Multiplicative noise removal through fractional order tv-based model and fast numerical schemes for its approximation

NASA Astrophysics Data System (ADS)

Ullah, Asmat; Chen, Wen; Khan, Mushtaq Ahmad

2017-07-01

This paper introduces a fractional order total variation (FOTV) based model with three different weights in the fractional order derivative definition for multiplicative noise removal purpose. The fractional-order Euler Lagrange equation which is a highly non-linear partial differential equation (PDE) is obtained by the minimization of the energy functional for image restoration. Two numerical schemes namely an iterative scheme based on the dual theory and majorization- minimization algorithm (MMA) are used. To improve the restoration results, we opt for an adaptive parameter selection procedure for the proposed model by applying the trial and error method. We report numerical simulations which show the validity and state of the art performance of the fractional-order model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding methods. Numerical experiments also demonstrate that MMAbased methodology is slightly better than that of an iterative scheme.

Fractional-order leaky integrate-and-fire model with long-term memory and power law dynamics.

PubMed

Teka, Wondimu W; Upadhyay, Ranjit Kumar; Mondal, Argha

2017-09-01

Pyramidal neurons produce different spiking patterns to process information, communicate with each other and transform information. These spiking patterns have complex and multiple time scale dynamics that have been described with the fractional-order leaky integrate-and-Fire (FLIF) model. Models with fractional (non-integer) order differentiation that generalize power law dynamics can be used to describe complex temporal voltage dynamics. The main characteristic of FLIF model is that it depends on all past values of the voltage that causes long-term memory. The model produces spikes with high interspike interval variability and displays several spiking properties such as upward spike-frequency adaptation and long spike latency in response to a constant stimulus. We show that the subthreshold voltage and the firing rate of the fractional-order model make transitions from exponential to power law dynamics when the fractional order α decreases from 1 to smaller values. The firing rate displays different types of spike timing adaptation caused by changes on initial values. We also show that the voltage-memory trace and fractional coefficient are the causes of these different types of spiking properties. The voltage-memory trace that represents the long-term memory has a feedback regulatory mechanism and affects spiking activity. The results suggest that fractional-order models might be appropriate for understanding multiple time scale neuronal dynamics. Overall, a neuron with fractional dynamics displays history dependent activities that might be very useful and powerful for effective information processing. Copyright © 2017 Elsevier Ltd. All rights reserved.

Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory

NASA Astrophysics Data System (ADS)

Ansari, R.; Faraji Oskouie, M.; Gholami, R.

2016-01-01

In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.

Memory in a fractional-order cardiomyocyte model alters properties of alternans and spontaneous activity

NASA Astrophysics Data System (ADS)

Comlekoglu, T.; Weinberg, S. H.

2017-09-01

Cardiac memory is the dependence of electrical activity on the prior history of one or more system state variables, including transmembrane potential (Vm), ionic current gating, and ion concentrations. While prior work has represented memory either phenomenologically or with biophysical detail, in this study, we consider an intermediate approach of a minimal three-variable cardiomyocyte model, modified with fractional-order dynamics, i.e., a differential equation of order between 0 and 1, to account for history-dependence. Memory is represented via both capacitive memory, due to fractional-order Vm dynamics, that arises due to non-ideal behavior of membrane capacitance; and ionic current gating memory, due to fractional-order gating variable dynamics, that arises due to gating history-dependence. We perform simulations for varying Vm and gating variable fractional-orders and pacing cycle length and measure action potential duration (APD) and incidence of alternans, loss of capture, and spontaneous activity. In the absence of ionic current gating memory, we find that capacitive memory, i.e., decreased Vm fractional-order, typically shortens APD, suppresses alternans, and decreases the minimum cycle length (MCL) for loss of capture. However, in the presence of ionic current gating memory, capacitive memory can prolong APD, promote alternans, and increase MCL. Further, we find that reduced Vm fractional order (typically less than 0.75) can drive phase 4 depolarizations that promote spontaneous activity. Collectively, our results demonstrate that memory reproduced by a fractional-order model can play a role in alternans formation and pacemaking, and in general, can greatly increase the range of electrophysiological characteristics exhibited by a minimal model.

Atmospheric Turbulence Modeling for Aerospace Vehicles: Fractional Order Fit

NASA Technical Reports Server (NTRS)

Kopasakis, George (Inventor)

2015-01-01

An improved model for simulating atmospheric disturbances is disclosed. A scale Kolmogorov spectral may be scaled to convert the Kolmogorov spectral into a finite energy von Karman spectral and a fractional order pole-zero transfer function (TF) may be derived from the von Karman spectral. Fractional order atmospheric turbulence may be approximated with an integer order pole-zero TF fit, and the approximation may be stored in memory.

Forecasting the Amount of Waste-Sewage Water Discharged into the Yangtze River Basin Based on the Optimal Fractional Order Grey Model

PubMed Central

Li, Shuliang; Meng, Wei; Xie, Yufeng

2017-01-01

With the rapid development of the Yangtze River economic belt, the amount of waste-sewage water discharged into the Yangtze River basin increases sharply year by year, which has impeded the sustainable development of the Yangtze River basin. The water security along the Yangtze River basin is very important for China, It is something about water security of roughly one-third of China’s population and the sustainable development of the 19 provinces, municipalities and autonomous regions among the Yangtze River basin. Therefore, a scientific prediction of the amount of waste-sewage water discharged into Yangtze River basin has a positive significance on sustainable development of industry belt along with Yangtze River basin. This paper builds the fractional DWSGM (1,1) (DWSGM (1,1) model is short for Discharge amount of Waste Sewage Grey Model for one order equation and one variable) model based on the fractional accumulating generation operator and fractional reducing operator, and calculates the optimal order of “r” by using particle swarm optimization (PSO) algorithm for solving the minimum average relative simulation error. Meanwhile, the simulation performance of DWSGM (1,1) model with the optimal fractional order is tested by comparing the simulation results of grey prediction models with different orders. Finally, the optimal fractional order DWSGM (1,1) grey model is applied to predict the amount of waste-sewage water discharged into the Yangtze River basin, and corresponding countermeasures and suggestions are put forward through analyzing and comparing the prediction results. This paper has positive significance on enriching the fractional order modeling method of the grey system. PMID:29295517

Forecasting the Amount of Waste-Sewage Water Discharged into the Yangtze River Basin Based on the Optimal Fractional Order Grey Model.

PubMed

Li, Shuliang; Meng, Wei; Xie, Yufeng

2017-12-23

With the rapid development of the Yangtze River economic belt, the amount of waste-sewage water discharged into the Yangtze River basin increases sharply year by year, which has impeded the sustainable development of the Yangtze River basin. The water security along the Yangtze River basin is very important for China, It is something aboutwater security of roughly one-third of China's population and the sustainable development of the 19 provinces, municipalities and autonomous regions among the Yangtze River basin. Therefore, a scientific prediction of the amount of waste-sewage water discharged into Yangtze River basin has a positive significance on sustainable development of industry belt along with Yangtze River basin. This paper builds the fractional DWSGM(1,1)(DWSGM(1,1) model is short for Discharge amount of Waste Sewage Grey Model for one order equation and one variable) model based on the fractional accumulating generation operator and fractional reducing operator, and calculates the optimal order of "r" by using particle swarm optimization(PSO)algorithm for solving the minimum average relative simulation error. Meanwhile, the simulation performance of DWSGM(1,1)model with the optimal fractional order is tested by comparing the simulation results of grey prediction models with different orders. Finally, the optimal fractional order DWSGM(1,1)grey model is applied to predict the amount of waste-sewage water discharged into the Yangtze River basin, and corresponding countermeasures and suggestions are put forward through analyzing and comparing the prediction results. This paper has positive significance on enriching the fractional order modeling method of the grey system.

High-order fractional partial differential equation transform for molecular surface construction

PubMed Central

Hu, Langhua; Chen, Duan; Wei, Guo-Wei

2013-01-01

Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model indicate that the proposed high-order fractional PDEs are robust, stable and efficient for biomolecular surface generation. PMID:24364020

Fractional order creep model for dam concrete considering degree of hydration

NASA Astrophysics Data System (ADS)

Huang, Yaoying; Xiao, Lei; Bao, Tengfei; Liu, Yu

2018-05-01

Concrete is a material that is an intermediate between an ideal solid and an ideal fluid. The creep of concrete is related not only to the loading age and duration, but also to its temperature and temperature history. Fractional order calculus is a powerful tool for solving physical mechanics modeling problems. Using a software element based on the generalized Kelvin model, a fractional order creep model of concrete considering the loading age and duration is established. Then, the hydration rate of cement is considered in terms of the degree of hydration, and the fractional order creep model of concrete considering the degree of hydration is established. Moreover, uniaxial tensile creep tests of dam concrete under different curing temperatures were conducted, and the results were combined with the creep test data and complex optimization method to optimize the parameters of a new creep model. The results show that the fractional tensile creep model based on hydration degree can better describe the tensile creep properties of concrete, and this model involves fewer parameters than the 8-parameter model.

Mathematical analysis of a power-law form time dependent vector-borne disease transmission model.

PubMed

Sardar, Tridip; Saha, Bapi

2017-06-01

In the last few years, fractional order derivatives have been used in epidemiology to capture the memory phenomena. However, these models do not have proper biological justification in most of the cases and lack a derivation from a stochastic process. In this present manuscript, using theory of a stochastic process, we derived a general time dependent single strain vector borne disease model. It is shown that under certain choice of time dependent transmission kernel this model can be converted into the classical integer order system. When the time-dependent transmission follows a power law form, we showed that the model converted into a vector borne disease model with fractional order transmission. We explicitly derived the disease-free and endemic equilibrium of this new fractional order vector borne disease model. Using mathematical properties of nonlinear Volterra type integral equation it is shown that the unique disease-free state is globally asymptotically stable under certain condition. We define a threshold quantity which is epidemiologically known as the basic reproduction number (R 0 ). It is shown that if R 0 > 1, then the derived fractional order model has a unique endemic equilibrium. We analytically derived the condition for the local stability of the endemic equilibrium. To test the model capability to capture real epidemic, we calibrated our newly proposed model to weekly dengue incidence data of San Juan, Puerto Rico for the time period 30th April 1994 to 23rd April 1995. We estimated several parameters, including the order of the fractional derivative of the proposed model using aforesaid data. It is shown that our proposed fractional order model can nicely capture real epidemic. Copyright © 2017 Elsevier Inc. All rights reserved.

Numerical simulation of time fractional dual-phase-lag model of heat transfer within skin tissue during thermal therapy.

PubMed

Kumar, Dinesh; Rai, K N

2017-07-01

In this paper, we investigated the thermal behavior in living biological tissues using time fractional dual-phase-lag bioheat transfer (DPLBHT) model subjected to Dirichelt boundary condition in presence of metabolic and electromagnetic heat sources during thermal therapy. We solved this bioheat transfer model using finite element Legendre wavelet Galerkin method (FELWGM) with help of block pulse function in sense of Caputo fractional order derivative. We compared the obtained results from FELWGM and exact method in a specific case, and found a high accuracy. Results are interpreted in the form of standard and anomalous cases for taking different order of time fractional DPLBHT model. The time to achieve hyperthermia position is discussed in both cases as standard and time fractional order derivative. The success of thermal therapy in the treatment of metastatic cancerous cell depends on time fractional order derivative to precise prediction and control of temperature. The effect of variability of parameters such as time fractional derivative, lagging times, blood perfusion coefficient, metabolic heat source and transmitted power on dimensionless temperature distribution in skin tissue is discussed in detail. The physiological parameters has been estimated, corresponding to the value of fractional order derivative for hyperthermia treatment therapy. Copyright © 2017 Elsevier Ltd. All rights reserved.

Fractional dynamics pharmacokinetics–pharmacodynamic models

PubMed Central

2010-01-01

While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokinetics–pharmacodynamic (PKPD) literature. One of the reasons is computational: while the analytical solution of fractional differential equations is available in special cases, it this turns out that even the simplest PKPD models that can be constructed using fractional calculus do not allow an analytical solution. In this paper, we first introduce new families of PKPD models incorporating fractional order integrals and differential equations, and, second, exemplify and investigate their qualitative behavior. The families represent extensions of frequently used PK link and PD direct and indirect action models, using the tools of fractional calculus. In addition the PD models can be a function of a variable, the active drug, which can smoothly transition from concentration to exposure, to hyper-exposure, according to a fractional integral transformation. To investigate the behavior of the models we propose, we implement numerical algorithms for fractional integration and for the numerical solution of a system of fractional differential equations. For simplicity, in our investigation we concentrate on the pharmacodynamic side of the models, assuming standard (integer order) pharmacokinetics. PMID:20455076

A continued fraction resummation form of bath relaxation effect in the spin-boson model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gong, Zhihao; Tang, Zhoufei; Wu, Jianlan, E-mail: jianlanwu@zju.edu.cn

2015-02-28

In the spin-boson model, a continued fraction form is proposed to systematically resum high-order quantum kinetic expansion (QKE) rate kernels, accounting for the bath relaxation effect beyond the second-order perturbation. In particular, the analytical expression of the sixth-order QKE rate kernel is derived for resummation. With higher-order correction terms systematically extracted from higher-order rate kernels, the resummed quantum kinetic expansion approach in the continued fraction form extends the Pade approximation and can fully recover the exact quantum dynamics as the expansion order increases.

Optimal Campaign Strategies in Fractional-Order Smoking Dynamics

NASA Astrophysics Data System (ADS)

Zeb, Anwar; Zaman, Gul; Jung, Il Hyo; Khan, Madad

2014-06-01

This paper deals with the optimal control problem in the giving up smoking model of fractional order. For the eradication of smoking in a community, we introduce three control variables in the form of education campaign, anti-smoking gum, and anti-nicotive drugs/medicine in the proposed fractional order model. We discuss the necessary conditions for the optimality of a general fractional optimal control problem whose fractional derivative is described in the Caputo sense. In order to do this, we minimize the number of potential and occasional smokers and maximize the number of ex-smokers. We use Pontryagin's maximum principle to characterize the optimal levels of the three controls. The resulting optimality system is solved numerically by MATLAB.

Complexity and Hopf Bifurcation Analysis on a Kind of Fractional-Order IS-LM Macroeconomic System

NASA Astrophysics Data System (ADS)

Ma, Junhai; Ren, Wenbo

On the basis of our previous research, we deepen and complete a kind of macroeconomics IS-LM model with fractional-order calculus theory, which is a good reflection on the memory characteristics of economic variables, we also focus on the influence of the variables on the real system, and improve the analysis capabilities of the traditional economic models to suit the actual macroeconomic environment. The conditions of Hopf bifurcation in fractional-order system models are briefly demonstrated, and the fractional order when Hopf bifurcation occurs is calculated, showing the inherent complex dynamic characteristics of the system. With numerical simulation, bifurcation, strange attractor, limit cycle, waveform and other complex dynamic characteristics are given; and the order condition is obtained with respect to time. We find that the system order has an important influence on the running state of the system. The system has a periodic motion when the order meets the conditions of Hopf bifurcation; the fractional-order system gradually stabilizes with the change of the order and parameters while the corresponding integer-order system diverges. This study has certain significance to policy-making about macroeconomic regulation and control.

Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization

NASA Astrophysics Data System (ADS)

Pang, Guofei; Perdikaris, Paris; Cai, Wei; Karniadakis, George Em

2017-11-01

The fractional advection-dispersion equation (FADE) can describe accurately the solute transport in groundwater but its fractional order has to be determined a priori. Here, we employ multi-fidelity Bayesian optimization to obtain the fractional order under various conditions, and we obtain more accurate results compared to previously published data. Moreover, the present method is very efficient as we use different levels of resolution to construct a stochastic surrogate model and quantify its uncertainty. We consider two different problem set ups. In the first set up, we obtain variable fractional orders of one-dimensional FADE, considering both synthetic and field data. In the second set up, we identify constant fractional orders of two-dimensional FADE using synthetic data. We employ multi-resolution simulations using two-level and three-level Gaussian process regression models to construct the surrogates.

Derivative with two fractional orders: A new avenue of investigation toward revolution in fractional calculus

NASA Astrophysics Data System (ADS)

Atangana, Abdon

2016-10-01

In order to describe more complex problems using the concept of fractional derivatives, we introduce in this paper the concept of fractional derivatives with orders. The new definitions are based upon the concept of power law together with the generalized Mittag-Leffler function. The first order is included in the power law function and the second one is in the generalized Mittag-Leffler function. Each order therefore plays an important role while modeling, for instance, problems with two layers with different properties. This is the case, for instance, in thermal science for a reaction diffusion within a media with two different layers with different properties. Another case is that of groundwater flowing within an aquifer where geological formation is formed with two layers with different properties. The paper presents new fractional operators that will open new doors for research and investigations in modeling real world problems. Some useful properties of the new operators are presented, in particular their relationship with existing integral transforms, namely the Laplace, Sumudu, Mellin and Fourier transforms. The numerical approximation of the new fractional operators are presented. We apply the new fractional operators on the model of groundwater plume with degradation and limited sorption and solve the new model numerically with some numerical simulations. The numerical simulation leaves no doubt in believing that the new fractional operators are powerfull mathematical tools able to portray complexes real world problems.

Fractional discrete-time consensus models for single- and double-summator dynamics

NASA Astrophysics Data System (ADS)

Wyrwas, Małgorzata; Mozyrska, Dorota; Girejko, Ewa

2018-04-01

The leader-following consensus problem of fractional-order multi-agent discrete-time systems is considered. In the systems, interactions between opinions are defined like in Krause and Cucker-Smale models but the memory is included by taking the fractional-order discrete-time operator on the left-hand side of the nonlinear systems. In this paper, we investigate fractional-order models of opinions for the single- and double-summator dynamics of discrete-time by analytical methods as well as by computer simulations. The necessary and sufficient conditions for the leader-following consensus are formulated by proposing a consensus control law for tracking the virtual leader.

A numerical solution for a variable-order reaction-diffusion model by using fractional derivatives with non-local and non-singular kernel

NASA Astrophysics Data System (ADS)

Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.

2018-02-01

A reaction-diffusion system can be represented by the Gray-Scott model. The reaction-diffusion dynamic is described by a pair of time and space dependent Partial Differential Equations (PDEs). In this paper, a generalization of the Gray-Scott model by using variable-order fractional differential equations is proposed. The variable-orders were set as smooth functions bounded in (0 , 1 ] and, specifically, the Liouville-Caputo and the Atangana-Baleanu-Caputo fractional derivatives were used to express the time differentiation. In order to find a numerical solution of the proposed model, the finite difference method together with the Adams method were applied. The simulations results showed the chaotic behavior of the proposed model when different variable-orders are applied.

Measuring memory with the order of fractional derivative

NASA Astrophysics Data System (ADS)

Du, Maolin; Wang, Zaihua; Hu, Haiyan

2013-12-01

Fractional derivative has a history as long as that of classical calculus, but it is much less popular than it should be. What is the physical meaning of fractional derivative? This is still an open problem. In modeling various memory phenomena, we observe that a memory process usually consists of two stages. One is short with permanent retention, and the other is governed by a simple model of fractional derivative. With the numerical least square method, we show that the fractional model perfectly fits the test data of memory phenomena in different disciplines, not only in mechanics, but also in biology and psychology. Based on this model, we find that a physical meaning of the fractional order is an index of memory.

A physics-based fractional order model and state of energy estimation for lithium ion batteries. Part I: Model development and observability analysis

NASA Astrophysics Data System (ADS)

Li, Xiaoyu; Fan, Guodong; Pan, Ke; Wei, Guo; Zhu, Chunbo; Rizzoni, Giorgio; Canova, Marcello

2017-11-01

The design of a lumped parameter battery model preserving physical meaning is especially desired by the automotive researchers and engineers due to the strong demand for battery system control, estimation, diagnosis and prognostics. In light of this, a novel simplified fractional order electrochemical model is developed for electric vehicle (EV) applications in this paper. In the model, a general fractional order transfer function is designed for the solid phase lithium ion diffusion approximation. The dynamic characteristics of the electrolyte concentration overpotential are approximated by a first-order resistance-capacitor transfer function in the electrolyte phase. The Ohmic resistances and electrochemical reaction kinetics resistance are simplified to a lumped Ohmic resistance parameter. Overall, the number of model parameters is reduced from 30 to 9, yet the accuracy of the model is still guaranteed. In order to address the dynamics of phase-change phenomenon in the active particle during charging and discharging, variable solid-state diffusivity is taken into consideration in the model. Also, the observability of the model is analyzed on two types of lithium ion batteries subsequently. Results show the fractional order model with variable solid-state diffusivity agrees very well with experimental data at various current input conditions and is suitable for electric vehicle applications.

Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics

NASA Astrophysics Data System (ADS)

Xu, Kaixuan; Wang, Jun

2017-02-01

In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model.

Fractional Order Modeling of Atmospheric Turbulence - A More Accurate Modeling Methodology for Aero Vehicles

NASA Technical Reports Server (NTRS)

Kopasakis, George

2014-01-01

The presentation covers a recently developed methodology to model atmospheric turbulence as disturbances for aero vehicle gust loads and for controls development like flutter and inlet shock position. The approach models atmospheric turbulence in their natural fractional order form, which provides for more accuracy compared to traditional methods like the Dryden model, especially for high speed vehicle. The presentation provides a historical background on atmospheric turbulence modeling and the approaches utilized for air vehicles. This is followed by the motivation and the methodology utilized to develop the atmospheric turbulence fractional order modeling approach. Some examples covering the application of this method are also provided, followed by concluding remarks.

Fractional two-compartmental model for articaine serum levels

NASA Astrophysics Data System (ADS)

Petronijevic, Branislava; Sarcev, Ivan; Zorica, Dusan; Janev, Marko; Atanackovic, Teodor M.

2016-06-01

Two fractional two-compartmental models are applied to the pharmacokinetics of articaine. Integer order derivatives are replaced by fractional derivatives, either of different, or of same orders. Models are formulated so that the mass balance is preserved. Explicit forms of the solutions are obtained in terms of the Mittag-Leffler functions. Pharmacokinetic parameters are determined by the use of the evolutionary algorithm and trust regions optimization to recover the experimental data.

Ultra wideband (0.5-16 kHz) MR elastography for robust shear viscoelasticity model identification.

PubMed

Liu, Yifei; Yasar, Temel K; Royston, Thomas J

2014-12-21

Changes in the viscoelastic parameters of soft biological tissues often correlate with progression of disease, trauma or injury, and response to treatment. Identifying the most appropriate viscoelastic model, then estimating and monitoring the corresponding parameters of that model can improve insight into the underlying tissue structural changes. MR Elastography (MRE) provides a quantitative method of measuring tissue viscoelasticity. In a previous study by the authors (Yasar et al 2013 Magn. Reson. Med. 70 479-89), a silicone-based phantom material was examined over the frequency range of 200 Hz-7.75 kHz using MRE, an unprecedented bandwidth at that time. Six viscoelastic models including four integer order models and two fractional order models, were fit to the wideband viscoelastic data (measured storage and loss moduli as a function of frequency). The 'fractional Voigt' model (spring and springpot in parallel) exhibited the best fit and was even able to fit the entire frequency band well when it was identified based only on a small portion of the band. This paper is an extension of that study with a wider frequency range from 500 Hz to 16 kHz. Furthermore, more fractional order viscoelastic models are added to the comparison pool. It is found that added complexity of the viscoelastic model provides only marginal improvement over the 'fractional Voigt' model. And, again, the fractional order models show significant improvement over integer order viscoelastic models that have as many or more fitting parameters.

A predictive universal fractional-order differential model of wall-turbulence

NASA Astrophysics Data System (ADS)

Song, Fangying; Karniadakis, George

2017-11-01

Fractional calculus has been around for centuries but its use in computational since and engineering has emerged only recently. Here we develop a relatively simple one-dimensional model for fully-developed wall-turbulence that involves a fractional operator with variable fractional order. We use available DNS data bases to ``learn'' the function that describes the fractional order, which has a high value at the wall and decays monotonically to an asymptotic value at the centerline. We show that this function is universal upon re-scaling and hence it can be used to predict the mean velocity profile at all Reynolds numbers. We demonstrate the accuracy of our universal fractional model for channel flow at high Reynolds number as well as for pipe flow and we obtain good agreement with the Princeton super-pipe data up to Reynolds numbers 35,000,000. This work was supported by an ARO MURI Number: W911NF-15-1-0562.

Tomographic imaging of non-local media based on space-fractional diffusion models

NASA Astrophysics Data System (ADS)

Buonocore, Salvatore; Semperlotti, Fabio

2018-06-01

We investigate a generalized tomographic imaging framework applicable to a class of inhomogeneous media characterized by non-local diffusive energy transport. Under these conditions, the transport mechanism is well described by fractional-order continuum models capable of capturing anomalous diffusion that would otherwise remain undetected when using traditional integer-order models. Although the underlying idea of the proposed framework is applicable to any transport mechanism, the case of fractional heat conduction is presented as a specific example to illustrate the methodology. By using numerical simulations, we show how complex inhomogeneous media involving non-local transport can be successfully imaged if fractional order models are used. In particular, results will show that by properly recognizing and accounting for the fractional character of the host medium not only allows achieving increased resolution but, in case of strong and spatially distributed non-locality, it represents the only viable approach to achieve a successful reconstruction.

A fractional model with parallel fractional Maxwell elements for amorphous thermoplastics

NASA Astrophysics Data System (ADS)

Lei, Dong; Liang, Yingjie; Xiao, Rui

2018-01-01

We develop a fractional model to describe the thermomechanical behavior of amorphous thermoplastics. The fractional model is composed of two parallel fractional Maxwell elements. The first fractional Maxwell model is used to describe the glass transition, while the second component is aimed at describing the viscous flow. We further derive the analytical solutions for the stress relaxation modulus and complex modulus through Laplace transform. We then demonstrate the model is able to describe the master curves of the stress relaxation modulus, storage modulus and loss modulus, which all show two distinct transition regions. The obtained parameters show that the modulus of the two fractional Maxwell elements differs in 2-3 orders of magnitude, while the relaxation time differs in 7-9 orders of magnitude. Finally, we apply the model to describe the stress response of constant strain rate tests. The model, together with the parameters obtained from fitting the master curve of stress relaxation modulus, can accurately predict the temperature and strain rate dependent stress response.

A non-local model of fractional heat conduction in rigid bodies

NASA Astrophysics Data System (ADS)

Borino, G.; di Paola, M.; Zingales, M.

2011-03-01

In recent years several applications of fractional differential calculus have been proposed in physics, chemistry as well as in engineering fields. Fractional order integrals and derivatives extend the well-known definitions of integer-order primitives and derivatives of the ordinary differential calculus to real-order operators. Engineering applications of fractional operators spread from viscoelastic models, stochastic dynamics as well as with thermoelasticity. In this latter field one of the main actractives of fractional operators is their capability to interpolate between the heat flux and its time-rate of change, that is related to the well-known second sound effect. In other recent studies a fractional, non-local thermoelastic model has been proposed as a particular case of the non-local, integral, thermoelasticity introduced at the mid of the seventies. In this study the autors aim to introduce a different non-local model of extended irreverible thermodynamics to account for second sound effect. Long-range heat flux is defined and it involves the integral part of the spatial Marchaud fractional derivatives of the temperature field whereas the second-sound effect is accounted for introducing time-derivative of the heat flux in the transport equation. It is shown that the proposed model does not suffer of the pathological problems of non-homogenoeus boundary conditions. Moreover the proposed model coalesces with the Povstenko fractional models in unbounded domains.

A new approach to the compartmental analysis in pharmacokinetics: fractional time evolution of diclofenac.

PubMed

Popović, Jovan K; Atanacković, Milica T; Pilipović, Ana S; Rapaić, Milan R; Pilipović, Stevan; Atanacković, Teodor M

2010-04-01

This study presents a new two compartmental model and its application to the evaluation of diclofenac pharmacokinetics in a small number of healthy adults, during a bioequivalence trial. In the model the integer order derivatives are replaced by derivatives of real order often called fractional order derivatives. Physically that means that a history (memory) of a biological process, realized as a transfer from one compartment to another one with the mass balance conservation, is taken into account. This kind of investigations in pharmacokinetics is founded by Dokoumetzidis and Macheras through the one compartmental models while our contribution is the analysis of multi-dimensional compartmental models with the applications of the two compartmental model in evaluation of diclofenac pharmacokinetics. Two experiments were preformed with 12 healthy volunteers with two slow release 100 mg diclofenac tablet formulations. The agreement of the values predicted by the proposed model with the values obtained through experiments is shown to be good. Thus, pharmacokinetics of slow release diclofenac can be described well by a specific two compartmental model with fractional derivatives of the same order. Parameters in the model are determined by the least-squares method and the Particle Swarm Optimization (PSO) numerical procedure is used. The results show that the fractional order two compartmental model for diclofenac is superior in comparison to the classical two compartmental model. Actually this is true in general case since the classical one is a special case of the fractional one.

Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.

2018-03-01

In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.

Epidemic outbreaks and its control using a fractional order model with seasonality and stochastic infection

NASA Astrophysics Data System (ADS)

He, Shaobo; Banerjee, Santo

2018-07-01

A fractional-order SIR epidemic model is proposed under the influence of both parametric seasonality and the external noise. The integer order SIR epidemic model originally is stable. By introducing seasonality and noise force to the model, behaviors of the system is changed. It is shown that the system has rich dynamical behaviors with different system parameters, fractional derivative order and the degree of seasonality and noise. Complexity of the stochastic model is investigated by using multi-scale fuzzy entropy. Finally, hard limiter controlled system is designed and simulation results show the ratio of infected individuals can converge to a small enough target ρ, which means the epidemic outbreak can be under control by the implementation of some effective medical and health measures.

Heterogeneous fractionation profiles of meta-analytic coactivation networks.

PubMed

Laird, Angela R; Riedel, Michael C; Okoe, Mershack; Jianu, Radu; Ray, Kimberly L; Eickhoff, Simon B; Smith, Stephen M; Fox, Peter T; Sutherland, Matthew T

2017-04-01

Computational cognitive neuroimaging approaches can be leveraged to characterize the hierarchical organization of distributed, functionally specialized networks in the human brain. To this end, we performed large-scale mining across the BrainMap database of coordinate-based activation locations from over 10,000 task-based experiments. Meta-analytic coactivation networks were identified by jointly applying independent component analysis (ICA) and meta-analytic connectivity modeling (MACM) across a wide range of model orders (i.e., d=20-300). We then iteratively computed pairwise correlation coefficients for consecutive model orders to compare spatial network topologies, ultimately yielding fractionation profiles delineating how "parent" functional brain systems decompose into constituent "child" sub-networks. Fractionation profiles differed dramatically across canonical networks: some exhibited complex and extensive fractionation into a large number of sub-networks across the full range of model orders, whereas others exhibited little to no decomposition as model order increased. Hierarchical clustering was applied to evaluate this heterogeneity, yielding three distinct groups of network fractionation profiles: high, moderate, and low fractionation. BrainMap-based functional decoding of resultant coactivation networks revealed a multi-domain association regardless of fractionation complexity. Rather than emphasize a cognitive-motor-perceptual gradient, these outcomes suggest the importance of inter-lobar connectivity in functional brain organization. We conclude that high fractionation networks are complex and comprised of many constituent sub-networks reflecting long-range, inter-lobar connectivity, particularly in fronto-parietal regions. In contrast, low fractionation networks may reflect persistent and stable networks that are more internally coherent and exhibit reduced inter-lobar communication. Copyright © 2017 Elsevier Inc. All rights reserved.

Heterogeneous fractionation profiles of meta-analytic coactivation networks

PubMed Central

Laird, Angela R.; Riedel, Michael C.; Okoe, Mershack; Jianu, Radu; Ray, Kimberly L.; Eickhoff, Simon B.; Smith, Stephen M.; Fox, Peter T.; Sutherland, Matthew T.

2017-01-01

Computational cognitive neuroimaging approaches can be leveraged to characterize the hierarchical organization of distributed, functionally specialized networks in the human brain. To this end, we performed large-scale mining across the BrainMap database of coordinate-based activation locations from over 10,000 task-based experiments. Meta-analytic coactivation networks were identified by jointly applying independent component analysis (ICA) and meta-analytic connectivity modeling (MACM) across a wide range of model orders (i.e., d = 20 to 300). We then iteratively computed pairwise correlation coefficients for consecutive model orders to compare spatial network topologies, ultimately yielding fractionation profiles delineating how “parent” functional brain systems decompose into constituent “child” sub-networks. Fractionation profiles differed dramatically across canonical networks: some exhibited complex and extensive fractionation into a large number of sub-networks across the full range of model orders, whereas others exhibited little to no decomposition as model order increased. Hierarchical clustering was applied to evaluate this heterogeneity, yielding three distinct groups of network fractionation profiles: high, moderate, and low fractionation. BrainMap-based functional decoding of resultant coactivation networks revealed a multi-domain association regardless of fractionation complexity. Rather than emphasize a cognitive-motor-perceptual gradient, these outcomes suggest the importance of inter-lobar connectivity in functional brain organization. We conclude that high fractionation networks are complex and comprised of many constituent sub-networks reflecting long-range, inter-lobar connectivity, particularly in fronto-parietal regions. In contrast, low fractionation networks may reflect persistent and stable networks that are more internally coherent and exhibit reduced inter-lobar communication. PMID:28222386

Dynamical models of happiness with fractional order

NASA Astrophysics Data System (ADS)

Song, Lei; Xu, Shiyun; Yang, Jianying

2010-03-01

This present study focuses on a dynamical model of happiness described through fractional-order differential equations. By categorizing people of different personality and different impact factor of memory (IFM) with different set of model parameters, it is demonstrated via numerical simulations that such fractional-order models could exhibit various behaviors with and without external circumstance. Moreover, control and synchronization problems of this model are discussed, which correspond to the control of emotion as well as emotion synchronization in real life. This study is an endeavor to combine the psychological knowledge with control problems and system theories, and some implications for psychotherapy as well as hints of a personal approach to life are both proposed.

Modeling and analysis of fractional order DC-DC converter.

PubMed

Radwan, Ahmed G; Emira, Ahmed A; AbdelAty, Amr M; Azar, Ahmad Taher

2017-07-11

Due to the non-idealities of commercial inductors, the demand for a better model that accurately describe their dynamic response is elevated. So, the fractional order models of Buck, Boost and Buck-Boost DC-DC converters are presented in this paper. The detailed analysis is made for the two most common modes of converter operation: Continuous Conduction Mode (CCM) and Discontinuous Conduction Mode (DCM). Closed form time domain expressions are derived for inductor currents, voltage gain, average current, conduction time and power efficiency where the effect of the fractional order inductor is found to be strongly present. For example, the peak inductor current at steady state increases with decreasing the inductor order. Advanced Design Systems (ADS) circuit simulations are used to verify the derived formulas, where the fractional order inductor is simulated using Valsa Constant Phase Element (CPE) approximation and Generalized Impedance Converter (GIC). Different simulation results are introduced with good matching to the theoretical formulas for the three DC-DC converter topologies under different fractional orders. A comprehensive comparison with the recently published literature is presented to show the advantages and disadvantages of each approach. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Robust control for fractional variable-order chaotic systems with non-singular kernel

NASA Astrophysics Data System (ADS)

Zuñiga-Aguilar, C. J.; Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Romero-Ugalde, H. M.

2018-01-01

This paper investigates the chaos control for a class of variable-order fractional chaotic systems using robust control strategy. The variable-order fractional models of the non-autonomous biological system, the King Cobra chaotic system, the Halvorsen's attractor and the Burke-Shaw system, have been derived using the fractional-order derivative with Mittag-Leffler in the Liouville-Caputo sense. The fractional differential equations and the control law were solved using the Adams-Bashforth-Moulton algorithm. To test the control stability efficiency, different statistical indicators were introduced. Finally, simulation results demonstrate the effectiveness of the proposed robust control.

Distributed containment control of heterogeneous fractional-order multi-agent systems with communication delays

NASA Astrophysics Data System (ADS)

Yang, Hongyong; Han, Fujun; Zhao, Mei; Zhang, Shuning; Yue, Jun

2017-08-01

Because many networked systems can only be characterized with fractional-order dynamics in complex environments, fractional-order calculus has been studied deeply recently. When diverse individual features are shown in different agents of networked systems, heterogeneous fractional-order dynamics will be used to describe the complex systems. Based on the distinguishing properties of agents, heterogeneous fractional-order multi-agent systems (FOMAS) are presented. With the supposition of multiple leader agents in FOMAS, distributed containment control of FOMAS is studied in directed weighted topologies. By applying Laplace transformation and frequency domain theory of the fractional-order operator, an upper bound of delays is obtained to ensure containment consensus of delayed heterogenous FOMAS. Consensus results of delayed FOMAS in this paper can be extended to systems with integer-order models. Finally, numerical examples are used to verify our results.

Anomalous NMR Relaxation in Cartilage Matrix Components and Native Cartilage: Fractional-Order Models

PubMed Central

Magin, Richard L.; Li, Weiguo; Velasco, M. Pilar; Trujillo, Juan; Reiter, David A.; Morgenstern, Ashley; Spencer, Richard G.

2011-01-01

We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena (T1 and T2). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T1 and T2 relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T2 relaxation of BNC can be described in a unique way by a single fractional-order parameter (α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T1 was observed in BNC. In the single-component gels, for T2 measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for microstructural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T2 NMR relaxation processes in biological tissues. PMID:21498095

Anomalous NMR relaxation in cartilage matrix components and native cartilage: Fractional-order models

NASA Astrophysics Data System (ADS)

Magin, Richard L.; Li, Weiguo; Pilar Velasco, M.; Trujillo, Juan; Reiter, David A.; Morgenstern, Ashley; Spencer, Richard G.

2011-06-01

We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena ( T1 and T2). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T1 and T2 relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T2 relaxation of BNC can be described in a unique way by a single fractional-order parameter ( α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T1 was observed in BNC. In the single-component gels, for T2 measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for micro-structural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T2 NMR relaxation processes in biological tissues.

Anomalous diffusion with linear reaction dynamics: from continuous time random walks to fractional reaction-diffusion equations.

PubMed

Henry, B I; Langlands, T A M; Wearne, S L

2006-09-01

We have revisited the problem of anomalously diffusing species, modeled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics. If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps then the long time asymptotic limit has a standard linear reaction kinetics term but a fractional order temporal derivative operating on a nonstandard diffusion term. Results from the above two models are compared with a phenomenological model with standard linear reaction kinetics and a fractional order temporal derivative operating on a standard diffusion term. We have also developed further extensions of the CTRW model to include more general reaction dynamics.

The use of fractional order derivatives for eddy current non-destructive testing

NASA Astrophysics Data System (ADS)

Sikora, Ryszard; Grzywacz, Bogdan; Chady, Tomasz

2018-04-01

The paper presents the possibility of using the fractional derivatives for non-destructive testing when a multi-frequency method based on eddy current is applied. It is shown that frequency characteristics obtained during tests can be approximated by characteristics of a proposed model in the form of fractional order transfer function, and values of parameters of this model can be utilized for detection and identification of defects.

Study on Fuzzy Adaptive Fractional Order PIλDμ Control for Maglev Guiding System

NASA Astrophysics Data System (ADS)

Hu, Qing; Hu, Yuwei

The mathematical model of the linear elevator maglev guiding system is analyzed in this paper. For the linear elevator needs strong stability and robustness to run, the integer order PID was expanded to the fractional order, in order to improve the steady state precision, rapidity and robustness of the system, enhance the accuracy of the parameter in fractional order PIλDμ controller, the fuzzy control is combined with the fractional order PIλDμ control, using the fuzzy logic achieves the parameters online adjustment. The simulations reveal that the system has faster response speed, higher tracking precision, and has stronger robustness to the disturbance.

Mittag-Leffler synchronization of fractional neural networks with time-varying delays and reaction-diffusion terms using impulsive and linear controllers.

PubMed

Stamova, Ivanka; Stamov, Gani

2017-12-01

In this paper, we propose a fractional-order neural network system with time-varying delays and reaction-diffusion terms. We first develop a new Mittag-Leffler synchronization strategy for the controlled nodes via impulsive controllers. Using the fractional Lyapunov method sufficient conditions are given. We also study the global Mittag-Leffler synchronization of two identical fractional impulsive reaction-diffusion neural networks using linear controllers, which was an open problem even for integer-order models. Since the Mittag-Leffler stability notion is a generalization of the exponential stability concept for fractional-order systems, our results extend and improve the exponential impulsive control theory of neural network system with time-varying delays and reaction-diffusion terms to the fractional-order case. The fractional-order derivatives allow us to model the long-term memory in the neural networks, and thus the present research provides with a conceptually straightforward mathematical representation of rather complex processes. Illustrative examples are presented to show the validity of the obtained results. We show that by means of appropriate impulsive controllers we can realize the stability goal and to control the qualitative behavior of the states. An image encryption scheme is extended using fractional derivatives. Copyright © 2017 Elsevier Ltd. All rights reserved.

Modeling and character analyzing of current-controlled memristors with fractional kinetic transport

NASA Astrophysics Data System (ADS)

Si, Gangquan; Diao, Lijie; Zhu, Jianwei; Lei, Yuhang; Babajide, Oresanya; Zhang, Yanbin

2017-07-01

Memristors have come into limelight again after it was realized by HP researchers. This paper proposes a memristor model which can be called fractional-order current-controlled memristor, and it is more general and comprehensive. We introduce the fractional integral/differential to the current-controlled memristor model and model memristor with fractional kinetic of charge transport. An interesting phenomena found out is that the I-V characteristic is a triple-loop curve (0 < α < 1) and not the conventional double-loop I-V curve (α=1). Memristance (RM) is analyzed versus the fractional order α and time(t), and it reach saturation faster when 0 < α < 1. The saturation (Rmin → Rmax) time is given and analyzed versus different orders α and frequencies ω, which increase with α increasing and ω decreasing. More importantly, the memristors can't reach the Rmax in some cases. Energy loss of the model is analyzed, and the I-P curves isn't origin-symmetric when 0 < α < 1 which is very different with curves when α = 1 .

Analysis of Drude model using fractional derivatives without singular kernels

NASA Astrophysics Data System (ADS)

Jiménez, Leonardo Martínez; García, J. Juan Rosales; Contreras, Abraham Ortega; Baleanu, Dumitru

2017-11-01

We report study exploring the fractional Drude model in the time domain, using fractional derivatives without singular kernels, Caputo-Fabrizio (CF), and fractional derivatives with a stretched Mittag-Leffler function. It is shown that the velocity and current density of electrons moving through a metal depend on both the time and the fractional order 0 < γ ≤ 1. Due to non-singular fractional kernels, it is possible to consider complete memory effects in the model, which appear neither in the ordinary model, nor in the fractional Drude model with Caputo fractional derivative. A comparison is also made between these two representations of the fractional derivatives, resulting a considered difference when γ < 0.8.

Atmospheric Turbulence Modeling for Aero Vehicles: Fractional Order Fits

NASA Technical Reports Server (NTRS)

Kopasakis, George

2015-01-01

Atmospheric turbulence models are necessary for the design of both inlet/engine and flight controls, as well as for studying coupling between the propulsion and the vehicle structural dynamics for supersonic vehicles. Models based on the Kolmogorov spectrum have been previously utilized to model atmospheric turbulence. In this paper, a more accurate model is developed in its representative fractional order form, typical of atmospheric disturbances. This is accomplished by first scaling the Kolmogorov spectral to convert them into finite energy von Karman forms and then by deriving an explicit fractional circuit-filter type analog for this model. This circuit model is utilized to develop a generalized formulation in frequency domain to approximate the fractional order with the products of first order transfer functions, which enables accurate time domain simulations. The objective of this work is as follows. Given the parameters describing the conditions of atmospheric disturbances, and utilizing the derived formulations, directly compute the transfer function poles and zeros describing these disturbances for acoustic velocity, temperature, pressure, and density. Time domain simulations of representative atmospheric turbulence can then be developed by utilizing these computed transfer functions together with the disturbance frequencies of interest.

Atmospheric Turbulence Modeling for Aero Vehicles: Fractional Order Fits

NASA Technical Reports Server (NTRS)

Kopasakis, George

2010-01-01

Atmospheric turbulence models are necessary for the design of both inlet/engine and flight controls, as well as for studying coupling between the propulsion and the vehicle structural dynamics for supersonic vehicles. Models based on the Kolmogorov spectrum have been previously utilized to model atmospheric turbulence. In this paper, a more accurate model is developed in its representative fractional order form, typical of atmospheric disturbances. This is accomplished by first scaling the Kolmogorov spectral to convert them into finite energy von Karman forms and then by deriving an explicit fractional circuit-filter type analog for this model. This circuit model is utilized to develop a generalized formulation in frequency domain to approximate the fractional order with the products of first order transfer functions, which enables accurate time domain simulations. The objective of this work is as follows. Given the parameters describing the conditions of atmospheric disturbances, and utilizing the derived formulations, directly compute the transfer function poles and zeros describing these disturbances for acoustic velocity, temperature, pressure, and density. Time domain simulations of representative atmospheric turbulence can then be developed by utilizing these computed transfer functions together with the disturbance frequencies of interest.

Disturbance observer-based adaptive sliding mode hybrid projective synchronisation of identical fractional-order financial systems

NASA Astrophysics Data System (ADS)

Khan, Ayub; Tyagi, Arti

2018-05-01

In this paper, we have studied the hybrid projective synchronisation for incommensurate, integer and commensurate fractional-order financial systems with unknown disturbance. To tackle the problem of unknown bounded disturbance, fractional-order disturbance observer is designed to approximate the unknown disturbance. Further, we have introduced simple sliding mode surface and designed adaptive sliding mode controllers incorporating with the designed fractional-order disturbance observer to achieve a bounded hybrid projective synchronisation between two identical fractional-order financial model with different initial conditions. It is shown that the slave system with disturbance can be synchronised with the projection of the master system generated through state transformation. Simulation results are presented to ensure the validity and effectiveness of the proposed sliding mode control scheme in the presence of external bounded unknown disturbance. Also, synchronisation error for commensurate, integer and incommensurate fractional-order financial systems is studied in numerical simulation.

Fractional domain varying-order differential denoising method

NASA Astrophysics Data System (ADS)

Zhang, Yan-Shan; Zhang, Feng; Li, Bing-Zhao; Tao, Ran

2014-10-01

Removal of noise is an important step in the image restoration process, and it remains a challenging problem in image processing. Denoising is a process used to remove the noise from the corrupted image, while retaining the edges and other detailed features as much as possible. Recently, denoising in the fractional domain is a hot research topic. The fractional-order anisotropic diffusion method can bring a less blocky effect and preserve edges in image denoising, a method that has received much interest in the literature. Based on this method, we propose a new method for image denoising, in which fractional-varying-order differential, rather than constant-order differential, is used. The theoretical analysis and experimental results show that compared with the state-of-the-art fractional-order anisotropic diffusion method, the proposed fractional-varying-order differential denoising model can preserve structure and texture well, while quickly removing noise, and yields good visual effects and better peak signal-to-noise ratio.

Design of distributed PID-type dynamic matrix controller for fractional-order systems

NASA Astrophysics Data System (ADS)

Wang, Dawei; Zhang, Ridong

2018-01-01

With the continuous requirements for product quality and safety operation in industrial production, it is difficult to describe the complex large-scale processes with integer-order differential equations. However, the fractional differential equations may precisely represent the intrinsic characteristics of such systems. In this paper, a distributed PID-type dynamic matrix control method based on fractional-order systems is proposed. First, the high-order approximate model of integer order is obtained by utilising the Oustaloup method. Then, the step response model vectors of the plant is obtained on the basis of the high-order model, and the online optimisation for multivariable processes is transformed into the optimisation of each small-scale subsystem that is regarded as a sub-plant controlled in the distributed framework. Furthermore, the PID operator is introduced into the performance index of each subsystem and the fractional-order PID-type dynamic matrix controller is designed based on Nash optimisation strategy. The information exchange among the subsystems is realised through the distributed control structure so as to complete the optimisation task of the whole large-scale system. Finally, the control performance of the designed controller in this paper is verified by an example.

Modeling vehicle operating speed on urban roads in Montreal: a panel mixed ordered probit fractional split model.

PubMed

Eluru, Naveen; Chakour, Vincent; Chamberlain, Morgan; Miranda-Moreno, Luis F

2013-10-01

Vehicle operating speed measured on roadways is a critical component for a host of analysis in the transportation field including transportation safety, traffic flow modeling, roadway geometric design, vehicle emissions modeling, and road user route decisions. The current research effort contributes to the literature on examining vehicle speed on urban roads methodologically and substantively. In terms of methodology, we formulate a new econometric model framework for examining speed profiles. The proposed model is an ordered response formulation of a fractional split model. The ordered nature of the speed variable allows us to propose an ordered variant of the fractional split model in the literature. The proposed formulation allows us to model the proportion of vehicles traveling in each speed interval for the entire segment of roadway. We extend the model to allow the influence of exogenous variables to vary across the population. Further, we develop a panel mixed version of the fractional split model to account for the influence of site-specific unobserved effects. The paper contributes substantively by estimating the proposed model using a unique dataset from Montreal consisting of weekly speed data (collected in hourly intervals) for about 50 local roads and 70 arterial roads. We estimate separate models for local roads and arterial roads. The model estimation exercise considers a whole host of variables including geometric design attributes, roadway attributes, traffic characteristics and environmental factors. The model results highlight the role of various street characteristics including number of lanes, presence of parking, presence of sidewalks, vertical grade, and bicycle route on vehicle speed proportions. The results also highlight the presence of site-specific unobserved effects influencing the speed distribution. The parameters from the modeling exercise are validated using a hold-out sample not considered for model estimation. The results indicate that the proposed panel mixed ordered probit fractional split model offers promise for modeling such proportional ordinal variables. Copyright © 2013 Elsevier Ltd. All rights reserved.

Finite element formulation of viscoelastic sandwich beams using fractional derivative operators

NASA Astrophysics Data System (ADS)

Galucio, A. C.; Deü, J.-F.; Ohayon, R.

This paper presents a finite element formulation for transient dynamic analysis of sandwich beams with embedded viscoelastic material using fractional derivative constitutive equations. The sandwich configuration is composed of a viscoelastic core (based on Timoshenko theory) sandwiched between elastic faces (based on Euler-Bernoulli assumptions). The viscoelastic model used to describe the behavior of the core is a four-parameter fractional derivative model. Concerning the parameter identification, a strategy to estimate the fractional order of the time derivative and the relaxation time is outlined. Curve-fitting aspects are focused, showing a good agreement with experimental data. In order to implement the viscoelastic model into the finite element formulation, the Grünwald definition of the fractional operator is employed. To solve the equation of motion, a direct time integration method based on the implicit Newmark scheme is used. One of the particularities of the proposed algorithm lies in the storage of displacement history only, reducing considerably the numerical efforts related to the non-locality of fractional operators. After validations, numerical applications are presented in order to analyze truncation effects (fading memory phenomena) and solution convergence aspects.

Modeling and Analysis of a Fractional-Order Generalized Memristor-Based Chaotic System and Circuit Implementation

NASA Astrophysics Data System (ADS)

Yang, Ningning; Xu, Cheng; Wu, Chaojun; Jia, Rong; Liu, Chongxin

2017-12-01

Memristor is a nonlinear “missing circuit element”, that can easily achieve chaotic oscillation. Memristor-based chaotic systems have received more and more attention. Research shows that fractional-order systems are more close to real systems. As an important parameter, the order can increase the flexibility and degree of freedom of the system. In this paper, a fractional-order generalized memristor, which consists of a diode bridge and a parallel circuit with an equivalent unit circuit and a linear resistance, is proposed. Frequency and electrical characteristics of the fractional-order memristor are analyzed. A chain structure circuit is used to implement the fractional-order unit circuit. Then replacing the conventional Chua’s diode by the fractional-order generalized memristor, a fractional-order memristor-based chaotic circuit is proposed. A large amount of research work has been done to investigate the influence of the order on the dynamical behaviors of the fractional-order memristor-based chaotic circuit. Varying with the order, the system enters the chaotic state from the periodic state through the Hopf bifurcation and period-doubling bifurcation. The chaotic state of the system has two types of attractors: single-scroll and double-scroll attractor. The stability theory of fractional-order systems is used to determine the minimum order occurring Hopf bifurcation. And the influence of the initial value on the system is analyzed. Circuit simulations are designed to verify the results of theoretical analysis and numerical simulation.

Model-based estimates of long-term persistence of induced HPV antibodies: a flexible subject-specific approach.

PubMed

Aregay, Mehreteab; Shkedy, Ziv; Molenberghs, Geert; David, Marie-Pierre; Tibaldi, Fabián

2013-01-01

In infectious diseases, it is important to predict the long-term persistence of vaccine-induced antibodies and to estimate the time points where the individual titers are below the threshold value for protection. This article focuses on HPV-16/18, and uses a so-called fractional-polynomial model to this effect, derived in a data-driven fashion. Initially, model selection was done from among the second- and first-order fractional polynomials on the one hand and from the linear mixed model on the other. According to a functional selection procedure, the first-order fractional polynomial was selected. Apart from the fractional polynomial model, we also fitted a power-law model, which is a special case of the fractional polynomial model. Both models were compared using Akaike's information criterion. Over the observation period, the fractional polynomials fitted the data better than the power-law model; this, of course, does not imply that it fits best over the long run, and hence, caution ought to be used when prediction is of interest. Therefore, we point out that the persistence of the anti-HPV responses induced by these vaccines can only be ascertained empirically by long-term follow-up analysis.

Finite-Strain Fractional-Order Viscoelastic (FOV) Material Models and Numerical Methods for Solving Them

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Diethelm, Kai; Gray, Hugh R. (Technical Monitor)

2002-01-01

Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.

Robust Takagi-Sugeno fuzzy control for fractional order hydro-turbine governing system.

PubMed

Wang, Bin; Xue, Jianyi; Wu, Fengjiao; Zhu, Delan

2016-11-01

A robust fuzzy control method for fractional order hydro-turbine governing system (FOHGS) in the presence of random disturbances is investigated in this paper. Firstly, the mathematical model of FOHGS is introduced, and based on Takagi-Sugeno (T-S) fuzzy rules, the generalized T-S fuzzy model of FOHGS is presented. Secondly, based on fractional order Lyapunov stability theory, a novel T-S fuzzy control method is designed for the stability control of FOHGS. Thirdly, the relatively loose sufficient stability condition is acquired, which could be transformed into a group of linear matrix inequalities (LMIs) via Schur complement as well as the strict mathematical derivation is given. Furthermore, the control method could resist random disturbances, which shows the good robustness. Simulation results indicate the designed fractional order T-S fuzzy control scheme works well compared with the existing method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Fractional Order Spatiotemporal Chaos with Delay in Spatial Nonlinear Coupling

NASA Astrophysics Data System (ADS)

Zhang, Yingqian; Wang, Xingyuan; Liu, Liyan; Liu, Jia

We investigate the spatiotemporal dynamics with fractional order differential logistic map with delay under nonlinear chaotic maps for spatial coupling connections. Here, the coupling methods between lattices are the nonlinear chaotic map coupling of lattices. The fractional order differential logistic map with delay breaks the limits of the range of parameter μ ∈ [3.75, 4] in the classical logistic map for chaotic states. The Kolmogorov-Sinai entropy density and universality, and bifurcation diagrams are employed to investigate the chaotic behaviors of the proposed model in this paper. The proposed model can also be applied for cryptography, which is verified in a color image encryption scheme in this paper.

Fractional-order TV-L2 model for image denoising

NASA Astrophysics Data System (ADS)

Chen, Dali; Sun, Shenshen; Zhang, Congrong; Chen, YangQuan; Xue, Dingyu

2013-10-01

This paper proposes a new fractional order total variation (TV) denoising method, which provides a much more elegant and effective way of treating problems of the algorithm implementation, ill-posed inverse, regularization parameter selection and blocky effect. Two fractional order TV-L2 models are constructed for image denoising. The majorization-minimization (MM) algorithm is used to decompose these two complex fractional TV optimization problems into a set of linear optimization problems which can be solved by the conjugate gradient algorithm. The final adaptive numerical procedure is given. Finally, we report experimental results which show that the proposed methodology avoids the blocky effect and achieves state-of-the-art performance. In addition, two medical image processing experiments are presented to demonstrate the validity of the proposed methodology.

A Novel Fractional Order Model for the Dynamic Hysteresis of Piezoelectrically Actuated Fast Tool Servo

PubMed Central

Zhu, Zhiwei; Zhou, Xiaoqin

2012-01-01

The main contribution of this paper is the development of a linearized model for describing the dynamic hysteresis behaviors of piezoelectrically actuated fast tool servo (FTS). A linearized hysteresis force model is proposed and mathematically described by a fractional order differential equation. Combining the dynamic modeling of the FTS mechanism, a linearized fractional order dynamic hysteresis (LFDH) model for the piezoelectrically actuated FTS is established. The unique features of the LFDH model could be summarized as follows: (a) It could well describe the rate-dependent hysteresis due to its intrinsic characteristics of frequency-dependent nonlinear phase shifts and amplitude modulations; (b) The linearization scheme of the LFDH model would make it easier to implement the inverse dynamic control on piezoelectrically actuated micro-systems. To verify the effectiveness of the proposed model, a series of experiments are conducted. The toolpaths of the FTS for creating two typical micro-functional surfaces involving various harmonic components with different frequencies and amplitudes are scaled and employed as command signals for the piezoelectric actuator. The modeling errors in the steady state are less than ±2.5% within the full span range which is much smaller than certain state-of-the-art modeling methods, demonstrating the efficiency and superiority of the proposed model for modeling dynamic hysteresis effects. Moreover, it indicates that the piezoelectrically actuated micro systems would be more suitably described as a fractional order dynamic system.

Desert soil clay content estimation using reflectance spectroscopy preprocessed by fractional derivative

PubMed Central

Tiyip, Tashpolat; Ding, Jianli; Zhang, Dong; Liu, Wei; Wang, Fei; Tashpolat, Nigara

2017-01-01

Effective pretreatment of spectral reflectance is vital to model accuracy in soil parameter estimation. However, the classic integer derivative has some disadvantages, including spectral information loss and the introduction of high-frequency noise. In this paper, the fractional order derivative algorithm was applied to the pretreatment and partial least squares regression (PLSR) was used to assess the clay content of desert soils. Overall, 103 soil samples were collected from the Ebinur Lake basin in the Xinjiang Uighur Autonomous Region of China, and used as data sets for calibration and validation. Following laboratory measurements of spectral reflectance and clay content, the raw spectral reflectance and absorbance data were treated using the fractional derivative order from the 0.0 to the 2.0 order (order interval: 0.2). The ratio of performance to deviation (RPD), determinant coefficients of calibration (Rc2), root mean square errors of calibration (RMSEC), determinant coefficients of prediction (Rp2), and root mean square errors of prediction (RMSEP) were applied to assess the performance of predicting models. The results showed that models built on the fractional derivative order performed better than when using the classic integer derivative. Comparison of the predictive effects of 22 models for estimating clay content, calibrated by PLSR, showed that those models based on the fractional derivative 1.8 order of spectral reflectance (Rc2 = 0.907, RMSEC = 0.425%, Rp2 = 0.916, RMSEP = 0.364%, and RPD = 2.484 ≥ 2.000) and absorbance (Rc2 = 0.888, RMSEC = 0.446%, Rp2 = 0.918, RMSEP = 0.383% and RPD = 2.511 ≥ 2.000) were most effective. Furthermore, they performed well in quantitative estimations of the clay content of soils in the study area. PMID:28934274

Fractional diffusion: recovering the distributed fractional derivative from overposed data

NASA Astrophysics Data System (ADS)

Rundell, W.; Zhang, Z.

2017-03-01

There has been considerable recent study in ‘subdiffusion’ models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one such is to realize that the order of the fractional derivative is related to the time scales of the underlying diffusion process. This raises the question of what order α of derivative should be taken and if a single value actually suffices. This has led to models that combine a finite number of these derivatives each with a different fractional exponent {αk} and different weighting value c k to better model a greater possible range of time scales. Ultimately, one wants to look at a situation that combines derivatives in a continuous way—the so-called distributional model with parameter μ ≤ft(α \\right) . However all of this begs the question of how one determines this ‘order’ of differentiation. Recovering a single fractional value has been an active part of the process from the beginning of fractional diffusion modeling and if this is the only unknown then the markers left by the fractional order derivative are relatively straightforward to determine. In the case of a finite combination of derivatives this becomes much more complex due to the more limited analytic tools available for such equations, but recent progress in this direction has been made, (Li et al 2015 Appl. Math. Comput. 257 381-97, Li and Yamamoto 2015 Appl. Anal. 94 570-9). This paper considers the full distributional model where the order is viewed as a function μ ≤ft(α \\right) on the interval (0, 1]. We show existence, uniqueness and regularity for an initial-boundary value problem including an important representation theorem in the case of a single spatial variable. This is then used in the inverse problem of recovering the distributional coefficient μ ≤ft(α \\right) from a time trace of the solution and a uniqueness result is proven.

Modelling of Piezothermoelastic Beam with Fractional Order Derivative

NASA Astrophysics Data System (ADS)

Kumar, Rajneesh; Sharma, Poonam

2016-04-01

This paper deals with the study of transverse vibrations in piezothermoelastic beam resonators with fractional order derivative. The fractional order theory of thermoelasticity developed by Sherief et al. [1] has been used to study the problem. The expressions for frequency shift and damping factor are derived for a thermo micro-electromechanical (MEM) and thermo nano-electromechanical (NEM) beam resonators clamped on one side and free on another. The effect of fractional order derivative on the derived expressions is observed analytically and shown graphically in the case of Lead Zirconate Titanate (PZT)-5A material. For α = 1, our results agree with those that are obtained by Grover and Sharma [20] and other particular cases of interest are also discussed.

An analytical study of physical models with inherited temporal and spatial memory

NASA Astrophysics Data System (ADS)

Jaradat, Imad; Alquran, Marwan; Al-Khaled, Kamel

2018-04-01

Du et al. (Sci. Reb. 3, 3431 (2013)) demonstrated that the fractional derivative order can be physically interpreted as a memory index by fitting the test data of memory phenomena. The aim of this work is to study analytically the joint effect of the memory index on time and space coordinates simultaneously. For this purpose, we introduce a novel bivariate fractional power series expansion that is accompanied by twofold fractional derivatives ordering α, β\\in(0,1]. Further, some convergence criteria concerning our expansion are presented and an analog of the well-known bivariate Taylor's formula in the sense of mixed fractional derivatives is obtained. Finally, in order to show the functionality and efficiency of this expansion, we employ the corresponding Taylor's series method to obtain closed-form solutions of various physical models with inherited time and space memory.

Coefficient of restitution in fractional viscoelastic compliant impacts using fractional Chebyshev collocation

NASA Astrophysics Data System (ADS)

Dabiri, Arman; Butcher, Eric A.; Nazari, Morad

2017-02-01

Compliant impacts can be modeled using linear viscoelastic constitutive models. While such impact models for realistic viscoelastic materials using integer order derivatives of force and displacement usually require a large number of parameters, compliant impact models obtained using fractional calculus, however, can be advantageous since such models use fewer parameters and successfully capture the hereditary property. In this paper, we introduce the fractional Chebyshev collocation (FCC) method as an approximation tool for numerical simulation of several linear fractional viscoelastic compliant impact models in which the overall coefficient of restitution for the impact is studied as a function of the fractional model parameters for the first time. Other relevant impact characteristics such as hysteresis curves, impact force gradient, penetration and separation depths are also studied.

A generic model for a single strain mosquito-transmitted disease with memory on the host and the vector.

PubMed

Sardar, Tridip; Rana, Sourav; Bhattacharya, Sabyasachi; Al-Khaled, Kamel; Chattopadhyay, Joydev

2015-05-01

In the present investigation, three mathematical models on a common single strain mosquito-transmitted diseases are considered. The first one is based on ordinary differential equations, and other two models are based on fractional order differential equations. The proposed models are validated using published monthly dengue incidence data from two provinces of Venezuela during the period 1999-2002. We estimate several parameters of these models like the order of the fractional derivatives (in case of two fractional order systems), the biting rate of mosquito, two probabilities of infection, mosquito recruitment and mortality rates, etc., from the data. The basic reproduction number, R0, for the ODE system is estimated using the data. For two fractional order systems, an upper bound for, R0, is derived and its value is obtained using the published data. The force of infection, and the effective reproduction number, R(t), for the three models are estimated using the data. Sensitivity analysis of the mosquito memory parameter with some important responses is worked out. We use Akaike Information Criterion (AIC) to identify the best model among the three proposed models. It is observed that the model with memory in both the host, and the vector population provides a better agreement with epidemic data. Finally, we provide a control strategy for the vector-borne disease, dengue, using the memory of the host, and the vector. Copyright © 2015 Elsevier Inc. All rights reserved.

Fractional viscoelasticity of soft elastomers and auxetic foams

NASA Astrophysics Data System (ADS)

Solheim, Hannah; Stanisauskis, Eugenia; Miles, Paul; Oates, William

2018-03-01

Dielectric elastomers are commonly implemented in adaptive structures due to their unique capabilities for real time control of a structure's shape, stiffness, and damping. These active polymers are often used in applications where actuator control or dynamic tunability are important, making an accurate understanding of the viscoelastic behavior critical. This challenge is complicated as these elastomers often operate over a broad range of deformation rates. Whereas research has demonstrated success in applying a nonlinear viscoelastic constitutive model to characterize the behavior of Very High Bond (VHB) 4910, robust predictions of the viscoelastic response over the entire range of time scales is still a significant challenge. An alternative formulation for viscoelastic modeling using fractional order calculus has shown significant improvement in predictive capabilities. While fractional calculus has been explored theoretically in the field of linear viscoelasticity, limited experimental validation and statistical evaluation of the underlying phenomena have been considered. In the present study, predictions across several orders of magnitude in deformation rates are validated against data using a single set of model parameters. Moreover, we illustrate the fractional order is material dependent by running complementary experiments and parameter estimation on the elastomer VHB 4949 as well as an auxetic foam. All results are statistically validated using Bayesian uncertainty methods to obtain posterior densities for the fractional order as well as the hyperelastic parameters.

On the origins of generalized fractional calculus

NASA Astrophysics Data System (ADS)

Kiryakova, Virginia

2015-11-01

In Fractional Calculus (FC), as in the (classical) Calculus, the notions of derivatives and integrals (of first, second, etc. or arbitrary, incl. non-integer order) are basic and co-related. One of the most frequent approach in FC is to define first the Riemann-Liouville (R-L) integral of fractional order, and then by means of suitable integer-order differentiation operation applied over it (or under its sign) a fractional derivative is defined - in the R-L sense (or in Caputo sense). The first mentioned (R-L type) is closer to the theoretical studies in analysis, but has some shortages - from the point of view of interpretation of the initial conditions for Cauchy problems for fractional differential equations (stated also by means of fractional order derivatives/ integrals), and also for the analysts' confusion that such a derivative of a constant is not zero in general. The Caputo (C-) derivative, arising first in geophysical studies, helps to overcome these problems and to describe models of applied problems with physically consistent initial conditions. The operators of the Generalized Fractional Calculus - GFC (integrals and derivatives) are based on commuting m-tuple (m = 1, 2, 3, …) compositions of operators of the classical FC with power weights (the so-called Erdélyi-Kober operators), but represented in compact and explicit form by means of integral, integro-differential (R-L type) or differential-integral (C-type) operators, where the kernels are special functions of most general hypergeometric kind. The foundations of this theory are given in Kiryakova 18. In this survey we present the genesis of the definitions of the GFC - the generalized fractional integrals and derivatives (of fractional multi-order) of R-L type and Caputo type, analyze their properties and applications. Their special cases are all the known operators of classical FC, their generalizations introduced by other authors, the hyper-Bessel differential operators of higher integer order m as a multi-order (1, 1,…, 1), the Gelfond-Leontiev generalized differentiation operators, many other integral and differential operators in Calculus that have been used in various topics, some of them not related to FC at all, others involved in differential and integral equations for treating fractional order models.

Random-order fractional bistable system and its stochastic resonance

NASA Astrophysics Data System (ADS)

Gao, Shilong; Zhang, Li; Liu, Hui; Kan, Bixia

2017-01-01

In this paper, the diffusion motion of Brownian particles in a viscous liquid suffering from stochastic fluctuations of the external environment is modeled as a random-order fractional bistable equation, and as a typical nonlinear dynamic behavior, the stochastic resonance phenomena in this system are investigated. At first, the derivation process of the random-order fractional bistable system is given. In particular, the random-power-law memory is deeply discussed to obtain the physical interpretation of the random-order fractional derivative. Secondly, the stochastic resonance evoked by random-order and external periodic force is mainly studied by numerical simulation. In particular, the frequency shifting phenomena of the periodical output are observed in SR induced by the excitation of the random order. Finally, the stochastic resonance of the system under the double stochastic excitations of the random order and the internal color noise is also investigated.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations. PMID:26064639

Fractional Modeling of the AC Large-Signal Frequency Response in Magnetoresistive Current Sensors

PubMed Central

Arias, Sergio Iván Ravello; Muñoz, Diego Ramírez; Moreno, Jaime Sánchez; Cardoso, Susana; Ferreira, Ricardo; de Freitas, Paulo Jorge Peixeiro

2013-01-01

Fractional calculus is considered when derivatives and integrals of non-integer order are applied over a specific function. In the electrical and electronic domain, the transfer function dependence of a fractional filter not only by the filter order n, but additionally, of the fractional order α is an example of a great number of systems where its input-output behavior could be more exactly modeled by a fractional behavior. Following this aim, the present work shows the experimental ac large-signal frequency response of a family of electrical current sensors based in different spintronic conduction mechanisms. Using an ac characterization set-up the sensor transimpedance function Zt(if) is obtained considering it as the relationship between sensor output voltage and input sensing current, Zt(jf)=Vo,sensor(jf)/Isensor(jf). The study has been extended to various magnetoresistance sensors based in different technologies like anisotropic magnetoresistance (AMR), giant magnetoresistance (GMR), spin-valve (GMR-SV) and tunnel magnetoresistance (TMR). The resulting modeling shows two predominant behaviors, the low-pass and the inverse low-pass with fractional index different from the classical integer response. The TMR technology with internal magnetization offers the best dynamic and sensitivity properties opening the way to develop actual industrial applications. PMID:24351648

Bounded diffusion impedance characterization of battery electrodes using fractional modeling

NASA Astrophysics Data System (ADS)

Gabano, Jean-Denis; Poinot, Thierry; Huard, Benoît

2017-06-01

This article deals with the ability of fractional modeling to describe the bounded diffusion behavior encountered in modern thin film and nanoparticles lithium battery electrodes. Indeed, the diffusion impedance of such batteries behaves as a half order integrator characterized by the Warburg impedance at high frequencies and becomes a classical integrator described by a capacitor at low frequencies. The transition between these two behaviors depends on the particles geometry. Three of them will be considered in this paper: planar, cylindrical and spherical ones. The fractional representation proposed is a gray box model able to perfectly fit the low and high frequency diffusive impedance behaviors while optimizing the frequency response transition. Identification results are provided using frequential simulation data considering the three electrochemical diffusion models based on the particles geometry. Furthermore, knowing this geometry allows to estimate the diffusion ionic resistance and time constant using the relationships linking these physical parameters to the structural fractional model parameters. Finally, other simulations using Randles impedance models including the charge transfer impedance and the external resistance demonstrate the interest of fractional modeling in order to identify properly not only the charge transfer impedance but also the diffusion physical parameters whatever the particles geometry.

Fractional-order gradient descent learning of BP neural networks with Caputo derivative.

PubMed

Wang, Jian; Wen, Yanqing; Gou, Yida; Ye, Zhenyun; Chen, Hua

2017-05-01

Fractional calculus has been found to be a promising area of research for information processing and modeling of some physical systems. In this paper, we propose a fractional gradient descent method for the backpropagation (BP) training of neural networks. In particular, the Caputo derivative is employed to evaluate the fractional-order gradient of the error defined as the traditional quadratic energy function. The monotonicity and weak (strong) convergence of the proposed approach are proved in detail. Two simulations have been implemented to illustrate the performance of presented fractional-order BP algorithm on three small datasets and one large dataset. The numerical simulations effectively verify the theoretical observations of this paper as well. Copyright © 2017 Elsevier Ltd. All rights reserved.

A Fractional PDE Approach to Turbulent Mixing; Part II: Numerical Simulation

NASA Astrophysics Data System (ADS)

Samiee, Mehdi; Zayernouri, Mohsen

2016-11-01

We propose a generalizing fractional order transport model of advection-diffusion kind with fractional time- and space-derivatives, governing the evolution of passive scalar turbulence. This approach allows one to incorporate the nonlocal and memory effects in the underlying anomalous diffusion i.e., sub-to-standard diffusion to model the trapping of particles inside the eddied, and super-diffusion associated with the sudden jumps of particles from one coherent region to another. For this nonlocal model, we develop a high order numerical (spectral) method in addition to a fast solver, examined in the context of some canonical problems. PhD student, Department of Mechanical Engineering, & Department Computational Mathematics, Science, and Engineering.

An explicit dissipation-preserving method for Riesz space-fractional nonlinear wave equations in multiple dimensions

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

2018-06-01

In this work, we investigate numerically a model governed by a multidimensional nonlinear wave equation with damping and fractional diffusion. The governing partial differential equation considers the presence of Riesz space-fractional derivatives of orders in (1, 2], and homogeneous Dirichlet boundary data are imposed on a closed and bounded spatial domain. The model under investigation possesses an energy function which is preserved in the undamped regime. In the damped case, we establish the property of energy dissipation of the model using arguments from functional analysis. Motivated by these results, we propose an explicit finite-difference discretization of our fractional model based on the use of fractional centered differences. Associated to our discrete model, we also propose discretizations of the energy quantities. We establish that the discrete energy is conserved in the undamped regime, and that it dissipates in the damped scenario. Among the most important numerical features of our scheme, we show that the method has a consistency of second order, that it is stable and that it has a quadratic order of convergence. Some one- and two-dimensional simulations are shown in this work to illustrate the fact that the technique is capable of preserving the discrete energy in the undamped regime. For the sake of convenience, we provide a Matlab implementation of our method for the one-dimensional scenario.

Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator

NASA Astrophysics Data System (ADS)

Owolabi, Kolade M.

2018-03-01

In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.

Fractional time-dependent apparent viscosity model for semisolid foodstuffs

NASA Astrophysics Data System (ADS)

Yang, Xu; Chen, Wen; Sun, HongGuang

2017-10-01

The difficulty in the description of thixotropic behaviors in semisolid foodstuffs is the time dependent nature of apparent viscosity under constant shear rate. In this study, we propose a novel theoretical model via fractional derivative to address the high demand by industries. The present model adopts the critical parameter of fractional derivative order α to describe the corresponding time-dependent thixotropic behavior. More interestingly, the parameter α provides a quantitative insight into discriminating foodstuffs. With the re-exploration of three groups of experimental data (tehineh, balangu, and natillas), the proposed methodology is validated in good applicability and efficiency. The results show that the present fractional apparent viscosity model performs successfully for tested foodstuffs in the shear rate range of 50-150 s^{ - 1}. The fractional order α decreases with the increase of temperature at low temperature, below 50 °C, but increases with growing shear rate. While the ideal initial viscosity k decreases with the increase of temperature, shear rate, and ingredient content. It is observed that the magnitude of α is capable of characterizing the thixotropy of semisolid foodstuffs.

A semi-analytical method for the computation of the Lyapunov exponents of fractional-order systems

NASA Astrophysics Data System (ADS)

Caponetto, Riccardo; Fazzino, Stefano

2013-01-01

Fractional-order differential equations are interesting for their applications in the construction of mathematical models in finance, materials science or diffusion. In this paper, an application of a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equation is employed for calculating Lyapunov exponents of fractional order systems. It is known that the Lyapunov exponents, first introduced by Oseledec, play a crucial role in characterizing the behaviour of dynamical systems. They can be used to analyze the sensitive dependence on initial conditions and the presence of chaotic attractors. The results reveal that the proposed method is very effective and simple and leads to accurate, approximately convergent solutions.

Toward lattice fractional vector calculus

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2014-09-01

An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.

Extending Maxwell's equations for dielectric materials using analytical principles from viscoelasticity based on the fractional calculus

NASA Astrophysics Data System (ADS)

Wharmby, Andrew William

Existing fractional calculus models having a non-empirical basis used to describe constitutive relationships between stress and strain in viscoelastic materials are modified to employ all orders of fractional derivatives between zero and one. Parallels between viscoelastic and dielectric theory are drawn so that these modified fractional calculus based models for viscoelastic materials may be used to describe relationships between electric flux density and electric field intensity in dielectric materials. The resulting fractional calculus based dielectric relaxation model is tested using existing complex permittivity data in the radio-frequency bandwidth of a wide variety of homogeneous materials. The consequences that the application of this newly developed fractional calculus based dielectric relaxation model has on Maxwell's equations are also examined through the effects of dielectric dissipation and dispersion.

Fractional-order Viscoelasticity (FOV): Constitutive Development Using the Fractional Calculus: First Annual Report

NASA Technical Reports Server (NTRS)

Freed, Alan; Diethelm, Kai; Luchko, Yury

2002-01-01

This is the first annual report to the U.S. Army Medical Research and Material Command for the three year project "Advanced Soft Tissue Modeling for Telemedicine and Surgical Simulation" supported by grant No. DAMD17-01-1-0673 to The Cleveland Clinic Foundation, to which the NASA Glenn Research Center is a subcontractor through Space Act Agreement SAA 3-445. The objective of this report is to extend popular one-dimensional (1D) fractional-order viscoelastic (FOV) materials models into their three-dimensional (3D) equivalents for finitely deforming continua, and to provide numerical algorithms for their solution.

Exploiting Fractional Order PID Controller Methods in Improving the Performance of Integer Order PID Controllers: A GA Based Approach

NASA Astrophysics Data System (ADS)

Mukherjee, Bijoy K.; Metia, Santanu

2009-10-01

The paper is divided into three parts. The first part gives a brief introduction to the overall paper, to fractional order PID (PIλDμ) controllers and to Genetic Algorithm (GA). In the second part, first it has been studied how the performance of an integer order PID controller deteriorates when implemented with lossy capacitors in its analog realization. Thereafter it has been shown that the lossy capacitors can be effectively modeled by fractional order terms. Then, a novel GA based method has been proposed to tune the controller parameters such that the original performance is retained even though realized with the same lossy capacitors. Simulation results have been presented to validate the usefulness of the method. Some Ziegler-Nichols type tuning rules for design of fractional order PID controllers have been proposed in the literature [11]. In the third part, a novel GA based method has been proposed which shows how equivalent integer order PID controllers can be obtained which will give performance level similar to those of the fractional order PID controllers thereby removing the complexity involved in the implementation of the latter. It has been shown with extensive simulation results that the equivalent integer order PID controllers more or less retain the robustness and iso-damping properties of the original fractional order PID controllers. Simulation results also show that the equivalent integer order PID controllers are more robust than the normal Ziegler-Nichols tuned PID controllers.

Fractional order analysis of Sephadex gel structures: NMR measurements reflecting anomalous diffusion

NASA Astrophysics Data System (ADS)

Magin, Richard L.; Akpa, Belinda S.; Neuberger, Thomas; Webb, Andrew G.

2011-12-01

We report the appearance of anomalous water diffusion in hydrophilic Sephadex gels observed using pulse field gradient (PFG) nuclear magnetic resonance (NMR). The NMR diffusion data was collected using a Varian 14.1 Tesla imaging system with a home-built RF saddle coil. A fractional order analysis of the data was used to characterize heterogeneity in the gels for the dynamics of water diffusion in this restricted environment. Several recent studies of anomalous diffusion have used the stretched exponential function to model the decay of the NMR signal, i.e., exp[-( bD) α], where D is the apparent diffusion constant, b is determined the experimental conditions (gradient pulse separation, durations and strength), and α is a measure of structural complexity. In this work, we consider a different case where the spatial Laplacian in the Bloch-Torrey equation is generalized to a fractional order model of diffusivity via a complexity parameter, β, a space constant, μ, and a diffusion coefficient, D. This treatment reverts to the classical result for the integer order case. The fractional order decay model was fit to the diffusion-weighted signal attenuation for a range of b-values (0 < b < 4000 s mm -2). Throughout this range of b values, the parameters β, μ and D, were found to correlate with the porosity and tortuosity of the gel structure.

Dynamic stability analysis of fractional order leaky integrator echo state neural networks

NASA Astrophysics Data System (ADS)

Pahnehkolaei, Seyed Mehdi Abedi; Alfi, Alireza; Tenreiro Machado, J. A.

2017-06-01

The Leaky integrator echo state neural network (Leaky-ESN) is an improved model of the recurrent neural network (RNN) and adopts an interconnected recurrent grid of processing neurons. This paper presents a new proof for the convergence of a Lyapunov candidate function to zero when time tends to infinity by means of the Caputo fractional derivative with order lying in the range (0, 1). The stability of Fractional-Order Leaky-ESN (FO Leaky-ESN) is then analyzed, and the existence, uniqueness and stability of the equilibrium point are provided. A numerical example demonstrates the feasibility of the proposed method.

Model-free adaptive sliding mode controller design for generalized projective synchronization of the fractional-order chaotic system via radial basis function neural networks

NASA Astrophysics Data System (ADS)

Wang, L. M.

2017-09-01

A novel model-free adaptive sliding mode strategy is proposed for a generalized projective synchronization (GPS) between two entirely unknown fractional-order chaotic systems subject to the external disturbances. To solve the difficulties from the little knowledge about the master-slave system and to overcome the bad effects of the external disturbances on the generalized projective synchronization, the radial basis function neural networks are used to approach the packaged unknown master system and the packaged unknown slave system (including the external disturbances). Consequently, based on the slide mode technology and the neural network theory, a model-free adaptive sliding mode controller is designed to guarantee asymptotic stability of the generalized projective synchronization error. The main contribution of this paper is that a control strategy is provided for the generalized projective synchronization between two entirely unknown fractional-order chaotic systems subject to the unknown external disturbances, and the proposed control strategy only requires that the master system has the same fractional orders as the slave system. Moreover, the proposed method allows us to achieve all kinds of generalized projective chaos synchronizations by turning the user-defined parameters onto the desired values. Simulation results show the effectiveness of the proposed method and the robustness of the controlled system.

A new analysis of the Fornberg-Whitham equation pertaining to a fractional derivative with Mittag-Leffler-type kernel

NASA Astrophysics Data System (ADS)

Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru

2018-02-01

The mathematical model of breaking of non-linear dispersive water waves with memory effect is very important in mathematical physics. In the present article, we examine a novel fractional extension of the non-linear Fornberg-Whitham equation occurring in wave breaking. We consider the most recent theory of differentiation involving the non-singular kernel based on the extended Mittag-Leffler-type function to modify the Fornberg-Whitham equation. We examine the existence of the solution of the non-linear Fornberg-Whitham equation of fractional order. Further, we show the uniqueness of the solution. We obtain the numerical solution of the new arbitrary order model of the non-linear Fornberg-Whitham equation with the aid of the Laplace decomposition technique. The numerical outcomes are displayed in the form of graphs and tables. The results indicate that the Laplace decomposition algorithm is a very user-friendly and reliable scheme for handling such type of non-linear problems of fractional order.

A physics-based fractional order model and state of energy estimation for lithium ion batteries. Part II: Parameter identification and state of energy estimation for LiFePO4 battery

NASA Astrophysics Data System (ADS)

Li, Xiaoyu; Pan, Ke; Fan, Guodong; Lu, Rengui; Zhu, Chunbo; Rizzoni, Giorgio; Canova, Marcello

2017-11-01

State of energy (SOE) is an important index for the electrochemical energy storage system in electric vehicles. In this paper, a robust state of energy estimation method in combination with a physical model parameter identification method is proposed to achieve accurate battery state estimation at different operating conditions and different aging stages. A physics-based fractional order model with variable solid-state diffusivity (FOM-VSSD) is used to characterize the dynamic performance of a LiFePO4/graphite battery. In order to update the model parameter automatically at different aging stages, a multi-step model parameter identification method based on the lexicographic optimization is especially designed for the electric vehicle operating conditions. As the battery available energy changes with different applied load current profiles, the relationship between the remaining energy loss and the state of charge, the average current as well as the average squared current is modeled. The SOE with different operating conditions and different aging stages are estimated based on an adaptive fractional order extended Kalman filter (AFEKF). Validation results show that the overall SOE estimation error is within ±5%. The proposed method is suitable for the electric vehicle online applications.

From the S U (2 ) quantum link model on the honeycomb lattice to the quantum dimer model on the kagome lattice: Phase transition and fractionalized flux strings

NASA Astrophysics Data System (ADS)

Banerjee, D.; Jiang, F.-J.; Olesen, T. Z.; Orland, P.; Wiese, U.-J.

2018-05-01

We consider the (2 +1 ) -dimensional S U (2 ) quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the kagome lattice. The model has crystalline confined phases with spontaneously broken translation invariance associated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges [which transform nontrivially under the Z (2 ) center of the S U (2 ) gauge group] are confined to each other by fractionalized strings with a delocalized Z (2 ) flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the three-dimensional Ising universality class separates two confining phases: one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.

Algorithms for the Fractional Calculus: A Selection of Numerical Methods

NASA Technical Reports Server (NTRS)

Diethelm, K.; Ford, N. J.; Freed, A. D.; Luchko, Yu.

2003-01-01

Many recently developed models in areas like viscoelasticity, electrochemistry, diffusion processes, etc. are formulated in terms of derivatives (and integrals) of fractional (non-integer) order. In this paper we present a collection of numerical algorithms for the solution of the various problems arising in this context. We believe that this will give the engineer the necessary tools required to work with fractional models in an efficient way.

Conformal field theory construction for non-Abelian hierarchy wave functions

NASA Astrophysics Data System (ADS)

Tournois, Yoran; Hermanns, Maria

2017-12-01

The fractional quantum Hall effect is the paradigmatic example of topologically ordered phases. One of its most fascinating aspects is the large variety of different topological orders that may be realized, in particular non-Abelian ones. Here we analyze a class of non-Abelian fractional quantum Hall model states which are generalizations of the Abelian Haldane-Halperin hierarchy. We derive their topological properties and show that the quasiparticles obey non-Abelian fusion rules of type su (q)k . For a subset of these states we are able to derive the conformal field theory description that makes the topological properties—in particular braiding—of the state manifest. The model states we study provide explicit wave functions for a large variety of interesting topological orders, which may be relevant for certain fractional quantum Hall states observed in the first excited Landau level.

A new fractional operator of variable order: Application in the description of anomalous diffusion

NASA Astrophysics Data System (ADS)

Yang, Xiao-Jun; Machado, J. A. Tenreiro

2017-09-01

In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Laplace and Fourier transforms are analyzed and the results for the anomalous diffusion equations of variable order are discussed. The new formulation is efficient in modeling a class of concentrations in the complex transport process.

Time-Domain Evaluation of Fractional Order Controllers’ Direct Discretization Methods

NASA Astrophysics Data System (ADS)

Ma, Chengbin; Hori, Yoichi

Fractional Order Control (FOC), in which the controlled systems and/or controllers are described by fractional order differential equations, has been applied to various control problems. Though it is not difficult to understand FOC’s theoretical superiority, realization issue keeps being somewhat problematic. Since the fractional order systems have an infinite dimension, proper approximation by finite difference equation is needed to realize the designed fractional order controllers. In this paper, the existing direct discretization methods are evaluated by their convergences and time-domain comparison with the baseline case. Proposed sampling time scaling property is used to calculate the baseline case with full memory length. This novel discretization method is based on the classical trapezoidal rule but with scaled sampling time. Comparative studies show good performance and simple algorithm make the Short Memory Principle method most practically superior. The FOC research is still at its primary stage. But its applications in modeling and robustness against non-linearities reveal the promising aspects. Parallel to the development of FOC theories, applying FOC to various control problems is also crucially important and one of top priority issues.

Spatial analysis of toxic emissions in LCA: a sub-continental nested USEtox model with freshwater archetypes.

PubMed

Kounina, Anna; Margni, Manuele; Shaked, Shanna; Bulle, Cécile; Jolliet, Olivier

2014-08-01

This paper develops continent-specific factors for the USEtox model and analyses the accuracy of different model architectures, spatial scales and archetypes in evaluating toxic impacts, with a focus on freshwater pathways. Inter-continental variation is analysed by comparing chemical fate and intake fractions between sub-continental zones of two life cycle impact assessment models: (1) the nested USEtox model parameterized with sub-continental zones and (2) the spatially differentiated IMPACTWorld model with 17 interconnected sub-continental regions. Substance residence time in water varies by up to two orders of magnitude among the 17 zones assessed with IMPACTWorld and USEtox, and intake fraction varies by up to three orders of magnitude. Despite this variation, the nested USEtox model succeeds in mimicking the results of the spatially differentiated model, with the exception of very persistent volatile pollutants that can be transported to polar regions. Intra-continental variation is analysed by comparing fate and intake fractions modelled with the a-spatial (one box) IMPACT Europe continental model vs. the spatially differentiated version of the same model. Results show that the one box model might overestimate chemical fate and characterisation factors for freshwater eco-toxicity of persistent pollutants by up to three orders of magnitude for point source emissions. Subdividing Europe into three archetypes, based on freshwater residence time (how long it takes water to reach the sea), improves the prediction of fate and intake fractions for point source emissions, bringing them within a factor five compared to the spatial model. We demonstrated that a sub-continental nested model such as USEtox, with continent-specific parameterization complemented with freshwater archetypes, can thus represent inter- and intra-continental spatial variations, whilst minimizing model complexity. Copyright © 2014 Elsevier Ltd. All rights reserved.

Modelling thermal radiation from one-meter diameter methane pool fires

NASA Astrophysics Data System (ADS)

Consalvi, J. L.; Demarco, R.

2012-06-01

The first objective of this article is to implement a comprehensive radiation model in order to predict the radiant fractions and radiative fluxes on remote surfaces in large-scale methane pool fires. The second aim is to quantify the importance of Turbulence-Radiation Interactions (TRIs) in such buoyant flames. The fire-induced flow is modelled by using a buoyancy-modified k-ɛ model and the Steady Laminar Flamelet (SLF) model coupled with a presumed probability density function (pdf) approach. Spectral radiation is modelled by using the Full-Spectrum Correlated-k (FSCK) method. TRIs are taken into account by considering the Optically-Thin Fluctuation Approximation (OTFA). The emission term and the mean absorption coefficient are closed by using a presumed pdf of the mixture fraction, scalar dissipation rate and enthalpy defect. Two 1m-diameter fires with Heat Release Rates (HRR) of 49 kW and 162 kW were simulated. Predicted radiant fractions and radiative heat fluxes are found in reasonable agreement with experimental data. The importance of TRIs is evidenced, computed radiant fractions and radiative heat fluxes being considerably higher than those obtained from calculations based on mean properties. Finally, model results show that the complete absorption coefficient-Planck function correlation should be considered in order to properly take into account the influence of TRIs on the emission term, whereas the absorption coefficient self-correlation in the absorption term reduces significantly the radiant fractions.

A new fractional order derivative based active contour model for colon wall segmentation

NASA Astrophysics Data System (ADS)

Chen, Bo; Li, Lihong C.; Wang, Huafeng; Wei, Xinzhou; Huang, Shan; Chen, Wensheng; Liang, Zhengrong

2018-02-01

Segmentation of colon wall plays an important role in advancing computed tomographic colonography (CTC) toward a screening modality. Due to the low contrast of CT attenuation around colon wall, accurate segmentation of the boundary of both inner and outer wall is very challenging. In this paper, based on the geodesic active contour model, we develop a new model for colon wall segmentation. First, tagged materials in CTC images were automatically removed via a partial volume (PV) based electronic colon cleansing (ECC) strategy. We then present a new fractional order derivative based active contour model to segment the volumetric colon wall from the cleansed CTC images. In this model, the regionbased Chan-Vese model is incorporated as an energy term to the whole model so that not only edge/gradient information but also region/volume information is taken into account in the segmentation process. Furthermore, a fractional order differentiation derivative energy term is also developed in the new model to preserve the low frequency information and improve the noise immunity of the new segmentation model. The proposed colon wall segmentation approach was validated on 16 patient CTC scans. Experimental results indicate that the present scheme is very promising towards automatically segmenting colon wall, thus facilitating computer aided detection of initial colonic polyp candidates via CTC.

Approximate solution of space and time fractional higher order phase field equation

NASA Astrophysics Data System (ADS)

Shamseldeen, S.

2018-03-01

This paper is concerned with a class of space and time fractional partial differential equation (STFDE) with Riesz derivative in space and Caputo in time. The proposed STFDE is considered as a generalization of a sixth-order partial phase field equation. We describe the application of the optimal homotopy analysis method (OHAM) to obtain an approximate solution for the suggested fractional initial value problem. An averaged-squared residual error function is defined and used to determine the optimal convergence control parameter. Two numerical examples are studied, considering periodic and non-periodic initial conditions, to justify the efficiency and the accuracy of the adopted iterative approach. The dependence of the solution on the order of the fractional derivative in space and time and model parameters is investigated.

Rate dependent constitutive behavior of dielectric elastomers and applications in legged robotics

NASA Astrophysics Data System (ADS)

Oates, William; Miles, Paul; Gao, Wei; Clark, Jonathan; Mashayekhi, Somayeh; Hussaini, M. Yousuff

2017-04-01

Dielectric elastomers exhibit novel electromechanical coupling that has been exploited in many adaptive structure applications. Whereas the quasi-static, one-dimensional constitutive behavior can often be accurately quantified by hyperelastic functions and linear dielectric relations, accurate predictions of electromechanical, rate-dependent deformation during multiaxial loading is non-trivial. In this paper, an overview of multiaxial electromechanical membrane finite element modeling is formulated. Viscoelastic constitutive relations are extended to include fractional order. It is shown that fractional order viscoelastic constitutive relations are superior to conventional integer order models. This knowledge is critical for transition to control of legged robotic structures that exhibit advanced mobility.

Ultrasound speckle reduction based on fractional order differentiation.

PubMed

Shao, Dangguo; Zhou, Ting; Liu, Fan; Yi, Sanli; Xiang, Yan; Ma, Lei; Xiong, Xin; He, Jianfeng

2017-07-01

Ultrasound images show a granular pattern of noise known as speckle that diminishes their quality and results in difficulties in diagnosis. To preserve edges and features, this paper proposes a fractional differentiation-based image operator to reduce speckle in ultrasound. An image de-noising model based on fractional partial differential equations with balance relation between k (gradient modulus threshold that controls the conduction) and v (the order of fractional differentiation) was constructed by the effective combination of fractional calculus theory and a partial differential equation, and the numerical algorithm of it was achieved using a fractional differential mask operator. The proposed algorithm has better speckle reduction and structure preservation than the three existing methods [P-M model, the speckle reducing anisotropic diffusion (SRAD) technique, and the detail preserving anisotropic diffusion (DPAD) technique]. And it is significantly faster than bilateral filtering (BF) in producing virtually the same experimental results. Ultrasound phantom testing and in vivo imaging show that the proposed method can improve the quality of an ultrasound image in terms of tissue SNR, CNR, and FOM values.

Numerical analysis for the fractional diffusion and fractional Buckmaster equation by the two-step Laplace Adam-Bashforth method

NASA Astrophysics Data System (ADS)

Jain, Sonal

2018-01-01

In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.

Fast classification and compositional analysis of cornstover fractions using Fourier transform near-infrared techniques.

PubMed

Philip Ye, X; Liu, Lu; Hayes, Douglas; Womac, Alvin; Hong, Kunlun; Sokhansanj, Shahab

2008-10-01

The objectives of this research were to determine the variation of chemical composition across botanical fractions of cornstover, and to probe the potential of Fourier transform near-infrared (FT-NIR) techniques in qualitatively classifying separated cornstover fractions and in quantitatively analyzing chemical compositions of cornstover by developing calibration models to predict chemical compositions of cornstover based on FT-NIR spectra. Large variations of cornstover chemical composition for wide calibration ranges, which is required by a reliable calibration model, were achieved by manually separating the cornstover samples into six botanical fractions, and their chemical compositions were determined by conventional wet chemical analyses, which proved that chemical composition varies significantly among different botanical fractions of cornstover. Different botanic fractions, having total saccharide content in descending order, are husk, sheath, pith, rind, leaf, and node. Based on FT-NIR spectra acquired on the biomass, classification by Soft Independent Modeling of Class Analogy (SIMCA) was employed to conduct qualitative classification of cornstover fractions, and partial least square (PLS) regression was used for quantitative chemical composition analysis. SIMCA was successfully demonstrated in classifying botanical fractions of cornstover. The developed PLS model yielded root mean square error of prediction (RMSEP %w/w) of 0.92, 1.03, 0.17, 0.27, 0.21, 1.12, and 0.57 for glucan, xylan, galactan, arabinan, mannan, lignin, and ash, respectively. The results showed the potential of FT-NIR techniques in combination with multivariate analysis to be utilized by biomass feedstock suppliers, bioethanol manufacturers, and bio-power producers in order to better manage bioenergy feedstocks and enhance bioconversion.

Fractional Diffusion Processes: Probability Distributions and Continuous Time Random Walk

NASA Astrophysics Data System (ADS)

Gorenflo, R.; Mainardi, F.

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By the space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order alpha in (0,2] and skewness theta (\\verttheta\\vertlemin \\{alpha ,2-alpha \\}), and the first-order time derivative with a Caputo derivative of order beta in (0,1] . The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process. We view it as a generalized diffusion process that we call fractional diffusion process, and present an integral representation of the fundamental solution. A more general approach to anomalous diffusion is however known to be provided by the master equation for a continuous time random walk (CTRW). We show how this equation reduces to our fractional diffusion equation by a properly scaled passage to the limit of compressed waiting times and jump widths. Finally, we describe a method of simulation and display (via graphics) results of a few numerical case studies.

Numerical Solution of Time-Dependent Problems with a Fractional-Power Elliptic Operator

NASA Astrophysics Data System (ADS)

Vabishchevich, P. N.

2018-03-01

A time-dependent problem in a bounded domain for a fractional diffusion equation is considered. The first-order evolution equation involves a fractional-power second-order elliptic operator with Robin boundary conditions. A finite-element spatial approximation with an additive approximation of the operator of the problem is used. The time approximation is based on a vector scheme. The transition to a new time level is ensured by solving a sequence of standard elliptic boundary value problems. Numerical results obtained for a two-dimensional model problem are presented.

Limit Theorems and Their Relation to Solute Transport in Simulated Fractured Media

NASA Astrophysics Data System (ADS)

Reeves, D. M.; Benson, D. A.; Meerschaert, M. M.

2003-12-01

Solute particles that travel through fracture networks are subject to wide velocity variations along a restricted set of directions. This may result in super-Fickian dispersion along a few primary scaling directions. The fractional advection-dispersion equation (FADE), a modification of the original advection-dispersion equation in which a fractional derivative replaces the integer-order dispersion term, has the ability to model rapid, non-Gaussian solute transport. The FADE assumes that solute particle motions converge to either α -stable or operator stable densities, which are modeled by spatial fractional derivatives. In multiple dimensions, the multi-fractional dispersion derivative dictates the order and weight of differentiation in all directions, which correspond to the statistics of large particle motions in all directions. This study numerically investigates the presence of super- Fickian solute transport through simulated two-dimensional fracture networks. An ensemble of networks is gen

Fractional Control of An Active Four-wheel-steering Vehicle

NASA Astrophysics Data System (ADS)

Wang, Tianting; Tong, Jun; Chen, Ning; Tian, Jie

2018-03-01

A four-wheel-steering (4WS) vehicle model and reference model with a drop filter are constructed. The decoupling of 4WS vehicle model is carried out. And a fractional PIλDμ controller is introduced into the decoupling strategy to reduce the effects of the uncertainty of the vehicle parameters as well as the unmodelled dynamics on the system performance. Based on optimization techniques, the design of fractional controller are obtained to ensure the robustness of 4WS vehicle during the special range of frequencies through proper choice of the constraints. In order to compare with fractional robust controller, an optimal controller for the same vehicle is also designed. The simulations of the two control systems are carried out and it reveals that the decoupling and fractional robust controller is able to make vehicle model trace the reference model very well with better robustness.

Volterra-type Lyapunov functions for fractional-order epidemic systems

NASA Astrophysics Data System (ADS)

Vargas-De-León, Cruz

2015-07-01

In this paper we prove an elementary lemma which estimates fractional derivatives of Volterra-type Lyapunov functions in the sense Caputo when α ∈ (0, 1) . Moreover, by using this result, we study the uniform asymptotic stability of some Caputo-type epidemic systems with a pair of fractional-order differential equations. These epidemic systems are the Susceptible-Infected-Susceptible (SIS), Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Recovered-Susceptible (SIRS) models and Ross-Macdonald model for vector-borne diseases. We show that the unique endemic equilibrium is uniformly asymptotically stable if the basic reproductive number is greater than one. We illustrate our theoretical results with numerical simulations using the Adams-Bashforth-Moulton scheme implemented in the fde12 Matlab function.

Regarding on the prototype solutions for the nonlinear fractional-order biological population model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baskonus, Haci Mehmet, E-mail: hmbaskonus@gmail.com; Bulut, Hasan

2016-06-08

In this study, we have submitted to literature a method newly extended which is called as Improved Bernoulli sub-equation function method based on the Bernoulli Sub-ODE method. The proposed analytical scheme has been expressed with steps. We have obtained some new analytical solutions to the nonlinear fractional-order biological population model by using this technique. Two and three dimensional surfaces of analytical solutions have been drawn by wolfram Mathematica 9. Finally, a conclusion has been submitted by mentioning important acquisitions founded in this study.

Physics of the Kitaev Model: Fractionalization, Dynamic Correlations, and Material Connections

NASA Astrophysics Data System (ADS)

Hermanns, M.; Kimchi, I.; Knolle, J.

2018-03-01

Quantum spin liquids have fascinated condensed matter physicists for decades because of their unusual properties such as spin fractionalization and long-range entanglement. Unlike conventional symmetry breaking, the topological order underlying quantum spin liquids is hard to detect experimentally. Even theoretical models are scarce for which the ground state is established to be a quantum spin liquid. The Kitaev honeycomb model and its generalizations to other tricoordinated lattices are chief counterexamples - they are exactly solvable, harbor a variety of quantum spin liquid phases, and are also relevant for certain transition metal compounds including the polymorphs of (Na,Li)2IrO3 iridates and RuCl3. In this review, we give an overview of the rich physics of the Kitaev model, including two-dimensional and three-dimensional fractionalization as well as dynamic correlations and behavior at finite temperatures. We discuss the different materials and argue how the Kitaev model physics can be relevant even though most materials show magnetic ordering at low temperatures.

Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T2 *-weighted magnetic resonance imaging at 7 T.

PubMed

Qin, Shanlin; Liu, Fawang; Turner, Ian W; Yu, Qiang; Yang, Qianqian; Vegh, Viktor

2017-04-01

To study the utility of fractional calculus in modeling gradient-recalled echo MRI signal decay in the normal human brain. We solved analytically the extended time-fractional Bloch equations resulting in five model parameters, namely, the amplitude, relaxation rate, order of the time-fractional derivative, frequency shift, and constant offset. Voxel-level temporal fitting of the MRI signal was performed using the classical monoexponential model, a previously developed anomalous relaxation model, and using our extended time-fractional relaxation model. Nine brain regions segmented from multiple echo gradient-recalled echo 7 Tesla MRI data acquired from five participants were then used to investigate the characteristics of the extended time-fractional model parameters. We found that the extended time-fractional model is able to fit the experimental data with smaller mean squared error than the classical monoexponential relaxation model and the anomalous relaxation model, which do not account for frequency shift. We were able to fit multiple echo time MRI data with high accuracy using the developed model. Parameters of the model likely capture information on microstructural and susceptibility-induced changes in the human brain. Magn Reson Med 77:1485-1494, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Model Drawing Strategy for Fraction Word Problem Solving of Fourth-Grade Students with Learning Disabilities

ERIC Educational Resources Information Center

Sharp, Emily; Shih Dennis, Minyi

2017-01-01

This study used a multiple probe across participants design to examine the effects of a model drawing strategy (MDS) intervention package on fraction comparing and ordering word problem-solving performance of three Grade 4 students. MDS is a form of cognitive strategy instruction for teaching word problem solving that includes explicit instruction…

How to bridge the gap between "unresolved" model and "resolved" model in CFD-DEM coupled method for sediment transport?

NASA Astrophysics Data System (ADS)

Liu, D.; Fu, X.; Liu, X.

2016-12-01

In nature, granular materials exist widely in water bodies. Understanding the fundamentals of solid-liquid two-phase flow, such as turbulent sediment-laden flow, is of importance for a wide range of applications. A coupling method combining computational fluid dynamics (CFD) and discrete element method (DEM) is now widely used for modeling such flows. In this method, when particles are significantly larger than the CFD cells, the fluid field around each particle should be fully resolved. On the other hand, the "unresolved" model is designed for the situation where particles are significantly smaller than the mesh cells. Using "unresolved" model, large amount of particles can be simulated simultaneously. However, there is a gap between these two situations when the size of DEM particles and CFD cell is in the same order of magnitude. In this work, the most commonly used void fraction models are tested with numerical sedimentation experiments. The range of applicability for each model is presented. Based on this, a new void fraction model, i.e., a modified version of "tri-linear" model, is proposed. Particular attention is paid to the smooth function of void fraction in order to avoid numerical instability. The results show good agreement with the experimental data and analytical solution for both single-particle motion and also group-particle motion, indicating great potential of the new void fraction model.

Fractional kinetics of compartmental systems: first approach with use digraph-based method

NASA Astrophysics Data System (ADS)

Markowski, Konrad Andrzej

2017-08-01

In the last two decades, integral and differential calculus of a fractional order has become a subject of great interest in different areas of physics, biology, economics and other sciences. The idea of such a generalization was mentioned in 1695 by Leibniz and L'Hospital. The first definition of the fractional derivative was introduced by Liouville and Riemann at the end of the 19th century. Fractional calculus was found to be a very useful tool for modelling the behaviour of many materials and systems. In this paper fractional calculus was applied to pharmacokinetic compartmental model. For introduced model determine all possible quasi-positive realisation based on one-dimensional digraph theory. The proposed method was discussed and illustrated in detail with some numerical examples.

Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions.

PubMed

Langlands, T A M; Henry, B I; Wearne, S L

2009-12-01

We introduce fractional Nernst-Planck equations and derive fractional cable equations as macroscopic models for electrodiffusion of ions in nerve cells when molecular diffusion is anomalous subdiffusion due to binding, crowding or trapping. The anomalous subdiffusion is modelled by replacing diffusion constants with time dependent operators parameterized by fractional order exponents. Solutions are obtained as functions of the scaling parameters for infinite cables and semi-infinite cables with instantaneous current injections. Voltage attenuation along dendrites in response to alpha function synaptic inputs is computed. Action potential firing rates are also derived based on simple integrate and fire versions of the models. Our results show that electrotonic properties and firing rates of nerve cells are altered by anomalous subdiffusion in these models. We have suggested electrophysiological experiments to calibrate and validate the models.

General solution of a fractional Parker diffusion-convection equation describing the superdiffusive transport of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, Ashraf M.; Fichtner, Horst; Elhanbaly, A.; Schlickeiser, Reinhard

2018-06-01

Anomalous diffusion models of energetic particles in space plasmas are developed by introducing the fractional Parker diffusion-convection equation. Analytical solution of the space-time fractional equation is obtained by use of the Caputo and Riesz-Feller fractional derivatives with the Laplace-Fourier transforms. The solution is given in terms of the Fox H-function. Profiles of particle densities are illustrated for different values of the space fractional order and the so-called skewness parameter.

A class of traveling wave solutions for space-time fractional biological population model in mathematical physics

NASA Astrophysics Data System (ADS)

Akram, Ghazala; Batool, Fiza

2017-10-01

The (G'/G)-expansion method is utilized for a reliable treatment of space-time fractional biological population model. The method has been applied in the sense of the Jumarie's modified Riemann-Liouville derivative. Three classes of exact traveling wave solutions, hyperbolic, trigonometric and rational solutions of the associated equation are characterized with some free parameters. A generalized fractional complex transform is applied to convert the fractional equations to ordinary differential equations which subsequently resulted in number of exact solutions. It should be mentioned that the (G'/G)-expansion method is very effective and convenient for solving nonlinear partial differential equations of fractional order whose balancing number is a negative integer.

Fractional cable model for signal conduction in spiny neuronal dendrites

NASA Astrophysics Data System (ADS)

Vitali, Silvia; Mainardi, Francesco

2017-06-01

The cable model is widely used in several fields of science to describe the propagation of signals. A relevant medical and biological example is the anomalous subdiffusion in spiny neuronal dendrites observed in several studies of the last decade. Anomalous subdiffusion can be modelled in several ways introducing some fractional component into the classical cable model. The Chauchy problem associated to these kind of models has been investigated by many authors, but up to our knowledge an explicit solution for the signalling problem has not yet been published. Here we propose how this solution can be derived applying the generalized convolution theorem (known as Efros theorem) for Laplace transforms. The fractional cable model considered in this paper is defined by replacing the first order time derivative with a fractional derivative of order α ∈ (0, 1) of Caputo type. The signalling problem is solved for any input function applied to the accessible end of a semi-infinite cable, which satisfies the requirements of the Efros theorem. The solutions corresponding to the simple cases of impulsive and step inputs are explicitly calculated in integral form containing Wright functions. Thanks to the variability of the parameter α, the corresponding solutions are expected to adapt to the qualitative behaviour of the membrane potential observed in experiments better than in the standard case α = 1.

Boundary layer flow of MHD generalized Maxwell fluid over an exponentially accelerated infinite vertical surface with slip and Newtonian heating at the boundary

NASA Astrophysics Data System (ADS)

Imran, M. A.; Riaz, M. B.; Shah, N. A.; Zafar, A. A.

2018-03-01

The aim of this article is to investigate the unsteady natural convection flow of Maxwell fluid with fractional derivative over an exponentially accelerated infinite vertical plate. Moreover, slip condition, radiation, MHD and Newtonian heating effects are also considered. A modern definition of fractional derivative operator recently introduced by Caputo and Fabrizio has been used to formulate the fractional model. Semi analytical solutions of the dimensionless problem are obtained by employing Stehfest's and Tzou's algorithms in order to find the inverse Laplace transforms for temperature and velocity fields. Temperature and rate of heat transfer for non-integer and integer order derivatives are computed and reduced to some known solutions from the literature. Finally, in order to get insight of the physical significance of the considered problem regarding velocity and Nusselt number, some graphical illustrations are made using Mathcad software. As a result, in comparison between Maxwell and viscous fluid (fractional and ordinary) we found that viscous (fractional and ordinary) fluids are swiftest than Maxwell (fractional and ordinary) fluids.

Design of set-point weighting PIλ + Dμ controller for vertical magnetic flux controller in Damavand tokamak.

PubMed

Rasouli, H; Fatehi, A

2014-12-01

In this paper, a simple method is presented for tuning weighted PI(λ) + D(μ) controller parameters based on the pole placement controller of pseudo-second-order fractional systems. One of the advantages of this controller is capability of reducing the disturbance effects and improving response to input, simultaneously. In the following sections, the performance of this controller is evaluated experimentally to control the vertical magnetic flux in Damavand tokamak. For this work, at first a fractional order model is identified using output-error technique in time domain. For various practical experiments, having desired time responses for magnetic flux in Damavand tokamak, is vital. To approach this, at first the desired closed loop reference models are obtained based on generalized characteristic ratio assignment method in fractional order systems. After that, for the identified model, a set-point weighting PI(λ) + D(μ) controller is designed and simulated. Finally, this controller is implemented on digital signal processor control system of the plant to fast/slow control of magnetic flux. The practical results show appropriate performance of this controller.

A novel interval type-2 fractional order fuzzy PID controller: Design, performance evaluation, and its optimal time domain tuning.

PubMed

Kumar, Anupam; Kumar, Vijay

2017-05-01

In this paper, a novel concept of an interval type-2 fractional order fuzzy PID (IT2FO-FPID) controller, which requires fractional order integrator and fractional order differentiator, is proposed. The incorporation of Takagi-Sugeno-Kang (TSK) type interval type-2 fuzzy logic controller (IT2FLC) with fractional controller of PID-type is investigated for time response measure due to both unit step response and unit load disturbance. The resulting IT2FO-FPID controller is examined on different delayed linear and nonlinear benchmark plants followed by robustness analysis. In order to design this controller, fractional order integrator-differentiator operators are considered as design variables including input-output scaling factors. A new hybridized algorithm named as artificial bee colony-genetic algorithm (ABC-GA) is used to optimize the parameters of the controller while minimizing weighted sum of integral of time absolute error (ITAE) and integral of square of control output (ISCO). To assess the comparative performance of the IT2FO-FPID, authors compared it against existing controllers, i.e., interval type-2 fuzzy PID (IT2-FPID), type-1 fractional order fuzzy PID (T1FO-FPID), type-1 fuzzy PID (T1-FPID), and conventional PID controllers. Furthermore, to show the effectiveness of the proposed controller, the perturbed processes along with the larger dead time are tested. Moreover, the proposed controllers are also implemented on multi input multi output (MIMO), coupled, and highly complex nonlinear two-link robot manipulator system in presence of un-modeled dynamics. Finally, the simulation results explicitly indicate that the performance of the proposed IT2FO-FPID controller is superior to its conventional counterparts in most of the cases. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

A simplified fractional order impedance model and parameter identification method for lithium-ion batteries

PubMed Central

Yang, Qingxia; Xu, Jun; Cao, Binggang; Li, Xiuqing

2017-01-01

Identification of internal parameters of lithium-ion batteries is a useful tool to evaluate battery performance, and requires an effective model and algorithm. Based on the least square genetic algorithm, a simplified fractional order impedance model for lithium-ion batteries and the corresponding parameter identification method were developed. The simplified model was derived from the analysis of the electrochemical impedance spectroscopy data and the transient response of lithium-ion batteries with different states of charge. In order to identify the parameters of the model, an equivalent tracking system was established, and the method of least square genetic algorithm was applied using the time-domain test data. Experiments and computer simulations were carried out to verify the effectiveness and accuracy of the proposed model and parameter identification method. Compared with a second-order resistance-capacitance (2-RC) model and recursive least squares method, small tracing voltage fluctuations were observed. The maximum battery voltage tracing error for the proposed model and parameter identification method is within 0.5%; this demonstrates the good performance of the model and the efficiency of the least square genetic algorithm to estimate the internal parameters of lithium-ion batteries. PMID:28212405

Fractional model for pharmacokinetics of high dose methotrexate in children with acute lymphoblastic leukaemia

NASA Astrophysics Data System (ADS)

Popović, Jovan K.; Spasić, Dragan T.; Tošić, Jela; Kolarović, Jovanka L.; Malti, Rachid; Mitić, Igor M.; Pilipović, Stevan; Atanacković, Teodor M.

2015-05-01

The aim of this study is to promote a model based on the fractional differential calculus related to the pharmacokinetic individualization of high dose methotrexate treatment in children with acute lymphoblastic leukaemia, especially in high risk patients. We applied two-compartment fractional model on 8 selected cases with the largest number (4-19) of measured concentrations, among 43 pediatric patients received 24-h methotrexate 2-5 g/m2 infusions. The plasma concentrations were determined by fluorescence polarization immunoassay. Our mathematical procedure, designed by combining Post's and Newton's method, was coded in Mathematica 8.0 and performed on Fujicu Celsius M470-2 PC. Experimental data show that most of the measured values of methotrexate were in decreasing order. However, in certain treatments local maximums were detected. On the other hand, integer order compartmental models do not give values which fit well with the observed data. By the use of our model, we obtained better results, since it gives more accurate behavior of the transmission, as well as the local maximums which were recognized in methotrexate monitoring. It follows from our method that an additional test with a small methotrexate dose can be suggested for the fractional system parameter identification and the prediction of a possible pattern with a full dose in the case of high risk patients. A special feature of the fractional model is that it can also recognize and better fit an observed non-monotonic behavior. A new parameter determination procedure can be successfully used.

Tunable Thermosetting Epoxies Based on Fractionated and Well-Characterized Lignins.

PubMed

Gioia, Claudio; Lo Re, Giada; Lawoko, Martin; Berglund, Lars

2018-03-21

Here we report the synthesis of thermosetting resins from low molar mass Kraft lignin fractions of high functionality, refined by solvent extraction. Such fractions were fully characterized by 31 P NMR, 2D-HSQC NMR, SEC, and DSC in order to obtain a detailed description of the structures. Reactive oxirane moieties were introduced on the lignin backbone under mild reaction conditions and quantified by simple 1 H NMR analysis. The modified fractions were chemically cross-linked with a flexible polyether diamine ( M n ≈ 2000), in order to obtain epoxy thermosets. Epoxies from different lignin fractions, studied by DSC, DMA, tensile tests, and SEM, demonstrated substantial differences in terms of thermo-mechanical properties. For the first time, strong relationships between lignin structures and epoxy properties could be demonstrated. The suggested approach provides unprecedented possibilities to tune network structure and properties of thermosets based on real lignin fractions, rather than model compounds.

A second-order bulk boundary-layer model

NASA Technical Reports Server (NTRS)

Randall, David A.; Shao, Qingqiu; Moeng, Chin-Hoh

1992-01-01

Bulk mass-flux models represent the large eddies that are primarily responsible for the turbulent fluxes in the planetary boundary layer as convective circulations, with an associated convective mass flux. In order for such models to be useful, it is necessary to determine the fractional area covered by rising motion in the convective circulations. This fraction can be used as an estimate of the cloud amount, under certain conditions. 'Matching' conditions have been developed that relate the convective mass flux to the ventilation and entrainment mass fluxes. These are based on conservation equations for the scalar means and variances in the entrainment and ventilation layers. Methods are presented to determine both the fractional area covered by rising motion and the convective mass flux. The requirement of variance balance is used to relax the 'well-mixed' assumption. The vertical structures of the mean state and the turbulent fluxes are determined analytically. Several aspects of this simple model's formulation are evaluated using results from large-eddy simulations.

Analytical study of fractional equations describing anomalous diffusion of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, A. M.; Fichtner, H.; Schlickeiser, R.; Elhanbaly, A.

2017-06-01

To present the main influence of anomalous diffusion on the energetic particle propagation, the fractional derivative model of transport is developed by deriving the fractional modified Telegraph and Rayleigh equations. Analytical solutions of the fractional modified Telegraph and the fractional Rayleigh equations, which are defined in terms of Caputo fractional derivatives, are obtained by using the Laplace transform and the Mittag-Leffler function method. The solutions of these fractional equations are given in terms of special functions like Fox’s H, Mittag-Leffler, Hermite and Hyper-geometric functions. The predicted travelling pulse solutions are discussed in each case for different values of fractional order.

Development of a second order closure model for computation of turbulent diffusion flames

NASA Technical Reports Server (NTRS)

Varma, A. K.; Donaldson, C. D.

1974-01-01

A typical eddy box model for the second-order closure of turbulent, multispecies, reacting flows developed. The model structure was quite general and was valid for an arbitrary number of species. For the case of a reaction involving three species, the nine model parameters were determined from equations for nine independent first- and second-order correlations. The model enabled calculation of any higher-order correlation involving mass fractions, temperatures, and reaction rates in terms of first- and second-order correlations. Model predictions for the reaction rate were in very good agreement with exact solutions of the reaction rate equations for a number of assumed flow distributions.

Nonclassical point of view of the Brownian motion generation via fractional deterministic model

NASA Astrophysics Data System (ADS)

Gilardi-Velázquez, H. E.; Campos-Cantón, E.

In this paper, we present a dynamical system based on the Langevin equation without stochastic term and using fractional derivatives that exhibit properties of Brownian motion, i.e. a deterministic model to generate Brownian motion is proposed. The stochastic process is replaced by considering an additional degree of freedom in the second-order Langevin equation. Thus, it is transformed into a system of three first-order linear differential equations, additionally α-fractional derivative are considered which allow us to obtain better statistical properties. Switching surfaces are established as a part of fluctuating acceleration. The final system of three α-order linear differential equations does not contain a stochastic term, so the system generates motion in a deterministic way. Nevertheless, from the time series analysis, we found that the behavior of the system exhibits statistics properties of Brownian motion, such as, a linear growth in time of mean square displacement, a Gaussian distribution. Furthermore, we use the detrended fluctuation analysis to prove the Brownian character of this motion.

Discrete maximal regularity of time-stepping schemes for fractional evolution equations.

PubMed

Jin, Bangti; Li, Buyang; Zhou, Zhi

2018-01-01

In this work, we establish the maximal [Formula: see text]-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order [Formula: see text], [Formula: see text], in time. These schemes include convolution quadratures generated by backward Euler method and second-order backward difference formula, the L1 scheme, explicit Euler method and a fractional variant of the Crank-Nicolson method. The main tools for the analysis include operator-valued Fourier multiplier theorem due to Weis (Math Ann 319:735-758, 2001. doi:10.1007/PL00004457) and its discrete analogue due to Blunck (Stud Math 146:157-176, 2001. doi:10.4064/sm146-2-3). These results generalize the corresponding results for parabolic problems.

NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.

PubMed

Liu, F; Meerschaert, M M; McGough, R J; Zhuang, P; Liu, Q

2013-03-01

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION

PubMed Central

Liu, F.; Meerschaert, M.M.; McGough, R.J.; Zhuang, P.; Liu, Q.

2013-01-01

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian. PMID:23772179

Surface response of a fractional order viscoelastic halfspace to surface and subsurface sources

PubMed Central

Meral, F. Can; Royston, Thomas J.; Magin, Richard L.

2009-01-01

Previous studies by the second author published in this journal focused on low audible frequency (40–400 Hz) shear and surface wave motion in and on a viscoelastic material representative of biological tissue. Specific cases considered were that of surface wave motion on a halfspace caused by a finite rigid circular disk located on the surface and oscillating normal to it [Royston et al., J. Acoust. Soc. Am. 106, 3678–3686 (1999)] and compression, shear, and surface wave motion in a halfspace generated by a subsurface finite dipole [Royston et al., J. Acoust. Soc. Am. 113, 1109–1121 (2003)]. In both studies, a Voigt model of viscoelasticity was assumed in the theoretical treatment, which resulted in agreement between theoretical predictions and experimental measurements over a limited frequency range. In the present article, the linear viscoelastic assumption in these two prior works is revisited to consider a (still linear) fractional order Voigt model, where the rate-dependent damping component that is dependent on the first derivative of time is replaced with a component that is dependent on a fractional derivative of time. It is shown that in both excitation source configurations, the fractional order Voigt model assumption improves the match of theory to experiment over a wider frequency range (in some cases up to the measured range of 700 Hz). PMID:20000941

Comparing the Caputo, Caputo-Fabrizio and Atangana-Baleanu derivative with fractional order: Fractional cubic isothermal auto-catalytic chemical system

NASA Astrophysics Data System (ADS)

Saad, K. M.

2018-03-01

In this work we extend the standard model for a cubic isothermal auto-catalytic chemical system (CIACS) to a new model of a fractional cubic isothermal auto-catalytic chemical system (FCIACS) based on Caputo (C), Caputo-Fabrizio (CF) and Atangana-Baleanu in the Liouville-Caputo sense (ABC) fractional time derivatives, respectively. We present approximate solutions for these extended models using the q -homotopy analysis transform method ( q -HATM). We solve the FCIACS with the C derivative and compare our results with those obtained using the CF and ABC derivatives. The ranges of convergence of the solutions are found and the optimal values of h , the auxiliary parameter, are derived. Finally, these solutions are compared with numerical solutions of the various models obtained using finite differences and excellent agreement is found.

Control of Initialized Fractional-Order Systems. Revised

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Lorenzo, Carl F.

2002-01-01

Due to the importance of historical effects in fractional-order systems, this paper presents a general fractional-order control theory that includes the time-varying initialization response. Previous studies have not properly accounted for these historical effects. The initialization response, along with the forced response, for fractional-order systems is determined. Stability properties of fractional-order systems are presented in the complex w-plane, which is a transformation of the s-plane. Time responses are discussed with respect to pole positions in the complex w-plane and frequency response behavior is included. A fractional-order vector space representation, which is a generalization of the state space concept, is presented including the initialization response. Control methods for vector representations of initialized fractional-order systems are shown. Nyquist, root-locus, and other input-output control methods are adapted to the control of fractional-order systems. Finally, the fractional-order differintegral is generalized to continuous order-distributions that have the possibility of including a continuum of fractional orders in a system element.

Control of Initialized Fractional-Order Systems

NASA Technical Reports Server (NTRS)

Hartly, Tom T.; Lorenzo, Carl F.

2002-01-01

Due to the importance of historical effects in fractional-order systems, this paper presents a general fractional-order control theory that includes the time-varying initialization response. Previous studies have not properly accounted for these historical effects. The initialization response, along with the forced response, for fractional-order systems is determined. Stability properties of fractional-order systems are presented in the complex Airplane, which is a transformation of the s-plane. Time responses are discussed with respect to pole positions in the complex Airplane and frequency response behavior is included. A fractional-order vector space representation, which is a generalization of the state space concept, is presented including the initialization response. Control methods for vector representations of initialized fractional-order systems are shown. Nyquist, root-locus, and other input-output control methods are adapted to the control of fractional-order systems. Finally, the fractional-order differintegral is generalized to continuous order-distributions that have the possibility of including a continuum of fractional orders in a system element.

One Adaptive Synchronization Approach for Fractional-Order Chaotic System with Fractional-Order 1 < q < 2

PubMed Central

Zhou, Ping; Bai, Rongji

2014-01-01

Based on a new stability result of equilibrium point in nonlinear fractional-order systems for fractional-order lying in 1 < q < 2, one adaptive synchronization approach is established. The adaptive synchronization for the fractional-order Lorenz chaotic system with fractional-order 1 < q < 2 is considered. Numerical simulations show the validity and feasibility of the proposed scheme. PMID:25247207

Stability analysis and nonstandard Grünwald-Letnikov scheme for a fractional order predator-prey model with ratio-dependent functional response

NASA Astrophysics Data System (ADS)

Suryanto, Agus; Darti, Isnani

2017-12-01

In this paper we discuss a fractional order predator-prey model with ratio-dependent functional response. The dynamical properties of this model is analyzed. Here we determine all equilibrium points of this model including their existence conditions and their stability properties. It is found that the model has two type of equilibria, namely the predator-free point and the co-existence point. If there is no co-existence equilibrium, i.e. when the coefficient of conversion from the functional response into the growth rate of predator is less than the death rate of predator, then the predator-free point is asymptotically stable. On the other hand, if the co-existence point exists then this equilibrium is conditionally stable. We also construct a nonstandard Grnwald-Letnikov (NSGL) numerical scheme for the propose model. This scheme is a combination of the Grnwald-Letnikov approximation and the nonstandard finite difference scheme. This scheme is implemented in MATLAB and used to perform some simulations. It is shown that our numerical solutions are consistent with the dynamical properties of our fractional predator-prey model.

Enriched reproducing kernel particle method for fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Ying, Yuping; Lian, Yanping; Tang, Shaoqiang; Liu, Wing Kam

2018-06-01

The reproducing kernel particle method (RKPM) has been efficiently applied to problems with large deformations, high gradients and high modal density. In this paper, it is extended to solve a nonlocal problem modeled by a fractional advection-diffusion equation (FADE), which exhibits a boundary layer with low regularity. We formulate this method on a moving least-square approach. Via the enrichment of fractional-order power functions to the traditional integer-order basis for RKPM, leading terms of the solution to the FADE can be exactly reproduced, which guarantees a good approximation to the boundary layer. Numerical tests are performed to verify the proposed approach.

Adaptive neural network backstepping control for a class of uncertain fractional-order chaotic systems with unknown backlash-like hysteresis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Yimin; Lv, Hui, E-mail: lvhui207@gmail.com

In this paper, we consider the control problem of a class of uncertain fractional-order chaotic systems preceded by unknown backlash-like hysteresis nonlinearities based on backstepping control algorithm. We model the hysteresis by using a differential equation. Based on the fractional Lyapunov stability criterion and the backstepping algorithm procedures, an adaptive neural network controller is driven. No knowledge of the upper bound of the disturbance and system uncertainty is required in our controller, and the asymptotical convergence of the tracking error can be guaranteed. Finally, we give two simulation examples to confirm our theoretical results.

[Evoked Potential Blind Extraction Based on Fractional Lower Order Spatial Time-Frequency Matrix].

PubMed

Long, Junbo; Wang, Haibin; Zha, Daifeng

2015-04-01

The impulsive electroencephalograph (EEG) noises in evoked potential (EP) signals is very strong, usually with a heavy tail and infinite variance characteristics like the acceleration noise impact, hypoxia and etc., as shown in other special tests. The noises can be described by a stable distribution model. In this paper, Wigner-Ville distribution (WVD) and pseudo Wigner-Ville distribution (PWVD) time-frequency distribution based on the fractional lower order moment are presented to be improved. We got fractional lower order WVD (FLO-WVD) and fractional lower order PWVD (FLO-PWVD) time-frequency distribution which could be suitable for a stable distribution process. We also proposed the fractional lower order spatial time-frequency distribution matrix (FLO-STFM) concept. Therefore, combining with time-frequency underdetermined blind source separation (TF-UBSS), we proposed a new fractional lower order spatial time-frequency underdetermined blind source separation (FLO-TF-UBSS) which can work in a stable distribution environment. We used the FLO-TF-UBSS algorithm to extract EPs. Simulations showed that the proposed method could effectively extract EPs in EEG noises, and the separated EPs and EEG signals based on FLO-TF-UBSS were almost the same as the original signal, but blind separation based on TF-UBSS had certain deviation. The correlation coefficient of the FLO-TF-UBSS algorithm was higher than the TF-UBSS algorithm when generalized signal-to-noise ratio (GSNR) changed from 10 dB to 30 dB and a varied from 1. 06 to 1. 94, and was approximately e- qual to 1. Hence, the proposed FLO-TF-UBSS method might be better than the TF-UBSS algorithm based on second order for extracting EP signal under an EEG noise environment.

Understanding agent-based models of financial markets: A bottom-up approach based on order parameters and phase diagrams

NASA Astrophysics Data System (ADS)

Lye, Ribin; Tan, James Peng Lung; Cheong, Siew Ann

2012-11-01

We describe a bottom-up framework, based on the identification of appropriate order parameters and determination of phase diagrams, for understanding progressively refined agent-based models and simulations of financial markets. We illustrate this framework by starting with a deterministic toy model, whereby N independent traders buy and sell M stocks through an order book that acts as a clearing house. The price of a stock increases whenever it is bought and decreases whenever it is sold. Price changes are updated by the order book before the next transaction takes place. In this deterministic model, all traders based their buy decisions on a call utility function, and all their sell decisions on a put utility function. We then make the agent-based model more realistic, by either having a fraction fb of traders buy a random stock on offer, or a fraction fs of traders sell a random stock in their portfolio. Based on our simulations, we find that it is possible to identify useful order parameters from the steady-state price distributions of all three models. Using these order parameters as a guide, we find three phases: (i) the dead market; (ii) the boom market; and (iii) the jammed market in the phase diagram of the deterministic model. Comparing the phase diagrams of the stochastic models against that of the deterministic model, we realize that the primary effect of stochasticity is to eliminate the dead market phase.

Stability Analysis of Distributed Order Fractional Chen System

PubMed Central

Aminikhah, H.; Refahi Sheikhani, A.; Rezazadeh, H.

2013-01-01

We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results. PMID:24489508

Enhanced Bulk-Edge Coulomb Coupling in Fractional Fabry-Perot Interferometers.

PubMed

von Keyserlingk, C W; Simon, S H; Rosenow, Bernd

2015-09-18

Recent experiments use Fabry-Perot (FP) interferometry to claim that the ν=5/2 quantum Hall state exhibits non-Abelian topological order. We note that the experiments appear inconsistent with a model neglecting bulk-edge Coulomb coupling and Majorana tunneling, so we reexamine the theory of FP devices. Even a moderate Coulomb coupling may strongly affect some fractional plateaus, but very weakly affect others, allowing us to model the data over a wide range of plateaus. While experiments are consistent with the ν=5/2 state harboring Moore-Read topological order, they may have measured Coulomb effects rather than an "even-odd effect" due to non-Abelian braiding.

Design of set-point weighting PI{sup λ} + D{sup μ} controller for vertical magnetic flux controller in Damavand tokamak

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rasouli, H.; Fatehi, A.

2014-12-15

In this paper, a simple method is presented for tuning weighted PI{sup λ} + D{sup μ} controller parameters based on the pole placement controller of pseudo-second-order fractional systems. One of the advantages of this controller is capability of reducing the disturbance effects and improving response to input, simultaneously. In the following sections, the performance of this controller is evaluated experimentally to control the vertical magnetic flux in Damavand tokamak. For this work, at first a fractional order model is identified using output-error technique in time domain. For various practical experiments, having desired time responses for magnetic flux in Damavand tokamak,more » is vital. To approach this, at first the desired closed loop reference models are obtained based on generalized characteristic ratio assignment method in fractional order systems. After that, for the identified model, a set-point weighting PI{sup λ} + D{sup μ} controller is designed and simulated. Finally, this controller is implemented on digital signal processor control system of the plant to fast/slow control of magnetic flux. The practical results show appropriate performance of this controller.« less

Fractional calculus in bioengineering, part 3.

PubMed

Magin, Richard L

2004-01-01

Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub-threshold nerve propagation. By expanding the range of mathematical operations to include fractional calculus, we can develop new and potentially useful functional relationships for modeling complex biological systems in a direct and rigorous manner. In Part 2 of this review (Crit Rev Biomed Eng 2004; 32(1):105-193), fractional calculus was applied to problems in nerve stimulation, dielectric relaxation, and viscoelastic materials by extending the governing differential equations to include fractional order terms. In this third and final installment, we consider distributed systems that represent shear stress in fluids, heat transfer in uniform one-dimensional media, and subthreshold nerve depolarization. Classic electrochemical analysis and impedance spectroscopy are also reviewed from the perspective of fractional calculus, and selected examples from recent studies in neuroscience, bioelectricity, and tissue biomechanics are analyzed to illustrate the vitality of the field.

PREFACE: Fractional Differentiation and its Applications (FDA08) Fractional Differentiation and its Applications (FDA08)

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Tenreiro Machado, J. A.

2009-10-01

The international workshop, Fractional Differentiation and its Applications (FDA08), held at Cankaya University, Ankara, Turkey on 5-7 November 2008, was the third in an ongoing series of conferences dedicated to exploring applications of fractional calculus in science, engineering, economics and finance. Fractional calculus, which deals with derivatives and integrals of any order, is now recognized as playing an important role in modeling multi-scale problems that span a wide range of time or length scales. Fractional calculus provides a natural link to the intermediate-order dynamics that often reflects the complexity of micro- and nanostructures through fractional-order differential equations. Unlike the more established techniques of mathematical physics, the methods of fractional differentiation are still under development; while it is true that the ideas of fractional calculus are as old as the classical integer-order differential operators, modern work is proceeding by both expanding the capabilities of this mathematical tool and by widening its range of applications. Hence, the interested reader will find papers here that focus on the underlying mathematics of fractional calculus, that extend fractional-order operators into new domains, and that apply well established methods to experimental and theoretical problems. The organizing committee invited presentations from experts representing the international community of scholars in fractional calculus and welcomed contributions from the growing number of researchers who are applying fractional differentiation to complex technical problems. The selection of papers in this topical issue of Physica Scripta reflects the success of the FDA08 workshop, with the emergence of a variety of novel areas of application. With these ideas in mind, the guest editors would like to honor the many distinguished scientists that have promoted the development of fractional calculus and, in particular, Professor George M Zaslavsky who supported this special issue but passed away recently. The organizing committee wishes to thank the sponsors and supporters of FDA08, namely Cankaya University represented by the President of the Board of Trustees Sitki Alp and Rector Professor Ziya B Güvenc, The Scientfic and Technological Research Council of Turkey (TUBITAK) and the IFAC for providing the resources needed to hold the workshop, the invited speakers for sharing their expertise and knowledge of fractional calculus, and the participants for their enthusiastic contributions to the discussions and debates.

Maximal regularity in lp spaces for discrete time fractional shifted equations

NASA Astrophysics Data System (ADS)

Lizama, Carlos; Murillo-Arcila, Marina

2017-09-01

In this paper, we are presenting a new method based on operator-valued Fourier multipliers to characterize the existence and uniqueness of ℓp-solutions for discrete time fractional models in the form where A is a closed linear operator defined on a Banach space X and Δα denotes the Grünwald-Letnikov fractional derivative of order α > 0. If X is a UMD space, we provide this characterization only in terms of the R-boundedness of the operator-valued symbol associated to the abstract model. To illustrate our results, we derive new qualitative properties of nonlinear difference equations with shiftings, including fractional versions of the logistic and Nagumo equations.

Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1 dimensions

NASA Astrophysics Data System (ADS)

Wen, Xiao-Gang

2017-05-01

We propose a generic construction of exactly soluble local bosonic models that realize various topological orders with gappable boundaries. In particular, we construct an exactly soluble bosonic model that realizes a (3+1)-dimensional [(3+1)D] Z2-gauge theory with emergent fermionic Kramers doublet. We show that the emergence of such a fermion will cause the nucleation of certain topological excitations in space-time without pin+ structure. The exactly soluble model also leads to a statistical transmutation in (3+1)D. In addition, we construct exactly soluble bosonic models that realize 2 types of time-reversal symmetry-enriched Z2 topological orders in 2+1 dimensions, and 20 types of simplest time-reversal symmetry-enriched topological (SET) orders which have only one nontrivial pointlike and stringlike topological excitation. Many physical properties of those topological states are calculated using the exactly soluble models. We find that some time-reversal SET orders have pointlike excitations that carry Kramers doublet, a fractionalized time-reversal symmetry. We also find that some Z2 SET orders have stringlike excitations that carry anomalous (nononsite) Z2 symmetry, which can be viewed as a fractionalization of Z2 symmetry on strings. Our construction is based on cochains and cocycles in algebraic topology, which is very versatile. In principle, it can also realize emergent topological field theory beyond the twisted gauge theory.

Sufficient conditions for asymptotic stability and stabilization of autonomous fractional order systems

NASA Astrophysics Data System (ADS)

Lenka, Bichitra Kumar; Banerjee, Soumitro

2018-03-01

We discuss the asymptotic stability of autonomous linear and nonlinear fractional order systems where the state equations contain same or different fractional orders which lie between 0 and 2. First, we use the Laplace transform method to derive some sufficient conditions which ensure asymptotic stability of linear fractional order systems. Then by using the obtained results and linearization technique, a stability theorem is presented for autonomous nonlinear fractional order system. Finally, we design a control strategy for stabilization of autonomous nonlinear fractional order systems, and apply the results to the chaotic fractional order Lorenz system in order to verify its effectiveness.

A structure-preserving method for a class of nonlinear dissipative wave equations with Riesz space-fractional derivatives

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

2017-12-01

In this manuscript, we consider an initial-boundary-value problem governed by a (1 + 1)-dimensional hyperbolic partial differential equation with constant damping that generalizes many nonlinear wave equations from mathematical physics. The model considers the presence of a spatial Laplacian of fractional order which is defined in terms of Riesz fractional derivatives, as well as the inclusion of a generic continuously differentiable potential. It is known that the undamped regime has an associated positive energy functional, and we show here that it is preserved throughout time under suitable boundary conditions. To approximate the solutions of this model, we propose a finite-difference discretization based on fractional centered differences. Some discrete quantities are proposed in this work to estimate the energy functional, and we show that the numerical method is capable of conserving the discrete energy under the same boundary conditions for which the continuous model is conservative. Moreover, we establish suitable computational constraints under which the discrete energy of the system is positive. The method is consistent of second order, and is both stable and convergent. The numerical simulations shown here illustrate the most important features of our numerical methodology.

Structure of the mixed-metal carbonate KAgCO₃ revisited: order-disorder (OD) polytypism and allotwinning.

PubMed

Hans, Philipp; Stöger, Berthold; Weil, Matthias; Zobetz, Erich

2015-04-01

Crystals of KAgCO3 belong to an order-disorder (OD) family of structures composed of layers of two kinds. There are two polytypes with a maximum degree of order [MDO1: Pccb; MDO2: Ibca, doubled a-axis compared with MDO1], which are both realised to a different extent in two crystals under investigation [volume fraction MDO1:MDO2 in crystal (I): 0.0216:0.9784 (3) and in crystal (II): 0.9657:0.0343 (3)]. Sharp diffraction spots and the absence of diffuse scattering indicate highly ordered macroscopic domains. The structure of KAgCO3 was refined concurrently against all reflections using an allotwin model (addition of the intensities of both domains). It is shown that a disorder model refined against reflections of only one domain can lead to a significant overestimation of the volume fraction of this domain.

Diversity of the Lyman continuum escape fractions of high-z galaxies and its origins

NASA Astrophysics Data System (ADS)

Sumida, Takumi; Kashino, Daichi; Hasegawa, Kenji

2018-04-01

The Lyman continuum (LyC) escape fraction is a key quantity to determine the contribution of galaxies to cosmic reionization. It has been known that the escape fractions estimated by observations and numerical simulations show a large diversity. However, the origins of the diversity are still uncertain. In this work, to understand what quantities of galaxies are responsible for controlling the escape fraction, we numerically evaluate the escape fraction by performing ray-tracing calculation with simplified disc galaxy models. With a smooth disc model, we explore the dependence of the escape fraction on the disposition of ionizing sources and find that the escape fraction varies up to ˜3 orders of magnitude. It is also found that the halo mass dependence of disc scale height determines whether the escape fraction increases or decreases with halo mass. With a clumpy disc model, it turns out that the escape fraction increases as the clump mass fraction increases because the density in the inter-clump region decreases. In addition, we find that clumpiness regulates the escape fraction via two ways when the total clump mass dominates the total gas mass; the escape fraction is controlled by the covering factor of clumps if the clumps are dense sufficient to block LyC photons, otherwise the clumpiness works to reduce the escape fraction by increasing the total number of recombination events in a galaxy.

On the Numerical Formulation of Parametric Linear Fractional Transformation (LFT) Uncertainty Models for Multivariate Matrix Polynomial Problems

NASA Technical Reports Server (NTRS)

Belcastro, Christine M.

1998-01-01

Robust control system analysis and design is based on an uncertainty description, called a linear fractional transformation (LFT), which separates the uncertain (or varying) part of the system from the nominal system. These models are also useful in the design of gain-scheduled control systems based on Linear Parameter Varying (LPV) methods. Low-order LFT models are difficult to form for problems involving nonlinear parameter variations. This paper presents a numerical computational method for constructing and LFT model for a given LPV model. The method is developed for multivariate polynomial problems, and uses simple matrix computations to obtain an exact low-order LFT representation of the given LPV system without the use of model reduction. Although the method is developed for multivariate polynomial problems, multivariate rational problems can also be solved using this method by reformulating the rational problem into a polynomial form.

Time fractional capital-induced labor migration model

NASA Astrophysics Data System (ADS)

Ali Balcı, Mehmet

2017-07-01

In this study we present a new model of neoclassical economic growth by considering that workers move from regions with lower density of capital to regions with higher density of capital. Since the labor migration and capital flow involves self-similarities in long range time, we use the fractional order derivatives for the time variable. To solve this model we proposed Variational Iteration Method, and studied numerically labor migration flow data from Turkey along with other countries throughout the period of 1966-2014.

[Effect of SO2 volume fraction in flue gas on the adsorption behaviors adsorbed by ZL50 activated carbon and kinetic analysis].

PubMed

Gao, Ji-xian; Wang, Tie-feng; Wang, Jin-fu

2010-05-01

The influence of SO2 dynamic adsorption behaviors using ZL50 activated carbon for flue gas desulphurization and denitrification under different SO2 volume fraction was investigated experimentally, and the kinetic analysis was conducted by kinetic models. With the increase of SO2 volume fraction in flue gas, the SO2 removal ratio and the activity ratio of ZL50 activated carbon decreased, respectively, and SO2 adsorption rate and capacity increased correspondingly. The calculated results indicate that Bangham model has the best prediction effect, the chemisorption processes of SO2 was significantly affected by catalytic oxidative reaction. The adsorption rate constant of Lagergren's pseudo first order model increased with the increase of inlet SO, volume fraction, which indicated that catalytic oxidative reaction of SO2 adsorbed by ZL50 activated carbon may be the rate controlling step in earlier adsorption stage. The Lagergren's and Bangham's initial adsorption rate were deduced and defined, respectively. The Ho's and Elovich's initial adsorption rate were also deduced in this paper. The Bangham's initial adsorption rate values were defined in good agreement with those of experiments. The defined Bangham's adsorptive reaction kinetic model can describe the SO2 dynamic adsorption rate well. The studied results indicated that the SO2 partial order of initial reaction rate was one or adjacent to one, while the O2 and water vapor partial order of initial reaction rate were constants ranging from 0.15-0.20 and 0.45-0.50, respectively.

Quantitative estimation of soil salinity by means of different modeling methods and visible-near infrared (VIS–NIR) spectroscopy, Ebinur Lake Wetland, Northwest China

PubMed Central

Wang, Jingzhe; Abulimiti, Aerzuna; Cai, Lianghong

2018-01-01

Soil salinization is one of the most common forms of land degradation. The detection and assessment of soil salinity is critical for the prevention of environmental deterioration especially in arid and semi-arid areas. This study introduced the fractional derivative in the pretreatment of visible and near infrared (VIS–NIR) spectroscopy. The soil samples (n = 400) collected from the Ebinur Lake Wetland, Xinjiang Uyghur Autonomous Region (XUAR), China, were used as the dataset. After measuring the spectral reflectance and salinity in the laboratory, the raw spectral reflectance was preprocessed by means of the absorbance and the fractional derivative order in the range of 0.0–2.0 order with an interval of 0.1. Two different modeling methods, namely, partial least squares regression (PLSR) and random forest (RF) with preprocessed reflectance were used for quantifying soil salinity. The results showed that more spectral characteristics were refined for the spectrum reflectance treated via fractional derivative. The validation accuracies showed that RF models performed better than those of PLSR. The most effective model was established based on RF with the 1.5 order derivative of absorbance with the optimal values of R2 (0.93), RMSE (4.57 dS m−1), and RPD (2.78 ≥ 2.50). The developed RF model was stable and accurate in the application of spectral reflectance for determining the soil salinity of the Ebinur Lake wetland. The pretreatment of fractional derivative could be useful for monitoring multiple soil parameters with higher accuracy, which could effectively help to analyze the soil salinity. PMID:29736341

Quantitative estimation of soil salinity by means of different modeling methods and visible-near infrared (VIS-NIR) spectroscopy, Ebinur Lake Wetland, Northwest China.

PubMed

Wang, Jingzhe; Ding, Jianli; Abulimiti, Aerzuna; Cai, Lianghong

2018-01-01

Soil salinization is one of the most common forms of land degradation. The detection and assessment of soil salinity is critical for the prevention of environmental deterioration especially in arid and semi-arid areas. This study introduced the fractional derivative in the pretreatment of visible and near infrared (VIS-NIR) spectroscopy. The soil samples ( n  = 400) collected from the Ebinur Lake Wetland, Xinjiang Uyghur Autonomous Region (XUAR), China, were used as the dataset. After measuring the spectral reflectance and salinity in the laboratory, the raw spectral reflectance was preprocessed by means of the absorbance and the fractional derivative order in the range of 0.0-2.0 order with an interval of 0.1. Two different modeling methods, namely, partial least squares regression (PLSR) and random forest (RF) with preprocessed reflectance were used for quantifying soil salinity. The results showed that more spectral characteristics were refined for the spectrum reflectance treated via fractional derivative. The validation accuracies showed that RF models performed better than those of PLSR. The most effective model was established based on RF with the 1.5 order derivative of absorbance with the optimal values of R 2 (0.93), RMSE (4.57 dS m -1 ), and RPD (2.78 ≥ 2.50). The developed RF model was stable and accurate in the application of spectral reflectance for determining the soil salinity of the Ebinur Lake wetland. The pretreatment of fractional derivative could be useful for monitoring multiple soil parameters with higher accuracy, which could effectively help to analyze the soil salinity.

Magnetic field effect on blood flow of Casson fluid in axisymmetric cylindrical tube: A fractional model

NASA Astrophysics Data System (ADS)

Ali, Farhad; Sheikh, Nadeem Ahmad; Khan, Ilyas; Saqib, Muhammad

2017-02-01

The effects of magnetohydrodynamics on the blood flow when blood is represented as a Casson fluid, along with magnetic particles in a horizontal cylinder is studied. The flow is due to an oscillating pressure gradient. The Laplace and finite Hankel transforms are used to obtain the closed form solutions of the fractional partial differential equations. Effects of various parameters on the flow of both blood and magnetic particles are shown graphically. The analysis shows that, the model with fractional order derivatives bring a remarkable changes as compared to the ordinary model. The study highlights that applied magnetic field reduces the velocities of both the blood and magnetic particles.

Estimation of Supercapacitor Energy Storage Based on Fractional Differential Equations.

PubMed

Kopka, Ryszard

2017-12-22

In this paper, new results on using only voltage measurements on supercapacitor terminals for estimation of accumulated energy are presented. For this purpose, a study based on application of fractional-order models of supercapacitor charging/discharging circuits is undertaken. Parameter estimates of the models are then used to assess the amount of the energy accumulated in supercapacitor. The obtained results are compared with energy determined experimentally by measuring voltage and current on supercapacitor terminals. All the tests are repeated for various input signal shapes and parameters. Very high consistency between estimated and experimental results fully confirm suitability of the proposed approach and thus applicability of the fractional calculus to modelling of supercapacitor energy storage.

A physically based connection between fractional calculus and fractal geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Butera, Salvatore, E-mail: sg.butera@gmail.com; Di Paola, Mario, E-mail: mario.dipaola@unipa.it

2014-11-15

We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose long memory and hereditary properties are mathematically modelled by differential operators of non integer order. Dealing with the relevant example of a viscous fluid seeping through a fractal shaped porous medium, we show that, once a physical phenomenon or process takes place on an underlying fractal geometry, then a power-law naturally comes up in ruling its evolution, whose order is related to the anomalousmore » dimension of such geometry, as well as to the model used to describe the physics involved. By linearizing the non linear dependence of the response of the system at hand to a proper forcing action then, exploiting the Boltzmann superposition principle, a fractional differential equation is found, describing the dynamics of the system itself. The order of such equation is again related to the anomalous dimension of the underlying geometry.« less

Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry.

PubMed

Miller, Jacob; Miyake, Akimasa

2018-04-27

An emerging insight is that ground states of symmetry-protected topological orders (SPTOs) possess latent computational complexity in terms of their many-body entanglement. By introducing a fractional symmetry of SPTO, which requires the invariance under 3-colorable symmetries of a lattice, we prove that every renormalization fixed-point state of 2D (Z_{2})^{m} SPTO with fractional symmetry can be utilized for universal quantum computation using only Pauli measurements, as long as it belongs to a nontrivial 2D SPTO phase. Our infinite family of fixed-point states may serve as a base model to demonstrate the idea of a "quantum computational phase" of matter, whose states share universal computational complexity ubiquitously.

Bifurcation and chaos of a new discrete fractional-order logistic map

NASA Astrophysics Data System (ADS)

Ji, YuanDong; Lai, Li; Zhong, SuChuan; Zhang, Lu

2018-04-01

The fractional-order discrete maps with chaotic behaviors based on the theory of ;fractional difference; are proposed in recent years. In this paper, instead of using fractional difference, a new fractionalized logistic map is proposed based on the numerical algorithm of fractional differentiation definition. The bifurcation diagrams of this map with various differential orders are given by numerical simulation. The simulation results show that the fractional-order logistic map derived in this manner holds rich dynamical behaviors because of its memory effect. In addition, new types of behaviors of bifurcation and chaos are found, which are different from those of the integer-order and the previous fractional-order logistic maps.

A bilayer Double Semion model with symmetry-enriched topological order

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ortiz, L., E-mail: lauraort@ucm.es; Martin-Delgado, M.A.

2016-12-15

We construct a new model of two-dimensional quantum spin systems that combines intrinsic topological orders and a global symmetry called flavour symmetry. It is referred as the bilayer Doubled Semion model (bDS) and is an instance of symmetry-enriched topological order. A honeycomb bilayer lattice is introduced to combine a Double Semion Topological Order with a global spin–flavour symmetry to get the fractionalization of its quasiparticles. The bDS model exhibits non-trivial braiding self-statistics of excitations and its dual model constitutes a Symmetry-Protected Topological Order with novel edge states. This dual model gives rise to a bilayer Non-Trivial Paramagnet that is invariantmore » under the flavour symmetry and the well-known spin flip symmetry.« less

Cascading failures in interdependent systems under a flow redistribution model

NASA Astrophysics Data System (ADS)

Zhang, Yingrui; Arenas, Alex; Yaǧan, Osman

2018-02-01

Robustness and cascading failures in interdependent systems has been an active research field in the past decade. However, most existing works use percolation-based models where only the largest component of each network remains functional throughout the cascade. Although suitable for communication networks, this assumption fails to capture the dependencies in systems carrying a flow (e.g., power systems, road transportation networks), where cascading failures are often triggered by redistribution of flows leading to overloading of lines. Here, we consider a model consisting of systems A and B with initial line loads and capacities given by {LA,i,CA ,i} i =1 n and {LB,i,CB ,i} i =1 n, respectively. When a line fails in system A , a fraction of its load is redistributed to alive lines in B , while remaining (1 -a ) fraction is redistributed equally among all functional lines in A ; a line failure in B is treated similarly with b giving the fraction to be redistributed to A . We give a thorough analysis of cascading failures of this model initiated by a random attack targeting p1 fraction of lines in A and p2 fraction in B . We show that (i) the model captures the real-world phenomenon of unexpected large scale cascades and exhibits interesting transition behavior: the final collapse is always first order, but it can be preceded by a sequence of first- and second-order transitions; (ii) network robustness tightly depends on the coupling coefficients a and b , and robustness is maximized at non-trivial a ,b values in general; (iii) unlike most existing models, interdependence has a multifaceted impact on system robustness in that interdependency can lead to an improved robustness for each individual network.

Cascading failures in interdependent systems under a flow redistribution model.

PubMed

Zhang, Yingrui; Arenas, Alex; Yağan, Osman

2018-02-01

Robustness and cascading failures in interdependent systems has been an active research field in the past decade. However, most existing works use percolation-based models where only the largest component of each network remains functional throughout the cascade. Although suitable for communication networks, this assumption fails to capture the dependencies in systems carrying a flow (e.g., power systems, road transportation networks), where cascading failures are often triggered by redistribution of flows leading to overloading of lines. Here, we consider a model consisting of systems A and B with initial line loads and capacities given by {L_{A,i},C_{A,i}}_{i=1}^{n} and {L_{B,i},C_{B,i}}_{i=1}^{n}, respectively. When a line fails in system A, a fraction of its load is redistributed to alive lines in B, while remaining (1-a) fraction is redistributed equally among all functional lines in A; a line failure in B is treated similarly with b giving the fraction to be redistributed to A. We give a thorough analysis of cascading failures of this model initiated by a random attack targeting p_{1} fraction of lines in A and p_{2} fraction in B. We show that (i) the model captures the real-world phenomenon of unexpected large scale cascades and exhibits interesting transition behavior: the final collapse is always first order, but it can be preceded by a sequence of first- and second-order transitions; (ii) network robustness tightly depends on the coupling coefficients a and b, and robustness is maximized at non-trivial a,b values in general; (iii) unlike most existing models, interdependence has a multifaceted impact on system robustness in that interdependency can lead to an improved robustness for each individual network.

Anomalous Diffusion Measured by a Twice-Refocused Spin Echo Pulse Sequence: Analysis Using Fractional Order Calculus

PubMed Central

2011-01-01

Purpose To theoretically develop and experimentally validate a formulism based on a fractional order calculus (FC) diffusion model to characterize anomalous diffusion in brain tissues measured with a twice-refocused spin-echo (TRSE) pulse sequence. Materials and Methods The FC diffusion model is the fractional order generalization of the Bloch-Torrey equation. Using this model, an analytical expression was derived to describe the diffusion-induced signal attenuation in a TRSE pulse sequence. To experimentally validate this expression, a set of diffusion-weighted (DW) images was acquired at 3 Tesla from healthy human brains using a TRSE sequence with twelve b-values ranging from 0 to 2,600 s/mm2. For comparison, DW images were also acquired using a Stejskal-Tanner diffusion gradient in a single-shot spin-echo echo planar sequence. For both datasets, a Levenberg-Marquardt fitting algorithm was used to extract three parameters: diffusion coefficient D, fractional order derivative in space β, and a spatial parameter μ (in units of μm). Using adjusted R-squared values and standard deviations, D, β and μ values and the goodness-of-fit in three specific regions of interest (ROI) in white matter, gray matter, and cerebrospinal fluid were evaluated for each of the two datasets. In addition, spatially resolved parametric maps were assessed qualitatively. Results The analytical expression for the TRSE sequence, derived from the FC diffusion model, accurately characterized the diffusion-induced signal loss in brain tissues at high b-values. In the selected ROIs, the goodness-of-fit and standard deviations for the TRSE dataset were comparable with the results obtained from the Stejskal-Tanner dataset, demonstrating the robustness of the FC model across multiple data acquisition strategies. Qualitatively, the D, β, and μ maps from the TRSE dataset exhibited fewer artifacts, reflecting the improved immunity to eddy currents. Conclusion The diffusion-induced signal attenuation in a TRSE pulse sequence can be described by an FC diffusion model at high b-values. This model performs equally well for data acquired from the human brain tissues with a TRSE pulse sequence or a conventional Stejskal-Tanner sequence. PMID:21509877

Anomalous diffusion measured by a twice-refocused spin echo pulse sequence: analysis using fractional order calculus.

PubMed

Gao, Qing; Srinivasan, Girish; Magin, Richard L; Zhou, Xiaohong Joe

2011-05-01

To theoretically develop and experimentally validate a formulism based on a fractional order calculus (FC) diffusion model to characterize anomalous diffusion in brain tissues measured with a twice-refocused spin-echo (TRSE) pulse sequence. The FC diffusion model is the fractional order generalization of the Bloch-Torrey equation. Using this model, an analytical expression was derived to describe the diffusion-induced signal attenuation in a TRSE pulse sequence. To experimentally validate this expression, a set of diffusion-weighted (DW) images was acquired at 3 Tesla from healthy human brains using a TRSE sequence with twelve b-values ranging from 0 to 2600 s/mm(2). For comparison, DW images were also acquired using a Stejskal-Tanner diffusion gradient in a single-shot spin-echo echo planar sequence. For both datasets, a Levenberg-Marquardt fitting algorithm was used to extract three parameters: diffusion coefficient D, fractional order derivative in space β, and a spatial parameter μ (in units of μm). Using adjusted R-squared values and standard deviations, D, β, and μ values and the goodness-of-fit in three specific regions of interest (ROIs) in white matter, gray matter, and cerebrospinal fluid, respectively, were evaluated for each of the two datasets. In addition, spatially resolved parametric maps were assessed qualitatively. The analytical expression for the TRSE sequence, derived from the FC diffusion model, accurately characterized the diffusion-induced signal loss in brain tissues at high b-values. In the selected ROIs, the goodness-of-fit and standard deviations for the TRSE dataset were comparable with the results obtained from the Stejskal-Tanner dataset, demonstrating the robustness of the FC model across multiple data acquisition strategies. Qualitatively, the D, β, and μ maps from the TRSE dataset exhibited fewer artifacts, reflecting the improved immunity to eddy currents. The diffusion-induced signal attenuation in a TRSE pulse sequence can be described by an FC diffusion model at high b-values. This model performs equally well for data acquired from the human brain tissues with a TRSE pulse sequence or a conventional Stejskal-Tanner sequence. Copyright © 2011 Wiley-Liss, Inc.

Phase-field simulations of coherent precipitate morphologies and coarsening kinetics

NASA Astrophysics Data System (ADS)

Vaithyanathan, Venugopalan

2002-09-01

The primary aim of this research is to enhance the fundamental understanding of coherent precipitation reactions in advanced metallic alloys. The emphasis is on a particular class of precipitation reactions which result in ordered intermetallic precipitates embedded in a disordered matrix. These precipitation reactions underlie the development of high-temperature Ni-base superalloys and ultra-light aluminum alloys. Phase-field approach, which has emerged as the method of choice for modeling microstructure evolution, is employed for this research with the focus on factors that control the precipitate morphologies and coarsening kinetics, such as precipitate volume fractions and lattice mismatch between precipitates and matrix. Two types of alloy systems are considered. The first involves L1 2 ordered precipitates in a disordered cubic matrix, in an attempt to model the gamma' precipitates in Ni-base superalloys and delta' precipitates in Al-Li alloys. The effect of volume fraction on coarsening kinetics of gamma' precipitates was investigated using two-dimensional (2D) computer simulations. With increase in volume fraction, larger fractions of precipitates were found to have smaller aspect ratios in the late stages of coarsening, and the precipitate size distributions became wider and more positively skewed. The most interesting result was associated with the effect of volume fraction on the coarsening rate constant. Coarsening rate constant as a function of volume fraction extracted from the cubic growth law of average half-edge length was found to exhibit three distinct regimes: anomalous behavior or decreasing rate constant with volume fraction at small volume fractions ( ≲ 20%), volume fraction independent or constant behavior for intermediate volume fractions (˜20--50%), and the normal behavior or increasing rate constant with volume fraction for large volume fractions ( ≳ 50%). The second alloy system considered was Al-Cu with the focus on understanding precipitation of metastable tetragonal theta'-Al 2Cu in a cubic Al solid solution matrix. In collaboration with Chris Wolverton at Ford Motor Company, a multiscale model, which involves a novel combination of first-principles atomistic calculations with a mesoscale phase-field microstructure model, was developed. Reliable energetics in the form of bulk free energy, interfacial energy and parameters for calculating the elastic energy were obtained using accurate first-principles calculations. (Abstract shortened by UMI.)

Initialization of a fractional order identification algorithm applied for Lithium-ion battery modeling in time domain

NASA Astrophysics Data System (ADS)

Nasser Eddine, Achraf; Huard, Benoît; Gabano, Jean-Denis; Poinot, Thierry

2018-06-01

This paper deals with the initialization of a non linear identification algorithm used to accurately estimate the physical parameters of Lithium-ion battery. A Randles electric equivalent circuit is used to describe the internal impedance of the battery. The diffusion phenomenon related to this modeling is presented using a fractional order method. The battery model is thus reformulated into a transfer function which can be identified through Levenberg-Marquardt algorithm to ensure the algorithm's convergence to the physical parameters. An initialization method is proposed in this paper by taking into account previously acquired information about the static and dynamic system behavior. The method is validated using noisy voltage response, while precision of the final identification results is evaluated using Monte-Carlo method.

Improved model reduction and tuning of fractional-order PI(λ)D(μ) controllers for analytical rule extraction with genetic programming.

PubMed

Das, Saptarshi; Pan, Indranil; Das, Shantanu; Gupta, Amitava

2012-03-01

Genetic algorithm (GA) has been used in this study for a new approach of suboptimal model reduction in the Nyquist plane and optimal time domain tuning of proportional-integral-derivative (PID) and fractional-order (FO) PI(λ)D(μ) controllers. Simulation studies show that the new Nyquist-based model reduction technique outperforms the conventional H(2)-norm-based reduced parameter modeling technique. With the tuned controller parameters and reduced-order model parameter dataset, optimum tuning rules have been developed with a test-bench of higher-order processes via genetic programming (GP). The GP performs a symbolic regression on the reduced process parameters to evolve a tuning rule which provides the best analytical expression to map the data. The tuning rules are developed for a minimum time domain integral performance index described by a weighted sum of error index and controller effort. From the reported Pareto optimal front of the GP-based optimal rule extraction technique, a trade-off can be made between the complexity of the tuning formulae and the control performance. The efficacy of the single-gene and multi-gene GP-based tuning rules has been compared with the original GA-based control performance for the PID and PI(λ)D(μ) controllers, handling four different classes of representative higher-order processes. These rules are very useful for process control engineers, as they inherit the power of the GA-based tuning methodology, but can be easily calculated without the requirement for running the computationally intensive GA every time. Three-dimensional plots of the required variation in PID/fractional-order PID (FOPID) controller parameters with reduced process parameters have been shown as a guideline for the operator. Parametric robustness of the reported GP-based tuning rules has also been shown with credible simulation examples. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

Persistence of low levels of plasma viremia and of the latent reservoir in patients under ART: A fractional-order approach

NASA Astrophysics Data System (ADS)

Pinto, Carla M. A.

2017-02-01

Low levels of viral load are found in HIV-infected patients, after many years under successful suppressive anti-retroviral therapy (ART). The factors leading to this persistence are still under debate, but it is now more or less accepted that the latent reservoir may be crucial to the maintenance of this residual viremia. In this paper, we study the role of the latent reservoir in the persistence of the latent reservoir and of the plasma viremia in a fractional-order (FO) model for HIV infection. Our model assumes that (i) the latently infected cells may undergo bystander proliferation, without active viral production, (ii) the latent cell activation rate decreases with time on ART, (iii) the productively infected cells' death rate is a function of the infected cell density. The proposed model provides new insights on the role of the latent reservoir in the persistence of the latent reservoir and of the plasma virus. Moreover, the fractional-order derivative distinguishes distinct velocities in the dynamics of the latent reservoir and of plasma virus. The later may be used to better approximations of HIV-infected patients data. To our best knowledge, this is the first FO model that deals with the role of the latent reservoir in the persistence of low levels of viremia and of the latent reservoir.

Multiswitching combination synchronisation of non-identical fractional-order chaotic systems

NASA Astrophysics Data System (ADS)

Bhat, Muzaffar Ahmad; Khan, Ayub

2018-06-01

In this paper, multiswitching combination synchronisation (MSCS) scheme has been investigated in a class of three non-identical fractional-order chaotic systems. The fractional-order Lorenz and Chen systems are taken as the drive systems. The combination of multidrive systems is then synchronised with the fractional-order Lü chaotic system. In MSCS, the state variables of the two drive systems synchronise with different state variables of the response system, simultaneously. Based on the stability of fractional-order chaotic systems, the MSCS of three fractional-order non-identical systems has been investigated. For the synchronisation of three non-identical fractional-order chaotic systems, suitable controllers have been designed. Theoretical analysis and numerical results are presented to demonstrate the validity and feasibility of the applied method.

Fractional order implementation of Integral Resonant Control - A nanopositioning application.

PubMed

San-Millan, Andres; Feliu-Batlle, Vicente; Aphale, Sumeet S

2017-10-04

By exploiting the co-located sensor-actuator arrangement in typical flexure-based piezoelectric stack actuated nanopositioners, the polezero interlacing exhibited by their axial frequency response can be transformed to a zero-pole interlacing by adding a constant feed-through term. The Integral Resonant Control (IRC) utilizes this unique property to add substantial damping to the dominant resonant mode by the use of a simple integrator implemented in closed loop. IRC used in conjunction with an integral tracking scheme, effectively reduces positioning errors introduced by modelling inaccuracies or parameter uncertainties. Over the past few years, successful application of the IRC control technique to nanopositioning systems has demonstrated performance robustness, easy tunability and versatility. The main drawback has been the relatively small positioning bandwidth achievable. This paper proposes a fractional order implementation of the classical integral tracking scheme employed in tandem with the IRC scheme to deliver damping and tracking. The fractional order integrator introduces an additional design parameter which allows desired pole-placement, resulting in superior closed loop bandwidth. Simulations and experimental results are presented to validate the theory. A 250% improvement in the achievable positioning bandwidth is observed with proposed fractional order scheme. Copyright © 2017. Published by Elsevier Ltd.

A method searching for optimum fractional order and its application in self-phase modulation induced nonlinear phase noise estimation in coherent optical fiber transmission systems

NASA Astrophysics Data System (ADS)

Huang, Chuan; Guo, Peng; Yang, Aiying; Qiao, Yaojun

2018-07-01

In single channel systems, the nonlinear phase noise only comes from the channel itself through self-phase modulation (SPM). In this paper, a fast-nonlinear effect estimation method is proposed based on fractional Fourier transformation (FrFT). The nonlinear phase noise caused by Self-phase modulation effect is accurately estimated for single model 10Gbaud OOK and RZ-QPSK signals with the fiber length range of 0-200 km and the launch power range of 1-10 mW. The pulse windowing is adopted to search the optimum fractional order for the OOK and RZ-QPSK signals. Since the nonlinear phase shift caused by the SPM effect is very small, the accurate optimum fractional order of the signal cannot be found based on the traditional method. In this paper, a new method magnifying the phase shift is proposed to get the accurate optimum order and thus the nonlinear phase shift is calculated. The simulation results agree with the theoretical analysis and the method is applicable to signals whose pulse type has the similar characteristics with Gaussian pulse.

Design and analysis of fractional order seismic transducer for displacement and acceleration measurements

NASA Astrophysics Data System (ADS)

Veeraian, Parthasarathi; Gandhi, Uma; Mangalanathan, Umapathy

2018-04-01

Seismic transducers are widely used for measurement of displacement, velocity, and acceleration. This paper presents the design of seismic transducer in the fractional domain for the measurement of displacement and acceleration. The fractional order transfer function for seismic displacement and acceleration transducer are derived using Grünwald-Letnikov derivative. Frequency response analysis of fractional order seismic displacement transducer (FOSDT) and fractional order seismic acceleration transducer (FOSAT) are carried out for different damping ratio with the different fractional order, and the maximum dynamic measurement range is identified. The results demonstrate that fractional order seismic transducer has increased dynamic measurement range and less phase distortion as compared to the conventional seismic transducer even with a lower damping ratio. Time response of FOSDT and FOSAT are derived analytically in terms of Mittag-Leffler function, the effect of fractional behavior in the time domain is evaluated from the impulse and step response. The fractional order system is found to have significantly reduced overshoot as compared to the conventional transducer. The fractional order seismic transducer design proposed in this paper is illustrated with a design example for FOSDT and FOSAT. Finally, an electrical equivalent of FOSDT and FOSAT is considered, and its frequency response is found to be in close agreement with the proposed fractional order seismic transducer.

A Class of time-fractional hemivariational inequalities with application to frictional contact problem

NASA Astrophysics Data System (ADS)

Zeng, Shengda; Migórski, Stanisław

2018-03-01

In this paper a class of elliptic hemivariational inequalities involving the time-fractional order integral operator is investigated. Exploiting the Rothe method and using the surjectivity of multivalued pseudomonotone operators, a result on existence of solution to the problem is established. Then, this abstract result is applied to provide a theorem on the weak solvability of a fractional viscoelastic contact problem. The process is quasistatic and the constitutive relation is modeled with the fractional Kelvin-Voigt law. The friction and contact conditions are described by the Clarke generalized gradient of nonconvex and nonsmooth functionals. The variational formulation of this problem leads to a fractional hemivariational inequality.

Design of broadband time-domain impedance boundary conditions using the oscillatory-diffusive representation of acoustical models.

PubMed

Monteghetti, Florian; Matignon, Denis; Piot, Estelle; Pascal, Lucas

2016-09-01

A methodology to design broadband time-domain impedance boundary conditions (TDIBCs) from the analysis of acoustical models is presented. The derived TDIBCs are recast exclusively as first-order differential equations, well-suited for high-order numerical simulations. Broadband approximations are yielded from an elementary linear least squares optimization that is, for most models, independent of the absorbing material geometry. This methodology relies on a mathematical technique referred to as the oscillatory-diffusive (or poles and cuts) representation, and is applied to a wide range of acoustical models, drawn from duct acoustics and outdoor sound propagation, which covers perforates, semi-infinite ground layers, as well as cavities filled with a porous medium. It is shown that each of these impedance models leads to a different TDIBC. Comparison with existing numerical models, such as multi-pole or extended Helmholtz resonator, provides insights into their suitability. Additionally, the broadly-applicable fractional polynomial impedance models are analyzed using fractional calculus.

Invariant domain watermarking using heaviside function of order alpha and fractional Gaussian field.

PubMed

Abbasi, Almas; Woo, Chaw Seng; Ibrahim, Rabha Waell; Islam, Saeed

2015-01-01

Digital image watermarking is an important technique for the authentication of multimedia content and copyright protection. Conventional digital image watermarking techniques are often vulnerable to geometric distortions such as Rotation, Scaling, and Translation (RST). These distortions desynchronize the watermark information embedded in an image and thus disable watermark detection. To solve this problem, we propose an RST invariant domain watermarking technique based on fractional calculus. We have constructed a domain using Heaviside function of order alpha (HFOA). The HFOA models the signal as a polynomial for watermark embedding. The watermark is embedded in all the coefficients of the image. We have also constructed a fractional variance formula using fractional Gaussian field. A cross correlation method based on the fractional Gaussian field is used for watermark detection. Furthermore the proposed method enables blind watermark detection where the original image is not required during the watermark detection thereby making it more practical than non-blind watermarking techniques. Experimental results confirmed that the proposed technique has a high level of robustness.

Invariant Domain Watermarking Using Heaviside Function of Order Alpha and Fractional Gaussian Field

PubMed Central

Abbasi, Almas; Woo, Chaw Seng; Ibrahim, Rabha Waell; Islam, Saeed

2015-01-01

Digital image watermarking is an important technique for the authentication of multimedia content and copyright protection. Conventional digital image watermarking techniques are often vulnerable to geometric distortions such as Rotation, Scaling, and Translation (RST). These distortions desynchronize the watermark information embedded in an image and thus disable watermark detection. To solve this problem, we propose an RST invariant domain watermarking technique based on fractional calculus. We have constructed a domain using Heaviside function of order alpha (HFOA). The HFOA models the signal as a polynomial for watermark embedding. The watermark is embedded in all the coefficients of the image. We have also constructed a fractional variance formula using fractional Gaussian field. A cross correlation method based on the fractional Gaussian field is used for watermark detection. Furthermore the proposed method enables blind watermark detection where the original image is not required during the watermark detection thereby making it more practical than non-blind watermarking techniques. Experimental results confirmed that the proposed technique has a high level of robustness. PMID:25884854

Axi-symmetric generalized thermoelastic diffusion problem with two-temperature and initial stress under fractional order heat conduction

NASA Astrophysics Data System (ADS)

Deswal, Sunita; Kalkal, Kapil Kumar; Sheoran, Sandeep Singh

2016-09-01

A mathematical model of fractional order two-temperature generalized thermoelasticity with diffusion and initial stress is proposed to analyze the transient wave phenomenon in an infinite thermoelastic half-space. The governing equations are derived in cylindrical coordinates for a two dimensional axi-symmetric problem. The analytical solution is procured by employing the Laplace and Hankel transforms for time and space variables respectively. The solutions are investigated in detail for a time dependent heat source. By using numerical inversion method of integral transforms, we obtain the solutions for displacement, stress, temperature and diffusion fields in physical domain. Computations are carried out for copper material and displayed graphically. The effect of fractional order parameter, two-temperature parameter, diffusion, initial stress and time on the different thermoelastic and diffusion fields is analyzed on the basis of analytical and numerical results. Some special cases have also been deduced from the present investigation.

Global Mittag-Leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons.

PubMed

Yang, Xujun; Li, Chuandong; Song, Qiankun; Chen, Jiyang; Huang, Junjian

2018-05-04

This paper talks about the stability and synchronization problems of fractional-order quaternion-valued neural networks (FQVNNs) with linear threshold neurons. On account of the non-commutativity of quaternion multiplication resulting from Hamilton rules, the FQVNN models are separated into four real-valued neural network (RVNN) models. Consequently, the dynamic analysis of FQVNNs can be realized by investigating the real-valued ones. Based on the method of M-matrix, the existence and uniqueness of the equilibrium point of the FQVNNs are obtained without detailed proof. Afterwards, several sufficient criteria ensuring the global Mittag-Leffler stability for the unique equilibrium point of the FQVNNs are derived by applying the Lyapunov direct method, the theory of fractional differential equation, the theory of matrix eigenvalue, and some inequality techniques. In the meanwhile, global Mittag-Leffler synchronization for the drive-response models of the addressed FQVNNs are investigated explicitly. Finally, simulation examples are designed to verify the feasibility and availability of the theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.

A Fractional Differential Kinetic Equation and Applications to Modelling Bursts in Turbulent Nonlinear Space Plasmas

NASA Astrophysics Data System (ADS)

Watkins, N. W.; Rosenberg, S.; Sanchez, R.; Chapman, S. C.; Credgington, D.

2008-12-01

Since the 1960s Mandelbrot has advocated the use of fractals for the description of the non-Euclidean geometry of many aspects of nature. In particular he proposed two kinds of model to capture persistence in time (his Joseph effect, common in hydrology and with fractional Brownian motion as the prototype) and/or prone to heavy tailed jumps (the Noah effect, typical of economic indices, for which he proposed Lévy flights as an exemplar). Both effects are now well demonstrated in space plasmas, notably in the turbulent solar wind. Models have, however, typically emphasised one of the Noah and Joseph parameters (the Lévy exponent μ and the temporal exponent β) at the other's expense. I will describe recent work in which we studied a simple self-affine stable model-linear fractional stable motion, LFSM, which unifies both effects and present a recently-derived diffusion equation for LFSM. This replaces the second order spatial derivative in the equation of fBm with a fractional derivative of order μ, but retains a diffusion coefficient with a power law time dependence rather than a fractional derivative in time. I will also show work in progress using an LFSM model and simple analytic scaling arguments to study the problem of the area between an LFSM curve and a threshold. This problem relates to the burst size measure introduced by Takalo and Consolini into solar-terrestrial physics and further studied by Freeman et al [PRE, 2000] on solar wind Poynting flux near L1. We test how expressions derived by other authors generalise to the non-Gaussian, constant threshold problem. Ongoing work on extension of these LFSM results to multifractals will also be discussed.

New Operational Matrices for Solving Fractional Differential Equations on the Half-Line

PubMed Central

2015-01-01

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques. PMID:25996369

New operational matrices for solving fractional differential equations on the half-line.

PubMed

Bhrawy, Ali H; Taha, Taha M; Alzahrani, Ebraheem O; Alzahrani, Ebrahim O; Baleanu, Dumitru; Alzahrani, Abdulrahim A

2015-01-01

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques.

Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials

PubMed Central

Khan, Rahmat Ali; Tajadodi, Haleh; Johnston, Sarah Jane

2014-01-01

In this paper we propose the Bernstein polynomials to achieve the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. We use operational matrices of fractional integration and multiplication of Bernstein polynomials, which turns the nonlinear fractional-order Brusselator system to a system of algebraic equations. Two illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques. PMID:25485293

Structural characterization of the packings of granular regular polygons.

PubMed

Wang, Chuncheng; Dong, Kejun; Yu, Aibing

2015-12-01

By using a recently developed method for discrete modeling of nonspherical particles, we simulate the random packings of granular regular polygons with three to 11 edges under gravity. The effects of shape and friction on the packing structures are investigated by various structural parameters, including packing fraction, the radial distribution function, coordination number, Voronoi tessellation, and bond-orientational order. We find that packing fraction is generally higher for geometrically nonfrustrated regular polygons, and can be increased by the increase of edge number and decrease of friction. The changes of packing fraction are linked with those of the microstructures, such as the variations of the translational and orientational orders and local configurations. In particular, the free areas of Voronoi tessellations (which are related to local packing fractions) can be described by log-normal distributions for all polygons. The quantitative analyses establish a clearer picture for the packings of regular polygons.

An actual load forecasting methodology by interval grey modeling based on the fractional calculus.

PubMed

Yang, Yang; Xue, Dingyü

2017-07-17

The operation processes for thermal power plant are measured by the real-time data, and a large number of historical interval data can be obtained from the dataset. Within defined periods of time, the interval information could provide important information for decision making and equipment maintenance. Actual load is one of the most important parameters, and the trends hidden in the historical data will show the overall operation status of the equipments. However, based on the interval grey parameter numbers, the modeling and prediction process is more complicated than the one with real numbers. In order not lose any information, the geometric coordinate features are used by the coordinates of area and middle point lines in this paper, which are proved with the same information as the original interval data. The grey prediction model for interval grey number by the fractional-order accumulation calculus is proposed. Compared with integer-order model, the proposed method could have more freedom with better performance for modeling and prediction, which can be widely used in the modeling process and prediction for the small amount interval historical industry sequence samples. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Modeling of Atmospheric Turbulence as Disturbances for Control Design and Evaluation of High Speed Propulsion Systems

NASA Technical Reports Server (NTRS)

Kopasakis, George

2010-01-01

Atmospheric turbulence models are necessary for the design of both inlet/engine and flight controls, as well as for studying integrated couplings between the propulsion and the vehicle structural dynamics for supersonic vehicles. Models based on the Kolmogorov spectrum have been previously utilized to model atmospheric turbulence. In this paper, a more accurate model is developed in its representative fractional order form, typical of atmospheric disturbances. This is accomplished by first scaling the Kolmogorov spectral to convert them into finite energy von Karman forms. Then a generalized formulation is developed in frequency domain for these scale models that approximates the fractional order with the products of first order transfer functions. Given the parameters describing the conditions of atmospheric disturbances and utilizing the derived formulations, the objective is to directly compute the transfer functions that describe these disturbances for acoustic velocity, temperature, pressure and density. Utilizing these computed transfer functions and choosing the disturbance frequencies of interest, time domain simulations of these representative atmospheric turbulences can be developed. These disturbance representations are then used to first develop considerations for disturbance rejection specifications for the design of the propulsion control system, and then to evaluate the closed-loop performance.

A Simulator for the Respiratory Tree in Healthy Subjects Derived from Continued Fractions Expansions

NASA Astrophysics Data System (ADS)

Muntean, Ionuţ; Ionescu, Clara; Naşcu, Ioan

2009-04-01

Taking into account the self-similar recurrent geometrical structure of the human respiratory tree, the total respiratory impedance can be represented using an electrical equivalent of a ladder network model. In this paper, the parameters of the respiratory tree are employed in simulation, based on clinical insight and morphology. Once the transfer function of the total input impedance model is calculated, it is further interpreted in its continued fraction expansion form. The purpose is to compare the ladder network structure with the continuous fraction expansion form of the impedance. The results are supporting the theory of fractional-order impedance appearance (also known as constant-phase behaviour) and help understanding the mathematical and morphological basis for constructing a physiology-based simulator of the human lungs.

Sudden spreading of infections in an epidemic model with a finite seed fraction

NASA Astrophysics Data System (ADS)

Hasegawa, Takehisa; Nemoto, Koji

2018-03-01

We study a simple case of the susceptible-weakened-infected-removed model in regular random graphs in a situation where an epidemic starts from a finite fraction of initially infected nodes (seeds). Previous studies have shown that, assuming a single seed, this model exhibits a kind of discontinuous transition at a certain value of infection rate. Performing Monte Carlo simulations and evaluating approximate master equations, we find that the present model has two critical infection rates for the case with a finite seed fraction. At the first critical rate the system shows a percolation transition of clusters composed of removed nodes, and at the second critical rate, which is larger than the first one, a giant cluster suddenly grows and the order parameter jumps even though it has been already rising. Numerical evaluation of the master equations shows that such sudden epidemic spreading does occur if the degree of the underlying network is large and the seed fraction is small.

3-D Forward modeling of Induced Polarization Effects of Transient Electromagnetic Method

NASA Astrophysics Data System (ADS)

Wu, Y.; Ji, Y.; Guan, S.; Li, D.; Wang, A.

2017-12-01

In transient electromagnetic (TEM) detection, Induced polarization (IP) effects are so important that they cannot be ignored. The authors simulate the three-dimensional (3-D) induced polarization effects in time-domain directly by applying the finite-difference time-domain method (FDTD) based on Cole-Cole model. Due to the frequency dispersion characteristics of the electrical conductivity, the computations of convolution in the generalized Ohm's law of fractional order system makes the forward modeling particularly complicated. Firstly, we propose a method to approximate the fractional order function of Cole-Cole model using a lower order rational transfer function based on error minimum theory in the frequency domain. In this section, two auxiliary variables are introduced to transform nonlinear least square fitting problem of the fractional order system into a linear programming problem, thus avoiding having to solve a system of equations and nonlinear problems. Secondly, the time-domain expression of Cole-Cole model is obtained by using Inverse Laplace transform. Then, for the calculation of Ohm's law, we propose an e-index auxiliary equation of conductivity to transform the convolution to non-convolution integral; in this section, the trapezoid rule is applied to compute the integral. We then substitute the recursion equation into Maxwell's equations to derive the iterative equations of electromagnetic field using the FDTD method. Finally, we finish the stimulation of 3-D model and evaluate polarization parameters. The results are compared with those obtained from the digital filtering solution of the analytical equation in the homogeneous half space, as well as with the 3-D model results from the auxiliary ordinary differential equation method (ADE). Good agreements are obtained across the three methods. In terms of the 3-D model, the proposed method has higher efficiency and lower memory requirements as execution times and memory usage were reduced by 20% compared with ADE method.

Viscoelastic properties of uncured resin composites: Dynamic oscillatory shear test and fractional derivative model.

PubMed

Petrovic, Ljubomir M; Zorica, Dusan M; Stojanac, Igor Lj; Krstonosic, Veljko S; Hadnadjev, Miroslav S; Janev, Marko B; Premovic, Milica T; Atanackovic, Teodor M

2015-08-01

In this study we analyze viscoelastic properties of three flowable (Wave, Wave MV, Wave HV) and one universal hybrid resin (Ice) composites, prior to setting. We developed a mathematical model containing fractional derivatives in order to describe their properties. Isothermal experimental study was conducted on a rheometer with parallel plates. In dynamic oscillatory shear test, storage and loss modulus, as well as the complex viscosity where determined. We assumed four different fractional viscoelastic models, each belonging to one particular class, derivable from distributed-order fractional constitutive equation. The restrictions following from the Second law of thermodynamics are imposed on each model. The optimal parameters corresponding to each model are obtained by minimizing the error function that takes into account storage and loss modulus, thus obtaining the best fit to the experimental data. In the frequency range considered, we obtained that for Wave HV and Wave MV there exist a critical frequency for which loss and storage modulus curves intersect, defining a boundary between two different types of behavior: one in which storage modulus is larger than loss modulus and the other in which the situation is opposite. Loss and storage modulus curves for Ice and Wave do not show this type of behavior, having either elastic, or viscous effects dominating in entire frequency range considered. The developed models may be used to predict behavior of four tested composites in different flow conditions (different deformation speed), thus helping to estimate optimal handling characteristics for specific clinical applications. Copyright © 2015 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

The Origins of Order: Self-Organization and Selection in Evolution

NASA Astrophysics Data System (ADS)

Kauffman, Stuart A.

The following sections are included: * Introduction * Fitness Landscapes in Sequence Space * The NK Model of Rugged Fitness Landscapes * The NK Model of Random Epistatic Interactions * The Rank Order Statistics on K = N - 1 Random Landscapes * The number of local optima is very large * The expected fraction of fitter 1-mutant neighbors dwindles by 1/2 on each improvement step * Walks to local optima are short and vary as a logarithmic function of N * The expected time to reach an optimum is proportional to the dimensionality of the space * The ratio of accepted to tried mutations scales as lnN/N * Any genotype can only climb to a small fraction of the local optima * A small fraction of the genotypes can climb to any one optimum * Conflicting constraints cause a "complexity catastrophe": as complexity increase accessible adaptive peaks fall toward the mean fitness * The "Tunable" NK Family of Correlated Landscapes * Other Combinatorial Optimization Problems and Their Landscapes * Summary * References

A fractional-order accumulative regularization filter for force reconstruction

NASA Astrophysics Data System (ADS)

Wensong, Jiang; Zhongyu, Wang; Jing, Lv

2018-02-01

The ill-posed inverse problem of the force reconstruction comes from the influence of noise to measured responses and results in an inaccurate or non-unique solution. To overcome this ill-posedness, in this paper, the transfer function of the reconstruction model is redefined by a Fractional order Accumulative Regularization Filter (FARF). First, the measured responses with noise are refined by a fractional-order accumulation filter based on a dynamic data refresh strategy. Second, a transfer function, generated by the filtering results of the measured responses, is manipulated by an iterative Tikhonov regularization with a serious of iterative Landweber filter factors. Third, the regularization parameter is optimized by the Generalized Cross-Validation (GCV) to improve the ill-posedness of the force reconstruction model. A Dynamic Force Measurement System (DFMS) for the force reconstruction is designed to illustrate the application advantages of our suggested FARF method. The experimental result shows that the FARF method with r = 0.1 and α = 20, has a PRE of 0.36% and an RE of 2.45%, is superior to other cases of the FARF method and the traditional regularization methods when it comes to the dynamic force reconstruction.

Order reduction of z-transfer functions via multipoint Jordan continued-fraction expansion

NASA Technical Reports Server (NTRS)

Lee, Ying-Chin; Hwang, Chyi; Shieh, Leang S.

1992-01-01

The order reduction problem of z-transfer functions is solved by using the multipoint Jordan continued-fraction expansion (MJCFE) technique. An efficient algorithm that does not require the use of complex algebra is presented for obtaining an MJCFE from a stable z-transfer function with expansion points selected from the unit circle and/or the positive real axis of the z-plane. The reduced-order models are exactly the multipoint Pade approximants of the original system and, therefore, they match the (weighted) time-moments of the impulse response and preserve the frequency responses of the system at some characteristic frequencies, such as gain crossover frequency, phase crossover frequency, bandwidth, etc.

Position control of an industrial robot using fractional order controller

NASA Astrophysics Data System (ADS)

Clitan, Iulia; Muresan, Vlad; Abrudean, Mihail; Clitan, Andrei; Miron, Radu

2017-02-01

This paper presents the design of a control structure that ensures no overshoot for the movement of an industrial robot, used for the evacuation of round steel blocks from inside a rotary hearth furnace. First, a mathematical model for the positioning system is derived from a set of experimental data, and further, the paper focuses on obtaining a PID type controller, using the relay method as tuning method in order to obtain a stable closed loop system. The controller parameters are further tuned in order to achieve the imposed set of performances for the positioning of the industrial robot through computer simulation, using trial and error method. Further, a fractional - order PID controller is obtained in order to improve the control signal variation, so as to fit within the range of unified current's variation, 4 to 20 mA.

Control of Initialized Fractional-Order Systems

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Lorenzo, Carl F.

2004-01-01

Fractional-Order systems, or systems containing fractional derivatives and integrals, have been studied by many in the engineering area. Additionally, very readable discussions, devoted specifically to the subject, are presented by Oldham and Spanier, Miller and Ross, and Pudlubny (1999a). It should be noted that there are a growing number of physical systems whose behavior can be compactly described using fractional system theory. Of specific interest to electrical engineers are long lines, electrochemical processes, dielectric polarization, colored noise, viscoelastic materials, and chaos. With the growing number of applications, it is important to establish a theory of control for these fractional-order systems, and for the potential use of fractional-order systems as feedback compensators. This topic is addressed in this paper. The first section discusses the control of fractional-order systems using a vector space representation, where initialization is included in the discussion. It should be noted that Bagley and Calico and Padovan and Sawicki both present a fractional state-space representation, which do not include the important historic effects. Incorporation of these effects based on the initialized fractional calculus is presented . The control methods presented in this paper are based on the initialized fractional order system theory. The second section presents an input-output approach. Some of the problems encountered in these sections are: a) the need to introduce a new complex plane to study the dynamics of fractional-order systems, b) the need to properly define the Laplace transform of the fractional derivative, and c) the proper inclusion of the initialization response in the system and control formulation. Following this, the next section generalizes the proportional-plus-integral-control (PI-control) and PID-control (PI-plus- derivative) concepts using fractional integrals. This is then further generalized using general fractional- order compensators. Finally the compensator concept is generalized by the use of a continuum of fractions in the compensator via the concept of order-distributions. The last section introduces fractional feedback in discrete-time.

Fractional Models Simulating Non-Fickian Behavior in Four-Stage Single-Well Push-Pull Tests

NASA Astrophysics Data System (ADS)

Chen, Kewei; Zhan, Hongbin; Yang, Qiang

2017-11-01

Four-stage single-well push-pull (SWPP) tracer tests, including injection, chasing, resting, and pumping, were conducted in a fractured aquifer at Newark basin. An anomalous transport phenomenon observed in the SWPP tests is the linear decline of breakthrough curves (BTCs) at late time with slope of -1.8 in log-log plots. A time-dependent fractional model is developed to interpret the anomalous transport behavior. This model considers a time-dependent power law memory function and a time-dependent fractional advection-dispersion operator. The fractional advection-dispersion equations (fADE) are solved in a radial coordinate system using the implicit Euler method. A semi-analytical solution of the first-order rate-limited mobile-immobile model (FORMIM) is derived for comparison. It is found that both the nonlocal transport in time and space can produce the long-tailed BTC. A smaller time-fractional or space-fractional index leads to a lower peak concentration and a larger late-time slope. The mass distribution of the fractional-in-space (FS) model exhibits power law decline at the leading plume edge. Early breakthrough during pumping is not observed because the mobile mass at the start of pumping is nonzero and more concentrated near the wellbore. The capacity ratio is an important factor that affects the peak concentration. A larger capacity ratio leads to greater peak concentration. A smaller time-fractional index in the injection, chasing, or resting stage will move the BTC downward and the slope of the late time BTC is determined by the space-fractional index over all stages and the time-fractional index in the pumping stage. The capability of the existing models to recover the BTC of the SWPP test is discussed and some guidelines for how to choose the appropriate model to interpret the SWPP test data are proposed.

New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models

NASA Astrophysics Data System (ADS)

Toufik, Mekkaoui; Atangana, Abdon

2017-10-01

Recently a new concept of fractional differentiation with non-local and non-singular kernel was introduced in order to extend the limitations of the conventional Riemann-Liouville and Caputo fractional derivatives. A new numerical scheme has been developed, in this paper, for the newly established fractional differentiation. We present in general the error analysis. The new numerical scheme was applied to solve linear and non-linear fractional differential equations. We do not need a predictor-corrector to have an efficient algorithm, in this method. The comparison of approximate and exact solutions leaves no doubt believing that, the new numerical scheme is very efficient and converges toward exact solution very rapidly.

Global asymptotical ω-periodicity of a fractional-order non-autonomous neural networks.

PubMed

Chen, Boshan; Chen, Jiejie

2015-08-01

We study the global asymptotic ω-periodicity for a fractional-order non-autonomous neural networks. Firstly, based on the Caputo fractional-order derivative it is shown that ω-periodic or autonomous fractional-order neural networks cannot generate exactly ω-periodic signals. Next, by using the contraction mapping principle we discuss the existence and uniqueness of S-asymptotically ω-periodic solution for a class of fractional-order non-autonomous neural networks. Then by using a fractional-order differential and integral inequality technique, we study global Mittag-Leffler stability and global asymptotical periodicity of the fractional-order non-autonomous neural networks, which shows that all paths of the networks, starting from arbitrary points and responding to persistent, nonconstant ω-periodic external inputs, asymptotically converge to the same nonconstant ω-periodic function that may be not a solution. Copyright © 2015 Elsevier Ltd. All rights reserved.

Diffusion control for a tempered anomalous diffusion system using fractional-order PI controllers.

PubMed

Juan Chen; Zhuang, Bo; Chen, YangQuan; Cui, Baotong

2017-05-09

This paper is concerned with diffusion control problem of a tempered anomalous diffusion system based on fractional-order PI controllers. The contribution of this paper is to introduce fractional-order PI controllers into the tempered anomalous diffusion system for mobile actuators motion and spraying control. For the proposed control force, convergence analysis of the system described by mobile actuator dynamical equations is presented based on Lyapunov stability arguments. Moreover, a new Centroidal Voronoi Tessellation (CVT) algorithm based on fractional-order PI controllers, henceforth called FOPI-based CVT algorithm, is provided together with a modified simulation platform called Fractional-Order Diffusion Mobile Actuator-Sensor 2-Dimension Fractional-Order Proportional Integral (FO-Diff-MAS2D-FOPI). Finally, extensive numerical simulations for the tempered anomalous diffusion process are presented to verify the effectiveness of our proposed fractional-order PI controllers. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Adaptive fractional order sliding mode control for Boost converter in the Battery/Supercapacitor HESS.

PubMed

Wang, Jianlin; Xu, Dan; Zhou, Huan; Zhou, Tao

2018-01-01

In this paper, an adaptive fractional order sliding mode control (AFSMC) scheme is designed for the current tracking control of the Boost-type converter in a Battery/Supercapacitor hybrid energy storage system (HESS). In order to stabilize the current, the adaptation rules based on state-observer and Lyapunov function are being designed. A fractional order sliding surface function is defined based on the tracking current error and adaptive rules. Furthermore, through fractional order analysis, the stability of the fractional order control system is proven, and the value of the fractional order (λ) is being investigated. In addition, the effectiveness of the proposed AFSMC strategy is being verified by numerical simulations. The advantages of good transient response and robustness to uncertainty are being indicated by this design, when compared with a conventional integer order sliding mode control system.

Suspension concentration distribution in turbulent flows: An analytical study using fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Kundu, Snehasis

2018-09-01

In this study vertical distribution of sediment particles in steady uniform turbulent open channel flow over erodible bed is investigated using fractional advection-diffusion equation (fADE). Unlike previous investigations on fADE to investigate the suspension distribution, in this study the modified Atangana-Baleanu-Caputo fractional derivative with a non-singular and non-local kernel is employed. The proposed fADE is solved and an analytical model for finding vertical suspension distribution is obtained. The model is validated against experimental as well as field measurements of Missouri River, Mississippi River and Rio Grande conveyance channel and is compared with the Rouse equation and other fractional model found in literature. A quantitative error analysis shows that the proposed model is able to predict the vertical distribution of particles more appropriately than previous models. The validation results shows that the fractional model can be equally applied to all size of particles with an appropriate choice of the order of the fractional derivative α. It is also found that besides particle diameter, parameter α depends on the mass density of particle and shear velocity of the flow. To predict this parameter, a multivariate regression is carried out and a relation is proposed for easy application of the model. From the results for sand and plastic particles, it is found that the parameter α is more sensitive to mass density than the particle diameter. The rationality of the dependence of α on particle and flow characteristics has been justified physically.

A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances.

PubMed

Pashaei, Shabnam; Badamchizadeh, Mohammadali

2016-07-01

This paper investigates the stabilization and disturbance rejection for a class of fractional-order nonlinear dynamical systems with mismatched disturbances. To fulfill this purpose a new fractional-order sliding mode control (FOSMC) based on a nonlinear disturbance observer is proposed. In order to design the suitable fractional-order sliding mode controller, a proper switching surface is introduced. Afterward, by using the sliding mode theory and Lyapunov stability theory, a robust fractional-order control law via a nonlinear disturbance observer is proposed to assure the existence of the sliding motion in finite time. The proposed fractional-order sliding mode controller exposes better control performance, ensures fast and robust stability of the closed-loop system, eliminates the disturbances and diminishes the chattering problem. Finally, the effectiveness of the proposed fractional-order controller is depicted via numerical simulation results of practical example and is compared with some other controllers. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Kinetic characteristic of phenanthrene sorption in aged soil amended with biochar

NASA Astrophysics Data System (ADS)

Kim, Chanyang; Kim, Yong-Seong; Hyun, Seunghun

2015-04-01

Biochar has been recently highlighted as an amendment that affects yield of the crops by increasing pH, cation exchange capacity and water retention, and reduces the lability of contaminants by increasing sorption capacity in the soil system. Biochar's physico-chemical properties, high CEC, surfaces containing abundant micropores and macropores, and various types of functional groups, play important roles in enhancing sorption capacity of contaminants. Aging through a natural weathering process might change physico-chemical properties of biochar amended in soils, which can affect the sorption behavior of contaminants. Thus, in this study, the sorption characteristics of phenanthrene (PHE) on biochar-amended soils were studied with various types of chars depending on aging time. To do this, 1) soil was amended with sludge waste char (SWC), wood char (WC), and municipal waste char (MWC) during 0, 6, and 12 month. Chars were applied to soil at 1% and 2.5% (w/w) ratio. 2) Several batch kinetic and equilibrium studies were conducted. One-compartment first order and two-compartment first order model apportioning the fraction of fast and slow sorbing were selected for kinetic models. Where, qt is PHE concentration in biochar-amended soils at each time t, qeis PHE concentration in biochar-amended soils at equilibrium. ff is fastly sorbing fraction and (1-ff) is slowly sorbing fraction. k is sorption rate constant from one-compartment first order model, k1 and k2 are sorption rate constant from two-compartment first order model, t is time (hr). The equilibrium sorption data were fitted with Fruendlich and Langmuir equation. 3) Change in physico-chemical properties of biochar-amended soils was investigated with aging time. Batch equilibrium sorption results suggested that sorbed amount of PHE on WC was greater than SWC and MWC. The more char contents added to soil, the greater sorption capacity of PHE. Sorption equilibrium was reached after 4 hours and equilibrium pH ranged from 6.5 to 8.0. Sorption capacity was reduced with aging time. From kinetic results, two-compartment first order model was more suitable than one-compartment first order model. Fast sorption site of biochar-amended soils dominated total sorption process (i.e., Fraction of fast sorption site ranged from 0.55 to 0.96). Reduced sorption capacity with aging time could be attributed to changes in physico-chemical properties of biochar-amended soils (e.g., reduced pores and increased hydrophilic carboxyl and carbonyl functional groups). Verification is FI-IR and SSA. It is assumed that biochar is a suitable material for PHE contaminated soil in order to reduce the lability of PHE. However, aging effects would lessen biochar benefit for reducing the sorption capacity of PHE by forming hydrophilic functional group and reducing pores.

Transient competitive complexation in biological kinetic isotope fractionation explains non-steady isotopic effects: Theory and application to denitrification in soils

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maggi, F.M.; Riley, W.J.

2009-06-01

The theoretical formulation of biological kinetic reactions in isotopic applications often assume first-order or Michaelis-Menten-Monod kinetics under the quasi-steady-state assumption to simplify the system kinetics. However, isotopic e ects have the same order of magnitude as the potential error introduced by these simpli cations. Both formulations lead to a constant fractionation factor which may yield incorrect estimations of the isotopic effect and a misleading interpretation of the isotopic signature of a reaction. We have analyzed the isotopic signature of denitri cation in biogeochemical soil systems by Menyailo and Hungate [2006], where high {sup 15}N{sub 2}O enrichment during N{sub 2}O productionmore » and inverse isotope fractionation during N{sub 2}O consumption could not be explained with first-order kinetics and the Rayleigh equation, or with the quasi-steady-state Michaelis-Menten-Monod kinetics. When the quasi-steady-state assumption was relaxed, transient Michaelis-Menten-Monod kinetics accurately reproduced the observations and aided in interpretation of experimental isotopic signatures. These results may imply a substantial revision in using the Rayleigh equation for interpretation of isotopic signatures and in modeling biological kinetic isotope fractionation with first-order kinetics or quasi-steady-state Michaelis-Menten-Monod kinetics.« less

Dysfunction Screening in Experimental Arteriovenous Grafts for Hemodialysis Using Fractional-Order Extractor and Color Relation Analysis.

PubMed

Wu, Ming-Jui; Chen, Wei-Ling; Kan, Chung-Dann; Yu, Fan-Ming; Wang, Su-Chin; Lin, Hsiu-Hui; Lin, Chia-Hung

2015-12-01

In physical examinations, hemodialysis access stenosis leading to dysfunction occurs at the venous anastomosis site or the outflow vein. Information from the inflow stenosis, such as blood pressure, pressure drop, and flow resistance increases, allows dysfunction screening from the stage of early clots and thrombosis to the progression of outflow stenosis. Therefore, this study proposes dysfunction screening model in experimental arteriovenous grafts (AVGs) using the fractional-order extractor (FOE) and the color relation analysis (CRA). A Sprott system was designed using an FOE to quantify the differences in transverse vibration pressures between the inflow and outflow sites of an AVG. Experimental analysis revealed that the degree of stenosis (DOS) correlated with an increase in fractional-order dynamic errors (FODEs). Exponential regression was used to fit a non-linear curve and can be used to quantify the relationship between the FODEs and DOS (R (2) = 0.8064). The specific ranges were used to evaluate the stenosis degree, such as DOS: <50, 50-80, and >80%. A CRA-based screening method was derived from the hue angle-saturation-value color model, which describes perceptual color relationships for the DOS. It has a flexibility inference manner with color visualization to represent the different stenosis degrees, which has average accuracy >90% superior to the traditional methods. This in vitro experimental study demonstrated that the proposed model can be used for dysfunction screening in stenotic AVGs.

Spatiotemporal chaos of fractional order logistic equation in nonlinear coupled lattices

NASA Astrophysics Data System (ADS)

Zhang, Ying-Qian; Wang, Xing-Yuan; Liu, Li-Yan; He, Yi; Liu, Jia

2017-11-01

We investigate a new spatiotemporal dynamics with fractional order differential logistic map and spatial nonlinear coupling. The spatial nonlinear coupling features such as the higher percentage of lattices in chaotic behaviors for most of parameters and none periodic windows in bifurcation diagrams are held, which are more suitable for encryptions than the former adjacent coupled map lattices. Besides, the proposed model has new features such as the wider parameter range and wider range of state amplitude for ergodicity, which contributes a wider range of key space when applied in encryptions. The simulations and theoretical analyses are developed in this paper.

Systematic void fraction studies with RELAP5, FRANCESCA and HECHAN

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stosic, Z.; Preusche, G.

1996-08-01

In enhancing the scope of standard thermal-hydraulic codes applications beyond its capabilities, i.e. coupling with a one and/or three-dimensional kinetics core model, the void fraction, transferred from thermal-hydraulics to the core model, plays a determining role in normal operating range and high core flow, as the generated heat and axial power profiles are direct functions of void distribution in the core. Hence, it is very important to know if the void quality models in the programs which have to be coupled are compatible to allow the interactive exchange of data which are based on these constitutive void-quality relations. The presentedmore » void fraction study is performed in order to give the basis for the conclusion whether a transient core simulation using the RELAP5 void fractions can calculate the axial power shapes adequately. Because of that, the void fractions calculated with RELAP5 are compared with those calculated by BWR safety code for licensing--FRANCESCA and the best estimate model for pre- and post-dryout calculation in BWR heated channel--HECHAN. In addition, a comparison with standard experimental void-quality benchmark tube data is performed for the HECHAN code.« less

Attempt to generalize fractional-order electric elements to complex-order ones

NASA Astrophysics Data System (ADS)

Si, Gangquan; Diao, Lijie; Zhu, Jianwei; Lei, Yuhang; Zhang, Yanbin

2017-06-01

The complex derivative {D}α +/- {{j}β }, with α, β \\in R+ is a generalization of the concept of integer derivative, where α=1, β=0. Fractional-order electric elements and circuits are becoming more and more attractive. In this paper, the complex-order electric elements concept is proposed for the first time, and the complex-order elements are modeled and analyzed. Some interesting phenomena are found that the real part of the order affects the phase of output signal, and the imaginary part affects the amplitude for both the complex-order capacitor and complex-order memristor. More interesting is that the complex-order capacitor can do well at the time of fitting electrochemistry impedance spectra. The complex-order memristor is also analyzed. The area inside the hysteresis loops increases with the increasing of the imaginary part of the order and decreases with the increasing of the real part. Some complex case of complex-order memristors hysteresis loops are analyzed at last, whose loop has touching points beyond the origin of the coordinate system.

Few Fractional Order Derivatives and Their Computations

ERIC Educational Resources Information Center

Bhatta, D. D.

2007-01-01

This work presents an introductory development of fractional order derivatives and their computations. Historical development of fractional calculus is discussed. This paper presents how to obtain computational results of fractional order derivatives for some elementary functions. Computational results are illustrated in tabular and graphical…

Fractional order PIλ controller synthesis for steam turbine speed governing systems.

PubMed

Chen, Kai; Tang, Rongnian; Li, Chuang; Lu, Junguo

2018-06-01

The current state of the art of fractional order stability theory is hardly to build connection between the time domain analysis and frequency domain synthesis. The existing tuning methodologies for fractional order PI λ D μ are not always satisfy the given gain crossover frequency and phase margin simultaneously. To overcome the drawbacks in the existing synthesis of fractional order controller, the synthesis of optimal fractional order PI λ controller for higher-order process is proposed. According to the specified phase margin, the corresponding upper boundary of gain crossover frequency and stability surface in parameter space are obtained. Sweeping the order parameter over λ∈(0,2), the complete set of stabilizing controller which guarantees both pre-specifying phase frequency characteristic can be collected. Whereafter, the optimal fractional order PI λ controller is applied to the speed governing systems of steam turbine generation units. The numerical simulation and hardware-in-the-loop simulation demonstrate the effectiveness and satisfactory closed-loop performance of obtained fractional order PI λ controller. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Adaptive fractional order sliding mode control for Boost converter in the Battery/Supercapacitor HESS

PubMed Central

Xu, Dan; Zhou, Huan; Zhou, Tao

2018-01-01

In this paper, an adaptive fractional order sliding mode control (AFSMC) scheme is designed for the current tracking control of the Boost-type converter in a Battery/Supercapacitor hybrid energy storage system (HESS). In order to stabilize the current, the adaptation rules based on state-observer and Lyapunov function are being designed. A fractional order sliding surface function is defined based on the tracking current error and adaptive rules. Furthermore, through fractional order analysis, the stability of the fractional order control system is proven, and the value of the fractional order (λ) is being investigated. In addition, the effectiveness of the proposed AFSMC strategy is being verified by numerical simulations. The advantages of good transient response and robustness to uncertainty are being indicated by this design, when compared with a conventional integer order sliding mode control system. PMID:29702696

Fractional flow in fractured chalk; a flow and tracer test revisited.

PubMed

Odling, N E; West, L J; Hartmann, S; Kilpatrick, A

2013-04-01

A multi-borehole pumping and tracer test in fractured chalk is revisited and reinterpreted in the light of fractional flow. Pumping test data analyzed using a fractional flow model gives sub-spherical flow dimensions of 2.2-2.4 which are interpreted as due to the partially penetrating nature of the pumped borehole. The fractional flow model offers greater versatility than classical methods for interpreting pumping tests in fractured aquifers but its use has been hampered because the hydraulic parameters derived are hard to interpret. A method is developed to convert apparent transmissivity and storativity (L(4-n)/T and S(2-n)) to conventional transmissivity and storativity (L2/T and dimensionless) for the case where flow dimension, 2

Fractional Hopfield Neural Networks: Fractional Dynamic Associative Recurrent Neural Networks.

PubMed

Pu, Yi-Fei; Yi, Zhang; Zhou, Ji-Liu

2017-10-01

This paper mainly discusses a novel conceptual framework: fractional Hopfield neural networks (FHNN). As is commonly known, fractional calculus has been incorporated into artificial neural networks, mainly because of its long-term memory and nonlocality. Some researchers have made interesting attempts at fractional neural networks and gained competitive advantages over integer-order neural networks. Therefore, it is naturally makes one ponder how to generalize the first-order Hopfield neural networks to the fractional-order ones, and how to implement FHNN by means of fractional calculus. We propose to introduce a novel mathematical method: fractional calculus to implement FHNN. First, we implement fractor in the form of an analog circuit. Second, we implement FHNN by utilizing fractor and the fractional steepest descent approach, construct its Lyapunov function, and further analyze its attractors. Third, we perform experiments to analyze the stability and convergence of FHNN, and further discuss its applications to the defense against chip cloning attacks for anticounterfeiting. The main contribution of our work is to propose FHNN in the form of an analog circuit by utilizing a fractor and the fractional steepest descent approach, construct its Lyapunov function, prove its Lyapunov stability, analyze its attractors, and apply FHNN to the defense against chip cloning attacks for anticounterfeiting. A significant advantage of FHNN is that its attractors essentially relate to the neuron's fractional order. FHNN possesses the fractional-order-stability and fractional-order-sensitivity characteristics.

Nonlocal electrical diffusion equation

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H.; Benavides-Cruz, M.; Calderón-Ramón, C.

2016-07-01

In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is 0<β≤1 and for the time domain is 0<γ≤2. We present solutions for the full fractional equation involving space and time fractional derivatives using numerical methods based on Fourier variable separation. The case with spatial fractional derivatives leads to Levy flight type phenomena, while the time fractional equation is related to sub- or super diffusion. We show that the mathematical concept of fractional derivatives can be useful to understand the behavior of semiconductors, the design of solar panels, electrochemical phenomena and the description of anomalous complex processes.

First observation of a mass independent isotopic fractionation in a condensation reaction

NASA Technical Reports Server (NTRS)

Thiemens, M. H.; Nelson, R.; Dong, Q. W.; Nuth, Joseph A., III

1994-01-01

Thiemens and Heidenreich (1983) first demonstrated that a chemically produced mass independent isotopic fractionation process could produce an isotopic composition which is identical to that observed in Allende inclusions. This raised the possibility that the meteoritic components could be produced by chemical, rather than nuclear processes. In order to develop a mechanistic model of the early solar system, it is important that relevant reactions be studied, particularly, those which may occur in the earliest condensation reactions. The isotopic results for isotopic fractionations associated with condensation processes are reported. A large mass independent isotopic fractionation is observed in one of the experiments.

Modeling the erythemal surface diffuse irradiance fraction for Badajoz, Spain

NASA Astrophysics Data System (ADS)

Sanchez, Guadalupe; Serrano, Antonio; Cancillo, María Luisa

2017-10-01

Despite its important role on the human health and numerous biological processes, the diffuse component of the erythemal ultraviolet irradiance (UVER) is scarcely measured at standard radiometric stations and therefore needs to be estimated. This study proposes and compares 10 empirical models to estimate the UVER diffuse fraction. These models are inspired from mathematical expressions originally used to estimate total diffuse fraction, but, in this study, they are applied to the UVER case and tested against experimental measurements. In addition to adapting to the UVER range the various independent variables involved in these models, the total ozone column has been added in order to account for its strong impact on the attenuation of ultraviolet radiation. The proposed models are fitted to experimental measurements and validated against an independent subset. The best-performing model (RAU3) is based on a model proposed by Ruiz-Arias et al. (2010) and shows values of r2 equal to 0.91 and relative root-mean-square error (rRMSE) equal to 6.1 %. The performance achieved by this entirely empirical model is better than those obtained by previous semi-empirical approaches and therefore needs no additional information from other physically based models. This study expands on previous research to the ultraviolet range and provides reliable empirical models to accurately estimate the UVER diffuse fraction.

Nanoclustering phase competition induces the resistivity hump in colossal magnetoresistive manganites

NASA Astrophysics Data System (ADS)

Pradhan, Kalpataru; Yunoki, Seiji

2017-12-01

Using a two-band double-exchange model with Jahn-Teller lattice distortions and superexchange interactions, supplemented by quenched disorder, at an electron density n =0.65 , we explicitly demonstrate the coexistence of the n =1 /2 -type (π ,π ) charge-ordered and the ferromagnetic nanoclusters above the ferromagnetic transition temperature Tc in colossal magnetoresistive (CMR) manganites. The resistivity increases due to the enhancement of the volume fraction of the charge-ordered and the ferromagnetic nanoclusters upon decreasing the temperature down to Tc. The ferromagnetic nanoclusters start to grow and merge, and the volume fraction of the charge-ordered nanoclusters decreases below Tc, leading to the sharp drop in the resistivity. By applying a small external magnetic field h , we show that the resistivity above Tc increases, as compared with the case when h =0 , a fact that further confirms the coexistence of the charge-ordered and the ferromagnetic nanoclusters. In addition, we show that the volume fraction of the charge-ordered nanoclusters decreases upon increasing the bandwidth, and consequently the resistivity hump diminishes for large bandwidth manganites, in good qualitative agreement with experiments. The obtained insights from our calculations provide a complete pathway to understand the phase competition in CMR manganites.

Influence of organic acids on kinetic release of chromium in soil contaminated with leather factory waste in the presence of some adsorbents.

PubMed

Taghipour, Marzieh; Jalali, Mohsen

2016-07-01

In this study, batch experiments were conducted to investigate the effects of nanoparticles (NPs) (MgO, ZnO, TiO2) and clay minerals (bentonite, zeolite) on the release of chromium (Cr) from leather factory waste (LFW) and LFW treated soil using organic acids. Chromium release from all treatments was studied in the presence of citric acid, oxalic acid and CaCl2 solutions. The results showed that, in all treatments, organic acids released more Cr than inorganic salt (CaCl2). The release of Cr by citric acid was higher than that by oxalic acid. In LFW treated soil and LFW, the release of Cr from the all treatments with NPs was less than that from the clay mineral treatments. On the other hand, in the presence of organic acids, Cr release by NPs and clay minerals decreased. Two kinetic models including pseudo-first- and pseudo-second-order model were tested to describe the time dependent Cr release data. Among the kinetic models used, the pseudo-second-order model generally gave the best fits to experimental data. Before and after release experiments, Cr in LFW, treated LFW, control soil and LFW treated soils were fractionated. In all treatments, the greatest amounts of Cr were found in the residual fraction (RES). The organic acids were effective in reducing the exchangeable (EXC), bound to organic matter (OM) and bound to carbonate (CAR) fractions of Cr in all treatments, whereas, after release of Cr from treated soils, Cr remained mainly in the RES fraction. The application of NPs and clay minerals in soil led to a significant transformation of Cr from mobile fractions to the RES fraction. Therefore, organic ligands played a dominant role in mobility and bioavailability of Cr and the removal of Cr by adsorbents. Copyright © 2016 Elsevier Ltd. All rights reserved.

A fractional calculus perspective of distributed propeller design

NASA Astrophysics Data System (ADS)

Tenreiro Machado, J.; Galhano, Alexandra M.

2018-02-01

A new generation of aircraft with distributed propellers leads to operational performances superior to those exhibited by standard designs. Computational simulations and experimental tests show a reduction of fuel consumption and noise. This paper proposes an analogy between aerodynamics and electrical circuits. The model reveals properties similar to those of fractional-order systems and gives a deeper insight into the dynamics of multi-propeller coupling.

Modeling of heat conduction via fractional derivatives

NASA Astrophysics Data System (ADS)

Fabrizio, Mauro; Giorgi, Claudio; Morro, Angelo

2017-09-01

The modeling of heat conduction is considered by letting the time derivative, in the Cattaneo-Maxwell equation, be replaced by a derivative of fractional order. The purpose of this new approach is to overcome some drawbacks of the Cattaneo-Maxwell equation, for instance possible fluctuations which violate the non-negativity of the absolute temperature. Consistency with thermodynamics is shown to hold for a suitable free energy potential, that is in fact a functional of the summed history of the heat flux, subject to a suitable restriction on the set of admissible histories. Compatibility with wave propagation at a finite speed is investigated in connection with temperature-rate waves. It follows that though, as expected, this is the case for the Cattaneo-Maxwell equation, the model involving the fractional derivative does not allow the propagation at a finite speed. Nevertheless, this new model provides a good description of wave-like profiles in thermal propagation phenomena, whereas Fourier's law does not.

Fractional calculus phenomenology in two-dimensional plasma models

NASA Astrophysics Data System (ADS)

Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill

2006-10-01

Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).

Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method

NASA Astrophysics Data System (ADS)

Rahmatullah; Ellahi, Rahmat; Mohyud-Din, Syed Tauseef; Khan, Umar

2018-03-01

We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses.

Improved Control Strategy for Subsynchronous Resonance Mitigation with Fractional-order PI Controller

NASA Astrophysics Data System (ADS)

Raju, D. Koteswara; Umre, Bhimrao S.; Junghare, A. S.; Chitti Babu, B.

2016-12-01

This paper explores a robust Fractional-order PI (FOPI) controller to diminish Subsynchronous Resonance (SSR) using Static Synchronous series compensator (SSSC). The diminution of SSR is accomplished by increasing the network damping with the injection of voltage of subsynchronous component into the line at those frequencies which are proximate to the torsional mode frequency of the turbine-generator shaft. The voltage of subsynchronous frequency component is extracted from the transmission line and further the similar quantity of series voltage is injected by SSSC into the line to make the current of subsynchronous frequency component to zero which is the major source of oscillations in the turbine-generator shaft. The insertion and fine tuning of Fractional-order PI controller in the control scheme of SSSC the subsynchronous oscillations are reduced to 4 % as compared to conventional PI controller. The studied system is modelled and simulated using MATLAB-Simulink and the results are analysed to show the precision and robustness of the proposed control strategy.

Lie Symmetry Analysis and Explicit Solutions of the Time Fractional Fifth-Order KdV Equation

PubMed Central

Wang, Gang wei; Xu, Tian zhou; Feng, Tao

2014-01-01

In this paper, using the Lie group analysis method, we study the invariance properties of the time fractional fifth-order KdV equation. A systematic research to derive Lie point symmetries to time fractional fifth-order KdV equation is performed. In the sense of point symmetry, all of the vector fields and the symmetry reductions of the fractional fifth-order KdV equation are obtained. At last, by virtue of the sub-equation method, some exact solutions to the fractional fifth-order KdV equation are provided. PMID:24523885

On the use of fractional order PK-PD models

NASA Astrophysics Data System (ADS)

Ionescu, Clara; Copot, Dana

2017-01-01

Quantifying and controlling depth of anesthesia is a challenging process due to lack of measurement technology for direct effects of drug supply into the body. Efforts are being made to develop new sensor techniques and new horizons are explored for modeling this intricate process. This paper introduces emerging tools available on the ‘engineering market’ imported from the area of fractional calculus. A novel interpretation of the classical drug-effect curve is given, enabling linear control. This enables broadening the horizon of signal processing and control techniques and suggests future research lines.

Uncertain viscoelastic models with fractional order: A new spectral tau method to study the numerical simulations of the solution

NASA Astrophysics Data System (ADS)

Ahmadian, A.; Ismail, F.; Salahshour, S.; Baleanu, D.; Ghaemi, F.

2017-12-01

The analysis of the behaviors of physical phenomena is important to discover significant features of the character and the structure of mathematical models. Frequently the unknown parameters involve in the models are assumed to be unvarying over time. In reality, some of them are uncertain and implicitly depend on several factors. In this study, to consider such uncertainty in variables of the models, they are characterized based on the fuzzy notion. We propose here a new model based on fractional calculus to deal with the Kelvin-Voigt (KV) equation and non-Newtonian fluid behavior model with fuzzy parameters. A new and accurate numerical algorithm using a spectral tau technique based on the generalized fractional Legendre polynomials (GFLPs) is developed to solve those problems under uncertainty. Numerical simulations are carried out and the analysis of the results highlights the significant features of the new technique in comparison with the previous findings. A detailed error analysis is also carried out and discussed.

Accounting for the dissociating properties of organic chemicals in LCIA: an uncertainty analysis applied to micropollutants in the assessment of freshwater ecotoxicity.

PubMed

Morais, Sérgio Alberto; Delerue-Matos, Cristina; Gabarrell, Xavier

2013-03-15

In life cycle impact assessment (LCIA) models, the sorption of the ionic fraction of dissociating organic chemicals is not adequately modeled because conventional non-polar partitioning models are applied. Therefore, high uncertainties are expected when modeling the mobility, as well as the bioavailability for uptake by exposed biota and degradation, of dissociating organic chemicals. Alternative regressions that account for the ionized fraction of a molecule to estimate fate parameters were applied to the USEtox model. The most sensitive model parameters in the estimation of ecotoxicological characterization factors (CFs) of micropollutants were evaluated by Monte Carlo analysis in both the default USEtox model and the alternative approach. Negligible differences of CFs values and 95% confidence limits between the two approaches were estimated for direct emissions to the freshwater compartment; however the default USEtox model overestimates CFs and the 95% confidence limits of basic compounds up to three orders and four orders of magnitude, respectively, relatively to the alternative approach for emissions to the agricultural soil compartment. For three emission scenarios, LCIA results show that the default USEtox model overestimates freshwater ecotoxicity impacts for the emission scenarios to agricultural soil by one order of magnitude, and larger confidence limits were estimated, relatively to the alternative approach. Copyright © 2013 Elsevier B.V. All rights reserved.

Pole-zero form fractional model identification in frequency domain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mansouri, R.; Djamah, T.; Djennoune, S.

2009-03-05

This paper deals with system identification in the frequency domain using non integer order models given in the pole-zero form. The usual identification techniques cannot be used in this case because of the non integer orders of differentiation which makes the problem strongly nonlinear. A general identification method based on Levenberg-Marquardt algorithm is developed and allows to estimate the (2n+2m+1) parameters of the model. Its application to identify the ''skin effect'' of a squirrel cage induction machine modeling is then presented.

Some operational tools for solving fractional and higher integer order differential equations: A survey on their mutual relations

NASA Astrophysics Data System (ADS)

Kiryakova, Virginia S.

2012-11-01

The Laplace Transform (LT) serves as a basis of the Operational Calculus (OC), widely explored by engineers and applied scientists in solving mathematical models for their practical needs. This transform is closely related to the exponential and trigonometric functions (exp, cos, sin) and to the classical differentiation and integration operators, reducing them to simple algebraic operations. Thus, the classical LT and the OC give useful tool to handle differential equations and systems with constant coefficients. Several generalizations of the LT have been introduced to allow solving, in a similar way, of differential equations with variable coefficients and of higher integer orders, as well as of fractional (arbitrary non-integer) orders. Note that fractional order mathematical models are recently widely used to describe better various systems and phenomena of the real world. This paper surveys briefly some of our results on classes of such integral transforms, that can be obtained from the LT by means of "transmutations" which are operators of the generalized fractional calculus (GFC). On the list of these Laplace-type integral transforms, we consider the Borel-Dzrbashjan, Meijer, Krätzel, Obrechkoff, generalized Obrechkoff (multi-index Borel-Dzrbashjan) transforms, etc. All of them are G- and H-integral transforms of convolutional type, having as kernels Meijer's G- or Fox's H-functions. Besides, some special functions (also being G- and H-functions), among them - the generalized Bessel-type and Mittag-Leffler (M-L) type functions, are generating Gel'fond-Leontiev (G-L) operators of generalized differentiation and integration, which happen to be also operators of GFC. Our integral transforms have operational properties analogous to those of the LT - they do algebrize the G-L generalized integrations and differentiations, and thus can serve for solving wide classes of differential equations with variable coefficients of arbitrary, including non-integer order. Throughout the survey, we illustrate the parallels in the relationships: Laplace type integral transforms - special functions as kernels - operators of generalized integration and differentiation generated by special functions - special functions as solutions of related differential equations. The role of the so-called Special Functions of Fractional Calculus is emphasized.

Control of polymer network topology in semi-batch systems

NASA Astrophysics Data System (ADS)

Wang, Rui; Olsen, Bradley; Johnson, Jeremiah

Polymer networks invariably possess topological defects: loops of different orders. Since small loops (primary loops and secondary loops) both lower the modulus of network and lead to stress concentration that causes material failure at low deformation, it is desirable to greatly reduce the loop fraction. We have shown that achieving loop fraction close to zero is extremely difficult in the batch process due to the slow decay of loop fraction with the polymer concentration and chain length. Here, we develop a modified kinetic graph theory that can model network formation reactions in semi-batch systems. We demonstrate that the loop fraction is not sensitive to the feeding policy if the reaction volume maintains constant during the network formation. However, if we initially put concentrated solution of small junction molecules in the reactor and continuously adding polymer solutions, the fractions of both primary loop and higher-order loops will be significantly reduced. There is a limiting value (nonzero) of loop fraction that can be achieved in the semi-batch system in condition of extremely slow feeding rate. This minimum loop fraction only depends on a single dimensionless variable, the product of concentration and with single chain pervaded volume, and defines an operating zone in which the loop fraction of polymer networks can be controlled through adjusting the feeding rate of the semi-batch process.

Fractional blood flow in oscillatory arteries with thermal radiation and magnetic field effects

NASA Astrophysics Data System (ADS)

Bansi, C. D. K.; Tabi, C. B.; Motsumi, T. G.; Mohamadou, A.

2018-06-01

A fractional model is proposed to study the effect of heat transfer and magnetic field on the blood flowing inside oscillatory arteries. The flow is due to periodic pressure gradient and the fractional model equations include body acceleration. The proposed velocity and temperature distribution equations are solved using the Laplace and Hankel transforms. The effect of the fluid parameters such as the Reynolds number (Re), the magnetic parameter (M) and the radiation parameter (N) is studied graphically with changing the fractional-order parameter. It is found that the fractional derivative is a valuable tool to control both the temperature and velocity of blood when flow parameters change under treatment, for example. Besides, this work highlights the fact that in the presence of strong magnetic field, blood velocity and temperature reduce. A reversed effect is observed where the applied thermal radiation increase; the velocity and temperature of blood increase. However, the temperature remains high around the artery centerline, which is appropriate during treatment to avoid tissues damage.

Silicate Inclusions in the Kodaikanal IIE Iron Meteorite

NASA Technical Reports Server (NTRS)

Kurat, G.; Varela, M. E.; Zinner, E.

2005-01-01

Silicate inclusions in iron meteorites display an astonishing chemical and mineralogical variety, ranging from chondritic to highly fractionated, silica- and alkali-rich assemblages. In spite of this, their origin is commonly considered to be a simple one: mixing of silicates, fractionated or unfractionated, with metal. The latter had to be liquid in order to accommodate the former in a pore-free way which all models accomplish by assuming shock melting. II-E iron meteorites are particularly interesting because they contain an exotic zoo of silicate inclusions, including some chemically strongly fractionated ones. They also pose a formidable conundrum: young silicates are enclosed by very old metal. This and many other incompatibilities between models and reality forced the formulation of an alternative genetic model for irons. Here we present preliminary findings in our study of Kodaikanal silicate inclusions.

NTCP modelling of lung toxicity after SBRT comparing the universal survival curve and the linear quadratic model for fractionation correction.

PubMed

Wennberg, Berit M; Baumann, Pia; Gagliardi, Giovanna; Nyman, Jan; Drugge, Ninni; Hoyer, Morten; Traberg, Anders; Nilsson, Kristina; Morhed, Elisabeth; Ekberg, Lars; Wittgren, Lena; Lund, Jo-Åsmund; Levin, Nina; Sederholm, Christer; Lewensohn, Rolf; Lax, Ingmar

2011-05-01

In SBRT of lung tumours no established relationship between dose-volume parameters and the incidence of lung toxicity is found. The aim of this study is to compare the LQ model and the universal survival curve (USC) to calculate biologically equivalent doses in SBRT to see if this will improve knowledge on this relationship. Toxicity data on radiation pneumonitis grade 2 or more (RP2+) from 57 patients were used, 10.5% were diagnosed with RP2+. The lung DVHs were corrected for fractionation (LQ and USC) and analysed with the Lyman- Kutcher-Burman (LKB) model. In the LQ-correction α/β = 3 Gy was used and the USC parameters used were: α/β = 3 Gy, D(0) = 1.0 Gy, [Formula: see text] = 10, α = 0.206 Gy(-1) and d(T) = 5.8 Gy. In order to understand the relative contribution of different dose levels to the calculated NTCP the concept of fractional NTCP was used. This might give an insight to the questions of whether "high doses to small volumes" or "low doses to large volumes" are most important for lung toxicity. NTCP analysis with the LKB-model using parameters m = 0.4, D(50) = 30 Gy resulted for the volume dependence parameter (n) with LQ correction n = 0.87 and with USC correction n = 0.71. Using parameters m = 0.3, D(50) = 20 Gy n = 0.93 with LQ correction and n = 0.83 with USC correction. In SBRT of lung tumours, NTCP modelling of lung toxicity comparing models (LQ,USC) for fractionation correction, shows that low dose contribute less and high dose more to the NTCP when using the USC-model. Comparing NTCP modelling of SBRT data and data from breast cancer, lung cancer and whole lung irradiation implies that the response of the lung is treatment specific. More data are however needed in order to have a more reliable modelling.

Effect of molecular mass on supramolecular organisation of poly(4,4''-dioctyl-2,2':5',2''-terthiophene).

PubMed

Jaroch, Tomasz; Knor, Marek; Nowakowski, Robert; Zagórska, Małgorzata; Proń, Adam

2008-10-28

The effect of the chain length on the type and extent of the 2D supramolecular organization in poly(4,4''-dioctyl-2,2':5',2''-terthiophene) (PDOTT) monomolecular layers deposited on highly oriented pyrolytic graphite (HOPG) is studied by scanning tunneling microscopy (STM) and analyzed in terms of molecular modeling. The strictly monodispersed fractions of increasing molecular mass used in this study were obtained by chromatographic fractionation of the crude product of 4,4''-dioctyl-2,2':5',2''-terthiophene oxidative polymerization. STM investigations of PDOTT layers, deposited on HOPG from poly- and monodispersed fractions, show that polydispersity can be considered as a key factor seriously limiting supramolecular ordering. This is a consequence of significant differences in the type of supramolecular order observed for molecules of different chain length. It has been demonstrated that shorter molecules (consisting of 6 and 9 thiophene units) form well-defined two-dimensional islands, while the interactions between longer molecules (consisting of 12 and 15 thiophene units) become anisotropic. Consequently, for higher molecular mass fractions, the supramolecular organization is one-dimensional and consists of more or less separated rows of ordered macromolecules. In this case an increase of the chain length leads to amplification of the intermolecular interactions proceeding via interdigitation of the alkyl substituents of adjacent molecules. Polydispersed fractions show much less ordered organization because of the incompatibility of the supramolecular structures of molecules of different molecular masses. This finding is of crucial importance for the application of polythiophene derivatives in organic and molecular electronics since ordered supramolecular organization constitutes the condition sine qua non of good electrical transport properties.

A Stochastic Fractional Dynamics Model of Space-time Variability of Rain

NASA Technical Reports Server (NTRS)

Kundu, Prasun K.; Travis, James E.

2013-01-01

Rainfall varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, that allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and times scales. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and in Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to the second moment statistics of radar data. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well without any further adjustment.

Superconductivity from fractionalized excitations in URu2Si2

NASA Astrophysics Data System (ADS)

Hsu, Chen-Hsuan; Chakravarty, Sudip

2014-10-01

An unconventional pairing mechanism in the heavy-fermion material URu2Si2 is studied. We propose a mixed singlet-triplet d-density wave to be the hidden-order state in URu2Si2. The exotic order is topologically nontrivial and supports a charge 2e skyrmionic spin texture, which is assumed to fractionalize into merons and antimerons at the deconfined quantum critical point. The interaction between these fractional particles results in a (pseudo)spin-singlet chiral d-wave superconducting state, which breaks time-reversal symmetry. Therefore, it is highly likely to produce a nonzero signal of the polar Kerr effect at the onset of the superconductivity, consistent with recent experiments. In addition, the nodal structures of the possible pairing functions in our model are consistent with the thermodynamic experiments in URu2Si2.

The generalised isodamping approach for robust fractional PID controllers design

NASA Astrophysics Data System (ADS)

Beschi, M.; Padula, F.; Visioli, A.

2017-06-01

In this paper, we present a novel methodology to design fractional-order proportional-integral-derivative controllers. Based on the description of the controlled system by means of a family of linear models parameterised with respect to a free variable that describes the real process operating point, we design the controller by solving a constrained min-max optimisation problem where the maximum sensitivity has to be minimised. Among the imposed constraints, the most important one is the new generalised isodamping condition, that defines the invariancy of the phase margin with respect to the free parameter variations. It is also shown that the well-known classical isodamping condition is a special case of the new technique proposed in this paper. Simulation results show the effectiveness of the proposed technique and the superiority of the fractional-order controller compared to its integer counterpart.

Propagation properties of hollow sinh-Gaussian beams through fractional Fourier transform optical systems

NASA Astrophysics Data System (ADS)

Tang, Bin; Jiang, ShengBao; Jiang, Chun; Zhu, Haibin

2014-07-01

A hollow sinh-Gaussian beam (HsG) is an appropriate model to describe the dark-hollow beam. Based on Collins integral formula and the fact that a hard-edged-aperture function can be expanded into a finite sum of complex Gaussian functions, the propagation properties of a HsG beam passing through fractional Fourier transform (FRFT) optical systems with and without apertures have been studied in detail by some typical numerical examples. The results obtained using the approximate analytical formula are in good agreement with those obtained using numerical integral calculation. Further, the studies indicate that the normalized intensity distribution of the HsG beam in FRFT plane is closely related with not only the fractional order but also the beam order and the truncation parameter. The FRFT optical systems provide a convenient way for laser beam shaping.

A pseudo energy-invariant method for relativistic wave equations with Riesz space-fractional derivatives

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.; Hendy, A. S.; De Staelen, R. H.

2018-03-01

In this work, we investigate a general nonlinear wave equation with Riesz space-fractional derivatives that generalizes various classical hyperbolic models, including the sine-Gordon and the Klein-Gordon equations from relativistic quantum mechanics. A finite-difference discretization of the model is provided using fractional centered differences. The method is a technique that is capable of preserving an energy-like quantity at each iteration. Some computational comparisons against solutions available in the literature are performed in order to assess the capability of the method to preserve the invariant. Our experiments confirm that the technique yields good approximations to the solutions considered. As an application of our scheme, we provide simulations that confirm, for the first time in the literature, the presence of the phenomenon of nonlinear supratransmission in Riesz space-fractional Klein-Gordon equations driven by a harmonic perturbation at the boundary.

Radical chiral Floquet phases in a periodically driven Kitaev model and beyond

NASA Astrophysics Data System (ADS)

Po, Hoi Chun; Fidkowski, Lukasz; Vishwanath, Ashvin; Potter, Andrew C.

2017-12-01

We theoretically discover a family of nonequilibrium fractional topological phases in which time-periodic driving of a 2D system produces excitations with fractional statistics, and produces chiral quantum channels that propagate a quantized fractional number of qubits along the sample edge during each driving period. These phases share some common features with fractional quantum Hall states, but are sharply distinct dynamical phenomena. Unlike the integer-valued invariant characterizing the equilibrium quantum Hall conductance, these phases are characterized by a dynamical topological invariant that is a square root of a rational number, inspiring the label: radical chiral Floquet phases. We construct solvable models of driven and interacting spin systems with these properties, and identify an unusual bulk-boundary correspondence between the chiral edge dynamics and bulk "anyon time-crystal" order characterized by dynamical transmutation of electric-charge into magnetic-flux excitations in the bulk.

Fractional order uncertainty estimator based hierarchical sliding mode design for a class of fractional order non-holonomic chained system.

PubMed

Deepika; Kaur, Sandeep; Narayan, Shiv

2018-06-01

This paper proposes a novel fractional order sliding mode control approach to address the issues of stabilization as well as tracking of an N-dimensional extended chained form of fractional order non-holonomic system. Firstly, the hierarchical fractional order terminal sliding manifolds are selected to procure the desired objectives in finite time. Then, a sliding mode control law is formulated which provides robustness against various system uncertainties or external disturbances. In addition, a novel fractional order uncertainty estimator is deduced mathematically to estimate and mitigate the effects of uncertainties, which also excludes the requirement of their upper bounds. Due to the omission of discontinuous control action, the proposed algorithm ensures a chatter-free control input. Moreover, the finite time stability of the closed loop system has been proved analytically through well known Mittag-Leffler and Fractional Lyapunov theorems. Finally, the proposed methodology is validated with MATLAB simulations on two examples including an application of fractional order non-holonomic wheeled mobile robot and its performances are also compared with the existing control approach. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

The phosphorus fractions and adsorption-desorption characteristics in the Wuliangsuhai Lake, China.

PubMed

Wang, Xinglei; Wei, Jinxing; Bai, Na; Cha, Hancaicike; Cao, Can; Zheng, Kexuan; Liu, Ying

2018-05-11

The phosphorus (P) fractions and adsorption-desorption characteristics in the Wuliangsuhai Lake were investigated through molybdenum blue/ascorbic acid method and indoor simulation experiments, respectively. The results showed that the highest total phosphorus concentration in overlying water (W-TP) was found in S1 which was in the hypereutrophic type. The mean concentration of particulate organic phosphorus (POP) was the most abundant P fraction (31.35% of the W-TP). The results of TP contents in sediments (S-TP) indicated that the most sampling sites were in the mild level of pollution. The contents of calcium-bound P (HCl-P) and residual P (Res-P) fractions together comprised 83.03-98.10% of the S-TP. Pseudo-second-order models fitted well with the adsorption-desorption kinetic of P fractions. The Langmuir and Freundlich models well described the adsorption isotherm of P fractions. The results of adsorption-desorption of P fractions indicated that the adsorption capacity was strong, the chemical adsorption was dominant, and the sediments was a source of P. Accordingly, we concluded that the Wuliangsuhai Lake was in the moderate pollution level, and the sediments as a source could desorb P in natural aquatic environment.

New optical solitons of space-time conformable fractional perturbed Gerdjikov-Ivanov equation by sine-Gordon equation method

NASA Astrophysics Data System (ADS)

Yaşar, Elif; Yıldırım, Yakup; Yaşar, Emrullah

2018-06-01

This paper devotes to conformable fractional space-time perturbed Gerdjikov-Ivanov (GI) equation which appears in nonlinear fiber optics and photonic crystal fibers (PCF). We consider the model with full nonlinearity in order to give a generalized flavor. The sine-Gordon equation approach is carried out to model equation for retrieving the dark, bright, dark-bright, singular and combined singular optical solitons. The constraint conditions are also reported for guaranteeing the existence of these solitons. We also present some graphical simulations of the solutions for better understanding the physical phenomena of the behind the considered model.

A Stable Clock Error Model Using Coupled First and Second Order Gauss-Markov Processes

NASA Technical Reports Server (NTRS)

Carpenter, Russell; Lee, Taesul

2008-01-01

Long data outages may occur in applications of global navigation satellite system technology to orbit determination for missions that spend significant fractions of their orbits above the navigation satellite constellation(s). Current clock error models based on the random walk idealization may not be suitable in these circumstances, since the covariance of the clock errors may become large enough to overflow flight computer arithmetic. A model that is stable, but which approximates the existing models over short time horizons is desirable. A coupled first- and second-order Gauss-Markov process is such a model.

Turbulent Dispersion of Pathogenic Spores Within and Above Plant Canopies: Field Experiments and Lagrangian Modeling

NASA Astrophysics Data System (ADS)

Gleicher, S.; Chamecki, M.; Isard, S.; Katul, G. G.

2012-12-01

Plant disease epidemics caused by pathogenic spores are a common and consequential threat to agricultural crops. In most cases, pathogenic spores are produced and released deep inside plant canopies and must be transported out of the canopy region in order to infect other fields and spread the disease. The fraction of spores that "escape" the canopy is crucial in determining how fast and far these plant diseases will spread. The goal of this work is to use a field experiment, coupled with a Lagrangian Stochastic Model (LSM), to investigate how properties of canopy turbulence impact the dispersion of spores inside the canopy and the fraction of spores that escape from the canopy. An extensive field experiment was conducted to study spore dispersion inside and outside a corn canopy. The spores were released from point sources located at various depths inside the canopy. Concentration measurements were obtained inside and above the canopy by a 3-dimensional grid of spore collectors. The experimental measurements of mean spore concentration are used to validate a LSM for spore dispersion. In the LSM, flow field statistics used to drive the particle dispersion are specified by a second-order closure model for turbulence within plant canopies. The dispersion model includes spore deposition on and rebound from canopy elements. The combination of experimental and numerical simulations is used to quantify the fraction of spores that escape the canopy. Effects of release height, friction velocity, and canopy architecture on the escape fraction of spores are explored using the LSM, and implications for disease propagation are discussed.

A fractal derivative model for the characterization of anomalous diffusion in magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Liang, Yingjie; Ye, Allen Q.; Chen, Wen; Gatto, Rodolfo G.; Colon-Perez, Luis; Mareci, Thomas H.; Magin, Richard L.

2016-10-01

Non-Gaussian (anomalous) diffusion is wide spread in biological tissues where its effects modulate chemical reactions and membrane transport. When viewed using magnetic resonance imaging (MRI), anomalous diffusion is characterized by a persistent or 'long tail' behavior in the decay of the diffusion signal. Recent MRI studies have used the fractional derivative to describe diffusion dynamics in normal and post-mortem tissue by connecting the order of the derivative with changes in tissue composition, structure and complexity. In this study we consider an alternative approach by introducing fractal time and space derivatives into Fick's second law of diffusion. This provides a more natural way to link sub-voxel tissue composition with the observed MRI diffusion signal decay following the application of a diffusion-sensitive pulse sequence. Unlike previous studies using fractional order derivatives, here the fractal derivative order is directly connected to the Hausdorff fractal dimension of the diffusion trajectory. The result is a simpler, computationally faster, and more direct way to incorporate tissue complexity and microstructure into the diffusional dynamics. Furthermore, the results are readily expressed in terms of spectral entropy, which provides a quantitative measure of the overall complexity of the heterogeneous and multi-scale structure of biological tissues. As an example, we apply this new model for the characterization of diffusion in fixed samples of the mouse brain. These results are compared with those obtained using the mono-exponential, the stretched exponential, the fractional derivative, and the diffusion kurtosis models. Overall, we find that the order of the fractal time derivative, the diffusion coefficient, and the spectral entropy are potential biomarkers to differentiate between the microstructure of white and gray matter. In addition, we note that the fractal derivative model has practical advantages over the existing models from the perspective of computational accuracy and efficiency.

Entanglement spectrum as a generalization of entanglement entropy: identification of topological order in non-Abelian fractional quantum Hall effect states.

PubMed

Li, Hui; Haldane, F D M

2008-07-04

We study the "entanglement spectrum" (a presentation of the Schmidt decomposition analogous to a set of "energy levels") of a many-body state, and compare the Moore-Read model wave function for the nu=5/2 fractional quantum Hall state with a generic 5/2 state obtained by finite-size diagonalization of the second-Landau-level-projected Coulomb interactions. Their spectra share a common "gapless" structure, related to conformal field theory. In the model state, these are the only levels, while in the "generic" case, they are separated from the rest of the spectrum by a clear "entanglement gap", which appears to remain finite in the thermodynamic limit. We propose that the low-lying entanglement spectrum can be used as a "fingerprint" to identify topological order.

An approach to design controllers for MIMO fractional-order plants based on parameter optimization algorithm.

PubMed

Xue, Dingyü; Li, Tingxue

2017-04-27

The parameter optimization method for multivariable systems is extended to the controller design problems for multiple input multiple output (MIMO) square fractional-order plants. The algorithm can be applied to search for the optimal parameters of integer-order controllers for fractional-order plants with or without time delays. Two examples are given to present the controller design procedures for MIMO fractional-order systems. Simulation studies show that the integer-order controllers designed are robust to plant gain variations. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Fractional cable equation for general geometry: A model of axons with swellings and anomalous diffusion.

PubMed

López-Sánchez, Erick J; Romero, Juan M; Yépez-Martínez, Huitzilin

2017-09-01

Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease, and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark of these diseases. The diffusion in the axons can become anomalous as a result of this abnormality. In this case the voltage propagation in axons is affected. Another hallmark of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for a general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increases, the voltage decreases. Similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.

Fractional cable equation for general geometry: A model of axons with swellings and anomalous diffusion

NASA Astrophysics Data System (ADS)

López-Sánchez, Erick J.; Romero, Juan M.; Yépez-Martínez, Huitzilin

2017-09-01

Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease, and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark of these diseases. The diffusion in the axons can become anomalous as a result of this abnormality. In this case the voltage propagation in axons is affected. Another hallmark of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for a general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increases, the voltage decreases. Similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.

Two-degree-of-freedom fractional order-PID controllers design for fractional order processes with dead-time.

PubMed

Li, Mingjie; Zhou, Ping; Zhao, Zhicheng; Zhang, Jinggang

2016-03-01

Recently, fractional order (FO) processes with dead-time have attracted more and more attention of many researchers in control field, but FO-PID controllers design techniques available for the FO processes with dead-time suffer from lack of direct systematic approaches. In this paper, a simple design and parameters tuning approach of two-degree-of-freedom (2-DOF) FO-PID controller based on internal model control (IMC) is proposed for FO processes with dead-time, conventional one-degree-of-freedom control exhibited the shortcoming of coupling of robustness and dynamic response performance. 2-DOF control can overcome the above weakness which means it realizes decoupling of robustness and dynamic performance from each other. The adjustable parameter η2 of FO-PID controller is directly related to the robustness of closed-loop system, and the analytical expression is given between the maximum sensitivity specification Ms and parameters η2. In addition, according to the dynamic performance requirement of the practical system, the parameters η1 can also be selected easily. By approximating the dead-time term of the process model with the first-order Padé or Taylor series, the expressions for 2-DOF FO-PID controller parameters are derived for three classes of FO processes with dead-time. Moreover, compared with other methods, the proposed method is simple and easy to implement. Finally, the simulation results are given to illustrate the effectiveness of this method. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Quantitative Analysis of First-Pass Contrast-Enhanced Myocardial Perfusion Multidetector CT Using a Patlak Plot Method and Extraction Fraction Correction During Adenosine Stress

NASA Astrophysics Data System (ADS)

Ichihara, Takashi; George, Richard T.; Silva, Caterina; Lima, Joao A. C.; Lardo, Albert C.

2011-02-01

The purpose of this study was to develop a quantitative method for myocardial blood flow (MBF) measurement that can be used to derive accurate myocardial perfusion measurements from dynamic multidetector computed tomography (MDCT) images by using a compartment model for calculating the first-order transfer constant (K1) with correction for the capillary transit extraction fraction (E). Six canine models of left anterior descending (LAD) artery stenosis were prepared and underwent first-pass contrast-enhanced MDCT perfusion imaging during adenosine infusion (0.14-0.21 mg/kg/min). K1 , which is the first-order transfer constant from left ventricular (LV) blood to myocardium, was measured using the Patlak plot method applied to time-attenuation curve data of the LV blood pool and myocardium. The results were compared against microsphere MBF measurements, and the extraction fraction of contrast agent was calculated. K1 is related to the regional MBF as K1=EF, E=(1-exp(-PS/F)), where PS is the permeability-surface area product and F is myocardial flow. Based on the above relationship, a look-up table from K1 to MBF can be generated and Patlak plot-derived K1 values can be converted to the calculated MBF. The calculated MBF and microsphere MBF showed a strong linear association. The extraction fraction in dogs as a function of flow (F) was E=(1-exp(-(0.2532F+0.7871)/F)) . Regional MBF can be measured accurately using the Patlak plot method based on a compartment model and look-up table with extraction fraction correction from K1 to MBF.

ICA model order selection of task co-activation networks.

PubMed

Ray, Kimberly L; McKay, D Reese; Fox, Peter M; Riedel, Michael C; Uecker, Angela M; Beckmann, Christian F; Smith, Stephen M; Fox, Peter T; Laird, Angela R

2013-01-01

Independent component analysis (ICA) has become a widely used method for extracting functional networks in the brain during rest and task. Historically, preferred ICA dimensionality has widely varied within the neuroimaging community, but typically varies between 20 and 100 components. This can be problematic when comparing results across multiple studies because of the impact ICA dimensionality has on the topology of its resultant components. Recent studies have demonstrated that ICA can be applied to peak activation coordinates archived in a large neuroimaging database (i.e., BrainMap Database) to yield whole-brain task-based co-activation networks. A strength of applying ICA to BrainMap data is that the vast amount of metadata in BrainMap can be used to quantitatively assess tasks and cognitive processes contributing to each component. In this study, we investigated the effect of model order on the distribution of functional properties across networks as a method for identifying the most informative decompositions of BrainMap-based ICA components. Our findings suggest dimensionality of 20 for low model order ICA to examine large-scale brain networks, and dimensionality of 70 to provide insight into how large-scale networks fractionate into sub-networks. We also provide a functional and organizational assessment of visual, motor, emotion, and interoceptive task co-activation networks as they fractionate from low to high model-orders.

ICA model order selection of task co-activation networks

PubMed Central

Ray, Kimberly L.; McKay, D. Reese; Fox, Peter M.; Riedel, Michael C.; Uecker, Angela M.; Beckmann, Christian F.; Smith, Stephen M.; Fox, Peter T.; Laird, Angela R.

2013-01-01

Independent component analysis (ICA) has become a widely used method for extracting functional networks in the brain during rest and task. Historically, preferred ICA dimensionality has widely varied within the neuroimaging community, but typically varies between 20 and 100 components. This can be problematic when comparing results across multiple studies because of the impact ICA dimensionality has on the topology of its resultant components. Recent studies have demonstrated that ICA can be applied to peak activation coordinates archived in a large neuroimaging database (i.e., BrainMap Database) to yield whole-brain task-based co-activation networks. A strength of applying ICA to BrainMap data is that the vast amount of metadata in BrainMap can be used to quantitatively assess tasks and cognitive processes contributing to each component. In this study, we investigated the effect of model order on the distribution of functional properties across networks as a method for identifying the most informative decompositions of BrainMap-based ICA components. Our findings suggest dimensionality of 20 for low model order ICA to examine large-scale brain networks, and dimensionality of 70 to provide insight into how large-scale networks fractionate into sub-networks. We also provide a functional and organizational assessment of visual, motor, emotion, and interoceptive task co-activation networks as they fractionate from low to high model-orders. PMID:24339802

Synchronization and an application of a novel fractional order King Cobra chaotic system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Muthukumar, P., E-mail: muthukumardgl@gmail.com; Balasubramaniam, P., E-mail: balugru@gmail.com; Ratnavelu, K., E-mail: kuru052001@gmail.com

2014-09-01

In this paper, we design a new three dimensional King Cobra face shaped fractional order chaotic system. The multi-scale synchronization scheme of two fractional order chaotic systems is described. The necessary conditions for the multi-scale synchronization of two identical fractional order King Cobra chaotic systems are derived through feedback control. A new cryptosystem is proposed for an image encryption and decryption by using synchronized fractional order King Cobra chaotic systems with the supports of multiple cryptographic assumptions. The security of the proposed cryptosystem is analyzed by the well known algebraic attacks. Numerical simulations are given to show the effectiveness ofmore » the proposed theoretical results.« less

Searches for Leptonic B Decays at BaBar

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nelson, Silke; /SLAC

2012-04-25

Measurements of the branching fractions of purely leptonic decays of B-mesons translate into constraints in the plane of the charged Higgs mass versus tan {beta} which are relatively insensitive to the particular theoretical model. Using the full BABAR dataset of 450 million B-decays we search for these decays. No significant signal is found in the decays into electrons or muons and we set upper limits on the branching fractions of the order of a 10{sup -6} at 90% confidence level. We measure the branching fraction of B {yields} {tau}{mu} to be (1.7 {+-} 0.6) x 10{sup -4}.

The role of fractional time-derivative operators on anomalous diffusion

NASA Astrophysics Data System (ADS)

Tateishi, Angel A.; Ribeiro, Haroldo V.; Lenzi, Ervin K.

2017-10-01

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties. Recently, researchers have proposed different fractional-time operators (namely: the Caputo-Fabrizio and Atangana-Baleanu) which, differently from the well-known Riemann-Liouville operator, are defined by non-singular memory kernels. Here we proposed to use these new operators to generalize the usual diffusion equation. By analyzing the corresponding fractional diffusion equations within the continuous time random walk framework, we obtained waiting time distributions characterized by exponential, stretched exponential, and power-law functions, as well as a crossover between two behaviors. For the mean square displacement, we found crossovers between usual and confined diffusion, and between usual and sub-diffusion. We obtained the exact expressions for the probability distributions, where non-Gaussian and stationary distributions emerged. This former feature is remarkable because the fractional diffusion equation is solved without external forces and subjected to the free diffusion boundary conditions. We have further shown that these new fractional diffusion equations are related to diffusive processes with stochastic resetting, and to fractional diffusion equations with derivatives of distributed order. Thus, our results suggest that these new operators may be a simple and efficient way for incorporating different structural aspects into the system, opening new possibilities for modeling and investigating anomalous diffusive processes.

Variable Order and Distributed Order Fractional Operators

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

2002-01-01

Many physical processes appear to exhibit fractional order behavior that may vary with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. This paper develops the concept of variable and distributed order fractional operators. Definitions based on the Riemann-Liouville definitions are introduced and behavior of the operators is studied. Several time domain definitions that assign different arguments to the order q in the Riemann-Liouville definition are introduced. For each of these definitions various characteristics are determined. These include: time invariance of the operator, operator initialization, physical realization, linearity, operational transforms. and memory characteristics of the defining kernels. A measure (m2) for memory retentiveness of the order history is introduced. A generalized linear argument for the order q allows the concept of "tailored" variable order fractional operators whose a, memory may be chosen for a particular application. Memory retentiveness (m2) and order dynamic behavior are investigated and applications are shown. The concept of distributed order operators where the order of the time based operator depends on an additional independent (spatial) variable is also forwarded. Several definitions and their Laplace transforms are developed, analysis methods with these operators are demonstrated, and examples shown. Finally operators of multivariable and distributed order are defined in their various applications are outlined.

Fractionalized Fermi liquid in a Kondo-Heisenberg model

DOE PAGES

Tsvelik, A. M.

2016-10-10

The Kondo-Heisenberg model is used as a controllable tool to demonstrate the existence of a peculiar metallic state with unbroken translational symmetry where the Fermi surface volume is not controlled by the total electron density. Here, I use a nonperturbative approach where the strongest interactions are taken into account by means of exact solution, and corrections are controllable. The resulting metallic state represents a fractionalized Fermi liquid where well defined quasiparticles coexist with gapped fractionalized collective excitations, in agreement with the general requirements formulated by T. Senthil et al. [Phys. Rev. Lett. 90, 216403 (2003)]. Furthermore, the system undergoes amore » phase transition to an ordered phase (charge density wave or superconducting), at the transition temperature which is parametrically small in comparison to the quasiparticle Fermi energy.« less

Ensemble brightening and enhanced quantum yield in size-purified silicon nanocrystals

DOE PAGES

Miller, Joseph B.; Van Sickle, Austin R.; Anthony, Rebecca J.; ...

2012-07-18

Here, we report on the quantum yield, photoluminescence (PL) lifetime and ensemble photoluminescent stability of highly monodisperse plasma-synthesized silicon nanocrystals (SiNCs) prepared though density-gradient ultracentrifugation in mixed organic solvents. Improved size uniformity leads to a reduction in PL line width and the emergence of entropic order in dry nanocrystal films. We find excellent agreement with the anticipated trends of quantum confinement in nanocrystalline silicon, with a solution quantum yield that is independent of nanocrystal size for the larger fractions but decreases dramatically with size for the smaller fractions. We also find a significant PL enhancement in films assembled from themore » fractions, and we use a combination of measurement, simulation and modeling to link this ‘brightening’ to a temporally enhanced quantum yield arising from SiNC interactions in ordered ensembles of monodisperse nanocrystals. Using an appropriate excitation scheme, we exploit this enhancement to achieve photostable emission.« less

An Expansion Formula with Higher-Order Derivatives for Fractional Operators of Variable Order

PubMed Central

Almeida, Ricardo

2013-01-01

We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is given. The efficiency of the approximation method is illustrated with examples. As applications, we show how the obtained results are useful to solve differential equations, and problems of the calculus of variations that depend on fractional derivatives of Marchaud type. PMID:24319382

In vivo wound healing activity and phytochemical screening of the crude extract and various fractions of Kalanchoe petitiana A. Rich (Crassulaceae) leaves in mice.

PubMed

Mekonnen, Awol; Sidamo, Temesgen; Asres, Kaleab; Engidawork, Ephrem

2013-01-30

The leaves of Kalanchoe petitiana A. Rich (Crassulaceae) are used in Ethiopian folk medicine for treatment of evil eye, fractured surface for bone setting and several skin disorders including for the treatment of sores, boils, and malignant wounds. In order to scientifically prove the claimed utilization of the plant, the effects of the extracts and the fractions were investigated using in vivo excision, incision and dead space wound models. Mice were used for wound healing study, while rats and rabbit were used for skin irritation test. For studying healing activity 80% methanolic extract and the fractions were formulated in strength of 5% and 10%, either as ointment (hydroalcoholic extract, aqueous and methanol fractions) or gel (chloroform fraction). Oral administration of the crude extract was used for dead space model. Negative controls were treated either with simple ointment or sodium carboxyl methyl cellulose xerogel, while positive controls with nitrofurazone (0.2 w/v) skin ointment. Negative controls for dead space model were treated with 1% carboxy methyl cellulose. Parameters, including rate of wound contraction, period of complete epithelializtion, hydroxyproline contents and skin breaking strength were evaluated. Significant wound healing activity was observed with ointment formulated from the crude extract at both 5% and 10% concentration (p<0.01) compared to controls in both excision and incision models. In dead space model, 600 mg/kg (p<0.01) but not 300 mg/kg significantly increased hydroxyproline content. Fractions showed variable effect, with the chloroform fraction lacking any significant effect. Both 5% and 10% formulations of the aqueous and methanolic fractions significantly increased wound contraction, decreased epithelializtion time and increased hydroxyproline content in excision wound model (p<0.05) as compared to controls. These fractions were also endowed with higher skin breaking strength in incision wound model (p<0.01). The present study provided evidence that the leaves of Kalanchoe petitiana A. Rich possess remarkable wound healing activities supporting the folkloric assertion of the plant. Fractionation revealed that polar or semi polar compound may play vital role, as both aqueous and methanolic fractions were endowed with wound healing activity. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

Phase transitions and adiabatic preparation of a fractional Chern insulator in a boson cold-atom model

NASA Astrophysics Data System (ADS)

Motruk, Johannes; Pollmann, Frank

2017-10-01

We investigate the fate of hardcore bosons in a Harper-Hofstadter model which was experimentally realized by Aidelsburger et al. [Nat. Phys. 11, 162 (2015), 10.1038/nphys3171] at half-filling of the lowest band. We discuss the stability of an emergent fractional Chern insulator (FCI) state in a finite region of the phase diagram that is separated from a superfluid state by a first-order transition when tuning the band topology following the protocol used in the experiment. Since crossing a first-order transition is unfavorable for adiabatically preparing the FCI state, we extend the model to stabilize a featureless insulating state. The transition between this phase and the topological state proves to be continuous, providing a path in parameter space along which an FCI state could be adiabatically prepared. To further corroborate this statement, we perform time-dependent DMRG calculations which demonstrate that the FCI state may indeed be reached by adiabatically tuning a simple product state.

Thermal and high pressure inactivation kinetics of blueberry peroxidase.

PubMed

Terefe, Netsanet Shiferaw; Delon, Antoine; Versteeg, Cornelis

2017-10-01

This study for the first time investigated the stability and inactivation kinetics of blueberry peroxidase in model systems (McIlvaine buffer, pH=3.6, the typical pH of blueberry juice) during thermal (40-80°C) and combined high pressure-thermal processing (0.1-690MPa, 30-90°C). At 70-80°C, the thermal inactivation kinetics was best described by a biphasic model with ∼61% labile and ∼39% stable fractions at temperature between 70 and 75°C. High pressure inhibited the inactivation of the enzyme with no inactivation at pressures as high as 690MPa and temperatures less than 50°C. The inactivation kinetics of the enzyme at 60-70°C, and pressures higher than 500MPa was best described by a first order biphasic model with ∼25% labile fraction and 75% stable fraction. The activation energy values at atmospheric pressure were 548.6kJ/mol and 324.5kJ/mol respectively for the stable and the labile fractions. Crown Copyright © 2017. Published by Elsevier Ltd. All rights reserved.

Fractional Order PIλDμ Control for Maglev Guiding System

NASA Astrophysics Data System (ADS)

Hu, Qing; Hu, Yuwei

To effectively suppress the external disturbances and parameter perturbation problem of the maglev guiding system, and improve speed and robustness, the electromagnetic guiding system is exactly linearized using state feedback method, Fractional calculus theory is introduced, the order of integer order PID control was extended to the field of fractional, then fractional order PIλDμ Controller was presented, Due to the extra two adjustable parameters compared with traditional PID controller, fractional order PIλDμ controllers were expected to show better control performance. The results of the computer simulation show that the proposed controller suppresses the external disturbances and parameter perturbation of the system effectively; the system response speed was increased; at the same time, it had flexible structure and stronger robustness.

Optimization of radioactive sources to achieve the highest precision in three-phase flow meters using Jaya algorithm.

PubMed

Roshani, G H; Karami, A; Khazaei, A; Olfateh, A; Nazemi, E; Omidi, M

2018-05-17

Gamma ray source has very important role in precision of multi-phase flow metering. In this study, different combination of gamma ray sources (( 133 Ba- 137 Cs), ( 133 Ba- 60 Co), ( 241 Am- 137 Cs), ( 241 Am- 60 Co), ( 133 Ba- 241 Am) and ( 60 Co- 137 Cs)) were investigated in order to optimize the three-phase flow meter. Three phases were water, oil and gas and the regime was considered annular. The required data was numerically generated using MCNP-X code which is a Monte-Carlo code. Indeed, the present study devotes to forecast the volume fractions in the annular three-phase flow, based on a multi energy metering system including various radiation sources and also one NaI detector, using a hybrid model of artificial neural network and Jaya Optimization algorithm. Since the summation of volume fractions is constant, a constraint modeling problem exists, meaning that the hybrid model must forecast only two volume fractions. Six hybrid models associated with the number of used radiation sources are designed. The models are employed to forecast the gas and water volume fractions. The next step is to train the hybrid models based on numerically obtained data. The results show that, the best forecast results are obtained for the gas and water volume fractions of the system including the ( 241 Am- 137 Cs) as the radiation source. Copyright © 2018 Elsevier Ltd. All rights reserved.

A stochastic fractional dynamics model of space-time variability of rain

NASA Astrophysics Data System (ADS)

Kundu, Prasun K.; Travis, James E.

2013-09-01

varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, which allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and time scales. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and on the Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to fit the second moment statistics of radar data at the smaller spatiotemporal scales. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well at these scales without any further adjustment.

A better way of representing stem area index in two-big-leaf models: the application and impact on canopy integration of leaf nitrogen content

NASA Astrophysics Data System (ADS)

Chen, M.; Butler, E. E.; Wythers, K. R.; Kattge, J.; Ricciuto, D. M.; Thornton, P. E.; Atkin, O. K.; Flores-Moreno, H.; Reich, P. B.

2017-12-01

In order to better estimate the carbon budget of the globe, accurately simulating gross primary productivity (GPP) in earth system models is critical. When upscaling leaf level photosynthesis to the canopy, climate models uses different big-leaf schemes. About half of the state-of-the-art earth system models use a "two-big-leaf" scheme that partitions canopies into direct and diffusively illuminated fractions to reduce high bias of GPP simulated by one-big-leaf models. Some two-big-leaf models, such as ACME (identical in this respect to CLM 4.5) add leaf area index (LAI) and stem area index (SAI) together when calculating canopy radiation transfer. This treatment, however, will result in higher fraction of sunlit leaves. It will also lead to an artificial overestimation of canopy nitrogen content. Here we introduce a new algorithm of simulating SAI in a two-big-leaf model. The new algorithm reduced the sunlit leave fraction of the canopy and conserved the nitrogen content from leaf to canopy level. The lower fraction of sunlit leaves reduced global GPP especially in tropical area. Compared to the default model, for the past 100 years (1909-2009), the averaged global annual GPP is lowered by 4.11 PgC year-1 using this new algorithm.

A comparison between the stability properties in a DDE model for leukemia and the modified fractional counterpart

NASA Astrophysics Data System (ADS)

Rǎdulescu, I. R.; Cândea, D.; Kaslik, E.

2017-01-01

In this paper, a delay differential equations (DDEs) model of leukemia is introduced and its dynamical properties are investigated in comparison with the modified fractional-order system where the Caputo's derivative is used. The model takes into account three types of division that a stem-like cell can undergo and cell competition between healthy and leukemia cell populations. The action of the immune system on the leukemic cell populations is also considered. The stability properties of the equilibrium points are established through numerical results and the differences between the two types of approaches are discussed. Medical conclusions are drawn in view of the obtained numerical simulations.

Lyα-emitting galaxies as a probe of reionization: large-scale bubble morphology and small-scale absorbers

NASA Astrophysics Data System (ADS)

Kakiichi, Koki; Dijkstra, Mark; Ciardi, Benedetta; Graziani, Luca

2016-12-01

The visibility of Lyα-emitting galaxies during the Epoch of Reionization is controlled by both diffuse H I patches in large-scale bubble morphology and small-scale absorbers. To investigate their impacts on Lyα transfer, we apply a novel combination of analytic modelling and cosmological hydrodynamical, radiative transfer simulations to three reionization models: (I) the `bubble' model, where only diffuse H I outside ionized bubbles is present; (II) the `web' model, where H I exists only in overdense self-shielded gas; and (III) the hybrid `web-bubble' model. The three models can explain the observed Lyα luminosity function equally well, but with very different H I fractions. This confirms a degeneracy between the ionization topology of the intergalactic medium (IGM) and the H I fraction inferred from Lyα surveys. We highlight the importance of the clustering of small-scale absorbers around galaxies. A combined analysis of the Lyα luminosity function and the Lyα fraction can break this degeneracy and provide constraints on the reionization history and its topology. Constraints can be improved by analysing the full MUV-dependent redshift evolution of the Lyα fraction of Lyman break galaxies. We find that the IGM-transmission probability distribution function is unimodal for bubble models and bimodal in web models. Comparing our models to observations, we infer that the neutral fraction at z ˜ 7 is likely to be of the order of tens of per cent when interpreted with bubble or web-bubble models, with a conservative lower limit ˜1 per cent when interpreted with web models.

On the Analysis of Fraction Subtraction Data: The DINA Model, Classification, Latent Class Sizes, and the Q-Matrix

ERIC Educational Resources Information Center

DeCarlo, Lawrence T.

2011-01-01

Cognitive diagnostic models (CDMs) attempt to uncover latent skills or attributes that examinees must possess in order to answer test items correctly. The DINA (deterministic input, noisy "and") model is a popular CDM that has been widely used. It is shown here that a logistic version of the model can easily be fit with standard software for…

A bilayer Double Semion Model with Symmetry-Enriched Topological Order

NASA Astrophysics Data System (ADS)

Ortiz, Laura; Martin-Delgado, Miguel Angel

We construct a new model of two-dimensional quantum spin systems that combines intrinsic topological orders and a global symmetry called flavour symmetry. It is referred as the bilayer Doubled Semion model (bDS) and is an instance of symmetry-enriched topological order. A honeycomb bilayer lattice is introduced to combine a Double Semion Topolgical Order with a global spin-flavour symmetry to get the fractionalization of its quasiparticles. The bDS model exhibits non-trival braiding self-statistics of excitations and its dual model constitutes a Symmetry-Protected Topological Order with novel edge states. This dual model gives rise to a bilayer Non-Trivial Paramagnet that is invariant under the flavour symmetry and the well-known spin flip symmetry. We acknowledge financial support from the Spanish MINECO Grants FIS2012-33152, FIS2015-67411, and the CAM research consortium QUITEMAD+, Grant No. S2013/ICE-2801. The research of M.A.M.-D. has been supported in part by the U.S. Army Research Office throu.

Magma differentiation rates from ( 226Ra / 230Th) and the size and power output of magma chambers

NASA Astrophysics Data System (ADS)

Blake, Stephen; Rogers, Nick

2005-08-01

We present a mathematical model for the evolution of the ( 226Ra / 230Th) activity ratio during simultaneous fractional crystallization and ageing of magma. The model is applied to published data for four volcanic suites that are independently known to have evolved by fractional crystallization. These are tholeiitic basalt from Ardoukoba, Djibouti, MORB from the East Pacific Rise, alkali basalt to mugearite from Vestmannaeyjar, Iceland, and basaltic andesites from Miyakejima, Izu-Bonin arc. In all cases ( 226Ra / 230Th) correlates with indices of fractional crystallization, such as Th, and the data fall close to model curves of constant fractional crystallization rate. The best fit rates vary from 2 to 6 × 10 - 4 yr - 1 . Consequently, the time required to generate moderately evolved magmas ( F ≤ 0.7) is of the order of 500 to 1500 yrs and closed magma chambers will have lifetimes of 1700 to 5000 yrs. These rates and timescales are argued to depend principally on the specific power output (i.e., power output per unit volume) of the magma chambers that are the sites of fractional crystallization. Equating the heat flux at the EPR to the heat flux from the sub-axial magma chamber that evolves at a rate of ca. 3 × 10 - 4 yr - 1 implies that the magma body is a sill of ca. 100 m thickness, a value which coincides with independent estimates from seismology. The similarity of the four inferred differentiation rates suggests that the specific power output of shallow magma chambers in a range of tectonic settings covers a similarly narrow range of ca. 10 to 50 MW km - 3 . Their differentiation rates are some two orders of magnitude slower than that of the basaltic Makaopuhi lava lake, Hawaii, that cooled to the atmosphere. This is consistent with the two orders of magnitude difference in heat flux between Makaopuhi and the East Pacific Rise. ( 226Ra / 230Th) data for magma suites related by fractional crystallization allow the magma differentiation rate to be estimated and, from this, the thermal budget of the magma chamber addressed, and where an independent measurement of heat flux exists, to place constraints on the size of the magma chamber. Such results have the potential to constrain the likely timescale and size of future eruptions of evolved magmas.

Grain-Size Based Additivity Models for Scaling Multi-rate Uranyl Surface Complexation in Subsurface Sediments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Xiaoying; Liu, Chongxuan; Hu, Bill X.

This study statistically analyzed a grain-size based additivity model that has been proposed to scale reaction rates and parameters from laboratory to field. The additivity model assumed that reaction properties in a sediment including surface area, reactive site concentration, reaction rate, and extent can be predicted from field-scale grain size distribution by linearly adding reaction properties for individual grain size fractions. This study focused on the statistical analysis of the additivity model with respect to reaction rate constants using multi-rate uranyl (U(VI)) surface complexation reactions in a contaminated sediment as an example. Experimental data of rate-limited U(VI) desorption in amore » stirred flow-cell reactor were used to estimate the statistical properties of multi-rate parameters for individual grain size fractions. The statistical properties of the rate constants for the individual grain size fractions were then used to analyze the statistical properties of the additivity model to predict rate-limited U(VI) desorption in the composite sediment, and to evaluate the relative importance of individual grain size fractions to the overall U(VI) desorption. The result indicated that the additivity model provided a good prediction of the U(VI) desorption in the composite sediment. However, the rate constants were not directly scalable using the additivity model, and U(VI) desorption in individual grain size fractions have to be simulated in order to apply the additivity model. An approximate additivity model for directly scaling rate constants was subsequently proposed and evaluated. The result found that the approximate model provided a good prediction of the experimental results within statistical uncertainty. This study also found that a gravel size fraction (2-8mm), which is often ignored in modeling U(VI) sorption and desorption, is statistically significant to the U(VI) desorption in the sediment.« less

H2-norm for mesh optimization with application to electro-thermal modeling of an electric wire in automotive context

NASA Astrophysics Data System (ADS)

Chevrié, Mathieu; Farges, Christophe; Sabatier, Jocelyn; Guillemard, Franck; Pradere, Laetitia

2017-04-01

In automotive application field, reducing electric conductors dimensions is significant to decrease the embedded mass and the manufacturing costs. It is thus essential to develop tools to optimize the wire diameter according to thermal constraints and protection algorithms to maintain a high level of safety. In order to develop such tools and algorithms, accurate electro-thermal models of electric wires are required. However, thermal equation solutions lead to implicit fractional transfer functions involving an exponential that cannot be embedded in a car calculator. This paper thus proposes an integer order transfer function approximation methodology based on a spatial discretization for this class of fractional transfer functions. Moreover, the H2-norm is used to minimize approximation error. Accuracy of the proposed approach is confirmed with measured data on a 1.5 mm2 wire implemented in a dedicated test bench.

Destruction of solid tumors by immune cells

NASA Astrophysics Data System (ADS)

López, Álvaro G.; Seoane, Jesús M.; Sanjuán, Miguel A. F.

2017-03-01

The fractional cell kill is a mathematical expression describing the rate at which a certain population of cells is reduced to a fraction of itself. In order to investigate the fractional cell kill that governs the rate at which a solid tumor is lysed by a cell population of cytotoxic CD8+ T cells (CTLs), we present several in silico simulations and mathematical analyses. When the CTLs eradicate efficiently the tumor cells, the models predict a correlation between the morphology of the tumors and the rate at which they are lysed. However, when the effectiveness of the immune cells is decreased, the mathematical function fails to reproduce the process of lysis. This limit is thoroughly discussed and a new fractional cell kill is proposed.

Method for analyzing E x B probe spectra from Hall thruster plumes.

PubMed

Shastry, Rohit; Hofer, Richard R; Reid, Bryan M; Gallimore, Alec D

2009-06-01

Various methods for accurately determining ion species' current fractions using E x B probes in Hall thruster plumes are investigated. The effects of peak broadening and charge exchange on the calculated values of current fractions are quantified in order to determine the importance of accounting for them in the analysis. It is shown that both peak broadening and charge exchange have a significant effect on the calculated current fractions over a variety of operating conditions, especially at operating pressures exceeding 10(-5) torr. However, these effects can be accounted for using a simple approximation for the velocity distribution function and a one-dimensional charge exchange correction model. In order to keep plume attenuation from charge exchange below 30%, it is recommended that pz < or = 2, where p is the measured facility pressure in units of 10(-5) torr and z is the distance from the thruster exit plane to the probe inlet in meters. The spatial variation of the current fractions in the plume of a Hall thruster and the error induced from taking a single-point measurement are also briefly discussed.

Microbially Mediated Kinetic Sulfur Isotope Fractionation: Reactive Transport Modeling Benchmark

NASA Astrophysics Data System (ADS)

Wanner, C.; Druhan, J. L.; Cheng, Y.; Amos, R. T.; Steefel, C. I.; Ajo Franklin, J. B.

2014-12-01

Microbially mediated sulfate reduction is a ubiquitous process in many subsurface systems. Isotopic fractionation is characteristic of this anaerobic process, since sulfate reducing bacteria (SRB) favor the reduction of the lighter sulfate isotopologue (S32O42-) over the heavier isotopologue (S34O42-). Detection of isotopic shifts have been utilized as a proxy for the onset of sulfate reduction in subsurface systems such as oil reservoirs and aquifers undergoing uranium bioremediation. Reactive transport modeling (RTM) of kinetic sulfur isotope fractionation has been applied to field and laboratory studies. These RTM approaches employ different mathematical formulations in the representation of kinetic sulfur isotope fractionation. In order to test the various formulations, we propose a benchmark problem set for the simulation of kinetic sulfur isotope fractionation during microbially mediated sulfate reduction. The benchmark problem set is comprised of four problem levels and is based on a recent laboratory column experimental study of sulfur isotope fractionation. Pertinent processes impacting sulfur isotopic composition such as microbial sulfate reduction and dispersion are included in the problem set. To date, participating RTM codes are: CRUNCHTOPE, TOUGHREACT, MIN3P and THE GEOCHEMIST'S WORKBENCH. Preliminary results from various codes show reasonable agreement for the problem levels simulating sulfur isotope fractionation in 1D.

Stable multi-domain spectral penalty methods for fractional partial differential equations

NASA Astrophysics Data System (ADS)

Xu, Qinwu; Hesthaven, Jan S.

2014-01-01

We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.

Multi-pathway exposure modelling of chemicals in cosmetics ...

EPA Pesticide Factsheets

We present a novel multi-pathway, mass balance based, fate and exposure model compatible with life cycle and high-throughput screening assessments of chemicals in cosmetic products. The exposures through product use as well as post-use emissions and environmental media were quantified based on the chemical mass originally applied via a product, multiplied by the product intake fractions (PiF, the fraction of a chemical in a product that is taken in by exposed persons) to yield intake rates. The average PiFs for the evaluated chemicals in shampoo ranged from 3 × 10− 4 up to 0.3 for rapidly absorbed ingredients. Average intake rates ranged between nano- and micrograms per kilogram bodyweight per day; the order of chemical prioritization was strongly affected by the ingredient concentration in shampoo. Dermal intake and inhalation (for 20% of the evaluated chemicals) during use dominated exposure, while the skin permeation coefficient dominated the estimated uncertainties. The fraction of chemical taken in by a shampoo user often exceeded, by orders of magnitude, the aggregated fraction taken in by the population through post-use environmental emissions. Chemicals with relatively high octanol-water partitioning and/or volatility, and low molecular weight tended to have higher use stage exposure. Chemicals with low intakes during use (< 1%) and subsequent high post-use emissions, however, may yield comparable intake for a member of the general population. The pre

Stochastic transitions and jamming in granular pipe flow

NASA Astrophysics Data System (ADS)

Brand, Samuel; Ball, Robin C.; Nicodemi, Mario

2011-03-01

We study a model granular suspension driven down a channel by an embedding fluid via computer simulations. We characterize the different system flow regimes and the stochastic nature of the transitions between them. For packing fractions below a threshold ϕm, granular flow is disordered and exhibits an Ostwald-de Waele-type power-law shear-stress constitutive relation. Above ϕm, two asymptotic states exist; disordered flow can persist indefinitely, yet, in a fraction of samples, the system self-organizes in an ordered form of flow where grains move in parallel ordered layers. In the latter regime, the Ostwald-de Waele relationship breaks down and a nearly solid plug appears in the center, with linear shear regions at the boundaries. Above a higher threshold ϕg, an abrupt jamming transition is observed if ordering is avoided.

Free convection flow of some fractional nanofluids over a moving vertical plate with uniform heat flux and heat source

NASA Astrophysics Data System (ADS)

Azhar, Waqas Ali; Vieru, Dumitru; Fetecau, Constantin

2017-08-01

Free convection flow of some water based fractional nanofluids over a moving infinite vertical plate with uniform heat flux and heat source is analytically and graphically studied. Exact solutions for dimensionless temperature and velocity fields, Nusselt numbers, and skin friction coefficients are established in integral form in terms of modified Bessel functions of the first kind. These solutions satisfy all imposed initial and boundary conditions and reduce to the similar solutions for ordinary nanofluids when the fractional parameters tend to one. Furthermore, they reduce to the known solutions from the literature when the plate is fixed and the heat source is absent. The influence of fractional parameters on heat transfer and fluid motion is graphically underlined and discussed. The enhancement of heat transfer in such flows is higher for fractional nanofluids in comparison with ordinary nanofluids. Moreover, the use of fractional models allows us to choose the fractional parameters in order to get a very good agreement between experimental and theoretical results.

A two-phase model for aluminized explosives on the ballistic and brisance performance

NASA Astrophysics Data System (ADS)

Kim, Wuhyun; Gwak, Min-cheol; Lee, Young-hun; Yoh, Jack J.

2018-02-01

The performance of aluminized high explosives is considered by varying the aluminum (Al) mass fraction in a heterogeneous mixture model. Since the time scales of the characteristic induction and combustion of high explosives and Al particles differ, the process of energy release behind the leading detonation wave front occurs over an extended period of time. For simulating the performance of aluminized explosives with varying Al mass fraction, HMX (1,3,5,7-tetrahexmine-1,3,5,7-tetrazocane) is considered as a base explosive when formulating the multiphase conservation laws of mass, momentum, and energy exchanges between the HMX product gases and Al particles. In the current study, a two-phase model is utilized in order to determine the effects of the Al mass fraction in a condensed phase explosive. First, two types of confined rate stick tests are considered to investigate the detonation velocity and the acceleration ability, which refers to the radial expansion velocity of the confinement shell. The simulation results of the confined rate stick test are compared with the experimental data for the Al mass fraction range of 0%-25%, and the optimal Al mass fraction is provided, which is consistent with the experimental observations. Additionally, a series of plate dent test simulations are conducted, the results of which show the same tendency as those of the experimental tests with varying Al mass fractions.

Parameter Estimation of Fractional-Order Chaotic Systems by Using Quantum Parallel Particle Swarm Optimization Algorithm

PubMed Central

Huang, Yu; Guo, Feng; Li, Yongling; Liu, Yufeng

2015-01-01

Parameter estimation for fractional-order chaotic systems is an important issue in fractional-order chaotic control and synchronization and could be essentially formulated as a multidimensional optimization problem. A novel algorithm called quantum parallel particle swarm optimization (QPPSO) is proposed to solve the parameter estimation for fractional-order chaotic systems. The parallel characteristic of quantum computing is used in QPPSO. This characteristic increases the calculation of each generation exponentially. The behavior of particles in quantum space is restrained by the quantum evolution equation, which consists of the current rotation angle, individual optimal quantum rotation angle, and global optimal quantum rotation angle. Numerical simulation based on several typical fractional-order systems and comparisons with some typical existing algorithms show the effectiveness and efficiency of the proposed algorithm. PMID:25603158

Analysis of Ingredient Lists to Quantitatively Characterize ...

EPA Pesticide Factsheets

The EPA’s ExpoCast program is developing high throughput (HT) approaches to generate the needed exposure estimates to compare against HT bioactivity data generated from the US inter-agency Tox21 and the US EPA ToxCast programs. Assessing such exposures for the thousands of chemicals in consumer products requires data on product composition. This is a challenge since quantitative product composition data are rarely available. We developed methods to predict the weight fractions of chemicals in consumer products from weight fraction-ordered chemical ingredient lists, and curated a library of such lists from online manufacturer and retailer sites. The probabilistic model predicts weight fraction as a function of the total number of reported ingredients, the rank of the ingredient in the list, the minimum weight fraction for which ingredients were reported, and the total weight fraction of unreported ingredients. Weight fractions predicted by the model compared very well to available quantitative weight fraction data obtained from Material Safety Data Sheets for products with 3-8 ingredients. Lists were located from the online sources for 5148 products containing 8422 unique ingredient names. A total of 1100 of these names could be located in EPA’s HT chemical database (DSSTox), and linked to 864 unique Chemical Abstract Service Registration Numbers (392 of which were in the Tox21 chemical library). Weight fractions were estimated for these 864 CASRN. Using a

Geometric confinement influences cellular mechanical properties I -- adhesion area dependence.

PubMed

Su, Judith; Jiang, Xingyu; Welsch, Roy; Whitesides, George M; So, Peter T C

2007-06-01

Interactions between the cell and the extracellular matrix regulate a variety of cellular properties and functions, including cellular rheology. In the present study of cellular adhesion, area was controlled by confining NIH 3T3 fibroblast cells to circular micropatterned islands of defined size. The shear moduli of cells adhering to islands of well defined geometry, as measured by magnetic microrheometry, was found to have a significantly lower variance than those of cells allowed to spread on unpatterned surfaces. We observe that the area of cellular adhesion influences shear modulus. Rheological measurements further indicate that cellular shear modulus is a biphasic function of cellular adhesion area with stiffness decreasing to a minimum value for intermediate areas of adhesion, and then increasing for cells on larger patterns. We propose a simple hypothesis: that the area of adhesion affects cellular rheological properties by regulating the structure of the actin cytoskeleton. To test this hypothesis, we quantified the volume fraction of polymerized actin in the cytosol by staining with fluorescent phalloidin and imaging using quantitative 3D microscopy. The polymerized actin volume fraction exhibited a similar biphasic dependence on adhesion area. Within the limits of our simplifying hypothesis, our experimental results permit an evaluation of the ability of established, micromechanical models to predict the cellular shear modulus based on polymerized actin volume fraction. We investigated the "tensegrity", "cellular-solids", and "biopolymer physics" models that have, respectively, a linear, quadratic, and 5/2 dependence on polymerized actin volume fraction. All three models predict that a biphasic trend in polymerized actin volume fraction as a function of adhesion area will result in a biphasic behavior in shear modulus. Our data favors a higher-order dependence on polymerized actin volume fraction. Increasingly better experimental agreement is observed for the tensegrity, the cellular solids, and the biopolymer models respectively. Alternatively if we postulate the existence of a critical actin volume fraction below which the shear modulus vanishes, the experimental data can be equivalently described by a model with an almost linear dependence on polymerized actin volume fraction; this observation supports a tensegrity model with a critical actin volume fraction.

Colored noise and a stochastic fractional model for correlated inputs and adaptation in neuronal firing.

PubMed

Pirozzi, Enrica

2018-04-01

High variability in the neuronal response to stimulations and the adaptation phenomenon cannot be explained by the standard stochastic leaky integrate-and-fire model. The main reason is that the uncorrelated inputs involved in the model are not realistic. There exists some form of dependency between the inputs, and it can be interpreted as memory effects. In order to include these physiological features in the standard model, we reconsider it with time-dependent coefficients and correlated inputs. Due to its hard mathematical tractability, we perform simulations of it for a wide investigation of its output. A Gauss-Markov process is constructed for approximating its non-Markovian dynamics. The first passage time probability density of such a process can be numerically evaluated, and it can be used to fit the histograms of simulated firing times. Some estimates of the moments of firing times are also provided. The effect of the correlation time of the inputs on firing densities and on firing rates is shown. An exponential probability density of the first firing time is estimated for low values of input current and high values of correlation time. For comparison, a simulation-based investigation is also carried out for a fractional stochastic model that allows to preserve the memory of the time evolution of the neuronal membrane potential. In this case, the memory parameter that affects the firing activity is the fractional derivative order. In both models an adaptation level of spike frequency is attained, even if along different modalities. Comparisons and discussion of the obtained results are provided.

A class of fractional differential hemivariational inequalities with application to contact problem

NASA Astrophysics Data System (ADS)

Zeng, Shengda; Liu, Zhenhai; Migorski, Stanislaw

2018-04-01

In this paper, we study a class of generalized differential hemivariational inequalities of parabolic type involving the time fractional order derivative operator in Banach spaces. We use the Rothe method combined with surjectivity of multivalued pseudomonotone operators and properties of the Clarke generalized gradient to establish existence of solution to the abstract inequality. As an illustrative application, a frictional quasistatic contact problem for viscoelastic materials with adhesion is investigated, in which the friction and contact conditions are described by the Clarke generalized gradient of nonconvex and nonsmooth functionals, and the constitutive relation is modeled by the fractional Kelvin-Voigt law.

Generalized Nonlinear Yule Models

NASA Astrophysics Data System (ADS)

Lansky, Petr; Polito, Federico; Sacerdote, Laura

2016-11-01

With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.

Fractional calculus and morphogen gradient formation

NASA Astrophysics Data System (ADS)

Yuste, Santos Bravo; Abad, Enrique; Lindenberg, Katja

2012-12-01

Some microscopic models for reactive systems where the reaction kinetics is limited by subdiffusion are described by means of reaction-subdiffusion equations where fractional derivatives play a key role. In particular, we consider subdiffusive particles described by means of a Continuous Time Random Walk (CTRW) model subject to a linear (first-order) death process. The resulting fractional equation is employed to study the developmental biology key problem of morphogen gradient formation for the case in which the morphogens are subdiffusive. If the morphogen degradation rate (reactivity) is constant, we find exponentially decreasing stationary concentration profiles, which are similar to the profiles found when the morphogens diffuse normally. However, for the case in which the degradation rate decays exponentially with the distance to the morphogen source, we find that the morphogen profiles are qualitatively different from the profiles obtained when the morphogens diffuse normally.

Cure models for estimating hospital-based breast cancer survival.

PubMed

Rama, Ranganathan; Swaminathan, Rajaraman; Venkatesan, Perumal

2010-01-01

Research on cancer survival is enriched by development and application of innovative analytical approaches in relation to standard methods. The aim of the present paper is to document the utility of a mixture model to estimate the cure fraction and compare it with other approaches. The data were for 1,107 patients with locally advanced breast cancer, who completed the neo-adjuvant treatment protocol during 1990-99 at the Cancer Institute (WIA), Chennai, India. Tumour stage, post-operative pathological node (PN) and tumour residue (TR) status were studied. Event free survival probability was estimated using the Kaplan-Meier method. Cure models under proportional and non-proportional hazard assumptions following log normal distribution for survival time were used to estimate both the cure fraction and the survival function for the uncured. Event free survival at 5 and 10 years were 64.2% and 52.6% respectively and cure fraction was 47.5% for all cases together. Follow up ranged between 0-15 years and survival probabilities showed minimal changes after 7 years of follow up. TR and PN emerged as independent prognostic factors using Cox and proportional hazard (PH) cure models. Proportionality condition was violated when tumour stage was considered and it was statistically significant only under PH and not under non PH cure models. However, TR and PN continued to be independent prognostic factors after adjusting for tumour stage using the non PH cure model. A consistent ordering of cure fractions with respect to factors of PN and TR was forthcoming across tumour stages using PH and non PH cure models, but perceptible differences in survival were observed between the two. If PH conditions are violated, analysis using a non PH model is advocated and mixture cure models are useful in estimating the cure fraction and constructing survival curves for non-cures.

A partially coupled, fraction-by-fraction modelling approach to the subsurface migration of gasoline spills

NASA Astrophysics Data System (ADS)

Fagerlund, F.; Niemi, A.

2007-01-01

The subsurface spreading behaviour of gasoline, as well as several other common soil- and groundwater pollutants (e.g. diesel, creosote), is complicated by the fact that it is a mixture of hundreds of different constituents, behaving differently with respect to e.g. dissolution, volatilisation, adsorption and biodegradation. Especially for scenarios where the non-aqueous phase liquid (NAPL) phase is highly mobile, such as for sudden spills in connection with accidents, it is necessary to simultaneously analyse the migration of the NAPL and its individual components in order to assess risks and environmental impacts. Although a few fully coupled, multi-phase, multi-constituent models exist, such models are highly complex and may be time consuming to use. A new, somewhat simplified methodology for modelling the subsurface migration of gasoline while taking its multi-constituent nature into account is therefore introduced here. Constituents with similar properties are grouped together into eight fractions. The migration of each fraction in the aqueous and gaseous phases as well as adsorption is modelled separately using a single-constituent multi-phase flow model, while the movement of the free-phase gasoline is essentially the same for all fractions. The modelling is done stepwise to allow updating of the free-phase gasoline composition at certain time intervals. The output is the concentration of the eight different fractions in the aqueous, gaseous, free gasoline and solid phases with time. The approach is evaluated by comparing it to a fully coupled multi-phase, multi-constituent numerical simulator in the modelling of a typical accident-type spill scenario, based on a tanker accident in northern Sweden. Here the PCFF method produces results similar to those of the more sophisticated, fully coupled model. The benefit of the method is that it is easy to use and can be applied to any single-constituent multi-phase numerical simulator, which in turn may have different strengths in incorporating various processes. The results demonstrate that the different fractions have significantly different migration behaviours and although the methodology involves some simplifications, it is a considerable improvement compared to modelling the gasoline constituents completely individually or as one single mixture.

A Stochastic Fractional Dynamics Model of Rainfall Statistics

NASA Astrophysics Data System (ADS)

Kundu, Prasun; Travis, James

2013-04-01

Rainfall varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, that allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is designed to faithfully reflect the scale dependence and is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and times scales. The main restriction is the assumption that the statistics of the precipitation field is spatially homogeneous and isotropic and stationary in time. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and in Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to the second moment statistics of the radar data. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well without any further adjustment. Some data sets containing periods of non-stationary behavior that involves occasional anomalously correlated rain events, present a challenge for the model.

Stochastic P-bifurcation and stochastic resonance in a noisy bistable fractional-order system

NASA Astrophysics Data System (ADS)

Yang, J. H.; Sanjuán, Miguel A. F.; Liu, H. G.; Litak, G.; Li, X.

2016-12-01

We investigate the stochastic response of a noisy bistable fractional-order system when the fractional-order lies in the interval (0, 2]. We focus mainly on the stochastic P-bifurcation and the phenomenon of the stochastic resonance. We compare the generalized Euler algorithm and the predictor-corrector approach which are commonly used for numerical calculations of fractional-order nonlinear equations. Based on the predictor-corrector approach, the stochastic P-bifurcation and the stochastic resonance are investigated. Both the fractional-order value and the noise intensity can induce an stochastic P-bifurcation. The fractional-order may lead the stationary probability density function to turn from a single-peak mode to a double-peak mode. However, the noise intensity may transform the stationary probability density function from a double-peak mode to a single-peak mode. The stochastic resonance is investigated thoroughly, according to the linear and the nonlinear response theory. In the linear response theory, the optimal stochastic resonance may occur when the value of the fractional-order is larger than one. In previous works, the fractional-order is usually limited to the interval (0, 1]. Moreover, the stochastic resonance at the subharmonic frequency and the superharmonic frequency are investigated respectively, by using the nonlinear response theory. When it occurs at the subharmonic frequency, the resonance may be strong and cannot be ignored. When it occurs at the superharmonic frequency, the resonance is weak. We believe that the results in this paper might be useful for the signal processing of nonlinear systems.

Diffusion weighted imaging for the differentiation of breast tumors: From apparent diffusion coefficient to high order diffusion tensor imaging.

PubMed

Teruel, Jose R; Goa, Pål E; Sjøbakk, Torill E; Østlie, Agnes; Fjøsne, Hans E; Bathen, Tone F

2016-05-01

To compare "standard" diffusion weighted imaging, and diffusion tensor imaging (DTI) of 2(nd) and 4(th) -order for the differentiation of malignant and benign breast lesions. Seventy-one patients were imaged at 3 Tesla with a 16-channel breast coil. A diffusion weighted MRI sequence including b = 0 and b = 700 in 30 directions was obtained for all patients. The image data were fitted to three different diffusion models: isotropic model - apparent diffusion coefficient (ADC), 2(nd) -order tensor model (the standard model used for DTI) and a 4(th) -order tensor model, with increased degrees of freedom to describe anisotropy. The ability of the fitted parameters in the different models to differentiate between malignant and benign tumors was analyzed. Seventy-two breast lesions were analyzed, out of which 38 corresponded to malignant and 34 to benign tumors. ADC (using any model) presented the highest discriminative ability of malignant from benign tumors with a receiver operating characteristic area under the curve (AUC) of 0.968, and sensitivity and specificity of 94.1% and 94.7% respectively for a 1.33 × 10(-3) mm(2) /s cutoff. Anisotropy measurements presented high statistical significance between malignant and benign tumors (P < 0.001), but with lower discriminative ability of malignant from benign tumors than ADC (AUC of 0.896 and 0.897 for fractional anisotropy and generalized anisotropy respectively). Statistical significant difference was found between generalized anisotropy and fractional anisotropy for cancers (P < 0.001) but not for benign lesions (P = 0.87). While anisotropy parameters have the potential to provide additional value for breast applications as demonstrated in this study, ADC exhibited the highest differentiation power between malignant and benign breast tumors. © 2015 Wiley Periodicals, Inc.

Analysis of tristable energy harvesting system having fractional order viscoelastic material

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oumbé Tékam, G. T.; Woafo, P.; Kitio Kwuimy, C. A.

2015-01-15

A particular attention is devoted to analyze the dynamics of a strongly nonlinear energy harvester having fractional order viscoelastic flexible material. The strong nonlinearity is obtained from the magnetic interaction between the end free of the flexible material and three equally spaced magnets. Periodic responses are computed using the KrylovBogoliubov averaging method, and the effects of fractional order damping on the output electric energy are analyzed. It is obtained that the harvested energy is enhanced for small order of the fractional derivative. Considering the order and strength of the fractional viscoelastic property as control parameter, the complexity of the systemmore » response is investigated through the Melnikov criteria for horseshoes chaos, which allows us to derive the mathematical expression of the boundary between intra-well motion and bifurcations appearance domain. We observe that the order and strength of the fractional viscoelastic property can be effectively used to control chaos in the system. The results are confirmed by the smooth and fractal shape of the basin of attraction as the order of derivative decreases. The bifurcation diagrams and the corresponding Lyapunov exponents are plotted to get insight into the nonlinear response of the system.« less

Observation of fractional Chern insulators in a van der Waals heterostructure

NASA Astrophysics Data System (ADS)

Spanton, Eric M.; Zibrov, Alexander A.; Zhou, Haoxin; Taniguchi, Takashi; Watanabe, Kenji; Zaletel, Michael P.; Young, Andrea F.

2018-04-01

Topologically ordered phases are characterized by long-range quantum entanglement and fractional statistics rather than by symmetry breaking. First observed in a fractionally filled continuum Landau level, topological order has since been proposed to arise more generally at fractional fillings of topologically nontrivial Chern bands. Here we report the observation of gapped states at fractional fillings of Harper-Hofstadter bands arising from the interplay of a magnetic field and a superlattice potential in a bilayer graphene–hexagonal boron nitride heterostructure. We observed phases at fractional filling of bands with Chern indices C=‑1, ±2, and ±3. Some of these phases, in C=‑1 and C=2 bands, are characterized by fractional Hall conductance—that is, they are known as fractional Chern insulators and constitute an example of topological order beyond Landau levels.

Variability estimation of urban wastewater biodegradable fractions by respirometry.

PubMed

Lagarde, Fabienne; Tusseau-Vuillemin, Marie-Hélène; Lessard, Paul; Héduit, Alain; Dutrop, François; Mouchel, Jean-Marie

2005-11-01

This paper presents a methodology for assessing the variability of biodegradable chemical oxygen demand (COD) fractions in urban wastewaters. Thirteen raw wastewater samples from combined and separate sewers feeding the same plant were characterised, and two optimisation procedures were applied in order to evaluate the variability in biodegradable fractions and related kinetic parameters. Through an overall optimisation on all the samples, a unique kinetic parameter set was obtained with a three-substrate model including an adsorption stage. This method required powerful numerical treatment, but improved the identifiability problem compared to the usual sample-to-sample optimisation. The results showed that the fractionation of samples collected in the combined sewer was much more variable (standard deviation of 70% of the mean values) than the fractionation of the separate sewer samples, and the slowly biodegradable COD fraction was the most significant fraction (45% of the total COD on average). Because these samples were collected under various rain conditions, the standard deviations obtained here on the combined sewer biodegradable fractions could be used as a first estimation of the variability of this type of sewer system.

Characterization of the Dynamics of Climate Systems and Identification of Missing Mechanisms Impacting the Long Term Predictive Capabilities of Global Climate Models Utilizing Dynamical Systems Approaches to the Analysis of Observed and Modeled Climate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhatt, Uma S.; Wackerbauer, Renate; Polyakov, Igor V.

The goal of this research was to apply fractional and non-linear analysis techniques in order to develop a more complete characterization of climate change and variability for the oceanic, sea ice and atmospheric components of the Earth System. This research applied two measures of dynamical characteristics of time series, the R/S method of calculating the Hurst exponent and Renyi entropy, to observational and modeled climate data in order to evaluate how well climate models capture the long-term dynamics evident in observations. Fractional diffusion analysis was applied to ARGO ocean buoy data to quantify ocean transport. Self organized maps were appliedmore » to North Pacific sea level pressure and analyzed in ways to improve seasonal predictability for Alaska fire weather. This body of research shows that these methods can be used to evaluate climate models and shed light on climate mechanisms (i.e., understanding why something happens). With further research, these methods show promise for improving seasonal to longer time scale forecasts of climate.« less

Condition of Mechanical Equilibrium at the Phase Interface with Arbitrary Geometry

NASA Astrophysics Data System (ADS)

Zubkov, V. V.; Zubkova, A. V.

2017-09-01

The authors produced an expression for the mechanical equilibrium condition at the phase interface within the force definition of surface tension. This equilibrium condition is the most general one from the mathematical standpoint and takes into account the three-dimensional aspect of surface tension. Furthermore, the formula produced allows describing equilibrium on the fractal surface of the interface. The authors used the fractional integral model of fractal distribution and took the fractional order integrals over Euclidean space instead of integrating over the fractal set.

Comments on “A Unified Representation of Deep Moist Convection in Numerical Modeling of the Atmosphere. Part I”

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Guang; Fan, Jiwen; Xu, Kuan-Man

2015-06-01

Arakawa and Wu (2013, hereafter referred to as AW13) recently developed a formal approach to a unified parameterization of atmospheric convection for high-resolution numerical models. The work is based on ideas formulated by Arakawa et al. (2011). It lays the foundation for a new parameterization pathway in the era of high-resolution numerical modeling of the atmosphere. The key parameter in this approach is convective cloud fraction. In conventional parameterization, it is assumed that <<1. This assumption is no longer valid when horizontal resolution of numerical models approaches a few to a few tens kilometers, since in such situations convective cloudmore » fraction can be comparable to unity. Therefore, they argue that the conventional approach to parameterizing convective transport must include a factor 1 - in order to unify the parameterization for the full range of model resolutions so that it is scale-aware and valid for large convective cloud fractions. While AW13’s approach provides important guidance for future convective parameterization development, in this note we intend to show that the conventional approach already has this scale awareness factor 1 - built in, although not recognized for the last forty years. Therefore, it should work well even in situations of large convective cloud fractions in high-resolution numerical models.« less

An explicit closed-form analytical solution for European options under the CGMY model

NASA Astrophysics Data System (ADS)

Chen, Wenting; Du, Meiyu; Xu, Xiang

2017-01-01

In this paper, we consider the analytical pricing of European path-independent options under the CGMY model, which is a particular type of pure jump Le´vy process, and agrees well with many observed properties of the real market data by allowing the diffusions and jumps to have both finite and infinite activity and variation. It is shown that, under this model, the option price is governed by a fractional partial differential equation (FPDE) with both the left-side and right-side spatial-fractional derivatives. In comparison to derivatives of integer order, fractional derivatives at a point not only involve properties of the function at that particular point, but also the information of the function in a certain subset of the entire domain of definition. This ;globalness; of the fractional derivatives has added an additional degree of difficulty when either analytical methods or numerical solutions are attempted. Albeit difficult, we still have managed to derive an explicit closed-form analytical solution for European options under the CGMY model. Based on our solution, the asymptotic behaviors of the option price and the put-call parity under the CGMY model are further discussed. Practically, a reliable numerical evaluation technique for the current formula is proposed. With the numerical results, some analyses of impacts of four key parameters of the CGMY model on European option prices are also provided.

Boundedness, Mittag-Leffler stability and asymptotical ω-periodicity of fractional-order fuzzy neural networks.

PubMed

Wu, Ailong; Zeng, Zhigang

2016-02-01

We show that the ω-periodic fractional-order fuzzy neural networks cannot generate non-constant ω-periodic signals. In addition, several sufficient conditions are obtained to ascertain the boundedness and global Mittag-Leffler stability of fractional-order fuzzy neural networks. Furthermore, S-asymptotical ω-periodicity and global asymptotical ω-periodicity of fractional-order fuzzy neural networks is also characterized. The obtained criteria improve and extend the existing related results. To illustrate and compare the theoretical criteria, some numerical examples with simulation results are discussed in detail. Crown Copyright © 2015. Published by Elsevier Ltd. All rights reserved.

On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system

NASA Astrophysics Data System (ADS)

Hajipour, Ahamad; Hajipour, Mojtaba; Baleanu, Dumitru

2018-05-01

This manuscript mainly focuses on the construction, dynamic analysis and control of a new fractional-order financial system. The basic dynamical behaviors of the proposed system are studied such as the equilibrium points and their stability, Lyapunov exponents, bifurcation diagrams, phase portraits of state variables and the intervals of system parameters. It is shown that the system exhibits hyperchaotic behavior for a number of system parameters and fractional-order values. To stabilize the proposed hyperchaotic fractional system with uncertain dynamics and disturbances, an efficient adaptive sliding mode controller technique is developed. Using the proposed technique, two hyperchaotic fractional-order financial systems are also synchronized. Numerical simulations are presented to verify the successful performance of the designed controllers.

Chaos in a Fractional Order Chua System

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.; Qammar, Helen Killory

1996-01-01

This report studies the effects of fractional dynamics in chaotic systems. In particular, Chua's system is modified to include fractional order elements. Varying the total system order incrementally from 2.6 to 3.7 demonstrates that systems of 'order' less than three can exhibit chaos as well as other nonlinear behavior. This effectively forces a clarification of the definition of order which can no longer be considered only by the total number of differentiations or by the highest power of the Laplace variable.

On the mathematical modeling of soccer dynamics

NASA Astrophysics Data System (ADS)

Machado, J. A. Tenreiro; Lopes, António M.

2017-12-01

This paper addresses the modeling and dynamical analysis of soccer teams. Two modeling perspectives based on the concepts of fractional calculus are adopted. In the first, the power law behavior and fractional-order integration are explored. In the second, a league season is interpreted in the light of a system where the teams are represented by objects (particles) that evolve in time and interact (collide) at successive rounds with dynamics driven by the outcomes of the matches. The two proposed models embed implicitly details of players and coaches, or strategical and tactical maneuvers during the matches. Therefore, the scale of observation focuses on the teams behavior in the scope of the observed variables. Data characterizing two European soccer leagues in the season 2015-2016 are adopted and processed. The model leads to the emergence of patterns that are analyzed and interpreted.

Dynamic Analysis and Adaptive Sliding Mode Controller for a Chaotic Fractional Incommensurate Order Financial System

NASA Astrophysics Data System (ADS)

Hajipour, Ahmad; Tavakoli, Hamidreza

2017-12-01

In this study, the dynamic behavior and chaos control of a chaotic fractional incommensurate-order financial system are investigated. Using well-known tools of nonlinear theory, i.e. Lyapunov exponents, phase diagrams and bifurcation diagrams, we observe some interesting phenomena, e.g. antimonotonicity, crisis phenomena and route to chaos through a period doubling sequence. Adopting largest Lyapunov exponent criteria, we find that the system yields chaos at the lowest order of 2.15. Next, in order to globally stabilize the chaotic fractional incommensurate order financial system with uncertain dynamics, an adaptive fractional sliding mode controller is designed. Numerical simulations are used to demonstrate the effectiveness of the proposed control method.

Tissue responses to fractional transient heating with sinusoidal heat flux condition on skin surface.

PubMed

Ezzat, Magdy A; El-Bary, Alaa A; Al-Sowayan, Noorah S

2016-10-01

A fractional model of Bioheat equation for describing quantitatively the thermal responses of skin tissue under sinusoidal heat flux conditions on skin surface is given. Laplace transform technique is used to obtain the solution in a closed form. The resulting formulation is applied to one-dimensional application to investigate the temperature distribution in skin with instantaneous surface heating for different cases. According to the numerical results and its graphs, conclusion about the fractional bioheat transfer equation has been constructed. Sensitivity analysis is performed to explore the thermal effects of various control parameters on tissue temperature. The comparisons are made with the results obtained in the case of the absence of time-fractional order. © 2016 Japanese Society of Animal Science. © 2016 Japanese Society of Animal Science.

Controllability of fractional higher order stochastic integrodifferential systems with fractional Brownian motion.

PubMed

Sathiyaraj, T; Balasubramaniam, P

2017-11-30

This paper presents a new set of sufficient conditions for controllability of fractional higher order stochastic integrodifferential systems with fractional Brownian motion (fBm) in finite dimensional space using fractional calculus, fixed point technique and stochastic analysis approach. In particular, we discuss the complete controllability for nonlinear fractional stochastic integrodifferential systems under the proved result of the corresponding linear fractional system is controllable. Finally, an example is presented to illustrate the efficiency of the obtained theoretical results. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Performance and robustness of optimal fractional fuzzy PID controllers for pitch control of a wind turbine using chaotic optimization algorithms.

PubMed

Asgharnia, Amirhossein; Shahnazi, Reza; Jamali, Ali

2018-05-11

The most studied controller for pitch control of wind turbines is proportional-integral-derivative (PID) controller. However, due to uncertainties in wind turbine modeling and wind speed profiles, the need for more effective controllers is inevitable. On the other hand, the parameters of PID controller usually are unknown and should be selected by the designer which is neither a straightforward task nor optimal. To cope with these drawbacks, in this paper, two advanced controllers called fuzzy PID (FPID) and fractional-order fuzzy PID (FOFPID) are proposed to improve the pitch control performance. Meanwhile, to find the parameters of the controllers the chaotic evolutionary optimization methods are used. Using evolutionary optimization methods not only gives us the unknown parameters of the controllers but also guarantees the optimality based on the chosen objective function. To improve the performance of the evolutionary algorithms chaotic maps are used. All the optimization procedures are applied to the 2-mass model of 5-MW wind turbine model. The proposed optimal controllers are validated using simulator FAST developed by NREL. Simulation results demonstrate that the FOFPID controller can reach to better performance and robustness while guaranteeing fewer fatigue damages in different wind speeds in comparison to FPID, fractional-order PID (FOPID) and gain-scheduling PID (GSPID) controllers. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Simulating soil C stability with mechanistic systems models: a multisite comparison of measured fractions and modelled pools

NASA Astrophysics Data System (ADS)

Robertson, Andy; Schipanski, Meagan; Sherrod, Lucretia; Ma, Liwang; Ahuja, Lajpat; McNamara, Niall; Smith, Pete; Davies, Christian

2016-04-01

Agriculture, covering more than 30% of global land area, has an exciting opportunity to help combat climate change by effectively managing its soil to promote increased C sequestration. Further, newly sequestered soil carbon (C) through agriculture needs to be stored in more stable forms in order to have a lasting impact on reducing atmospheric CO2 concentrations. While land uses in different climates and soils require different management strategies, the fundamental mechanisms that regulate C sequestration and stabilisation remain the same. These mechanisms are used by a number of different systems models to simulate C dynamics, and thus assess the impacts of change in management or climate. To evaluate the accuracy of these model simulations, our research uses a multidirectional approach to compare C stocks of physicochemical soil fractions collected at two long-term agricultural sites. Carbon stocks for a number of soil fractions were measured at two sites (Lincoln, UK; Colorado, USA) over 8 and 12 years, respectively. Both sites represent managed agricultural land but have notably different climates and levels of disturbance. The measured soil fractions act as proxies for varying degrees of stability, with C contained within these fractions relatable to the C simulated within the soil pools of mechanistic systems models1. Using stable isotope techniques at the UK site, specific turnover times of C within the different fractions were determined and compared with those simulated in the pools of 3 different models of varying complexity (RothC, DayCent and RZWQM2). Further, C dynamics and N-mineralisation rates of the measured fractions at the US site were assessed and compared to results of the same three models. The UK site saw a significant increase in C stocks within the most stable fractions, with topsoil (0-30cm) sequestration rates of just over 0.3 tC ha-1 yr-1 after only 8 years. Further, the sum of all fractions reported C sequestration rates of nearly 1.0 tC ha-1 yr-1. At the US site, however, topsoil C sequestration was less consistent noting considerable variation over the 12 years of measured data. Both sites showed noteworthy discrepancies when model-simulated C was compared with measured C. While all three models were able to simulate the bulk C stocks within reasonable degrees of uncertainty, the accuracy broke down considerably when this bulk soil was split into fractions/pools. Using the data collected and accounting for the differences in model structure, we present potential next steps in model development as well as the variables that should be measured when aiming to reduce the uncertainties inherent in mechanistic systems models. References 1 - Zimmermann et al., 2007. Measured soil organic matter fractions can be related to pools in the RothC model. European Journal of Soil Science, 58:658-667.

Spatial variability of intake fractions for Canadian emission scenarios: a comparison between three resolution scales.

PubMed

Manneh, Rima; Margni, Manuele; Deschênes, Louise

2010-06-01

Spatially differentiated intake fractions (iFs) linked to Canadian emissions of toxic organic chemicals were developed using the multimedia and multipathways fate and exposure model IMPACT 2002. The fate and exposure of chemicals released to the Canadian environment were modeled with a single regional mass-balance model and three models that provided multiple mass-balance regions within Canada. These three models were based on the Canadian subwatersheds (172 zones), ecozones (15 zones), and provinces (13 zones). Releases of 32 organic chemicals into water and air were considered. This was done in order to (i) assess and compare the spatial variability of iFs within and across the three levels of regionalization and (ii) compare the spatial iFs to nonspatial ones. Results showed that iFs calculated using the subwatershed resolution presented a higher spatial variability (up to 10 orders of magnitude for emissions into water) than the ones based on the ecozones and provinces, implying that higher spatial resolution could potentially reduce uncertainty in iFs and, therefore, increase the discriminating power when assessing and comparing toxic releases for known emission locations. Results also indicated that, for an unknown emission location, a model with high spatial resolution such as the subwatershed model could significantly improve the accuracy of a generic iF. Population weighted iFs span up to 3 orders of magnitude compared to nonspatial iFs calculated by the one-box model. Less significant differences were observed when comparing spatial versus nonspatial iFs from the ecozones and provinces, respectively.

The response analysis of fractional-order stochastic system via generalized cell mapping method.

PubMed

Wang, Liang; Xue, Lili; Sun, Chunyan; Yue, Xiaole; Xu, Wei

2018-01-01

This paper is concerned with the response of a fractional-order stochastic system. The short memory principle is introduced to ensure that the response of the system is a Markov process. The generalized cell mapping method is applied to display the global dynamics of the noise-free system, such as attractors, basins of attraction, basin boundary, saddle, and invariant manifolds. The stochastic generalized cell mapping method is employed to obtain the evolutionary process of probability density functions of the response. The fractional-order ϕ 6 oscillator and the fractional-order smooth and discontinuous oscillator are taken as examples to give the implementations of our strategies. Studies have shown that the evolutionary direction of the probability density function of the fractional-order stochastic system is consistent with the unstable manifold. The effectiveness of the method is confirmed using Monte Carlo results.

Khater method for nonlinear Sharma Tasso-Olever (STO) equation of fractional order

NASA Astrophysics Data System (ADS)

Bibi, Sadaf; Mohyud-Din, Syed Tauseef; Khan, Umar; Ahmed, Naveed

In this work, we have implemented a direct method, known as Khater method to establish exact solutions of nonlinear partial differential equations of fractional order. Number of solutions provided by this method is greater than other traditional methods. Exact solutions of nonlinear fractional order Sharma Tasso-Olever (STO) equation are expressed in terms of kink, travelling wave, periodic and solitary wave solutions. Modified Riemann-Liouville derivative and Fractional complex transform have been used for compatibility with fractional order sense. Solutions have been graphically simulated for understanding the physical aspects and importance of the method. A comparative discussion between our established results and the results obtained by existing ones is also presented. Our results clearly reveal that the proposed method is an effective, powerful and straightforward technique to work out new solutions of various types of differential equations of non-integer order in the fields of applied sciences and engineering.

Quasi-projective synchronization of fractional-order complex-valued recurrent neural networks.

PubMed

Yang, Shuai; Yu, Juan; Hu, Cheng; Jiang, Haijun

2018-08-01

In this paper, without separating the complex-valued neural networks into two real-valued systems, the quasi-projective synchronization of fractional-order complex-valued neural networks is investigated. First, two new fractional-order inequalities are established by using the theory of complex functions, Laplace transform and Mittag-Leffler functions, which generalize traditional inequalities with the first-order derivative in the real domain. Additionally, different from hybrid control schemes given in the previous work concerning the projective synchronization, a simple and linear control strategy is designed in this paper and several criteria are derived to ensure quasi-projective synchronization of the complex-valued neural networks with fractional-order based on the established fractional-order inequalities and the theory of complex functions. Moreover, the error bounds of quasi-projective synchronization are estimated. Especially, some conditions are also presented for the Mittag-Leffler synchronization of the addressed neural networks. Finally, some numerical examples with simulations are provided to show the effectiveness of the derived theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.

A K-BKZ Formulation for Soft-Tissue Viscoelasticity

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Diethelm, Kai

2005-01-01

A viscoelastic model of the K-BKZ (Kaye 1962; Bernstein et al. 1963) type is developed for isotropic biological tissues, and applied to the fat pad of the human heel. To facilitate this pursuit, a class of elastic solids is introduced through a novel strain-energy function whose elements possess strong ellipticity, and therefore lead to stable material models. The standard fractional-order viscoelastic (FOV) solid is used to arrive at the overall elastic/viscoelastic structure of the model, while the elastic potential via the K-BKZ hypothesis is used to arrive at the tensorial structure of the model. Candidate sets of functions are proposed for the elastic and viscoelastic material functions present in the model, including a regularized fractional derivative that was determined to be the best. The Akaike information criterion (AIC) is advocated for performing multi-model inference, enabling an objective selection of the best material function from within a candidate set.

Antioxidant and Cytoprotective Activities of Fucus spiralis Seaweed on a Human Cell in Vitro Model.

PubMed

Pinteus, Susete; Silva, Joana; Alves, Celso; Horta, André; Thomas, Olivier P; Pedrosa, Rui

2017-01-29

Antioxidants play an important role as Reactive Oxygen Species (ROS) chelating agents and, therefore, the screening for potent antioxidants from natural sources as potential protective agents is of great relevance. The main aim of this study was to obtain antioxidant-enriched fractions from the common seaweed Fucus spiralis and evaluate their activity and efficiency in protecting human cells (MCF-7 cells) on an oxidative stress condition induced by H₂O₂. Five fractions, F1-F5, were obtained by reversed-phase vacuum liquid chromatography. F3, F4 and F5 revealed the highest phlorotannin content, also showing the strongest antioxidant effects. The cell death induced by H₂O₂ was reduced by all fractions following the potency order F4 > F2 > F3 > F5 > F1. Only fraction F4 completely inhibited the H₂O₂ effect. To understand the possible mechanisms of action of these fractions, the cellular production of H₂O₂, the mitochondrial membrane potential and the caspase 9 activity were studied. Fractions F3 and F4 presented the highest reduction on H₂O₂ cell production. All fractions decreased both caspase-9 activity and cell membrane depolarization (except F1). Taken all together, the edible F. spiralis reveal that they provide protection against oxidative stress induced by H₂O₂ on the human MCF-7 cellular model, probably acting as upstream blockers of apoptosis.

Bone marrow fat quantification in the presence of trabecular bone: initial comparison between water-fat imaging and single-voxel MRS

PubMed Central

Karampinos, Dimitrios C.; Melkus, Gerd; Baum, Thomas; Bauer, Jan S.; Rummeny, Ernst J.; Krug, Roland

2013-01-01

Purpose The purpose of the present study was to test the relative performance of chemical shift-based water-fat imaging in measuring bone marrow fat fraction in the presence of trabecular bone, having as reference standard the single-voxel magnetic resonance spectroscopy (MRS). Methods Six-echo gradient echo imaging and single-voxel MRS measurements were performed on the proximal femur of seven healthy volunteers. The bone marrow fat spectrum was characterized based on the magnitude of measurable fat peaks and an a priori knowledge of the chemical structure of triglycerides, in order to accurately extract the water peak from the overlapping broad fat peaks in MRS. The imaging-based fat fraction results were then compared to the MRS-based results both without and with taking into consideration the presence of short T2* water components in MRS. Results There was a significant underestimation of the fat fraction using the MRS model not accounting for short T2* species with respect to the imaging-based water fraction. A good equivalency was observed between the fat fraction using the MRS model accounting for short T2* species and the imaging-based fat fraction (R2=0.87). Conclusion The consideration of the short T2* water species effect on bone marrow fat quantification is essential when comparing MRS-based and imaging-based fat fraction results. PMID:23657998

Molecular dynamics simulations of stratum corneum lipid models: fatty acids and cholesterol.

PubMed

Höltje, M; Förster, T; Brandt, B; Engels, T; von Rybinski, W; Höltje, H D

2001-03-09

We report the results of an investigation on stratum corneum lipids, which present the main barrier of the skin. Molecular dynamics simulations, thermal analysis and FTIR measurements were applied. The primary objective of this work was to study the effect of cholesterol on skin structure and dynamics. Two molecular models were constructed, a free fatty acid bilayer (stearic acid, palmitic acid) and a fatty acid/cholesterol mixture at a 1:1 molar ratio. Our simulations were performed at constant pressure and temperature on a nanosecond time scale. The resulting model structures were characterized by calculating surface areas per headgroup, conformational properties, atom densities and order parameters of the fatty acids. Analysis of the simulations indicates that the free fatty acid fraction of stratum corneum lipids stays in a highly ordered crystalline state at skin temperatures. The phase behavior is strongly influenced when cholesterol is added. Cholesterol smoothes the rigid phases of the fatty acids: the order of the hydrocarbon tails (mainly of the last eight bonds) is reduced, the area per molecule becomes larger, the fraction of trans dihedrals is lower and the hydrophobic thickness is reduced. The simulation results are in good agreement with our experimental data from FTIR analysis and NIR-FT Raman spectroscopy.

Modeling of biomass fractionation in a lab-scale biorefinery: Solubilization of hemicellulose and cellulose from holm oak wood using subcritical water.

PubMed

Cabeza, A; Piqueras, C M; Sobrón, F; García-Serna, J

2016-01-01

Lignocellulose fractionation is a key biorefinery process that need to be understood. In this work, a comprehensive study on hydrothermal-fractionation of holm oak in a semi-continuous system was conducted. The aim was to develop a physicochemical model in order to reproduce the role of temperature and water flow over the products composition. The experiments involved two sets: at constant flow (6mL/min) and two different ranges of temperature (140-180 and 240-280°C) and at a constant temperature range (180-260°C) and different flows: 11.0, 15.0 and 27.9mL/min. From the results, temperature has main influence and flow effect was observed only if soluble compounds were produced. The kinetic model was validated against experimental data, reproducing the total organic carbon profile (e.g. deviation of 33%) and the physicochemical phenomena observed in the process. In the model, it was also considered the variations of molecular weight of each biopolymer, successfully reproducing the biomass cleaving. Copyright © 2015 Elsevier Ltd. All rights reserved.

An analysis of carbon and radiocarbon profiles across a range ecosystems types

NASA Astrophysics Data System (ADS)

Heckman, K. A.; Gallo, A.; Hatten, J. A.; Swanston, C.; Strahm, B. D.; Sanclements, M.

2016-12-01

Soil carbon stocks have become recognized as increasingly important in the context of climate change and global C cycle modeling. As modelers seek to identify key parameters affecting the size and stability of belowground C stocks, attention has been drawn to the mineral matrix and the soil physiochemical factors influenced by it. Though clay content has often been utilized as a convenient and key explanatory variable for soil C dynamics, its utility has recently come under scrutiny as new paradigms of soil organic matter stabilization have been developed. We utilized soil cores from a range of National Ecological Observatory Network (NEON) experimental plots to examine the influence of mineralogical parameters on soil C stocks and turnover and their relative importance in comparison to climatic variables. Results are presented for a total of 11 NEON sites, spanning Alfisols, Entisols, Mollisols and Spodosols. Soils were sampled by genetic horizon, density separated according to density fractionation: light fractions (particulate organics neither occluded within aggregates nor associated with mineral surfaces), occluded fractions (particulate organics occluded within aggregates), and heavy fractions (organics associated with mineral surfaces). Bulk soils and density fractions were measured for % C and radiocarbon abundance (as a measure of C stability). Carbon and radiocarbon abundances were examined among fractions and in the context of climatic variables (temperature, precipitation, elevation) and soil physiochemical variables (% clay and pH). No direct relationships between temperature and soil C or radiocarbon abundances were found. As a whole, soil radiocarbon abundance in density fractions decreased in the order of light>heavy>occluded, highlighting the importance of both surface sorption and aggregation to the preservation of organics. Radiocarbon concentrations of the heavy fraction (mineral adsorbed) were significantly, though weakly, correlated with pH (r2 = 0.35, p = 0.02), though C concentrations were not. Data suggest an important role for both aggregation and soil chemistry in regulating soil C cycling across a diversity of soil orders. The current presented results serve as a preliminary report on a project spanning 40 NEON sites and a range of physiochemical analyses.

Dynamics analysis of fractional order Yu-Wang system

NASA Astrophysics Data System (ADS)

Bhalekar, Sachin

2013-10-01

Fractional order version of a dynamical system introduced by Yu and Wang (Engineering, Technology & Applied Science Research, 2, (2012) 209-215) is discussed in this article. The basic dynamical properties of the system are studied. Minimum effective dimension 0.942329 for the existence of chaos in the proposed system is obtained using the analytical result. For chaos detection, we have calculated maximum Lyapunov exponents for various values of fractional order. Feedback control method is then used to control chaos in the system. Further, the system is synchronized with itself and with fractional order financial system using active control technique. Modified Adams-Bashforth-Moulton algorithm is used for numerical simulations.

Dynamic evolution characteristics of a fractional order hydropower station system

NASA Astrophysics Data System (ADS)

Gao, Xiang; Chen, Diyi; Yan, Donglin; Xu, Beibei; Wang, Xiangyu

2018-01-01

This paper investigates the dynamic evolution characteristics of the hydropower station by introducing the fractional order damping forces. A careful analysis of the dynamic characteristics of the generator shaft system is carried out under different values of fractional order. It turns out the vibration state of the axis coordinates has a certain evolution law with the increase of the fractional order. Significantly, the obtained law exists in the horizontal evolution and vertical evolution of the dynamical behaviors. Meanwhile, some interesting dynamical phenomena were found in this process. The outcomes of this study enrich the nonlinear dynamic theory from the engineering practice of hydropower stations.

Taming stochastic bifurcations in fractional-order systems via noise and delayed feedback

NASA Astrophysics Data System (ADS)

Sun, Zhongkui; Zhang, Jintian; Yang, Xiaoli; Xu, Wei

2017-08-01

The dynamics in fractional-order systems have been widely studied during the past decade due to the potential applications in new materials and anomalous diffusions, but the investigations have been so far restricted to a fractional-order system without time delay(s). In this paper, we report the first study of random responses of fractional-order system coupled with noise and delayed feedback. Stochastic averaging method has been utilized to determine the stationary probability density functions (PDFs) by means of the principle of minimum mean-square error, based on which stochastic bifurcations could be identified through recognizing the shape of the PDFs. It has been found that by changing the fractional order the shape of the PDFs can switch from unimodal distribution to bimodal one, or from bimodal distribution to unimodal one, thus announcing the onset of stochastic bifurcation. Further, we have demonstrated that by merely modulating the time delay, the feedback strengths, or the noise intensity, the shapes of PDFs can transit between a single peak and a double peak. Therefore, it provides an efficient candidate to control, say, induce or suppress, the stochastic bifurcations in fractional-order systems.

(N+1)-dimensional fractional reduced differential transform method for fractional order partial differential equations

NASA Astrophysics Data System (ADS)

Arshad, Muhammad; Lu, Dianchen; Wang, Jun

2017-07-01

In this paper, we pursue the general form of the fractional reduced differential transform method (DTM) to (N+1)-dimensional case, so that fractional order partial differential equations (PDEs) can be resolved effectively. The most distinct aspect of this method is that no prescribed assumptions are required, and the huge computational exertion is reduced and round-off errors are also evaded. We utilize the proposed scheme on some initial value problems and approximate numerical solutions of linear and nonlinear time fractional PDEs are obtained, which shows that the method is highly accurate and simple to apply. The proposed technique is thus an influential technique for solving the fractional PDEs and fractional order problems occurring in the field of engineering, physics etc. Numerical results are obtained for verification and demonstration purpose by using Mathematica software.

Formation of double front detonations of a condensed-phase explosive with powdered aluminium

NASA Astrophysics Data System (ADS)

Kim, Wuhyun; Gwak, Min-cheol; Yoh, Jack J.

2018-03-01

The performance characteristics of aluminised high explosive are considered by varying the aluminium (Al) mass fraction in a hybrid non-ideal detonation model. Since the time scales of the characteristic induction and combustion of high explosives and Al particles differ, the process of energy release behind the leading detonation wave front occurs over an extended period of time. Two cardinal observations are reported: a decrease in detonation velocity with an increase in Al mass fraction and a double front detonation (DFD) feature when anaerobic Al reaction occurs behind the front. In order to simulate the performance characteristics due to the varying Al mass fraction, the tetrahexamine tetranitramine (HMX) is considered as a base high explosive when formulating the multiphase conservation laws of mass, momentum, and energy exchanges between particles and HMX product gases. While experimental studies have been reported on the effect of Al mass fraction on both gas-phase and solid-phase detonations, the numerical investigations have been limited to only gas-phase detonation for the varying Al particles in the mixture. In the current study, a two-phase model is utilised for understanding the volumetric effects of Al mass fraction in condensed phase detonations. A series of unconfined and confined rate sticks are considered for characterising the performance of aluminised HMX with a maximum Al mass fraction of 50%. The simulated results are compared with the experimental data for 5-25% mass fractions, and the higher mass fraction behaviours are consistent with the experimental observations.

Observer-based adaptive backstepping control for fractional order systems with input saturation.

PubMed

Sheng, Dian; Wei, Yiheng; Cheng, Songsong; Wang, Yong

2017-07-03

An observer-based fractional order anti-saturation adaptive backstepping control scheme is proposed for incommensurate fractional order systems with input saturation and partial measurable state in this paper. On the basis of stability analysis, a novel state observer is established first since the only information we could acquire is the system output. In order to compensate the saturation, a series of virtual signals are generated via the construction of fractional order auxiliary system. Afterwards, the controller design is carried out in accordance with the adaptive backstepping control method by introduction of the indirect Lyapunov method. To highlight the effectiveness of the proposed control scheme, simulation examples are demonstrated at last. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

A Model for Partitioning CO2 Flux and Calculating Transformation of Soil C Fractions

NASA Astrophysics Data System (ADS)

Zhang, S.; Noormets, A.; Tu, C.; King, J.

2011-12-01

It has been recognized that mechanistic understanding of soil organic carbon (SOC) mineralization requires partitioning of SOM to different sub-pools, whose turnover kinetics differ. Different fractionation methods have been developed to separate and analyze SOC fractions with different turnover rates, but some recent studies have called to questions earlier assumptions about chemical structure of C compounds and their recalcitrance to decomposition. To our knowledge, there is also no model that would bring together the information on various indicators of recalcitrance in a kinetic model framework . Here we deploy an analytical framework to partition soil net CO2 emissions to three density fractions (F1, F2, and F3, in the order of increasing density) in a peat soil and follow mineralization-related transformations (from lighter to heavier fractions). We followed the changes in total C content [C] and 13C of each three density fractions through a 3-month incubation study. We partitioned the CO2 produced by the soil between the different fractions using 13C and [C] change data. Applying this approach to a factorial experiment, we found that partitioning of CO2 emission and transformation rates among fractions differed between the organic top soil and deeper sandy soil. At depth of 45-75cm, almost no C was released through CO2 emission for all three fractions, while at 0-30cm, emission reached 0.2 g C/g soil over the incubation period, an average of 99% of which was from F2. Mineralization-related transformation rate at 45-75cm was 0.02 g soil/g soil with no significant differences among fractions. At 0-30cm, out of one gram of initial bulk soil, an average of 0.31g F1 transformed to F2, whereas no F2 was transformed to F3. Although the current study was carried out on a high-organic soil, the partitioning method is applicable to all soil types.

Kalman filters for fractional discrete-time stochastic systems along with time-delay in the observation signal

NASA Astrophysics Data System (ADS)

Torabi, H.; Pariz, N.; Karimpour, A.

2016-02-01

This paper investigates fractional Kalman filters when time-delay is entered in the observation signal in the discrete-time stochastic fractional order state-space representation. After investigating the common fractional Kalman filter, we try to derive a fractional Kalman filter for time-delay fractional systems. A detailed derivation is given. Fractional Kalman filters will be used to estimate recursively the states of fractional order state-space systems based on minimizing the cost function when there is a constant time delay (d) in the observation signal. The problem will be solved by converting the filtering problem to a usual d-step prediction problem for delay-free fractional systems.

Fractional System Identification: An Approach Using Continuous Order-Distributions

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Lorenzo, Carl F.

1999-01-01

This paper discusses the identification of fractional- and integer-order systems using the concept of continuous order-distribution. Based on the ability to define systems using continuous order-distributions, it is shown that frequency domain system identification can be performed using least squares techniques after discretizing the order-distribution.

Impact of leakage delay on bifurcation in high-order fractional BAM neural networks.

PubMed

Huang, Chengdai; Cao, Jinde

2018-02-01

The effects of leakage delay on the dynamics of neural networks with integer-order have lately been received considerable attention. It has been confirmed that fractional neural networks more appropriately uncover the dynamical properties of neural networks, but the results of fractional neural networks with leakage delay are relatively few. This paper primarily concentrates on the issue of bifurcation for high-order fractional bidirectional associative memory(BAM) neural networks involving leakage delay. The first attempt is made to tackle the stability and bifurcation of high-order fractional BAM neural networks with time delay in leakage terms in this paper. The conditions for the appearance of bifurcation for the proposed systems with leakage delay are firstly established by adopting time delay as a bifurcation parameter. Then, the bifurcation criteria of such system without leakage delay are successfully acquired. Comparative analysis wondrously detects that the stability performance of the proposed high-order fractional neural networks is critically weakened by leakage delay, they cannot be overlooked. Numerical examples are ultimately exhibited to attest the efficiency of the theoretical results. Copyright © 2017 Elsevier Ltd. All rights reserved.

An Avoidance Model for Short-Range Order Induced by Soft Repulsions in Systems of Rigid Rods

NASA Astrophysics Data System (ADS)

Han, Jining; Herzfeld, Judith

1996-03-01

The effects of soft repulsions on hard particle systems are calculated using an avoidance model which improves upon the simple mean field approximation. Avoidance reduces, but does not eliminate, the energy due to soft repulsions. On the other hand, it also reduces the configurational entropy. Under suitable conditions, this simple trade-off yields a free energy that is lower than the mean field value. In these cases, the variationally determined avoidance gives an estimate for the short-range positional order induced by soft repulsions. The results indicate little short-range order for isotropically oriented rods. However, for parallel rods, short-range order increases to significant levels as the particle axial ratio increases. The implications for long- range positional ordering are also discussed. In particular, avoidance may explain the smectic ordering of tobacco mosaic virus at volume fractions lower than those necessary for smectic ordering of hard particles.

Gauge invariant fractional electromagnetic fields

NASA Astrophysics Data System (ADS)

Lazo, Matheus Jatkoske

2011-09-01

Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators.

Exact solutions for STO and (3+1)-dimensional KdV-ZK equations using (G‧/G2) -expansion method

NASA Astrophysics Data System (ADS)

Bibi, Sadaf; Mohyud-Din, Syed Tauseef; Ullah, Rahmat; Ahmed, Naveed; Khan, Umar

This article deals with finding some exact solutions of nonlinear fractional differential equations (NLFDEs) by applying a relatively new method known as (G‧/G2) -expansion method. Solutions of space-time fractional Sharma-Tasso-Olever (STO) equation of fractional order and (3+1)-dimensional KdV-Zakharov Kuznetsov (KdV-ZK) equation of fractional order are reckoned to demonstrate the validity of this method. The fractional derivative version of modified Riemann-Liouville, linked with Fractional complex transform is employed to transform fractional differential equations into the corresponding ordinary differential equations.

THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.

PubMed

Jiang, H; Liu, F; Meerschaert, M M; McGough, R J

2013-01-01

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n ) ( n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko's Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian.

Binary Star Fractions from the LAMOST DR4

NASA Astrophysics Data System (ADS)

Tian, Zhi-Jia; Liu, Xiao-Wei; Yuan, Hai-Bo; Chen, Bing-Qiu; Xiang, Mao-Sheng; Huang, Yang; Wang, Chun; Zhang, Hua-Wei; Guo, Jin-Cheng; Ren, Juan-Juan; Huo, Zhi-Ying; Yang, Yong; Zhang, Meng; Bi, Shao-Lan; Yang, Wu-Ming; Liu, Kang; Zhang, Xian-Fei; Li, Tan-Da; Wu, Ya-Qian; Zhang, Jing-Hua

2018-05-01

Stellar systems composed of single, double, triple or higher-order systems are rightfully regarded as the fundamental building blocks of the Milky Way. Binary stars play an important role in formation and evolution of the Galaxy. Through comparing the radial velocity variations from multi-epoch observations, we analyze the binary fraction of dwarf stars observed with LAMOST. Effects of different model assumptions, such as orbital period distributions on the estimate of binary fractions, are investigated. The results based on log-normal distribution of orbital periods reproduce the previous complete analyses better than the power-law distribution. We find that the binary fraction increases with T eff and decreases with [Fe/H]. We first investigate the relation between α-elements and binary fraction in such a large sample as provided by LAMOST. The old stars with high [α/Fe] dominate with a higher binary fraction than young stars with low [α/Fe]. At the same mass, earlier forming stars possess a higher binary fraction than newly forming ones, which may be related with evolution of the Galaxy.

Electrical conductivity of basaltic and carbonatite melt-bearing peridotites at high pressures: Implications for melt distribution and melt fraction in the upper mantle

NASA Astrophysics Data System (ADS)

Yoshino, Takashi; Laumonier, Mickael; McIsaac, Elizabeth; Katsura, Tomoo

2010-07-01

Electrical impedance measurements were performed on two types of partial molten samples with basaltic and carbonatitic melts in a Kawai-type multi-anvil apparatus in order to investigate melt fraction-conductivity relationships and melt distribution of the partial molten mantle peridotite under high pressure. The silicate samples were composed of San Carlos olivine with various amounts of mid-ocean ridge basalt (MORB), and the carbonate samples were a mixture of San Carlos olivine with various amounts of carbonatite. High-pressure experiments on the silicate and carbonate systems were performed up to 1600 K at 1.5 GPa and up to at least 1650 K at 3 GPa, respectively. The sample conductivity increased with increasing melt fraction. Carbonatite-bearing samples show approximately one order of magnitude higher conductivity than basalt-bearing ones at the similar melt fraction. A linear relationship between log conductivity ( σbulk) and log melt fraction ( ϕ) can be expressed well by the Archie's law (Archie, 1942) ( σbulk/ σmelt = Cϕn) with parameters C = 0.68 and 0.97, n = 0.87 and 1.13 for silicate and carbonate systems, respectively. Comparison of the electrical conductivity data with theoretical predictions for melt distribution indicates that the model assuming that the grain boundary is completely wetted by melt is the most preferable melt geometry. The gradual change of conductivity with melt fraction suggests no permeability jump due to melt percolation at a certain melt fraction. The melt fraction of the partial molten region in the upper mantle can be estimated to be 1-3% and ˜ 0.3% for basaltic melt and carbonatite melt, respectively.

Predicting First Traversal Times for Virions and Nanoparticles in Mucus with Slowed Diffusion

PubMed Central

Erickson, Austen M.; Henry, Bruce I.; Murray, John M.; Klasse, Per Johan; Angstmann, Christopher N.

2015-01-01

Particle-tracking experiments focusing on virions or nanoparticles in mucus have measured mean-square displacements and reported diffusion coefficients that are orders of magnitude smaller than the diffusion coefficients of such particles in water. Accurate description of this subdiffusion is important to properly estimate the likelihood of virions traversing the mucus boundary layer and infecting cells in the epithelium. However, there are several candidate models for diffusion that can fit experimental measurements of mean-square displacements. We show that these models yield very different estimates for the time taken for subdiffusive virions to traverse through a mucus layer. We explain why fits of subdiffusive mean-square displacements to standard diffusion models may be misleading. Relevant to human immunodeficiency virus infection, using computational methods for fractional subdiffusion, we show that subdiffusion in normal acidic mucus provides a more effective barrier against infection than previously thought. By contrast, the neutralization of the mucus by alkaline semen, after sexual intercourse, allows virions to cross the mucus layer and reach the epithelium in a short timeframe. The computed barrier protection from fractional subdiffusion is some orders of magnitude greater than that derived by fitting standard models of diffusion to subdiffusive data. PMID:26153713

Application of the principal fractional meta-trigonometric functions for the solution of linear commensurate-order time-invariant fractional differential equations.

PubMed

Lorenzo, C F; Hartley, T T; Malti, R

2013-05-13

A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on the R-function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics.

Correlation Structure of Fractional Pearson Diffusions.

PubMed

Leonenko, Nikolai N; Meerschaert, Mark M; Sikorskii, Alla

2013-09-01

The stochastic solution to a diffusion equations with polynomial coefficients is called a Pearson diffusion. If the first time derivative is replaced by a Caputo fractional derivative of order less than one, the stochastic solution is called a fractional Pearson diffusion. This paper develops an explicit formula for the covariance function of a fractional Pearson diffusion in steady state, in terms of Mittag-Leffler functions. That formula shows that fractional Pearson diffusions are long range dependent, with a correlation that falls off like a power law, whose exponent equals the order of the fractional derivative.

Synchronization of fractional-order complex-valued neural networks with time delay.

PubMed

Bao, Haibo; Park, Ju H; Cao, Jinde

2016-09-01

This paper deals with the problem of synchronization of fractional-order complex-valued neural networks with time delays. By means of linear delay feedback control and a fractional-order inequality, sufficient conditions are obtained to guarantee the synchronization of the drive-response systems. Numerical simulations are provided to show the effectiveness of the obtained results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Variational iteration method — a promising technique for constructing equivalent integral equations of fractional order

NASA Astrophysics Data System (ADS)

Wang, Yi-Hong; Wu, Guo-Cheng; Baleanu, Dumitru

2013-10-01

The variational iteration method is newly used to construct various integral equations of fractional order. Some iterative schemes are proposed which fully use the method and the predictor-corrector approach. The fractional Bagley-Torvik equation is then illustrated as an example of multi-order and the results show the efficiency of the variational iteration method's new role.

Repopulation Kinetics and the Linear-Quadratic Model

NASA Astrophysics Data System (ADS)

O'Rourke, S. F. C.; McAneney, H.; Starrett, C.; O'Sullivan, J. M.

2009-08-01

The standard Linear-Quadratic (LQ) survival model for radiotherapy is used to investigate different schedules of radiation treatment planning for advanced head and neck cancer. We explore how these treament protocols may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al. [1], which was concerned with the case of exponential repopulation between treatments. Treatment schedules investigated include standarized and accelerated fractionation. Calculations based on the present work show, that even with growth laws scaled to ensure that the repopulation kinetics for advanced head and neck cancer are comparable, considerable variation in the survival fraction to orders of magnitude emerged. Calculations show that application of the Gompertz model results in a significantly poorer prognosis for tumour eradication. Gaps in treatment also highlight the differences in the LQ model with the effect of repopulation kinetics included.

Alternative solution model for the ternary carbonate system CaCO3 - MgCO3 - FeCO3 - I. A ternary Bragg-Williams ordering model

USGS Publications Warehouse

McSwiggen, P.L.

1993-01-01

The minerals of the ternary carbonate system CaCO3 - MgCO3 - FeCO3 represent a complex series of solid solutions and ordering states. An understanding of those complexities requires a solution model that can both duplicate the subsolidus phase relationships and generate correct values for the activities. Such a solution model must account for the changes in the total energy of the system resulting from a change in the ordering state of the individual constituents. Various ordering models have been applied to binary carbonate systems, but no attempts have previously been made to model the ordering in the ternary system. This study derives a new set of equations that allow for the equilibrium degree of order to be calculated for a system involving three cations mixing on two sites, as in the case of the ternary carbonates. The method is based on the Bragg-Williams approach. From the degree of order, the mole fractions of the three cations in each of the two sites can be determined. Once the site occupancies have been established, a Margules-type mixing model can be used to determine the free energy of mixing in the solid solution and therefore the activities of the various components. ?? 1993 Springer-Verlag.

Isotopic fractionation of gases during its migration: experiments and 2D numerical simulation

NASA Astrophysics Data System (ADS)

Kara, S.; Prinzhofer, A.

2003-04-01

Several works have been developed in the last decade on the experimental isotope fractionation of gases during migration (Prinzhofer et al., 1997 and Zhang &Krooss, 2001 among others). We add to these results new experiments on diffusion of CO_2, which becomes currently a crucial subject for environmental purpose. Our experiments showed that transport by diffusion of CO_2 through a water saturated shale induces a significant and systematic carbon isotopic fractionation with heavier (13C enriched) CO_2 migrating first. In all experiments, significant isotope fractionation was found but still remains without quantitative interpretation. To interpret these data, we developed a 2D numerical model at the pore scale. The general principle of this model is the study of transport by water solubilization/diffusion of gas in a capillary saturated with water with two different media : a mobile zone representing free water and a immobile zone representing bounded water. The model takes also into account solubilization coefficients of gas in water, as well as the migration distance and the volume of upstream and downstream reservoirs. Using our numerical model, we could reproduce the evolution of isotopic fractionations and the velocity of CO_2 migration versus the production factor F (proportion of diffused gas). We determined some physical parameters of the porous medium (bentonite) which are not directly measurable at the present time. Furthermore, we used these parameters to reproduce the curves of isotopic fractionation obtained by Pernaton (1998) on methane migration with the same porous rock. We used also a modified version of this model with infinite reservoirs to reproduce the curves of isotopic fractionation of Zhang &Krooss (2001). Application of this model to geological scale is under progress, in order to implement it into sedimentary basins modelling. REFERENCES: Zhang T. and Krooss M. (2001). Geochim. Cosmochim. Acta, Vol. 65, No.16, pp. 2723-2742. Pernaton E. (1998) PhD. Thesis, Université de Paris VII, 272 pp. Prinzhofer A. and Pernaton E. (1997) Chem. Geol., vol. 142, 193-200.

Volatile inventory of Mars-2: Primordial sources and fractionating processes

NASA Technical Reports Server (NTRS)

Pepin, R. O.

1987-01-01

The total volatile inventory of Mars has been modeled using meteoritic and presumed primordial abundances in the early solar system. Evidence is presented which indicates that the elemental abundances of the noble gases on Earth and Mars are similar, and their ratios are comparable to those in average carbonaceous chondrites with the exception of xenon and krypton. In order to account for presently observed variations in gas abundances, two primordial sources were used. One was the solar composition similar to the solar wind, and the other of carbonaceous grains that were the source for trace exotic components. For Mars, a model in which the early, high solar EUV flux with continued hydrogen production by differentiation results in mass fractionation of the primordial atmosphere, early depletion of xenon, and later depletion of gases lighter than krypton. The result is that the primordial Mars water inventory may have been on the order of 20 to 30 km if spread over the planet.

Quenching oscillating behaviors in fractional coupled Stuart-Landau oscillators

NASA Astrophysics Data System (ADS)

Sun, Zhongkui; Xiao, Rui; Yang, Xiaoli; Xu, Wei

2018-03-01

Oscillation quenching has been widely studied during the past several decades in fields ranging from natural sciences to engineering, but investigations have so far been restricted to oscillators with an integer-order derivative. Here, we report the first study of amplitude death (AD) in fractional coupled Stuart-Landau oscillators with partial and/or complete conjugate couplings to explore oscillation quenching patterns and dynamics. It has been found that the fractional-order derivative impacts the AD state crucially. The area of the AD state increases along with the decrease of the fractional-order derivative. Furthermore, by introducing and adjusting a limiting feedback factor in coupling links, the AD state can be well tamed in fractional coupled oscillators. Hence, it provides one an effective approach to analyze and control the oscillating behaviors in fractional coupled oscillators.

Estimation of stochastic volatility with long memory for index prices of FTSE Bursa Malaysia KLCI

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Kho Chia; Kane, Ibrahim Lawal; Rahman, Haliza Abd

In recent years, modeling in long memory properties or fractionally integrated processes in stochastic volatility has been applied in the financial time series. A time series with structural breaks can generate a strong persistence in the autocorrelation function, which is an observed behaviour of a long memory process. This paper considers the structural break of data in order to determine true long memory time series data. Unlike usual short memory models for log volatility, the fractional Ornstein-Uhlenbeck process is neither a Markovian process nor can it be easily transformed into a Markovian process. This makes the likelihood evaluation and parametermore » estimation for the long memory stochastic volatility (LMSV) model challenging tasks. The drift and volatility parameters of the fractional Ornstein-Unlenbeck model are estimated separately using the least square estimator (lse) and quadratic generalized variations (qgv) method respectively. Finally, the empirical distribution of unobserved volatility is estimated using the particle filtering with sequential important sampling-resampling (SIR) method. The mean square error (MSE) between the estimated and empirical volatility indicates that the performance of the model towards the index prices of FTSE Bursa Malaysia KLCI is fairly well.« less

Theoretical results on fractionally integrated exponential generalized autoregressive conditional heteroskedastic processes

NASA Astrophysics Data System (ADS)

Lopes, Sílvia R. C.; Prass, Taiane S.

2014-05-01

Here we present a theoretical study on the main properties of Fractionally Integrated Exponential Generalized Autoregressive Conditional Heteroskedastic (FIEGARCH) processes. We analyze the conditions for the existence, the invertibility, the stationarity and the ergodicity of these processes. We prove that, if { is a FIEGARCH(p,d,q) process then, under mild conditions, { is an ARFIMA(q,d,0) with correlated innovations, that is, an autoregressive fractionally integrated moving average process. The convergence order for the polynomial coefficients that describes the volatility is presented and results related to the spectral representation and to the covariance structure of both processes { and { are discussed. Expressions for the kurtosis and the asymmetry measures for any stationary FIEGARCH(p,d,q) process are also derived. The h-step ahead forecast for the processes {, { and { are given with their respective mean square error of forecast. The work also presents a Monte Carlo simulation study showing how to generate, estimate and forecast based on six different FIEGARCH models. The forecasting performance of six models belonging to the class of autoregressive conditional heteroskedastic models (namely, ARCH-type models) and radial basis models is compared through an empirical application to Brazilian stock market exchange index.

Revisiting the Potential of Melt Pond Fraction as a Predictor for the Seasonal Arctic Sea Ice Extent Minimum

NASA Technical Reports Server (NTRS)

Liu, Jiping; Song, Mirong; Horton, Radley M.; Hu, Yongyun

2015-01-01

The rapid change in Arctic sea ice in recent decades has led to a rising demand for seasonal sea ice prediction. A recent modeling study that employed a prognostic melt pond model in a stand-alone sea ice model found that September Arctic sea ice extent can be accurately predicted from the melt pond fraction in May. Here we show that satellite observations show no evidence of predictive skill in May. However, we find that a significantly strong relationship (high predictability) first emerges as the melt pond fraction is integrated from early May to late June, with a persistent strong relationship only occurring after late July. Our results highlight that late spring to mid summer melt pond information is required to improve the prediction skill of the seasonal sea ice minimum. Furthermore, satellite observations indicate a much higher percentage of melt pond formation in May than does the aforementioned model simulation, which points to the need to reconcile model simulations and observations, in order to better understand key mechanisms of melt pond formation and evolution and their influence on sea ice state.

Global Modeling of Uranium Molecular Species Formation Using Laser-Ablated Plasmas

NASA Astrophysics Data System (ADS)

Curreli, Davide; Finko, Mikhail; Azer, Magdi; Armstrong, Mike; Crowhurst, Jonathan; Radousky, Harry; Rose, Timothy; Stavrou, Elissaios; Weisz, David; Zaug, Joseph

2016-10-01

Uranium is chemically fractionated from other refractory elements in post-detonation nuclear debris but the mechanism is poorly understood. Fractionation alters the chemistry of the nuclear debris so that it no longer reflects the chemistry of the source weapon. The conditions of a condensing fireball can be simulated by a low-temperature plasma formed by vaporizing a uranium sample via laser heating. We have developed a global plasma kinetic model in order to model the chemical evolution of U/UOx species within an ablated plasma plume. The model allows to track the time evolution of the density and energy of an uranium plasma plume moving through an oxygen atmosphere of given fugacity, as well as other relevant quantities such as average electron and gas temperature. Comparison of model predictions with absorption spectroscopy of uranium-ablated plasmas provide preliminary insights on the key chemical species and evolution pathways involved during the fractionation process. This project was sponsored by the DoD, Defense Threat Reduction Agency, Grant HDTRA1-16-1-0020. This work was performed in part under the auspices of the U.S. DoE by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Estimation of stochastic volatility with long memory for index prices of FTSE Bursa Malaysia KLCI

NASA Astrophysics Data System (ADS)

Chen, Kho Chia; Bahar, Arifah; Kane, Ibrahim Lawal; Ting, Chee-Ming; Rahman, Haliza Abd

2015-02-01

In recent years, modeling in long memory properties or fractionally integrated processes in stochastic volatility has been applied in the financial time series. A time series with structural breaks can generate a strong persistence in the autocorrelation function, which is an observed behaviour of a long memory process. This paper considers the structural break of data in order to determine true long memory time series data. Unlike usual short memory models for log volatility, the fractional Ornstein-Uhlenbeck process is neither a Markovian process nor can it be easily transformed into a Markovian process. This makes the likelihood evaluation and parameter estimation for the long memory stochastic volatility (LMSV) model challenging tasks. The drift and volatility parameters of the fractional Ornstein-Unlenbeck model are estimated separately using the least square estimator (lse) and quadratic generalized variations (qgv) method respectively. Finally, the empirical distribution of unobserved volatility is estimated using the particle filtering with sequential important sampling-resampling (SIR) method. The mean square error (MSE) between the estimated and empirical volatility indicates that the performance of the model towards the index prices of FTSE Bursa Malaysia KLCI is fairly well.

Impact of dose escalation and adaptive radiotherapy for cervical cancers on tumour shrinkage—a modelling study

NASA Astrophysics Data System (ADS)

Røthe Arnesen, Marius; Paulsen Hellebust, Taran; Malinen, Eirik

2017-03-01

Tumour shrinkage occurs during fractionated radiotherapy and is regulated by radiation induced cellular damage, repopulation of viable cells and clearance of dead cells. In some cases additional tumour shrinkage during external beam therapy may be beneficial, particularly for locally advanced cervical cancer where a small tumour volume may simplify and improve brachytherapy. In the current work, a mathematical tumour model is utilized to investigate how local dose escalation affects tumour shrinkage, focusing on implications for brachytherapy. The iterative two-compartment model is based upon linear-quadratic radiation response, a doubling time for viable cells and a half-time for clearance of dead cells. The model was individually fitted to clinical tumour volume data from fractionated radiotherapy of 25 cervical cancer patients. Three different fractionation patterns for dose escalation, all with an additional dose of 12.2 Gy, were simulated and compared to standard fractionation in terms of tumour shrinkage. An adaptive strategy where dose escalation was initiated after one week of treatment was also considered. For 22 out of 25 patients, a good model fit was achieved to the observed tumour shrinkage. A large degree of inter-patient variation was seen in predicted volume reduction following dose escalation. For the 10 best responding patients, a mean tumour volume reduction of 34  ±  3% (relative to standard treatment) was estimated at the time of brachytherapy. Timing of initiating dose escalation had a larger impact than the number of fractions applied. In conclusion, the model was found useful in evaluating the impact from dose escalation on tumour shrinkage. The results indicate that dose escalation could be conducted from the start of external beam radiotherapy in order to obtain additional tumour shrinkage before brachytherapy.

Adsorption characterizations of fulvic acid fractions onto kaolinite.

PubMed

Li, Aimin; Xu, Minjuan; Li, Wenhui; Wang, Xuejun; Dai, Jingyu

2008-01-01

Fulvic acids extracted from a typical rice-production region near Taihu Lake of China were fractionated into three fractions including F4.8, F7.0 and F11.0 (eluted by pH 4.8 buffer, pH 7.0 buffer and pH 11.0 buffer, respectively). Sorption of fulvic acid (FA) fractions onto kaolinite was studied by batch adsorption experiments, and characterizations of kaolinite before and after adsorption were investigated using scanning electron microscopy (SEM). Adsorption isotherms of kaolinite for three FA fractions fit well with the Langmuir adsorption model. The adsorption density of the three fractions was positively correlated with the ratio of the amount of the alkyl carbon to that of carboxyl and carbonyl carbon in FA fractions and followed an order of F11.0 > F7.0 > F4.8. Hydrophobic interaction was one of the control mechanisms for the sorption of FA fraction onto kaolinite. SEM images confirmed that compared to blank kaolinite samples, kaolinite samples coated by a FA fraction displayed an opener and more dispersed conformation resulting from the disruption of the floc structure in complex. Dispersion of kaolinite after adsorption was due to the repulsion between negatively charged FA-coated particles, which is closely related to the amount of FA fractions absorbed on kaolinite.

Stabilization of an inverted pendulum-cart system by fractional PI-state feedback.

PubMed

Bettayeb, M; Boussalem, C; Mansouri, R; Al-Saggaf, U M

2014-03-01

This paper deals with pole placement PI-state feedback controller design to control an integer order system. The fractional aspect of the control law is introduced by a dynamic state feedback as u(t)=K(p)x(t)+K(I)I(α)(x(t)). The closed loop characteristic polynomial is thus fractional for which the roots are complex to calculate. The proposed method allows us to decompose this polynomial into a first order fractional polynomial and an integer order polynomial of order n-1 (n being the order of the integer system). This new stabilization control algorithm is applied for an inverted pendulum-cart test-bed, and the effectiveness and robustness of the proposed control are examined by experiments. Crown Copyright © 2013. Published by Elsevier Ltd. All rights reserved.

Error Patterns in Ordering Fractions among At-Risk Fourth-Grade Students

PubMed Central

Malone, Amelia S.; Fuchs, Lynn S.

2016-01-01

The 3 purposes of this study were to: (a) describe fraction ordering errors among at-risk 4th-grade students; (b) assess the effect of part-whole understanding and accuracy of fraction magnitude estimation on the probability of committing errors; and (c) examine the effect of students' ability to explain comparing problems on the probability of committing errors. Students (n = 227) completed a 9-item ordering test. A high proportion (81%) of problems were completed incorrectly. Most (65% of) errors were due to students misapplying whole number logic to fractions. Fraction-magnitude estimation skill, but not part-whole understanding, significantly predicted the probability of committing this type of error. Implications for practice are discussed. PMID:26966153

Stability analysis of fractional-order Hopfield neural networks with time delays.

PubMed

Wang, Hu; Yu, Yongguang; Wen, Guoguang

2014-07-01

This paper investigates the stability for fractional-order Hopfield neural networks with time delays. Firstly, the fractional-order Hopfield neural networks with hub structure and time delays are studied. Some sufficient conditions for stability of the systems are obtained. Next, two fractional-order Hopfield neural networks with different ring structures and time delays are developed. By studying the developed neural networks, the corresponding sufficient conditions for stability of the systems are also derived. It is shown that the stability conditions are independent of time delays. Finally, numerical simulations are given to illustrate the effectiveness of the theoretical results obtained in this paper. Copyright © 2014 Elsevier Ltd. All rights reserved.

Assessing Soil Organic C Stability at the Continental Scale: An Analysis of Soil C and Radiocarbon Profiles Across the NEON Sites

NASA Astrophysics Data System (ADS)

Heckman, K. A.; Gallo, A.; Hatten, J. A.; Swanston, C.; McKnight, D. M.; Strahm, B. D.; Sanclements, M.

2017-12-01

Soil carbon stocks have become recognized as increasingly important in the context of climate change and global C cycle modeling. As modelers seek to identify key parameters affecting the size and stability of belowground C stocks, attention has been drawn to the mineral matrix and the soil physiochemical factors influenced by it. Though clay content has often been utilized as a convenient and key explanatory variable for soil C dynamics, its utility has recently come under scrutiny as new paradigms of soil organic matter stabilization have been developed. We utilized soil cores from a range of National Ecological Observatory Network (NEON) experimental plots to examine the influence of physicochemical parameters on soil C stocks and turnover, and their relative importance in comparison to climatic variables. Soils were cored at NEON sites, sampled by genetic horizon, and density separated into light fractions (particulate organics neither occluded within aggregates nor associated with mineral surfaces), occluded fractions (particulate organics occluded within aggregates), and heavy fractions (organics associated with mineral surfaces). Bulk soils and density fractions were measured for % C and radiocarbon abundance (as a measure of C stability). Carbon and radiocarbon abundances were examined among fractions and in the context of climatic variables (temperature, precipitation, elevation) and soil physiochemical variables (% clay and pH). No direct relationships between temperature and soil C or radiocarbon abundances were found. As a whole, soil radiocarbon abundance in density fractions decreased in the order of light>heavy>occluded, highlighting the importance of both surface sorption and aggregation to the preservation of organics. Radiocarbon abundance was correlated with pH, with variance also grouping by dominate vegetation type. Soil order was also identified as an important proxy variable for C and radiocarbon abundance. Preliminary results suggest that both integrative proxies as well as physicochemical properties may be needed to account for variation in soil C abundance and stability at the continental scale.

Maintenance of order in a moving strong condensate

NASA Astrophysics Data System (ADS)

Whitehouse, Justin; Costa, André; Blythe, Richard A.; Evans, Martin R.

2014-11-01

We investigate the conditions under which a moving condensate may exist in a driven mass transport system. Our paradigm is a minimal mass transport model in which n - 1 particles move simultaneously from a site containing n > 1 particles to the neighbouring site in a preferred direction. In the spirit of a zero-range process the rate u(n) of this move depends only on the occupation of the departure site. We study a hopping rate u(n) = 1 + b/nα numerically and find a moving strong condensate phase for b > bc(α) for all α > 0. This phase is characterised by a condensate that moves through the system and comprises a fraction of the system's mass that tends to unity. The mass lost by the condensate as it moves is constantly replenished from the trailing tail of low occupancy sites that collectively comprise a vanishing fraction of the mass. We formulate an approximate analytical treatment of the model that allows a reasonable estimate of bc(α) to be obtained. We show numerically (for α = 1) that the transition is of mixed order, exhibiting a discontinuity in the order parameter as well as a diverging length scale as b\\searrow bc .

Generalized characteristic ratios assignment for commensurate fractional order systems with one zero.

PubMed

Tabatabaei, Mohammad

2017-07-01

In this paper, a new method for determination of the desired characteristic equation and zero location of commensurate fractional order systems is presented. The concept of the characteristic ratio is extended for zero-including commensurate fractional order systems. The generalized version of characteristic ratios is defined such that the time-scaling property of characteristic ratios is also preserved. The monotonicity of the magnitude frequency response is employed to assign the generalized characteristic ratios for commensurate fractional order transfer functions with one zero. A simple pattern for characteristic ratios is proposed to reach a non-overshooting step response. Then, the proposed pattern is revisited to reach a low overshoot (say for example 2%) step response. Finally, zero-including controllers such as fractional order PI or lag (lead) controllers are designed using generalized characteristic ratios assignment method. Numerical simulations are provided to show the efficiency of the so designed controllers. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Transport, biodegradation and isotopic fractionation of chlorinated ethenes: modeling and parameter estimation methods

NASA Astrophysics Data System (ADS)

Béranger, Sandra C.; Sleep, Brent E.; Lollar, Barbara Sherwood; Monteagudo, Fernando Perez

2005-01-01

An analytical, one-dimensional, multi-species, reactive transport model for simulating the concentrations and isotopic signatures of tetrachloroethylene (PCE) and its daughter products was developed. The simulation model was coupled to a genetic algorithm (GA) combined with a gradient-based (GB) method to estimate the first order decay coefficients and enrichment factors. In testing with synthetic data, the hybrid GA-GB method reduced the computational requirements for parameter estimation by a factor as great as 300. The isotopic signature profiles were observed to be more sensitive than the concentration profiles to estimates of both the first order decay constants and enrichment factors. Including isotopic data for parameter estimation significantly increased the GA convergence rate and slightly improved the accuracy of estimation of first order decay constants.

Does the dose-solubility ratio affect the mean dissolution time of drugs?

PubMed

Lánský, P; Weiss, M

1999-09-01

To present a new model for describing drug dissolution. On the basis of the new model to characterize the dissolution profile by the distribution function of the random dissolution time of a drug molecule, which generalizes the classical first order model. Instead of assuming a constant fractional dissolution rate, as in the classical model, it is considered that the fractional dissolution rate is a decreasing function of the dissolved amount controlled by the dose-solubility ratio. The differential equation derived from this assumption is solved and the distribution measures (half-dissolution time, mean dissolution time, relative dispersion of the dissolution time, dissolution time density, and fractional dissolution rate) are calculated. Finally, instead of monotonically decreasing the fractional dissolution rate, a generalization resulting in zero dissolution rate at time origin is introduced. The behavior of the model is divided into two regions defined by q, the ratio of the dose to the solubility level: q < 1 (complete dissolution of the dose, dissolution time) and q > 1 (saturation of the solution, saturation time). The singular case q = 1 is also treated and in this situation the mean as well as the relative dispersion of the dissolution time increase to infinity. The model was successfully fitted to data (1). This empirical model is descriptive without detailed physical reasoning behind its derivation. According to the model, the mean dissolution time is affected by the dose-solubility ratio. Although this prediction appears to be in accordance with preliminary application, further validation based on more suitable experimental data is required.

Exact solutions to the time-fractional differential equations via local fractional derivatives

NASA Astrophysics Data System (ADS)

Guner, Ozkan; Bekir, Ahmet

2018-01-01

This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.

Mesoscale Particle-Based Model of Electrophoretic Deposition

DOE PAGES

Giera, Brian; Zepeda-Ruiz, Luis A.; Pascall, Andrew J.; ...

2016-12-20

In this paper, we present and evaluate a semiempirical particle-based model of electrophoretic deposition using extensive mesoscale simulations. We analyze particle configurations in order to observe how colloids accumulate at the electrode and arrange into deposits. In agreement with existing continuum models, the thickness of the deposit increases linearly in time during deposition. Resulting colloidal deposits exhibit a transition between highly ordered and bulk disordered regions that can give rise to an appreciable density gradient under certain simulated conditions. The overall volume fraction increases and falls within a narrow range as the driving force due to the electric field increasesmore » and repulsive intercolloidal interactions decrease. We postulate ordering and stacking within the initial layer(s) dramatically impacts the microstructure of the deposits. Finally, we find a combination of parameters, i.e., electric field and suspension properties, whose interplay enhances colloidal ordering beyond the commonly known approach of only reducing the driving force.« less

Crude extract and fractions from Eugenia uniflora Linn leaves showed anti-inflammatory, antioxidant, and antibacterial activities.

PubMed

Falcão, Tamires Rocha; de Araújo, Aurigena Antunes; Soares, Luiz Alberto Lira; de Moraes Ramos, Rhayanne Thaís; Bezerra, Isabelle Cristinne Ferraz; Ferreira, Magda Rhayanny Assunção; de Souza Neto, Manoel André; Melo, Maria Celeste Nunes; de Araújo, Raimundo Fernandes; de Aguiar Guerra, Andreza Conceição Véras; de Medeiros, Juliana Silva; Guerra, Gerlane Coelho Bernardo

2018-03-09

This study showed phytochemical composition and evaluates the anti-inflammatory, and analgesic activities of crude extract (CE) and fractions from E. uniflora Linn leaves. Polyphenols present in crude extract (CE), in aqueous fraction (AqF), and ethyl acetate (EAF) treated fractions from E. uniflora Linn leaves were shown by chromatographic analysis in order to conduct a phytochemical characterization. Antibacterial activity was evaluated based on minimum inhibitory concentrations (MICs) determined using the agar dilution method. Doses of 50, 100, and 200 mg/kg of the CE and fractions were applied for conducting in vivo models (male Swiss mice, 8-10 weeks old). The peritonitis experimental model was induced by carrageenan following of Myeloperoxidase activity (MPO), Total glutathione and malondialdehyde (MDA), IL-1β and TNF-α levels by spectroscopic UV/VIS analysis. Antinociceptive activity was evaluated based on an abdominal writhing model and hot plate test. The results were statistically evaluated using one-way analysis of variance (ANOVA), followed by Bonferroni's post-hoc test. The level of statistical significance was p < 0.05. High-performance liquid chromatography with photodiode array detection (HPLC-DAD) detected varying concentrations of gallic acid, ellagic acid, and myricitrin in the CE and fractions obtained from E. uniflora Linn leaves (0.05-0.87%w/w, 0.20-0.32%w/w, and 1.71-6.56%w/w, respectively). In general, the CE had lower MIC values than the fractions, including the lowest MIC against the MRSA strain. The CE and AqF also significantly reduced leukocyte migration and MPO activity (p < 0.05). In addition, AqF significantly reduced IL-1β and TNF-α levels (p < 0.05). Furthermore, the CE and fractions exhibited an antioxidant effect (p < 0.05) and peripheral analgesic activity (p < 0.05). The CE and fractions from the studied E. uniflora Linn leaves exhibited antibacterial, anti-inflammatory, antioxidant, and analgesic activity in the performed assays.

Order-disorder transitions in lattice gases with annealed reactive constraints

NASA Astrophysics Data System (ADS)

Dudka, Maxym; Bénichou, Olivier; Oshanin, Gleb

2018-04-01

We study equilibrium properties of catalytically-activated reactions taking place on a lattice of adsorption sites. The particles undergo continuous exchanges with a reservoir maintained at a constant chemical potential μ and react when they appear at the neighbouring sites, provided that some reactive conditions are fulfilled. We model the latter in two different ways: in the Model I some fraction p of the bonds connecting neighbouring sites possesses special catalytic properties such that any two As appearing on the sites connected by such a bond instantaneously react and desorb. In the Model II some fraction p of the adsorption sites possesses such properties and neighbouring particles react if at least one of them resides on a catalytic site. For the case of annealed disorder in the distribution of the catalyst, which is tantamount to the situation when the reaction may take place at any point on the lattice but happens with a finite probability p, we provide an exact solution for both models for the interior of an infinitely large Cayley tree—the so-called Bethe lattice. We show that both models exhibit a rich critical behaviour: for the annealed Model I it is characterised by a transition into an ordered state and a re-entrant transition into a disordered phase, which both are continuous. For the annealed Model II, which represents a rather exotic model of statistical mechanics in which interactions of any particle with its environment have a peculiar Boolean form, the transition to an ordered state is always continuous, while the re-entrant transition into the disordered phase may be either continuous or discontinuous, depending on the value of p.

3D heart motion from single-plane angiography of the coronary vasculature: a model-based approach

NASA Astrophysics Data System (ADS)

Sherknies, Denis; Meunier, Jean; Tardif, Jean-Claude

2004-05-01

In order to complete a thorough examination of a patient heart muscle, physicians practice two common invasive procedures: the ventriculography, which allows the determination of the ejection fraction, and the coronarography, giving among other things, information on stenosis of arteries. We propose a method that allows the determination of a contraction index similar to ejection fraction, using only single-plane coronarography. Our method first reconstructs in 3D, selected points on the angiogram, using a 3D model devised from data published by Dodge ea. ['88, '92]. We then follow the point displacements through a complete heart contraction cycle. The objective function, minimizing the RMS distances between the angiogram and the model, relies on affine transformations, i.e. translation, rotation and isotropic scaling. We validate our method on simulated projections using cases from Dodge data. In order to avoid any bias, a leave-one-out strategy was used, which excludes the reference case when constructing the 3D coronary heart model. The simulated projections are created by transforming the reference case, with scaling, translation and rotation transformations, and by adding random 3D noise for each frame in the contraction cycle. Comparing the true scaling parameters to the reconstructed sequence, our method is quite robust (R2=96.6%, P<1%), even when noise error level is as high as 1 cm. Using 10 clinical cases we then proceeded to reconstruct the contraction sequence for a complete cardiac cycle starting at end-diastole. A simple heart contraction mathematical model permitted us to link the measured ejection fraction of the different cases to the maximum heart contraction amplitude (R2=57%, P<1%) determined by our method.

Size effects in martensitic microstructures: Finite-strain phase field model versus sharp-interface approach

NASA Astrophysics Data System (ADS)

Tůma, K.; Stupkiewicz, S.; Petryk, H.

2016-10-01

A finite-strain phase field model for martensitic phase transformation and twinning in shape memory alloys is developed and confronted with the corresponding sharp-interface approach extended to interfacial energy effects. The model is set in the energy framework so that the kinetic equations and conditions of mechanical equilibrium are fully defined by specifying the free energy and dissipation potentials. The free energy density involves the bulk and interfacial energy contributions, the latter describing the energy of diffuse interfaces in a manner typical for phase-field approaches. To ensure volume preservation during martensite reorientation at finite deformation within a diffuse interface, it is proposed to apply linear mixing of the logarithmic transformation strains. The physically different nature of phase interfaces and twin boundaries in the martensitic phase is reflected by introducing two order-parameters in a hierarchical manner, one as the reference volume fraction of austenite, and thus of the whole martensite, and the second as the volume fraction of one variant of martensite in the martensitic phase only. The microstructure evolution problem is given a variational formulation in terms of incremental fields of displacement and order parameters, with unilateral constraints on volume fractions explicitly enforced by applying the augmented Lagrangian method. As an application, size-dependent microstructures with diffuse interfaces are calculated for the cubic-to-orthorhombic transformation in a CuAlNi shape memory alloy and compared with the sharp-interface microstructures with interfacial energy effects.

Thermal-noise-limited higher-order mode locking of a reference cavity

NASA Astrophysics Data System (ADS)

Zeng, X. Y.; Ye, Y. X.; Shi, X. H.; Wang, Z. Y.; Deng, K.; Zhang, J.; Lu, Z. H.

2018-04-01

Higher-order mode locking has been proposed to reduce the thermal noise limit of reference cavities. By locking a laser to the HG02 mode of a 10-cm long all ULE cavity, and measure its performance with the three-cornered-hat method among three independently stabilized lasers, we demonstrate a thermal noise limited performance of a fractional frequency instability of 4.9E-16. The results match the theoretical models with higher-order optical modes. The achieved laser instability improves the all ULE short cavity results to a new low level.

Antioxidant and Cytoprotective Activities of Fucus spiralis Seaweed on a Human Cell in Vitro Model

PubMed Central

Pinteus, Susete; Silva, Joana; Alves, Celso; Horta, André; Thomas, Olivier P.; Pedrosa, Rui

2017-01-01

Antioxidants play an important role as Reactive Oxygen Species (ROS) chelating agents and, therefore, the screening for potent antioxidants from natural sources as potential protective agents is of great relevance. The main aim of this study was to obtain antioxidant-enriched fractions from the common seaweed Fucus spiralis and evaluate their activity and efficiency in protecting human cells (MCF-7 cells) on an oxidative stress condition induced by H2O2. Five fractions, F1–F5, were obtained by reversed-phase vacuum liquid chromatography. F3, F4 and F5 revealed the highest phlorotannin content, also showing the strongest antioxidant effects. The cell death induced by H2O2 was reduced by all fractions following the potency order F4 > F2 > F3 > F5 > F1. Only fraction F4 completely inhibited the H2O2 effect. To understand the possible mechanisms of action of these fractions, the cellular production of H2O2, the mitochondrial membrane potential and the caspase 9 activity were studied. Fractions F3 and F4 presented the highest reduction on H2O2 cell production. All fractions decreased both caspase-9 activity and cell membrane depolarization (except F1). Taken all together, the edible F. spiralis reveal that they provide protection against oxidative stress induced by H2O2 on the human MCF-7 cellular model, probably acting as upstream blockers of apoptosis. PMID:28146076

Carbon turnover in an agricultural sub-soil

NASA Astrophysics Data System (ADS)

Collins, Chris

2010-05-01

Maize was added to a grassland subsoil (10 - 50 cm) and the fate of the carbon from the plant material followed for 520 days with nine sampling points over an exponential time series. The carbon and delta 13C signature in five soil fractions: POM (particulate organic matter), fine sand, coarse silt, fine silt and clay were monitored. Over the course of the experiment there was a 57% decline in the total C of the soil principally from the particulate organic matter which contained the added maize equivalent to a half life of 533 days. A single exponential was the best fit to the data indicating that the slower turnover pools proposed in models such as Roth C were not observed in the time course of this experiment. Carbon rapidly entered the fine sand and coarse silt fractions, it then passed into the clay fraction. The fine silt fraction was not significantly changed. The maize carbon showed a delay to this pattern, but there was accumulation of maize carbon in the fine sand and fine silt fractions. The largest increases in % carbon as a consequence of the introduction of the maize carbon were of the following order clay > fine sand > coarse silt >fine silt. The results suggest that all these fractions are actively being turnover in this soil and that carbon is most protected in the fine sand and silt fractions, not clay as has been observed by other workers. The results are also discussed in the wider contexts of representative pools for modeling.

Sliding Mode Control of Fractional-Order Delayed Memristive Chaotic System with Uncertainty and Disturbance

NASA Astrophysics Data System (ADS)

Ding, Da-Wei; Liu, Fang-Fang; Chen, Hui; Wang, Nian; Liang, Dong

2017-12-01

In this paper, a simplest fractional-order delayed memristive chaotic system is proposed in order to control the chaos behaviors via sliding mode control strategy. Firstly, we design a sliding mode control strategy for the fractional-order system with time delay to make the states of the system asymptotically stable. Then, we obtain theoretical analysis results of the control method using Lyapunov stability theorem which guarantees the asymptotic stability of the non-commensurate order and commensurate order system with and without uncertainty and an external disturbance. Finally, numerical simulations are given to verify that the proposed sliding mode control method can eliminate chaos and stabilize the fractional-order delayed memristive system in a finite time. Supported by the National Nature Science Foundation of China under Grant No. 61201227, Funding of China Scholarship Council, the Natural Science Foundation of Anhui Province under Grant No. 1208085M F93, 211 Innovation Team of Anhui University under Grant Nos. KJTD007A and KJTD001B

Fractional Order and Dynamic Simulation of a System Involving an Elastic Wide Plate

NASA Astrophysics Data System (ADS)

David, S. A.; Balthazar, J. M.; Julio, B. H. S.; Oliveira, C.

2011-09-01

Numerous researchers have studied about nonlinear dynamics in several areas of science and engineering. However, in most cases, these concepts have been explored mainly from the standpoint of analytical and computational methods involving integer order calculus (IOC). In this paper we have examined the dynamic behavior of an elastic wide plate induced by two electromagnets of a point of view of the fractional order calculus (FOC). The primary focus of this study is on to help gain a better understanding of nonlinear dynamic in fractional order systems.

Fractional-order Fourier analysis for ultrashort pulse characterization.

PubMed

Brunel, Marc; Coetmellec, Sébastien; Lelek, Mickael; Louradour, Frédéric

2007-06-01

We report what we believe to be the first experimental demonstration of ultrashort pulse characterization using fractional-order Fourier analysis. The analysis is applied to the interpretation of spectral interferometry resolved in time (SPIRIT) traces [which are spectral phase interferometry for direct electric field reconstruction (SPIDER)-like interferograms]. First, the fractional-order Fourier transformation is shown to naturally allow the determination of the cubic spectral phase coefficient of pulses to be analyzed. A simultaneous determination of both cubic and quadratic spectral phase coefficients of the pulses using the fractional-order Fourier series expansion is further demonstrated. This latter technique consists of localizing relative maxima in a 2D cartography representing decomposition coefficients. It is further used to reconstruct or filter SPIRIT traces.

Optimization in fractional aircraft ownership

NASA Astrophysics Data System (ADS)

Septiani, R. D.; Pasaribu, H. M.; Soewono, E.; Fayalita, R. A.

2012-05-01

Fractional Aircraft Ownership is a new concept in flight ownership management system where each individual or corporation may own a fraction of an aircraft. In this system, the owners have privilege to schedule their flight according to their needs. Fractional management companies (FMC) manages all aspects of aircraft operations, including utilization of FMC's aircraft in combination of outsourced aircrafts. This gives the owners the right to enjoy the benefits of private aviations. However, FMC may have complicated business requirements that neither commercial airlines nor charter airlines faces. Here, optimization models are constructed to minimize the number of aircrafts in order to maximize the profit and to minimize the daily operating cost. In this paper, three kinds of demand scenarios are made to represent different flight operations from different types of fractional owners. The problems are formulated as an optimization of profit and a daily operational cost to find the optimum flight assignments satisfying the weekly and daily demand respectively from the owners. Numerical results are obtained by Genetic Algorithm method.

Non-integer viscoelastic constitutive law to model soft biological tissues to in-vivo indentation.

PubMed

Demirci, Nagehan; Tönük, Ergin

2014-01-01

During the last decades, derivatives and integrals of non-integer orders are being more commonly used for the description of constitutive behavior of various viscoelastic materials including soft biological tissues. Compared to integer order constitutive relations, non-integer order viscoelastic material models of soft biological tissues are capable of capturing a wider range of viscoelastic behavior obtained from experiments. Although integer order models may yield comparably accurate results, non-integer order material models have less number of parameters to be identified in addition to description of an intermediate material that can monotonically and continuously be adjusted in between an ideal elastic solid and an ideal viscous fluid. In this work, starting with some preliminaries on non-integer (fractional) calculus, the "spring-pot", (intermediate mechanical element between a solid and a fluid), non-integer order three element (Zener) solid model, finally a user-defined large strain non-integer order viscoelastic constitutive model was constructed to be used in finite element simulations. Using the constitutive equation developed, by utilizing inverse finite element method and in vivo indentation experiments, soft tissue material identification was performed. The results indicate that material coefficients obtained from relaxation experiments, when optimized with creep experimental data could simulate relaxation, creep and cyclic loading and unloading experiments accurately. Non-integer calculus viscoelastic constitutive models, having physical interpretation and modeling experimental data accurately is a good alternative to classical phenomenological viscoelastic constitutive equations.

Adaptative synchronization in multi-output fractional-order complex dynamical networks and secure communications

NASA Astrophysics Data System (ADS)

Mata-Machuca, Juan L.; Aguilar-López, Ricardo

2018-01-01

This work deals with the adaptative synchronization of complex dynamical networks with fractional-order nodes and its application in secure communications employing chaotic parameter modulation. The complex network is composed of multiple fractional-order systems with mismatch parameters and the coupling functions are given to realize the network synchronization. We introduce a fractional algebraic synchronizability condition (FASC) and a fractional algebraic identifiability condition (FAIC) which are used to know if the synchronization and parameters estimation problems can be solved. To overcome these problems, an adaptative synchronization methodology is designed; the strategy consists in proposing multiple receiver systems which tend to follow asymptotically the uncertain transmitters systems. The coupling functions and parameters of the receiver systems are adjusted continually according to a convenient sigmoid-like adaptative controller (SLAC), until the measurable output errors converge to zero, hence, synchronization between transmitter and receivers is achieved and message signals are recovered. Indeed, the stability analysis of the synchronization error is based on the fractional Lyapunov direct method. Finally, numerical results corroborate the satisfactory performance of the proposed scheme by means of the synchronization of a complex network consisting of several fractional-order unified chaotic systems.

Condensation and fractionation of rare earths in the solar nebula

NASA Technical Reports Server (NTRS)

Davis, A. M.; Grossman, L.

1979-01-01

The condensation behavior of the rare earth elements in the solar nebula is calculated on the basis of the most recent thermodynamic data in order to construct a model explaining group II rare earth element patterns in Allende inclusions. Models considered all involve the removal of large fractions of the more refractory heavy rare earth elements in an early condensate, followed by the condensation of the remainder at a lower temperature. It is shown that the model of Boynton (1975) in which one rare earth element component is dissolved nonideally in perovskite according to relative activity coefficients can not reasonably be made to fit the observed group II patterns. A model in which two rare earth components control the patterns and dissolve ideally in perovskite is proposed and shown to be able to account for the 20 patterns by variations of the perovskite removal temperature and the relative proportions of the two components.

A 2D multi-term time and space fractional Bloch-Torrey model based on bilinear rectangular finite elements

NASA Astrophysics Data System (ADS)

Qin, Shanlin; Liu, Fawang; Turner, Ian W.

2018-03-01

The consideration of diffusion processes in magnetic resonance imaging (MRI) signal attenuation is classically described by the Bloch-Torrey equation. However, many recent works highlight the distinct deviation in MRI signal decay due to anomalous diffusion, which motivates the fractional order generalization of the Bloch-Torrey equation. In this work, we study the two-dimensional multi-term time and space fractional diffusion equation generalized from the time and space fractional Bloch-Torrey equation. By using the Galerkin finite element method with a structured mesh consisting of rectangular elements to discretize in space and the L1 approximation of the Caputo fractional derivative in time, a fully discrete numerical scheme is derived. A rigorous analysis of stability and error estimation is provided. Numerical experiments in the square and L-shaped domains are performed to give an insight into the efficiency and reliability of our method. Then the scheme is applied to solve the multi-term time and space fractional Bloch-Torrey equation, which shows that the extra time derivative terms impact the relaxation process.

Experimental investigation, model development and sensitivity analysis of rheological behavior of ZnO/10W40 nano-lubricants for automotive applications

NASA Astrophysics Data System (ADS)

Hemmat Esfe, Mohammad; Saedodin, Seyfolah; Rejvani, Mousa; Shahram, Jalal

2017-06-01

In the present study, rheological behavior of ZnO/10W40 nano-lubricant is investigated by an experimental approach. Firstly, ZnO nanoparticles of 10-30 nm were dispersed in 10W40 engine oil with solid volume fractions of 0.25-2%, then the viscosity of the composed nano-lubricant was measured in temperature ranges of 5-55 °C and in various shear rates. From analyzing the results, it was revealed that both of the base oil and nano-lubricants are non-Newtonian fluids which exhibit shear thinning behavior. Sensitivity of viscosity to the solid volume fraction enhancement was calculated by a new correlation which was proposed in terms of solid volume fraction and temperature. In order to attain an accurate model by which experimental data are predicted, an artificial neural network (ANN) with a hidden layer and 5 neurons was designed. This model was considerably accurate in predicting experimental data of dynamic viscosity as R-squared and average absolute relative deviation (AARD %) were respectively 0.9999 and 0.0502.

Identification of Hierarchies of Student Learning about Percentages Using Rasch Analysis

ERIC Educational Resources Information Center

Burfitt, Joan

2013-01-01

A review of the research literature indicated that there were probable orders in which students develop understandings and skills for calculating with percentages. Such calculations might include using models to represent percentages, knowing fraction equivalents, selection of strategies to solve problems and determination of percentage change. To…

Duality in an asset exchange model for wealth distribution

NASA Astrophysics Data System (ADS)

Li, Jie; Boghosian, Bruce M.

2018-05-01

Asset exchange models are agent-based economic models with binary transactions. Previous investigations have augmented these models with mechanisms for wealth redistribution, quantified by a parameter χ, and for trading bias favoring wealthier agents, quantified by a parameter ζ. By deriving and analyzing a Fokker-Planck equation for a particular asset exchange model thus augmented, it has been shown that it exhibits a second-order phase transition at ζ / χ = 1, between regimes with and without partial wealth condensation. In the "subcritical" regime with ζ / χ < 1, all of the wealth is classically distributed; in the "supercritical" regime with ζ / χ > 1, a fraction 1 - χ / ζ of the wealth is condensed. Intuitively, one may associate the supercritical, wealth-condensed regime as reflecting the presence of "oligarchy," by which we mean that an infinitesimal fraction of the total agents hold a finite fraction of the total wealth in the continuum limit. In this paper, we further elucidate the phase behavior of this model - and hence of the generalized solutions of the Fokker-Planck equation that describes it - by demonstrating the existence of a remarkable symmetry between its supercritical and subcritical regimes in the steady-state. Noting that the replacement { ζ → χ , χ → ζ } , which clearly has the effect of inverting the order parameter ζ / χ, provides a one-to-one correspondence between the subcritical and supercritical states, we demonstrate that the wealth distribution of the subcritical state is identical to that of the corresponding supercritical state when the oligarchy is removed from the latter. We demonstrate this result analytically, both from the microscopic agent-level model and from its macroscopic Fokker-Planck description, as well as numerically. We argue that this symmetry is a kind of duality, analogous to the famous Kramers-Wannier duality between the subcritical and supercritical states of the Ising model, and to the Maldacena duality that underlies AdS/CFT theory.

Identifying Glacial Meltwater in the Amundsen Sea, Antarctica

NASA Astrophysics Data System (ADS)

Biddle, L. C.; Heywood, K. J.; Jenkins, A.; Kaiser, J.

2016-02-01

Pine Island Glacier, located in the Amundsen Sea, is losing mass rapidly due to relatively warm ocean waters melting its ice shelf from below. The resulting increase in meltwater production may be the root of the freshening in the Ross Sea over the last 30 years. Tracing the meltwater travelling away from the ice sheets is important in order to identify the regions most affected by the increased input of this water type. We use water mass characteristics (temperature, salinity, O2 concentration) derived from 105 CTD casts during the Ocean2ice cruise on RRS James Clark Ross in January-March 2014 to calculate meltwater fractions north of Pine Island Glacier. The data show maximum meltwater fractions at the ice front of up to 2.4 % and a plume of meltwater travelling away from the ice front along the 1027.7 kg m-3 isopycnal. We investigate the reliability of these results and attach uncertainties to the measurements made to ascertain the most reliable method of meltwater calculation in the Amundsen Sea. Processes such as atmospheric interaction and biological activity also affect the calculated apparent meltwater fractions. We analyse their effects on the reliability of the calculated meltwater fractions across the region using a bulk mixed layer model based on the one-dimensional Price-Weller-Pinkel model (Price et al., 1986). The model includes sea ice, dissolved oxygen concentrations and a simple respiration model, forced by NCEP climatology and an initial linear mixing profile between Winter Water (WW) and Circumpolar Deep Water (CDW). The model mimics the seasonal cycle of mixed layer warming and freshening and simulates how increases in sea ice formation and the influx of slightly cooler Lower CDW impact on the apparent meltwater fractions. These processes could result in biased meltwater signatures across the eastern Amundsen Sea.

Identifying glacial meltwater in the Amundsen Sea, Antarctica

NASA Astrophysics Data System (ADS)

Biddle, Louise; Heywood, Karen; Jenkins, Adrian; Kaiser, Jan

2016-04-01

Pine Island Glacier, located in the Amundsen Sea, is losing mass rapidly due to relatively warm ocean waters melting its ice shelf from below. The resulting increase in meltwater production may be the root of the freshening in the Ross Sea over the last 30 years. Tracing the meltwater travelling away from the ice sheets is important in order to identify the regions most affected by the increased input of this water type. We use water mass characteristics (temperature, salinity, O2 concentration) derived from 105 CTD casts during the Ocean2ice cruise on RRS James Clark Ross in January-March 2014 to calculate meltwater fractions north of Pine Island Glacier. The data show maximum meltwater fractions at the ice front of up to 2.4 % and a plume of meltwater travelling away from the ice front along the 1027.7 kg m-3 isopycnal. We investigate the reliability of these results and attach uncertainties to the measurements made to ascertain the most reliable method of meltwater calculation in the Amundsen Sea. Processes such as atmospheric interaction and biological activity also affect the calculated apparent meltwater fractions. We analyse their effects on the reliability of the calculated meltwater fractions across the region using a bulk mixed layer model based on the one-dimensional Price-Weller-Pinkel model (1986). The model includes sea ice, dissolved oxygen concentrations and a simple respiration model, forced by NCEP climatology and an initial linear mixing profile between Winter Water (WW) and Circumpolar Deep Water (CDW). The model mimics the seasonal cycle of mixed layer warming and freshening and simulates how increases in sea ice formation and the influx of slightly cooler Lower CDW impact on the apparent meltwater fractions. These processes could result in biased meltwater signatures across the eastern Amundsen Sea.

A CFD modeling study in an urban street canyon for ultrafine particles and population exposure: The intake fraction approach.

PubMed

Habilomatis, George; Chaloulakou, Archontoula

2015-10-15

Air quality in street canyons is of major importance, since the highest pollution levels are often encountered in these microenvironments. The canyon effect (reduced natural ventilation) makes them "hot spots" for particulate pollution contributing to adverse health effects for the exposed population. In this study we tried to characterize the influence of UFP (ultrafine particle) emissions from traffic on population exposure in an urban street canyon, by applying the intake fraction (iF) approach. One month long measurements of UFP levels have been monitored and used for the need of this study. We applied a three dimensional computational fluid dynamic (CFD) model based on real measurements for the simulation of UFP levels. We used infiltration factors, evaluated on a daily basis for the under study area, to estimate the indoor UFP levels. As a result the intake fraction for the pedestrians, residents and office workers is in the range of (1E-5)-(1E-4). The street canyon is mostly residential justifying partially the higher value of intake fraction for residents (1E-4). The above iF value is on the same order of magnitude with the corresponding one evaluated in a relative street canyon study. The total iF value in this microenvironment is one order of magnitude higher than ours, explained partially by the different use and activities. Two specific applications of iF to assess prioritization among emission sources and environmental justice issues are also examined. We ran a scenario with diesel and gasoline cars and diesel fueled vehicle seems to be a target source to improve overall iF. Our application focus on a small residential area, typical of urban central Athens, in order to evaluate high resolution iF. The significance of source-exposure relationship study in a micro scale is emphasized by recent research. Copyright © 2015 Elsevier B.V. All rights reserved.

Continued-fraction representation of the Kraus map for non-Markovian reservoir damping

NASA Astrophysics Data System (ADS)

van Wonderen, A. J.; Suttorp, L. G.

2018-04-01

Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative dynamics as determined by the unitary evolution of system and reservoir is described by a Kraus map consisting of an infinite number of matrices. For all Laplace-transformed Kraus matrices exact solutions are constructed in terms of continued fractions that depend on the pair correlation functions of the reservoir. By performing factorizations in the Kraus map a perturbation theory is set up that conserves in arbitrary perturbative order both positivity and probability of the density matrix. The latter is determined by an integral equation for a bitemporal matrix and a finite hierarchy for Kraus matrices. In the lowest perturbative order this hierarchy reduces to one equation for one Kraus matrix. Its solution is given by a continued fraction of a much simpler structure as compared to the non-perturbative case. In the lowest perturbative order our non-Markovian evolution equations are applied to the damped Jaynes–Cummings model. From the solution for the atomic density matrix it is found that the atom may remain in the state of maximum entropy for a significant time span that depends on the initial energy of the radiation field.

The convergence of the order sequence and the solution function sequence on fractional partial differential equation

NASA Astrophysics Data System (ADS)

Rusyaman, E.; Parmikanti, K.; Chaerani, D.; Asefan; Irianingsih, I.

2018-03-01

One of the application of fractional ordinary differential equation is related to the viscoelasticity, i.e., a correlation between the viscosity of fluids and the elasticity of solids. If the solution function develops into function with two or more variables, then its differential equation must be changed into fractional partial differential equation. As the preliminary study for two variables viscoelasticity problem, this paper discusses about convergence analysis of function sequence which is the solution of the homogenous fractional partial differential equation. The method used to solve the problem is Homotopy Analysis Method. The results show that if given two real number sequences (αn) and (βn) which converge to α and β respectively, then the solution function sequences of fractional partial differential equation with order (αn, βn) will also converge to the solution function of fractional partial differential equation with order (α, β).

Modelling of slaughterhouse solid waste anaerobic digestion: determination of parameters and continuous reactor simulation.

PubMed

López, Iván; Borzacconi, Liliana

2010-10-01

A model based on the work of Angelidaki et al. (1993) was applied to simulate the anaerobic biodegradation of ruminal contents. In this study, two fractions of solids with different biodegradation rates were considered. A first-order kinetic was used for the easily biodegradable fraction and a kinetic expression that is function of the extracellular enzyme concentration was used for the slowly biodegradable fraction. Batch experiments were performed to obtain an accumulated methane curve that was then used to obtain the model parameters. For this determination, a methodology derived from the "multiple-shooting" method was successfully used. Monte Carlo simulations allowed a confidence range to be obtained for each parameter. Simulations of a continuous reactor were performed using the optimal set of model parameters. The final steady-states were determined as functions of the operational conditions (solids load and residence time). The simulations showed that methane flow peaked at a flow rate of 0.5-0.8 Nm(3)/d/m(reactor)(3) at a residence time of 10-20 days. Simulations allow the adequate selection of operating conditions of a continuous reactor. (c) 2010 Elsevier Ltd. All rights reserved.

Pasta Nucleosynthesis: Molecular dynamics simulations of nuclear statistical equilibrium

NASA Astrophysics Data System (ADS)

Caplan, Matthew; Horowitz, Charles; da Silva Schneider, Andre; Berry, Donald

2014-09-01

We simulate the decompression of cold dense nuclear matter, near the nuclear saturation density, in order to study the role of nuclear pasta in r-process nucleosynthesis in neutron star mergers. Our simulations are performed using a classical molecular dynamics model with 51 200 and 409 600 nucleons, and are run on GPUs. We expand our simulation region to decompress systems from initial densities of 0.080 fm-3 down to 0.00125 fm-3. We study proton fractions of YP = 0.05, 0.10, 0.20, 0.30, and 0.40 at T = 0.5, 0.75, and 1 MeV. We calculate the composition of the resulting systems using a cluster algorithm. This composition is in good agreement with nuclear statistical equilibrium models for temperatures of 0.75 and 1 MeV. However, for proton fractions greater than YP = 0.2 at a temperature of T = 0.5 MeV, the MD simulations produce non-equilibrium results with large rod-like nuclei. Our MD model is valid at higher densities than simple nuclear statistical equilibrium models and may help determine the initial temperatures and proton fractions of matter ejected in mergers.

Performance analysis of two-degree of freedom fractional order PID controllers for robotic manipulator with payload.

PubMed

Sharma, Richa; Gaur, Prerna; Mittal, A P

2015-09-01

The robotic manipulators are multi-input multi-output (MIMO), coupled and highly nonlinear systems. The presence of external disturbances and time-varying parameters adversely affects the performance of these systems. Therefore, the controller designed for these systems should effectively deal with such complexities, and it is an intriguing task for control engineers. This paper presents two-degree of freedom fractional order proportional-integral-derivative (2-DOF FOPID) controller scheme for a two-link planar rigid robotic manipulator with payload for trajectory tracking task. The tuning of all controller parameters is done using cuckoo search algorithm (CSA). The performance of proposed 2-DOF FOPID controllers is compared with those of their integer order designs, i.e., 2-DOF PID controllers, and with the traditional PID controllers. In order to show effectiveness of proposed scheme, the robustness testing is carried out for model uncertainties, payload variations with time, external disturbance and random noise. Numerical simulation results indicate that the 2-DOF FOPID controllers are superior to their integer order counterparts and the traditional PID controllers. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Modeling and Testing of the Viscoelastic Properties of a Graphite Nanoplatelet/Epoxy Composite

NASA Technical Reports Server (NTRS)

Odegard, Gregory M.; Gates, Thomas S.

2005-01-01

In order to facilitate the interpretation of experimental data, a micromechanical modeling procedure is developed to predict the viscoelastic properties of a graphite nanoplatelet/epoxy composite as a function of volume fraction and nanoplatelet diameter. The predicted storage and loss moduli for the composite are compared to measured values from the same material using three test methods; Dynamical Mechanical Analysis, nanoindentation, and quasi-static tensile tests. In most cases, the model and experiments indicate that for increasing volume fractions of nanoplatelets, both the storage and loss moduli increase. Also, the results indicate that for nanoplatelet sizes above 15 microns, nanoindentation is capable of measuring properties of individual constituents of a composite system. Comparison of the predicted values to the measured data helps illustrate the relative similarities and differences between the bulk and local measurement techniques.

Coordination of fractional-order nonlinear multi-agent systems via distributed impulsive control

NASA Astrophysics Data System (ADS)

Ma, Tiedong; Li, Teng; Cui, Bing

2018-01-01

The coordination of fractional-order nonlinear multi-agent systems via distributed impulsive control method is studied in this paper. Based on the theory of impulsive differential equations, algebraic graph theory, Lyapunov stability theory and Mittag-Leffler function, two novel sufficient conditions for achieving the cooperative control of a class of fractional-order nonlinear multi-agent systems are derived. Finally, two numerical simulations are verified to illustrate the effectiveness and feasibility of the proposed method.

Boundary particle method for Laplace transformed time fractional diffusion equations

NASA Astrophysics Data System (ADS)

Fu, Zhuo-Jia; Chen, Wen; Yang, Hai-Tian

2013-02-01

This paper develops a novel boundary meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation in Laplace space and then employs a truly boundary-only meshless boundary particle method (BPM) to solve this Laplace-transformed problem. Unlike the other boundary discretization methods, the BPM does not require any inner nodes, since the recursive composite multiple reciprocity technique (RC-MRM) is used to convert the inhomogeneous problem into the higher-order homogeneous problem. Finally, the Stehfest numerical inverse Laplace transform (NILT) is implemented to retrieve the numerical solutions of time fractional diffusion equations from the corresponding BPM solutions. In comparison with finite difference discretization, the LTBPM introduces Laplace transform and Stehfest NILT algorithm to deal with time fractional derivative term, which evades costly convolution integral calculation in time fractional derivation approximation and avoids the effect of time step on numerical accuracy and stability. Consequently, it can effectively simulate long time-history fractional diffusion systems. Error analysis and numerical experiments demonstrate that the present LTBPM is highly accurate and computationally efficient for 2D and 3D time fractional diffusion equations.

Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space-bandwidth product.

PubMed

Oktem, Figen S; Ozaktas, Haldun M

2010-08-01

Linear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and ordered by the corresponding fractional order parameter and provides insight into the evolution of light through an optical system modeled by LCTs. If a set of signals is highly confined to finite intervals in two arbitrary LCT domains, the space-frequency (phase space) support is a parallelogram. The number of degrees of freedom of this set of signals is given by the area of this parallelogram, which is equal to the bicanonical width product but usually smaller than the conventional space-bandwidth product. The bicanonical width product, which is a generalization of the space-bandwidth product, can provide a tighter measure of the actual number of degrees of freedom, and allows us to represent and process signals with fewer samples.

Gabor-based kernel PCA with fractional power polynomial models for face recognition.

PubMed

Liu, Chengjun

2004-05-01

This paper presents a novel Gabor-based kernel Principal Component Analysis (PCA) method by integrating the Gabor wavelet representation of face images and the kernel PCA method for face recognition. Gabor wavelets first derive desirable facial features characterized by spatial frequency, spatial locality, and orientation selectivity to cope with the variations due to illumination and facial expression changes. The kernel PCA method is then extended to include fractional power polynomial models for enhanced face recognition performance. A fractional power polynomial, however, does not necessarily define a kernel function, as it might not define a positive semidefinite Gram matrix. Note that the sigmoid kernels, one of the three classes of widely used kernel functions (polynomial kernels, Gaussian kernels, and sigmoid kernels), do not actually define a positive semidefinite Gram matrix either. Nevertheless, the sigmoid kernels have been successfully used in practice, such as in building support vector machines. In order to derive real kernel PCA features, we apply only those kernel PCA eigenvectors that are associated with positive eigenvalues. The feasibility of the Gabor-based kernel PCA method with fractional power polynomial models has been successfully tested on both frontal and pose-angled face recognition, using two data sets from the FERET database and the CMU PIE database, respectively. The FERET data set contains 600 frontal face images of 200 subjects, while the PIE data set consists of 680 images across five poses (left and right profiles, left and right half profiles, and frontal view) with two different facial expressions (neutral and smiling) of 68 subjects. The effectiveness of the Gabor-based kernel PCA method with fractional power polynomial models is shown in terms of both absolute performance indices and comparative performance against the PCA method, the kernel PCA method with polynomial kernels, the kernel PCA method with fractional power polynomial models, the Gabor wavelet-based PCA method, and the Gabor wavelet-based kernel PCA method with polynomial kernels.

Well-conditioned fractional collocation methods using fractional Birkhoff interpolation basis

NASA Astrophysics Data System (ADS)

Jiao, Yujian; Wang, Li-Lian; Huang, Can

2016-01-01

The purpose of this paper is twofold. Firstly, we provide explicit and compact formulas for computing both Caputo and (modified) Riemann-Liouville (RL) fractional pseudospectral differentiation matrices (F-PSDMs) of any order at general Jacobi-Gauss-Lobatto (JGL) points. We show that in the Caputo case, it suffices to compute F-PSDM of order μ ∈ (0 , 1) to compute that of any order k + μ with integer k ≥ 0, while in the modified RL case, it is only necessary to evaluate a fractional integral matrix of order μ ∈ (0 , 1). Secondly, we introduce suitable fractional JGL Birkhoff interpolation problems leading to new interpolation polynomial basis functions with remarkable properties: (i) the matrix generated from the new basis yields the exact inverse of F-PSDM at "interior" JGL points; (ii) the matrix of the highest fractional derivative in a collocation scheme under the new basis is diagonal; and (iii) the resulted linear system is well-conditioned in the Caputo case, while in the modified RL case, the eigenvalues of the coefficient matrix are highly concentrated. In both cases, the linear systems of the collocation schemes using the new basis can be solved by an iterative solver within a few iterations. Notably, the inverse can be computed in a very stable manner, so this offers optimal preconditioners for usual fractional collocation methods for fractional differential equations (FDEs). It is also noteworthy that the choice of certain special JGL points with parameters related to the order of the equations can ease the implementation. We highlight that the use of the Bateman's fractional integral formulas and fast transforms between Jacobi polynomials with different parameters, is essential for our algorithm development.

Continuous fractional-order Zero Phase Error Tracking Control.

PubMed

Liu, Lu; Tian, Siyuan; Xue, Dingyu; Zhang, Tao; Chen, YangQuan

2018-04-01

A continuous time fractional-order feedforward control algorithm for tracking desired time varying input signals is proposed in this paper. The presented controller cancels the phase shift caused by the zeros and poles of controlled closed-loop fractional-order system, so it is called Fractional-Order Zero Phase Tracking Controller (FZPETC). The controlled systems are divided into two categories i.e. with and without non-cancellable (non-minimum-phase) zeros which stand in unstable region or on stability boundary. Each kinds of systems has a targeted FZPETC design control strategy. The improved tracking performance has been evaluated successfully by applying the proposed controller to three different kinds of fractional-order controlled systems. Besides, a modified quasi-perfect tracking scheme is presented for those systems which may not have available future tracking trajectory information or have problem in high frequency disturbance rejection if the perfect tracking algorithm is applied. A simulation comparison and a hardware-in-the-loop thermal peltier platform are shown to validate the practicality of the proposed quasi-perfect control algorithm. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Fractional order PID controller for improvement of PMSM speed control in aerospace applications

NASA Astrophysics Data System (ADS)

Saraji, Ali Motalebi; Ghanbari, Mahmood

2014-12-01

Because of the benefits reduced size, cost and maintenance, noise, CO2 emissions and increased control flexibility and precision, to meet these expectations, electrical equipment increasingly utilize in modern aircraft systems and aerospace industry rather than conventional mechanic, hydraulic, and pneumatic power systems. Electric motor drives are capable of converting electrical power to drive actuators, pumps, compressors, and other subsystems at variable speeds. In the past decades, permanent magnet synchronous motor (PMSM) and brushless dc (BLDC) motor were investigated for aerospace applications such as aircraft actuators. In this paper, the fractional-order PID controller is used in the design of speed loop of PMSM speed control system. Having more parameters for tuning fractional order PID controller lead to good performance ratio to integer order. This good performance is shown by comparison fractional order PID controller with the conventional PI and tuned PID controller by Genetic algorithm in MATLAB soft wear.

Fractional-order positive position feedback compensator for active vibration control of a smart composite plate

NASA Astrophysics Data System (ADS)

Marinangeli, L.; Alijani, F.; HosseinNia, S. Hassan

2018-01-01

In this paper, Active Vibration Control (AVC) of a rectangular carbon fibre composite plate with free edges is presented. The plate is subjected to out-of-plane excitation by a modal vibration exciter and controlled by Macro Fibre Composite (MFC) transducers. Vibration measurements are performed by using a Laser Doppler Vibrometer (LDV) system. A fractional-order Positive Position Feedback (PPF) compensator is proposed, implemented and compared to the standard integer-order PPF. MFC actuator and sensor are positioned on the plate based on maximal modal strain criterion, so as to control the second natural mode of the plate. Both integer and fractional-order PPF allowed for the effective control of the second mode of vibration. However, the newly proposed fractional-order controller is found to be more efficient in achieving the same performance with less actuation voltage. Moreover, it shows promising performance in reducing spillover effect due to uncontrolled modes.

Convergence of fractional adaptive systems using gradient approach.

PubMed

Gallegos, Javier A; Duarte-Mermoud, Manuel A

2017-07-01

Conditions for boundedness and convergence of the output error and the parameter error for various Caputo's fractional order adaptive schemes based on the steepest descent method are derived in this paper. To this aim, the concept of sufficiently exciting signals is introduced, characterized and related to the concept of persistently exciting signals used in the integer order case. An application is designed in adaptive indirect control of integer order systems using fractional equations to adjust parameters. This application is illustrated for a pole placement adaptive problem. Advantages of using fractional adjustment in control adaptive schemes are experimentally obtained. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Axisymmetric deformation in a micropolar thermoelastic medium under fractional order theory of thermoelasticity

NASA Astrophysics Data System (ADS)

Kumar, Rajneesh; Singh, Kulwinder; Pathania, Devinder Singh

2017-07-01

The purpose of this paper is to study the variations in temperature, radial and normal displacement, normal stress, shear stress and couple stress in a micropolar thermoelastic solid in the context of fractional order theory of thermoelasticity. Eigen value approach together with Laplace and Hankel transforms are employed to obtain the general solution of the problem. The field variables corresponding to different fractional order theories of thermoelasticity have been obtained in the transformed domain. The general solution is applied to an infinite space subjected to a concentrated load at the origin. To obtained solution in the physical domain numerical inversion technique has been applied and numerically computed results are depicted graphically to analyze the effects of fractional order parameter on the field variables.

Assessment of normal tissue complications following prostate cancer irradiation: Comparison of radiation treatment modalities using NTCP models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Takam, Rungdham; Bezak, Eva; Yeoh, Eric E.

2010-09-15

Purpose: Normal tissue complication probability (NTCP) of the rectum, bladder, urethra, and femoral heads following several techniques for radiation treatment of prostate cancer were evaluated applying the relative seriality and Lyman models. Methods: Model parameters from literature were used in this evaluation. The treatment techniques included external (standard fractionated, hypofractionated, and dose-escalated) three-dimensional conformal radiotherapy (3D-CRT), low-dose-rate (LDR) brachytherapy (I-125 seeds), and high-dose-rate (HDR) brachytherapy (Ir-192 source). Dose-volume histograms (DVHs) of the rectum, bladder, and urethra retrieved from corresponding treatment planning systems were converted to biological effective dose-based and equivalent dose-based DVHs, respectively, in order to account for differences inmore » radiation treatment modality and fractionation schedule. Results: Results indicated that with hypofractionated 3D-CRT (20 fractions of 2.75 Gy/fraction delivered five times/week to total dose of 55 Gy), NTCP of the rectum, bladder, and urethra were less than those for standard fractionated 3D-CRT using a four-field technique (32 fractions of 2 Gy/fraction delivered five times/week to total dose of 64 Gy) and dose-escalated 3D-CRT. Rectal and bladder NTCPs (5.2% and 6.6%, respectively) following the dose-escalated four-field 3D-CRT (2 Gy/fraction to total dose of 74 Gy) were the highest among analyzed treatment techniques. The average NTCP for the rectum and urethra were 0.6% and 24.7% for LDR-BT and 0.5% and 11.2% for HDR-BT. Conclusions: Although brachytherapy techniques resulted in delivering larger equivalent doses to normal tissues, the corresponding NTCPs were lower than those of external beam techniques other than the urethra because of much smaller volumes irradiated to higher doses. Among analyzed normal tissues, the femoral heads were found to have the lowest probability of complications as most of their volume was irradiated to lower equivalent doses compared to other tissues.« less

a Maximum Entropy Model of the Bearded Capuchin Monkey Habitat Incorporating Topography and Spectral Unmixing Analysis

NASA Astrophysics Data System (ADS)

Howard, A. M.; Bernardes, S.; Nibbelink, N.; Biondi, L.; Presotto, A.; Fragaszy, D. M.; Madden, M.

2012-07-01

Movement patterns of bearded capuchin monkeys (Cebus (Sapajus) libidinosus) in northeastern Brazil are likely impacted by environmental features such as elevation, vegetation density, or vegetation type. Habitat preferences of these monkeys provide insights regarding the impact of environmental features on species ecology and the degree to which they incorporate these features in movement decisions. In order to evaluate environmental features influencing movement patterns and predict areas suitable for movement, we employed a maximum entropy modelling approach, using observation points along capuchin monkey daily routes as species presence points. We combined these presence points with spatial data on important environmental features from remotely sensed data on land cover and topography. A spectral mixing analysis procedure was used to generate fraction images that represent green vegetation, shade and soil of the study area. A Landsat Thematic Mapper scene of the area of study was geometrically and atmospherically corrected and used as input in a Minimum Noise Fraction (MNF) procedure and a linear spectral unmixing approach was used to generate the fraction images. These fraction images and elevation were the environmental layer inputs for our logistic MaxEnt model of capuchin movement. Our models' predictive power (test AUC) was 0.775. Areas of high elevation (>450 m) showed low probabilities of presence, and percent green vegetation was the greatest overall contributor to model AUC. This work has implications for predicting daily movement patterns of capuchins in our field site, as suitability values from our model may relate to habitat preference and facility of movement.

From Fractals to Fractional Vector Calculus: Measurement in the Correct Metric

NASA Astrophysics Data System (ADS)

Wheatcraft, S. W.; Meerschaert, M. M.; Mortensen, J.

2005-12-01

Traditional (stationary) stochastic theories have been fairly successful in reproducing transport behavior at relatively homogeneous field sites such as the Borden and Cape Code sites. However, the highly heterogeneous MADE site has produced tracer data that can not be adequately explained with traditional stochastic theories. In recent years, considerable attention has been focused on developing more sophisticated theories that can predict or reproduce the behavior of complex sites such as the MADE site. People began to realize that the model for geologic complexity may in many cases be very different than the model required for stochastic theory. Fractal approaches were useful in conceptualizing scale-invariant heterogeneity by demonstrating that scale dependant transport was just an artifact of our measurement system. Fractal media have dimensions larger than the dimension that measurement is taking place in, thus assuring the scale-dependence of parameters such as dispersivity. What was needed was a rigorous way to develop a theory that was consistent with the fractal dimension of the heterogeneity. The fractional advection-dispersion equation (FADE) was developed with this idea in mind. The second derivative in the dispersion term of the advection-dispersion equation is replaced with a fractional derivative. The order of differentiation, α, is fractional. Values of α in the range: 1 < α < 2 produce super-Fickian dispersion; in essence, the dispersion scaling is controlled by the value of α. When α = 2, the traditional advection-dispersion equation is recovered. The 1-D version of the FADE has been used successfully to back-predict tracer test behavior at several heterogeneous field sites, including the MADE site. It has been hypothesized that the order of differentiation in the FADE is equivalent to (or at least related to) the fractal dimension of the particle tracks (or geologic heterogeneity). With this way of thinking, one can think of the FADE as a governing equation written for the correct dimension, thus eliminating scale-dependent behavior. Before a generalized multi-dimensional form of the FADE can be developed, it has been necessary to develop a generalized fractional vector calculus. The authors have recently developed generalized canonical fractional forms of the gradient, divergence and curl. This fractional vector calculus will be useful in developing fractional forms of many governing equations in physics.

Phase behavior and orientational ordering in block copolymers doped with anisotropic nanoparticles

NASA Astrophysics Data System (ADS)

Osipov, M. A.; Gorkunov, M. V.; Berezkin, A. V.; Kudryavtsev, Y. V.

2018-04-01

A molecular field theory and coarse-grained computer simulations with dissipative particle dynamics have been used to study the spontaneous orientational ordering of anisotropic nanoparticles in the lamellar and hexagonal phases of diblock copolymers and the effect of nanoparticles on the phase behavior of these systems. Both the molecular theory and computer simulations indicate that strongly anisotropic nanoparticles are ordered orientationally mainly in the boundary region between the domains and the nematic order parameter possesses opposite signs in adjacent domains. The orientational order is induced by the boundary and by the interaction between nanoparticles and the monomer units in different domains. In simulations, sufficiently long and strongly selective nanoparticles are ordered also inside the domains. The nematic order parameter and local concentration profiles of nanoparticles have been calculated numerically using the model of a nanoparticle with two interaction centers and also determined using the results of computer simulations. A number of phase diagrams have been obtained which illustrate the effect of nanoparticle selectivity and molar fraction of the stability ranges of various phases. Different morphologies have been identified by analyzing the static structure factor and a phase diagram has been constructed in coordinates' nanoparticle concentration-copolymer composition. Orientational ordering of even a small fraction of nanoparticles may result in a significant increase of the dielectric anisotropy of a polymer nanocomposite, which is important for various applications.

A Solution to the Fundamental Linear Fractional Order Differential Equation

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Lorenzo, Carl F.

1998-01-01

This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.

Insights Into the Fractional Order Initial Value Problem via Semi-Infinite Systems

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Lorenzo, Carl F.

1998-01-01

This paper considers various aspects of the initial value problem for fractional order differential equations. The main contribution of this paper is to use the solutions to known spatially distributed systems to demonstrate that fractional differintegral operators require an initial condition term that is time-varying due to past distributed storage of information.

Error Patterns in Ordering Fractions among At-Risk Fourth-Grade Students

ERIC Educational Resources Information Center

Malone, Amelia Schneider; Fuchs, Lynn S.

2015-01-01

The 3 purposes of this study were to: (a) describe fraction ordering errors among at-risk 4th-grade students; (b) assess the effect of part-whole understanding and accuracy of fraction magnitude estimation on the probability of committing errors; and (c) examine the effect of students' ability to explain comparing problems on the probability of…

Error Patterns in Ordering Fractions among At-Risk Fourth-Grade Students

ERIC Educational Resources Information Center

Malone, Amelia S.; Fuchs, Lynn S.

2017-01-01

The three purposes of this study were to (a) describe fraction ordering errors among at-risk fourth grade students, (b) assess the effect of part-whole understanding and accuracy of fraction magnitude estimation on the probability of committing errors, and (c) examine the effect of students' ability to explain comparing problems on the probability…

Optimization of thiamethoxam adsorption parameters using multi-walled carbon nanotubes by means of fractional factorial design.

PubMed

Panić, Sanja; Rakić, Dušan; Guzsvány, Valéria; Kiss, Erne; Boskovic, Goran; Kónya, Zoltán; Kukovecz, Ákos

2015-12-01

The aim of this work was to evaluate significant factors affecting the thiamethoxam adsorption efficiency using oxidized multi-walled carbon nanotubes (MWCNTs) as adsorbents. Five factors (initial solution concentration of thiamethoxam in water, temperature, solution pH, MWCNTs weight and contact time) were investigated using 2V(5-1) fractional factorial design. The obtained linear model was statistically tested using analysis of variance (ANOVA) and the analysis of residuals was used to investigate the model validity. It was observed that the factors and their second-order interactions affecting the thiamethoxam removal can be divided into three groups: very important, moderately important and insignificant ones. The initial solution concentration was found to be the most influencing parameter on thiamethoxam adsorption from water. Optimization of the factors levels was carried out by minimizing those parameters which are usually critical in real life: the temperature (energy), contact time (money) and weight of MWCNTs (potential health hazard), in order to maximize the adsorbed amount of the pollutant. The results of maximal adsorbed thiamethoxam amount in both real and optimized experiments indicate that among minimized parameters the adsorption time is one that makes the largest difference. The results of this study indicate that fractional factorial design is very useful tool for screening the higher number of parameters and reducing the number of adsorption experiments. Copyright © 2015 Elsevier Ltd. All rights reserved.

Jump Resonance in Fractional Order Circuits

NASA Astrophysics Data System (ADS)

Buscarino, Arturo; Caponetto, Riccardo; Famoso, Carlo; Fortuna, Luigi

The occurrence of an hysteretic loop in the frequency response of a driven nonlinear system is a phenomenon deeply investigated in nonlinear control theory. Such a phenomenon, which is linked to the multistable behavior of the system, is called jump resonance, since the magnitude of the frequency response is subjected to an abrupt jump up/down with respect to the increasing/decreasing of the frequency of the driving signal. In this paper, we aim at investigating fractional order nonlinear systems showing jump resonance, that is systems in which the order of the derivative is noninteger and their frequency response has a magnitude that is a multivalued function in a given range of frequencies. Furthermore, a strategy for designing fractional order systems showing jump resonance is presented along with the procedure to design and implement an analog circuit based on the approximation of the fractional order derivative. An extensive numerical analysis allows one to assess that the phenomenon is robust to the difference in the derivative order, enlightening the first example of a system with order lower than two which is able to demonstrate a jump resonance behavior.

Rheology of water and ammonia-water ices

NASA Technical Reports Server (NTRS)

Goldsby, D. L.; Kohlstedt, D. L.; Durham, W. B.

1993-01-01

Creep experiments on fine-grained water and ammonia-water ices have been performed at one atmosphere and high confining pressure in order to develop constitutive relationships necessary to model tectonic processes and interpret surface features of icy moons of the outer solar system. The present series of experiments explores the effects of temperature, strain rate, grain size, and melt fraction on creep strength. In general, creep strength decreases with increasing temperature, decreasing strain rate, and increasing melt fraction. A transition from dislocation creep to diffusion creep occurs at finer grain sizes, higher temperatures, and lower strain rates.

ECG artifact cancellation in surface EMG signals by fractional order calculus application.

PubMed

Miljković, Nadica; Popović, Nenad; Djordjević, Olivera; Konstantinović, Ljubica; Šekara, Tomislav B

2017-03-01

New aspects for automatic electrocardiography artifact removal from surface electromyography signals by application of fractional order calculus in combination with linear and nonlinear moving window filters are explored. Surface electromyography recordings of skeletal trunk muscles are commonly contaminated with spike shaped artifacts. This artifact originates from electrical heart activity, recorded by electrocardiography, commonly present in the surface electromyography signals recorded in heart proximity. For appropriate assessment of neuromuscular changes by means of surface electromyography, application of a proper filtering technique of electrocardiography artifact is crucial. A novel method for automatic artifact cancellation in surface electromyography signals by applying fractional order calculus and nonlinear median filter is introduced. The proposed method is compared with the linear moving average filter, with and without prior application of fractional order calculus. 3D graphs for assessment of window lengths of the filters, crest factors, root mean square differences, and fractional calculus orders (called WFC and WRC graphs) have been introduced. For an appropriate quantitative filtering evaluation, the synthetic electrocardiography signal and analogous semi-synthetic dataset have been generated. The examples of noise removal in 10 able-bodied subjects and in one patient with muscle dystrophy are presented for qualitative analysis. The crest factors, correlation coefficients, and root mean square differences of the recorded and semi-synthetic electromyography datasets showed that the most successful method was the median filter in combination with fractional order calculus of the order 0.9. Statistically more significant (p < 0.001) ECG peak reduction was obtained by the median filter application compared to the moving average filter in the cases of low level amplitude of muscle contraction compared to ECG spikes. The presented results suggest that the novel method combining a median filter and fractional order calculus can be used for automatic filtering of electrocardiography artifacts in the surface electromyography signal envelopes recorded in trunk muscles. Copyright © 2017 Elsevier Ireland Ltd. All rights reserved.

Multiscale high-order/low-order (HOLO) algorithms and applications

NASA Astrophysics Data System (ADS)

Chacón, L.; Chen, G.; Knoll, D. A.; Newman, C.; Park, H.; Taitano, W.; Willert, J. A.; Womeldorff, G.

2017-02-01

We review the state of the art in the formulation, implementation, and performance of so-called high-order/low-order (HOLO) algorithms for challenging multiscale problems. HOLO algorithms attempt to couple one or several high-complexity physical models (the high-order model, HO) with low-complexity ones (the low-order model, LO). The primary goal of HOLO algorithms is to achieve nonlinear convergence between HO and LO components while minimizing memory footprint and managing the computational complexity in a practical manner. Key to the HOLO approach is the use of the LO representations to address temporal stiffness, effectively accelerating the convergence of the HO/LO coupled system. The HOLO approach is broadly underpinned by the concept of nonlinear elimination, which enables segregation of the HO and LO components in ways that can effectively use heterogeneous architectures. The accuracy and efficiency benefits of HOLO algorithms are demonstrated with specific applications to radiation transport, gas dynamics, plasmas (both Eulerian and Lagrangian formulations), and ocean modeling. Across this broad application spectrum, HOLO algorithms achieve significant accuracy improvements at a fraction of the cost compared to conventional approaches. It follows that HOLO algorithms hold significant potential for high-fidelity system scale multiscale simulations leveraging exascale computing.

Numerical treatment for solving two-dimensional space-fractional advection-dispersion equation using meshless method

NASA Astrophysics Data System (ADS)

Cheng, Rongjun; Sun, Fengxin; Wei, Qi; Wang, Jufeng

2018-02-01

Space-fractional advection-dispersion equation (SFADE) can describe particle transport in a variety of fields more accurately than the classical models of integer-order derivative. Because of nonlocal property of integro-differential operator of space-fractional derivative, it is very challenging to deal with fractional model, and few have been reported in the literature. In this paper, a numerical analysis of the two-dimensional SFADE is carried out by the element-free Galerkin (EFG) method. The trial functions for the SFADE are constructed by the moving least-square (MLS) approximation. By the Galerkin weak form, the energy functional is formulated. Employing the energy functional minimization procedure, the final algebraic equations system is obtained. The Riemann-Liouville operator is discretized by the Grünwald formula. With center difference method, EFG method and Grünwald formula, the fully discrete approximation schemes for SFADE are established. Comparing with exact results and available results by other well-known methods, the computed approximate solutions are presented in the format of tables and graphs. The presented results demonstrate the validity, efficiency and accuracy of the proposed techniques. Furthermore, the error is computed and the proposed method has reasonable convergence rates in spatial and temporal discretizations.

Box-modeling of 15N/14N in mammals.

PubMed

Balter, Vincent; Simon, Laurent; Fouillet, Hélène; Lécuyer, Christophe

2006-03-01

The 15N/14N signature of animal proteins is now commonly used to understand their physiology and quantify the flows of nutrient in trophic webs. These studies assume that animals are predictably 15N-enriched relative to their food, but the isotopic mechanism which accounts for this enrichment remains unknown. We developed a box model of the nitrogen isotope cycle in mammals in order to predict the 15N/14N ratios of body reservoirs as a function of time, N intake and body mass. Results of modeling show that a combination of kinetic isotope fractionation during the N transfer between amines and equilibrium fractionation related to the reversible conversion of N-amine into ammonia is required to account for the well-established approximately 4 per thousand 15N-enrichment of body proteins relative to the diet. This isotopic enrichment observed in proteins is due to the partial recycling of 15N-enriched urea and the urinary excretion of a fraction of the strongly 15N-depleted ammonia reservoir. For a given body mass and diet delta15N, the isotopic compositions are mainly controlled by the N intake. Increase of the urea turnover combined with a decrease of the N intake lead to calculate a delta15N increase of the proteins, in agreement with the observed increase of collagen delta15N of herbivorous animals with aridity. We further show that the low delta15N collagen values of cave bears cannot be attributed to the dormancy periods as it is commonly thought, but inversely to the hyperphagia behavior. This model highlights the need for experimental investigations performed with large mammals in order to improve our understanding of natural variations of delta15N collagen.

Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations

PubMed Central

Song, Junqiang; Leng, Hongze; Lu, Fengshun

2014-01-01

We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique. PMID:24511303

Phytochemical analysis, antioxidant and anti-inflammatory activity of calyces from Physalis peruviana.

PubMed

Toro, Reina M; Aragón, Diana M; Ospina, Luis F; Ramos, Freddy A; Castellanos, Leonardo

2014-11-01

Physalis peruviana calyces are used extensively in folk medicine. The crude ethanolic extract and some fractions of calyces were evaluated in order to explore antioxidant and anti-inflammatory activities. The anti-inflammatory activity was evaluated by the TPA-induced ear edema model. The antioxidant in vitro activity was measured by means of the superoxide and nitric oxide scavenging activity of the extracts and fractions. The butanolic fraction was found to be promising due to its anti-inflammatory and antioxidant activities. Therefore, a bio-assay guided approach was employed to isolate and identify rutin (1) and nicotoflorin (2) from their NMR spectroscopic and MS data. The identification of rutin in calyces of P. peruviana supports the possible use of this waste material for phytotherapeutic, nutraceutical and cosmetic preparations.

Microwave response of hole and patch arrays

NASA Astrophysics Data System (ADS)

Taylor, Melita C.; Edmunds, James D.; Hendry, Euan; Hibbins, Alastair P.; Sambles, J. Roy

2010-10-01

The electromagnetic response of two-dimensional square arrays of perfectly conducting square patches, and their complementary structures, is modeled utilizing a modal matching technique and employing Babinet’s principle. This method allows for the introduction of progressively higher diffracted orders and waveguide modes to be included in the calculation, hence aiding understanding of the underlying causal mechanism for the observed response. At frequencies close to, but below, the onset of diffraction, a near-complete reflection condition is predicted, even for low filling fractions: conversely, for high filling fractions a near-complete transmission condition results. These resonance phenomena are associated with evanescent diffraction, which is sufficiently strong to reverse the step change in transmission upon establishment of electrical continuity; i.e., the connected structure demonstrates increased transmission with increasing filling fraction.

Analyzing signal attenuation in PFG anomalous diffusion via a non-Gaussian phase distribution approximation approach by fractional derivatives.

PubMed

Lin, Guoxing

2016-11-21

Anomalous diffusion exists widely in polymer and biological systems. Pulsed-field gradient (PFG) techniques have been increasingly used to study anomalous diffusion in nuclear magnetic resonance and magnetic resonance imaging. However, the interpretation of PFG anomalous diffusion is complicated. Moreover, the exact signal attenuation expression including the finite gradient pulse width effect has not been obtained based on fractional derivatives for PFG anomalous diffusion. In this paper, a new method, a Mainardi-Luchko-Pagnini (MLP) phase distribution approximation, is proposed to describe PFG fractional diffusion. MLP phase distribution is a non-Gaussian phase distribution. From the fractional derivative model, both the probability density function (PDF) of a spin in real space and the PDF of the spin's accumulating phase shift in virtual phase space are MLP distributions. The MLP phase distribution leads to a Mittag-Leffler function based PFG signal attenuation, which differs significantly from the exponential attenuation for normal diffusion and from the stretched exponential attenuation for fractional diffusion based on the fractal derivative model. A complete signal attenuation expression E α (-D f b α,β * ) including the finite gradient pulse width effect was obtained and it can handle all three types of PFG fractional diffusions. The result was also extended in a straightforward way to give a signal attenuation expression of fractional diffusion in PFG intramolecular multiple quantum coherence experiments, which has an n β dependence upon the order of coherence which is different from the familiar n 2 dependence in normal diffusion. The results obtained in this study are in agreement with the results from the literature. The results in this paper provide a set of new, convenient approximation formalisms to interpret complex PFG fractional diffusion experiments.

Two-component Structure in the Entanglement Spectrum of Highly Excited States

NASA Astrophysics Data System (ADS)

Yang, Zhi-Cheng; Chamon, Claudio; Hamma, Alioscia; Mucciolo, Eduardo

We study the entanglement spectrum of highly excited eigenstates of two known models which exhibit a many-body localization transition, namely the one-dimensional random-field Heisenberg model and the quantum random energy model. Our results indicate that the entanglement spectrum shows a ``two-component'' structure: a universal part that is associated to Random Matrix Theory, and a non-universal part that is model dependent. The non-universal part manifests the deviation of the highly excited eigenstate from a true random state even in the thermalized phase where the Eigenstate Thermalization Hypothesis holds. The fraction of the spectrum containing the universal part decreases continuously as one approaches the critical point and vanishes in the localized phase in the thermodynamic limit. We use the universal part fraction to construct a new order parameter for the many-body delocalized-to-localized transition. Two toy models based on Rokhsar-Kivelson type wavefunctions are constructed and their entanglement spectra are shown to exhibit the same structure.

Adaptive two-degree-of-freedom PI for speed control of permanent magnet synchronous motor based on fractional order GPC.

PubMed

Qiao, Wenjun; Tang, Xiaoqi; Zheng, Shiqi; Xie, Yuanlong; Song, Bao

2016-09-01

In this paper, an adaptive two-degree-of-freedom (2Dof) proportional-integral (PI) controller is proposed for the speed control of permanent magnet synchronous motor (PMSM). Firstly, an enhanced just-in-time learning technique consisting of two novel searching engines is presented to identify the model of the speed control system in a real-time manner. Secondly, a general formula is given to predict the future speed reference which is unavailable at the interval of two bus-communication cycles. Thirdly, the fractional order generalized predictive control (FOGPC) is introduced to improve the control performance of the servo drive system. Based on the identified model parameters and predicted speed reference, the optimal control law of FOGPC is derived. Finally, the designed 2Dof PI controller is auto-tuned by matching with the optimal control law. Simulations and real-time experimental results on the servo drive system of PMSM are provided to illustrate the effectiveness of the proposed strategy. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Anaerobic biodegradability of fish remains: experimental investigation and parameter estimation.

PubMed

Donoso-Bravo, Andres; Bindels, Francoise; Gerin, Patrick A; Vande Wouwer, Alain

2015-01-01

The generation of organic waste associated with aquaculture fish processing has increased significantly in recent decades. The objective of this study is to evaluate the anaerobic biodegradability of several fish processing fractions, as well as water treatment sludge, for tilapia and sturgeon species cultured in recirculated aquaculture systems. After substrate characterization, the ultimate biodegradability and the hydrolytic rate were estimated by fitting a first-order kinetic model with the biogas production profiles. In general, the first-order model was able to reproduce the biogas profiles properly with a high correlation coefficient. In the case of tilapia, the skin/fin, viscera, head and flesh presented a high level of biodegradability, above 310 mLCH₄gCOD⁻¹, whereas the head and bones showed a low hydrolytic rate. For sturgeon, the results for all fractions were quite similar in terms of both parameters, although viscera presented the lowest values. Both the substrate characterization and the kinetic analysis of the anaerobic degradation may be used as design criteria for implementing anaerobic digestion in a recirculating aquaculture system.

On the solutions of fractional order of evolution equations

NASA Astrophysics Data System (ADS)

Morales-Delgado, V. F.; Taneco-Hernández, M. A.; Gómez-Aguilar, J. F.

2017-01-01

In this paper we present a discussion of generalized Cauchy problems in a diffusion wave process, we consider bi-fractional-order evolution equations in the Riemann-Liouville, Liouville-Caputo, and Caputo-Fabrizio sense. Through Fourier transforms and Laplace transform we derive closed-form solutions to the Cauchy problems mentioned above. Similarly, we establish fundamental solutions. Finally, we give an application of the above results to the determination of decompositions of Dirac type for bi-fractional-order equations and write a formula for the moments for the fractional vibration of a beam equation. This type of decomposition allows us to speak of internal degrees of freedom in the vibration of a beam equation.

Crystallization of Deformable Spherical Colloids

NASA Astrophysics Data System (ADS)

Batista, Vera M. O.; Miller, Mark A.

2010-08-01

We introduce and characterize a first-order model for a generic class of colloidal particles that have a preferred spherical shape but can undergo deformations while always maintaining hard-body interactions. The model consists of hard spheres that can continuously change shape at fixed volume into prolate or oblate ellipsoids of revolution, subject to an energetic penalty. The severity of this penalty is specified by a single parameter that determines the flexibility of the particles. The deformable hard spheres crystallize at higher packing fractions than rigid hard spheres, have a narrower solid-fluid coexistence region and can reach high densities by a second transition to an orientationally ordered crystal.

Nucleation in Sheared Granular Matter

NASA Astrophysics Data System (ADS)

Rietz, Frank; Radin, Charles; Swinney, Harry L.; Schröter, Matthias

2018-02-01

We present an experiment on crystallization of packings of macroscopic granular spheres. This system is often considered to be a model for thermally driven atomic or colloidal systems. Cyclically shearing a packing of frictional spheres, we observe a first order phase transition from a disordered to an ordered state. The ordered state consists of crystallites of mixed fcc and hcp symmetry that coexist with the amorphous bulk. The transition, initiated by homogeneous nucleation, overcomes a barrier at 64.5% volume fraction. Nucleation consists predominantly of the dissolving of small nuclei and the growth of nuclei that have reached a critical size of about ten spheres.

Thermal-noise-limited higher-order mode locking of a reference cavity.

PubMed

Zeng, X Y; Ye, Y X; Shi, X H; Wang, Z Y; Deng, K; Zhang, J; Lu, Z H

2018-04-15

Higher-order mode locking has been proposed to reduce the thermal noise limit of reference cavities. By locking a laser to the HG 02 mode of a 10-cm long all ultra-low expansion (ULE) cavity and measuring its performance with the three-cornered-hat method among three independently stabilized lasers, we demonstrate a thermal-noise-limited performance of a fractional frequency instability of 4.9×10 -16 . The results match the theoretical models with higher-order optical modes. The achieved laser instability improves the all ULE short cavity results to a new low level.

Finite-time synchronization of fractional-order memristor-based neural networks with time delays.

PubMed

Velmurugan, G; Rakkiyappan, R; Cao, Jinde

2016-01-01

In this paper, we consider the problem of finite-time synchronization of a class of fractional-order memristor-based neural networks (FMNNs) with time delays and investigated it potentially. By using Laplace transform, the generalized Gronwall's inequality, Mittag-Leffler functions and linear feedback control technique, some new sufficient conditions are derived to ensure the finite-time synchronization of addressing FMNNs with fractional order α:1<α<2 and 0<α<1. The results from the theory of fractional-order differential equations with discontinuous right-hand sides are used to investigate the problem under consideration. The derived results are extended to some previous related works on memristor-based neural networks. Finally, three numerical examples are presented to show the effectiveness of our proposed theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.

Comparative study on the antioxidant activity of peptides from pearl oyster ( Pinctada martensii) mantle type V collagen and tilapia ( Oreochromis niloticus) scale type I collagen

NASA Astrophysics Data System (ADS)

Xia, Guanghua; Zhang, Xueying; Dong, Zhenghua; Shen, Xuanri

2017-12-01

In this study, Pearl oyster mantle type V collagen (POMC) and tilapia scale type I collagen (TSC) were extracted and hydrolyzed by various proteases in order to obtain peptides. The antioxidant activity of the peptides was investigated by DPPH, hydroxyl radical scavenging experiments and a dynamic digestion model in vitro. The results show that there are significant differences in amino acid composition between POMC and TSC. The collagen peptides obtained from pearl oyster mantle (POMCP) by treating with alkaline protease exhibited higher antioxidant activity than that from tilapia scale (TSCP) treated with papaya protease, and both of them showed greater DPPH and hydroxyl radical scavenging activity than other peptides. After being separated via Sephadex G-25 chromatography, the M1 fraction isolated from POMCP, and the S1 fraction from TSCP with which both had higher molecular weights showed the strongest antioxidant activity than other fractions, and the M1 fraction exhibited stronger antioxidant activity than the S1 fraction in scavenging free-radicals and protecting cells from the oxidation damage. Furthermore, after treating the dynamic digestion system model in vitro, the DPPH and hydroxyl radical scavenging activity of the M1 fraction increased slightly. These results suggest that POMCP exhibits stronger antioxidant activity than TSCP, which means that PMOP may be a good candidate to be a potential natural antioxidant in the food-processing industry.

Anti-Diabetic Potential of Ocimum gratissimum Leaf Fractions in Fortified Diet-Fed Streptozotocin Treated Rat Model of Type-2 Diabetes

PubMed Central

Umar, Isamila A.; James, Dorcas B.; Inuwa, Hajiya M.

2017-01-01

Background: Ocimum gratissimum (OG) is used in the traditional management of diabetes in Nigeria. This study investigated the anti-diabetic potential of OG leaf fractions (OGLF) in a rat model of Type-2 diabetes (T2D). Methods: Methanol crude extract of OG leaf was fractionated with solvents of increasing order of polarity (n-hexane, chloroform, ethyl-acetate, n-butanol and water). The anti-diabetic potential of the fractions was evaluated in vivo. T2D was induced in Albino Wistar rats and treated with OGLF. Results: The T2D rats showed significant elevation in serum levels of fasting blood glucose (FBG), liver and kidney function biomarkers. At 4-week of intervention with OGLF, the untreated diabetic control group maintained severe hyperglycaemia in the presence of 61.7% serum insulin, 17.3% pancreatic β-cell function (HOMA-β) and 51.5% Insulin sensitivity. The glucose tolerance ability was enhanced in the n-butanol-fraction (OGb) treated group. With 74.8% available serum insulin and 38.6% improvement in insulin sensitivity, the OGb treated group had a 63.5% reduction in FBG and it was found to be most effective as it ameliorates a majority of the changes caused in the studied parameters in diabetic rats. Conclusions: The data from this study suggest that OGb fraction is a potential candidate for the development of an effective drug for the management of T2D. PMID:29019956

Anti-Diabetic Potential of Ocimum gratissimum Leaf Fractions in Fortified Diet-Fed Streptozotocin Treated Rat Model of Type-2 Diabetes.

PubMed

Okoduwa, Stanley I R; Umar, Isamila A; James, Dorcas B; Inuwa, Hajiya M

2017-10-11

Background : Ocimum gratissimum (OG) is used in the traditional management of diabetes in Nigeria. This study investigated the anti-diabetic potential of OG leaf fractions (OGLF) in a rat model of Type-2 diabetes (T2D). Method : Methanol crude extract of OG leaf was fractionated with solvents of increasing order of polarity ( n -hexane, chloroform, ethyl-acetate, n -butanol and water). The anti-diabetic potential of the fractions was evaluated in vivo. T2D was induced in Albino Wistar rats and treated with OGLF. Result : The T2D rats showed significant elevation in serum levels of fasting blood glucose (FBG), liver and kidney function biomarkers. At 4-weeks of intervention with OGLF, the untreated diabetic control group maintained severe hyperglycaemia in the presence of 61.7% serum insulin, 17.3% pancreatic β-cell function (HOMA-β) and 51.5% Insulin sensitivity. The glucose tolerance ability was enhanced in the n -butanol-fraction (OGb) treated group. With 74.8% available serum insulin and 38.6% improvement in insulin sensitivity, the OGb treated group had a 63.5% reduction in FBG and it was found to be most effective as it ameliorates a majority of the changes caused in the studied parameters in diabetic rats. Conclusions : The data from this study suggest that OGb fraction is a potential candidate for the development of an effective drug for the management of T2D.

Fundamental studies on kinetic isotope effect (KIE) of hydrogen isotope fractionation in natural gas systems

USGS Publications Warehouse

Ni, Y.; Ma, Q.; Ellis, G.S.; Dai, J.; Katz, B.; Zhang, S.; Tang, Y.

2011-01-01

Based on quantum chemistry calculations for normal octane homolytic cracking, a kinetic hydrogen isotope fractionation model for methane, ethane, and propane formation is proposed. The activation energy differences between D-substitute and non-substituted methane, ethane, and propane are 318.6, 281.7, and 280.2cal/mol, respectively. In order to determine the effect of the entropy contribution for hydrogen isotopic substitution, a transition state for ethane bond rupture was determined based on density function theory (DFT) calculations. The kinetic isotope effect (KIE) associated with bond rupture in D and H substituted ethane results in a frequency factor ratio of 1.07. Based on the proposed mathematical model of hydrogen isotope fractionation, one can potentially quantify natural gas thermal maturity from measured hydrogen isotope values. Calculated gas maturity values determined by the proposed mathematical model using ??D values in ethane from several basins in the world are in close agreement with similar predictions based on the ??13C composition of ethane. However, gas maturity values calculated from field data of methane and propane using both hydrogen and carbon kinetic isotopic models do not agree as closely. It is possible that ??D values in methane may be affected by microbial mixing and that propane values might be more susceptible to hydrogen exchange with water or to analytical errors. Although the model used in this study is quite preliminary, the results demonstrate that kinetic isotope fractionation effects in hydrogen may be useful in quantitative models of natural gas generation, and that ??D values in ethane might be more suitable for modeling than comparable values in methane and propane. ?? 2011 Elsevier Ltd.

Single image super-resolution using self-optimizing mask via fractional-order gradient interpolation and reconstruction.

PubMed

Yang, Qi; Zhang, Yanzhu; Zhao, Tiebiao; Chen, YangQuan

2017-04-04

Image super-resolution using self-optimizing mask via fractional-order gradient interpolation and reconstruction aims to recover detailed information from low-resolution images and reconstruct them into high-resolution images. Due to the limited amount of data and information retrieved from low-resolution images, it is difficult to restore clear, artifact-free images, while still preserving enough structure of the image such as the texture. This paper presents a new single image super-resolution method which is based on adaptive fractional-order gradient interpolation and reconstruction. The interpolated image gradient via optimal fractional-order gradient is first constructed according to the image similarity and afterwards the minimum energy function is employed to reconstruct the final high-resolution image. Fractional-order gradient based interpolation methods provide an additional degree of freedom which helps optimize the implementation quality due to the fact that an extra free parameter α-order is being used. The proposed method is able to produce a rich texture detail while still being able to maintain structural similarity even under large zoom conditions. Experimental results show that the proposed method performs better than current single image super-resolution techniques. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Chemical and isotopic fractionations by evaporation and their cosmochemical implications

NASA Astrophysics Data System (ADS)

Ozawa, Kazuhito; Nagahara, Hiroko

2001-07-01

A kinetic model for evaporation of a multi-component condensed phase with a fixed rate constant of the reaction is developed. A binary system with two isotopes for one of the components undergoing simple thermal histories (e.g., isothermal heating) is investigated in order to evaluate the extent of isotopic and chemical fractionations during evaporation. Diffusion in the condensed phase and the effect of back reaction from ambient gas are taken into consideration. Chemical and isotopic fractionation factors and the Péclet number for evaporation are the three main parameters that control the fractionation. Dust enrichment factor (η), the ratio of the initial dust quantity to that required for attainment of gas-dust equilibrium, is critical when back reactions become significant. Dust does not reach equilibrium with gas at η < 1. Notable chemical and isotopic fractionations usually take place under these conditions. There are two circumstances in which isotopic fractionation of a very volatile element does not accompany chemical fractionation during isothermal heating. One is free evaporation when diffusion in the condensed phase is very slow (η = 0), and the other is evaporation in the presence of ambient gas (η > 0). In the former case, a quasi-steady state in the diffusion boundary layer is maintained for isotopic fractionation but not for chemical fractionation. In the latter case, the back reaction brings the strong isotopic fractionation generated in the earlier stage of evaporation back to a negligibly small value in the later stage before complete evaporation. The model results are applied to cosmochemical fractionation of volatile elements during evaporation from a condensed phase that can be regarded as a binary solution phase. The wide range of potassium depletion without isotopic fractionation in various types of chondrules (Alexander et al., 2000) is explained by instantaneous heating followed by cooling in a closed system with various degrees of dust enrichment (η = 0.001-10) and cooling rates of less than ˜5°C/min. The extent of decoupling between isotopic and chemical fractionations of various elements in chondrules and matrix minerals may constrain the time scale and the conditions of heating and cooling processes in the early solar nebula.

Scalar excursions in large-eddy simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matheou, Georgios; Dimotakis, Paul E.

Here, the range of values of scalar fields in turbulent flows is bounded by their boundary values, for passive scalars, and by a combination of boundary values, reaction rates, phase changes, etc., for active scalars. The current investigation focuses on the local conservation of passive scalar concentration fields and the ability of the large-eddy simulation (LES) method to observe the boundedness of passive scalar concentrations. In practice, as a result of numerical artifacts, this fundamental constraint is often violated with scalars exhibiting unphysical excursions. The present study characterizes passive-scalar excursions in LES of a shear flow and examines methods formore » diagnosis and assesment of the problem. The analysis of scalar-excursion statistics provides support of the main hypothesis of the current study that unphysical scalar excursions in LES result from dispersive errors of the convection-term discretization where the subgrid-scale model (SGS) provides insufficient dissipation to produce a sufficiently smooth scalar field. In the LES runs three parameters are varied: the discretization of the convection terms, the SGS model, and grid resolution. Unphysical scalar excursions decrease as the order of accuracy of non-dissipative schemes is increased, but the improvement rate decreases with increasing order of accuracy. Two SGS models are examined, the stretched-vortex and a constant-coefficient Smagorinsky. Scalar excursions strongly depend on the SGS model. The excursions are significantly reduced when the characteristic SGS scale is set to double the grid spacing in runs with the stretched-vortex model. The maximum excursion and volume fraction of excursions outside boundary values show opposite trends with respect to resolution. The maximum unphysical excursions increase as resolution increases, whereas the volume fraction decreases. The reason for the increase in the maximum excursion is statistical and traceable to the number of grid points (sample size) which increases with resolution. In contrast, the volume fraction of unphysical excursions decreases with resolution because the SGS models explored perform better at higher grid resolution.« less

Scalar excursions in large-eddy simulations

DOE PAGES

Matheou, Georgios; Dimotakis, Paul E.

2016-08-31

Here, the range of values of scalar fields in turbulent flows is bounded by their boundary values, for passive scalars, and by a combination of boundary values, reaction rates, phase changes, etc., for active scalars. The current investigation focuses on the local conservation of passive scalar concentration fields and the ability of the large-eddy simulation (LES) method to observe the boundedness of passive scalar concentrations. In practice, as a result of numerical artifacts, this fundamental constraint is often violated with scalars exhibiting unphysical excursions. The present study characterizes passive-scalar excursions in LES of a shear flow and examines methods formore » diagnosis and assesment of the problem. The analysis of scalar-excursion statistics provides support of the main hypothesis of the current study that unphysical scalar excursions in LES result from dispersive errors of the convection-term discretization where the subgrid-scale model (SGS) provides insufficient dissipation to produce a sufficiently smooth scalar field. In the LES runs three parameters are varied: the discretization of the convection terms, the SGS model, and grid resolution. Unphysical scalar excursions decrease as the order of accuracy of non-dissipative schemes is increased, but the improvement rate decreases with increasing order of accuracy. Two SGS models are examined, the stretched-vortex and a constant-coefficient Smagorinsky. Scalar excursions strongly depend on the SGS model. The excursions are significantly reduced when the characteristic SGS scale is set to double the grid spacing in runs with the stretched-vortex model. The maximum excursion and volume fraction of excursions outside boundary values show opposite trends with respect to resolution. The maximum unphysical excursions increase as resolution increases, whereas the volume fraction decreases. The reason for the increase in the maximum excursion is statistical and traceable to the number of grid points (sample size) which increases with resolution. In contrast, the volume fraction of unphysical excursions decreases with resolution because the SGS models explored perform better at higher grid resolution.« less

Anharmonic 1D actuator model including electrostatic and Casimir forces with fractional damping perturbed by an external force

NASA Astrophysics Data System (ADS)

Mansoori Kermani, Maryam; Dehestani, Maryam

2018-06-01

We modeled a one-dimensional actuator including the Casimir and electrostatic forces perturbed by an external force with fractional damping. The movable electrode was assumed to oscillate by an anharmonic elastic force originated from Murrell-Mottram or Lippincott potential. The nonlinear equations have been solved via the Adomian decomposition method. The behavior of the displacement of the electrode from equilibrium position, its velocity and acceleration were described versus time. Also, the changes of the displacement have been investigated according to the frequency of the external force and the voltage of the electrostatic force. The convergence of the Adomian method and the effect of the orders of expansion on the displacement versus time, frequency, and voltage were discussed. The pull-in parameter was obtained and compared with the other models in the literature. This parameter was described versus the equilibrium position and anharmonicity constant.

Alfvén ionization in an MHD-gas interactions code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wilson, A. D.; Diver, D. A.

A numerical model of partially ionized plasmas is developed in order to capture their evolving ionization fractions as a result of Alfvén ionization (AI). The mechanism of, and the parameter regime necessary for, AI is discussed and an expression for the AI rate based on fluid parameters, from a gas-MHD model, is derived. This AI term is added to an existing MHD-gas interactions' code, and the result is a linear, 2D, two-fluid model that includes momentum transfer between charged and neutral species as well as an ionization rate that depends on the velocity fields of both fluids. The dynamics ofmore » waves propagating through such a partially ionized plasma are investigated, and it is found that AI has a significant influence on the fluid dynamics as well as both the local and global ionization fraction.« less

Forecasting municipal solid waste generation using prognostic tools and regression analysis.

PubMed

Ghinea, Cristina; Drăgoi, Elena Niculina; Comăniţă, Elena-Diana; Gavrilescu, Marius; Câmpean, Teofil; Curteanu, Silvia; Gavrilescu, Maria

2016-11-01

For an adequate planning of waste management systems the accurate forecast of waste generation is an essential step, since various factors can affect waste trends. The application of predictive and prognosis models are useful tools, as reliable support for decision making processes. In this paper some indicators such as: number of residents, population age, urban life expectancy, total municipal solid waste were used as input variables in prognostic models in order to predict the amount of solid waste fractions. We applied Waste Prognostic Tool, regression analysis and time series analysis to forecast municipal solid waste generation and composition by considering the Iasi Romania case study. Regression equations were determined for six solid waste fractions (paper, plastic, metal, glass, biodegradable and other waste). Accuracy Measures were calculated and the results showed that S-curve trend model is the most suitable for municipal solid waste (MSW) prediction. Copyright © 2016 Elsevier Ltd. All rights reserved.

Analyses of a heterogeneous lattice hydrodynamic model with low and high-sensitivity vehicles

NASA Astrophysics Data System (ADS)

Kaur, Ramanpreet; Sharma, Sapna

2018-06-01

Basic lattice model is extended to study the heterogeneous traffic by considering the optimal current difference effect on a unidirectional single lane highway. Heterogeneous traffic consisting of low- and high-sensitivity vehicles is modeled and their impact on stability of mixed traffic flow has been examined through linear stability analysis. The stability of flow is investigated in five distinct regions of the neutral stability diagram corresponding to the amount of higher sensitivity vehicles present on road. In order to investigate the propagating behavior of density waves non linear analysis is performed and near the critical point, the kink antikink soliton is obtained by driving mKdV equation. The effect of fraction parameter corresponding to high sensitivity vehicles is investigated and the results indicates that the stability rise up due to the fraction parameter. The theoretical findings are verified via direct numerical simulation.

Anharmonic 1D actuator model including electrostatic and Casimir forces with fractional damping perturbed by an external force

NASA Astrophysics Data System (ADS)

Mansoori Kermani, Maryam; Dehestani, Maryam

2018-03-01

We modeled a one-dimensional actuator including the Casimir and electrostatic forces perturbed by an external force with fractional damping. The movable electrode was assumed to oscillate by an anharmonic elastic force originated from Murrell-Mottram or Lippincott potential. The nonlinear equations have been solved via the Adomian decomposition method. The behavior of the displacement of the electrode from equilibrium position, its velocity and acceleration were described versus time. Also, the changes of the displacement have been investigated according to the frequency of the external force and the voltage of the electrostatic force. The convergence of the Adomian method and the effect of the orders of expansion on the displacement versus time, frequency, and voltage were discussed. The pull-in parameter was obtained and compared with the other models in the literature. This parameter was described versus the equilibrium position and anharmonicity constant.

A Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

NASA Technical Reports Server (NTRS)

Solakiewicz, Richard; Attele, Rohan; Koshak, William

2011-01-01

A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a (low earth orbiting or geostationary) satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters, a scalar function was minimized by a numerical method. In order to improve this optimization, we introduce a Grobner basis solution to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. Using the Grobner basis, we show that there are exactly 2 solutions involving the first 3 moments of the (exponentially distributed) data. When the mean of the ground flash optical characteristic (e.g., such as the Maximum Group Area, MGA) is larger than that for cloud flashes, then a unique solution can be obtained.

Competition of the connectivity with the local and the global order in polymer melts and crystals

NASA Astrophysics Data System (ADS)

Bernini, S.; Puosi, F.; Barucco, M.; Leporini, D.

2013-11-01

The competition between the connectivity and the local or global order in model fully flexible chain molecules is investigated by molecular-dynamics simulations. States with both missing (melts) and high (crystal) global order are considered. Local order is characterized within the first coordination shell (FCS) of a tagged monomer and found to be lower than in atomic systems in both melt and crystal. The role played by the bonds linking the tagged monomer to FCS monomers (radial bonds), and the bonds linking two FCS monomers (shell bonds) is investigated. The detailed analysis in terms of Steinhardt's orientation order parameters Ql (l = 2 - 10) reveals that increasing the number of shell bonds decreases the FCS order in both melt and crystal. Differently, the FCS arrangements organize the radial bonds. Even if the molecular chains are fully flexible, the distribution of the angle formed by adjacent radial bonds exhibits sharp contributions at the characteristic angles θ ≈ 70°, 122°, 180°. The fractions of adjacent radial bonds with θ ≈ 122°, 180° are enhanced by the global order of the crystal, whereas the fraction with 70° ≲ θ ≲ 110° is nearly unaffected by the crystallization. Kink defects, i.e., large lateral displacements of the chains, are evidenced in the crystalline state.

Stochastic optimization model for order acceptance with multiple demand classes and uncertain demand/supply

NASA Astrophysics Data System (ADS)

Yang, Wen; Fung, Richard Y. K.

2014-06-01

This article considers an order acceptance problem in a make-to-stock manufacturing system with multiple demand classes in a finite time horizon. Demands in different periods are random variables and are independent of one another, and replenishments of inventory deviate from the scheduled quantities. The objective of this work is to maximize the expected net profit over the planning horizon by deciding the fraction of the demand that is going to be fulfilled. This article presents a stochastic order acceptance optimization model and analyses the existence of the optimal promising policies. An example of a discrete problem is used to illustrate the policies by applying the dynamic programming method. In order to solve the continuous problems, a heuristic algorithm based on stochastic approximation (HASA) is developed. Finally, the computational results of a case example illustrate the effectiveness and efficiency of the HASA approach, and make the application of the proposed model readily acceptable.

DEM simulation of dendritic grain random packing: application to metal alloy solidification

NASA Astrophysics Data System (ADS)

Olmedilla, Antonio; Založnik, Miha; Combeau, Hervé

2017-06-01

The random packing of equiaxed dendritic grains in metal-alloy solidification is numerically simulated and validated via an experimental model. This phenomenon is characterized by a driving force which is induced by the solid-liquid density difference. Thereby, the solid dendritic grains, nucleated in the melt, sediment and pack with a relatively low inertia-to-dissipation ratio, which is the so-called Stokes number. The characteristics of the particle packed porous structure such as solid packing fraction affect the final solidified product. A multi-sphere clumping Discrete Element Method (DEM) approach is employed to predict the solid packing fraction as function of the grain geometry under the solidification conditions. Five different monodisperse noncohesive frictionless particle collections are numerically packed by means of a vertical acceleration: a) three dendritic morphologies; b) spheres and c) one ellipsoidal geometry. In order to validate our numerical results with solidification conditions, the sedimentation and packing of two monodisperse collections (spherical and dendritic) is experimentally carried out in a viscous quiescent medium. The hydrodynamic similarity is respected between the actual phenomenon and the experimental model, that is a low Stokes number, o(10-3). In this way, the experimental average solid packing fraction is employed to validate the numerical model. Eventually, the average packing fraction is found to highly depend on the equiaxed dendritic grain sphericity, with looser packings for lower sphericity.

Influence of the nucleus area distribution on the survival fraction after charged particles broad beam irradiation.

PubMed

Wéra, A-C; Barazzuol, L; Jeynes, J C G; Merchant, M J; Suzuki, M; Kirkby, K J

2014-08-07

It is well known that broad beam irradiation with heavy ions leads to variation in the number of hit(s) received by each cell as the distribution of particles follows the Poisson statistics. Although the nucleus area will determine the number of hit(s) received for a given dose, variation amongst its irradiated cell population is generally not considered. In this work, we investigate the effect of the nucleus area's distribution on the survival fraction. More specifically, this work aims to explain the deviation, or tail, which might be observed in the survival fraction at high irradiation doses. For this purpose, the nucleus area distribution was added to the beam Poisson statistics and the Linear-Quadratic model in order to fit the experimental data. As shown in this study, nucleus size variation, and the associated Poisson statistics, can lead to an upward survival trend after broad beam irradiation. The influence of the distribution parameters (mean area and standard deviation) was studied using a normal distribution, along with the Linear-Quadratic model parameters (α and β). Finally, the model proposed here was successfully tested to the survival fraction of LN18 cells irradiated with a 85 keV µm(- 1) carbon ion broad beam for which the distribution in the area of the nucleus had been determined.

Multi-pathway exposure modeling of chemicals in cosmetics with application to shampoo.

PubMed

Ernstoff, Alexi S; Fantke, Peter; Csiszar, Susan A; Henderson, Andrew D; Chung, Susie; Jolliet, Olivier

2016-01-01

We present a novel multi-pathway, mass balance based, fate and exposure model compatible with life cycle and high-throughput screening assessments of chemicals in cosmetic products. The exposures through product use as well as post-use emissions and environmental media were quantified based on the chemical mass originally applied via a product, multiplied by the product intake fractions (PiF, the fraction of a chemical in a product that is taken in by exposed persons) to yield intake rates. The average PiFs for the evaluated chemicals in shampoo ranged from 3×10(-4) up to 0.3 for rapidly absorbed ingredients. Average intake rates ranged between nano- and micrograms per kilogram bodyweight per day; the order of chemical prioritization was strongly affected by the ingredient concentration in shampoo. Dermal intake and inhalation (for 20% of the evaluated chemicals) during use dominated exposure, while the skin permeation coefficient dominated the estimated uncertainties. The fraction of chemical taken in by a shampoo user often exceeded, by orders of magnitude, the aggregated fraction taken in by the population through post-use environmental emissions. Chemicals with relatively high octanol-water partitioning and/or volatility, and low molecular weight tended to have higher use stage exposure. Chemicals with low intakes during use (<1%) and subsequent high post-use emissions, however, may yield comparable intake for a member of the general population. The presented PiF based framework offers a novel and critical advancement for life cycle assessments and high-throughput exposure screening of chemicals in cosmetic products demonstrating the importance of consistent consideration of near- and far-field multi-pathway exposures. Copyright © 2016 Elsevier Ltd. All rights reserved.

Geochemical and Nd-Sr-Pb isotope characteristics of synorogenic lower crust-derived granodiorites (Central Damara orogen, Namibia)

NASA Astrophysics Data System (ADS)

Simon, I.; Jung, S.; Romer, R. L.; Garbe-Schönberg, D.; Berndt, J.

2017-03-01

The 547 ± 7 Ma old Achas intrusion (Damara orogen, Namibia) includes magnesian, metaluminous to slightly peraluminous, calcic to calc-alkalic granodiorites and ferroan, metaluminous to slightly peraluminous, calc-alkalic to alkali-calcic leucogranites. For the granodiorites, major and trace element variations show weak if any evidence for fractional crystallization whereas some leucogranites are highly fractionated. Both, granodiorites and leucogranites are isotopically evolved (granodiorites: εNdinit: - 12.4 to - 20.5; TDM: 2.4-1.9; leucogranites: εNdinit: - 12.1 to - 20.6, TDM: 2.5-2.0), show similar Pb isotopic compositions, and may be derived from late Archean to Paleoproterozoic crustal source rocks. Comparison with melting experiments and simple partial melting modeling indicate that the granodiorites may be derived by extensive melting (> 40%) at 900-950 °C under water-undersaturated conditions (< 5 wt.% H2O) of felsic gneisses. Al-Ti and zircon saturation thermometry of the most primitive granodiorite sample yielded temperatures of ca. 930 °C and ca. 800 °C. In contrast to other lower crust-derived granodiorites and granites of the Central Damara orogen, the composition of the magma source is considered the first-order cause of the compositional diversity of the Achas granite. Second-order processes such as fractional crystallization at least for the granodiorites were minor and evidence for coupled assimilation-fractional crystallization processes is lacking. The most likely petrogenetic model involves high temperature partial melting of a Paleoproterozoic felsic source in the lower crust ca. 10-20 Ma before the first peak of regional high-temperature metamorphism. Underplating of the lower crust by magmas derived from the lithospheric mantle may have provided the heat for melting of the basement to produce anhydrous granodioritic melts.

Numerical investigation of a helicopter combustion chamber using LES and tabulated chemistry

NASA Astrophysics Data System (ADS)

Auzillon, Pierre; Riber, Eléonore; Gicquel, Laurent Y. M.; Gicquel, Olivier; Darabiha, Nasser; Veynante, Denis; Fiorina, Benoît

2013-01-01

This article presents Large Eddy Simulations (LES) of a realistic aeronautical combustor device: the chamber CTA1 designed by TURBOMECA. Under nominal operating conditions, experiments show hot spots observed on the combustor walls, in the vicinity of the injectors. These high temperature regions disappear when modifying the fuel stream equivalence ratio. In order to account for detailed chemistry effects within LES, the numerical simulation uses the recently developed turbulent combustion model F-TACLES (Filtered TAbulated Chemistry for LES). The principle of this model is first to generate a lookup table where thermochemical variables are computed from a set of filtered laminar unstrained premixed flamelets. To model the interactions between the flame and the turbulence at the subgrid scale, a flame wrinkling analytical model is introduced and the Filtered Density Function (FDF) of the mixture fraction is modeled by a β function. Filtered thermochemical quantities are stored as a function of three coordinates: the filtered progress variable, the filtered mixture fraction and the mixture fraction subgrid scale variance. The chemical lookup table is then coupled with the LES using a mathematical formalism that ensures an accurate prediction of the flame dynamics. The numerical simulation of the CTA1 chamber with the F-TACLES turbulent combustion model reproduces fairly the temperature fields observed in experiments. In particular the influence of the fuel stream equivalence ratio on the flame position is well captured.

Evaluation of the potential of different high calorific waste fractions for the preparation of solid recovered fuels.

PubMed

Garcés, Diego; Díaz, Eva; Sastre, Herminio; Ordóñez, Salvador; González-LaFuente, José Manuel

2016-01-01

Solid recovered fuels constitute a valuable alternative for the management of those non-hazardous waste fractions that cannot be recycled. The main purpose of this research is to assess the suitability of three different wastes from the landfill of the local waste management company (COGERSA), to be used as solid recovered fuels in a cement kiln near their facilities. The wastes analyzed were: End of life vehicles waste, packaging and bulky wastes. The study was carried out in two different periods of the year: November 2013 and April 2014. In order to characterize and classify these wastes as solid recovered fuels, they were separated into homogeneous fractions in order to determine different element components, such as plastics, cellulosic materials, packagings or textile compounds, and the elemental analysis (including chlorine content), heavy metal content and the heating value of each fraction were determined. The lower heating value of the waste fractions on wet basis varies between 10 MJ kg(-1) and 42 MJ kg(-1). One of the packaging wastes presents a very high chlorine content (6.3 wt.%) due to the presence of polyvinylchloride from pipe fragments, being the other wastes below the established limits. Most of the wastes analyzed meet the heavy metals restrictions, except the fine fraction of the end of life vehicles waste. In addition, none of the wastes exceed the mercury limit content, which is one of the parameters considered for the solid recovered fuels classification. A comparison among the experimental higher heating values and empirical models that predict the heating value from the elemental analysis data was carried out. Finally, from the three wastes measured, the fine fraction of the end of life vehicles waste was discarded for its use as solid recovered fuels due to the lower heating value and its high heavy metals content. From the point of view of the heating value, the end of life vehicles waste was the most suitable residue with a lower heating value of 35.89 MJ kg(-1), followed by the packaging waste and the bulky waste, respectively. When mixing the wastes studied a global waste was obtained, whose classification as solid recovered fuels was NCV 1 Cl 3 Hg 3. From the empirical models used for calculating higher heating value from elemental content, Scheurer-Kestner was the model that best fit the experimental data corresponding to the wastes collected in November 2013, whereas Chang equation was the most approximate to the experimental heating values for April 2014 fractions. This difference is due to higher chlorine content of the second batch of wastes, since Chang equation is the only one that incorporates the chlorine content. Copyright © 2015 Elsevier Ltd. All rights reserved.

Wiener-Hopf optimal control of a hydraulic canal prototype with fractional order dynamics.

PubMed

Feliu-Batlle, Vicente; Feliu-Talegón, Daniel; San-Millan, Andres; Rivas-Pérez, Raúl

2017-06-26

This article addresses the control of a laboratory hydraulic canal prototype that has fractional order dynamics and a time delay. Controlling this prototype is relevant since its dynamics closely resembles the dynamics of real main irrigation canals. Moreover, the dynamics of hydraulic canals vary largely when the operation regime changes since they are strongly nonlinear systems. All this makes difficult to design adequate controllers. The controller proposed in this article looks for a good time response to step commands. The design criterium for this controller is minimizing the integral performance index ISE. Then a new methodology to control fractional order processes with a time delay, based on the Wiener-Hopf control and the Padé approximation of the time delay, is developed. Moreover, in order to improve the robustness of the control system, a gain scheduling fractional order controller is proposed. Experiments show the adequate performance of the proposed controller. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Robust fractional order sliding mode control of doubly-fed induction generator (DFIG)-based wind turbines.

PubMed

Ebrahimkhani, Sadegh

2016-07-01

Wind power plants have nonlinear dynamics and contain many uncertainties such as unknown nonlinear disturbances and parameter uncertainties. Thus, it is a difficult task to design a robust reliable controller for this system. This paper proposes a novel robust fractional-order sliding mode (FOSM) controller for maximum power point tracking (MPPT) control of doubly fed induction generator (DFIG)-based wind energy conversion system. In order to enhance the robustness of the control system, uncertainties and disturbances are estimated using a fractional order uncertainty estimator. In the proposed method a continuous control strategy is developed to achieve the chattering free fractional order sliding-mode control, and also no knowledge of the uncertainties and disturbances or their bound is assumed. The boundedness and convergence properties of the closed-loop signals are proven using Lyapunov׳s stability theory. Simulation results in the presence of various uncertainties were carried out to evaluate the effectiveness and robustness of the proposed control scheme. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Fractional order PID controller for improvement of PMSM speed control in aerospace applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saraji, Ali Motalebi; Ghanbari, Mahmood

Because of the benefits reduced size, cost and maintenance, noise, CO2 emissions and increased control flexibility and precision, to meet these expectations, electrical equipment increasingly utilize in modern aircraft systems and aerospace industry rather than conventional mechanic, hydraulic, and pneumatic power systems. Electric motor drives are capable of converting electrical power to drive actuators, pumps, compressors, and other subsystems at variable speeds. In the past decades, permanent magnet synchronous motor (PMSM) and brushless dc (BLDC) motor were investigated for aerospace applications such as aircraft actuators. In this paper, the fractional-order PID controller is used in the design of speed loopmore » of PMSM speed control system. Having more parameters for tuning fractional order PID controller lead to good performance ratio to integer order. This good performance is shown by comparison fractional order PID controller with the conventional PI and tuned PID controller by Genetic algorithm in MATLAB soft wear.« less

Central Antinociceptive and Mechanism of Action of Pereskia bleo Kunth Leaves Crude Extract, Fractions, and Isolated Compounds

PubMed Central

Guilhon, Carolina Carvalho; Abdul Wahab, Ikarastika Rahayu; Boylan, Fabio; Fernandes, Patricia Dias

2015-01-01

Pereskia bleo (Kunth) DC. (Cactaceae) is a plant commonly used in popular medicine in Malaysia. In this work, we evaluate the antinociceptive effect of P. bleo leaf extracts and isolated compounds in central antinociceptive model. Ethanol extract (E), hexane (H), ethyl acetate (EA), or butanol (B) fractions (30, 50, or 100 mg/kg, p.o.), sitosterol (from hexane) and vitexin (from ethyl acetate), were administered to mice. Antinociceptive effect was evaluated in the hot plate and capsaicin- or glutamate-induced licking models. Morphine (1 mg/kg, p.o.) was used as reference drug. Naloxone (1 mg/kg, i.p.), atropine (1 mg/kg, i.p.), and L-nitro arginine methyl ester (L-NAME, 3 mg/kg, i.p.) were administered 30 min earlier (100 mg/kg, p.o.) in order to evaluate the mechanism of the antinociceptive action. Higher dose of B developed an effect significantly superior to morphine-treated group. Naloxone prevented the antinociceptive effect of all fractions. L-NAME demonstrated effect against E, EA, and B. In all fractions, sitosterol and vitexin reduced the licking time after capsaicin injection. Glutamate-induced licking response was blocked by H, EA, and B. Our results indicate that Pereskia bleo fractions, sitosterol and vitexin, possessed a central antinociceptive effect. Part of this effect is mediated by opioid receptors and nitrergic pathway. PMID:26273315

Reduced-Order Structure-Preserving Model for Parallel-Connected Three-Phase Grid-Tied Inverters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, Brian B; Purba, Victor; Jafarpour, Saber

Next-generation power networks will contain large numbers of grid-connected inverters satisfying a significant fraction of system load. Since each inverter model has a relatively large number of dynamic states, it is impractical to analyze complex system models where the full dynamics of each inverter are retained. To address this challenge, we derive a reduced-order structure-preserving model for parallel-connected grid-tied three-phase inverters. Here, each inverter in the system is assumed to have a full-bridge topology, LCL filter at the point of common coupling, and the control architecture for each inverter includes a current controller, a power controller, and a phase-locked loopmore » for grid synchronization. We outline a structure-preserving reduced-order inverter model with lumped parameters for the setting where the parallel inverters are each designed such that the filter components and controller gains scale linearly with the power rating. By structure preserving, we mean that the reduced-order three-phase inverter model is also composed of an LCL filter, a power controller, current controller, and PLL. We show that the system of parallel inverters can be modeled exactly as one aggregated inverter unit and this equivalent model has the same number of dynamical states as any individual inverter in the system. Numerical simulations validate the reduced-order model.« less

New Approaches to Minimum-Energy Design of Integer- and Fractional-Order Perfect Control Algorithms

NASA Astrophysics Data System (ADS)

Hunek, Wojciech P.; Wach, Łukasz

2017-10-01

In this paper the new methods concerning the energy-based minimization of the perfect control inputs is presented. For that reason the multivariable integer- and fractional-order models are applied which can be used for describing a various real world processes. Up to now, the classical approaches have been used in forms of minimum-norm/least squares inverses. Notwithstanding, the above-mentioned tool do not guarantee the optimal control corresponding to optimal input energy. Therefore the new class of inversebased methods has been introduced, in particular the new σ- and H-inverse of nonsquare parameter and polynomial matrices. Thus a proposed solution remarkably outperforms the typical ones in systems where the control runs can be understood in terms of different physical quantities, for example heat and mass transfer, electricity etc. A simulation study performed in Matlab/Simulink environment confirms the big potential of the new energy-based approaches.

Architectures for Parafermionic Topological Matter in Two Dimensions

NASA Astrophysics Data System (ADS)

Burrello, Michele; van Heck, Bernard; Cobanera, Emilio

2013-03-01

Recent proposals exploit edge modes of fractional topological insulators (FTIs), induced superconducting pairing, and back-scattering to realize one-dimensional systems of parafermions. We extend these proposals to two dimensions and analyze the effect of the superconducting islands' charging energy on the parafermions they host. We focus on two two-dimensional architectures, the tile and stripe configurations, characterized by different distributions of FTIs and derive the associated parafermionic effective Hamiltonians. The tile model realizes the Z2 m toric code in low-order perturbation theory and hence possesses full topological quantum order. By exploiting dualities, we obtain the phase diagram and generalized order parameters for both the tile and stripe models of parafermions. This work was supported by the Dutch Science Foundation NWO/FOM and an ERC Advanced Investigator grant.

Correlated disorder in the Kuramoto model: Effects on phase coherence, finite-size scaling, and dynamic fluctuations.

PubMed

Hong, Hyunsuk; O'Keeffe, Kevin P; Strogatz, Steven H

2016-10-01

We consider a mean-field model of coupled phase oscillators with quenched disorder in the natural frequencies and coupling strengths. A fraction p of oscillators are positively coupled, attracting all others, while the remaining fraction 1-p are negatively coupled, repelling all others. The frequencies and couplings are deterministically chosen in a manner which correlates them, thereby correlating the two types of disorder in the model. We first explore the effect of this correlation on the system's phase coherence. We find that there is a critical width γ c in the frequency distribution below which the system spontaneously synchronizes. Moreover, this γ c is independent of p. Hence, our model and the traditional Kuramoto model (recovered when p = 1) have the same critical width γ c . We next explore the critical behavior of the system by examining the finite-size scaling and the dynamic fluctuation of the traditional order parameter. We find that the model belongs to the same universality class as the Kuramoto model with deterministically (not randomly) chosen natural frequencies for the case of p < 1.

Uncertainty Aware Structural Topology Optimization Via a Stochastic Reduced Order Model Approach

NASA Technical Reports Server (NTRS)

Aguilo, Miguel A.; Warner, James E.

2017-01-01

This work presents a stochastic reduced order modeling strategy for the quantification and propagation of uncertainties in topology optimization. Uncertainty aware optimization problems can be computationally complex due to the substantial number of model evaluations that are necessary to accurately quantify and propagate uncertainties. This computational complexity is greatly magnified if a high-fidelity, physics-based numerical model is used for the topology optimization calculations. Stochastic reduced order model (SROM) methods are applied here to effectively 1) alleviate the prohibitive computational cost associated with an uncertainty aware topology optimization problem; and 2) quantify and propagate the inherent uncertainties due to design imperfections. A generic SROM framework that transforms the uncertainty aware, stochastic topology optimization problem into a deterministic optimization problem that relies only on independent calls to a deterministic numerical model is presented. This approach facilitates the use of existing optimization and modeling tools to accurately solve the uncertainty aware topology optimization problems in a fraction of the computational demand required by Monte Carlo methods. Finally, an example in structural topology optimization is presented to demonstrate the effectiveness of the proposed uncertainty aware structural topology optimization approach.

Local structure of dilute aqueous DMSO solutions, as seen from molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Idrissi, Abdenacer; Marekha, Bogdan A.; Barj, Mohammed; Miannay, François Alexandre; Takamuku, Toshiyuki; Raptis, Vasilios; Samios, Jannis; Jedlovszky, Pál

2017-06-01

The information about the structure of dimethyl sulfoxide (DMSO)-water mixtures at relatively low DMSO mole fractions is an important step in order to understand their cryoprotective properties as well as the solvation process of proteins and amino acids. Classical MD simulations, using the potential model combination that best reproduces the free energy of mixing of these compounds, are used to analyze the local structure of DMSO-water mixtures at DMSO mole fractions below 0.2. Significant changes in the local structure of DMSO are observed around the DMSO mole fraction of 0.1. The array of evidence, based on the cluster and the metric and topological parameters of the Voronoi polyhedra distributions, indicates that these changes are associated with the simultaneous increase of the number of DMSO-water and decrease of water-water hydrogen bonds with increasing DMSO concentration. The inversion between the dominance of these two types of H-bonds occurs around XDMSO = 0.1, above which the DMSO-DMSO interactions also start playing an important role. In other words, below the DMSO mole fraction of 0.1, DMSO molecules are mainly solvated by water molecules, while above it, their solvation shell consists of a mixture of water and DMSO. The trigonal, tetrahedral, and trigonal bipyramidal distributions of water shift to lower corresponding order parameter values indicating the loosening of these orientations. Adding DMSO does not affect the hydrogen bonding between a reference water molecule and its first neighbor hydrogen bonded water molecules, while it increases the bent hydrogen bond geometry involving the second ones. The close-packed local structure of the third, fourth, and fifth water neighbors also is reinforced. In accordance with previous theoretical and experimental data, the hydrogen bonding between water and the first, the second, and the third DMSO neighbors is stronger than that with its corresponding water neighbors. At a given DMSO mole fraction, the behavior of the intensity of the high orientational order parameter values indicates that water molecules are more ordered in the vicinity of the hydrophilic group while their structure is close-packed near the hydrophobic group of DMSO.

Modelling the seismic properties of fast-spreading ridge crustal Low-Velocity Zones: insights from Oman gabbro textures

NASA Astrophysics Data System (ADS)

Lamoureux, Gwenaëlle; Ildefonse, Benoı̂t; Mainprice, David

1999-11-01

Although considerable progress has been made in the study of fast-spreading, mid-ocean ridge magma chambers over the past fifteen years, the fraction of melt present in the chamber remains poorly constrained and controversial. We present new constraints obtained by modelling the seismic properties of partially molten gabbros at the ridge axis. P-wave velocities at low frequencies are calculated in the foliation/lineation reference frame using a differential effective medium technique. The model takes into account the lattice preferred orientation of the crystalline phase and the average shape of the melt phase. The structural parameters are obtained from the Oman ophiolite. The structural reference frame is given by the general trend of the gabbro foliation and the melt fraction and shape are estimated using the textures of nine upper gabbro samples. The estimated melt fraction and shape depend on the assumptions regarding which part of the observed textures represent the melt in the gabbroic mush of the magma chamber. However, we can put limits on the reasonable values for the melt fraction and shape. Our results are consistent with a melt fraction of the order of 10 to 20% in the Low-Velocity Zone (i.e. the magma chamber), which is anisotropically distributed with the melt pockets preferentially aligned parallel to the foliation and approximated by oblate ellipsoids with approximate dimensions of 4 : 4 : 1. These results are also consistent with the seismic structure of the East Pacific rise at 9°30'. The anisotropic melt distribution can, at least partially, explain the vertical velocity gradient described in the LVZ.

Demonstrative fractional order - PID controller based DC motor drive on digital platform.

PubMed

Khubalkar, Swapnil W; Junghare, Anjali S; Aware, Mohan V; Chopade, Amit S; Das, Shantanu

2017-09-21

In industrial drives applications, fractional order controllers can exhibit phenomenal impact due to realization through digital implementation. Digital fractional order controllers have created wide scope as it possess the inherent advantages like robustness against the plant parameter variation. This paper provides brief design procedure of fractional order proportional-integral-derivative (FO-PID) controller through the indirect approach of approximation using constant phase technique. The new modified dynamic particle swarm optimization (IdPSO) technique is proposed to find controller parameters. The FO-PID controller is implemented using floating point digital signal processor. The building blocks are designed and assembled with all peripheral components for the 1.5kW industrial DC motor drive. The robust operation for parametric variation is ascertained by testing the controller with two separately excited DC motors with the same rating but different parameters. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Network overload due to massive attacks

NASA Astrophysics Data System (ADS)

Kornbluth, Yosef; Barach, Gilad; Tuchman, Yaakov; Kadish, Benjamin; Cwilich, Gabriel; Buldyrev, Sergey V.

2018-05-01

We study the cascading failure of networks due to overload, using the betweenness centrality of a node as the measure of its load following the Motter and Lai model. We study the fraction of survived nodes at the end of the cascade pf as a function of the strength of the initial attack, measured by the fraction of nodes p that survive the initial attack for different values of tolerance α in random regular and Erdös-Renyi graphs. We find the existence of a first-order phase-transition line pt(α ) on a p -α plane, such that if p pt , pf is large and the giant component of the network is still present. Exactly at pt, the function pf(p ) undergoes a first-order discontinuity. We find that the line pt(α ) ends at a critical point (pc,αc) , in which the cascading failures are replaced by a second-order percolation transition. We find analytically the average betweenness of nodes with different degrees before and after the initial attack, we investigate their roles in the cascading failures, and we find a lower bound for pt(α ) . We also study the difference between localized and random attacks.

Hipergeometric solutions to some nonhomogeneous equations of fractional order

NASA Astrophysics Data System (ADS)

Olivares, Jorge; Martin, Pablo; Maass, Fernando

2017-12-01

In this paper a study is performed to the solution of the linear non homogeneous fractional order alpha differential equation equal to I 0(x), where I 0(x) is the modified Bessel function of order zero, the initial condition is f(0)=0 and 0 < alpha < 1. Caputo definition for the fractional derivatives is considered. Fractional derivatives have become important in physical and chemical phenomena as visco-elasticity and visco-plasticity, anomalous diffusion and electric circuits. In particular in this work the values of alpha=1/2, 1/4 and 3/4. are explicitly considered . In these cases Laplace transform is applied, and later the inverse Laplace transform leads to the solutions of the differential equation, which become hypergeometric functions.

[Using fractional polynomials to estimate the safety threshold of fluoride in drinking water].

PubMed

Pan, Shenling; An, Wei; Li, Hongyan; Yang, Min

2014-01-01

To study the dose-response relationship between fluoride content in drinking water and prevalence of dental fluorosis on the national scale, then to determine the safety threshold of fluoride in drinking water. Meta-regression analysis was applied to the 2001-2002 national endemic fluorosis survey data of key wards. First, fractional polynomial (FP) was adopted to establish fixed effect model, determining the best FP structure, after that restricted maximum likelihood (REML) was adopted to estimate between-study variance, then the best random effect model was established. The best FP structure was first-order logarithmic transformation. Based on the best random effect model, the benchmark dose (BMD) of fluoride in drinking water and its lower limit (BMDL) was calculated as 0.98 mg/L and 0.78 mg/L. Fluoride in drinking water can only explain 35.8% of the variability of the prevalence, among other influencing factors, ward type was a significant factor, while temperature condition and altitude were not. Fractional polynomial-based meta-regression method is simple, practical and can provide good fitting effect, based on it, the safety threshold of fluoride in drinking water of our country is determined as 0.8 mg/L.

Adaptive convex combination approach for the identification of improper quaternion processes.

PubMed

Ujang, Bukhari Che; Jahanchahi, Cyrus; Took, Clive Cheong; Mandic, Danilo P

2014-01-01

Data-adaptive optimal modeling and identification of real-world vector sensor data is provided by combining the fractional tap-length (FT) approach with model order selection in the quaternion domain. To account rigorously for the generality of such processes, both second-order circular (proper) and noncircular (improper), the proposed approach in this paper combines the FT length optimization with both the strictly linear quaternion least mean square (QLMS) and widely linear QLMS (WL-QLMS). A collaborative approach based on QLMS and WL-QLMS is shown to both identify the type of processes (proper or improper) and to track their optimal parameters in real time. Analysis shows that monitoring the evolution of the convex mixing parameter within the collaborative approach allows us to track the improperness in real time. Further insight into the properties of those algorithms is provided by establishing a relationship between the steady-state error and optimal model order. The approach is supported by simulations on model order selection and identification of both strictly linear and widely linear quaternion-valued systems, such as those routinely used in renewable energy (wind) and human-centered computing (biomechanics).

Characterization of Flow Dynamics and Reduced-Order Description of Experimental Two-Phase Pipe Flow

NASA Astrophysics Data System (ADS)

Viggiano, Bianca; SkjæRaasen, Olaf; Tutkun, Murat; Cal, Raul Bayoan

2017-11-01

Multiphase pipe flow is investigated using proper orthogonal decomposition for tomographic X-ray data, where holdup, cross sectional phase distributions and phase interface characteristics are obtained. Instantaneous phase fractions of dispersed flow and slug flow are analyzed and a reduced order dynamical description is generated. The dispersed flow displays coherent structures in the first few modes near the horizontal center of the pipe, representing the liquid-liquid interface location while the slug flow case shows coherent structures that correspond to the cyclical formation and breakup of the slug in the first 10 modes. The reconstruction of the fields indicate that main features are observed in the low order dynamical descriptions utilizing less than 1 % of the full order model. POD temporal coefficients a1, a2 and a3 show interdependence for the slug flow case. The coefficients also describe the phase fraction holdup as a function of time for both dispersed and slug flow. These flows are highly applicable to petroleum transport pipelines, hydroelectric power and heat exchanger tubes to name a few. The mathematical representations obtained via proper orthogonal decomposition will deepen the understanding of fundamental multiphase flow characteristics.

In Vitro Determination of Drug Transfer from Drug-Coated Balloons

PubMed Central

Seidlitz, Anne; Kotzan, Nadine; Nagel, Stefan; Reske, Thomas; Grabow, Niels; Harder, Claus; Petersen, Svea; Sternberg, Katrin; Weitschies, Werner

2013-01-01

Drug-coated balloons are medical devices designed to locally deliver drug to diseased segments of the vessel wall. For these dosage forms, drug transfer to the vessel wall needs to be examined in detail, since drug released into the blood is cleared from the site. In order to examine drug transfer, a new in vitro setup was developed combining the estimation of drug loss during advancement to the site of application in a model coronary artery pathway with a hydrogel compartment representing, as a very simplified model, the vessel wall. The transfer of fluorescent model substances as well as the drug paclitaxel from coated balloons to the simulated vessel wall was evaluated using this method. The model was suitable to quantify the fractions transferred to the hydrogel and also to qualitatively assess distribution patterns in the hydrogel film. In the case of fluorescein sodium, rhodamin b and paclitaxel, vast amounts of the coated substance were lost during the simulated passage and only very small fractions of about 1% of the total load were transferred to the gel. This must be attributed to good water solubility of the fluorescent substances and the mechanical instability of the paclitaxel coating. Transfer of the hydrophobic model substance triamterene was however nearly unaffected by the preliminary tracking procedure with transferred fractions ranging from 8% to 14%. Analysis of model substance distribution yielded inhomogeneous distributions indicating that the coating was not evenly distributed on the balloon surface and that a great fraction of the coating liquid did not penetrate the folds of the balloon. This finding is contradictory to the generally accepted assumption of a drug depot inside the folds and emphasizes the necessity to thoroughly characterize in vitro performance of drug-coated balloons to support the very promising clinical data. PMID:24391863

The implementation of biofiltration systems, rainwater tanks and urban irrigation in a single-layer urban canopy model

NASA Astrophysics Data System (ADS)

Demuzere, Matthias; Coutts, Andrew; Goehler, Maren; Broadbent, Ashley; Wouters, Hendrik; van Lipzig, Nicole; Gebert, Luke

2015-04-01

Urban vegetation is generally considered as a key tool to modify the urban energy balance through enhanced evapotranspiration (ET). Given that vegetation is most effective when it is healthy, stormwater harvesting and retention strategies (such as water sensitive urban design) could be used to support vegetation and promote ET. This study presents the implementation of a vegetated lined bio-filtration system (BFS) combined with a rainwater tank (RWT) and urban irrigation system in the single-layer urban canopy model Community Land Model-Urban. Runoff from roof and impervious road surface fractions is harvested and used to support an adequate soil moisture level for vegetation in the BFS. In a first stage, modelled soil moisture dynamics are evaluated and found reliable compared to observed soil moisture levels from biofiltration pits in Smith Street, Melbourne (Australia). Secondly, the impact of BFS, RWT and urban irrigation on ET is illustrated for a two-month period in 2012 using varying characteristics for all components. Results indicate that (i) a large amount of stormwater is potentially available for indoor and outdoor water demands, including irrigation of urban vegetation, (ii) ET from the BFS is an order of magnitude larger compared to the contributions from the impervious surfaces, even though the former only covers 10% of the surface fraction and (iii) attention should be paid to the cover fraction and soil texture of the BFS, size of the RWT and the surface fractions contributing to the collection of water in the RWT. Overall, this study reveals that this model development can effectuate future research with state-of-the-art urban climate models to further explore the benefits of vegetated biofiltration systems as a water sensitive urban design tool optimised with an urban irrigation system to maintain healthy vegetation.

Using dust, gas and stellar mass-selected samples to probe dust sources and sinks in low-metallicity galaxies

NASA Astrophysics Data System (ADS)

De Vis, P.; Gomez, H. L.; Schofield, S. P.; Maddox, S.; Dunne, L.; Baes, M.; Cigan, P.; Clark, C. J. R.; Gomez, E. L.; Lara-López, M.; Owers, M.

2017-10-01

We combine samples of nearby galaxies with Herschel photometry selected on their dust, metal, H I and stellar mass content, and compare these to chemical evolution models in order to discriminate between different dust sources. In a companion paper, we used an H I-selected sample of nearby galaxies to reveal a subsample of very gas-rich (gas fraction >80 per cent) sources with dust masses significantly below predictions from simple chemical evolution models, and well below Md/M* and Md/Mgas scaling relations seen in dust and stellar-selected samples of local galaxies. We use a chemical evolution model to explain these dust-poor, but gas-rich, sources as well as the observed star formation rates (SFRs) and dust-to-gas ratios. We find that (I) a delayed star formation history is required to model the observed SFRs; (II) inflows and outflows are required to model the observed metallicities at low gas fractions; (III) a reduced contribution of dust from supernovae (SNe) is needed to explain the dust-poor sources with high gas fractions. These dust-poor, low stellar mass galaxies require a typical core-collapse SN to produce 0.01-0.16 M⊙ of dust. To match the observed dust masses at lower gas fractions, significant grain growth is required to counteract the reduced contribution from dust in SNe and dust destruction from SN shocks. These findings are statistically robust, though due to intrinsic scatter it is not always possible to find one single model that successfully describes all the data. We also show that the dust-to-metal ratio decreases towards lower metallicity.

Assessing composition and structure of soft biphasic media from Kelvin-Voigt fractional derivative model parameters

NASA Astrophysics Data System (ADS)

Zhang, Hongmei; Wang, Yue; Fatemi, Mostafa; Insana, Michael F.

2017-03-01

Kelvin-Voigt fractional derivative (KVFD) model parameters have been used to describe viscoelastic properties of soft tissues. However, translating model parameters into a concise set of intrinsic mechanical properties related to tissue composition and structure remains challenging. This paper begins by exploring these relationships using a biphasic emulsion materials with known composition. Mechanical properties are measured by analyzing data from two indentation techniques—ramp-stress relaxation and load-unload hysteresis tests. Material composition is predictably correlated with viscoelastic model parameters. Model parameters estimated from the tests reveal that elastic modulus E 0 closely approximates the shear modulus for pure gelatin. Fractional-order parameter α and time constant τ vary monotonically with the volume fraction of the material’s fluid component. α characterizes medium fluidity and the rate of energy dissipation, and τ is a viscous time constant. Numerical simulations suggest that the viscous coefficient η is proportional to the energy lost during quasi-static force-displacement cycles, E A . The slope of E A versus η is determined by α and the applied indentation ramp time T r. Experimental measurements from phantom and ex vivo liver data show close agreement with theoretical predictions of the η -{{E}A} relation. The relative error is less than 20% for emulsions 22% for liver. We find that KVFD model parameters form a concise features space for biphasic medium characterization that described time-varying mechanical properties. The experimental work was carried out at the Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. Methodological development, including numerical simulation and all data analysis, were carried out at the school of Life Science and Technology, Xi’an JiaoTong University, 710049, China.

Air-Parcel Residence Times Within Forest Canopies

NASA Astrophysics Data System (ADS)

Gerken, Tobias; Chamecki, Marcelo; Fuentes, Jose D.

2017-10-01

We present a theoretical model, based on a simple model of turbulent diffusion and first-order chemical kinetics, to determine air-parcel residence times and the out-of-canopy export of reactive gases emitted within forest canopies under neutral conditions. Theoretical predictions of the air-parcel residence time are compared to values derived from large-eddy simulation for a range of canopy architectures and turbulence levels under neutral stratification. Median air-parcel residence times range from a few sec in the upper canopy to approximately 30 min near the ground and the distribution of residence times is skewed towards longer times in the lower canopy. While the predicted probability density functions from the theoretical model and large-eddy simulation are in good agreement with each other, the theoretical model requires only information on canopy height and eddy diffusivities inside the canopy. The eddy-diffusivity model developed additionally requires the friction velocity at canopy top and a parametrized profile of the standard deviation of vertical velocity. The theoretical model of air-parcel residence times is extended to include first-order chemical reactions over a range of of Damköhler numbers ( Da) characteristic of plant-emitted hydrocarbons. The resulting out-of-canopy export fractions range from near 1 for Da =10^{-3} to less than 0.3 at Da = 10. These results highlight the necessity for dense and tall forests to include the impacts of air-parcel residence times when calculating the out-of-canopy export fraction for reactive trace gases.

Application of fractional derivative with exponential law to bi-fractional-order wave equation with frictional memory kernel

NASA Astrophysics Data System (ADS)

Cuahutenango-Barro, B.; Taneco-Hernández, M. A.; Gómez-Aguilar, J. F.

2017-12-01

Analytical solutions of the wave equation with bi-fractional-order and frictional memory kernel of Mittag-Leffler type are obtained via Caputo-Fabrizio fractional derivative in the Liouville-Caputo sense. Through the method of separation of variables and Laplace transform method we derive closed-form solutions and establish fundamental solutions. Special cases with homogeneous Dirichlet boundary conditions and nonhomogeneous initial conditions, as well as for the external force are considered. Numerical simulations of the special solutions were done and novel behaviors are obtained.

Generalized quantum kinetic expansion: Higher-order corrections to multichromophoric Förster theory

NASA Astrophysics Data System (ADS)

Wu, Jianlan; Gong, Zhihao; Tang, Zhoufei

2015-08-01

For a general two-cluster energy transfer network, a new methodology of the generalized quantum kinetic expansion (GQKE) method is developed, which predicts an exact time-convolution equation for the cluster population evolution under the initial condition of the local cluster equilibrium state. The cluster-to-cluster rate kernel is expanded over the inter-cluster couplings. The lowest second-order GQKE rate recovers the multichromophoric Förster theory (MCFT) rate. The higher-order corrections to the MCFT rate are systematically included using the continued fraction resummation form, resulting in the resummed GQKE method. The reliability of the GQKE methodology is verified in two model systems, revealing the relevance of higher-order corrections.

Evaluation of the Possible Mechanisms of Antihypertensive Activity of Loranthus micranthus: An African Mistletoe

PubMed Central

Iwalokun, Bamidele A.; Hodonu, Sedoten A.; Nwoke, Stella; Ojo, Olabisi; Agomo, Phillip U.

2011-01-01

Loranthus micranthus (LM), also called African mistletoe is a major Nigerian Loranthaceae plant used traditionally to treat hypertension. The methanolic leaf extract of the plant (LMME) has been shown to elicit anti-hypertensive activity in rats but mechanism remains unclear. This study was undertaken to study the effect of LM on pressor-induced contraction of rat aorta smooth muscles and serum lipid profiles in mice. The LMME was partitioned to produce n-butanol (NBF-LMME), chloroform (CF-LMME), ethyl acetate (EAF-LMME) and water (WF-LMME) fractions. The median effective concentrations and maximum relaxation of the fractions were determined against epinephrine and KCl pre-contracted rat aorta ring model. Serum lipid profiles and nitric oxide (NO) were determined spectrophotometrically in mice administered per orally 250 mg/kg b.w. of each fraction for 21 days. Data were analyzed statistically. NBF-LMME elicited the highest dose-dependent inhibitory effect on rat aorta pre-contracted with norepinephrine and KCl, followed in decreasing order by WF-LMME > CF-LMME > EAF-LMME. Similar order of activity was observed in the ability of these fractions to inhibit elevation in artherogenic lipids, raise serum nitric oxide and reduce cardiac arginase in mice. We conclude the anti-hypertensive activity of L. micranthus involve anti-artherogenic events, vasorelaxation, cardiac arginase reduction and NO elevation. PMID:21918720

Exploration of the wound healing potential of Helichrysum graveolens (Bieb.) Sweet: isolation of apigenin as an active component.

PubMed

Süntar, Ipek; Küpeli Akkol, Esra; Keles, Hikmet; Yesilada, Erdem; Sarker, Satyajit D

2013-08-26

In Turkish traditional medicine, the flowers of Helichrysum graveolens (Bieb.) Sweet (Asteraceae) have been used for the treatment of jaundice, for wound-healing and as a diuretic. In order to find scientific evidence for the traditional utilization of this plant in wound-healing, the effect of the plant extract was investigated by using in vivo and in vitro experimental models. Then through bioassay-guided fractionation procedures active wound-healing component(s) was isolated and its possible role in the wound-healing process was also determined. The linear incision and the circular excision wound models were applied in order to evaluate in vivo wound-healing potential of Helichrysum graveolens. Anti-inflammatory and antioxidant activities, which are known to involve in wound-healing process, were also assessed by the Whittle method and the DPPH (2,2-diphenyl-1-picrylhydrazyl) radical-scavenging assay, respectively. The total phenolic content of the crude extract and solvent fractions was estimated to find correlation between the phenolic content and the antioxidant activity. Combined application of the chromatographic separation techniques on sephadex and silica gel columns, and bioassay techniques have yielded the active wound-healing principle of Helichrysum graveolens. Moreover, in vitro inhibitory effect of active principle on hyaluronidase, collagenase and elastase enzymes were investigated to explore the activity pathways. The 85% methanol (MeOH) extract of Helichrysum graveolens flowers displayed significant wound-healing, anti-inflammatory and antioxidant activities. Then the crude extract was partitioned by successive solvent extractions, in increasing polarity, to give five solvent fractions. Among the solvent fractions, the ethyl acetate (EtOAc) fraction exerted the highest activity. The EtOAc fraction was further subjected to chromatographic separations to yield active constituent and its structure was elucidated to be apigenin by spectrometric methods. Further in vivo and in vitro assays revealed that apigenin was one of the components responsible for the wound-healing effect of the plant remedy and also found to possess significant anti-inflammatory, antioxidant, anti-hyaluronidase and anti-collagenase activities. Present study supported the traditional use of Helichrysum graveolens flowers for wound-healing and through bioassay-guided fractionation procedures from the crude extract apigenin was isolated as one of the active components. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Computational Algorithms or Identification of Distributed Parameter Systems

DTIC Science & Technology

1993-04-24

delay-differential equations, Volterra integral equations, and partial differential equations with memory terms . In particular we investigated a...tested for estimating parameters in a Volterra integral equation arising from a viscoelastic model of a flexible structure with Boltzmann damping. In...particular, one of the parameters identified was the order of the derivative in Volterra integro-differential equations containing fractional

Obtaining mathematical models for assessing efficiency of dust collectors using integrated system of analysis and data management STATISTICA Design of Experiments

NASA Astrophysics Data System (ADS)

Azarov, A. V.; Zhukova, N. S.; Kozlovtseva, E. Yu; Dobrinsky, D. R.

2018-05-01

The article considers obtaining mathematical models to assess the efficiency of the dust collectors using an integrated system of analysis and data management STATISTICA Design of Experiments. The procedure for obtaining mathematical models and data processing is considered by the example of laboratory studies on a mounted installation containing a dust collector in counter-swirling flows (CSF) using gypsum dust of various fractions. Planning of experimental studies has been carried out in order to reduce the number of experiments and reduce the cost of experimental research. A second-order non-position plan (Box-Bencken plan) was used, which reduced the number of trials from 81 to 27. The order of statistical data research of Box-Benken plan using standard tools of integrated system for analysis and data management STATISTICA Design of Experiments is considered. Results of statistical data processing with significance estimation of coefficients and adequacy of mathematical models are presented.

Tidal streams from axion miniclusters and direct axion searches

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tinyakov, Peter; Tkachev, Igor; Zioutas, Konstantin, E-mail: petr.tiniakov@ulb.ac.be, E-mail: tkachev@inr.ru, E-mail: konstantin.zioutas@cern.ch

In some axion dark matter models a dominant fraction of axions resides in dense small-scale substructures, axion miniclusters. A fraction of these substructures is disrupted and forms tidal streams where the axion density may still be an order of magnitude larger than the average. We discuss implications of these streams for the direct axion searches. We estimate the fraction of disrupted miniclusters and the parameters of the resulting streams, and find that stream-crossing events would occur at a rate of about 1/(20 yr) for 2–3 days, during which the signal in axion detectors would be amplified by a factor ∼ 10. Thesemore » estimates suggest that the effect of the tidal disruption of axion miniclusters may be important for direct axion searches and deserves a more thorough study.« less

Application of the Aquifer Impact Model to support decisions at a CO 2 sequestration site: Modeling and Analysis: Application of the Aquifer Impact Model to support decisions at a CO 2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bacon, Diana Holford; Locke II, Randall A.; Keating, Elizabeth

The National Risk Assessment Partnership (NRAP) has developed a suite of tools to assess and manage risk at CO2 sequestration sites (1). The NRAP tool suite includes the Aquifer Impact Model (AIM), based on reduced order models developed using site-specific data from two aquifers (alluvium and carbonate). The models accept aquifer parameters as a range of variable inputs so they may have more broad applicability. Guidelines have been developed for determining the aquifer types for which the ROMs should be applicable. This paper considers the applicability of the aquifer models in AIM to predicting the impact of CO2 or Brinemore » leakage were it to occur at the Illinois Basin Decatur Project (IBDP). Based on the results of the sensitivity analysis, the hydraulic parameters and leakage source term magnitude are more sensitive than clay fraction or cation exchange capacity. Sand permeability was the only hydraulic parameter measured at the IBDP site. More information on the other hydraulic parameters, such as sand fraction and sand/clay correlation lengths, could reduce uncertainty in risk estimates. Some non-adjustable parameters, such as the initial pH and TDS and the pH no-impact threshold, are significantly different for the ROM than for the observations at the IBDP site. The reduced order model could be made more useful to a wider range of sites if the initial conditions and no-impact threshold values were adjustable parameters.« less