Extent Of Nonlinearity Research Articles

Understanding fast adsorption in single-solute breakthrough curves

To design efficient adsorption separations and select high-performing materials, understanding the relationship between adsorption equilibria and the movement of solute waves along the fluid is critical. While approximate-analytical methods are useful to combat nonlinearities in the differential equations and efficiently investigate the myriad of materials, their utility is limited by the lack of a clear physical interpretation and mathematical relationship to well-established models. In this work, we show that the two popular methods can be understood with regular perturbation theory and boundary layer theory in small ɛ, where a dilute solute travels from fluid to solid much faster than along the column. We consider conditions associated with a popular experimental technique used to characterize solute wave movement, where the column is initially at steady state and the fluid concentrations exiting, or breaking through, are time-monitored in response to a step change in inlet concentration. Our transformations and asymptotic analyses illustrate the time scales associated with popular techniques. We generalize their applicability to equilibria possessing inflection points while considering both adsorption and desorption modes. We use numerical simulations to estimate convergence orders of asymptotic approximations of breakthrough concentrations. For the leading-order approximation of regular perturbation theory, rarefaction waves possess positive convergence orders, depending on the extent of nonlinearity, while shock waves do not. Boundary-layer theory affords a more accurate approximation of the breakthrough curve than a shock wave, without guaranteeing a positive convergence order. This lack of positive convergence order is likely due to the evolution of the boundary layer, as illustrated with numerical simulations. An improved understanding of fast adsorption sets the stage for more realistic selection of high-performing materials and design configurations from thousands of available candidates.

Artificial synapse based on carbon quantum dots dispersed in indigo molecular layer for neuromorphic applications

Conventional computers are limited in their performance due to the physical separation of the memory and processing units. To overcome this, parallel computation using artificial synapses has been thought of as a possible replacement in computing architecture. The development of nanoelectronic devices that can show synaptic functionalities is very important. Here, we report the robust synaptic functionalities of carbon quantum dots embedded in two terminal indigo-based organic synapses. The carbon quantum dots (CQDs) are prepared using an easy-to-do process from commercial jaggery. The CQDs have a size range between 3.5 and 4.5 nm with excellent light emission in the green region. CQD+indigo-based devices show extremely stable memory characteristics, with ON and OFF states differing by more than 10 Mohm. Devices show excellent long-term potentiation and long-term depression characteristics, with both synaptic weight updates following a double exponential behavior. The extent of nonlinearity is explained using the nonlinearity factor. The linear increase in memory is established with repeated learning and forgetting (or potentiation and depression) curves. This study gives a robust way to make an artificial synapse work efficiently at room temperature with excellent memory and synaptic behavior.

Impact of HHP-treated starches on LAOS, tribology, and steady shear behavior of reduced-fat O/W emulsions

The present study aimed to scrutinize the influence of high hydrostatic pressure (HHP)-treated starches, including wheat starch (HPWS), corn starch (HPCS), and waxy corn starch (HPWCS) at different concentrations (10%, 15%, and 20%) as fat replacers on the large amplitude oscillatory shear (LAOS), tribological, and steady shear rheological characteristics of model O/W emulsions at three fat reduction (FR) levels (25%, 50%, and 75%). By increasing the FR level, greater nonlinearity, higher friction factor, and lower recovery percentage were observed for HPWS- and HPCS-contained samples, though HPWCS-contained samples showed lower nonlinearity. Using HHP-treated starches with higher concentration at each FR level, the extent of nonlinearity (regardless of elastic or viscous) and the quantities of friction factor decreased meaningfully and the values of strain stiffening and shear thickening factors increased. The values of G3′/G1′ of reduced-fat emulsions were significantly higher (24%–72%) than the magnitudes of G3"/G1" (except for the 75% reduced-fat samples).

On the relationship between inhibition and receptor occupancy by nondepolarizing neuromuscular blocking drugs

BackgroundNondepolarizing neuromuscular blocking drugs (NDNBs) are clinically used to produce muscle relaxation during general anesthesia. To better understand clinical properties of NDNBs, comparative in vitro pharmacologic studies have been performed. In these studies, a receptor binding model, which relies on the assumption that the inhibition, i.e., the effect of an NDNB, is proportional to the receptor occupancy by the drug, has been effectively used to describe obtained experimental data. However, it has not been studied in literature under which conditions the above assumption can be justified nor the assumption still holds in vivo. The purpose of this study is to explore the in vivo relationship between the inhibition and the receptor occupancy by an NDNB and to draw implications on how in vitro experimental results can be used to discuss the in vivo properties of NDNBs.MethodsAn ordinary differential equation model is employed to simulate physiologic processes of the activation of receptors by acetylcholine (ACh) as well as inhibition by an NDNB. With this model, the degree of inhibition is quantified by the fractional amount of receptors that are not activated by ACh due to the presence of an NDNB. The results are visualized by plotting the fractional amounts of the activated receptors as a function of the receptor occupancy.ResultsNumerical investigations reflecting in vivo conditions show that the degree of inhibition is not proportional to the receptor occupancy, i.e., there is a nonlinear relationship between the inhibition and the receptor occupancy. However, under a setting of high concentration of ACh reflecting a typical situation of in vitro experiments, the relationship between the inhibition and the receptor occupancy becomes linear, suggesting the validity of the receptor binding model. Also, it is found that the extent of nonlinearity depends on the selectivity of NDNBs for the two binding sites of the receptors.ConclusionsWhile the receptor binding model may be effective for estimating affinity of an NDNB through in vitro experiments, these models do not directly describe in vivo properties of NDNBs, because the nonlinearity between the inhibition and the receptor occupancy causes the modulation of the resultant concentration-effect relationships of NDNBs.

Effect of wheel polygonalization on the Degree of Non-linearity of dynamic response of high-speed vehicle system

Polygonalization of the wheel describes the growth of out-of-round profiles of the wheels of railway vehicle. This problem was identified in the 1980s but its mechanism is still not well understood. The wheel-rail disturbance formed by wheel polygonalization will accelerate the fatigue fracture of the key parts of rail vehicles and seriously threaten the safety of rail vehicle. This fact has led to significant efforts in detecting and diagnosing wheel polygonalization, in particular in setting the criteria for health monitoring. Currently, the time-domain feature parameters extraction method based on data statistics and frequency-domain feature parameters extraction method based on spectrum estimation are widely applied to detect wheel polygonalization. However, the basis of spectral estimation is the Fourier transform, which is not good at dealing with non-linear vibration systems (such as vehicle-track coupled system). Aiming at the wheel polygonalization problem existing in high-speed train, the non-linear extent of vibration response of vehicle system caused by wheel polygonalization is analyzed based on vehicle-track coupled dynamics and adaptive data analysis method. A typical high-speed train model is established according to the vehicle-track coupled dynamics theory. The wheel polygonalization model is introduced and vehicle system vibration response is calculated by numerical integration. The vibration response signal is decomposed by empirical mode decomposition (EMD) to produce the intrinsic mode functions (IMFs). By calculating the intra-wave frequency modulation of IMFs, that is, the difference between instantaneous and mean frequencies and amplitudes, the non-linearity of the dynamic response is quantified. Influences of wheel polygonalization on the non-linearity of steady-state and unsteady vibration responses of vehicle system are analyzed in detail. An objective criterion for wheel polygonalization health monitoring based on Degree of Non-linearity is proposed, which provides an effective tool for prognostics and health management of trains.

Designing the design of experiments (DOE) – An investigation on the influence of different factorial designs on the characterization of complex systems

Although a general set of guidelines and procedures for performing the design of experiments (DOE) exists, the literature lacks a recommended course of action for finding and selecting the optimal design of experiments among a large range of possible designs. This research tries to fill this gap by comprehensively testing more than thirty different DOEs through nearly half a million simulated experimental runs. The performance of various DOEs in the characterization of the thermal behaviour of a double skin façade (DSF) is assessed by comparing the outcomes of the different designs and using the full factorial design (FFD) as the ground truth. Besides the finding for the specific case study used in this investigation, this research allowed us to obtain some broad conclusions on the behaviour of different DOEs, which are summarized and translated into recommendations and a general decision tree chart for selecting the suitable DOE(s). The outcomes of this study help researchers and designers to apply DOEs that consider the extent of nonlinearity and interaction of factors in the investigated process in order to select the most successful and the most efficient designs for the specific process characterization.

Design of a lateral velocity observer based on synthesis of different sources

This paper is mainly devoted to estimating the lateral velocity of vehicle with an observer synthesis method using a cost-effective 6D inertial measurement unit. The four sources of observer to be synthesized come from the dynamics model, the kinematics model, and a LuGre tire model, respectively. The weight of each source is calculated by considering the nonlinear extent of each tire by means of the adaptation of tire cornering stiffness, which is adapted and updated using the dynamics model observer with the information obtained from the kinematics model observer. Then using the weighted sum of the four sources as the reference information for a modified kinematics observer, the final estimation can provide smooth and accurate results that are robust to sensor drifts and measurement noise, which is verified with several dSPACE based hardware-in-the-loop simulations.

Diagnosis of plant-wide oscillations by combining multivariate empirical mode decomposition and delay vector variance

A combination of multivariate empirical mode decomposition (MEMD) and the delay vector variance (DVV) method is explored for the diagnosis of plant-wide oscillations. The proposed algorithm improves upon the already presented method based solely on the DVV approach. The proposed modification makes it possible for the DVV method to work not only for the non-stationary data but also the case where multiple oscillations sources are present in the control loop. The focus of this work has been to distinguish between linear and non-linear causes of oscillations and isolating the source of non-linearity. A noise assisted multivariate empirical mode decomposition is used to sift out different oscillating components in the plant wide data and the nature of the oscillation is then ascertained using the already presented DVV approach. In the case of oscillations due to non-linear causes the method can isolate the source using the extent of non-linearity. The method is tested on simulated and industrial case studies and the results are compared with existing methods based on higher order statistics [8] and surrogate based methods [27].

Detecting and Measuring Nonlinearity

This paper proposes an approach to measure the extent of nonlinearity of the exposure of a financial asset to a given risk factor. The proposed measure exploits the decomposition of a conditional expectation into its linear and nonlinear components. We illustrate the method with the measurement of the degree of nonlinearity of a European style option with respect to the underlying asset. Next, we use the method to identify the empirical patterns of the return-risk trade-off on the SP500. The results are strongly supportive of a nonlinear relationship between expected return and expected volatility. The data seem to be driven by two regimes: one regime with a positive return-risk trade-off and one with a negative trade-off.

Effects of multivalent hexacyanoferrates and their ion pairs on water molecule dynamics measured with terahertz spectroscopy.

The valency of aqueous solutes plays a large role in determining the extent of ion-water dynamics, which can greatly influence the chemical and physical properties of solutions. In these experiments, broadband Fourier transform terahertz spectroscopy is used to probe perturbations to the low-frequency dynamics of water molecules by three different multivalent hexacyanoferrate salts. K3Fe(CN)6, K4Fe(CN)6 and Na4Fe(CN)6 were investigated as a function of concentration up to their solubility limits using spectral subtractions and fitting with damped harmonic lineshapes. Regions with subtle nonlinearities in amplitude with respect to solute concentration provide insight into ion-pairing events. The extent of nonlinearity suggests that ion pairs are major constituents in solution for all concentrations measured and is consistent with ion-pairing observed at millimolar concentrations by potentiometric and spectroscopic measurements. A lower estimate for the number of water molecules that are influenced by each ion is obtained from the damped harmonic fits. Values of 19, 28 and 25 water molecules with perturbed dynamics are obtained for KFe(CN)62-, KFe(CN)63- and NaFe(CN)63- ion pairs, respectively. These values represent dynamical perturbations into a second solvation shell and are consistent with the long-range structural effects observed in recent aqueous nanodrop spectroscopy experiments. Furthermore, the spectral absorptions for hexacyanoferrates are in agreement with a wide range of solutes studied previously using the developing methodology for interpreting terahertz spectra.

Enhanced Multi-Channel Adaptive Noise Control Compensating Nonlinear Distortions

In fields of controlling acoustical noises, the overall adaptive control system is nonlinear due to the loudspeaker, amplifiers, converters, and microphones, etc. and the performance of noise control is decreased by the extent of nonlinearities, so an adaptive control system compensating nonlinear distortions is needed. In this paper, a new multi-channel adaptive noise controller was proposed, which was combined with the adaptive compensator to effectively linearize nonlinear distortions in the overall adaptive control system. Through computer simulations, the proposed adaptive compensator could linearize the nonlinear distortions and the proposed noise controller had better capability of controlling the noises than the conventional LMS controller.

An Efficient Measure for Quantification of Nonlinearity in Chemical Engineering Processes Based on I/O Steady-State Loci

Nonlinearity is virtually ubiquitous in chemical engineering plants, and assessing the degree of nonlinearity involved in a process is of special interest for process control purposes. In this paper, we introduce a simple nonlinearity measure to quantify the extent of nonlinearity in a dynamic system based on its normalized steady-state input/output loci. Our nonlinearity measure obviates the limitations of previous metrics in terms of computational effort and correct identification of highly nonlinear relationships. The measure is satisfactorily applicable to various I/O relationships—from truly linear to sinusoidal, for instance. In order to illustrate the efficiency of the proposed measure, four numerical examples concerning a double-effect evaporator, a jacketed continuously stirred tank reactor (CSTR) with an irreversible reaction, a CSTR involving van de Vusse reactions, and the Henson–Seborg–Pottmann CSTR are presented.

Metal Atom Dynamics in Superbulky Metallocenes: A Comparison of (CpBIG)2Sn and (CpBIG)2Eu

Cp(BIG)2Sn (Cp(BIG) = (4-n-Bu-C6H4)5cyclopentadienyl), prepared by reaction of 2 equiv of Cp(BIG)Na with SnCl2, crystallized isomorphous to other known metallocenes with this ligand (Ca, Sr, Ba, Sm, Eu, Yb). Similarly, it shows perfect linearity, C-H···C(π) bonding between the Cp(BIG) rings and out-of-plane bending of the aryl substituents toward the metal. Whereas all other Cp(BIG)2M complexes show large disorder in the metal position, the Sn atom in Cp(BIG)2Sn is perfectly ordered. In contrast, (119)Sn and (151)Eu Mößbauer investigations on the corresponding Cp(BIG)2M metallocenes show that Sn(II) is more dynamic and loosely bound than Eu(II). The large displacement factors in the group 2 and especially in the lanthanide(II) metallocenes Cp(BIG)2M can be explained by static metal disorder in a plane parallel to the Cp(BIG) rings. Despite parallel Cp(BIG) rings, these metallocenes have a nonlinear Cpcenter-M-Cpcenter geometry. This is explained by an ionic model in which metal atoms are polarized by the negatively charged Cp rings. The extent of nonlinearity is in line with trends found in M(2+) ion polarizabilities. The range of known calculated dipole polarizabilities at the Douglas-Kroll CCSD(T) level was extended with values (atomic units) for Sn(2+) 15.35, Sm(2+)(4f(6) (7)F) 9.82, Eu(2+)(4f(7) (8)S) 8.99, and Yb(2+)(4f(14) (1)S) 6.55. This polarizability model cannot be applied to predominantly covalently bound Cp(BIG)2Sn, which shows a perfectly ordered structure. The bent geometry of Cp*2Sn should therefore not be explained by metal polarizability but is due to van der Waals Cp*···Cp* attraction and (to some extent) to a small p-character component in the Sn lone pair.

Prediction of Wave Attenuation across Multiple Joints with an Improved Elastic Nonlinear Model

The study on nonlinear displacement discontinuity model has been investigated in the researches of normal incident wave attenuation across rock joints. But the studies were limited only on the effects of joint with single type deformation behavior, without considering the influence of different extent in model nonlinearity. The improved elastic nonlinear normal deformational model can descript the extent of nonlinearity quantitatively. Based on this model, a displacement discontinuity model for normally incident wave propagation across multiple parallel joints was established in an elastic half-space. Using one-dimensional wave equation characteristics method, the time-domain numerical difference scheme of transmitted particle velocity was proposed, making computational programs to obtain semi-numerical solutions, and transmission coefficients. Parameter studies were conducted to get an insight into the effects of number of joints and the extent of nonlinearity, the incident wave maximum amplitude on transmission coefficients and transmission energy rate, waveform distortion and delay time.

Time distribution characteristics of cat-eye reflected light from moving optical target

By using the Collins diffraction formula and expanding the aperture function into a finite sum of complex Gaussian functions, an analytical formula of the time light intensity distribution for oblique Gaussian beams passing through a moving cat-eye optical lens and going back along the entrance way is deduced. By numerical computation, the variation laws of the time intensity distributions of the cat-eye reflected light with the viewing angle, imaging distance, aperture and instantaneous field of view are given. The results show that the relationship between the light intensity at the return place and the detection time is linear, and it is of inverse proportion only when the viewing angle is very large. For the staring imaging optical lens, the nonlinear extent of the time distribution curve becomes larger with the decrease of the viewing angle. For the instantaneous imaging optical lens, there is still some cat-eye reflected light when the detection system is out of the viewing field of the target lens.

SINGLE-PARTICLE AND PAIR DYNAMICAL PROPERTIES OF ACETONE–METHANOL MIXTURES CONTAINING CHARGED AND NEUTRAL SOLUTES: A MOLECULAR DYNAMICS STUDY

The dynamical properties of acetone–methanol mixtures containing either an ionic or a neutral hydrophobic solute are investigated by means of a series of molecular dynamics simulations. The primary goal has been to study how the solute and solvent dynamical properties change with variation of composition of the mixture ranging from pure acetone to pure methanol. The variations of structure and energetics of the mixture with composition are also calculated. The diffusion coefficients of both ionic and neutral solutes are found to show nonlinear variation with composition of the mixture, although the extent of nonlinearity in the diffusion of the neutral solute is much weaker. Calculations of appropriate solute-solvent distribution functions reveal the extent and nature of selective solvation of these solute species which play a role in determining the nonideal dynamical characteristics of these solutes. The free energies of solvation of the ionic solutes are also calculated and the results are discussed in the context of their dynamical behavior. The hydrogen bond statistics and dynamics of these mixtures are also calculated over their entire composition range. The energies and lifetimes of hydrogen bonds between an acetone and a methanol molecule or between two methanol molecules are found to increase with increase of acetone mole fraction of the mixture. Residence times of methanol molecules in solvation shells of acetone and methanol are also found to follow the same trend as relaxation times. However, these pair dynamical properties show essentially linear dependence on composition, thus behave almost ideally with respect to changes in composition of the mixture.

Precise determination of the pressure distortion coefficient of new controlled-clearance piston-cylinders based on the Heydemann–Welch model

A new controlled-clearance (CC) pressure balance has been developed with the aim of improving hydraulic pressure standards up to pressures of 1 GPa. The pressure balance is equipped with a weight-loading unit that can load/unload selected weights automatically and a CC piston-cylinder that is designed for the jacket pressure to be applied independently. In this paper, the effective area A(e) of two kinds of the CC piston-cylinders for pressures of 200 and 500 MPa was examined based on the Heydemann-Welch model. The two parameters in the model, the jacket pressure coefficient and the zero clearance jacket pressure, were precisely determined by the characterization experiments, after which the pressure dependence of A(e) and its uncertainty were estimated. The uncertainty due to the pressure dependence of A(e) for the 500 MPa CC piston-cylinder was less than 7.5x10(-8) MPa(-1). To confirm the consistency of the estimations, the results of the two CC piston-cylinders were compared through a free-deformation (FD) piston-cylinder; the two estimations were in agreement with each other. Moreover, it was shown that the extent of nonlinearity in the pressure dependence of A(e) of the FD piston-cylinder can be evaluated by calibration against the CC piston-cylinder.

Nonlinear pharmacokinetics of therapeutic proteins resulting from receptor mediated endocytosis

Receptor mediated endocytosis (RME) plays a major role in the disposition of therapeutic protein drugs in the body. It is suspected to be a major source of nonlinear pharmacokinetic behavior observed in clinical pharmacokinetic data. So far, mostly empirical or semi-mechanistic approaches have been used to represent RME. A thorough understanding of the impact of the properties of the drug and of the receptor system on the resulting nonlinear disposition is still missing, as is how to best represent RME in pharmacokinetic models. In this article, we present a detailed mechanistic model of RME that explicitly takes into account receptor binding and trafficking inside the cell and that is used to derive reduced models of RME which retain a mechanistic interpretation. We find that RME can be described by an extended Michaelis–Menten model that accounts for both the distribution and the elimination aspect of RME. If the amount of drug in the receptor system is negligible a standard Michaelis–Menten model is capable of describing the elimination by RME. Notably, a receptor system can efficiently eliminate drug from the extracellular space even if the total number of receptors is small. We find that drug elimination by RME can result in substantial nonlinear pharmacokinetics. The extent of nonlinearity is higher for drug/receptor systems with higher receptor availability at the membrane, or faster internalization and degradation of extracellular drug. Our approach is exemplified for the epidermal growth factor receptor system.Electronic supplementary materialThe online version of this article (doi:10.1007/s10928-009-9120-1) contains supplementary material, which is available to authorized users.

On-orbit calibration of HALOE detector linearity

The Halogen Occultation Experiment (HALOE) conducted satellite solar occultation measurements for 14 years ending on 21 November 2005. HALOE contained a calibration wheel, which included three neutral density filters that were used to examine response linearity through a combination of ground and on-orbit measurements. Although measurement uncertainties preclude a confident assessment of the true extent of nonlinearity, the on-orbit data lead to the conclusion that any existing response nonlinearity has changed by less than 2% over the mission lifetime. This conclusion eliminates a potentially significant uncertainty when using HALOE data for studies of long-term atmospheric trends.

A comparison of methods for the fitting of generalized additive models

There are several procedures for fitting generalized additive models, i.e. regression models for an exponential family response where the influence of each single covariates is assumed to have unknown, potentially non-linear shape. Simulated data are used to compare a smoothing parameter optimization approach for selection of smoothness and of covariates, a stepwise approach, a mixed model approach, and a procedure based on boosting techniques. In particular it is investigated how the performance of procedures is linked to amount of information, type of response, total number of covariates, number of influential covariates, and extent of non-linearity. Measures for comparison are prediction performance, identification of influential covariates, and smoothness of fitted functions. One result is that the mixed model approach returns sparse fits with frequently over-smoothed functions, while the functions are less smooth for the boosting approach and variable selection is less strict. The other approaches are in between with respect to these measures. The boosting procedure is seen to perform very well when little information is available and/or when a large number of covariates is to be investigated. It is somewhat surprising that in scenarios with low information the fitting of a linear model, even with stepwise variable selection, has not much advantage over the fitting of an additive model when the true underlying structure is linear. In cases with more information the prediction performance of all procedures is very similar. So, in difficult data situations the boosting approach can be recommended, in others the procedures can be chosen conditional on the aim of the analysis.