Time Exponent Research Articles

The microstructural development and erosion mechanism of BaZrO3/Al2O3 double ceramics by Ti–46Al–8Nb alloy melt

In this study, the erosion of BaZrO3/Al2O3 double ceramics by Ti–46Al–8Nb alloy melt was investigated at different melting temperatures (1833 K, 1873 K and 1913 K) and time (1800 s, 3600 s, 5400 s and 7200 s). The microstructure of erosion layer and the alloy ingot were analyzed as well as the oxygen content of the alloy ingot. The erosion mechanism was clarified in the kinetic perspectives. The results showed that the new oxide BaAl2O4 production was attached on the ingot surface, and two kinds of inclusions, i.e., (Ti, Zr)5(Si, Al)3 and YAlO3, were formed in the ingot matrix. The thickness of erosion layer, the oxygen content of ingot, and the volume fraction of inclusions increased with increasing melting temperatures and time. In addition, these three phenomena were controlled by the kinetics of dissolution, and the time exponents were approximately equaled to 0.5, indicating that the erosion mechanism was dissolution controlled by mutual diffusion between the double ceramics and alloy melts. The activation energies of three phenomena were determined by Arrhenius equation, and three kinetic models were further established.

Spectral induced polarization tomography inversion: Hybridizing homotopic continuation with Bayesian inversion

Induced polarization tomography offers the potential to better characterize the subsurface structures by considering spectral content from data acquisition over a broad frequency range. Spectral induced polarization (SIP) tomography is generally defined as a nonlinear inverse problem commonly solved through deterministic gradient-based methods. To this end, the spectral parameters, i.e., direct current resistivity, chargeability, relaxation time, and frequency exponent, are resolved by individually or simultaneously inverting all frequency data, followed by fitting a generalized Cole-Cole model to the inverted complex resistivities. Due to the high correlation between the Cole-Cole model parameters and a lack of knowledge about the initial approximation of the spectral parameters, using the classical least-squares methods may lead to inaccurate solutions and impede reliable uncertainty analysis. To cope with these limitations, we introduce a new approach based on a hybrid application of a globally convergent homotopic continuation method and a Bayesian inference to reconstruct the distribution of the subsurface spectral parameters. The homotopic optimization, owing to its fast and global convergence, is first implemented to invert multifrequency SIP data sets aimed at retrieving the complex-valued resistivity. Then, Bayesian inversion based on a Markov chain Monte Carlo (MCMC) sampling method, along with a priori information including the lower and upper bounds of the prior distributions, is used to invert the complex resistivity for the Cole-Cole model parameters. By applying the MCMC inversion algorithm, a full nonlinear uncertainty appraisal can be provided. We numerically evaluate the performance of our method using synthetic and real data examples in the presence of topographical effects. Numerical results prove that the homotopic continuation method outperforms the classic, smooth inversion algorithm in the sense of approximation accuracy and computational efficiency. In addition, we determine that our hybrid inversion strategy provides reliable representations of the main features and structure of the earth’s subsurface in terms of the spectral parameters.

Sharp corner singularity of the White–Metzner model

The stress singularity is determined using matched asymptotics for complete flow of a White–Metzner (WM) fluid around a re-entrant corner. The model is considered in the absence of a solvent viscosity, with power-law forms for the relaxation time and polymer viscosity. In this form, the model shares the same stress singularity as the upper convected Maxwell (UCM) model, but its wall boundary layers may be thinner or thicker than those for UCM depending upon the relative difference in the power-law exponents. If the exponent for the relaxation time is greater than that for the polymer viscosity, the boundary layer is narrower, whilst it is thicker if the polymer viscosity exponent exceeds that of the relaxation time. When the exponents are the same, the WM boundary layer thickness is the same size as that for UCM. A self-similar solution is derived for the stress and velocity fields and matched to both upstream and downstream boundary layers. Restrictions on the sizes of the power-law exponents are also given for validity of this solution.

Faster Modular Composition

A new Las Vegas algorithm is presented for the composition of two polynomials modulo a third one, over an arbitrary field. When the degrees of these polynomials are bounded by n , the algorithm uses O ( n 1.43 ) field operations, breaking through the 3/2 barrier in the exponent for the first time. The previous fastest algebraic algorithms, due to Brent and Kung in 1978, require O ( n 1.63 ) field operations in general, and n 3/2+ o (1) field operations in the special case of power series over a field of large enough characteristic. If cubic-time matrix multiplication is used, the new algorithm runs in n 5/3+ o (1) operations, while previous ones run in O ( n 2 ) operations. Our approach relies on the computation of a matrix of algebraic relations that is typically of small size. Randomization is used to reduce arbitrary input to this favorable situation.

Metastability for the degenerate Potts Model with positive external magnetic field under Glauber dynamics

We consider the ferromagnetic q-state Potts model on a finite grid graph with non-zero external field and periodic boundary conditions. The system evolves according to Glauber-type dynamics described by the Metropolis algorithm, and we focus on the low temperature asymptotic regime. We analyze the case of positive external magnetic field associated to one spin value. In this energy landscape there is one stable configuration and q−1 metastable states. We study the asymptotic behavior of the first hitting time from any metastable state to the stable configuration as β→∞ in probability, in expectation, and in distribution. We also identify the exponent of the mixing time and find an upper and a lower bound for the spectral gap. Finally, we identify all the minimal gates and the tube of typical trajectories for the transition from any metastable state to the unique stable configuration by giving a geometric characterization.

Interface reactions between copper and 50In-50Pb (wt%) alloy by solid-state aging

This study investigated the interface microstructure that developed between 50In-50Pb (wt%) solder and copper (Cu) base material as a function of solid-state aging. The aging temperatures and times were in the range of 55°C – 170°C and 1 – 350 days, respectively. The analysis examined the intermetallic compound (IMC) layer compositions; the rate kinetics of IMC layer growth; and the role of the IMC layer on solder joint shear strength. The IMC layer transitioned from pseudo-equilibrium compositions towards an equilibrium composition of Cu11In9 (φ phase) with an increased degree of aging, illustrating the non-equilibrium nature of the interface. The rate kinetics for solid-state IMC formation exhibited a time exponent, n, of 0.47±0.09, which indicated a diffusion-controlled reaction. The relatively low, apparent activation energy, ΔH, of 23±4 kJ/mol implied an anomalously-fast diffusion mechanism. The shear stresses were 22±2 MPa and 19±1 MPa for the 0.190 mm and 0.380 mm joint clearances, respectively, representing the as-fabricated condition; the difference reflected the plane strain effect. The crack path remained in the In-Pb solder so that the In-Pb microstructure, not the thickness, composition, or morphology of the IMC layer, controlled shear strength for either joint clearance. The shear strength trends differed between joint clearances due to competing processes in the In-Pb solder. Precipitation and re-solutionization of Cu dissolved in the In-Pb solder controlled the effects of aging on the shear strength of the 0.190 mm joint clearance while traditional recovery and recrystallization mechanisms determined the aging response of the 0.380 mm solder joints.

Quantum control and quantum speed limits of single-well systems

Achieving precise control and efficient manipulation of different quantum states is one of the most important goals of quantum technology. We study the quantum control and quantum speed limits of single-well systems by taking a harmonic oscillator whose frequency is a power function of time as an example when the transitionless quantum driving is imposed. For different eigenstates, we reveal the effects of control time and power exponent on Bures angle, fidelity, time-averaged cost, and quantum-speed-limit time. We find that the shortest control time for any eigenstate is proportional to the control parameter (i.e., power exponent). For different eigenstates meeting the same high fidelity requirements, it is shown that an optimal control parameter can always be obtained. Our findings provide theoretical support for the rapid and efficient manipulation of quantum states in single-well systems by using shortcut-to-adiabaticity technique experimentally.

Effects of Al3Ni compound on localized plastic deformation and creep strain of Al/Si hypoeutectic material

The mechanical resistance of AS10/xNi hypoeutectic alloy with (x = 0.05% and 0.1%) has been investigated. Vickers hardness (HV) was determined for the samples before and after sintering. All samples were subjected to a compressive creep test at a constant temperature of 298 K and a constant load of 45 MPa. Creep parameters, such as creep rate, sensitivity (m), time exponent (n), β, and ɣ have been calculated and related to the Ni content. Microstructure investigation was conducted using the scanning electron microscope technique (SEMT). After sintering, the results showed that there was a significant improvement in the hardness with the addition of nickel. There is an increase in creep resistance as a result of the distribution of Al3Ni chemical compound across grain boundaries, which stops additional dislocation movement and hence reduces the creep rate.

Cosmological complexity in K-essence

We calculate the cosmological complexity under the framework of scalar curvature perturbations for a K-essence model with constant potential. In particular, the squeezed quantum states are defined by acting a two-mode squeezed operator which is characterized by squeezing parameters rk and ϕk on vacuum state. The evolution of these squeezing parameters are governed by the Schrödinger equation, in which the Hamiltonian operator is derived from the cosmological perturbative action. With aid of the solutions of rk and ϕk, one can calculate the quantum circuit complexity between unsqueezed vacuum state and squeezed quantum states via the wave-function approach. One advantage of K-essence is that it allows us to explore the effects of varied sound speeds on evolution of cosmological complexity. Besides, this model also provides a way for us to distinguish the different cosmological phases by extracting some basic information, like the scrambling time and Lyapunov exponent etc, from the evolution of cosmological complexity.

Dynamic stability of the sandwich nano-beam system

This article explores the stochastic stability of a three nanobeam system connected by Kerr type elastic layer, subjected to the magnetic effects and compressive axial forces. While considering nano beams rotary inertia is taken into account and differential equations of nanobeams are given according to Eringen's nonlocal elasticity theory. The impact of a longitudinal magnetic field on the behavior of the nanobeam system is described using Lorentz magnetic forces. The objective of this research paper is to investigate the moment and almost sure stability of the system. It analyzes the system's stability under white noise excitation by employing the contact transformation method and perturbation approach. Notably, we consider the case where the system exhibits low damping. The study focuses on examining the system's dynamic behavior and stability characteristics under these conditions. The stochastic stability of this system is investigated through moment Lyapunov exponents and Lyapunov exponents for the first time and interesting conclusions regarding the stability region of this system were obtained by varying various system parameters. These conclusions are presented in a visual manner and discussed.

A Simplified Model of Activation and Deactivation of Human Rod Phototransduction-An Electroretinographic Study.

To test the hypothesis that a simple model having properties consistent with activation and deactivation in the rod approximates the whole time course of the photoresponse. Routinely, an exponential of the form f = α·(1 - exp(-(τ·(t - teff)s-1))), with amplitude α, rate constant τ (often scaled by intensity), irreducible delay teff, and time exponent s-1, is fit to the early period of the flash electroretinogram. Notably, s (an integer) represents the three integrating stages in the rod amplification cascade (rhodopsin isomerization, transducin activation, and cGMP hydrolysis). The time course of the photoresponse to a 0.17 cd·s·m-2 conditioning flash (CF) was determined in 21 healthy eyes by presenting the CF plus a bright probe flash (PF) in tandem, separated by interstimulus intervals (ISIs) of 0.01 to 1.4 seconds, and calculating the proportion of the PF a-wave suppressed by the CF at each ISI. To test if similar kinetics describe deactivation, difference of exponential (DoE) functions with common α and teff parameters, respective rate constants for the initiation (I) and quenching (Q) phases of the response, and specified values of s (sI, sQ), were compared to the photoresponse time course. As hypothesized, the optimal values of sI and sQ were 3 and 2, respectively. Mean ± SD α was 0.80 ± 0.066, I was 7700 ± 2400 m2·cd-1·s-3, and Q was 1.4 ± 0.47 s-1. Overall, r2 was 0.93. A method, including a DoE model with just three free parameters (α, I, Q), that robustly captures the magnitude and time-constants of the complete rod response, was produced. Only two steps integrate to quench the rod photoresponse.

A Study on the Interfacial Reactions between Gallium and Cu/Ni/Au(Pd) Multilayer Metallization.

This research introduces low-temperature soldering of Ga with practical metallization structures, namely, Cu/Ni/Pd and Cu/Ni/Au, applied to contemporary microelectronic packages. Through these multilayer configurations, the study investigates the stability of the Ni diffusion barrier by examining changes in the interfacial microstructure as Ni is consumed. The interfacial reactions are conducted across a temperature spectrum of 160, 200, 240, and 280 °C, with reaction durations ranging from 30 to 270 min. Valuable insights for low-temperature soldering with Ga are extracted from the data. At lower reaction temperatures, the presence of Ga-rich intermetallic compounds (IMCs), specifically GaxNi (x = 89 to 95 at%), on the Ga7Ni3 layer is notably confirmed. As the reaction temperature and duration increase, the gradual consumption of the Ni layer occurs. This gives rise to the formation of Ga-Cu IMCs, specifically CuGa2 and γ3-Cu9Ga4, beneath the Ga-Ni IMC layer. Concurrently, the gap between the Ga-Ni and Ga-Cu IMC layers widens, allowing molten Ga to infiltrate. The rate of Ga7Ni3 growth follows a time exponent ranging approximately from 1.1 to 1.7. This highlights the significant influence of interface reaction-controlled kinetics on Ga7Ni3 IMC growth. The activation energy for Ga7Ni3 growth is determined to be 61.5 kJ/mol. The growth of Ga7Ni3 is believed to be primarily driven by the diffusion of Ga atoms along grain boundaries, with the porous microstructure inherent in the Ga7Ni3 layer providing additional diffusion pathways.

A spall and diffraction study of nanosecond pressure release across the iron ε-α phase boundary

The extreme response of polycrystalline iron at high pressures and high strain rates is revealed by means of high-power laser pulses. The compression portion of the pulse coupled with x-ray diffraction identifies the expected body-centered cubic (α) to hexagonal close packed (ε) displacive transformation. Upon release, observation shows that the complete reverse transformation takes approximately 8 ns and that the structure returns to its initial microstructural configuration, in a reversible transformation path. This is in good agreement with molecular dynamics (MD) simulations which predict an inverse dependence between transformation time and strain rate. The grain size is reduced from μm to nm range during compression and begins increasing back to the original grain size on decompression. The kinetics of the transition is dictated by heterogenous nucleation as it follows the Johnson-Mehl-Avrami-Kolmogorov equation with the appropriate time exponent of ∼1. This is confirmed by MD simulations which also identify profuse twinning and dislocation generation. The tensile pulse generated upon reflection at the free surface is captured by time-resolved free surface velocity measurements from which a peak tensile stress of 7 GPa is obtained, in stark contrast with its quasi-static value of ∼200 MPa. At these strain rates, the strength of grain interiors, which is determined by twinning and slip exceeds the strength of the boundaries, and failure initiates preferentially in the latter.

Investigation of degradation and recovery characteristics of NBTI in 28-nm high-k metal gate process

Degradation induced by the negative bias temperature instability (NBTI) can be attributed to three mutually uncoupled physical mechanisms, i.e., the generation of interface traps (ΔV IT), hole trapping in pre-existing gate oxide defects (ΔV HT), and the generation of gate oxide defects (ΔV OT). In this work, the characteristic of NBTI for p-type MOSFET fabricated by using a 28-nm high-k metal gate (HKMG) process is thoroughly studied. The experimental results show that the degradation is enhanced at a larger stress bias and higher temperature. The effects of the three underlying subcomponents are evaluated by using the comprehensive models. It is found that the generation of interface traps dominates the NBTI degradation during long-time NBTI stress. Moreover, the NBTI parameters of the power-law time exponent and temperature activation energy as well as the gate oxide field acceleration are extracted. The dependence of operating lifetime on stress bias and temperature is also discussed. It is observed that NBTI lifetime significantly decreases as the stress increases. Furthermore, the decrease of charges related to interface traps and hole detrapping in pre-existing gate oxide defects are used to explain the recovery mechanism after stress.

Entropy generation and flow characteristics of Powell Eyring fluid under effects of time sale and viscosities parameters

Shear thinning fluids are widely used in the food and polymer industries due to their unique flow characteristics. The flow behavior of these fluids has been commonly studied using the Powell Eyring model under a small shear rate assumption. However, this assumption is not always valid. In this study, we explore the transport characteristics of a Powell Eyring fluid over a variable thicker sheet, not only at small shear rates but also at medium and high shear rates. Furthermore, we calculate the rate of entropy generation based on the assumptions. Generalized Powell–Eyring model of viscosity is used for the fluid, representing the re-arrangements of molecules in the forward and backward directions through the theory of potential energy. The model concludes the sensitivity of the viscosity from zero to infinite shear rate along time sale and exponent parameters. The model is used in the transport phenomena equations. The solution of the equation is obtained by using the numerical method and used to calculate the rate of entropy generation. The results are presented in the form of velocity and temperature profiles, the average rate of entropy generation, skin friction coefficient and Nusselt number under the influence of various viscosity parameters. It is found that velocity and temperature profiles are decreased and increased respectively against the time scale parameter.

Diffusion of knots in nanochannel-confined DNA molecules.

We used Langevin dynamics simulations without hydrodynamic interactions to probe knot diffusion mechanisms and the time scales governing the evolution and the spontaneous untying of trefoil knots in nanochannel-confined DNA molecules in the extended de Gennes regime. The knot untying follows an "opening up process," wherein the initially tight knot continues growing and fluctuating in size as it moves toward the end of the DNA molecule before its annihilation at the chain end. The mean knot size increases significantly and sub-linearly with increasing chain contour length. The knot diffusion in nanochannel-confined DNA molecules is subdiffusive, with the unknotting time scaling with chain contour length with an exponent of 2.64 ± 0.23 to within a 95% confidence interval. The scaling exponent for the mean unknotting time vs chain contour length, along with visual inspection of the knot conformations, suggests that the knot diffusion mechanism is a combination of self-reptation and knot region breathing for the simulated parameters.

Unintentional force drifts in the lower extremities.

We explored the phenomenon of unintentional force drift seen in the absence of visual feedback during knee extension contractions in isometric conditions. Based on the importance of knee extensors for the anti-gravity function, we hypothesized that such force drifts would be slower and smaller compared to those reported for the upper extremities. We also explored possible effects of foot dominance and gender on the force drifts. Young healthy persons produced isometric knee extension contractions to different levels, ranging from 15 to 25% of maximal voluntary contraction force, with the help of visual feedback, and then, the visual feedback was turned off. Force change over the time interval without visual feedback was quantified. In the absence of visual feedback, force drifted to smaller magnitudes. The drift magnitude expressed in percent of the initial force magnitude was smaller for smaller initial force levels, ranging between 8 and 15% of the initial force for the initial force magnitude of 15% and 25% of maximal voluntary contraction force. The time exponent of the force drift was independent of the initial force magnitude and was, on average, 6.45s. There were no significant effects of foot dominance or gender, although the male subjects tended to show stronger scaling of the drift magnitude with the initial force level compared to the female subjects. The results show that unintentional force drift is a common phenomenon across limbs and muscle groups. This conclusion fits the theory of control with spatial referent coordinates and the general tendency of all natural systems to drift to states with lower potential energy.

Non-uniform mechanical behaviour of uniaxially rolled Ti–6Al–4V with micro-texture regions

Uniaxial strain rate controlled and creep behavior of a unidirectionally rolled Ti–6Al–4V with micro-texture regions (MTR) were studied. The presence of MTR was identified and characterized using polarized light microscopy (PLM) and correlated with electron back-scatter diffraction (EBSD). Uniaxial tests were carried out along the rolling (RD), transverse (TD) and normal (ND) directions. Uniaxial strain rate controlled tests at strain rates of 10−3, 10−4 and 10−5 s−1 showed noticeable strain rate sensitivity at both room temperature (RT) and 200 °C. The yield strength in RD and TD was higher than ND by 16% and 8%, respectively. Creep behavior was sensitive to the initial strain rate during loading. The creep strain was fitted to a Norton-Bailey power law, ε=Aσntα, where ε, σ and t are creep strain, stress and time, respectively and A, n and α are constants, and showed a primary stress exponent, n, of 15 at RT and 10.4 at 200 °C and a time exponent, α, of 0.31 at RT and 0.125 at 200°C. In a first-of-its-kind exercise, PLM-EBSD was augmented with DIC in uniaxial strain rate controlled and creep tests for precise strain measurement and microstructural correlation with the directionality of testing. It revealed a significant effect of MTR on strain localization which may explain the role of MTR in failure nucleation.

Discovering a formula for the high temperature oxidation behavior of FeCrAlCoNi based high entropy alloys by domain knowledge-guided machine learning

A mathematical formula of high physical interpretation, and accurate prediction and large generalization power is highly desirable for science, technology and engineering. In this study, we performed a domain knowledge-guided machine learning to discover high interpretive formula describing the high-temperature oxidation behavior of FeCrAlCoNi-based high entropy alloys (HEAs). The domain knowledge suggests that the exposure time dependent and thermally activated oxidation behavior can be described by the synergy formula of power law multiplying Arrhenius equation. The pre-factor, time exponent (m), and activation energy (Q) are dependent on the chemical compositions of eight elements in the FeCrAlCoNi-based HEAs. The Tree-Classifier for Linear Regression (TCLR) algorithm utilizes the two experimental features of exposure time (t) and temperature (T) to extract the spectrums of activation energy (Q) and time exponent (m) from the complex and high dimensional feature space, which automatically gives the spectrum of pre-factor. The three spectrums are assembled by using the element features, which leads to a general and interpretive formula with high prediction accuracy of the determination coefficient R2=0.971. The role of each chemical element in the high-temperature oxidation behavior is analytically illustrated in the three spectrums, thereby the discovered interpretative formula provides a guidance to the inverse design of HEAs against high-temperature oxidation. The present work demonstrates the significance of domain knowledge in the development of materials informatics.

Bifurcations, relaxation time, and critical exponents in a dissipative or conservative Fermi model.

We investigated the time evolution for the stationary state at different bifurcations of a dissipative version of the Fermi-Ulam accelerator model. For local bifurcations, as period-doubling bifurcations, the convergence to the inactive state is made using a homogeneous and generalized function at the bifurcation parameter. It leads to a set of three critical exponents that are universal for such bifurcation. Near bifurcation, an exponential decay describes convergence whose relaxation time is characterized by a power law. For global bifurcation, as noticed for a boundary crisis, where a chaotic transient suddenly replaces a chaotic attractor after a tiny change of control parameters, the survival probability is described by an exponential decay whose transient time is given by a power law.