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In this article, the performance of brass electrode was investigated in a Zn-air (charcoal-based cathode) rechargeable battery. The construction of the battery was carried out with biodegradable materials, namely a cotton cloth diaphragm and carboxymethyl cellulose sodium salt (CMC-Na) viscosity modifier, while the battery skeleton was printed by 3D printing technology. The brass acted as a collector and a preferable surface for the metallic Zn deposition on the brass anode surface. The electrochemical behavior of the brass anode was investigated by cyclic voltammetry (CV). Cyclic performance tests were carried out, which showed stable cell operation even in the presence or absence of additives up to more than 100 cycles. Furthermore, high energy (Eeff) and Coulomb (Ceff) efficiencies, 80% (Eeff), 95% (Ceff), 75% (Eeff), and 95% (Ceff) were obtained, respectively. The Shepherd model was applied to describe the discharging processes of the Zn-air battery containing brass as anode in the presence of additive-free electrolyte or electrolyte with CMC-Na salt additive. It was found that the Shepherd equation described only approximately the resulting discharge curves. In order to attain a more precise mathematical description, stretched exponential function was implemented into the last term of the Shepherd equation. The need for such a correction shows the complexity of the electrochemical processes occurring in these systems. In addition, the surface of the brass anode was also investigated by scanning electron microscopy (SEM) and the composition of the brass alloys was determined by X-ray fluorescence spectroscopy (XRF). Importantly, the formation of dendritic deposition was successfully suppressed and a smooth and uniform surface was obtained after the cycling tests.

In this study, we investigated the threshold voltage (Vth) instability of solution-processed indium zinc oxide (IZO) thin film transistors (TFTs) prior to and after negative bias illumination stress (NBIS) with varying carrier suppressors (Ga, Al, Hf, and Zr). Variations in electrical properties of the IZO-based TFTs as a function of carrier suppressors were attributed to the differences in metal-oxygen bonding energy of the materials, which was numerically verified by calculating the relative oxygen deficient ratio from the X-ray photoelectron spectroscopy analysis. Furthermore, the values of Vth shift (ΔVth) of the devices subjected to negative gate bias stress under 635 nm (red), 530 nm (green), and 480 nm (blue) wavelength light irradiation increased as the incident photon energy increased. IZO TFTs doped with Ga atoms demonstrated weaker metal-oxygen bonding energy compared to the others and exhibited the largest ΔVth. This result was attributed to the suppressor-dependent distribution of neutral oxygen vacancies which determine the degrees of photon energy absorption in the IZO films. Then, the ΔVth instability of IZO-based TFTs under NBIS correlated well with a stretched exponential function.

We present the comprehensive analysis and the compact modeling methodology of fast electron detrapping from the bandgap engineered tunneling oxide (BE-TOX) in 3-D NAND flash memories. To this end, we develop a physics-based detrapping model considering the detailed electron dynamics in the BE-TOX and various emission paths of the detrapping mechanism. By the aid of the carrier density rates from the accurately calibrated model, we find that the major path of the charge loss can be direct tunneling (DT) or trap-to-band tunneling (TBT) depending on the temperature and the nitride layer position in the BE-TOX. In addition, we compare the model result and the fitted stretched exponential function. From those comparisons, we correlate several indicators (time constant and curve shape) of the retention characteristics with the major paths of the charge loss. Finally, our model facilitates the quantitative separation of the detrapping mechanism into different paths.

In this work, we study the relaxation behavior of a densified sodium aluminoborate glass by means of coupled Raman spectroscopy, Brillouin spectroscopy, and differential scanning calorimetry analyses. First, we show that the changes in elastic properties upon densification are largely associated with structural modifications in the glass network at short- and medium-range orders. Then, the evolution of the structural and elastic properties of the densified glass has been monitored in situ in the coupled DSC-Brillouin-Raman setup during isothermal annealing at different temperatures below the glass transition temperature. The stretched exponential function is found to well describe the observed relaxation kinetics, however, the stretching factor β varies non-monotonically with temperature. In contrast, the Arrhenius behavior of the characteristic decay times is deduced by lifetime distribution analysis, revealing three different relaxation processes with typical activation energies of 170±25, 200±5, and 280±15 kJ/mol. The relative contributions of these processes to the overall relaxation kinetics are found to vary with the temperature as well as the type of parameter considered (structural, elastic, or thermal), and hence, the relaxation kinetics cannot be properly understood using the stretched exponent function. The possible origins of the different relaxation processes are discussed.

This work reports the effect of thermal annealing (353–413 K) on structure and physical properties of thermally evaporated In10Ag10Sb10Se70 chalcogenide films. The samples were characterized by X-ray diffraction, transmission electron microscopy, TEM, Raman spectroscopy, optical absorption and photoconductivity measurements. Thermal annealing favours amorphous to polycrystalline structure transition with the growth of Se, AgInSe2 and AgSbSe2 phases. A significant change in position/shape of Raman bands upon annealing has been observed. The indirect optical gap decreases from 1.44 to 0.68 eV while tailing parameter increases with annealing. Photosensitivity decreases from 29.3 to 14.2 with annealing temperature. The decay of photocurrents is well fitted to stretched exponential function; the value of decay time constant increases while local minimum value of dispersion parameter at 353 K has been observed. These results are explained on the basis of amorphous crystalline phase transformation in chalcogenides and are important for developing new materials for emerging technologies.

Modeling of non-idealities in ion-sensitive field-effect transistors (ISFET) is crucial for obtaining precise pH-sensing characteristics. This paper presents an accurate Simulation Program with Integrated Circuit Emphasis (SPICE) macromodel of a $$\hbox {Si}_{3}\hbox {N}_{4}$$–gate ISFET pH sensor which takes into account the temperature and temporal drift. The robust model includes surface site densities of both the silanol and primary amine sites, which were approximated in previously reported ISFET macromodels. We use a thermodynamic model to incorporate the variation of dissociation constants with temperature to achieve a better fit with experimental data reported in the literature. Several regression iterations are performed, and an average adjusted R-squared value of 0.9992 is obtained. The transfer characteristics of the device obtained from the extracted parameters are in good agreement with the experimentally reported values, with an error of 3.53% and 2.29% between the reported and modeled isothermal points for gate voltage ($${V}_{\mathrm{GS}}$$) and drain current ($${I}_{\mathrm{DS}}$$), respectively. The developed macromodel is imported in a constant voltage/constant current (CVCC) readout circuit as a subcircuit block and simulated in a temperature range of 15–$$45\, ^{\circ }\hbox {C}$$. Simulations of the CVCC readout circuit show that operating the device near the isothermal point reduces the temperature drift to approximately 0.015 pH for the pH range of human blood, i.e., pH 7.35 to 7.45. Temporal drift modeling and simulation are performed, and show a stretched exponential dependence on time, which is in good agreement with experimental results reported in the literature. Finally, we demonstrate the combined effect of temporal and temperature drift, where it is found that the temporal drift rate increases with temperature as a stretched exponential function, validating the experimentally reported values.

We have reported novel 2D monoclinic, P63/mnm, δ-MnO2 nanowhiskers synthesized through a simple and facile hydrothermal route under optimized conditions without using any template. The X-ray diffraction pattern shows the formation of the δ phase of MnO2, which is further confirmed by Fourier transform infrared (FT-IR) spectroscopy and Raman spectroscopy. The transmission electron micrograph revealed nanowhiskers having a diameter of ∼7 nm and the high-resolution TEM and SAED patterns demonstrated the interplanar spacing and distinguished diffraction rings corresponding to the monoclinic phase of δ-MnO2. Fitting the temperature-dependent susceptibility with the Curie–Weiss law confirms the strong antiferromagnetic ordering and high effective magnetic moment of Mn4+ present in δ-MnO2. The large effective magnetic moment is attributed to the presence of both Mn3+ and Mn4+, as confirmed by XPS. The reduced valency of Mn from 4 to 3 is accompanied with oxygen vacancies, affording the exact composition of MnO1.58. The dynamic magnetic properties of the δ-MnO2 nanowhiskers were investigated using the frequency-dependent AC susceptibility fitted with various phenomenological models like the Vogel–Fulcher law and power law, indicating the existence of interacting spin clusters, which could freeze at ∼11.2 K. The time dependence of thermoremanent magnetization fitted well with a stretched exponential function, supporting the existence of relaxing spin clusters. Thus, the spin glass relaxation in the δ-MnO2 nanowhiskers is attributed to the interaction between Mn4+ and Mn3+, which results in intrinsic magnetic frustration and weak ferromagnetism with finite coercivity below Tf.

We have constructed the basic dielectric relaxations evolution expression for relaxing current as convolution operation of the chosen memory kernel and rate of change of applied voltage. We have studied types of memory kernels singular, non-singular and combination of singular and non-singular (mixed) decaying functions. With these, we form constitutive equations for relaxation dynamics of dielectrics; i.e. capacitor. We observe that though mathematically we can use non-singular kernels yet this does not give presently much useful practical or physically realizable results and interpretations. We relate our observations to relaxation currents given via Curie-von Schweidler and Kohlraush laws. The Curie-von Schweidler law gives singular function power law as basic relaxation current in dielectric relaxation; whereas the Kohlraush law is Electric field relaxation in dielectric as non-Debye function taken as stretched exponential i.e. non-singular function. These two laws are used since late nineteenth century for various dielectric relaxation and characterization studies. Here we arrive at general constitutive equation for capacitor and with each type of memory kernel we give corresponding impedance function and in some cases equivalent circuit representation for the capacitor element. We classify these systems as Curie-von Shweidler type for system with singular memory kernel function and Kohlraush type for system evolved via using non-singular function or mixed functions as memory kernel. We note that use of singular memory kernel gives constituent relations and impedance functions that are experimentally verified in large number of cases of dielectric studies. Therefore, we have a question, does natural relaxation dynamics for dielectrics have a singular memory kernel, and the relaxation current function is singular in nature? Is it the singular relaxation function for capacitor dynamics with singular memory kernel remains universal law for dielectric relaxation? However, we are not questioning researchers modeling relaxation of dielectric via non-singular functions, yet we are hinting about complexity and lack of interpretability of basic constituent equation of dielectric relaxation dynamics thus obtained via considering non-singular and mixed memory kernels; perhaps due to insufficient experimental evidences presently. However, the method employed in this study is general method. This method can be used to form memorized constituent equations for other systems (say Radioactive Decay/Growth, Diffusion and Wave phenomena) from basic evolution equation, i.e. effect function as convolution of memory kernel with cause function.

We present a treatment of the non-Markovian character of memory by incorporating different forms of Mittag-Leffler (ML) function, which generally arises in the solution of a fractional master equation, as different memory functions in the Generalized Kolmogorov-Feller Equation (GKFE). The cross-over from the short time (stretched exponential) to long time (inverse power law) approximations of the ML function incorporated in the GKFE is proven. We have found that the GKFE solutions are the same for negative exponential and upto first order expansion of the stretched exponential function for very small $$\tau \rightarrow 0$$ . A generalized integro-differential equation form of the GKFE along with an asymptotic case is provided.

Multiple-quantum (MQ) nuclear magnetic resonance (NMR) was used to characterize the proton distribution in methyltrimethoxysilane gel (MS gel, [CH3SiO3/2]n) and octavinylsilsesquioxane (OVS, [CH2=CHSiO3/2]8). The Gaussian model of distribution of MQ coherence intensities was used to determine the effective 1H spin-cluster size (N). The growth rate was described by the exponents α in the scaling law of the form N ~ τα. The obtained values of α were 1.65 for MS gel and 1.78 for OVS. The magnitudes of the growth exponents were compared to the previously obtained values for hybrid organic–inorganic gels. The influence of the dipolar coupling strength and the arrangement of spins in these systems on the growth of MQ NMR coherences is discussed. The shape of MQ NMR coherence profiles was investigated. It was found that the intensity profiles of MQ NMR coherences at different excitation times in the investigated hybrid silica gels are similar and may be well approximated by a stretched exponential function.

We study a stochastic lattice model describing the dynamics of a group chasing and escaping between two species in an environment that contains obstacles. The Monte Carlo simulations are carried out on a two-dimensional square lattice. Obstacles are represented by non-overlapping lattice shapes that are randomly placed on the lattice. The model includes smart pursuit (chasers to targets) and evasion (targets from chasers). Both species can affect their movement by visual perception within their finite sighting range σ . We concentrate here on the role that density and shape of the obstacles plays in the time evolution of the number of targets, N T ( t ) . Temporal evolution of the number of targets N T ( t ) is found to be stretched-exponential, of the form N T ( t ) = N T ( 0 ) − δ N T ( ∞ ) 1 − exp [ − ( t ∕ τ ) β ] , regardless of whether the obstacles are present or not. The characteristic timescale τ is found to decrease with the initial density of targets ρ 0 T according to a power-law, i.e., τ ∝ ( ρ 0 T ) − γ . Furthermore, temporal dependences of the number of targets N T ( t ) are compared for various combinations of chasers and targets with different sighting ranges, σ = 1 , 2 , in order to analyze the relationship between the ability of species and the capture dynamics in the presence of obstacles.

The stretched exponential function (SEF) was used to analyze and interpret saturation recovery (SR) electron paramagnetic resonance (EPR) data obtained from spin-labeled porcine eye-lens membranes. This function has two fitting parameters: the characteristic spin–lattice relaxation rate (T1str−1) and the stretching parameter (β), which ranges between zero and one. When β =1, the function is a single exponential. It is assumed that the SEF arises from a distribution of single exponential functions, each described by a T1 value. Because T 1 −1 s are determined primarily by the rotational diffusion of spin labels, they are a measure of membrane fluidity. Since β describes the distribution of T 1 −1 s, it can be interpreted as a measure of membrane heterogeneity. The SEF was used to analyze SR data obtained from intact cortical and nuclear fiber cell plasma membranes extracted from the eye lenses of 2-year-old animals and spin labeled with phospholipid and cholesterol analogs. The lipid environment sensed by these probe molecules was found to be less fluid and more heterogeneous in nuclear membranes than in cortical membranes. Parameters T 1str −1 and β were also used for a multivariate K-means cluster analysis of stretched exponential data. This analysis indicates that SEF data can be assigned accurately to clusters in nuclear or cortical membranes. In future work, the SEF will be applied to analyze data from human eye lenses of donors with differing health histories.

We present a study on decay kinetics for a recovery process depending on the light wavelength selected in optical instability measurements against amorphous In-Ga-Zn-O (a-IGZO) thin-film devices. To quantitatively analyze optically-induced instability behaviors, a stretched exponential function (SEF) and its inverse Laplace transform are employed for a time- and energy-dependent analysis, respectively. The analyzed results indicate that a shorter wavelength light activates electrons largely from the valence band while metastable states are deionized with the respective photon energy (hv). In contrast, a longer wavelength illumination is mainly activating trapped electrons at metastable states, e.g. oxygen defects. In particular, at 500 nm wavelength (hv ~ 2.5 eV), it shows an early persistency with a much higher activation energy. This also implies that the majority of metastable states remain ionized, thus the deionization energy >2.5 eV. However, the decay trend at 600 nm wavelength (hv ~ 2 eV) is found to be less persistent and lower current level compared to the case at 500 nm wavelength, suggesting the ionization energy of metastable states >2 eV. Finally, it is deduced that majority of oxygen defects before the illumination reside within the energy range between 2 eV and 2.5 eV from the conduction band edge.

We have developed a numerical model based on finite element analysis (FEA) with a viscoelastic material model coupling stress relaxation and structural relaxation, using the Mauro-Allan-Potuzak (MAP) non-equilibrium viscosity equation as the shift function. A modeling study of the delayed elasticity behavior in glass under different equilibrium viscosity and non-equilibrium viscosity conditions is conducted. The delayed elastic response is found to be well described by a stretched exponential function with three parameters: the maximum delayed elasticity response, the retardation time of delayed elasticity response, and the stretching exponent of delayed elasticity response. The delayed elasticity magnitude is seen to increase with lower values of the stretching exponent bstress. At equilibrium viscosity, the retardation time shows a linear relationship with the stress relaxation time. However, when the temperature drops sharply in the non-equilibrium viscosity cases, the delayed elastic response may be frozen resulting in a lower magnitude for the delayed elasticity and the retardation time is not linear any more with the stress relaxation time. The delayed elasticity stretching exponent is seen to vary slightly at different relaxation times and normalized delayed elasticity response can roughly be collapsed into a single master curve. The impact of liquid fragility is also studied.

For the requirement in container nursery culture that growing media should be achieved the appropriate degree compaction, this paper presents an experiment on the compaction dynamics of air-dried soil under repetitive drop shocks, as a preliminary step toward the mechanization of this compaction method. The drop height used to adjust the shock intensity included 2 mm, 4 mm, 5 mm and 6 mm. And the overall packing density of soil in a vertically stratified cylinder vessel and the local packing density in each layer were taken as indicators of soil compaction states. The stretched exponential function derived from KWW law than the empirical inverse-logarithmic function has been found to be more suitable for expressing the temporal evolution of soil compaction, according to the results of curve-fitting to test values of the overall and local density. It is inherent in this experimental configuration that the drop shock intensity even at a constant drop height varies with drop times, owing to the interaction between the soil packing itself and drop shocks caused by the combination of the packing and the container. But the function t/τf(t,H) is manifested as a straight line on the drop times t with the line slope related to the drop height H, so the soil compaction dynamics caused by its drop shocks and that under the condition with actively controlled intensity actually share the common relaxation law. In addition, the soil’s one-dimensional distribution of local packing density showed a slight positive gradient as similar as monodisperse particles did.

Supercapacitors are prone to self-discharging, which is most often measured as a voltage decrease with time under open circuit conditions. It is of substantial interest to find simple and general methods to extract information about the processes going on in the supercapacitor during self-discharge. The current work fits a stretched exponential function to experimental data available in the literature, thus extracting parameters that allows one to probe the internal processes of the supercapacitor. In particular, experimental data related to charge holding time, charging rate before self-discharge and temperature dependence are investigated. It is demonstrated how the fitting data can be understood in terms of a kinetic model exhibiting a distribution of rate constants which are related to the fitting parameters. The current work therefore proposes a method that allows one to quickly map the internal processes of a self-discharging supercapacitors with only two variables, and might therefore become a useful tool. publishedVersion

A stretched exponential function taking the form, f(x) = exp(-x^β), x ∈ [0, ∞), β ∈ (0, 1], characterizes decay, diffusion, and relaxation phenomena known as Kohlrausch-Williams-Watts (KWW) processes. Recent work, particularly on relaxation kinetics in metallic glasses, has described the conditions under the shape parameter β deviates from its usual value. Where β > 1, the corresponding exponential function is compressed rather than stretched. The β-generalized exponential function provides good parametric fits for two measures of influence in legal academia: law review impact factors and Social Science Research Network (SSRN) downloads per author. A stretched exponential function models impact factors from 2007 through 2019. A compressed exponential function describes SSRN downloads per author by law school, except the single outlier atop the rankings. A power law distribution fits the SSRN data, but only for the top 100 schools. The fact that the value of the exponent β straddles the value of 1, which characterizes an ordinary exponential function, is not a trivial artifact of fitting a model to observed bibliometric data. Treating the reciprocal of β as a rough measure of heterogeneity, h = 1/β, suggests that impact factors and SSRN downloads measure different aspects of academic influence in law. Law reviews, especially as the stigma of online publishing recedes, have become more heterogeneous. By contrast, the compressed rather than stretched exponential kinetics of SSRN data implies the presence of avalanche-like processes in the posting and sharing of preprints among legal scholars.

A probability distribution of rate constants contained within an exponential-like saturation recovery (SR) electron paramagnetic resonance signal can be constructed using stretched exponential function fitting parameters. Previously (Stein et al. Appl. Magn. Reson. 2019.), application of this method was limited to the case where only one relaxation process, namely spin-lattice relaxations due to the rotational diffusion of the spin labels in the intact eye-lens membranes, contributed to an exponential-like SR signal. These conditions were achieved for thoroughly deoxygenated samples. Here, the case is described where the second relaxation process, namely Heisenberg exchange between the spin label and molecular oxygen that occurs during bimolecular collisions, contributes to the decay of SR signals. We have further developed the theory for application of stretched exponential function to analyze SR signals involving these two processes. This new approach allows separation of stretched exponential parameters, namely characteristic stretched rates and heterogeneity parameters for both processes. Knowing these parameters allowed us to separately construct the probability distributions of spin-lattice relaxation rates determined by the rotational diffusion of spin labels and the distribution of relaxations induced strictly by collisions with molecular oxygen. The later distribution is determined by the distribution of oxygen diffusion concentration products within the membrane, which forms a sensitive new way to describe membrane fluidity and heterogeneity. This method was validated in silico and by fitting SR signals from spin-labeled intact nuclear fiber cell plasma membranes extracted from porcine eye lenses equilibrated with different fractions of air.Statement of SignificanceMulti-exponential spin-lattice relaxation in complex membranous systems can be described by a stretched exponential function that provides a continuous probability distribution of relaxation rates rather than discreet relaxations from separate domains. The stretched exponential function has two fitting parameters, the characteristic spin-lattice relaxation rate (T1str−1) and the stretching parameter (β), obtained without any assumption about the number of membrane domains and their homogeneity. For membranes equilibrated with air, collisions with molecular oxygen provide an additional relaxation pathway for spin labels that depends on the oxygen-diffusion-concentration product in the vicinity of spin labels. This new approach allows separation of membrane fluidity and heterogeneity sensed by motion of lipid spin labels from those described by the translational diffusion of molecular oxygen.

"Water-in-salt" (WIS) and "water-in-bisalt" (WIBS) electrolytes have recently been developed for Li-ion batteries, combining the safety and environmental friendliness of aqueous electrolytes with a larger operating window made possible by a solid-electrolyte interphase. We report quasielastic neutron scattering (QENS) measurements on solutions of a WIS electrolyte at two concentrations, 13.9 and 21 m (molal) lithium bis(trifluoromethane)sulfonimide LiTFSI in H2O/D2O and a WIBS electrolyte at (21 m LiTFSI + 7 m lithium triflate (LiOTf)) in H2O/D2O. The data were Fourier transformed to obtain experimental intermediate scattering functions (ISFs) and compared with corresponding quantities obtained from molecular dynamics (MD) simulations. Both QENS and MD ISFs could be fitted well by a single stretched exponential function to obtain apparent translational diffusion coefficients for the water molecules. The QENS values agree well with the MD simulations for the 13.9 and 21 m solutions, but MD simulations predict a slower relaxation of water compared to QENS for the WIBS electrolyte. Comparison of the incoherent and coherent scattering reveals much faster water dynamics compared with structural relaxation of the ionic framework, consistent with the nanodomain picture where the lithium diffusion occurs through the tortuous water domain around the slower relaxing ionic matrix, leading to highly non-Gaussian water motion.

The light-soaking effect is the observation that under constant illumination the measured power conversion efficiency of certain solar cells changes as a function of time. The theory of the light-soaking in metal halide perovskites is at present incomplete. In this report, we employ steady-state microwave conductivity, a contactless probe of electronic properties of semiconductors, to study the light-soaking effect in metal halide perovskites. By illuminating isolated thin films of two mixed-cation perovskites with AM1.5 solar illumination, we observe a continual increase in photoconductance over a period of many (>12) hours. We can fit the experimentally observed changes in photoconductance to a stretched exponential function, in an analogous manner to bias-stressed thin-film transistors. The information provided in this report should help the community better understand one of the most perplexing open problems in the field of perovskite solar cells and, ultimately, lead to more robust and predictable devices. The light soaking effect is when the power conversion efficiency of a solar cell changes over time while the illumination remains constant. Here, the authors investigate the underlying mechanisms of the light soaking effect in metal halide perovskites using steady-state microwave conductivity. Under constant illumination they observe an increase in photoconductance over many hours.

This chapter deals with dielectric properties, especially the relaxation time and electric modulus, and explores why oxide glass composites can be used for dielectric purposes. The oxide glass nanocomposite, xAgI-(1 − x)(0.5Ag2O-0.5P2O5) for x = 0.1, 0.2, 0.3, and 0.4, have been prepared by the melt-quenching technique. Frequency-dependent permittivity and the modulus of the present system have been well investigated. The real part of dielectric permittivity shows saturation at higher frequencies and a strong dispersion at lower frequencies. The variation of M// data with frequency has been characterized by KWW stretched exponential function. It is noted from the study that the value of the exponent parameter β

Mud sediments can exhibit a complex rheological behaviour particularly a thixotropic character or structural recovery after breakup due to the presence of organic matter/biopolymer. Such biopolymers can lead towards the development of flocculated structures having multiple length scales which are sensitive to shearing rate and history. In this study, the extent and rate of structural recovery of mud sediments was studied by measuring the storage modulus as a function of time using small amplitude oscillatory tests after a destructive steady shearing. This linear viscoelastic response of the sediments was further investigated as a function of several parameters including pre-shear rate, pre-shear time, measuring geometry, mud density and organic matter content. The equilibrium storage modulus (G∞ ') and the characteristic time (tr) for the structural recovery of the sediment matrix were estimated by fitting the experimental data to a stretched exponential function. The normalized storage modulus, G'/G0 ' (i.e., structural parameter) was used to relate it with the yield stresses of mud sediments. The results showed that the recovery of structure after shearing was instantaneous (tr being of the order of seconds), however, the extent of recovery was highly dependent on the studied parameters. The extent of recovery was higher for the samples with lower density and lower organic matter content. The effect of the shearing time on tr and G∞ ' was almost negligible, which implies that the destruction of the structure was achieved within seconds. Using vane geometry, the extent of recovery was higher than using Couette geometry which is linked with the distribution of shear stresses within the cell for each geometry. Yield stresses showed a strong dependency on structural parameter, until it reaches very small values. At low values of structural parameter, the yield stresses were constant as the structural recovery was even faster than the time required to perform the amplitude sweep tests. This study provides an extensive knowledge about the structural recovery in mud sediments under different shearing conditions which can be useful for sediment management.

Stretched exponential relaxation is a ubiquitous feature of homogeneous glasses. The stretched exponential decay function can be derived from the diffusion-trap model, which predicts certain critical values of the fractional stretching exponent, β . In practical implementations of glass relaxation models, it is computationally convenient to represent the stretched exponential function as a Prony series of simple exponentials. Here, we perform a comprehensive mathematical analysis of the Prony series approximation of the stretched exponential relaxation, including optimized coefficients for certain critical values of β . The fitting quality of the Prony series is analyzed as a function of the number of terms in the series. With a sufficient number of terms, the Prony series can accurately capture the time evolution of the stretched exponential function, including its “fat tail” at long times. However, it is unable to capture the divergence of the first-derivative of the stretched exponential function in the limit of zero time. We also present a frequency-domain analysis of the Prony series representation of the stretched exponential function and discuss its physical implications for the modeling of glass relaxation behavior.

The magnetic phase transitions and their thermal transformation arrest (TTA) behavior of Cr-substituted Mn 2 Sb were investigated. Mn 1.92 Cr 0.08 Sb showed the first-order magnetic transition between antiferromagnetic (AFM) and ferrimagnetic (FRI) state. The TTA phenomenon was observed in field-cooling process under magnetic field of μ 0 H ≥ 4 T. The relaxation process from the arrested FRI to AFM state was explained by stretched exponential function. As decreasing temperature, the magnetic relaxation changed from Arrhenius-type to non-Arrhenius ones. The characteristic relaxation time was evaluated to be the order of 10 5 ∼ 10 6 s, which indicated indeed arresting of the magnetic transition. During the process, the decrease in the magnetization due to the relaxation changed into an increase with the thermal fluctuation of ∼1%. These relaxation behaviors are explained by the density and the frequency of the reversal of triple-layered magnetic moments.

The fractional conformable derivative and its properties have been introduced recently. Using this derivative we obtain a new class of smooth solutions for the Newton’s law of cooling in terms of a stretched exponential function depending on the fractional order parameter 0 < γ ≤ 1. In addition, the convection coefficient of fractional order k(γ) can be calculated easily. Also, it is shown, that in the particular case γ = 1 these solutions become the ordi- nary ones.

Retardation and relaxation spectra of modified asphalt binders with nonlinear time, or in other words a stretched exponential function of time, were used for the description of accumulated compliance in the repeated creep and recovery test, as well as in transient shear flows such as startup flow. The experimental results were successfully fitted to the accumulated compliance function as well as to the stress (stress growth coefficient) in transient shear flows of several polymer-modified asphalt binders. The concept of stretched time exponential, used in this contribution, seems to be useful for the description of nonlinear behavior of modified asphalt binders and hence possibly more generally to describe other complex materials.

Experimental results of studying the conductivity response to methane of ZnO-Ag ceramics with different amounts of silver additive are presented. Kinetic dependences of the response were processed with the use of a stretched exponential function Kohlrausch-Williams-Watts stretched exponential function. Based on the obtained results, parameters of transients occurring on the sensor surface were evaluated.

The kinetic arrest (KA) of martensitic transformation (MT) observed in Ni 45 Co 5 Mn 36.8 In 13.2 melt-spun ribbons has been studied. These alloy ribbons show an ordered columnar-like grain microstructure with the longer grain axis growing perpendicular to ribbon plane and transform martensitically from a single austenitic (AST) parent phase with the L2 1 -type crystal structure to a monoclinic incommensurate 6 M modulated martensite (MST). Results show that the volume fraction of austenite frozen into the martensitic matrix is proportional to the applied magnetic field. A fully arrest of the structural transition is found for a magnetic field of 7 T. The metastable character of the non-equilibrium field-cooled glassy state was characterized by introducing thermal and magnetic field fluctuations or measuring the relaxation of magnetization. The relaxation of magnetization from a field-cooled kinetically arrested state at 5 and 7 T follows the Kohlrausch–Williams–Watts (KWW) stretched exponential function with a β exponent around 0.95 indicating the weak metastable nature of the system under the strong magnetic fields. The relationship between the occurrence of exchange bias and the frozen fraction of AST into the MST matrix was studied.

The room temperature crystal structure as well as the magnetic ground state of Ba(Fe1/2Nb1/2)O3 (BFN) are controversial. The results of Rietveld refinements using high-resolution synchrotron x-ray powder diffraction (SXRPD) data are presented to show that BFN belongs to cubic perovskite structure in the Pm 3 ¯ m space group and not in the cubic Fm 3 ¯ m or monoclinic symmetries, proposed by some earlier workers based on the analysis of the laboratory source XRD data. The temperature dependent specific heat measurements in the 1.8 to 300 K range on well characterized BFN samples are presented to show the absence of any long-range ordered (LRO) antiferromagnetic (AFM) transition, proposed by some earlier workers based on the observation of a peak in the temperature dependence of zero-field cooled (ZFC) DC magnetization around 25 to 32 K. Results of temperature dependent magnetization measurements during warming cycle on ZFC and field cooled (FC) BFN samples reveal history dependent bifurcation with a peak in the ZFC M (T) curve at Tf ~ 29 K, in agreement with some previous results where it was attributed to a spin-glass transition even though such an irreversibility can result from superparamagnetic (SPM) blocking as well. The appearance of a short plateau in our FC M (T) curve below Tf suggests a cluster spin-glass phase of BFN below Tf. This was confirmed by us through the ac susceptibility χ' (T, ω) studies which reveal divergence of spin dynamics at the spin-glass transition temperature TSG ~ (28 ± 1) K with a large characteristic spin relaxation time τ0 ~ 10−6 s following Vogel-Fulcher as well as power-law type critical dynamics. The existence of the magnetic glassy state in BFN is further supported by the observation of (1) magnetic field dependent shift of Tf with increasing magnetic field along the de Almeida-Thouless line in the T-H plane with a characteristic exponent of m = 2/3, (2) weak remanent magnetization Mr below Tf with exponentially decreasing Mr on approaching Tf, (3) extremely slow decay of the thermoremanent magnetization below Tf with time as per a stretched exponential function, and (4) characteristic aging, rejuvenation and memory effects below Tf. These results provide the first unambiguous confirmation of the cluster spin-glass state of BFN and settle the existing controversies related to its magnetic ground state.

We have investigated photoinduced effects in as-deposited Ge40−xSbxSe60 (x = 8, 15, and 20) films via in situ measurements of transmission spectra for wavelengths λ = 500 to 950 nm. The absorption coefficient increases initially, indicating the photodarkening (PD) effect, which rapidly saturates in tens of seconds. Then the absorption coefficient starts decreasing representing photobleaching (PB). The evolution of PD and PB can be described by stretched exponential function, yielding the time constants for the changes in absorption coefficients. The kinetics of PD is faster than that of PB. The coexistence of PB and PD suggests that the Sb and Ge based structural units of Ge-Sb-Se films respond to bandgap radiation independently. The structural origins of the observed opposing photoinduced effects are discussed.

It has been long observed that cumbersome parameters are required for the traditional viscoelastic models to describe complex rheological behaviors. Inspired by the relationship between normal and anomalous diffusions, this paper tentatively employs t α to replace t, called as the scaling transformation, in the traditional creep compliance and relaxation modulus. With this methodology, the relaxation modulus is found to agree with the well-known Kohlrausch-Williams-Watts (KWW) stretched exponential function. The fitting results confirm that the proposed models accurately characterize rheological behaviors only with one more parameter α. Moreover, it is noted that the present formulations are directly related to the fractal derivative viscoelastic models and the index α is actually the order of the fractal derivative.

The effects of cellulose powder and water activity (aw) on the equilibrium water content, glass transition temperature (Tg), mechanical relaxation, and caking of freeze-dried amorphous carbohydrate blend powders (dextrin-glucose mixture) were investigated. Water sorption isotherm and Tg-curve were obtained, and critical water activity (awc) was determined as the aw at Tg = 25 °C. There was a minor effect of cellulose powder on the awc. The degree of caking was negligible below the awc (glassy state), but increased remarkably above the awc (rubbery state). Cellulose powder played a dispersive role in the powder, and thus diminished the degree of caking. The caking behavior could be described by a stretched exponential function, and an experimental formula to predict the degree of caking as a function of aw/awc was obtained. The results for a food powder, with a more complex composition, largely deviated from the formula. Mechanical relaxation was evaluated as a force-reduction during isothermal compression. It was found that the relationship between the degree of caking and force-reduction could be described as a linear function independent of aw and cellulose powder content. The results for the food powder partially followed the linear relationship.