation of stress field and temperature have been evaluated. With the consideration of locking effect, the recovery characteristics have been modelled and discussed.

Extinction phase transitions in a model of ecological and evolutionary dynamics

We study the non-equilibrium phase transition between survival and extinction of spatially extended biological populations using an agent-based model. We especially focus on the effects of global temporal fluctuations of the environmental conditions, i.e., temporal disorder. Using large-scale Monte-Carlo simulations of up to $3\times 10^7$ organisms and $10^5$ generations, we find the extinction transition in time-independent environments to be in the well-known directed percolation universality class. In contrast, temporal disorder leads to a highly unusual extinction transition characterized by logarithmically slow population decay and enormous fluctuations even for large populations. The simulations provide strong evidence for this transition to be of exotic infinite-noise type, as recently predicted by a renormalization group theory. The transition is accompanied by temporal Griffiths phases featuring a power-law dependence of the life time on the population size.

Nearly Constant Loss (NCL) in Lithium Metasilicate Glass at Low Temperatures—Anisotropic and Dynamical Caging from Molecular Dynamics Simulations

Ions in ionically conducting materials show complex but universal trends in the time development of the mean squared displacements (MSD) of ions, which correspond to the complex frequency dependence conductivity spectra or susceptibility. Molecular dynamics simulations enable us to characterize the details of such motions including the initial nearly logarithmic or weak power law time dependence of the MSD of caged ions, showing up in susceptibility as the nearly constant loss (NCL) and the important connections of the caged ion dynamics to ion hopping dynamics in ionically conducting materials. In previous works, the motion of ions in the NCL region for lithium metasilicate was characterized at 700 and 500 K. Since each time region of MSD becomes longer and longer with decreasing temperature, the NCL region will cover the entire observation time during the MD run at lower temperatures, and thus enabling a more detailed study of the properties of the NCL. This paper reports results from new simulations at...

Modelling Transient Dynamics of Granular Slopes: MPM and DEM

Transient granular flows, such as rock falls, debris flows, and aerial and submarine avalanches, occur very often in nature. In the geotechnical context, transient movements of large granular slopes are a substantial factor of risk due to their destructive force and the transformations they may produce in the landscape. This paper investigates the ability of MPM, a continuum approach, to reproduce the evolution of a granular slope destabilised by an external energy source. In particular, a central issue is whether the power-law dependence of run-out distance and time observed with respect to the initial geometry or energy can be reproduced by a simple Mohr-Coulomb plastic behaviour. The effect of base friction on the run-out kinematics is studied by comparing the data obtained from the DEM and MPM simulations. The mechanism of energy dissipation is primarily through friction and the MPM is able to predict the run-out response in good agreement with the DEM simulations. At very low excitation energies, the DEM simulations show longer run-out in comparison to the MPM due to local destabilization at the flow front. At low input energies, a larger fraction of the energy is consumed in the destabilisation process, hence the amount energy available for flow is less. However, at higher input energy, where most of the energy is dissipated during the spreading phase, the run-out distance has a weak dependence on the distribution of velocity in the granular mass.

Kinetics of the hydration reaction at the electrolyte–insulator interface

The instability of the dc operating point in the pH-sensitive ion-selective field effect transistors (ISFETs) has been ascribed to a chemical ageing at the electrolyte–insulator. This instability, commonly referred to as a drift, is believed to involve formation of a chemically-modified insulator surface layer as a result of hydration of the insulator material. A kinetic model for hydration of the amorphous insulator material is presented. The kinetics of hydration is limited by the hopping and/or trap-limited transport mechanism known as dispersive transport, the key characteristic of which is a power-law time dependence of the diffusion coefficient. The power-law time dependence of the diffusion coefficient will be shown to lead to a stretchedexponential decay in the form exp[–(t/τ)β] for the excess density of sites or traps occupied by the hydrating chemical species undergoing dispersive diffusion, where τ is the time constant associated with a structural relaxation and β is the dispersion parameter satisfying 0 < β < 1. The kinetics associated with a hydration reaction limited by the dispersive diffusion has been shown to lead to a hydrated layer thickness exhibiting a time dependence in the form {1–exp[–(t/τ)β]}. The first order rate equation describing the kinetics of the hydration reaction is characterized by the time-dependent rate coefficient.

Analysis of Incubation Times for the Self-Induced Formation of GaN Nanowires: Influence of the Substrate on the Nucleation Mechanism

Surprisingly long incubation times for the self-induced formation of GaN nanowires on different substrates can reach hundreds of minutes and remain a mystery in GaN crystal growth. Herein, we examine the incubation times of GaN islands that subsequently give rise to nanowires on amorphous AlxOy/Si and SiNx/Si substrates versus the temperature and gallium flux. Experimental data are obtained by in situ monitoring of the surface morphology by reflection high energy electron diffraction during plasma-assisted molecular beam epitaxy. We develop a model that confirms an inverse power-law dependence of the incubation time on the gallium flux and the Arrhenius-type temperature dependence. The power exponent p and the activation energy Einc are related to the nucleation mechanism and the island growth regime. We find the values p ≅ 1, Einc = 6.0 eV for AlxOy, and p ≅ 2, Einc = 10.2 eV for SiNx buffer. The dominant nucleation mechanism on amorphous AlxOy should be heterogeneous. Homogeneous nucleation dominates on...

Addendum to “relaxation and creep in twist and flexure”

Purpose In this addendum, the purpose of this paper is to introduce the new creep law for the description of the different stages of creep. The introduced creep law generalizes the creep law used in Kobelev (2014). Design/methodology/approach The new generalized creep law demonstrates the relationship between creep rate and stress as well as accounts the time dependence in different creep regimes. In the stage of primary creep there is explicit time dependence of creep rate. In the stage of secondary creep the creep rate exhibits – analogously to the original creep law – no explicit dependence on time. Findings The closed form expressions giving the torque and bending moment as a function of the time are provided. The method is applicable for definite other stress functions in the creep law. Research limitations/implications The arbitrary creep law allows the separation of time and spatial variables; exponential and power-law time dependence. Practical implications The results of creep simulation are applied to practically important problem of engineering, namely for simulation of creep and relaxation of helical and disk spring, driveshafts, torque elements of machine dynamics. Originality/value The new creep model with fractional derivative of time dependence is introduced. The closed form solutions for new creep model allow simple formulas for creep effect on stress and deformation and the implications for high temperature design.

Correlated anomalous phase diffusion of coupled phononic modes in a sideband-driven resonator.

The dynamical backaction from a periodically driven optical cavity can reduce the damping of a mechanical resonator, leading to parametric instability accompanied by self-sustained oscillations. Here we study experimentally and theoretically new aspects of the backaction and the discrete time-translation symmetry of a driven system using a micromechanical resonator with two nonlinearly coupled vibrational modes with strongly differing frequencies and decay rates. We find self-sustained oscillations in both the low- and high-frequency modes. Their frequencies and amplitudes are determined by the nonlinearity, which also leads to bistability and hysteresis. The phase fluctuations of the two modes show near-perfect anti-correlation, a consequence of the discrete time-translation symmetry. Concurrently, the phase of each mode undergoes anomalous diffusion. The phase variance follows a power law time dependence, with an exponent determined by the 1/f-type resonator frequency noise. Our findings enable compensating for the fluctuations using a feedback scheme to achieve stable frequency downconversion.

Anomalously slow relaxation of the system of strongly interacting liquid clusters in a disordered nanoporous medium: Self-organized criticality

Abstract It has been shown that changes in the energy of a system of nonwetting liquid clusters confined in a random nanoporous medium in the process of relaxation can be written in the quasiparticle approximation in the form of the sum of the energies of local (metastable) configurations of liquid clusters interacting with clusters in the connected nearest pores. The energy spectrum and density of states of the local configuration have been calculated. It has been shown that the relaxation of the state of the system occurs through the scenario of self-organized criticality (SOC). The process is characterized by the expectation of a fluctuation necessary for overcoming a local energy barrier of the metastable state with the subsequent rapid hydrodynamic extrusion of the liquid under the action of the surface buoyancy forces of the nonwetting framework. In this case, the dependence of the interaction between local configurations on the number of filled pores belonging to the infinite percolation cluster of filled pores serves as an internal feedback initiating the SOC process. The calculations give a power-law time dependence of the relative volume of the confined liquid θ ∼ t − α ( α ∼ 0.1 ) . The developed model of the relaxation of the porous medium with the nonwetting liquid demonstrates possible mechanisms and scenarios of SOC for disordered atomic systems.

Anomalously slow relaxation of the system of liquid clusters in a disordered nanoporous medium according to the self-organized criticality scenario

We propose a physical model of a relaxation of states of clusters of nonwetting liquid confined in a random nanoporous medium. The relaxation is occurred by the self-organized criticality (SOC) scenario. Process is characterized by waiting for fluctuation necessary for overcoming of a local energy barrier with the subsequent avalanche hydrodynamic extrusion of the liquid by surface forces of the nonwetting frame. The dependence of the interaction between local configurations on the number of filled pores belonging to the infinite percolation cluster of filled pores serves as an internal feedback initiating the SOC process. The calculations give a power-law time dependence of the relative volume θ of the confined liquid θ∼t−ν (ν∼0.2) as in the picture of relaxation in the mean field approximation. The model of the relaxation of the porous medium with the nonwetting liquid demonstrates possible mechanisms and scenarios of SOC for relaxation of other disordered systems.

Field Structure of a Quasisoliton Approaching the Critical Point

Within the framework of an approximate approach based on the representation of the Gardnerequation solitons as compound structures (different-polarity kinks), the non-quasistationary evolution of such solitary waves, which is stipulated by the variable quadratic-nonlinearity parameter α. The structure of the composite soliton is studied in cases that are critical for the quasistationary description where the predicted increase in the solitary-wave scales becomes unbounded on finite spatio-temporal intervals. The dependence of the spatial scales of the quasisoliton-field distribution on the quadratic-nonlinearity coefficient near the critical point for the power-law time dependence α(t) is studied in detail. The obtained solution is compared with the results of direct numerical simulation of the Gardner equation with variable coefficients.

Origin of Initial Rapid Cell Current Reduction in Non-Volatile One-Time Programming Memory

The fast bit cell current (BCC) reduction in a one-time programming (OTP) device during high-temperature annealing will severely decrease the data retention (DR) capability. It is found that negative bias temperature instability-like degradation is responsible for this fast BCC shift, which is different from the well-known DR mechanism. The rapid floating gate charge diminution at the initial stage can be attributed to the recombination by hydrogen species as a result of the depassivation of Si–H bonds at the Si/SiO2 interface. Our experiments show that the BCC reduction rate follows a power-law time dependence $t^{-0.73}$ , which is in agreement with a simple analytical model based on interface state ( $N_{{\mathrm{it}}}$ ) generation and floating-gate voltage shift. These observations pave the way for further OTP DR reliability improvement.

Abnormal positive bias stress instability of In–Ga–Zn–O thin-film transistors with low-temperature Al2O3 gate dielectric

Low-temperature atomic layer deposition (ALD) was employed to deposit Al2O3 as a gate dielectric in amorphous In–Ga–Zn–O thin-film transistors fabricated at temperatures below 120 °C. The devices exhibited a negligible threshold voltage shift (ΔVT) during negative bias stress, but a more pronounced ΔVT under positive bias stress with a characteristic turnaround behavior from a positive ΔVT to a negative ΔVT. This abnormal positive bias instability is explained using a two-process model, including both electron trapping and hydrogen release and migration. Electron trapping induces the initial positive ΔVT, which can be fitted using the stretched exponential function. The breakage of residual AlO-H bonds in low-temperature ALD Al2O3 is triggered by the energetic channel electrons. The hydrogen atoms then diffuse toward the In–Ga–Zn–O channel and induce the negative ΔVT through electron doping with power-law time dependence. A rapid partial recovery of the negative ΔVT after stress is also observed during relaxation.

Self-similar nonequilibrium dynamics of a many-body system with power-law interactions.

The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic gases, which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a self-similar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration, and results in a scale invariance of the structure factor. Our findings show that in dissipative Rydberg gases out of equilibrium the characteristic distance among excitations-often referred to as the blockade radius-is not a static but rather a dynamic quantity.

An Experimental Perspective of Trap Generation Under BTI Stress

A gated-diode or direct current IV method is used to characterize trap generation (TG) under negative-bias temperature instability (NBTI) and positive-bias temperature instability (PBTI) stress in different planar high-k metal gate p-channel and n-channel MOSFETs, respectively. After correction of the measurement delay, very similar time (tSTR), voltage (VG,STR), temperature (T), AC pulse duty cycle, and frequency ( f ) dependence of TG is seen for NBTI and PBTI. Measured TG shows power-law time dependence with a time exponent of n ~ 0.16 for NBTI and PBTI and for DC and AC stress. Uncoupled nature of voltage acceleration (Γ) and T activation (EA) is seen. Interlayer scaling has a similar impact on EA and Γ for NBTI and PBTI. However, the physical location of TG is shown to be different for NBTI and PBTI stress.