Exponential Parameter Research Articles

Ortho–para nuclear-spin isomerization energies for all bound vibrational states of ditritium (T2) from non-Born–Oppenheimer variational calculations performed with explicitly correlated all-particle Gaussian functions

Direct variational calculations, where the Born–Oppenheimer (BO) approximation is not assumed, are performed for all 26 bound rovibrational states corresponding to the lowest rotational excitation (i.e. the N=1 states) of the tritium molecule (T2). The non-BO energies are used to determine the ortho–para isomerization energies. All-particle explicitly correlated Gaussian basis functions are employed in the calculations and over 11000 Gaussians independently generated for each state are used. The exponential parameters of the Gaussians are optimized with the aid of analytically calculated energy gradient determined with respect to these parameters. The non-BO wave functions are used to calculate expectation values of the inter-particle distances and the triton–triton correlation functions.

Impulsive control for synchronization and parameters identification of uncertain multi-links complex network

In this paper, the exponential and finite-time synchronization and parameters identification for uncertain multi-links complex network are investigated by using the impulsive control method. It is known that impulsive control, as an effective and ideal control technique, can not only realize the synchronization goal but also reduce the control cost. The paper proposes an impulsive complex network model with uncertain parameter. Two different kinds of adaptive feedback controllers are further designed based on impulsive delay differential inequalities, and the purpose is to achieve the exponential synchronization, finite-time synchronization and obtain parameters identification simultaneously. Several novel and useful exponential and finite-time synchronization criteria are also derived based on global exponential stability theory and finite-time stability theory. Finally, two numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

Nuclear Magnetic Resonance Investigation of the Fractionation of Water–Ethanol Mixtures with Cellulose and Its Cross-Linked Biopolymer Forms

Cellulose (CE) was cross-linked with epichlorohydrin (EPI) at variable compositions, and the fractionation properties were investigated in binary water–ethanol (W–E) solutions, including the pure solvent systems. The relative uptake of each solvent was measured using quantitative 1H nuclear magnetic resonance (qNMR) spectroscopy. This study highlights the utility of qNMR as a rapid screening method for estimation of solvent selective fractionation in binary mixtures. The uptake properties of CE–EPI cross-linked polymers with ethanol and water were well-described using the Sips isotherm model. Modeling shows that the monolayer surface coverage (Qm) of ethanol and water onto the polymer materials covers a range (1.13–2.44 g/g) of values with heterogeneous adsorption behavior, in agreement with the Sips exponential fitting parameter (ns ≠ 1). The CE–EPI adsorbents display unique fractionation with water and ethanol from binary solutions, as evidenced by the relative selectivity (Rselectivity) value in binary W–E solvent systems. The Rselectivity [Qm(W)/Qm(E)] values at saturative conditions varied (from 1.10 to 2.03) and further illustrate that CE materials display molecular selective solvent fractionation in binary W–E solutions. This study provides a greater molecular level understanding for the adsorptive uptake properties of CE that are relevant to developing CE-based adsorbent technology for the fractionation of biofuels and related chemical separations.

Dexmedetomidine pharmacokinetics in the obese

This study aims to characterize the influence of body weight and composition on the pharmacokinetics of dexmedetomidine. Twenty obese patients and 20 non-obese patients scheduled for elective laparoscopic surgery were given dexmedetomidine infusion schemes. Venous blood samples were taken during and after dexmedetomidine administration. Population pharmacokinetic modeling was undertaken to investigate fat free mass (FFM) and normal fat mass (NFM) as size descriptors of volumes and clearances using non-linear mixed effects modeling. NFM partitions total body weight into FFM and fat mass calculated from total body weight (TBW) minus FFM. The relative influence of fat mass compared to FFM is described by the fraction of fat mass that makes fat equivalent to FFM (Ffat). Theory-based allometric scaling using FFM best described weight and body composition differences in clearances and volumes A negative effect of fat mass of with an exponential parameter of -0.00541/kg (95% CI -0.0118 to -0.00246) was estimated for clearance which indicates increased fat mass is associated with impairment of clearance. The use of theory-based allometry with predictions of fat free mass has been able to separate the influences of weight and body composition and indicates that size-normalized clearance of dexmedetomidine is impaired in patients who are obese.

Flow equation forf(R)gravity and some of its exact solutions

We write a Renormalization Group (RG) equation for the function f in a theory of gravity in the f(R) truncation. Our equation differs from previous ones due to the exponential parametrization of the quantum fluctuations and to the choice of gauge. The cutoff procedure depends on three free parameters, and we find that there exist discrete special choices of parameters for which the flow equation has fixed points where f=f_0+f_1 R+f_2 R^2. For other values of the parameters the solution seems to be continuously deformed.

ICT distribution-based contact model for delay tolerant networks

Characteristics of inter contact time( ICT) are essential for delay tolerant networks( DTNs),which are beneficial to network performance analysis,routing protocol design and algorithm optimization,but existing ICT models lack general applicability. Based on the general assumptions,a reliability mathematical model was proposed,which is called ICT distribution-based contact model( IDCM),to demonstrate that the ICT between two mobile nodes was exponentially distributed and to verify that the exponential parameter of node pairs only related to the historical contact numbers and cumulative ICTs. Based on random direction( RD) mobility model dataset,random way point( RWP) mobility model dataset,Beijing taxi network dataset,pocket switch network dataset,extensive experimental simulations were conducted and comparison to parameter-aggregated exponential model was made. The simulation results show that IDCM characterizes contacts of node pairs accurately and have better accuracy than parameter-aggregated exponential model.

Anomalous T2 relaxation in normal and degraded cartilage.

To compare the ordinary monoexponential model with three anomalous relaxation models-the stretched Mittag-Leffler, stretched exponential, and biexponential functions-using both simulated and experimental cartilage relaxation data. Monte Carlo simulations were used to examine both the ability of identifying a given model under high signal-to-noise ratio (SNR) conditions and the accuracy and precision of parameter estimates under more modest SNR as would be encountered clinically. Experimental transverse relaxation data were analyzed from normal and enzymatically degraded cartilage samples under high SNR and rapid echo sampling to compare each model. Both simulation and experimental results showed improvement in signal representation with the anomalous relaxation models. The stretched exponential model consistently showed the lowest mean squared error in experimental data and closely represents the signal decay over multiple decades of the decay time (e.g., 1-10 ms, 10-100 ms, and >100 ms). The stretched exponential parameter αse showed an inverse correlation with biochemically derived cartilage proteoglycan content. Experimental results obtained at high field suggest potential application of αse as a measure of matrix integrity. Simulation reflecting more clinical imaging conditions, indicate the ability to robustly estimate αse and distinguish between normal and degraded tissue, highlighting its potential as a biomarker for human studies. Magn Reson Med 76:953-962, 2016. © 2015 Wiley Periodicals, Inc.

Unsteady MHD radiative flow and heat transfer of a dusty nanofluid over an exponentially stretching surface

We analyzed the unsteady magnetohydrodynamic radiative flow and heat transfer characteristics of a dusty nanofluid over an exponentially permeable stretching surface in presence of volume fraction of dust and nano particles. We considered two types of nanofluids namely Cu-water and CuO-water embedded with conducting dust particles. The governing equations are transformed into nonlinear ordinary differential equations by using similarity transformation and solved numerically using Runge–Kutta based shooting technique. The effects of non-dimensional governing parameters namely magneticfield parameter, mass concentration of dust particles, fluid particle interaction parameter, volume fraction of dust particles, volume fraction of nano particles, unsteadiness parameter, exponential parameter, radiation parameter and suction/injection parameter on velocity profiles for fluid phase, dust phase and temperature profiles are discussed and presented through graphs. Also, friction factor and Nusselt numbers are discussed and presented for two dusty nanofluids separately. Comparisons of the present study were made with existing studies under some special assumptions. The present results have an excellent agreement with existing studies. Results indicated that the enhancement in fluid particle interaction increases the heat transfer rate and depreciates the wall friction. Also, radiation parameter has the tendency to increase the temperature profiles of the dusty nanofluid.

Scaling and renormalization in two dimensional quantum gravity

We study scaling and renormalization in two dimensional quantum gravity in a covariant framework. After reviewing the definition of a proper path integral measure, we use scaling arguments to rederive the KPZ relations, the fractal dimension of the theory and the scaling of the reparametrization-invariant two point function. Then we compute the scaling exponents entering in this relations by means of the functional RG. We show that a key ingredient to obtain the correct results already known from Liouville theory is the use of the exponential parametrization for metric fluctuations. We also show that with this parametrization we can recover the correct finite part of the effective action as the $\epsilon \to 0$ continuation of gravity in $d=2+\epsilon$ dimensions.

Exact likelihood inference for two exponential populations based on a joint generalized Type-I hybrid censored sample

Following the work of Chen and Bhattacharyya [Exact confidence bounds for an exponential parameter under hybrid censoring. Comm Statist Theory Methods. 1988;17:1857–1870], several results have been developed regarding the exact likelihood inference of exponential parameters based on different forms of censored samples. In this paper, the conditional maximum likelihood estimators (MLEs) of two exponential mean parameters are derived under joint generalized Type-I hybrid censoring on the two samples. The moment generating functions (MGFs) and the exact densities of the conditional MLEs are obtained, using which exact confidence intervals are then developed for the model parameters. We also derive the means, variances, and mean squared errors of these estimates. An efficient computational method is developed based on the joint MGF. Finally, an example is presented to illustrate the methods of inference developed here.

Switching mechanism for TiO2 memristor and quantitative analysis of exponential model parameters**Project supported by the National Natural Science Foundation of China (Grant Nos. 61374150 and 61374171), the State Key Program of the National Natural Science Foundation of China (Grant No. 61134012), the National Basic Research Program of China (Grant No. 2011CB710606), and the Fundamental Research Funds for the Central Universities,

The memristor, as the fourth basic circuit element, has drawn worldwide attention since its physical implementation was released by HP Labs in 2008. However, at the nano-scale, there are many difficulties for memristor physical realization. So a better understanding and analysis of a good model will help us to study the characteristics of a memristor. In this paper, we analyze a possible mechanism for the switching behavior of a memristor with a Pt/TiO2/Pt structure, and explain the changes of electronic barrier at the interface of Pt/TiO2. Then, a quantitative analysis about each parameter in the exponential model of memristor is conducted based on the calculation results. The analysis results are validated by simulation results. The efforts made in this paper will provide researchers with theoretical guidance on choosing appropriate values for (α, β, χ, γ) in this exponential model.

Dynamic finite element simulations of composite stiffened panels with a transverse-isotropic viscoelastic energy dissipation model

This paper presents a methodology for predicting the damped response and energy dissipation of laminated composite structures, subjected to dynamic loads. Starting from simple coupon tests to characterize the material, the numerical simulation of damping properties is made possible by a novel linear viscoelastic model that has been developed and implemented in the finite element code B2000++. A nonlinear optimization procedure is adopted to fit experimental data and define the exponential Maxwell parameter model. To illustrate the potentialities of the method, the post-buckling analysis of a relatively complex aeronautical panel is presented, accounting not only for geometric nonlinearities, but also for viscoelastic effects. The results illustrate the effects due to material dissipation, their relation to the effects of inertia, and the influence of geometric imperfections on the response of the panel.

Distributions of Autocorrelated First-Order Kinetic Outcomes: Illness Severity.

Many complex systems produce outcomes having recurring, power law-like distributions over wide ranges. However, the form necessarily breaks down at extremes, whereas the Weibull distribution has been demonstrated over the full observed range. Here the Weibull distribution is derived as the asymptotic distribution of generalized first-order kinetic processes, with convergence driven by autocorrelation, and entropy maximization subject to finite positive mean, of the incremental compounding rates. Process increments represent multiplicative causes. In particular, illness severities are modeled as such, occurring in proportion to products of, e.g., chronic toxicant fractions passed by organs along a pathway, or rates of interacting oncogenic mutations. The Weibull form is also argued theoretically and by simulation to be robust to the onset of saturation kinetics. The Weibull exponential parameter is shown to indicate the number and widths of the first-order compounding increments, the extent of rate autocorrelation, and the degree to which process increments are distributed exponential. In contrast with the Gaussian result in linear independent systems, the form is driven not by independence and multiplicity of process increments, but by increment autocorrelation and entropy. In some physical systems the form may be attracting, due to multiplicative evolution of outcome magnitudes towards extreme values potentially much larger and smaller than control mechanisms can contain. The Weibull distribution is demonstrated in preference to the lognormal and Pareto I for illness severities versus (a) toxicokinetic models, (b) biologically-based network models, (c) scholastic and psychological test score data for children with prenatal mercury exposure, and (d) time-to-tumor data of the ED01 study.

Predicting chemical degradation during storage from two successive concentration ratios: Theoretical investigation

When a vitamin's, pigment's or other food component's chemical degradation follows a known fixed order kinetics, and its rate constant's temperature-dependence follows a two parameter model, then, at least theoretically, it is possible to extract these two parameters from two successive experimental concentration ratios determined during the food's non-isothermal storage. This requires numerical solution of two simultaneous equations, themselves the numerical solutions of two differential rate equations, with a program especially developed for the purpose. Once calculated, these parameters can be used to reconstruct the entire degradation curve for the particular temperature history and predict the degradation curves for other temperature histories. The concept and computation method were tested with simulated degradation under rising and/or falling oscillating temperature conditions, employing the exponential model to characterize the rate constant's temperature-dependence. In computer simulations, the method's predictions were robust against minor errors in the two concentration ratios. The program to do the calculations was posted as freeware on the Internet. The temperature profile can be entered as an algebraic expression that can include ‘If’ statements, or as an imported digitized time–temperature data file, to be converted into an Interpolating Function by the program. The numerical solution of the two simultaneous equations requires close initial guesses of the exponential model's parameters. Programs were devised to obtain these initial values by matching the two experimental concentration ratios with a generated degradation curve whose parameters can be varied manually with sliders on the screen. These programs too were made available as freeware on the Internet and were tested with published data on vitamin A.

Dispersion interactions in dimers of inert gases: Investigation by means of explicitly correlated coupled clusters CCSD(F12)(T)

Dispersion interactions in He2, Ne2, and Ar2 dimers are investigated using the explicitly correlated method CCSD(F12)(T) with numerical quadratures. The obtained energies of interaction agree well with the results from highly accurate CCSD(T) calculations described in works in which sets of bonded functions are used. It is shown that in order to attain high accuracy in estimating energies of interaction, the exponential parameter of Slater-type geminals in the CCSD(F12)(T) method must be optimized. The higher accuracy of the values of C 6 asymptotic coefficients found using the CCSD(F12)(T) method instead of the conventional CCSD(T) approach is established, demonstrating the importance of considering short-range electron correlation effects in asymptotic regions of potential surfaces where the interaction between atoms is of a long-range dispersion nature.

Direct non-Born-Oppenheimer variational calculations of all bound vibrational states corresponding to the first rotational excitation of D2 performed with explicitly correlated all-particle Gaussian functions.

Direct variational calculations where the Born-Oppenheimer approximation is not assumed are done for all rovibrational states of the D2 molecule corresponding to first excited rotational level (the N = 1 states). All-particle explicitly correlated Gaussian basis functions are used in the calculations. The exponential parameters of the Gaussians are optimized with the aid of analytically calculated energy gradient determined with respect to these parameters. The results allow to determine the ortho-para spin isomerization energies as a function of the vibrational quantum number.

On the regionalization of input–output tables with an industry-specific location quotient

The purpose of this study is to contribute to the ongoing debate about the performance of several location quotients (LQs), including Flegg’s location quotient (FLQ) and the industry-specific FLQ (SFLQ), which was newly developed by Kowalewski (Reg Stud, 240–250, 2015). Unlike FLQ, which has one unique $$\delta $$ -value for all industries in a region, SFLQ allows for a variation in the exponential parameter value of $$\delta $$ for each industrial sector in order to capture specialization and to reduce the tendency for overestimation or underestimation of each of the industries in a given region. Since the national and regional survey data are available for South Korea, this study evaluates and compares the results for SFLQ against those of other non-survey techniques. The findings prove that SFLQ is superior to other LQs, including FLQ and augmented FLQ. In addition, empirical evidence shows that the optimal values for the exponential parameters vary drastically among industries. SFLQ provides more detailed information on regional industries with individual $$\delta $$ values, which is definitely helpful when analyzing regional specialization and shifts in industrial structure. Furthermore, to determine the optimal exponential $$\delta ({\delta _j })$$ value in FLQ and SFLQ in advance, Flegg’s and Kowalewski’s regression models are tested with the use of Korean data. The statistics indicate that the regression equations are debatable and still need major improvement.

An analysis of dietary restraint and obesity using a dynamic model of cumulative food intake curves

BackgroundIn 1980, Kissileff et al. developed the universal eating monitor permitting investigators to calculate cumulative food intake curves. In this landmark study, cumulative food intake curves were fit using linear and quadratic functions. Yet, these models are artificial since cumulative food intake will never decrease, but rather saturate toward a carrying capacity.Methods: We used the Verhulst differential equation model that describes rapid growth followed by saturation to a carrying capacity and estimated model parameters for different food intake curves. The Verhulst model consists of two parameters, r (exponential growth rate) and the carrying capacity (K). Model parameters were calculated for unrestrained and restrained eaters who were guided to eat 1) as much as they feel comfortable with and 2) and as much as you can.Results: Model parameters were r=0.04, K=1500 g for the unrestrained eat as much as you can condition, and r=0.14, K=450 g for the unrestrained eat as much as you feel comfortable with condition. For restrained eaters, the eat as much as you can condition yielded r=0.05, K=1100 g while the eat as much as you feel comfortable with condition generated the parameters r=0.06, K=800 g.ConclusionNormalizing all cumulative food intake curves differentiated unrestrained eaters who were directed to eat as much as they could from all other scenarios. Mechanistically, the exponential growth rate parameter, r, associated with early increases in the rate of food intake was nearly three times larger than growth rates in all other cases. Identifying and classifying individuals who exhibit a high value of r can be useful for detecting and potentially changing eating rates to decrease energy intake.

Excitability of the infraspinatus, but not the middle deltoid, is affected by shoulder elevation angle.

Although both the rotator cuff and deltoid muscle serve as shoulder abductors, they play different roles in shoulder movement. While the deltoid is a primary abductor, the rotator cuff is a stabilizer. They have different anatomic structures for force production and demonstrate different neuromuscular control at different shoulder angles, as measured by electromyographic activity. Corticospinal excitability may be associated with different neuromuscular control of the deltoid and rotator cuff at different angles. The purpose of this study was to investigate how shoulder joint position influences the corticospinal excitability of the deltoid and rotator cuff muscles. Transcranial magnetic stimulation was used to measure the corticospinal excitability of the middle deltoid and infraspinatus at 0° and 90° of arm elevation. Three parameters, a plateau value, exponential parameter, and threshold, were calculated from the input-output curve of the corticospinal pathway. The plateau value of the infraspinatus was significantly higher at 90° of arm elevation, while there is no difference in the excitability in the middle deltoid between elevation angles. The plateau value of the middle deltoid at 90° was 5 % lower than that at 0°, but the plateau value of infraspinatus at 90° was 55 % higher than that at 0°. This suggests that the modulation of excitability varies with shoulder angle and reveals different neurological mechanism for the roles of the deltoid and rotator cuff.

Crashworthiness design for functionally graded foam-filled bumper beam

Automotive bumper beam is an important component to protect passenger and vehicle from injury and damage induced by severe collapse. Recent studies showed that foam-filled structures have significant advantages in light weight and high energy absorption. In this paper, a novel bumper beam filled with functionally graded foam (FGF) is considered here to explore its crashworthiness. To validate the FGF bumper beam model, the experiments at both component and full vehicle levels are conducted. Parametric study shows that gradient exponential parameter m that controls the variation of foam density has significant effect on bumper beam’s crashworthiness; and the crashworthiness of FGF-filled bumper beam is found much better than that of uniform foam (UF) filled and hollow bumper beam. The multiobjective optimization of FGF-filled bumper beam is also performed by considering specific energy absorption (SEA) and peak impact force as the design objectives, and the wall thickness t, foam densities ρf1 and ρf2 (foam densities at the end and at mid cross section, respectively) and gradient exponential parameter m as design variables. The Kriging surrogate modeling technique and multiobjective particle swarm optimization (MOPSO) algorithm were implemented to optimize the FGF-filled bumper beam. The optimized FGF-filled bumper beam is of great advantages and it can avoid the harmful local bending behavior and absorb more energy than UF filled and hollow bumper beam. Finally, the optimized FGF-filled bumper beam is installed to a passenger car model, and the results demonstrate that the FGF-filled bumper beam ensures the crashworthiness performance of the passenger car while reduces weight about 14.4% compared with baseline bumper beam.