Change In Exponent Research Articles

Estimation of Covid-19 Infection Growth Rate Based on the Imbedding Method

An analysis is presented of universal stages in the development of the COVID-19 virus infection epidemic. It is assumed that during a pandemic the growth rate in the number of infections in a country occurs similarly to the process of virion replication in an infected organism. The exponent of the growth rate of the number of infection cases reflects not only biomedical parameters of a virus infection but also distinctive features of the social behavior of the population of a country. The dynamics of the change in the growth rate exponents is simulated by a system of relaxation-type ordinary differential equations. In applied mathematics, based on the imbedding method, limit values are forecast for exponents of the growth rate of the number of cases using the currently available experimental data. These values “forecast ahead” are subsequently approached by the actual exponents of growth in the number of infectees. The search for unknown parameters is carried out by minimizing a specially constructed quadratic functional accounting for all confirmed cases of COVID-19 infection. The functional minimum is found via iterations by solving a system of ordinary differential equations.

Influence of Different Gases on the Design Point of an Industrial Axial Compressor and Deduced Aerodynamical Rematching Methodology

This paper presents a numerical investigation of the effects of compressing various gases, for example, carbon dioxide (CO2) and methane (CH4), on an eight-stage axial air compressor. Several adaptation methods are applied to achieve a similar operating point as for air. Theoretically, the operating point depends on Mach number, flow angles, Reynolds number and isentropic exponent. Numerical results show mismatch effects which arise in the parameters using a non-adapted geometry. A rematching procedure is described, including deduced speed adjustments, in order to achieve Mach number equality at compressor inlet. Only shroud modifications are performed to rematch the flow angles of the air simulation. Although Reynolds and Mach number are kept constant at compressor inlet, an inevitable deviation in downstream flow causes mismatches in efficiency and pressure ratio. Both analytical and numerical methodologies show that the scale of shroud adjustments, as well as the size of mismatch in Mach and Reynolds number, can be correlated to the isentropic gas exponent. In summary, the main impact on gas behavior in an axial air compressor is attributable to the change in isentropic exponent. Derivations of shroud adaptation and analyses of inevitable aerodynamic mismatch are therefore developed depending on the isentropic exponent.

Reduction of the synchronization time in random logistic maps.

We report on the effects of additive noises in a nonchaotic logistic map. In this system, the Lyapunov exponent changes from negative to positive as the noise intensity is increased. When the Lyapunov exponent is negative, the synchronization of orbits with different initial conditions occurs. We find that the synchronization time cannot be determined solely by the Lyapunov exponent when the noise intensity is greater than a point at which the Lyapunov exponent is minimum. We show that this reduction of the synchronization time is attributed to initial nonstationary behaviors, where the critical point of the logistic map plays an important role.

Exploring the level of urbanization based on Zipf’s scaling exponent

The rank–size distribution of cities follows Zipf’s law, and the Zipf scaling exponent often tends to a constant 1. This seems to be a general rule. However, a recent numerical experiment shows that there exists a contradiction between the Zipf exponent 1 and high urbanization level in a large population country. In this paper, mathematical modeling, computational analysis, and the method of proof by contradiction are employed to reveal the numerical relationships between urbanization level and Zipf scaling exponent. The main findings are as follows. (1) If Zipf scaling exponent equals 1, the urbanization rate of a large populous country can hardly exceed 50%. (2) If Zipf scaling exponent is less than 1, the urbanization level of large populous countries can exceeds 80%. A conclusion can be drawn that the Zipf exponent is the control parameter for the urbanization dynamics. In order to improve the urbanization level of large population countries, it is necessary to reduce the Zipf scaling exponent. Allometric growth law is employed to interpret the change of Zipf exponent, and scaling transform is employed to prove that different definitions of cities do no influence the above analytical conclusion essentially. This study provides a new way of looking at Zipf’s law of city-size distribution and urbanization dynamics.

Conditions of inertial-viscous transition and related jetting in large cavity collapse

Viscosity and surface tension of fluids regulates the collapse dynamics of a large cavity where collapse is initially inertial with the minimum radius ${r}_{m}\ensuremath{\sim}({t}_{0}\ensuremath{-}t{)}^{1/2}$, where ${t}_{0}\ensuremath{-}t$ is the time remaining for collapse. In low-viscosity fluids, an inertial-capillary transition occurs (exponent changes from 1/2 to 2/3), while it is inertial-viscous (exponent changes from 1/2 to 1) in viscous fluids at a late stage of collapse. The inertial-viscous transition occurs when the local capillary number is greater than 1 and the local Ohnesorge number is greater than 0.1.

Effect of Loading Rate on Creep Properties of HgCdTe Epitaxial Films

Nanoindentation creep studies were performed on Hg1-xCdxTe (x~0.29) epitaxial films using different loading rates of 0.5 mN.s-1, 1 mN.s-1, 2 mN.s-1 and 4 mN.s-1, keeping a constant peak load of 10 mN. A constant hold time of 20 sec at peak load was maintained for all experiments. The effect of loading rate on creep behaviour of material has been investigated. Creep displacement had shown increasing trend with increase of loading rates. Stress exponents were extracted using creep curve fitting with an empirical equation. A strong dependence of loading rate on stress exponent was observed. The value of stress exponent was found varying in the range 0.60-1.76, 0.96-2.23, 0.98-2,87 and 0.90-2.81 for loading rates 0.5 mN.s-1, 1 mN.s-1, 2 mN.s-1 and 4 mN.s-1, respectively. The change of stress exponent was attributed to change of creep mechanism. Hardness and elastic modulus were extracted from load-displacement curves and it was found that with the increase of the loading rate hardness increases, while elastic modulus remains constant. A correlation between variation of hardness and creep displacement has also been presented.

Melting of the critical behavior of a Tomonaga-Luttinger liquid under dephasing

Strongly correlated quantum systems often display universal behavior as, in certain regimes, their properties are found to be independent of the microscopic details of the underlying system. An example of such a situation is the Tomonaga-Luttinger liquid description of one-dimensional strongly correlated bosonic or fermionic systems. Here, we investigate how such a quantum liquid responds under dissipative dephasing dynamics and, in particular, we identify how the universal Tomonaga-Luttinger liquid properties melt away. Our study, based on adiabatic elimination, shows that dephasing first translates into the damping of the oscillations present in the density-density correlations, a behavior accompanied by a change in the Tomonaga-Luttinger liquid exponent. This first regime is followed by a second one characterized by the diffusive propagation of featureless correlations as expected for an infinite temperature state. We support these analytical predictions by numerically exact simulations carried out using a number-conserving implementation of the matrix product states algorithm adapted to open systems.

Nucleation and growth of cholesteric collagen tactoids: A time-series statistical analysis based on integration of direct numerical simulation (DNS) and long short-term memory recurrent neural network (LSTM-RNN)

HypothesisLiquid-crystalline phase separation by nucleation and growth (NG) is a crucial step in the formation of collagen-based biomaterials. However, the fundamental mechanisms are not completely understood for chiral lyotropic colloidal mesogens such as collagen. MethodologyTo capture the dynamics of NG under a quenching process into the biphasic equilibrium zone, we use direct numerical simulation based on the time-dependent Ginzburg-Landau model allowing minimization of the total free energy comprised of five key contributions: phase separation (Flory-Huggins), ordering (Landau-de Gennes), chiral orientational elasticity (Frank-Oseen-Mermin), interfacial and coupling effects. LSTM-RNN is applied as a surrogate model to greatly enrich the results. Significant correlations are established using Symbolic Regression. FindingsWe quantify the NG boundaries existing in the collagen phase diagram that has recently been developed and validated by our thermodynamic model (Khadem and Rey, 2019 [1]). We characterize the three NG stages (induction, nucleation, and coarsening) in terms of tactoids’ shape, morphology, growth laws, and population across the NG zone. Wide-range generic correlations are developed, revealing the quench depth dependence of NG characteristics and connecting the sequential NG stages. We confirm experimental observations on time-dependent growth law exponent changes from an initial n≈0.5 for the mass transfer limited regime to n≈1 for the volume-driven phase ordering regime upon increasing quench depth during the nucleation period and having exclusively a value of n≈0.5 for the coarsening period regardless of quench depth. We lastly uncover the underlying physics behind the NG phenomena.

Frameworks for investigation of nonlinear dynamics: Experimental study of the turbulent jet

Analysis methods that have been developed in the field of nonlinear dynamics have provided valuable insights into the physics of turbulent flows, although their application to open flows is less well explored. The nonlinear dynamics of a turbulent jet with a low-to-moderate Reynolds number is investigated by using the single-trajectory framework and ensemble framework. We have used Lyapunov exponents to calculate the spectra of scaling indices of the attractor. First, we evaluated the frameworks on two theoretical models, one with a stationary attractor (Lorenz-63) and the other with time-varying characteristics (Lorenz-84). Theoretical studies showed that in dynamical systems with a stable attractor, both frameworks estimated the same largest Lyapunov exponent. The ensemble framework enables us to resolve the unsteady characteristics of a time-varying strange attractor. Second, we applied both frameworks to time-resolved planar velocity fields in a turbulent jet at local Reynolds numbers (Reδ) of 3000 and 5000. Time-resolved particle image velocimetry was utilized to measure streamwise and transverse velocity components. Results support the presence of a low-dimensional attractor in the reconstructed phase space with a chaotic characteristic. Despite considerable changes in the dynamics for the higher Reynolds number case, the system’s fractal dimension did not change significantly. We have used Lagrangian Coherent Structures (LCSs) to study the relationship between changes in the Lyapunov exponent with flow topological features. Results suggest that holes in the stable LCSs provide a path for the entrainment of the coflow, which is shown to be one of the main contributors to high Lyapunov exponents.

Catastrophic Failure: How and When? Insights From 4‐D In Situ X‐ray Microtomography

AbstractCatastrophic failure of brittle rocks is important in managing risk associated with system‐sized material failure. Such failure is caused by nucleation, growth, and coalescence of microcracks that spontaneously self‐organize along localized damage zones under compressive stress. Here we present X‐ray microtomography observations that elucidate the in situ micron‐scale processes, obtained from novel tri‐axial compression experiments conducted in a synchrotron. We examine the effect of microstructural heterogeneity in the starting material (Ailsa Craig microgranite; known for being virtually crack‐free) on crack network evolution and localization. To control for heterogeneity, we introduced a random nanoscale crack network into one sample by thermal stressing, leaving a second sample as‐received. By assessing the time‐dependent statistics of crack size and spatial distribution, we test the hypothesis that the degree of starting heterogeneity influences the order and predictability of the phase transition between intact and failed states. We show that this is indeed the case at the system‐scale. The initially more heterogeneous (heat‐treated) sample showed clear evidence for a second‐order transition: inverse power law acceleration in correlation length with a well‐defined singularity near failure and distinct changes in the scaling exponents. The more homogeneous (untreated) sample showed evidence for a first‐order transition: exponential increase in correlation length associated with distributed damage and unstable crack nucleation ahead of abrupt failure. In both cases, anisotropy in the initial porosity dictated the fault orientation, and system‐sized failure occurred when the correlation length approached the grain size. These results have significant implications for the predictability of catastrophic failure in different materials.

Directional Droplet Transport Mediated by Circular Groove Arrays. Part I: Experimental Findings.

Directional transport of liquid droplets is crucial for various applications including water harvesting, anti-icing, and condensation heat transfer. Here, bouncing of water droplets with patterned superhydrophobic surfaces composed of circular equidistant grooves was studied. The directional transport of droplets toward the pole of the grooves was observed. The impact of the Weber number, initial polar distance r, and geometrical parameters of the surface on the directional droplet bouncing was experimentally explored. The nature of bouncing was switched when the Weber numbers exceeded We ≅ 20-25. The rebouncing height was slightly dependent on the initial polar coordinate of the impact point for a fixed We, whereas it grew for We > 20. The weak dependence of the droplet spreading time on the Weber number was close to the dependence predicted by the Hertz bouncing, thus evidencing the negligible influence of viscosity in the process. Change in the scaling exponent describing the dependence of the normalized spreading time on the Weber number was registered for We ≅ 25. The universal dependence of the offset distance ΔL of the droplets on the Weber number ΔL/D0 ∼ We1.5 was established. The normalized offset distance decreased with the normalized initial polar distance as ΔL/D0 ∼ (r/S)-1, where D0 and S are the droplet diameter and groove width, respectively. This research may yield more insights into droplet bouncing on patterned surfaces and offer more options in directed droplet transportation.

Inhomogeneous parametric scaling and variable-order fractional diffusion equations

We discuss the derivation and the solutions of integrodifferential equations (variable-order time-fractional diffusion equations) following as continuous limits for lattice continuous time random walk schemes with power-law waiting-time probability density functions whose parameters are position-dependent. We concentrate on subdiffusive cases and discuss two situations as examples: A system consisting of two parts with different exponents of subdiffusion, and a system in which the subdiffusion exponent changes linearly from one end of the interval to another one. In both cases we compare the numerical solutions of generalized master equations describing the process on the lattice to the corresponding solutions of the continuous equations, which follow by exact solution of the corresponding equations in the Laplace domain with subsequent numerical inversion using the Gaver-Stehfest algorithm.

Compressive creep of SiC whisker/Ti3SiC2 composites at high temperature in air

AbstractThe compressive creep of a SiC whisker (SiCw) reinforced Ti3SiC2 MAX phase‐based ceramic matrix composites (CMCs) was studied in the temperature range 1100‐1300°C in air for a stress range 20‐120 MPa. Ti3SiC2 containing 0, 10, and 20 vol% of SiCw was sintered by spark plasma sintering (SPS) for subsequent creep tests. The creep rate of Ti3SiC2 decreased by around two orders of magnitude with every additional 10 vol% of SiCw. The main creep mechanisms of monolithic Ti3SiC2 and the 10% CMCs appeared to be the same, whereas for the 20% material, a different mechanism is indicated by changes in stress exponents. The creep rates of 20% composites tend to converge to that of 10% at higher stress. Viscoplastic and viscoelastic creep is believed to be the deformation mechanism for the CMCs, whereas monolithic Ti3SiC2 might have undergone only dislocation‐based deformation. The rate controlling creep is believed to be dislocation based for all the materials which is also supported by similar activation energies in the range 650‐700 kJ/mol.

Evaluation of the depressive state of mobile technical systems operator subjected to electromagnetic noise radiation

This paper presents the results of the work aimed at a study of the patterns of changes in the nonlinear electroencephalogram (EEG) parameters, including fractal dimension and self-similarity exponent, when the operator is irradiated with electromagnetic noise radiation. Together with the above-mentioned nonlinear parameters, a change in the spectral power density of the rhythmic components in EEG (delta-, theta-, alpha-, and beta-rhythms) has been studied. Investigation of the fractal dimension, self-similarity exponent, and spectral power density during irradiation was associated with possible changes of the parameters in the case of operator’s depression or minor depression. The radiation source was represented by a transistor electromagnetic-noise generator with the power of 30 mW operating over the frequency range of 5 GHz. The methods for calculation of the nonlinear parameters including fractal dimension and self-similarity exponent have been described. To realize the principal objectives of the work, the Java-based software was developed. The relevant literature demonstrating the changes in fractal dimension, self-similarity exponent, spectral power density of the delta-, theta-, alpha-, beta-rhythms in the case of depression and minor depression has been reviewed. Electroencephalograms were registered according to the “10/20” scheme using the MBN Neurocartograph electroencephalograph. The analyzed leads were Fp1, Fp2, T3, T4, P3, P4, O1, O2, F3, F4, C3, C4. As shown by the results of this work, there is no distinct depressive state of the operator exposed to electromagnetic noise radiation, judging by changes in the self-similarity exponent, fractal dimension, and spectral power density. However, when the operator was irradiated with electromagnetic noise radiation, the observed tendency in variation of the parameters was characteristic for minor depression.

Fracture attribute and topology characteristics of a geothermal reservoir: Southern Negros, Philippines

The characterization of fracture networks using attribute and topological analyses has not been widely applied to the understanding and prediction of the secondary porosity, permeability and fluid flow characteristics of geothermal resources. We acquired fracture length, aperture, intensity and topological data from remotely sensed images and surface exposures of the Cuernos de Negros region and compared these data with well cores and thin sections from the underlying active geothermal reservoir: the Southern Negros Geothermal Field, west central Philippines. We show that the fracture attributes of the analogue and reservoir are best described by a power law distribution of fracture length and aperture intensity across six to eight orders of magnitude. This characterization of outcrop and borehole fractures validates the use of surface exposures as analogues for the Southern Negros Geothermal Field reservoir rocks at depth. An observed change in the scaling exponent in the 100–500 m length scale suggests that regional to sub-regional fracture systems scale differently from those at the meso- and macroscale, which may be a strata-bound effect or a sampling issue. Topological analyses show a dominance of Y-nodes and doubly connected branches, that indicates a high degree of fracture connectivity, which is important for effective fluid flow. Supplementary Material: Slopes, coefficient of determination and Aikake information criterion values of the cumulative frequency v. length and aperture plots of all fracture transects are available at https://doi.org/10.6084/m9.figshare.c.4960559 Thematic collection: This article is part of the The Geology of Fractured Reservoirs collection available at: https://www.lyellcollection.org/cc/the-geology-of-fractured-reservoirs

Nonlocal modeling and analysis of spatiotemporal patterns in non-isothermal phase transformation of NiTi strips

The spatiotemporal evolution of macro-domain patterns in a NiTi thin strip during stress-induced non-isothermal phase transformation (PT) are investigated through 2D FEM simulations using nonconvex nonlocal continuum model and 1D theoretical analysis. The FEM simulations shows that, with the increase of applied stretching rate (nominal strain rate), the way of PT in a thin strip (30 mm × 2.5 mm × 0.5 mm) changes from the sequential nucleation and growth mode in the low rates range (≤0.03/s) to the emergence of periodic patterns in the medium rates range (0.03/s~3.0/s) and eventually to stable homogeneous deformation mode in the high rates range (≥3.0/s). The domain spacing is governed by a power-law scaling to the strain rate, where the exponent changes from −1/2 (low rates range) to −1/6 (medium rates range). The 1D theoretical analysis further demonstrates that the rate-dependent patterns are essentially governed by a nondimensional internal material parameter A-0 and a nondimensional external driving parameter k-. A-0 represents the ratio of adiabatic hardening to isothermal softening in PT of the material, while k- controls the time scale competition of heat release and heat conduction, through which the thermodynamic condition of PT changes from near isothermal (k-→∞) to near adiabatic (k-→0) with the increase of the strain rate. It is shown that, as long as the material has the properties of isothermal softening and adiabatic hardening (i.e., A-0>1), the conventional nucleation-growth paradigm of PT will eventually break down for small k- (or large stain rate). This is due to the fact that the increase of the energy barrier caused by the thermal and the interfacial effects can convexify the energy landscape of the system near the adiabatic condition and suppress the nucleation events at the macroscopic level.

Dynamic changes in rhythmic and arrhythmic neural signatures in the subthalamic nucleus induced by anaesthesia and tracheal intubation

BackgroundSubcortical structures, including the basal ganglia, have been proposed to be crucial for arousal, consciousness, and behavioural responsiveness. How the basal ganglia contribute to the loss and recovery of consciousness during anaesthesia has, however, not yet been well characterised. MethodsTwelve patients with advanced Parkinson's disease, who were undergoing deep brain stimulation (DBS) electrode implantation in the subthalamic nucleus (STN), were included in this study. Local field potentials (LFPs) were recorded from the DBS electrodes and EEG was recorded from the scalp during induction of general anaesthesia (with propofol and sufentanil) and during tracheal intubation. Neural signatures of loss of consciousness and of the expected arousal during intubation were sought in the STN and EEG recordings. ResultsPropofol–sufentanil anaesthesia resulted in power increases in delta, theta, and alpha frequencies, and broadband power decreases in higher frequencies in both STN and frontal cortical areas. This was accompanied by increased STN–frontal cortical coherence only in the alpha frequency band (119 [68]%; P=0.0049). We observed temporal activity changes in STN after tracheal intubation, including power increases in high-beta (22–40 Hz) frequency (98 [123]%; P=0.0064) and changes in the power-law exponent in the power spectra at lower frequencies (2–80 Hz), which were not observed in the frontal cortex. During anaesthesia, the dynamic changes in the high-gamma power in STN LFPs correlated with the power-law exponent in the power spectra at lower frequencies (2–80 Hz). ConclusionsApart from similar activity changes in both STN and cortex associated with anaesthesia-induced unresponsiveness, we observed specific neuronal activity changes in the STN in response to the anaesthesia and tracheal intubation. We also show that the power-law exponent in the power spectra in the STN was modulated by tracheal intubation in anaesthesia. Our results support the hypothesis that subcortical nuclei may play an important role in the loss and return of responsiveness.

Dielectric study and AC conduction mechanism of gamma irradiated nano‑composite of polyvinyl alcohol matrix with Cd0.9Mn0.1S

Nanocomposite of PVA and Cd0.9Mn0.1S was prepared by solution casting technique. The formed nanocomposite was irradiated by γ-ray with dosage ranging from 10 to 120 kGy. The dielectric properties of PVA/Cd0.9Mn0.1S nanocomposites were studied as a function of frequency (100 Hz–5 MHz) in a temperature range of (303–413 K). The data were analyzed in the dielectric loss (e″), electric modulus (M″) and conductivity representation (σ′). Contributions from the polymer matrix and reinforcing phase are discerned in the relaxation response. The α-relaxation and a strong frequency dispersion are identified in the e″ spectra at high temperatures, which are attributed to the segmental motion of the polymer main chain and to conductivity contribution and /or interfacial polarization, respectively. However, two peaks are detected in the M″ spectra: a main α-relaxation at high frequency and ρ-relaxation relating to the conduction process at low frequency. The temperature dependence of both the ρ-relaxation time obtained from the modulus and dc conductivity (σdc) obeys the Arrhenius law with almost similar activation energies, ≈ 0.67 eV. The change of the frequency exponent, s, with temperature reveals that the ac conductivity is governed by the correlated barrier hopping (CBH) mechanism. The dielectric constant (e′) and dielectric loss (e″) are dose dependent showing highest value for 30 kGy irradiated sample in the α-dipolar relaxation region. With increasing γ dose, the ac conductivity increases whereas the binding energy of the charge carriers Wm decreases supporting the dominance of the chain scission in polymer.

New rate-decline forecast approach for low-permeability gas reservoirs with hydraulic fracturing treatments

Estimating production in low-permeability gas reservoirs accurately has been of more concern to oil and gas industries in recent years. Until now, various techniques to estimate well production have been developed. Among them, decline curve analysis models have been recognized as the most efficient and easiest approach to be applied. Unfortunately, each decline curve model has its own limitation and will not allow us to forecast production in low-permeability gas reservoirs with confidence. In this paper, firstly, the review of Arps, stretched exponential production decline (SEPD), and Duong methods is conducted explicitly to illustrate the reasons resulted in their limitations. Subsequently, a new empirical decline model with two fitting parameters is developed based on the proposed linear relation of logarithmic production versus the product of square root of time and logarithmic time, which takes the change of decline exponent with production time into account. In addition, a detailed procedure applying this novel decline model for low-permeability gas wells is presented, which is reliable and easy to be utilized. Furthermore, this new model is validated by numerically simulated cases and field observations, which appears good match between forecast rates calculated by this proposed method and numerically simulated rates/field rates. The comparison between this novel method and several traditional methods are further conducted, which indicates that this new approach leads to more reliable forecast than commonly utilized approaches. This work should provide a theoretical guidance to assist analysts in estimating hydrocarbon production rapidly and efficiently in low-permeability reservoirs.

Scale-invariant relaxation dynamics in two-component Bose-Einstein condensates with large particle-number imbalance

We theoretically study the scale-invariant relaxation dynamics in segregating two-component Bose-Einstein condensates with large particle-number imbalance, and uncover that random walk of droplet for the minor component plays a fundamental role in the relaxation process. Our numerical simulations based on the binary Gross-Pitaevskii model reveal the emergence of the dynamical scaling during the relaxation, which is a hallmark of scale-invariant dynamics, in a correlation function for the minor condensate. Tracking exponents characterizing the dynamical scaling in time, we find out a crossover phenomenon that features the change in power exponents of the correlation length. To understand the fundamental mechanism inherent in the scale-invariant relaxation dynamics, we construct a random walk model for droplets. Employing the model, we analytically derive the $1/3$ and $1/2$ power laws and predict the crossover of the scaling. These exponents are in reasonable agreement with the values obtained in the numerical calculations. We also discuss a possible experimental setup for observing the scale-invariant dynamics.