Exponential Dependence Research Articles

Global population: from Super-Malthus behavior to Doomsday criticality.

The report discusses global population changes from the Holocene beginning to 2023, via two Super Malthus (SM) scaling equations. SM-1 is the empowered exponential dependence: , and SM-2 is the Malthus-type relation with the time-dependent growth rate or relaxation time τ : . Population data from a few sources were numerically filtered to obtain a 'smooth' dataset, allowing the distortions-sensitive and derivative-based analysis. The test recalling SM-1 equation revealed the essential transition near the year 1970 (population: ~ 3 billion): from the compressed exponential behavior ( to the stretched exponential one ( ). For SM-2 dependence, linear changes of during the Industrial Revolutions period, since ~ 1700, led to the constrained critical behavior , where is the extrapolated year of the infinite population. The link to the 'hyperbolic' von Foerster Doomsday equation is shown. Results are discussed in the context of complex systems physics, the Weibull distribution in extreme value theory, and significant historic and prehistoric issues revealed by the distortions-sensitive analysis.

Superconducting nanostrip single photon detectors fabricated of aluminum thin-films

We systematically investigated the detection performance of Al nanostrips for single photons at various wavelengths. The Al films were deposited using magnetron sputtering, and the sophisticated nanostructures and morphology of the deposited films were revealed through high-resolution transmission electron microscopy. The fabricated Al meander nanostrips, with a thickness of 4.2 nm and a width of 178 nm, exhibited a superconducting transition temperature of 2.4 K and a critical current of approximately 5 μA at 0.85 K. While the Al nanostrips demonstrated a saturated internal quantum efficiency for 405-nm photons, the internal detection efficiency exhibited an exponential dependence on bias current without any saturation tendency for 1550-nm photons. This behavior can be attributed to the relatively large diffusion coefficient and coherence length of the Al films. By further narrowing the nanostrip width, the Al-SNSPDs remain capable of effectively detecting single telecom photons to facilitate practical applications.

Beyond fitness: The information imparted in population states by selection throughout lifecycles

We approach the questions, what part of evolutionary change results from selection, and what is the adaptive information flow into a population undergoing selection, as a problem of quantifying the divergence of typical trajectories realized under selection from the expected dynamics of their counterparts under a null stochastic-process model representing the absence of selection. This approach starts with a formulation of adaptation in terms of information and from that identifies selection from the genetic parameters that generate information flow; it is the reverse of a historical approach that defines selection in terms of fitness, and then identifies adaptive characters as those amplified in relative frequency by fitness. Adaptive information is a relative entropy on distributions of histories computed directly from the generators of stochastic evolutionary population processes, which in large population limits can be approximated by its leading exponential dependence as a large-deviation function. We study a particular class of generators that represent the genetic dependence of explicit transitions around reproductive cycles in terms of stoichiometry, familiar from chemical reaction networks. Following Smith (2023), which showed that partitioning evolutionary events among genetically distinct realizations of lifecycles yields a more consistent causal analysis through the Price equation than the construction from units of selection and fitness, here we show that it likewise yields more complete evolutionary information measures.

Mathematical expressions for simulation of supercapacitor voltammetry curves and capacitance dependence on scan rate

A straightforward RC series circuit model was proposed to fit the cyclic voltammetry experimental data of various symmetrical electrochemical supercapacitors. The model simulated the experimental behavior for exponential dependence of capacitance on the scan rate. In this model, the zero-scan rate capacitance was considered as a constant, and the equivalent serial resistance depended on the scan rate. Neither the equivalent parallel resistance nor a possible intrinsic dependence of capacitance on applied voltage was considered in the modelling.

Application of kinetic models to study the sorption rate in the ‘ammonium ions–calcined sorbent’ system

This study examines sorption kinetics for the extraction of ammonium ions from an aqueous solution under static conditions using 5 g of sorbent. The sorbent was obtained by calcining ash and slag waste accumulated in the ash dump following hydraulic ash removal. The initial concentrations of ammonium ions in the model solutions were 5, 20, 50 and 100 mg/dm3. The volume of the model solution was 50 cm3. For each initial concentration, the kinetic curves of the ammonium ion sorption at the sorption duration of 10, 30, 60, 90, 120, 150 and 180 min were obtained. The kinetic curves were processed using the Lagergren (pseudo-first order), Ho and McKay (pseudo-second order), Morris-Weber (diffusion) and Elovich kinetic equations. It was demonstrated that all kinetic equations adequately describe the experimental data. The linear correlation of the equations was given. The Boyd equation was used to determine the limiting stage in the Morris–Weber model. It was established that the external diffusion mechanism is limiting for the sorption of ammonium ions by a calcined sorbent. The Lagergren model, with a coefficient of determination R2 of 0.9801–0.9949, best described the experimental data on sorption kinetics. Sorption rate curves as a function of the adsorption value and sorption time were given. The latter are described by exponential and polynomial dependence according to the Lagergren model, polynomial dependence according to the Ho and McKay model and exponential dependence according to the Morris–Weber and Elovich models. The sorption rate was the highest at the initial stage of sorption for all dependencies, which is consistent with previous studies on the sorption of pollutants from aqueous solutions using various sorbents.

Mathematical Modeling of Initial Exothermic Behavior and Thixotropic Properties in Nanoclay-Enhanced Cementitious Materials.

In the realm of cementitious materials, integrating nanoclay shows promise in enhancing properties relevant to additive manufacturing. This paper presents a novel mathematical model that combines simple empirical dissolution/nucleation Avrami-like kinetics with a thixotropic kinetics equation. To analyze the initial exothermic peak, two sets of the calculation parameter function are built to describe the exothermic rate as a function of time, following an exponential pattern. This allows for the prediction of the changes in cumulative heat and heat rate during hydration, considering different concentrations of nanoclay. In the rheological aspect, the relationship between shear stress, shear rate, and time is modeled as a combination of exponential dependencies. This enables the prediction of the variations in shear stress with one variable while holding the other constant (either time or shear rate). By integrating these aspects, this model effectively describes both the first exothermal peak and the rheological behavior during cement hydration with the inclusion of nanoclay. Validated against experimental results, these models demonstrate good accuracy (overall below 3% error), reliability, and applicability. The findings offer valuable insights into the thermal and rheological aspects of concrete printing, enabling informed design decisions for both scientific and industrial applications.

Signatures of nearly compensated magnetism and spin glass behavior in highly frustrated β-Mn-type Mn50Fe25+xAl25-x Heusler alloys.

The present study examines the effect of Fe/Al concentration on the structural and magnetic properties of Mn-rich Mn50Fe25+xAl25-x (x = 5, 10, 15) Heusler alloys through x-ray diffraction, temperature- and field-dependent DC magnetization, thermoremanent magnetization, magnetic memory effect, AC susceptibility measurements, and DFT calculations. The samples crystallize in a cubic β-Mn structure. The trend shows a reduction in lattice parameters (unit cell volume) with the increasing Fe proportion. These alloys exhibit strong antiferromagnetic interactions with large frustration parameters, indicating the presence of competing magnetic interactions. The DC magnetization data reveal spin glass-like features with a peak at spin glass freezing temperature (Tf). The observation of bifurcation in temperature-dependent zero-field-cooled and field-cooled magnetization curves, exponential dependence of the temperature variation of remanence and coercivity, magnetic relaxation, and magnetic memory effect below Tf support the spin-glass character of these alloys. The frequency dependence of Tf is also examined in the context of dynamic scaling laws, such as the Vogel-Fulcher law and critical slowing down model, which further supports the presence of spin glass behavior. In the theoretical DFT calculations, the electronic structure is found to be metallic and similar for both spin projections. Moreover, the antiferromagnetic arrangement of the magnetic moments, in line with the experimental observations, is stabilized by exchange interactions, resulting in an almost compensated total magnetic moment of 0.02-0.38µB/f.u. This is probably caused by the frustrated structure and non-stoichiometric compositions of Mn50Fe25+xAl25-x.

ИМПЕДАНСНЫЙ АНАЛИЗ ПРОЦЕССОВ ПЕРЕНОСА ЗАРЯДА В СТРУКТУРЕ МЕТАЛЛ/ПОЛИМЕР/МЕТАЛЛ

The reaserch is devoted to the experimental study of charge transfer processes in thin films of an electroactive polymer from the class of polyarylene phthalides – poly (diphenylene phthalide). The method of impedance analysis of thin polymer films was used in this work. The material is quite well studied using other methods, such as thermally stimulated methods, optical spectroscopy, etc. However, frequency measurements were carried out mainly only in the field of determining capacitance-voltage characteristics. And since the polymer is electroactive, we should expect to identify features associated with charge transfer in the alternating field mode. In this regard, the work carried out an impedance analysis of thin films of poly (diphenylene phthalide) in the frequency range from 0.1 to 106 Hz. Typically, in impedance analysis, in addition to an ac field, a small DC bias voltage is applied to the metal/polymer/metal structure. This makes it possible to obtain data on surface polarization, charge carrier mobility, and the Maxwell-Wagner effect in the case of studying multilayer films. However, taking into account the electrical activity of the studied material, even impedance analysis in an alternating field, but with an effective voltage range from 0.1 to 10 V, made it possible to evaluate some of the electrophysical characteristics of the behavior of thin films. It was found that the slope of the impedance curve depends on the mechanism of transport of charge carriers in the polymer film. As the voltage increases from 0.1 to 10 V, an increase in the slope of the graph is observed. With an increase in the magnitude of the effective voltage, a transition occurs from the ohmic to the injection mechanism of transport of charge carriers limited by traps. When reaching 2 V, a mode of complete filling of the traps is observed, as a result of which an increase in voltage ceases to affect the slope of the frequency response. The dependence of the transition frequency fc on voltage has been plotted. This frequency corresponds to the transition from the predominance of the active to the reactive component of the impedance. Here, an exponential dependence on the magnitude of the applied voltage is observed, which also indicates the dependence of the mechanisms of transport of charge carriers in the polymer film on voltage (electric field).

Graphene Failure under MPa: Nanowear of Step Edges Initiated by Interfacial Mechanochemical Reactions.

The low wear resistance of macroscale graphene coatings does not match the ultrahigh mechanical strength and chemical inertness of the graphene layer itself; however, the wear mechanism responsible for this issue at low mechanical stress is still unclear. Here, we demonstrate that the susceptibility of the graphene monolayer to wear at its atomic step edges is governed by the mechanochemistry of frictional interfaces. The mechanochemical reactions activated by chemically active SiO2 microspheres result in atomic attrition rather than mechanical damage such as surface fracture and folding by chemically inert diamond tools. Correspondingly, the threshold contact stress for graphene edge wear decreases more than 30 times to the MPa level, and mechanochemical wear can be described well with the mechanically assisted Arrhenius-type kinetic model, i.e., exponential dependence of the removal rate on the contact stress. These findings provide a strategy for improving the antiwear of graphene-based materials by reducing the mechanochemical interactions at tribological interfaces.

Effects of the crystallinity of fluoropolymer binders components in polymer-bonded explosives on shock Hugoniots: A computational study

Fluoropolymers play a crucial role as binders in polymer-bonded explosive (PBX) formulations. However, there is a lack of clear understanding of the effects of increased fluoropolymer crystallinity on the shock response of PBXs in the service environment. This study investigated the shock Hugoniots of two widely applied fluoropolymer binders: (1) F2314 from China—a copolymer with a molar ratio of vinylidene fluoride (VDF) to chlorotrifluoroethylene (CTFE) of 1:4 and (2) F2313 from the United States, also known as Kel F-800, with a VDF to CTFE molar ratio of 1:3. The Hugoniot curves of both fluoropolymers were calculated based on equilibrium molecular dynamics (MD) and a mixing rule. Furthermore, the corresponding P–V curves were obtained through fitting using the Tait equation of state (EOS). Their calculated parameters, including zero-pressure bulk modulus (κo) and sound velocity (co), agreed well with experimental data. The results reveal that the Hugoniots of amorphous F2314 and F2313 exhibited negligible differences. However, increasing crystallinity significantly impacted the Hugoniot curves of both fluoropolymers, especially for F2314 with high crystallinity. The obtained macroscopic characteristic parameters, namely κo and co, exhibited an exponential dependence on crystallinity. Physically, this phenomenon can be attributed to a reduction in the compressible free volume of the fluoropolymers due to a more orderly chain arrangement. Additionally, under the same compression ratio, the shock temperature of the fluoropolymers increased with the crystallinity, posing potential safety risks to explosives. These findings establish a correlation between the crystallinity of fluoropolymers and the shock properties of PBXs, providing a theoretical reference for the formulation design of fluoropolymer-based PBXs.

A new empirical formula for calculation of (n,3n) cross sections of heavy mass nuclei in the energy region 22–27.5 MeV

In this paper we want to study (n,3n) reactions using an empirical formula derived on the basis of the statistical model considering reaction Q-value dependence. This formula was obtained by taking into account the exponential dependence on asymmetry parameter (N−Z)/A for neutron-induced reactions in Levkovskii's empirical formula. In addition, the present formula depends also on incident energy En, reaction Q-value and symmetry term (N−Z)2/A. Herein, a new analysis of experimental data of (n,3n) reactions in the energy region 22–27.5 MeV was carried out for quick estimation of cross sections of the heavy mass isotopes of odd Z-even N nuclides in the region of A = 151 to 209. We observed a good agreement of the experimental cross section data with the calculations performed using the present empirical formula.

Approaching the Curie temperature of ferromagnetic (Ga,Mn)P prepared by ion implantation and pulsed laser melting

This work aims to estimate the Curie temperature and critical exponents in the critical regime of III-V ferromagnetic semiconductor (FS) (Ga,Mn)P film using various methods, including Arrott and Kouvel-Fisher plots, as well as electrical transport measurements. The (Ga,Mn)P film was prepared by implanting Mn ions into an intrinsic (001) GaP wafer, followed by pulsed laser melting (PLM). The magnetic properties of the (Ga,Mn)P layer were systematically investigated. The study investigated the accuracy of four different methods in determining the critical behaviors for the magnetic properties close to TC. The results suggest that the critical exponents are similar to those of the mean-field model, as indicated by the modified Arrot plots and temperature dependent effective critical exponents. However, the accuracy of the temperature-dependent resistance Rxx(T) method and Kouvel-Fisher (K-F) analysis is limited due to the Gaussian distribution of Mn ions in the film.

Glass spectrum, excess wing phenomenon, and master curves in molecular glass formers: A multi-method approach.

The relaxation spectra of glass formers solely displaying an α-peak and excess wing contribution collected by various methods are reanalyzed to pin down their different spectral evolution. We show that master curve construction encompassing both α-peak and emerging excess wing works for depolarized light scattering (DLS) and nuclear magnetic resonance (NMR) relaxometry. It reveals the self-part of the slow dynamics' spectrum. Master curves are to be understood as a result of a more extensive scaling covering all temperatures instead of strict frequency-temperature superposition. DLS and NMR display identical relaxation spectra; yet, comparing different systems, we do not find a generic structural relaxation at variance with recent claims. Dielectric spectroscopy (DS) spectra show particularities, which render master curve construction obsolete. The DS α-peak is enhanced or suppressed with respect to that of DLS or NMR, yet, not correlated to the polarity of the liquid. Attempting to single out the excess wing from the overall spectrum discloses a stronger exponential temperature dependence of its amplitude compared to that below Tg and a link between its exponent and that of the fast dynamics' spectrum. Yet, such a decomposition of α-peak and excess wing appears to be unphysical. Among many different glasses, the amplitude of the excess wing power-law spectrum is found to be identical at Tg, interpreted as a relaxation analog to the Lindemann criterion.

Cooling and instabilities in colliding radiative flows with toroidal magnetic fields

ABSTRACT We report on the results of a simulation-based study of colliding magnetized plasma flows. Our set-up mimics pulsed power laboratory astrophysical experiments but, with an appropriate frame change, is relevant to astrophysical jets with internal velocity variations. We track the evolution of the interaction region where the two flows collide. Cooling via radiative losses is included in the calculation. We systematically vary plasma beta (βm) in the flows, the strength of the cooling (Λ0), and the exponent (α) of temperature dependence of the cooling function. We find that for strong magnetic fields a counter-propagating jet called a ‘spine’ is driven by pressure from shocked toroidal fields. The spines eventually become unstable and break apart. We demonstrate how formation and evolution of the spines depend on initial flow parameters and provide a simple analytical model that captures the basic features of the flow.

Biomechanical properties of nasal tissues

Introduction. Plastic rhinosurgery and augmentation rhinoplasty are very relevant today. Especially in relation to patients with congenital saddle deformity of the nasal dorsum, as well as patients with iatrogenic disorders of the nose shape, which dramatically reduce the quality of human life. There are violations of the function of the nose. The purpose of the work. Purpose. Within the framework of the necessity of performing silicone implantation rhinoplasty, the strength, elastic and hyperelastic properties of the soft tissues of the nasal fascia and periosteum were studied, the dynamic viscosity of the tissues of the nasal fascia and periosteum was evaluated, determining their relaxation properties using elastic, hyperelastic and rheological models. Methods. Linear, bilinear (with two Young modules), exponential, hyperelastic (neohookean, Mooney-Rivlin, Ogden, Yeoh, polynomial and Veronda-Westmann) and elastic-viscous (Maxwell) models of biological tissues were used. We used the Mathcad 15.0 computer algebra system and the universal package of interdisciplinary programs ANSYS Multiphysics Software (version 2022 R2). The accuracy of replacing the properties of real tissues with the results of calculations was calculated on the basis of indicators of descriptive statistics (standard deviation, maximum absolute error, maximum relative error and correlation coefficient). Results. It is proved that the bilinear model for the exact reproduction of the stress-strain curve assumes at the molecular level of tissues an initial linear reaction of elastin fibers, passing at ε=εcr into the final linear reaction of the collagen matrix. It was found that the properties of the periosteum (correlation coefficient R=0.9999) and nasal fascia (correlation coefficient R=0.9999) are described most adequately by the 5-parametric polynomial model of the 2nd order and the Yeoh model of the 3rd order (R=0.999 and R=1, respectively), the least accurately by the simple 1-parameter neohookean model (R=0.898 for the periosteum and R=0.905 for the fascia). Among elastic models, the exponential dependence characterizes the behavior of nasal materials quite well. Conclusion. Biomechanically verified that the periosteum is thicker, stronger and more rigid than the fascia. The established very high viscosity values indicate the slowness of relaxation processes in tissues. The periosteum relaxes tension more slowly, which improves the result of implant fixation. On the contrary, the relaxation time of the periosteum is higher than that of the fascia, from which it is concluded that it is preferable not to cut the periosteum during subcostal implantation.

Theoretical study of kinetic arrest, shear elastic modulus, and yielding in simple biphasic colloidal mixtures.

Based on integrating microscopic statistical mechanical theories for structure and ideal kinetic arrest at the naive mode coupling level, we study dynamic localization, the linear elastic shear modulus, applied stress induced modulus softening, and the absolute yielding of simple biphasic binary mixtures composed of equal diameter hard and attractive spheres. The kinetic arrest map is a rich function of total packing fraction, strength of attraction, and mixture composition. The gel to attractive ideal glass transition, the degree of glass melting re-entrancy, and the crossover boundary separating repulsive glasses from attractive glasses vary with the mixture composition. Exponential and/or apparent (high) power law dependences of the elastic shear modulus on the total packing fraction are predicted with effective exponents or exponential prefactors that are sensitive to mixture composition and location in the kinetic arrest map. An analysis of the effective mean square force on a tagged particle that induces dynamic localization reveals a compensation effect between structural correlations and degree of particle localization, resulting in the emergence of a weaker dependence of the shear modulus on mixture composition at very high attraction strengths. Based on a microrheologically inspired formulation of how external stress weakens particle localization and the shear modulus, we analyze mechanical-induced modulus softening and absolute yielding, defined as a discontinuous solid-to-fluid stress-induced transition that can occur in either one or two steps. Estimates of the corresponding yield strains predict that the binary mixture becomes more brittle with increasing sticky particle composition and/or attraction strength.

Study of Lightweight Ceramic Matrix-Less Syntactic Foam Composed of Cenosphere Using Spark Plasma Sintering.

The current investigation presents porous ceramic materials prepared with cenospheres (CS) by using spark plasma sintering. The impact of sintering temperature, mould diameter (20, 30 and 50 mm) and cenosphere size on the properties of the sintered material was investigated. Shrinkage of the samples during sintering started at 900 °C. Total sample shrinkage during sintering increases with increasing temperature and decreases with increasing mould size; increasing sample sintering temperature increases the apparent density of all sample series CS 63-150 µm in a 20 mm mould from 0.97 to 2.3 g·cm-3 at 1050-1300 °C; in a 30 mm mould, 0.81-1.87 g·cm-3 at 1050-1200 °C; in 50 mm mould, 0.54-0.75 g·cm-3 at 1050-1150 °C; while CS 150-250 µm in a 20 mm mould is 0.93-1.96 g·cm-3 at 1050-1200 °C. Total porosity decreases from 61.5% to 3.9% by increasing sintering temperature from 1050 to 1250 °C, while open porosity reduces at lower temperatures, with closed porosity being highest in samples sintered at 1150 °C. When the sintering temperature increases from 1050 to 1300 °C, the compressive strength of the CS 63-150 samples produced in a 20 mm mould increases from 11 MPa to 312 MPa. These results correlate with the Rice model, which describes an exponential dependence of compressive strength on material porosity and fully dense material compressive strength.

Thermophysical properties and rapid solidification mechanism of liquid Zr<sub>60</sub>Ni<sub>25</sub>Al<sub>15</sub> alloy under electrostatic levitation condition

In this study, the thermophysical properties and rapid solidification mechanism of highly undercooled liquid Zr<sub>60</sub>Ni<sub>25</sub>Al<sub>15</sub> alloy are investigated through the electrostatic levitation technique. The maximum undercooling of this alloy reaches 316 K (0.25<i>T</i><sub>L</sub>). Both density and surface tension display a linear relationship with temperature, while viscosity is related to temperature exponentially. When alloy undercooling is less than 259 K, two significant recalescence events are observed during solidification, corresponding to the formation of pseudobinary (Zr<sub>6</sub>Al<sub>2</sub>Ni + Zr<sub>5</sub>Ni<sub>4</sub>Al) eutectic and ternary (Zr<sub>6</sub>Al<sub>2</sub>Ni + Zr<sub>5</sub>Ni<sub>4</sub>Al + Zr<sub>2</sub>Ni) eutectic. The growth velocity of the binary eutectic phase gradually increases with further undercooling and reaches a maximum undercooling value of 259 K. In contrast, once undercooling exceeds 259 K, a single recalescence event occurs, leading to the independent nucleation of all three compound phases from alloy melt and the rapid growth of a ternary anomalous eutectic structure. Notably, the growth velocity of the ternary eutectic phase exhibits a gradual decline with further undercooling. This diminishing trend of the growth velocity suggests that further undercooling might entirely suppress crystal growth dynamically at a threshold of 385 K. With classical nucleation theory and the Kolmogorov-Johnson-Mehl-Avrami (KJMA) model, the onsets of crystallization for the three phases are calculated, thereby constructing a time–temperature-transformation (TTT) diagram. This diagram elucidates the competitive nucleation among the three phases in the undercooled melt. Both theoretical and experimental evidence reveal that Zr<sub>6</sub>Al<sub>2</sub>Ni phase is primarily nucleated at lower undercooling levels, whereas under higher cooling condition, it is possible for all three phases to nucleate simultaneously.

Brownian motion in a viscous fluid of particles with constant and time-dependent friction

The Brownian motion (BM) of particles in a fluid under the influence of a moving harmonic potential is described analytically. It is assumed that the bath is viscous and particles constituting it experience Stokes' force with friction coefficients that can depend on time. The generalized Langevin equation (GLE) is derived from the equations of motion for the bath and Brownian particles. It has a familiar form, but its memory kernel generalizes the expressions known from the literature even in the case of constant friction. Analytical solutions of the found GLE are obtained for the mean and mean squared displacements of the Brownian particle, assuming the overdamped character of its motion and both the overdamped and underdamped dynamics of bath particles. In the case of constant friction, the model well describes the BM when the external potential does not move so that the system is in equilibrium. The results determined by the time-dependent friction of the bath particles must be specified for concrete fluids. An example of Lennard–Jones atomic liquid is considered with the recently proposed exponential time dependence of the friction coefficient.

A Capacitance Varying Charge Pump with Exponential Stage-Number Dependence and Its Implementation by MEMS Technology

A Capacitance Varying Charge Pump with Exponential Stage-Number Dependence and Its Implementation by MEMS Technology