Exponential Behavior Research Articles

An investigation of a gas–liquid swirling flow with shear-thinning power-law liquids

A gas–liquid swirling flow with shear-thinning liquid rheology exhibits complex behavior. In order to investigate its flow characteristics, experiments and computational fluid dynamics (CFD) simulations are conducted based on dimensional analysis. A Malvern particle size analyzer and electrical resistance tomography are applied to obtain the bubble size distribution and section void fraction. A Coriolis mass flowmeter is applied to obtain the mixture flow rate and mixture density for an entrance gas volume fraction smaller than 7%. The CFD coupled mixture multiphase model and large eddy simulation model are applied, considering the liquid shear-thinning power-law rheology. The results show that the swirling flow can be divided into developing and decaying sections according to the swirl intensity evolution in the axial direction. A gas–liquid swirl flow with shear-thinning liquid prohibits a core-annulus flow structure. A smaller index n contributes to maintaining the development of the swirl flow field and its core-annulus flow structure so that the swirl flow can form over a shorter distance with a stronger intensity. For a more uniform distribution of the apparent viscosity, the gas column in the pipe center is thinner. On the other hand, a larger consistency k enlarges the stress tensor. The amplitude of the velocity and the pressure of the core-annulus flow structure are reduced. A weaker swirl intensity appears with a wider gas column appearing as a consequence. Furthermore, the swirl number decays with an exponential behavior with parameters sensitive to the consistency k and index n of the decaying section of the swirling flow field. These are beneficial to gas–liquid separator design and optimization when encountering the shear-thinning power-law liquid phase in the petroleum industry.

Temporal and spatial evolution of the distribution related to the number of COVID-19 pandemic

This work systematically conducts a data analysis based on the numbers of both cumulative and daily confirmed COVID-19 cases and deaths in a time span through April 2020 to June 2022 for over 200 countries around the world. Such research feature aims to reveal the temporal and spatial evolution of the country-level distribution observed in COVID-19 pandemic, and obtains some interesting results as follows. (1) The distributions of the numbers for cumulative confirmed cases and deaths obey power-law in early stages of COVID-19 and stretched exponential function in subsequent course. (2) The distributions of the numbers for daily confirmed cases and deaths obey power-law in early and late stages of COVID-19 and stretched exponential function in middle stages. The crossover region between power-law and stretched exponential behavior seems to depend on the evolution of “infection” event and “death” event. Such observation implies a kind of important symmetry related to the dynamics process of COVID-19 spreading. (3) The distributions of the normalized numbers for each metric show a temporal scaling behavior in 2-year period, and are well described by stretched exponential function. The observation of power-law and stretched exponential behavior in such country-level distributions suggests underlying intrinsic dynamics of a virus spreading process in human interconnected society. And thus it is important for understanding and mathematically modeling the COVID-19 pandemic.

Elliptic‐ and hyperbolic‐function solutions of the nonlocal reverse‐time and reverse‐space‐time nonlinear Schrödinger equations

In this paper, we obtain the stationary elliptic‐ and hyperbolic‐function solutions of the nonlocal reverse‐time and reverse‐space‐time nonlinear Schrödinger (NLS) equations based on their connection with the standard Weierstrass elliptic equation. The reverse‐time NLS equation possesses the bounded ‐, ‐, ‐, ‐, and ‐function solutions. Of special interest, the ‐function solution can display both the dark‐ and antidark‐soliton profiles. The reverse‐space‐time NLS equation admits the general Jacobian elliptic‐function solutions (which are exponentially growing at one infinity or display the periodical oscillation in ), the bounded ‐ and ‐function solutions, as well as the ‐shifted ‐ and function solutions. In addition, the hyperbolic‐function solutions may exhibit an exponential growth behavior at one infinity, or show the gray/bright‐soliton profiles.

Understanding Heavy Tails of Flood Peak Distributions

AbstractStatistical distributions of flood peak discharge often show heavy tail behavior, that is, extreme floods are more likely to occur than would be predicted by commonly used distributions that have exponential asymptotic behavior. This heavy tail behavior may surprise flood managers and citizens, as human intuition tends to expect light tail behavior, and the heaviness of the tails is very difficult to predict, which may lead to unnecessarily high flood damage. Despite its high importance, the literature on the heavy tail behavior of flood distributions is rather fragmented. In this review, we provide a coherent overview of the processes causing heavy flood tails and the implications for science and practice. Specifically, we propose nine hypotheses on the mechanisms causing heavy tails in flood peak distributions related to processes in the atmosphere, the catchment, and the river system. We then discuss to which extent the current knowledge supports or contradicts these hypotheses. We also discuss the statistical conditions for the emergence of heavy tail behavior based on derived distribution theory and relate them to the hypotheses and flood generation mechanisms. We review the degree to which the heaviness of the tails can be predicted from process knowledge and data. Finally, we recommend further research toward testing the hypotheses and improving the prediction of heavy tails.

Going beyond soft plus virtual

We present a formalism that sums up the soft-virtual (SV) and next-to-SV (NSV) diagonal contributions to inclusive colorless productions in hadron colliders to all orders in perturbative QCD. Using factorisation theorem, renormalisation group invariance and employing the transcendental structure of perturbative results, we show the exponential behavior of soft-collinear function. This allows us to predict certain SV and NSV terms to all orders from lower order information. We also present an integral representation for the coefficient functions which is suitable for Mellin $N$-space resummation.

Photoluminescence characteristics of Ln3+-doped phosphors derived from sustainable resources for solid state lightning applications

Di-calcium silicate (Ca2SiO4) phosphors doped with series of Ln3+ ions have been prepared by using high temperature solid-state reaction technique. The required raw chemicals of CaO from egg shell and SiO2 from rice husk powders have been used instead of chemicals which were derived from non-renewable minerals. The structural, morphological and photoluminescence characteristics were studied through XRD, SEM and FLS 980 spectrometer measurements, respectively. The XRD patterns of all the phosphors are fit well with the established ICDD card No.01–083–0464 with monoclinic crystal structure. Photoluminescence spectra of Ce3+, Pr3+, Sm3+, Eu3+, Tb3+, Dy3+ and Er3+-doped phosphors exhibit characteristic sharp intense emission peaks at 385 (d-f), 606 (1D2→3H4), 600 (4G5/2→6H7/2), 703 (5D0→7F4), 544 (5D4→7F5), 573 (4F9/2→6H13/2) and 545 nm (4S3/2→4I15/2), respectively. Emission characteristics of developed phosphors such as CIE co-ordinates, correlated colour temperature, colour purity, lifetimes of fluorescent level, etc., of Ln3+ have been quantified. The decay curves for lower concentrations of Ln3+ ion exhibit single exponential behaviour and turns into bi-exponential behaviour accompanied with shortening in lifetime for higher concentrations. These results have been discussed with reported values and found to be better than many of the reported phosphors derived from non-renewable minerals. Therefore, Ca2SiO4:Ln3+ phosphors could also be useful to design and develop low-cost solid state lightning devices besides effective utilization of renewable agricultural and food waste materials.

Krylov complexity in saddle-dominated scrambling

In semi-classical systems, the exponential growth of the out-of-time-order correlator (OTOC) is believed to be the hallmark of quantum chaos. However, on several occasions, it has been argued that, even in integrable systems, OTOC can grow exponentially due to the presence of unstable saddle points in the phase space. In this work, we probe such an integrable system exhibiting saddle-dominated scrambling through Krylov complexity and the associated Lanczos coefficients. In the realm of the universal operator growth hypothesis, we demonstrate that the Lanczos coefficients follow the linear growth, which ensures the exponential behavior of Krylov complexity at early times. The linear growth arises entirely due to the saddle, which dominates other phase-space points even away from itself. Our results reveal that the exponential growth of Krylov complexity can be observed in integrable systems with saddle-dominated scrambling and thus need not be associated with the presence of chaos.

Nanostructured Colloidal Solutions of Malachite Green Formulated: Nonlinear Optical Properties and Simulation.

Malachite green (MG) is a dye that has been presented to use as photosensitizers for photodynamic therapy (PDT). Nonlinear absorption coefficient (β) and nonlinear refractive index (n2) of MG formulations with micelles and its encapsulation are studied aiming PDT. Encapsulation of MG was prepared by the mixture of water droplet in the continuous phase of oil, stabilized with surfactant. MG interacts with micelles and reverses micelle (RM), and the results are related to the size and concentration of micelles, RM, surfactant charge types. At low capsule size, the 1/β linearly increases by the increase of volume fraction of water droplet, while, an exponential behavior was observed in the higher capsule size.

Adaptive Rejection of a Sinusoidal Disturbance with Unknown Frequency in a Flexible Rotor with Lubricated Journal Bearings

Frequency-dependent adaptive noise cancellation-based tracking controller (ANC-TC) is a known technique for the stabilization of several nonlinear dynamical systems. In recent years, this control strategy has been introduced and applied for the stabilization of a flexible rotor supported on full-lubricated journal bearings. This paper proposes a theoretical investigation, based on robust immersion and invariance (I&I) theory, of a novel ANC-frequency estimation (FE) technique designed to stabilize a flexible rotor shaft affected by self-generated sinusoidal disturbances, generalized to the case of unknown frequency. A structural proof, under assumptions on closed-loop output signals, shows that the sinusoidal disturbance rejection is exponential. Numerical simulations are presented to validate the mathematical results in silico. The iterative Inexact Newton method is applied to the disturbance frequency and phase estimation error point series. The data fitting confirms that the phase estimation succession has an exponential convergence behavior and that the asymptotical frequency estimation is a warm-up phase of the overall close-loop disturbance estimation process. In two different operating conditions, the orders of convergence obtained by phase and frequency estimate timeseries are pφ=1, pω,unc=0.9983 and pω,cav=1.005. Rejection of the rotor dynamic disturbance occurs approximately 76% before in the cavitated than in the uncavitated condition, 2 (s) and 8.5 (s), respectively.

Hardness targeted design and modulation of food textures in the elastic-regime using 3D printing of closed-cell foams in point lattice systems

Recently, 3D printing has become an innovative technique in the structuring and modulation of food textures. The objective is to systematically extended 3D food printing to allow the production of cellular structures with specifically targeted textural properties. This study presents an approach for 3D printing structures with predefined hardness. As a step in the foundation of textural design, parameter fitting of 3D printed foams and finite element simulations was used to obtain a generalized hardness design formula for the 3D printing of closed-cell foams. Structures incorporating spherical bubbles arranged in point lattice cubic configurations were printed at different porosity levels. A complete 3D printing-stabilization method was applied with an integrated on-board layer-based heating and optimized for targeting heat induced material transitions to actively modulate the material's mechanical properties. FEM simulations were performed at different Young's moduli adjusted using variable heating speeds where the results showed an independency of hardness on the foam configuration and the distance between the closed-cell bubbles. Comparable hardness results were observed between the 3D printed and simulated samples where the same exponential decrease behavior was achieved. The hardness design formula was developed in relation to the material's Young's modulus, porosity, and printed geometry. The performance of the obtained relation showed comparable results to the FEM simulations and the 3D printed structures. • Texture modulation of foods using 3D printing of closed-cell structures. • 3D printing and porosity variation is applied through spherical bubble designs in cubic configurations. • Manipulation of material mechanical properties is performed using variable in-line thermal stabilization. • Design of textural properties in the elastic regime using FEM simulations and 3D printing.

Infinite density and relaxation for Lévy walks in an external potential: Hermite polynomial approach.

Lévy walks are continuous-time random-walk processes with a spatiotemporal coupling of jump lengths and waiting times. We here apply the Hermite polynomial method to study the behavior of LWs with power-law walking time density for four different cases. First we show that the known result for the infinite density of an unconfined, unbiased LW is consistently recovered. We then derive the asymptotic behavior of the probability density function (PDF) for LWs in a constant force field, and we obtain the corresponding qth-order moments. In a harmonic external potential we derive the relaxation dynamic of the LW. For the case of a Poissonian walking time an exponential relaxation behavior is shown to emerge. Conversely, a power-law decay is obtained when the mean walking time diverges. Finally, we consider the case of an unconfined, unbiased LW with decaying speed v(τ)=v_{0}/sqrt[τ]. When the mean walking time is finite, a universal Gaussian law for the position-PDF of the walker is obtained explicitly.

Simple Formulae, Deep Learning and Elaborate Modelling for the COVID-19 Pandemic

Predictive modelling of infectious diseases is very important in planning public health policies, particularly during outbreaks. This work reviews the forecasting and mechanistic models published earlier. It is emphasized that researchers’ forecasting models exhibit, for large t, algebraic behavior, as opposed to the exponential behavior of the classical logistic-type models used usually in epidemics. Remarkably, a newly introduced mechanistic model also exhibits, for large t, algebraic behavior in contrast to the usual Susceptible-Exposed-Infectious-Removed (SEIR) models, which exhibit exponential behavior. The unexpected success of researchers’ simple forecasting models provides a strong support for the validity of this novel mechanistic model. It is also shown that the mathematical tools used for the analysis of the first wave may also be useful for the analysis of subsequent waves of the COVID-19 pandemic.

Reddish-orange emissions from Sm3+ doped zinc alumino borosilicate glasses: A correlative study on structural, thermal, and optical properties

The present study investigates the structural, thermal, and optical properties of Sm3+-doped Zinc Alumino Borosilicate (ZABS) glasses obtained through the melt-quenching method. The prepared glasses clearly exhibit an amorphous nature confirmed by XRD analysis. Through FTIR studies, the vibrations of metal cations, B2O3, SiO2, Al2O3 network groups and OH groups were analysed. This study helps to determine the bridging and non-bridging oxygen quantity in glass structures including Sm2O3. Through differential thermal studies, the thermal stability factor and its related calculations were carried out. Glasses showed a thermal stability (ΔT) value > 100 °C. Absorption spectra of the glasses showed thirteen peaks emerged from the lower ground state 6H5/2. The bonding parameter calculation showed that the glasses exhibit ionic bonding. The Judd-Ofelt (J-O) parameters followed the same trend Ω4 >Ω2> Ω6 for the synthesized glasses. The bandgap values of the glasses decrease with higher content of NBOs in the glass network, and the Urbach energy (EU) increases. The luminescence spectra of the glasses show four emission peaks such that the intense emission is seen at transition 4G5/2 → 6H7/2 at 599 nm. The radiative parameters calculation showed that Sm3+- 0.5 mol% glass has a higher emission cross section (σse) and transition probability (AR). Decay curves were recorded for all the glasses that show single exponential behavior with extended lifetimes (ms). Glasses produce reddish-orange emissions under 402 nm excitation and the values of correlated color temperature (CCT) lie in the range of 1500–1600 K. Overall, the prepared Sm3+-doped ZABS glasses act as a good candidate for luminescent display applications and laser materials.

Carrier Trapping in Wrinkled 2D Monolayer MoS2 for Ultrathin Memory.

Atomically thin two-dimensional (2D) semiconductors are promising for next-generation memory to meet the scaling down of semiconductor industry. However, the controllability of carrier trapping status, which is the key figure of merit for memory devices, still halts the application of 2D semiconductor-based memory. Here, we introduce a scheme for 2D material based memory using wrinkles in monolayer 2D semiconductors as controllable carrier trapping centers. Memory devices based on wrinkled monolayer MoS2 show multilevel storage capability, an on/off ratio of 106, and a retention time of >104 s, as well as tunable linear and exponential behaviors at the stimulation of different gate voltages. We also reveal an interesting wrinkle-based carrier trapping mechanism by using conductive atomic force microscopy. This work offers a configuration to control carriers in ultrathin memory devices and for in-memory calculations.

Improved Maxwell model with structural dashpot for characterization of ultraslow creep in concrete

Ultraslow creep follows a logarithmic law, which exists in high strength self-compacting concrete. The traditional and fractal derivative rheology models can respectively capture exponential and power law behaviors, but are not capable of characterizing ultraslow creep. The Lomnitz model is feasible to describe ultraslow creep, but it is an empirical model without clear physical meaning. In this study, an improved Maxwell model is developed to describe ultraslow creep behavior based on structural dashpot, which is constructed by using the local structural derivative. The structural Maxwell model provides a physical interpretation of the Lomnitz model. The creep deformations of a high strength self-compacting concrete at the early ages of 12 h, 16 h, 20 h, and 24 h are used to test the structural Maxwell model. The results show that the structural Maxwell model can accurately fit the experimental data, and the values of the goodness of fit for the structural Maxwell model and the Lomnitz model are much closer to 1. The creep processes of the self-compacting concrete at the ages of 12 h, 16 h, 20 h, and 24 h belong to ultraslow dynamics, and can well be interpreted by using the structural Maxwell model.

A comprehensive study of the liquid transfer from the front to the back of a vertical perforated sheet

AbstractPerforations contribute to liquid redistribution in corrugated sheet packings. We focus on a simplified but relevant experimental configuration where a vertical perforated flat sheet is supplied with liquid on its front side. We examine how the perforations irrigate the back of the plate. We successively consider a single perforation, a spanwise row of perforations, and a staggered array of perforations. We quantify the liquid transfer through a single row of perforations and find that the transferred flow rate per unit perforation diameter varies linearly with the supply flow rate per unit width. We also analyze the spreading of the rivulets leaking from the perforations, their merging into a continuous wavy film, and the leveling of this film as it falls down the plate. The spreading and the merging exhibit a power‐law behavior in agreement with theoretical models. The leveling exhibits exponential decay behavior.

K\xe4ll\xe9n\u2013Lehmann spectral representation of the scalar SU(2) glueball

The estimation of the Källén–Lehmann spectral density from gauge invariant lattice QCD two point correlation functions is proposed, and explored via an appropriate inversion method. As proof of concept the SU(2) glueball spectrum for the quantum numbers J^{PC} = 0^{++} is investigated for various values of the lattice spacing. The spectral density and the glueball spectrum are estimated using the published data of Yamanaka et al. (Phys Rev D 102(5):054507, https://doi.org/10.1103/PhysRevD.102.054507, arXiv:1910.07756 [hep-lat], 2020). Our estimates for the ground state mass are in good agreement with the traditional approach published therein, which is based on the large time exponential behaviour of the correlation functions. Furthermore, the spectral density also contains hints of excites states in the spectrum.

Disentangling Component Dynamics in an All-Polymer Nanocomposite Based on Single-Chain Nanoparticles by Quasielastic Neutron Scattering.

We have investigated an all-polymer nanocomposite (NC) consisting of single-chain nanoparticles (SCNPs) immersed in a matrix of linear chains of their precursors (25/75% composition in weight). The SCNPs were previously synthesized via “click” chemistry, which induces intramolecular cross-links in the individual macromolecules accompanied by a slight shift (5–8 K) of the glass transition temperature toward higher values and a broadening of the dynamic response with respect to the raw precursor material. The selective investigation of the dynamics of the NC components has been possible by using properly isotopically labeled materials and applying quasielastic neutron scattering techniques. Results have been analyzed in the momentum transfer range where the coherent scattering contribution is minimal, as determined by complementary neutron diffraction experiments with polarization analysis. We observe the development of dynamic heterogeneity in the intermediate scattering function of the NC components, which grows with increasing time. Local motions in the precursor matrix of the NC are accelerated with respect to the reference bulk behavior, while the displacements of SCNPs’ hydrogens show enhanced deviations from Gaussian and exponential behavior compared with the pure melt of SCNPs. The resulting averaged behavior in the NC coincides with that of the pure precursor, in accordance with the macroscopic observations by differential scanning calorimetry (DSC) experiments.

Wearable Sensors Based on Graphene Nanoplatelets Reinforced Polydimethylsiloxane for Human Motion Monitoring: Analysis of Crack Propagation and Cycling Load Monitoring

The use of graphene and other carbon nanoparticles is now of interest for developing chemical (gas and compounds detectors) and physical sensors. In this work, a graphene nanoplatelet (GNP)-PDMS sensor is proposed. More specifically, its strain-sensing capabilities under consecutive cycles as well as the crack propagation mechanisms are widely analyzed. First, an analysis of the electrical properties shows that the increase of the GNP content leads, as expected, to an increase of the electrical conductivity, ranging from values around 10−3 to 1 S/m for 5 and 11 wt.% samples. The analysis of crack propagation monitoring capabilities shows an exceptional sensitivity of the proposed flexible sensors, with a highly exponential behavior of the electrical resistance due to the prevalent breakage of the electrical pathways as crack propagation occurs. Furthermore, the analysis of the electrical response under cyclic load proves a very high robustness, with a similar response when comparing different cycles and an electrical sensitivity that increases when decreasing the GNP content (from 15–25 to 25–50 at 7 and 11 wt.% GNP content, respectively), a fact that is explained by the prevalence of tunneling mechanisms at low contents. Finally, a proof-of-concept of human motion monitoring by the detection of neck, wrist and facial movements is successfully achieved, indicating the high applicability of the proposed sensors.

Resistive switching memory based on chitosan/polyvinylpyrrolidone blend as active layers

We report on resistive switching in ReRAM devices that use chitosan/PVP composite as the active layers. Al/chitosan+PVP/Ag and ITO/chitosan+PVP/Ag devices, each consisting of chitosan/PVP active layer having 1:3, 1:1 and 3:1 chitosan to PVP ratio were studied. Asymmetric threshold switching with Vth=−1.21 V and Vhold=−0.34 V only in the negative voltage bias was obtained for the Al/chitosan+PVP(1:3)/Ag device. The Al/chitosan+PVP(1:1)/Ag device showed better memory behaviour relatively. This device showed bipolar switching with VSET=+0.75 V, and VRESET=−0.28 V, then asymmetric TS with Vth=+0.84 V and Vhold=+0.19 V and lastly back to bipolar switching with VSET=+0.77 V and VRESET=−045 V, during the first, second and third voltage sweeping cycles. We attributed the switching in this device to the formation and rupture of conductive filaments due to Ag ions migration. On the other hand, the Al/chitosan+PVP(3:1)/Ag showed no memory behaviour. In comparison, all ITO/chitosan+PVP/Ag devices did not show any memory characteristics. This indicating the role of the Al/chitosan+PVP interface in the Al/chitosan+PVP/Ag system. Furthermore, we observed the possibility of compliance current dependent or sweeping cycle-dependent decrease in resistance and change from linear to exponential current behaviour in ITO/chitosan+PVP/Ag devices. Resistive switching based on chitosan/PVP blend is essential for biodegradable and environmentally friendly devices. Our results reveal the applicability of chitosan/PVP blend in memory device fabrication and that both the memory and switching can be exploited by varying the ratio of chitosan to PVP in the composite. Lastly, our results demonstrate the importance of electrode material in ReRAM devices.