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Single particle level microscopy of immobilized FAPbBr3 nanocrystals (NCs) has elucidated the involvement of different processes in their photoluminescence (PL) intermittency. Four different blinking patterns are observed in the data from more than 100 NCs. The dependence of PL decays on PL intensities brought out in fluorescence lifetime intensity distribution (FLID) plots is rationalized by the interplay of exciton- and trion-mediated recombinations along with hot carrier (HC) trapping. The high intensity-long lifetime component is attributed to neutral exciton recombination, the low intensity-short lifetime component is attributed to trion assisted recombination, and the low intensity-long lifetime component is attributed to hot carrier recombination. Change-point analysis (CPA) of the PL blinking data reveals the involvement of multiple intermediate states. Truncated power law distribution is found to be more appropriate than power law and lognormal distribution for on and off events. Probability distributions of PL trajectories of single NCs are obtained for two different excitation fluences and wavelengths (λex = 400, 440 nm). Trapping rate (kT) prevails at higher power densities for both excitation wavelengths. From a careful analysis of the FLID and probability distributions, it is concluded that there is competition between the HC and trion assisted blinking pathways and that the contribution of these mechanisms varies with excitation wavelength as well as fluence. [ABSTRACT FROM AUTHOR]

During the synthesis of tellurium (Te) crystals, the coexistence of multiple crystalline phases (α-Te, β-Te, and γ-Te) with diverse structures commonly occurs, leading to instability and complexity in the performance of Te-based optoelectronic devices. This study employs physical vapor deposition to synthesize Te crystals of various sizes and morphologies, followed by spatially and temperature-dependent evaluation using Raman mapping and infrared photoluminescence (PL) spectroscopy. Spatially resolved results reveal that the size and morphology of Te crystals significantly influence the energy and peak profiles of Raman and PL spectra. Statistical analysis of spatially random sampling indicates the PL peak energies of Te crystals follow a lognormal distribution in terms of their occurrence frequencies, reflecting the complex interplay of multiple factors during crystal growth. This results in the coexistence of α-Te and β-Te phases, forming α/β-Te heterophase homojunction (HPHJ). Meanwhile, temperature-dependent PL results, obtained for the range of 3–290 K, reveal multi-peak competitive behavior in the PL spectra, accompanied by S-shaped shifts in peak energy. These features can be rationally explained by an interface transition-recombination mechanism based on the I-type α/β-Te HPHJ model. It also confirms infrared PL spectroscopy is an effective method for identifying the crystalline phase composition of Te crystals. [ABSTRACT FROM AUTHOR]

Integral geometry uses four geometric invariants—the Minkowski functionals—to characterize certain subsets of three-dimensional (3D) space. The question was, how is the fluid flow in a 3D porous system related to these invariants? In this work, we systematically study the dependency of permeability on the geometrical characteristics of two categories of 3D porous systems generated: (i) stochastic and (ii) deterministic. For the stochastic systems, we investigated both normal and lognormal size distribution of grains. For the deterministic porous systems, we checked for a cubic arrangement and a hexagonal arrangement of grains of equal size. Our studies reveal that for any three-dimensional porous system, ordered or disordered, permeability k follows a unique scaling relation with the Minkowski functionals: (a) volume of the pore space, (b) integral mean curvature, (c) Euler characteristic, and (d) critical cross-sectional area of the pore space. The cubic and the hexagonal symmetrical systems formed the upper and lower bounds of the scaling relations, respectively. The disordered systems lay between these bounds. Moreover, we propose a combinatoric F that weaves together the four Minkowski functionals and follows a power-law scaling with permeability. The scaling exponent is independent of particle size and distribution and has a universal value of 0.428 for 3D porous systems built of spherical grains. [ABSTRACT FROM AUTHOR]

The size of drops generated by the capillary-driven disintegration of liquid ligaments plays a fundamental role in several important natural phenomena, ranging from heat and mass transfer at the ocean-atmosphere interface to pathogen transmission. The inherent nonlinearity of the equations governing the ligament destabilization leads to significant differences in the resulting drop sizes, owing to small fluctuations in the myriad initial conditions. Previous experiments and simulations reveal a variety of drop size distributions, corresponding to competing underlying physical interpretations. Here, we perform numerical simulations of individual ligaments, the deterministic breakup of which is triggered by random initial surface corrugations. The simulations are grouped in a large ensemble, each corresponding to a random initial configuration. The resulting probability distributions reveal three stable drop sizes, generated via a sequence of two distinct stages of breakup. Four different distributions are tested, volume-based Poisson, Gaussian, Gamma, and Log-Normal. Depending on the time, range of droplet sizes and criteria for success, each distribution has successes and failures. However, the Log-Normal distribution roughly describes the data when fitting both the primary peak and the tail of the distribution while the number of droplets generated is the highest, while the Gamma and Log-Normal distributions perform equally well when fitting the tail. The study demonstrates a precisely controllable and reproducible framework, which can be employed to investigate the mechanisms responsible for the polydispersity of drop sizes found in complex fluid fragmentation scenarios. [ABSTRACT FROM AUTHOR]

We determined the size distribution of helium droplets produced in a pulsed beam in the condensation regime from the gas phase. Following electron-impact ionization, the mass-to-charge ratios of the positively charged droplets were determined by measuring their kinetic energies and velocities using an electrostatic cylindrical deflector setup. Over a range of different source conditions, we observed bimodal velocity distributions and log-normal size distributions. Our results are similar to those reported for continuous beams, but with mean sizes larger by a factor of around 100. The log-normal size distributions reported here differ strongly from the exponential distributions recently reported for a pulsed beam produced using a different nozzle design. [ABSTRACT FROM AUTHOR]

The synthesis of metal nanoparticles holds significant promise for various applications ranging from electronics to catalysis. Their high specific surface area makes them more applicable in the form of lubricant and sorbent. Some of the metal nano-powders, such as silver, copper, and zinc, possess anti-microbial properties; hence, they are very useful in medical sciences. This paper presents a novel approach to the design and implementation of a compact metal nano-powder generator of 273 MW average power through the electrical explosion of wire method. The design focuses on achieving the automatic and repetitive operation of a compact metal nano-powder generator and minimizing its geometric inductance to achieve a fast rise time current across the exploding wire load. Copper nano-powder is produced with a copper wire of 450 μm thickness and 30 mm length at charging voltages of 8.5, 9.0, and 9.5 kV and achieving a superheat of 1.75, 1.92, and 2.06, respectively. The synthesis process is characterized by a detailed analysis of the copper nano-powder's structural, morphological, and chemical composition using techniques such as x-ray diffraction, scanning electron microscopy, and energy-dispersive x-ray spectroscopy. The particle size distribution studies are performed by adopting the log-normal probability distribution. The results demonstrate the effectiveness of the proposed compact nano-powder generator in producing copper nano-powder with tailored properties suitable for diverse applications. [ABSTRACT FROM AUTHOR]

Spray cooling is an effective solution for high heat flux dissipation challenges. Accurate prediction of heat transfer efficiency by numerical simulation can reduce the cost of spray cooling in engineering applications. To improve the accuracy of numerical simulation, this study develops a mathematical model for droplet collision and heat transfer response based on experimental data. In spray cooling experiments, droplets are sprayed onto a 200 °C aluminum alloy thermal wall using an atomizing nozzle, temperature is monitored, and the curve of heat flux variation during cooling is estimated from temperature data. Analysis of high-speed photography results provides the droplet diameter, velocity, and spatial distribution. We discover that the average Weber number of droplets, We, has a power-law relationship with the volumetric flow rate, Q, as We ∼ Q1.55. The velocity and position of spray droplets approximately follow a normal distribution, while the diameter follows a Log-normal distribution. By analyzing the relation between heat flux and spray distribution, an experimental-data-based model, named Droplet Collision-Associated Heat Transfer Model, is designed. Integrating this experimental-data-based model with the discrete phase model (DPM), the heat transfer evolution process in spray cooling is simulated with high reliability. Particles sources are generated based on the experimentally obtained droplet parameter probability distributions, DPM is used to capture the trajectories of droplets, and the droplet impact heat transfer correlation model calculates the thermal response of the wall. Compared with experimental results, the simulation error is only 7.49%. Simulation results indicate that spray cooling at high flow rates has better temperature uniformity. [ABSTRACT FROM AUTHOR]

Impedance spectroscopy experiments are able to reveal the fundamental charge transport properties of a wide variety of complex disordered and nano-structured materials provided that appropriate modeling tools are used. In this paper, we present a numerical simulation-based approach to model the dynamical conductivity of networks formed by self-assembled metal nanoparticles. Inter-particle nano-resistance and nano-capacitance are implemented at the nano-scale assuming inter-particle charge transfer and accumulation mechanisms that can be adapted depending on the nature of the nano-particles and the surrounding medium. The actual positions and spatial arrangements of the nanoparticles within the network are taken into consideration, allowing the attributes of percolating conducting routes to be extracted, classified, and compared in terms of path conductance and statistical distribution of path lengths. Our findings are contrasted to those obtained using analytic models, which are commonly used, but rely on strong assumptions about the electric properties of the conducting paths. We address these assumptions and show that in the case of weakly disordered systems, there is a general agreement between numerical simulations and analytic modeling-based approaches. In the case of disordered networks where the nano-particle size and position fluctuations are included, we show that the path length distribution is frequency-dependent and can differ significantly from the lognormal distribution usually assumed in the analytic models. The impedance of individual pathways may be extracted from the numerical simulations; we discovered that the conductance and susceptance of a specific path are frequency-dependent and inversely proportional to the path length only in ordered networks. Strong scattering of conductance values is caused by disorder effects. The developed numerical approach is generic and applies to most nano-devices where charge transport relies on percolation; it allows to bridge the gap between the nano-scale and micro-scale electric characteristics and, thus, permits a deeper understanding of the charge transport properties of nano-structured materials. [ABSTRACT FROM AUTHOR]

Passive control of twin-fluid atomization can be achieved by changing the orifice shape of the injector. In this study, the characteristics of twin-fluid atomization in the outside-in-liquid injector with circular, square, and rectangular orifices at various aspect ratios were investigated experimentally and computationally. The morphology of the spray was captured by shadowgraph, the diameter and velocity of the droplets were measured by the phase Doppler particle analyzer, and numerical simulations were performed for the central gaseous core. Comparing the sprays with square and circular orifices, droplets from the non-circular orifice are generally smaller with less disparities in droplet sizes due to the more intensive turbulent disturbances and corner effect. Furthermore, the non-circular orifice also results in better spatial distribution of the spray. The droplet diameters of the spray with a square orifice do not satisfy the log-normal distribution near the orifice along the centerline of the spray, which may be attributed to the different entrainment of spray droplets by the central gas flow for the sprays with circular and non-circular orifices. The twin-fluid sprays produced by the rectangular orifice also exhibit the same axial switching effect as in the high-pressure gaseous jet flow, in which the spray diffusion in the minor axis is more extensive than that in the major axis. Moreover, the droplets' Sauter mean diameter produced by the rectangular orifice is more sensitive to the size in the minor axis of the orifice and decreases as the aspect ratio of the orifice increases given the same cross-sectional area. [ABSTRACT FROM AUTHOR]

Wire explosion is a technically straightforward green method for nanoparticle production; however, the determination of polydisperse and multimodal particle size distribution and thereby the assessment of the efficiency of the process pose serious challenges. Fitting extinction spectra derived from the Mie theory to the measured extinction spectra of colloidal solutions produced by the explosion of copper wires of 70 μm diameter and 20 mm length by discharging a capacitor of 435 nF charged to voltages ranging from 4 to 12 kV in an aqueous environment allows for determining the size distribution of the particles in the 10–300 nm diameter range and provides information on their oxidation state as well. In underwater wire explosion of copper, the vast majority of the nanoparticles transforms into copper oxides already during the process. The size distribution remains bimodal throughout the whole charging voltage range investigated. The nanoparticles follow a lognormal size distribution with a mode at 30 nm, while the fine particle population extending from 100 to 300 nm in diameter is dominated by rather normally distributed copper droplets with modes at 160–170 nm. The energy injected into the wire controls the individual concentration of both the fine and nanoparticles with the modes and ranges remaining hardly affected. The number concentration of the nanoparticles increases monotonically with the energy, spanning more than one order of magnitude. The throughput assessed by the total mass of the nanoparticles divided by the total mass of all species identified in the sol within the 0–300 nm diameter range increases monotonically from 1% at 4 kV up to 41% at 12 kV, revealing that wire explosion can be optimized for efficient nanoparticle production. [ABSTRACT FROM AUTHOR]

Using Monte Carlo simulations, we systematically investigate the effect of particle size distribution on the phase behavior of polydisperse hard disks. Compared with the commonly used Gaussian-like polydisperse hard disks [P. Sampedro Ruiz, Q.-l. Lei, and R. Ni, Commun. Phys. 2, 70 (2019)], we find that the phase behavior of polydisperse hard-disk systems with lognormal and triangle distributions is significantly different. In polydisperse hard-disk systems of lognormal distributions, although the phase diagram appears similar to that of Gaussian-like polydisperse hard disks, the re-entrant melting of the hexatic or solid phase cannot be observed in sedimentation experiments. For polydisperse hard-disk systems of triangle distributions, the phase behavior is qualitatively different from the Gaussian-like and lognormal distributions, and we cannot reach any system of true polydispersity larger than 0.06, which is due to the special shape of the triangle distribution. Our results suggest that the exact particle size distribution is of primary importance in determining the phase behavior of polydisperse hard disks, and we do not have a universal phase diagram for different polydisperse hard-disk systems. [ABSTRACT FROM AUTHOR]

Analysis of first-order reversal curves (FORCs) is a powerful tool to probe irreversible switching events in nanomagnet assemblies. As in essence switching events are related to the intrinsic properties of the constituents and their interactions, the resulting FORC diagrams contain much information that can be cross-linked and complex to deconvolute. In order to quantify the relevant parameters that drive the FORC diagrams of arrays of perpendicularly magnetized nanomagnets, we present step-by-step simulations of assemblies of hysterons to determine the specific signatures related to different known inputs. While we explored the consequences of dipolar interactions using either mean field or magnetostatic approaches, we completed by taking the hysteron switching field distribution (SFD) as either normal or lognormal. We demonstrated that the transition between FORC diagrams composed of an isolated interaction field distribution (IFD) and a wishbone shape operates via the SFD deviation, σ H s w , in the presence of a weakly dispersed interaction field. In the presence of a magnetostatic interaction field, the IFD profile is peaked and a coercive field distribution (CFD) sums to the IFD as σ H s w increases. A transition between IFD + CFD and wishbone shapes is clearly demonstrated as a function of the interaction field deviation σ H i n t . In addition, we demonstrate that whatever the considered cases, σ H s w can be quantitatively extracted from the FORC diagrams within an error inferior to 10%. These findings are of interest for dipolar coupled perpendicularly magnetized nanomagnets, as in assemblies of magnetic nanowires and nanopillars, as well as bit patterned media. [ABSTRACT FROM AUTHOR]

Colloidal clogging is typically studied in pores with constrictions arranged in parallel or series. In these systems, clogging statistics are governed by Poisson processes; the time interval between clogging events exhibits an exponential distribution. However, an entirely different phenomenon is observed in a gently tapered pore geometry. Unlike in non-tapered constrictions, rigid particles clogging tapered microchannels form discrete and discontinuous clogs. In a parallelized system of tapered microchannels, we analyze distributions of clog dimensions for different flow conditions. Clog width distributions reveal a lognormal process, arising from concurrent clogging across independent parallel microchannels. Clog lengths, however, which are analogous to growth time, are exponentially distributed. This indicates a Poisson process where events do not occur simultaneously. These two processes are contradictory: clogging events are statistically dependent within each channel, while clogs grow simultaneously across independent channels. The coexistence of Poisson and lognormal processes suggests a transient Markov process in which clogs occur both independently of, and dependently on, other clogs. Therefore, discussions of the stochastic character of clogging may require holistic consideration of the quantities used to assess it. This study reveals small adjustments to pore spaces can lead to qualitative differences in clogging dynamics, suggesting the importance of geometry. [ABSTRACT FROM AUTHOR]

The magnetic hysteresis curve can provide information about magnetic properties, particle size, and its distribution. For superparamagnetic materials, the characteristics of the hysteresis curve are very typical, that is, Hc is equal to zero with a certain Ms value related to particle size in the order of nanometers. Here, we report the analysis of the magnetization hysteresis curve by applying a modified Langevin equation with and without a log-normal distribution for nearly superparamagnetic Fe3O4 and Fe3O4 encapsulated by SiO2 (Fe3O4–SiO2). To study the reliability of the modified Langevin equation, we compared the particle size values obtained from fittings analysis of the modified Langevin equation with those obtained from the TEM measurement. It was found that particle size from TEM measurement for Fe3O4 and Fe3O4–SiO2 is 11 and 14 nm, respectively. These values had a very high match with the particle size obtained from fitting analysis of the modified Langevin equation with or without a log-normal distribution, which is 12.6 and 12.9 nm for Fe3O4 and 13.8 and 14.5 nm for Fe3O4–SiO2, respectively. The fitting results of the modified Langevin equation with a log-normal distribution showed a value closer to the measurement results. By using the modified Langevin equation with a log-normal distribution, it was also obtained that the probability density function for Fe3O4 was 20.69% and that for Fe3O4–SiO2 was 0.55%. It was concluded that the modified Langevin equation with and without log-normal distribution was able to be used to obtain the particle size and its distribution for nearly superparamagnetic samples. [ABSTRACT FROM AUTHOR]

Eolian sand transport in the atmospheric surface layer (ASL) is a typical kind of gas–solid two-phase flow at a very high Reynolds number that fluctuates over a wide range of spatial and temporal scales. Based on the high-frequency time series of streamwise wind speed (u) and total saltation mass flux (q) measure at three different observation sites, the fluctuating characteristics of u and q in the near-neutral ASL have been analyzed. Our study suggests that the probability density function (PDF) of the normalized streamwise wind speed fluctuations at the height of approximately 0.5 m follows a standard normal distribution, and the PDF of the q presents a lognormal distribution in the near-neutral ASL during strong and steady wind-blown sand. The investigations on the premultiplied spectral of q and u show that, as the energy of very large-scale motions (VLSMs) increases, the influence of the VLSMs on q becomes more significant. In addition, the stochastic couplings between u and q have been analyzed by using space–time correlations and linear coherence spectrum. Our results suggest that the VLSMs have a significant effect on the low-frequency fluctuations of q in the near-neutral ASL. [ABSTRACT FROM AUTHOR]

The characteristics of twin-fluid atomization operating in the annular flow regime were studied experimentally under various gas-to-liquid ratios (GLRs) and injection pressures. The macroscopic morphology of the spray was obtained by shadowgraph, while the droplet size and velocity were measured using a phase-Doppler particle analyzer technique. It was found that the spray cone angle increases almost linearly with the GLR, and the axial distance required for droplet coalescence to outweigh the breakup decreases with increasing GLR. The Sauter mean diameter (SMD) first decreases and then increases along the axial direction due to the competition between turbulent breakup and droplet coalescence. The droplet size follows a lognormal distribution; the droplet velocity distribution is closer to a lognormal distribution under large GLRs, while it follows normal distribution with GLR = 3%. Regarding the radial distribution, low GLRs (3% and 5%) lead to a bimodal spatial velocity distribution, while for large GLRs, the droplet velocity decreases monotonically toward the far field. The spray tends to become more stable with increasing GLR and injection pressure P inj , whereas the SMD increases with increasing P inj . The underlying atomization mechanism in a twin-fluid injector in the annular flow state can be regarded as the disintegration of the initial liquid sheet by longitudinal Kelvin–Helmholtz instability followed by transverse Rayleigh–Taylor instability, which yields a direct proportionality of the droplet size to the initial liquid sheet thickness Δ L . Subsequently, for high P inj , the gas core shrinks and Δ L increases, which results in an increased SMD but enhanced atomization efficiency Δ L / SMD . [ABSTRACT FROM AUTHOR]

An extended Tauc–Lorentz model is proposed to incorporate the bandgap variation in different grains in the polycrystalline semiconductors. The probability of a certain bandgap in the Tauc–Lorentz model is assumed to follow a log-normal distribution. After a Kramer–Kronig transform, the real part of this model is suggested as well. A comparison between this model and the experimental data in polycrystalline Si is carried out to validate this model. The experimental variation of grain size in the polycrystalline Si thin film can be correlated with the width of log-normal distribution of bandgap energies. [ABSTRACT FROM AUTHOR]

The effect of Gaussian dynamics on the line shapes in linear absorption and two-dimensional correlation spectroscopy is well understood as the second-order cumulant expansion provides exact spectra. Gaussian solvent dynamics can be well analyzed using slope line analysis of two-dimensional correlation spectra as a function of the waiting time between pump and probe fields. Non-Gaussian effects are not as well understood, even though these effects are common in nature. The interpretation of the spectra, thus far, relies on complex case to case analysis. We investigate spectra resulting from two physical mechanisms for non-Gaussian dynamics, one relying on the anharmonicity of the bath and the other on non-linear couplings between bath coordinates. These results are compared with outcomes from a simpler log-normal dynamics model. We find that the skewed spectral line shapes in all cases can be analyzed in terms of the log-normal model, with a minimal number of free parameters. The effect of log-normal dynamics on the spectral line shapes is analyzed in terms of frequency correlation functions, maxline slope analysis, and anti-diagonal linewidths. A triangular line shape is a telltale signature of the skewness induced by log-normal dynamics.We find that maxline slope analysis, as for Gaussian dynamics, is a good measure of the solvent dynamics for log-normal dynamics. [ABSTRACT FROM AUTHOR]

Fire is a typical scenario for nuclear accidents, in which uranium-containing materials will release uranium aerosols. Limited by many aspects, uranium aerosols cannot be used directly to carry out nuclear emergency training and equipment development research under real conditions. Therefore, it is necessary to filter and evaluate available surrogate materials through experiments. In this paper, metallic zinc is used to study the source term and particle size distribution of zinc aerosols under fire conditions, and the feasibility of zinc as a surrogate material for uranium aerosol research is evaluated based on the data of uranium aerosols in the literature. The experimental results show that the mass median aerodynamic diameter obtained by fitting with lognormal distribution is between 0.36 and 0.59 µm. The cumulative mass fraction distribution data are consistent with those given in the literature, indicating that the zinc aerosols generated under fire have a nice simulation effect on uranium aerosols in terms of particle size distribution. As for air release fraction (ARF) and respirable fraction (RF), the experiment of zinc aerosols is greater than that of uranium aerosols, which means the simulation in ARF and RF is not so good. [ABSTRACT FROM AUTHOR]

The power-law distribution is ubiquitous and seems to have various mechanisms. We find a general mechanism for the distribution. The distribution of a geometrically growing system can be approximated by a log-completely squared chi distribution with one degree of freedom (log-CS χ 1), which reaches asymptotically a power-law distribution, or by a lognormal distribution, which has an infinite asymptotic slope, at the upper limit. For the log-CS χ 1 , the asymptotic exponent of the power-law or the slope in a log–log diagram seems to be related only to the variances of the system parameters and their mutual correlation but independent of an initial distribution of the system or any mean value of parameters. We can take the log-CS χ 1 as a unique approximation when the system should have a singular initial distribution. The mechanism shows comprehensiveness to be applicable to wide practice. We derive a simple formula for Zipf's exponent, which will probably demand that the exponent should be near − 1 rather than exactly − 1. We show that this approach can explain statistics of the COVID-19 pandemic. [ABSTRACT FROM AUTHOR]

Forecasting epidemic scenarios has been critical to many decision-makers in imposing various public health interventions. Despite progresses in determining the magnitude and timing of epidemics, epidemic peak time predictions for H1N1 and COVID-19 were inaccurate, with the peaks delayed with respect to predictions. Here, we show that infection and recovery rate fluctuations play a critical role in peak timing. Using a susceptible–infected–recovered model with daily fluctuations on control parameters, we show that infection counts follow a lognormal distribution at the beginning of an epidemic wave, similar to price distributions for financial assets. The epidemic peak time of the stochastic solution exhibits an inverse Gaussian probability distribution, fitting the spread of the epidemic peak times observed across Italian regions. We also show that, for a given basic reproduction number R 0 , the deterministic model anticipates the peak with respect to the most probable and average peak time of the stochastic model. The epidemic peak time distribution allows one for a robust estimation of the epidemic evolution. Considering these results, we believe that the parameters' dynamical fluctuations are paramount to accurately predict the epidemic peak time and should be introduced in epidemiological models. [ABSTRACT FROM AUTHOR]

We reconstruct glass equations of state for polydisperse hard spheres with the help of computer simulations. To perform the reconstructions, we assume that hard-sphere glass equations of state have the form Zg(φ, φJ) = Zg(φJ/φ), where Zg, φ, and φJ are the reduced glass pressure (PV/NkBT), sphere volume fraction (packing density), and jamming density of the current basin of attraction, respectively. Specifically, we use the form X = ∑iciYi, where X = (φJ/φ) − 1 and Y = 1/(Zg − 1). Our reconstructions converge to the well-known Salsburg–Wood and free volume equations of state in the limit φ → φJ, but they are also applicable for values of φ ≪ φJ. We support the ansatz Zg(φ, φJ) = Zg(φJ/φ) with extensive computer simulations. We use log-normal distributions of particle radii (r) and polydispersities δ = ⟨ Δ r 2 ⟩ / ⟨ r ⟩ = 0.1 − 0.3 in steps of 0.05. By supplying the fluid equation of state (EOS) into the new glass EOS, we evaluate equilibrium jamming densities φEJ for a range of φ. By using the ideal glass transition densities φg as an input φ, we estimate the corresponding glass close packing limits φGCP = φEJ(φg). We use the Boublík–Mansoori–Carnahan–Starling–Leland fluid EOS, and we estimate φg from the Vogel–Fulcher–Tammann fits—but our method can work with any choice of the fluid EOS and φg estimates. We show that our glass EOS leads to much better predictions for φEJ(φ) than the standard Salsburg–Wood glass EOS. [ABSTRACT FROM AUTHOR]

COVID-19 has forced quarantine measures in several countries across the world. These measures have proven to be effective in signifi- cantly reducing the prevalence of the virus. To date, no effective treatment or vaccine is available. In the effort of preserving both public health and the economical and social textures, France and Italy governments have partially released lockdown measures. Here, we extrapo- late the long-term behavior of the epidemic in both countries using a susceptible-exposed-infected-recovered model, where parameters are stochastically perturbed with a lognormal distribution to handle the uncertainty in the estimates of COVID-19 prevalence and to simulate the presence of super-spreaders. Our results suggest that uncertainties in both parameters and initial conditions rapidly propagate in the model and can result in different outcomes of the epidemic leading or not to a second wave of infections. Furthermore, the presence of super- spreaders adds instability to the dynamics, making the control of the epidemic more difficult. Using actual knowledge, asymptotic estimates of COVID-19 prevalence can fluctuate of the order of 10 x 106 units in both countries. [ABSTRACT FROM AUTHOR]

Orange luminescence attributable to a core of silicon atoms in alkyl-capped crystalline quantum dots excited at λa=355 and 405 nm is investigated as a function of applied intensity and time. The intensity of luminescence displays a linear power dependence on the intensity of the applied field, from which an exponent n=0.94±0.02 commensurate with single-photon absorption is derived. The dependence of luminescence on time is observed to be strongly nonexponential and is optimally accounted for by a probability density function which describes a continuous distribution of two decay times: the behavior is characteristic of a pair of elementary steps connected with light emission within a distribution of local environments, or a single rate process supported by two environments. Nonlinear least-squares fits to the time dependent luminescence formulated on this basis with a Gaussian, Lorentzian, or log-normal distribution of rates return most probable lifetimes T1=21±1 μs and T2=3.7±0.8 μs. The widths of the distributions vary between σ1=0.01–0.03 μs-1 and σ2=0.14–1.1 μs-1 associated with 1/T1 and 1/T2, respectively. [ABSTRACT FROM AUTHOR]

In the current study, carbon black (CB) filled ethylene butylacrylate copolymer samples, which are submitted to a uniaxial creep, are probed with a sub-100-nm spatial resolution using atomic force microscopy in tapping mode. We demonstrate the significant effect of the long-time application of stress, at low strain amplitude well below the breaking threshold, on the crack occurrence along the interfaces between polymer and CB aggregates. The data analysis indicates a log-normal distribution of crack width whose average value follows an exponential saturation as a function of aging time. A possible model realizing this behavior is the rate dependent theory of fracture for polymers. [ABSTRACT FROM AUTHOR]

The electromigration (EM) lifetime in short copper interconnects is modeled using a previously developed means of generating realistic interconnect microstructures combined with the one-dimensional stress evolution equation of Korhonen et al. [J. Appl. Phys. 73, 3790 (1993)]. This initial analysis describes the void nucleation and subsequent growth in lines blocked at one end and terminated with a pad at the other. For short copper interconnects, the failure time is largely spent on void growth, and, for sufficiently short lines (<=50 mm), the growth is largely steady state. This allows for the development of a simple expression for the variation of the failure time with microstructure. Assuming that the diffusion activation energies are normally distributed, the permanence property of summed lognormals leads to a roughly lognormal distribution for EM failure times. Importantly for EM design rules, linear extrapolation on lognormal plot is found to slightly underestimate interconnect reliability. [ABSTRACT FROM AUTHOR]

Traditionally, the lognormal distribution has been used to analyze electromigration (EM) failure data for both Al- and Cu-based interconnect technologies. However, from a statistical perspective, the lognormal distribution is found to be inappropriate for submicron interconnects because their resistance degradation profiles are no longer “gradual” as compared to the wider interconnects. In such cases, the gamma distribution is found to be a good choice to represent such failures which are initially “gradual” and later “catastrophic” in nature. The invalidity of the lognormal model for submicron interconnects is assessed and a statistical proof in favor of the gamma statistics is presented. Experimental EM test data for submicron Cu interconnects are analyzed and it is found that the data fitting is generally more accurate for submicron interconnects when the gamma distribution is used. The use of a gamma distribution also changes the field operation lifetime estimates obtained through reliability extrapolation. [ABSTRACT FROM AUTHOR]

We have investigated the magnetization and relaxation dynamics of diluted, freeze-dried superparamagnetic magnetite (Fe3O4) nanoparticle samples with organic shells using a differential fluxgate magnetorelaxometry system. The experimental data were analyzed within the framework of the moment superposition model (MSM), providing information on size and size distribution of particle cores as well as on magnetic properties such as saturation magnetization and anisotropy constant. The MSM was refined by introducing an expression for the Néel time constant depending on magnetic field, anisotropy energy, saturation magnetization, and orientation of the magnetic moment of an individual magnetic nanoparticle (MNP) with respect to the external magnetic field. It is shown that especially the dependence of the magnetization and relaxation curves on magnetizing field and magnetization time provides valuable information for an unambiguous and comprehensive determination of MNP core parameters. All experimental findings could be explained with the refined MSM; however, so far, no self-consistent parameter set was obtained quantitatively explaining all measured data. Deviations from the assumed lognormal distribution of core sizes and yet too simplified expressions for the Néel time constant are discussed as potential reasons for the observed discrepancies. [ABSTRACT FROM AUTHOR]

Integrated circuit chip metallization reliability under use conditions is extrapolated from failure distributions of test structures tested under accelerated conditions. Lognormally plotted electromigration failure time distributions for via/line contact configurations with no redundant conductive path usually display two features that are different from failure time distributions for configurations that have well-defined redundant conductive paths. First, the failure times are more widely distributed (larger standard deviation or σ), and second, the left portion of the distribution (early failures) bends downward (if the sample size is large enough) as the failure times become shorter, in contrast to the straight line behavior that is usually observed for structures with good redundancy. The downward deviation from a straight line distribution erodes the goodness of fit relative to the commonly used two-parameter (t50,σ) lognormal distribution model, and the large σ produces a lifetime projection under use conditions that can be unacceptable for chip reliability. A three-parameter lognormal distribution model (t50,σ,X0) greatly improves the goodness of fit, especially for the downward bending early failure region, and produces projected failure times that are acceptable for chip reliability. The third parameter, X0, is interpreted as the threshold failure time for the distribution, or the time needed to form the absolute minimum size void that will cause failure. All recorded failure times for a given distribution will be greater than X0. Failure distributions for a via/line configuration with no redundancy are compared to those for via/line configurations with varying degrees and types of redundancy to demonstrate the behavior. [ABSTRACT FROM AUTHOR]

A new approach has been presented herein to prepare nano titanium carbide based on the underwater electrical explosion approach. Scanning electron microscopy and x-ray photoelectron spectroscopy were used to investigate the morphology and composition of the electrical explosion products. A numerical model was established to investigate the nanoparticle formation process. The results show that the average diameter of the formed nanoparticles was ∼60 nm and approximately conformed to a lognormal distribution. Compared with the nanoparticles prepared by electrical explosion in gas, the nanoparticles prepared by the underwater electrical explosion had a smaller size distribution range and better sphericity. During the formation process of nanoparticles, the distribution of nanoparticles formed in a narrow temperature range near the specific temperature directly determined the characteristics of the final electrical explosion products. The specific temperature was ∼3400 K, which was also the specific temperature of the saturation ratio, the nucleation rate, the average diameter of the formed nuclei, the number of monomers, and the number of the formed nanoparticles. The diameters of nanoparticles obtained in the experiment were mainly concentrated between 50 and 70 nm, and the calculated diameters of the nanoparticles were mainly concentrated between 55 and 65 nm; therefore, the data obtained through the model were consistent with the experimental ones. These provide a way to synthesize the nano titanium carbide and a method to estimate their size and distribution, and it is hoped for understanding the evolution of the titanium wire underwater electrical explosion and the formation of nanoparticles. [ABSTRACT FROM AUTHOR]

In 4H silicon carbide (SiC) metal-oxide-semiconductor field-effect transistors (MOSFETs), slow drain current transients and strong sweep hysteresis govern the subthreshold regime, in particular, after negative gate stress. Although these are clearly charge carrier trapping and emission phenomena, a physical model describing the effect to a full extent is missing. In this paper, we investigate a-face n-channel 4H-SiC trench MOSFETs and record drain current transients over seven decades of time for gate voltages below and above threshold. We find clear evidence that the transients result from electron capture rather than from hole emission. Thereby, the time constant for electron capture into interface or near-interfacial defects is broadly distributed and is well characterized by a lognormal distribution. Based on the findings, we propose a physical model that consistently describes the time-dependent measured data in the full gate voltage range. The resulting trap density for the investigated MOSFETs equals 4.2 × 1012 cm–2 with a median electrical capture cross section of 2.5 × 10 − 19 cm2. The distribution of capture time constants has a width of 1.6 orders of magnitude. [ABSTRACT FROM AUTHOR]

The three-dimensional Monterey–Miami parabolic equation model is used to simulate a nonlinear internal wave (NIW) crossing the sound field in a shallow water environment. The impetus for this research stems from acoustic measurements taken during the Shallow Water '06 (SW06) field experiment, where a NIW traversed the water column such that soliton wavecrests were nearly parallel to the source–receiver path. Horizontal refraction effects are important in this scenario. A sound speed profile adapted from experimental SW06 data is used to simulate the NIW, assuming variations along the wavecrests (e.g., curvature) are negligible. Broadband and modal energy metrics show acoustic fluctuations due to internal wave activity. Repeated model runs simulate the NIW crossing the parabolic equation (PE) field over space and time. Statistical analysis shows the PE data are best fit by a lognormal distribution but tends to an exponential distribution during certain scenarios. Small angle differences between the acoustic track and the propagating NIW cause substantial differences in energy distribution throughout the PE field. While refraction effects due to the leading edge of the NIW's arrival are important in all cases, the impacts of focusing and defocusing in the perfectly parallel case dominate the field fluctuations. In the non-parallel case, the strong fluctuations introduced by the passage of the NIW are of similar order to the refraction off the leading edge. [ABSTRACT FROM AUTHOR]

Reports on various distributions that were proposed on the basis of geometrical or semi-empirical grounds as suitable for characterizing the mass distribution from fracture or spallation. Expression for the cumulative fragment number distribution for the Mott distribution; Discussion on fractals, multiplicative processes and the lognormal distribution.

Presents information on a study which developed a statistical model of electromigration, incorporating the statistics of microstructure and concomittant variations in the activation energy for grain-boundary diffusion. Problem of scaling when applying the lognormal distribution to a line under stress; Model for electromigration induced failure; Derivation of element life distribution; Discussion on multilognormal as the fine line failure distribution.