Simple Exponential Function Research Articles

Long-time structural relaxation of glass-forming liquids: Simple or stretched exponential?

This paper presents data for the physical aging of the density of squalane upon both non-linear and nearly linear temperature jumps from states of thermal equilibrium. Invoking the single-parameter-aging scenario [Hecksher et al., J. Chem. Phys. 142, 241103 (2015); Proc. Natl. Acad. Sci. U. S. A. 116, 16736-16741 (2019)], the linear-response aging relaxation function is extracted from the data. Based on this, it is shown that the relaxation toward equilibrium follows a simple exponential function at long times; a stretched-exponential function provides a poor fit. This demonstrates the existence of a terminal relaxation rate for the physical aging of squalane, corresponding to an effective long-time cutoff in the spectrum of structural relaxation times.

Carbon Sequestration Due to Commercial Forestry: An Equilibrium Analysis

Abstract Carbon sequestration is one of the tools being used to respond to climate change risks. It is known that carbon stored in wood products is a type of sequestration. However, time frames for evaluating wood use can affect conclusions about sequestration benefits; a long-term perspective and large spatial scale may help clarify these issues. Therefore, I undertook an equilibrium analysis of ongoing commercial forestry operations, relative to carbon sequestration, at the landscape scale. I found that for simple exponential decay functions for wood remaining in use over time, the total sequestered wood at equilibrium is simply the integral of the decay function multiplied by wood product produced. I show that this simple multiplier is a linear function of half-life. For a 50-year wood half-life, this equilibrium multiplier is 72.1. The half-life depends on the specific wood product (lumber, etc.). For waste wood used for energy at mills, typical values yielded a 100-year sequestration (avoided emissions) value of 12H where H is tons of carbon in logs delivered to the mill. This exercise demonstrates that commercial forestry is a significant provider of carbon sequestration through wood products, in addition to other sequestration benefits. The simple multipliers developed here are intuitive and can be easily used with operational wood product data at any scale.

Simple analytical solutions of one-equation modelling for steady/decaying homogeneous turbulence sensitized to small strain

This study presents a simple mathematical solution describing the turbulent kinetic energy in steady or decaying homogeneous turbulence sensitized to small strain. Small strain is found to have little effect on the anisotropy of decaying homogeneous turbulence, which is consistent with a previous experiment. The effect of small strain on dissipation in the governing equations of turbulent kinetic energy is examined using the standard k-ε model. Two temporal profiles, namely a constant profile and a linear profile, with small strain are used. The steady homogeneous turbulence is maintained by linear forcing, as previously reported. This study mainly focuses on the effects of small strain on the turbulence time scale. When the magnitude of the small strain is small, the effects on the turbulence time scale can be negligibly small, especially for a constant profile. Based on this result, the governing equations for steady or decaying homogeneous turbulence sensitized to small strain can be reduced to simple linear equations. The analytical solution of these equations, a simple exponential function, is the same for the two types of homogeneous turbulence.

Analytical evaluation of the Uehling potential using binomial expansion theorems

In this paper, we have introduced a new method to study of Uehling potential using binomial expansion theorems. Note that, the Uehling potential is a powerful tool to determine the effect of vacuum polarization in atomic and muon-atomic systems. The correcting of vacuum-polarization for an electron in a nuclear Coulomb field can be defined more precisely by the use of Uehling potential. From this point of view, the determination of explicit and closed-form analytical expressions for Uehling potential is very important. Therefore, presented method is illustrated by analytically calculation of the Uehling potential with the simple binomial coefficients and exponential integral functions. As can be seen from table and figure, the newly derived analytical expression well avoids the computational difficulties. An evaluation analysis of the Uehling potential is reported for arbitrary values of parameters. Because of its simple form the suggested method can be generally applied to the quantum thermodynamical problems.

Turbines’ effects on water renewal within a marine tidal stream energy site

As tidal stream energy sites contribute to a significant part of water transport in coastal shelf seas, turbines’ implementation may lead to system-wide changes of the hydrodynamic circulation with potential effects on marine water quality. These aspects were investigated in north-western coastal waters of Brittany (France, western Europe) by simulating the decay of a tracer concentration within a control domain surrounding the tidal stream energy site of the Fromveur Strait. Simplified simulations were adopted to analyse the sensitivity of tracer distribution to stream energy extraction. While this marine area showed important renewal capacity with a 50% loss of tracer concentration in less than three days, residual values were still present after two months. This result exhibited that the concentration decay could not be calibrated by simple exponential functions. The renewal of marine waters appeared furthermore dependent on tracer release time during a tidal cycle. A full energy-extraction scenario was finally simulated suggesting weak effects of turbines on the renewal capacity with changes in residence times below 5%. The spatio-temporal Eulerian evolution of the concentration revealed, however, local trapping areas in close correlation with the Lagrangian residual circulation that vanished after two months.

Global α - nucleus optical model based on an Dirac Brueckner Hartree Fock approach

The global α-nucleus optical model is studied based on the nucleon self-energies in an Dirac-Brueckner-Hartree-Fock (DBHF) approach. The newly developed nucleon-nucleus optical model CTOM derived from DBHF, is used as the basis to consistently generate the real and imaginary potentials of the α-nucleus optical potential by double-folding model. The same range correction a of the improved local density approximation (ILDA) in CTOM is adopted, which is also suitable to modify the nucleon interaction range in α-nucleus systems. To get better description of experimental data, the re-normalization factors (NR,NI) are introduced in α-nucleus scattering calculations, and the individual optimized (NR,NI) for all nuclei and energies are searched out under the guidance of χ2 criterion. We systematically explore the energy dependence of NR and NI by considering the α elastic scattering from 12C to 208Pb at incident energies below 120MeV/nucleon and a simple exponential function is extracted. With this global α-nucleus optical potential, a reasonable description of all available experimental data for α scattering from nuclei is achieved.

Denitrification Rate and Its Potential to Predict Biogenic N2O Field Emissions in a Mediterranean Maize-Cropped Soil in Southern Italy

The denitrification rate in C2H2-amended intact soil cores and soil N2O fluxes in closed static chambers were monitored in a Mediterranean irrigated maize-cropped field. The measurements were carried out during: (i) a standard fertilization management (SFM) activity and (ii) a manipulation experimental (ME) test on the effects of increased and reduced application rates of urea at the late fertilization. In the course of the SFM, the irrigations following early and late nitrogen fertilization led to pulses of denitrification rates (up to 1300 μg N2O-N m−2 h−1) and N2O fluxes (up to 320 μg N2O-N m−2 h−1), thanks to the combined action of high soil temperatures and not limiting nitrates and water filled pore space (WFPS). During the ME, high soil nitrates were noted in all the treatments in the first one month after the late fertilization, which promoted marked N-losses by microbial denitrification (from 500 to 1800 μg N2O-N m−2 h−1) every time the soil WFPS was not limiting. At similar maize yield responses to fertilizer treatments, this result suggested no competition for N between plant roots and soil microbial community and indicated a probable surplus of nitrogen fertilizer input at the investigated farm. Correlation and regression analyses (CRA) on the whole set of data showed significant relations between both the denitrification rates and the N2O fluxes with three soil physical-chemical parameters: nitrate concentration, WFPS and temperature. Specifically, the response functions of denitrification rate to soil nitrates, WFPS and temperature could be satisfactorily modelled according to simple Michaelis-Menten kinetic, exponential and linear functions, respectively. Furthermore, the CRA demonstrated a significant exponential relationship between N2O fluxes and denitrification and simple empirical functions to predict N2O emissions from the denitrification rate appeared more fitting (higher concordance correlation coefficient) than the predictive empirical algorithm based on soil nitrates, WFPS and temperature. In this regard, the empirically established relationships between the denitrification rate on intact soil cores under field conditions and the soil variables provided local-specific threshold values and coefficients which may effectively work to calibrate and adapt existing N2O process-based simulation models to the local pedo-climatic conditions.

Hurst Exponent with ARIMA and Simple Exponential Smoothing for Measuring Persistency of M3- Competition Series

The Hurst exponent is a metric used to evaluate whether a time series exhibits long-term memory, and it is used to identify its complexity. Besides, forecasting methods are tested using time series from Makridakis competition. Additionally, Exponential Smoothing is among the best forecasting methods of this competition, and ARIMA is one of the most used for many applications. Nevertheless, the quality of using the Hurst exponent in Makridakis M3-Competition for measuring how well Simple Exponential Smoothing and ARIMA are adapted to a specific time series is unknown. In this work, we show the impact of applying the Hurst exponent using the complete set of series from the M3-Competition. We used k-means as clustering algorithm for the 3003 Hurst exponent values of these series, improving the visualization of all of the data to identify a relationship between Hurst exponent with MAPE and sMAPE forecasting error of the Simple Exponential Smoothing and ARIMA. Finally, the experimentation shows that Hurst exponent and MAPE for the tested methods are inversely related in most of the cases and that there is a trend between them.

Multiple-Change-Point Modeling and Exact Bayesian Inference of Degradation Signal for Prognostic Improvement

Prognostics play an increasingly important role in modern engineering systems for smart maintenance decision-making. In parametric regression-based approaches, the parametric models are often too rigid to model degradation signals in many applications. In this paper, we propose a Bayesian multiple-change-point (CP) modeling framework to better capture the degradation path and improve the prognostics. At the offline modeling stage, a novel stochastic process is proposed to model the joint prior of CPs and positions. All hyperparameters are estimated through an empirical two-stage process. At the online monitoring and remaining useful life (RUL) prediction stage, a recursive updating algorithm is developed to exactly calculate the posterior distribution and RUL prediction sequentially. To control the computational cost, a fixed-support-size strategy in the online model updating and a partial Monte Carlo strategy in the RUL prediction are proposed. The effectiveness and advantages of the proposed method are demonstrated through thorough simulation and real case studies. Note to Practitioners —Degradation signals have been widely used in determining the current health condition and estimate the remaining useful life (RUL) of a component or a system. Most of the existing prognostics utilize a parametric regression model to describe the evolution path of degradation signals for RUL prediction. The common functional forms of these models include simple linear, quadratic, and exponential functions. However, in many applications, the degradation signals show multiple-segment characteristics and the existing parametric forms are inadequate to capture the degradation trend. Motivated by such issue, this paper presents a multiple-change-point (CP) modeling approach, where the degradation signal is divided into several consecutive segments by CPs, and each segment is modeled by a unique parametric model. To capture the heterogeneity across different units, all the parameters, including the number and locations of CPs and model parameters of each segment, are assumed to be random variables following certain distributions. Then, we develop a statistical method to estimate these distributions using historical data. At the online monitoring stage, we develop an innovative updating algorithm to exactly calculate the closed forms of the posterior distributions of the latest CP, the current segment, and model parameters of the current segment. We also derive a closed form for the RUL distribution estimation. Later, several efficient approximation strategies are proposed to reduce the computational burden. Simulation studies and real case studies have shown that the proposed methodology has much better performance than those of existing approaches in handling degradation signals of multiple-segment characteristics.

Intermittent demand forecasting in the Enterprise: Empirical verification

AbstractForecasting methods are often valued by means of simulation studies. For intermittent demand items there are often very few non–zero observations, so it is hard to check any assumptions, because statistical information is often too weak to determine, for example, distribution of a variable. Therefore, it seems important to verify the forecasting methods on the basis of real data. The main aim of the article is an empirical verification of several forecasting methods applicable in case of intermittent demand. Some items are sold only in specific subperiods (in given month in each year, for example), but most forecasting methods (such as Croston's method) give non–zero forecasts for all periods. For example, summer work clothes should have non–zero forecasts only for summer months and many methods will usually provide non–zero forecasts for all months under consideration. This was the motivation for proposing and testing a new forecasting technique which can be applicable to seasonal items. In the article six methods were applied to construct separate forecasting systems: Croston's, SBA (Syntetos–Boylan Approximation), TSB (Teunter, Syntetos, Babai), MA (Moving Average), SES (Simple Exponential Smoothing) and SESAP (Simple Exponential Smoothing for Analogous subPeriods). The latter method (SESAP) is an author's proposal dedicated for companies facing the problem of seasonal items. By analogous subperiods the same subperiods in each year are understood, for example, the same months in each year. A data set from the real company was used to apply all the above forecasting procedures. That data set contained monthly time series for about nine thousand products. The forecasts accuracy was tested by means of both parametric and non–parametric measures. The scaled mean and the scaled root mean squared error were used to check biasedness and efficiency. Also, the mean absolute scaled error and the shares of best forecasts were estimated. The general conclusion is that in the analyzed company a forecasting system should be based on two forecasting methods: TSB and SESAP, but the latter method should be applied only to seasonal items (products sold only in specific subperiods). It also turned out that Croston's and SBA methods work worse than much simpler methods, such as SES or MA. The presented analysis might be helpful for enterprises facing the problem of forecasting intermittent items (and seasonal intermittent items as well).

Templates for Modeling Temperature Response of Passive Greenhouses

A previous publication [1] Stiles, M. 2018. “A Simple Model for Temperature Response of Single Zone Passive Buildings,” Journal of Building Physics, April 2018. Available at http://journals.sagepub.com/doi/full/10.1177/1744259118763843 (last accessed November 27, 2018). [Google Scholar] introduced a model of interior air temperature response to exterior temperature for a single-zone structure with no active heating, ventilation, or cooling. The model was based on a simple exponential step response function relating the two temperatures. Results were sufficiently encouraging to apply the model to other simple passive structures. This article applies the model to two cases of passive greenhouses. One of the greenhouses is a rudimentary plastic-covered hoop house. The other is a super-insulated net-zero structure that grows summer crops in cold climates using sunlight as the source of heating. A model for the interior air temperature of both of these structures was developed using two time-series templates. The first template is an exponential step response function of outdoor air temperature. This template synchronizes the model to the actual interior temperature but does not match its amplitude. A second template was developed by subtracting the model using the first template from the actual interior air temperature data. The second template scaled according to available sunlight as measured by an inexpensive photometric sensor. The superposition of the two templates tracks the actual interior temperature reasonably well given the limitations described in this article. Average difference between actual and modeled data for both structures was within 2°F, although maximum deviations ranged up to 30°F. This article concludes with a discussion of refinements to the model and of its commercial deployment should it prove generally applicable to passive greenhouses.

Analysis of in-beam PET time-profiles in proton therapy

Background: treatment verification with PET imaging in charged particle therapy is conventionally done by comparing measurements of spatial distributions with Monte Carlo (MC) predictions. However, decay curves can provide additional independent information about the treatment and the irradiated tissue. Most studies performed so far focus on long time intervals. Here we investigate the reliability of MC predictions of space and time (decay rate) profiles shortly after irradiation, and we show how the decay rates can give an indication about the elements of which the phantom is made up. Methods and Materials: various phantoms were irradiated in clinical and near-clinical conditions at the Cyclotron Centre of the Bronowice proton therapy centre. PET data were acquired with a planar 16×16 cm2 PET system. MC simulations of particle interactions and photon propagation in the phantoms were performed using the FLUKA code. The analysis included a comparison between experimental data and MC simulations of space and time profiles, as well as a fitting procedure to obtain the various isotope contributions in the phantoms. Results and conclusions: there was a good agreement between data and MC predictions in 1-dimensional space and decay rate distributions. The fractions of 11C, 15O and 10C that were obtained by fitting the decay rates with multiple simple exponentials generally agreed well with the MC expectations. We found a small excess of 10C in data compared to what was predicted in MC, which was clear especially in the PE phantom.

Beta Weil pairing revisited

In this paper, we extend the $$\beta $$ -Weil pairing, initially introduced in the setting of ordinary elliptic curves with even embedding degree by Aranha et al. [2], to ordinary elliptic curves of any embedding degree. We also propose a new optimal pairing which is the product of some rational functions with the same Miller loop and having a simple final exponentiation. The new pairing is appropriated for using the multi-pairing technique for an efficient implementation. We focus our computation at high security level. Exploiting the fact that the $$\beta $$ -Weil pairing is suitable for parallel execution, we first show that calculating the extended $$\beta $$ -Weil pairing over pairing-friendly elliptic curves with embedding degree 27 is more efficient than calculating the optimal ate pairing. Finally we show that calculating our new pairing over Barreto–Lynn–Scott curves with embedding degree 12 (BLS12) and pairing-friendly elliptic curves with embedding degree 15 is more efficient than calculating the optimal ate pairing.

Limitations of the lumped model for in‐tube laminar forced convection interacting with cross forced convection flows

AbstractThe short communication addresses forced convection heat transfer of a viscous fluid flowing in a tube with fully developed laminar velocity and uniform entrance temperature that exchanges heat convection with a surrounding fluid. The idea is to implement the lumped model following the footsteps of the potent lumped model within unsteady heat conduction, instead of the differential model. The computed mean bulk temperatures of the viscous fluid expressed by a simple exponential function agrees well with the baseline numerical mean bulk temperatures when the internal fluid is air, water or crude oil and the external fluid is air for small values of the modified Biot numbers and maximum Reynolds numbers are satisfied.

A Practical Collision-Based Power Analysis on RSA Prime Generation and Its Countermeasure

We analyze the security of RSA prime generation implemented on embedded devices by a practical power analysis attack. Unlike previous differential power analysis-based attack on primality tests of RSA prime generation exploiting the deterministic relationship among multiple prime candidates manipulated by consecutive primality tests, we propose a collision-based power analysis attack on the Miller-Rabin test for a single prime candidate which can recover the secret prime with a single attempt by exploiting collision characteristics of simple power analysis resistant modular exponentiation algorithms. Hence, our attack does not require the incremental prime search assumption and is applicable when countermeasures against previous attacks are deployed since it also does not require the assumption of trial divisions with small primes on prime candidates. For a realistic setting, where five 512-bit modular exponentiations are operated on an ARM Cortex-M4 microcontroller as recommended by FIPS 186-4 standard, we successfully recover the secret exponent to an extent that a feasible exhaustive search is needed for the full recovery of the secret prime. This is a first practical result of recovering a full secret of modular exponentiation which manipulates 512-bit RSA primitives with collision-based power analysis in a single attempt, where the previous attack demonstrates the result for 192-bit ECC primitive implementations. We also present a countermeasure against our attack which requires only one additional modular subtraction for the loop of square-and-multiply-always exponentiation algorithm. An experimental result for the effectiveness of our proposed countermeasure is presented.

Drying kinetics of jabuticaba pulp by regression models

Abstract Jabuticaba tree is native to the Atlantic Forest in Southern Brazil, and its fruit is widely consumed in the fresh form, but it is highly perishable, requiring conservation techniques. The aim of this study was to describe the drying kinetics of jabuticaba pulp at temperatures of 50 and 60°C, comparing the Henderson, Simple Three-Parameter Exponential, Lewis, Thompson, Fick and Wang and Sing regression models and estimating the Absolute Drying Rate (ADR) for the best model. Parameters were estimated using the SAS software. The evaluation of the quality in the adjustment and selection of models was made based on the adjusted determination coefficient, Residual Standard Deviation and Akaike Information Criterion. Models presented good adjustment to data, and the Lewis model was the most suitable to describe the drying kinetics of jabuticaba pulp at temperatures of 50 and 60°C, with drying rate of 0.000063 and 0.000082 g of water/s respectively. ADR indicated that in one third of the drying time, 70% of moisture loss occurred at both temperatures and after this period, there was a deceleration of moisture loss until stabilization, when equilibrium moisture content is reached.

Capturing complexity of the diffusion-weighted MR signal decay

Diffusion-weighted MRI (dMRI) is a key component of clinical radiology. When analyzing diffusion-weighted images, radiologists often seek to infer microscopic tissue structure through measurements of the diffusion coefficient, D0 (mm2/s). This multi-scale problem is framed by the creation of diffusion models of signal decay based on physical laws, histological structure, and biophysical constraints. The purpose of this paper is to simplify the model building process by focusing on the observed decay in the effective diffusion coefficient as a function of diffusion weighting (b-value), D(b), that is often observed in complex biological tissues. We call this approach the varying diffusion curvature (VDC) model. Since this is a heuristic model, the exact functional form of this decay is not important, so here we examine a simple exponential function, D(b) = D0exp(−bD1), where D0 and D1 capture aspects of hindered and restricted diffusion, respectively. As an example of the potential of the VDC model, we applied it to dMRI data collected from normal and diseased human brain tissue using Stejskal-Tanner diffusion gradient pulses. In order to illustrate the connection between D0 and D1 and the sub-voxel structure we also analyzed dMRI data from families of Sephadex beads selected with increasing tortuosity. Finally, we applied the VDC model to dMRI simulations of nested muscle fiber phantoms whose permeability, atrophy, and fiber size distribution could be changed. These results demonstrate that the VDC model is sensitive to sub-voxel tissue structure and composition (porosity, tortuosity, and permeability), hence can capture tissue complexity in a manner that could be easily applied in clinical dMRI.

On the Prony series representation of stretched exponential relaxation

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

Multilevel Supply-Modulated Chireix Outphasing With Continuous Input Modulation

This paper presents a dynamic characterization of a multilevel (ML) Chireix outphasing (ML-CO) power amplifier (PA) with modulated signals. The ML-CO technique combines the advantages of envelope tracking and outphasing architectures by limiting the supply modulation to discrete levels with an efficient power-DAC modulator and using outphasing for fine amplitude control. We describe an experimental test bench that supplies the required phase- and time-aligned modulated signals for outphasing and supply modulation simultaneously. Pulsed characterization is used to design an ML memoryless polynomial DPD. The linearized ML-CO GaN X-band MMIC PA is demonstrated with fixed input drive levels for 9.3-dB peak-to-average power ratio (PAPR), 1.4-MHz and 11.3-dB PAPR, 10-MHz LTE signals with a 9.7-GHz carrier. For both signals, the average total power consumption is reduced by a factor of two when supply modulation is used. An investigation of control signal generation strategies is presented, including combinations of discrete supply and continuous input modulation. A simple exponential function tracks the optimal efficiency trajectory of the ML-CO PA, enabling overall efficiency improvements within 9 and 27 percentage points. This control strategy is applied to radar pulses with amplitude shaping and frequency chirp, with the efficiency improvement of up to 11.8 percentage points compared with constant-supply operation, with 29-dB improvement in spectral confinement.

The mechanical properties of fly ash concrete prepared and cured at high temperatures

Results of an experimental investigation on the effect of fly ash content, water cement (w/c) ratio of concrete prepared and cured at temperatures of ambience, 40°C and 60°C are presented in this paper. The mechanical properties investigated here include its workability, its behaviour under compression and splitting tension. Microscopic investigations were also carried out using SEM micrographic images to gain understanding of concrete at its microstructural level.The results indicate that high temperature increases early compressive strengths of concrete, but has decreasing effects on the strengths at later ages. The use of fly ash in concretes cast and cured at elevated temperatures improves the physical and mechanical properties of fresh as well as those of hardened concrete.Various mathematical models describing the properties of such concretes are considered at the end of this paper. The strength properties of high temperature fly ash concrete were best represented by a simple exponential function of time, while its stress-strain relationship could be best described by an exponential function of strain of a more complicated form.