Exponential Research Articles

Propagators for molecular dynamics in a magnetic field

ABSTRACT Ab initio molecular dynamics in a magnetic field requires solving equations of motion with velocity-dependent forces – namely, the Lorentz force arising from the nuclear charges moving in a magnetic field and the Berry force arising from the shielding of these charges from the magnetic field by the surrounding electrons. In this work, we revisit two existing propagators for these equations of motion, the auxiliary-coordinates-and-momenta (ACM) propagator and the Tajima propagator (TAJ), and compare them with a new exponential (EXP) propagator based on the Magnus expansion. Additionally, we explore limits (for example, the zero-shielding limit), the implementation of higher-order integration schemes, and series truncation to reduce computational cost by carrying out simulations of a HeH + model system for a wide range of field strengths. While being as efficient as the TAJ propagator, the EXP propagator is the only propagator that converges to both the schemes of Spreiter and Walter (derived for systems without shielding of the Lorentz force) and to the exact cyclotronic motion of a charged particle. Since it also performs best in our model simulations, we conclude that the EXP propagator is the recommended propagator for molecules in magnetic fields.

The temporally evolving energy and waiting time statistics of two repeating fast radio bursts

ABSTRACT Based on two very large samples of repeating fast radio bursts (FRBs), i.e. FRB 20121102A and FRB 20201124A observed by the FAST telescope, we study the statistical properties of energy and waiting time. The bent power-law (BPL) model, thresholded power-law (TPL) model, and Band function are used to fit the distribution of energy, and the BPL model and exponential (EXP) model are used to fit the distribution of waiting time. It is found that no single model can fit the distribution of energy or waiting time well in the full range. To investigate the possible temporal evolution, we divide the full samples into several subsamples according to the observing sessions. We find that the distribution of energy for all subsamples can be well fitted by both BPL model and TPL model, while the distribution of waiting time for all subsamples can be well fitted by both BPL model and EXP model. Importantly, for the distribution of energy, the BPL index β of all the subsamples is almost invariant, but the median value parameter xb varies significantly. Similar situation happens in the distribution of waiting time. Furthermore, for the distribution of waiting time, the occurrence rate parameter λ in EXP model varies significantly. These features show that there may be a common emission mechanism for repeating FRBs, but the burst energy and occurrence rate are temporally evolving.

Theoretical thermoelastic frequency prediction of multi (uni/bi) directional graded porous panels and experimental verification

A novel finite element algorithm has been developed to analyse the eigenvalue characteristics of porous functionally graded (FG) curved panel under a thermal environment, considering the material gradings along the length and thickness, i.e. unidirectional (1D) and bidirectional (2D). In this research, exponential (EN), sigmoid (SM) and power-law (PL) gradings and porosity variations, i.e. even (POT-I) and uneven (POT-II), are adopted. The finite element (FE) computational algorithm has been prepared using a mathematical model of the FG panel based on the higher-order theory (HSDT). The structural governing equation is derived via Hamilton’s principle and solved numerically (FE solutions) to predict the eigenvalues. The obtained solution’s convergence is verified to establish the necessary stability. The difference between the present and published results is below 3.7%, and that between the present and experimental results is under 9.1%, which shows the accuracy of the developed model. A few natural fibre-reinforced (linearly varying through the thickness) polymeric layered FG plates are prepared for experimental validation. Finally, regarding the applicability of the proposed computational FE algorithm, a few parametric studies have been conducted to examine the effect of input variables on the thermal frequencies of the graded panel.

Accuracy Evaluation of Standardized Precipitation Index (SPI) Estimation under Conventional Assumption in Yeşilırmak, Kızılırmak, and Konya Closed Basins, Turkey

The doubt in the calculation algorithm of the standardized precipitation index (SPI), which is widely preferred in the evaluation and monitoring of drought, still remains up-to-date because its calculation process is performed in the form of standardization or normalization with a default probability distribution. Therefore, the success of this index is directly affected by the choice of the probability distribution model. This study is based on the effect of three different parameter estimation methods on the calculation process, as well as the comparison of the SPI results calculated based on the default Gamma distribution and the distribution with the best ability to represent the 3-and 12-month consecutive summed rainfall data among the 15 candidate distributions namely Gamma (GAM), Generalized Extreme Value (GEV), Pearson Type III (P III), Log Pearson Type III (LP III), two-parameter Lognormal (LN2), three-parameter Lognormal (LN3), Generalized Logistic (GLOG), Extreme Value Type I (EVI), Generalized Pareto (GPAR), Weilbul (W), Normal (N), Exponential (EXP), Logistic (LOG), four-parameter Wakeby (WK4), and five-parameter Wakeby (WK5) distributions. Approximately 68.4% and 18.4% of the 3-month data considered had the best fit to the Weibull and Pearson III distribution, while approximately 24% and 18% of the 12-month data had the best fit to the Weibull and Logistic distribution. On the other hand, it was found that the default Gamma distribution calculated the extreme drought categories significantly more than the best-fit distribution model. In terms of parameter estimation methods, L-moments for 3-month series and maximum likelihood approaches for 12-month series were most dominant.

IMPROVING ACCURACY AND REPEATABILITY OF T2 MAPPING IN THE OAI DATA THROUGH EXTEND PHASE GRAPH MODELING

IMPROVING ACCURACY AND REPEATABILITY OF T2 MAPPING IN THE OAI DATA THROUGH EXTEND PHASE GRAPH MODELING

The meaning distributions on different levels of granularity

The meaning distributions of certain linguistic forms generally follow a Zipfian distribution. However, since the meanings can be observed and classified on different levels of granularity, it is thus interesting to ask whether their distributions on different levels can be fitted by the same model and whether the parameters are the same. In this study, we investigate three quasi-prepositions in Shanghainese, a dialect of Wu Chinese, and test whether the meaning distributions on two levels of granularity can be fitted by the same model and whether the parameters are close. The results first show that the three models proposed by modern quantitative linguists can both achieve a good fit for all cases, while both the exponential (EXP) model and the right-truncated negative binomial (RTBN) models behave better than the modified right-truncated Zipf-Alekseev distribution (MRTZA), in terms of the consistency of the goodness of fit, parameter change, rationality, and simplicity. Second, the parameters of the distributions on the two levels and the curves are not exactly the same or even close to each other. This has supported a weak view of the concept of ‘scaling’ in complex sciences. Finally, differences are found to lie between the distributions on the two levels. The fine-grained meaning distributions are more right-skewed and more non-linear. This is attributed to the openness of the categories of systems. The finer semantic differentiation behaves like systems with open set of categories, while the coarse-grained meaning distribution resembles those having a close set of few categories.

Modeling of Diurnal Variation Characteristics of VLF Wave Propagation in Earth-Ionosphere Waveguide With FDTD Method

In this letter, Wait's exponential (EXP) model and international reference ionosphere (IRI) model are combined to study the diurnal variation characteristics of very low frequency (VLF) wave propagation. The EXP model is used below the IRI model to compensate for the subionosphere electron density lack of the IRI. The major EXP parameters are reconstructed from the lower IRI electron density for different times of the day. Being capable of characterizing the subionosphere details, the combined IRIEXP model gets higher accuracy than the pure IRI model for VLF diurnal variation prediction. The measurement result is replicated by using the finite-difference time-domain method to validate the presented model.

A Unified Passivity-Based Framework for Control of Modular Islanded AC Microgrids

Voltage and frequency control in an islanded ac microgrid (ImG) amounts to stabilizing an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> unknown ImG equilibrium induced by loads and changes in topology. This article puts forth a unified control framework, which, while guaranteeing such stability, allows for modular ImGs interconnecting multiple subsystems, that is, dynamic <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$RLC$ </tex-math></inline-formula> lines, nonlinear constant impedance, current, power (ZIP) and exponential (EXP) loads, and inverter-based distributed generation units (DGUs) controlled with different types of primary controllers. The underlying idea of the framework is based on the equilibrium-independent passivity (EIP) of the ImG subsystems, which enables stability certificates of ImG equilibria without explicit knowledge of these equilibria. In order to render DGUs EIP, we propose a decentralized controller synthesis algorithm based on port-Hamiltonian systems (PHSs). We also show that EIP, being the key to stability, provides a general framework, which can embrace other solutions available in the literature. Furthermore, we provide a novel argument based on LaSalle’s theorem for proving asymptotic voltage and frequency stability. Finally, we analyze the impact of actuator saturation on the stability results by exploiting the inherent EIP properties of the PHS DGU model. Theoretical findings are backed up by realistic simulations based on the medium-voltage CIGRE benchmark network.

Geometrical nonlinear numerical frequency prediction of porous functionally graded shell panel under thermal environment

The nonlinear eigenfrequency responses of a functionally graded material (FGM) panel in a thermal environment are numerically estimated in the present article using the finite element method (FEM). The constituents of the FGM are considered as the function of the temperature. For the evaluation of material properties of the FGM panel, Voigt’s micromechanical model is used in conjunction with three distinct types of material distribution patterns, namely power-law (PL), sigmoid (SM), and exponential (EN). Also, two kinds of porosity distributions, i.e. even (PT-I) and uneven (PT-II) through the panel thickness are considered in the present work. HSDT kinematics and Green–Lagrange nonlinear strain terms are employed to prepare a mathematical model of the FG panel. The governing equation is obtained using Hamilton’s principle, and a direct iterative technique is used to compute the final vibration responses. The convergence and validation are performed to check the stability and accuracy of the proposed model. Afterwards, several numerical examples are solved to demonstrate the proposed model efficacy in terms of currently adopted input parameters on the frequency (nonlinear) responses deliberated in detail.

A new single formula for the law of the wall and its application to wall-modeled large-eddy simulation

In this work, a new single formula is proposed for the law of the wall, which is dubbed as the LOG–EXP (logarithmic–exponential) formula, for predicting the mean velocity profile in different regions near the wall. When deriving the LOG–EXP formula, a correction term instead of a damping function is introduced to model the difference between the mixing-length eddy viscosity model and the actual Reynolds shear stress for the near-wall effect. The formula is tested using the direct numerical simulation (DNS) data of turbulent channel flows, the experimental data of the boundary layer flow over a flat plate, and the circular pipe flow for different Reynolds numbers. The formula is then employed as the wall model in wall-modeled large-eddy simulation (WMLES) and tested using the turbulent channel flow at three different Reynolds numbers. An overall good performance of the LOG–EXP formula is observed for all the considered cases. When refining the grid, no significant improvements are observed for the Reynolds stresses, as there are several factors, e.g., the grid employed, and the subgrid-scale model, affecting the predictive capability of WMLES. Further work is needed to quantify their effects and improve the WMLES predictions on a fine grid but not fine enough for a wall-resolved large-eddy simulation.

Improving daily rainfall extremes simulation using the generalized Pareto distribution: a case study in Western Iran

Prediction of the occurrence or non-occurrence of daily rainfall plays a significant role in agricultural planning and water resource management projects. In this study, gamma distribution function (GDF), kernel, and exponential (EXP) distributions were coupled (piecewise) with a generalized Pareto distribution. Thus, the gamma-generalized Pareto (GGP), kernel-generalized Pareto (KGP), and exponential-generalized Pareto (EGP) models were used. The aim of the present study was to introduce new methods to modify the simulated generation of extreme rainfall amounts of rainy seasons based on the preserved spatial correlation. The best approach was identified using the normalized root mean square error (NRMSE) criterion. For this purpose, the 30-yr daily rainfall datasets of 21 synoptic weather stations located in different climates of West Iran were analyzed. The first, second, and third-order Markov chain (MC) models were used to describe rainfall time series frequencies. The best MC model order was detected using the Akaike information criterion and Bayesian information criterion. Based on the best identified MC model order, the best piecewise distribution models, and the Wilks approach, rainfall events were modeled with regard to the spatial correlation among the study stations. The performance of the Wilks approach was verified using the coefficient of determination. The daily rainfall simulation resulted in a good agreement between the observed and the generated rainfall data. Hence, the proposed approach is capable of helping water resource managers in different contexts of agricultural planning.

Photosynthesis, Growth and Dry Biomass Production in Euglena gracilis Klebs as Affected by Three Growth Irradiance Levels

Aims: The research aimed to investigate the shade response of E. gracilis Klebs while making the irradiance a crucial factor for photosynthesis based physiological activities and its applicability for industrial level culture conditions.&#x0D; Study Design: Euglena was cultured at three different light intensities of 30, 90, and 210 mol m-2s-1 photoautotrophically and axenically in modified Cramer-Meyer medium at 25 ˚C as batch cultures.&#x0D; Methodology: The photosynthesis O2 evaluation of Euglena cultures was measured under exponential (EP), transitional (TP), and stationary phases (SP). The light compensation point (LCP), light saturation point (LSP), and dark respiration rate (DRR) were obtained. Cell volume and cell number in each culture were measured simultaneously. Cells were collected and obtained dry mass (DM) after drying aliquots at 80˚C. Specific growth rate (SGR) and relative growth rate (RGR) were calculated. Tests for homogeneity of variance were performed on all parameters and LSDs were used for the mean separation.&#x0D; Results: In the TP, the lowest LCP was achieved in the higher light culture. The values of both the DRR and the LSP were the same as in EP. The DRR, LCP and LSP are lower in lower PFD cultures and decreased with increasing cell titers. The cellular growth levels were lower in lower light culture and decreased as each culture grew. Cellular DM was maintained constant in the EP, where SGR almost equaled RGR. In the EP, SGR was maintained constant in each culture, SGR displayed a saturation phenomenon. In the later TP, SGR became equal to RGR and all the cultures revealed constant DM.&#x0D; Conclusion: Euglena photoautotrophic cultures can tolerate low light intensities. With the SGR and RGR behavior under the shade conditions, they can maintain the constant photosynthesis rate and constant dry matter level.

Non-linear Tree Height (h-d) Model Development and Forest Resource Productivity Assessment of Diguyo Limestone Forest within Northern Sierra Madre Natural Park

Forest resource monitoring of different forest types is of great importance in sustainable forest management and climate change mitigation. Monitoring the productivity of forest resources could be achieved by modeling the basic tree parameters necessary for forest growth and yield. This study was conducted to develop a height-diameter at breast height (h-d) model necessary for tree height (h) estimation since h measurement is difficult in the field, especially in dense forests, and to estimate the forest productivity of the Diguyo limestone forest within the Northern Sierra Madre Natural Park (NSMNP). The diameter at breast height (d) and h of 124 trees were measured in seven 400-m2 plots as the basis for the model development. The h-d model was developed using different non-linear models such as the Chapman-Richards (CR), exponential (EX), Korf/Lundqvist (KL), modified logistic (ML), Schnute (SC), and Weibull (WE) models. The models were evaluated using the adjusted coefficient of determination (R2 adjusted), Akaike information criterion (AIC), Bayesian information criterion (BIC), mean absolute error (MAE), root mean square error (RMSE), percentage root mean squared error (PRMSE), and root mean squared percentage error (RMSPE). The performance of the species-specific allometric models and the generic models were compared for the biomass productivity of the limestone forest. Results showed that the CR h-d model performed best with MAE, RMSE, PRMSE, RMSPE, R2 adjusted, AIC, and BIC values of 1.47 m, 1.74 m, 19.31%, 28.71%, 0.79, 32.46, and 36.00, respectively. The highest average predicted tree biomass and carbon stock of the Diguyo limestone forest was 112.52 ± 97.65 t/ha and 50.64 ± 43.94 tC/ha, respectively, which is lower than other karst forests in Asia. The low forest resource productivity is due to the physical condition of the forest aggravated by natural and anthropogenic disturbances, thereby needing immediate attention to achieve forest sustainability.

Systematic Analysis of Wind Resources for Eolic Potential in Bangladesh

Energy consumption in Bangladesh increased for economic, industrial, and digitalization growth. Reductions in conventional sources such as natural gas (54%) and coal (5.6%) are calls to enhance renewable resources. This paper aims to investigate the atmospheric variables for potential wind zones and develop a statistical power-forecasting model. The study-site is Bangladesh, focusing on eight divisions across two regions. First, the southern zone includes Dhaka (Capital), Chittagong, Barishal, and Khulna. The northern regions are Rajshahi, Rangpur, Mymensingh, and Sylhet. This investigation illustrates wind (m/s) speeds at various heights (m) and analyzes the boundary layer height (BLH) from the European Center for Medium Range Weather Forecast reanalysis 5th generation (ERA5). The data is from a period of 40 years from 1979 to 2018, assessing with a climatic base of 20 years (1979 to 2000). The climatological analysis comprises trends, time series, anomalies, and linear correlations. The results for the wind speed (BLH) indicate that the weakest (lower) and strongest (higher) regions are Sylhet and Barishal, respectively. Based on power-curve relationships, a simple power predictive model (SPPM) is developed using global wind atlas (GWA) data (sample: 1100) to estimate the power density (W/m2) and found an accuracy of 0.918 and 0.892 for Exponential (EXP) and Polynomial (PN) with mean absolute percentage errors (MAPE) of 22.92 and 21.8%, respectively. For validation, SPPM also forecasts power incorporating historical observations for Chittagong and obtains correlations of 0.970 and 0.974 for EXP and PN with a MAPE of 10.26 and 7.69% individually. Furthermore, calculations for annual energy production reveal an average megawattage of 1748 and 1070 in the southern and northern regions, with an MAPE of 15.71 and 5.85% for EXP and PN models, except Sylhet. The SPPM’s predictability can be improved with observed wind speeds and turbine types. The research wishes to apply SPPM for estimating energy in operational power plants.

A design strategy of bio-inspired defensive structures with stiffness programmability for reusable impact-resistance protection

As a natural defensive structure, insect cuticle exhibits fascinating impact resistance properties in their body protection due to their spatial hierarchical architecture and the stiffness distribution along their thickness designed by nature. In this study, inspired by the pattern of insect cuticle, we present a novel design strategy of graded elastic ring systems with programmable stiffness gradients to enhance the protective properties. By studying the influence of the elastic modulus, radius and thickness of rings on the impact response of the bio-inspired graded ring systems, the optimal solution of programing the stiffness gradient can be obtained. The mechanical analyses of the single-column ring systems and the bio-inspired ring array architectures with different stiffness gradients under impact loading show that both the distributions of stiffness gradients along the impact direction and the concavity and convexity of the stiffness profiles have a great influence on preventing stress wave propagation and improving impact-tolerance. Compared with convex stiffness gradients, the concave stiffness gradients significantly improve the protective properties as well as reduce the peak value of collision force applied to inner structures. In concave stiffness gradients, the results show that the bio-inspired ring array architectures with exponential (EXP) stiffness gradient have been identified to result in the minimum values of stress, collision force and impulse under impact loading. The strategy proposed in this paper greatly improves the impact resistance property and defensive effect compared with that of the case without protection. The knowledge gained from this work will inspire the designs of novel advanced reusable and lightweight protective structures with improved impact resistance capability by programming reasonable stiffness distributions.

Hidden Scale Invariance in Polydisperse Mixtures of Exponential Repulsive Particles

Polydisperse systems of particles interacting by the purely repulsive exponential (EXP) pair potential are studied in regard to how structure and dynamics vary along isotherms, isochores, and isomorphs. The sizable size polydispersities of 23%, 29%, 35%, and 40%, as well as energy polydispersity 35%, were considered. For each system an isomorph was traced out covering about one decade in density. For all systems studied, the structure and dynamics vary significantly along the isotherms and isochores but are invariant to a good approximation along the isomorphs. We conclude that the single-component EXP system's hidden scale invariance (implying isomorph invariance of structure and dynamics) is maintained even when a sizable polydispersity is introduced into the system.

Comparison of different mathematical models to assess seasonal variations in the longevity of DNA integrity of cooled‐stored stallion sperm

Dynamic assessment of sperm DNA fragmentation (SDF) has shown to give fuller understanding of stallion semen quality; however, there have been limited attempts to use this parameter to investigate seasonal changes in productive functions. The aims of this study were to: (a) establish a reliable mathematical model to describe the longevity of cooled-stored sperm DNA integrity; (b) to examine the effect of seasonal variations on SDF. Ejaculates were cooled to 5°C, and SDF was analysed after 0, 6 and 24hr of storage. The coefficient of determination (R2 ) was calculated after fine-tuning linear (LIN), exponential (EXP) and second order polynomial (POL) models. R2 was significantly higher (p<.001) for POL than for LIN and EXP. The rate of DNA degradation was calculated using the slopes of POL equations. After assessing the rate of change of the POL functions, significant differences between the acceleration of DNA fragmentation were found (p<.01) among seasons, being higher for winter and summer than spring and autumn. In conclusion, DNA analysis of stallion sperm fits better to a second order polynomial mathematical model, being spring the best season to collect and process cooled stallion semen in order to maintain the DNA integrity of the stallion sperm.

Accurate Empirical Path-Loss Model Based on Particle Swarm Optimization for Wireless Sensor Networks in Smart Agriculture

Wireless sensor networks (WSNs) have received significant attention in the last few years in the agriculture field. Among the major challenges for sensor nodes’ deployment in agriculture is the path loss in the presence of dense grass or the height of trees. This results in degradation of communication link quality due to absorption, scattering, and attenuation through the crop’s foliage or trees. In this study, two new path-loss models were formulated based on the MATLAB curve-fitting tool for ZigBee WSN in a farm field. The path loss between the router node (mounted on a drone) and the coordinator node was modeled and derived based on the received signal strength indicator (RSSI) measurements with the particle swarm optimization (PSO) algorithm in the farm field. Two path-loss models were formulated based on exponential (EXP) and polynomial (POLY) functions. Both functions were combined with PSO, namely, the hybrid EXP-PSO and POLY-PSO algorithms, to find the optimal coefficients of functions that would result in accurate path-loss models. The results show that the hybrid EXP-PSO and POLY-PSO models noticeably improved the coefficient of determination (R2) of the regression line, with the mean absolute error (MAE) found to be 1.6 and 2.7 dBm for EXP-PSO and POLY-PSO algorithms. The achieved R2 in this study outperformed the previous state-of-the-art models. An accurate path-loss model is essential for smart agriculture application to determine the behavior of the propagated signals and to deploy the nodes in the WSN in a position that ensures data communication without unnecessary packets’ loss between nodes.

Comparative analysis of probability distributions for the Standardized Precipitation Index and drought evolution in China during 1961–2015

As a representative index for monitoring and assessing drought, the Standardized Precipitation Index (SPI) relies on a suitable probability distribution function (PDF) to describe a precipitation series, which allows interregional comparisons following normalization. In this study, we considered nine PDFs (exponential (EXP), extreme value (EV), gamma (GAM), generalized Pareto (GP), logistic (LO), log-logistic (LOL), log-normal (LON), normal (NOR), and Weibull (WEI)) as candidates for use in SPI calculations. Based on monthly precipitation time series data (1961–2015) from 582 stations across China, together with the Kolmogorov–Smirnov (K–S) and Akaike Information Criterion (AIC) methods, differences in optimal PDFs for SPI calculations were compared comprehensively from the perspectives of timescale, record length, and index value. Based on the SPI calculated using the optimal PDF at the 6-month timescale (SPI6-opt), we analyzed the spatiotemporal characteristics of drought trends in China using the Mann–Kendall method. Results indicated both the timescale and the record length would affect the selection of the optimal PDF. The performance of the WEI and GAM distributions was superior to other distributions in describing monthly precipitation (especially for long precipitation records) at short and multiple timescales, respectively. During the entire study period, areas of China with high frequency of drought have transferred from the northwest (1960s), to the northeast (2000s), and to the southwest (most recent 5 years). Trend analysis revealed a noticeable wetting tendency confined mainly to Northwest, Northeast, and Southeast China and a significant trend toward drought in Southwest China and on the North China Plain.

Three-dimensional static black hole with Λ and nonlinear electromagnetic fields and its thermodynamics

Static black hole with the Power Maxwell invariant (PMI), Born–Infeld (BI), logarithmic (LN), exponential (EN) electromagnetic fields in three-dimensional spacetime with cosmological constant was studied. It was shown that the LN and EN fields represent the Born–Infeld type of nonlinear electrodynamics. It the framework of General Relativity the exact solutions of the field equations were obtained, corresponding thermodynamic functions were calculated and the [Formula: see text] criticality of the black holes in the extended phase-space thermodynamics was investigated.