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.

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.

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.

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.

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.

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.

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.

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

Universal block diagram based modeling and simulation schemes for fractional-order control systems.

PubMed

Bai, Lu; Xue, Dingyü

2017-05-08

Universal block diagram based schemes are proposed for modeling and simulating the fractional-order control systems in this paper. A fractional operator block in Simulink is designed to evaluate the fractional-order derivative and integral. Based on the block, the fractional-order control systems with zero initial conditions can be modeled conveniently. For modeling the system with nonzero initial conditions, the auxiliary signal is constructed in the compensation scheme. Since the compensation scheme is very complicated, therefore the integrator chain scheme is further proposed to simplify the modeling procedures. The accuracy and effectiveness of the schemes are assessed in the examples, the computation results testify the block diagram scheme is efficient for all Caputo fractional-order ordinary differential equations (FODEs) of any complexity, including the implicit Caputo FODEs. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

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.

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.

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

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.

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.

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.

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.

A conformal mapping based fractional order approach for sub-optimal tuning of PID controllers with guaranteed dominant pole placement

NASA Astrophysics Data System (ADS)

Saha, Suman; Das, Saptarshi; Das, Shantanu; Gupta, Amitava

2012-09-01

A novel conformal mapping based fractional order (FO) methodology is developed in this paper for tuning existing classical (Integer Order) Proportional Integral Derivative (PID) controllers especially for sluggish and oscillatory second order systems. The conventional pole placement tuning via Linear Quadratic Regulator (LQR) method is extended for open loop oscillatory systems as well. The locations of the open loop zeros of a fractional order PID (FOPID or PIλDμ) controller have been approximated in this paper vis-à-vis a LQR tuned conventional integer order PID controller, to achieve equivalent integer order PID control system. This approach eases the implementation of analog/digital realization of a FOPID controller with its integer order counterpart along with the advantages of fractional order controller preserved. It is shown here in the paper that decrease in the integro-differential operators of the FOPID/PIλDμ controller pushes the open loop zeros of the equivalent PID controller towards greater damping regions which gives a trajectory of the controller zeros and dominant closed loop poles. This trajectory is termed as "M-curve". This phenomena is used to design a two-stage tuning algorithm which reduces the existing PID controller's effort in a significant manner compared to that with a single stage LQR based pole placement method at a desired closed loop damping and frequency.

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.

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.

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.

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.

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.

Optimal control problem for linear fractional-order systems, described by equations with Hadamard-type derivative

NASA Astrophysics Data System (ADS)

Postnov, Sergey

2017-11-01

Two kinds of optimal control problem are investigated for linear time-invariant fractional-order systems with lumped parameters which dynamics described by equations with Hadamard-type derivative: the problem of control with minimal norm and the problem of control with minimal time at given restriction on control norm. The problem setting with nonlocal initial conditions studied. Admissible controls allowed to be the p-integrable functions (p > 1) at half-interval. The optimal control problem studied by moment method. The correctness and solvability conditions for the corresponding moment problem are derived. For several special cases the optimal control problems stated are solved analytically. Some analogies pointed for results obtained with the results which are known for integer-order systems and fractional-order systems describing by equations with Caputo- and Riemann-Liouville-type derivatives.

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.

Performance comparison of optimal fractional order hybrid fuzzy PID controllers for handling oscillatory fractional order processes with dead time.

PubMed

Das, Saptarshi; Pan, Indranil; Das, Shantanu

2013-07-01

Fuzzy logic based PID controllers have been studied in this paper, considering several combinations of hybrid controllers by grouping the proportional, integral and derivative actions with fuzzy inferencing in different forms. Fractional order (FO) rate of error signal and FO integral of control signal have been used in the design of a family of decomposed hybrid FO fuzzy PID controllers. The input and output scaling factors (SF) along with the integro-differential operators are tuned with real coded genetic algorithm (GA) to produce optimum closed loop performance by simultaneous consideration of the control loop error index and the control signal. Three different classes of fractional order oscillatory processes with various levels of relative dominance between time constant and time delay have been used to test the comparative merits of the proposed family of hybrid fractional order fuzzy PID controllers. Performance comparison of the different FO fuzzy PID controller structures has been done in terms of optimal set-point tracking, load disturbance rejection and minimal variation of manipulated variable or smaller actuator requirement etc. In addition, multi-objective Non-dominated Sorting Genetic Algorithm (NSGA-II) has been used to study the Pareto optimal trade-offs between the set point tracking and control signal, and the set point tracking and load disturbance performance for each of the controller structure to handle the three different types of processes. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Improving the position control of a two degrees of freedom robotic sensing antenna using fractional-order controllers

NASA Astrophysics Data System (ADS)

Feliu-Talegon, D.; Feliu-Batlle, V.

2017-06-01

Flexible links combined with force and torque sensors can be used to detect obstacles in mobile robotics, as well as for surface and object recognition. These devices, called sensing antennae, perform an active sensing strategy in which a servomotor system moves the link back and forth until it hits an object. At this instant, information of the motor angles combined with force and torque measurements allow calculating the positions of the hitting points, which are valuable information about the object surface. In order to move the antenna fast and accurately, this article proposes a new closed-loop control for driving this flexible link-based sensor. The control strategy is based on combining a feedforward term and a feedback phase-lag compensator of fractional order. We demonstrate that some drawbacks of the control of these sensing devices like the apparition of spillover effects when a very fast positioning of the antenna tip is desired, and actuator saturation caused by high-frequency sensor noise, can be significantly reduced by using our newly proposed fractional-order controllers. We have applied these controllers to the position control of a prototype of sensing antenna and experiments have shown the improvements attained with this technique in the accurate and vibration free motion of its tip (the fractional-order controller reduced ten times the residual vibration obtained with the integer-order controller).

Enhanced robust fractional order proportional-plus-integral controller based on neural network for velocity control of permanent magnet synchronous motor.

PubMed

Zhang, Bitao; Pi, YouGuo

2013-07-01

The traditional integer order proportional-integral-differential (IO-PID) controller is sensitive to the parameter variation or/and external load disturbance of permanent magnet synchronous motor (PMSM). And the fractional order proportional-integral-differential (FO-PID) control scheme based on robustness tuning method is proposed to enhance the robustness. But the robustness focuses on the open-loop gain variation of controlled plant. In this paper, an enhanced robust fractional order proportional-plus-integral (ERFOPI) controller based on neural network is proposed. The control law of the ERFOPI controller is acted on a fractional order implement function (FOIF) of tracking error but not tracking error directly, which, according to theory analysis, can enhance the robust performance of system. Tuning rules and approaches, based on phase margin, crossover frequency specification and robustness rejecting gain variation, are introduced to obtain the parameters of ERFOPI controller. And the neural network algorithm is used to adjust the parameter of FOIF. Simulation and experimental results show that the method proposed in this paper not only achieve favorable tracking performance, but also is robust with regard to external load disturbance and parameter variation. Crown Copyright © 2013. Published by Elsevier Ltd. All rights reserved.

Design, implementation and application of distributed order PI control.

PubMed

Zhou, Fengyu; Zhao, Yang; Li, Yan; Chen, YangQuan

2013-05-01

In this paper, a series of distributed order PI controller design methods are derived and applied to the robust control of wheeled service robots, which can tolerate more structural and parametric uncertainties than the corresponding fractional order PI control. A practical discrete incremental distributed order PI control strategy is proposed basing on the discretization method and the frequency criterions, which can be commonly used in many fields of fractional order system, control and signal processing. Besides, an auto-tuning strategy and the genetic algorithm are applied to the distributed order PI control as well. A number of experimental results are provided to show the advantages and distinguished features of the discussed methods in fairways. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

Projective synchronization of nonidentical fractional-order neural networks based on sliding mode controller.

PubMed

Ding, Zhixia; Shen, Yi

2016-04-01

This paper investigates global projective synchronization of nonidentical fractional-order neural networks (FNNs) based on sliding mode control technique. We firstly construct a fractional-order integral sliding surface. Then, according to the sliding mode control theory, we design a sliding mode controller to guarantee the occurrence of the sliding motion. Based on fractional Lyapunov direct methods, system trajectories are driven to the proposed sliding surface and remain on it evermore, and some novel criteria are obtained to realize global projective synchronization of nonidentical FNNs. As the special cases, some sufficient conditions are given to ensure projective synchronization of identical FNNs, complete synchronization of nonidentical FNNs and anti-synchronization of nonidentical FNNs. Finally, one numerical example is given to demonstrate the effectiveness of the obtained results. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

Adaptive Fractional-order Control for Synchronization of Two Coupled Neurons in the External Electrical Stimulation

PubMed Central

Mehdiabadi, M. R. Rahmani; Rouhani, E.; Mashhadi, S. K. Mousavi; Jalali, A. A.

2014-01-01

This paper addresses synchronizing two coupled chaotic FitzHugh–Nagumo (FHN) neurons with weakly gap junction under external electrical stimulation (EES). To transmit information among coupled neurons, by generalization of the integer-order FHN equations of the coupled system into the fractional-order in frequency domain using Crone approach, the behavior of each coupled neuron relies on its past behavior and the memorized system can be a better fit for the neuron response. An adaptive fractional-order controller based on the Lyaponuv stability theory was designed to synchronize two neurons electrically coupled with gap junction in EES. The proposed controller is also robust to the inevitable random noise such as disturbances of ionic channels. The simulation results demonstrate the effectiveness of the control scheme. PMID:25337373

On the fragility of fractional-order PID controllers for FOPDT processes.

PubMed

Padula, Fabrizio; Visioli, Antonio

2016-01-01

This paper analyzes the fragility issue of fractional-order proportional-integral-derivative controllers applied to integer first-order plus-dead-time processes. In particular, the effects of the variations of the controller parameters on the achieved control system robustness and performance are investigated. Results show that this kind of controllers is more fragile with respect to the standard proportional-integral-derivative controllers and therefore a significant attention should be paid by the user in their tuning. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

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.

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

Numerical analysis for trajectory controllability of a coupled multi-order fractional delay differential system via the shifted Jacobi method

NASA Astrophysics Data System (ADS)

Priya, B. Ganesh; Muthukumar, P.

2018-02-01

This paper deals with the trajectory controllability for a class of multi-order fractional linear systems subject to a constant delay in state vector. The solution for the coupled fractional delay differential equation is established by the Mittag-Leffler function. The necessary and sufficient condition for the trajectory controllability is formulated and proved by the generalized Gronwall's inequality. The approximate trajectory for the proposed system is obtained through the shifted Jacobi operational matrix method. The numerical simulation of the approximate solution shows the theoretical results. Finally, some remarks and comments on the existing results of constrained controllability for the fractional dynamical system are also presented.

High-performance fractional order terminal sliding mode control strategy for DC-DC Buck converter

PubMed Central

Xu, Dan; Zhou, Huan; Bai, Anning; Lu, Wei

2017-01-01

This paper presents an adaption of the fractional order terminal sliding mode control (AFTSMC) strategy for DC-DC Buck converter. The following strategy aims to design a novel nonlinear sliding surface function, with a double closed-loop structure of voltage and current. This strategy is a fusion of two characteristics: terminal sliding mode control (TSMC) and fractional order calculation (FOC). In addition, the influence of “the controller parameters” on the “performance of double closed-loop system” is investigated. It is observed that the value of terminal power has to be chosen to make a compromise between start-up and transient response of the converter. Therefore the AFTSMC strategy chooses the value of the terminal power adaptively, and this strategy can lead to the appropriate number of fractional order as well. Furthermore, through the fractional order analysis, the system can reach the sliding mode surface in a finite time. And the theoretical considerations are verified by numerical simulation. The performance of the AFTSMC and TSMC strategies is tested by computer simulations. And the comparison simulation results show that the AFTSMC exhibits a considerable improvement in terms of a faster output voltage response during load changes. Moreover, AFTSMC obtains a faster dynamical response, smaller steady-state error rate and lower overshoot. PMID:29084255

High-performance fractional order terminal sliding mode control strategy for DC-DC Buck converter.

PubMed

Wang, Jianlin; Xu, Dan; Zhou, Huan; Bai, Anning; Lu, Wei

2017-01-01

This paper presents an adaption of the fractional order terminal sliding mode control (AFTSMC) strategy for DC-DC Buck converter. The following strategy aims to design a novel nonlinear sliding surface function, with a double closed-loop structure of voltage and current. This strategy is a fusion of two characteristics: terminal sliding mode control (TSMC) and fractional order calculation (FOC). In addition, the influence of "the controller parameters" on the "performance of double closed-loop system" is investigated. It is observed that the value of terminal power has to be chosen to make a compromise between start-up and transient response of the converter. Therefore the AFTSMC strategy chooses the value of the terminal power adaptively, and this strategy can lead to the appropriate number of fractional order as well. Furthermore, through the fractional order analysis, the system can reach the sliding mode surface in a finite time. And the theoretical considerations are verified by numerical simulation. The performance of the AFTSMC and TSMC strategies is tested by computer simulations. And the comparison simulation results show that the AFTSMC exhibits a considerable improvement in terms of a faster output voltage response during load changes. Moreover, AFTSMC obtains a faster dynamical response, smaller steady-state error rate and lower overshoot.

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

PubMed

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.

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

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.

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.

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.

Robust fast controller design via nonlinear fractional differential equations.

PubMed

Zhou, Xi; Wei, Yiheng; Liang, Shu; Wang, Yong

2017-07-01

A new method for linear system controller design is proposed whereby the closed-loop system achieves both robustness and fast response. The robustness performance considered here means the damping ratio of closed-loop system can keep its desired value under system parameter perturbation, while the fast response, represented by rise time of system output, can be improved by tuning the controller parameter. We exploit techniques from both the nonlinear systems control and the fractional order systems control to derive a novel nonlinear fractional order controller. For theoretical analysis of the closed-loop system performance, two comparison theorems are developed for a class of fractional differential equations. Moreover, the rise time of the closed-loop system can be estimated, which facilitates our controller design to satisfy the fast response performance and maintain the robustness. Finally, numerical examples are given to illustrate the effectiveness of our methods. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

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.

Fractional order absolute vibration suppression (AVS) controllers

NASA Astrophysics Data System (ADS)

Halevi, Yoram

2017-04-01

Absolute vibration suppression (AVS) is a control method for flexible structures. The first step is an accurate, infinite dimension, transfer function (TF), from actuation to measurement. This leads to the collocated, rate feedback AVS controller that in some cases completely eliminates the vibration. In case of the 1D wave equation, the TF consists of pure time delays and low order rational terms, and the AVS controller is rational. In all other cases, the TF and consequently the controller are fractional order in both the delays and the "rational parts". The paper considers stability, performance and actual implementation in such cases.

Calculation of controllability and observability matrices for special case of continuous-time multi-order fractional systems.

PubMed

Hassanzadeh, Iman; Tabatabaei, Mohammad

2017-03-28

In this paper, controllability and observability matrices for pseudo upper or lower triangular multi-order fractional systems are derived. It is demonstrated that these systems are controllable and observable if and only if their controllability and observability matrices are full rank. In other words, the rank of these matrices should be equal to the inner dimension of their corresponding state space realizations. To reduce the computational complexities, these matrices are converted to simplified matrices with smaller dimensions. Numerical examples are provided to show the usefulness of the mentioned matrices for controllability and observability analysis of this case of multi-order fractional systems. These examples clarify that the duality concept is not necessarily true for these special systems. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

An Implementation Method of the Fractional-Order PID Control System Considering the Memory Constraint and its Application to the Temperature Control of Heat Plate

NASA Astrophysics Data System (ADS)

Sasano, Koji; Okajima, Hiroshi; Matsunaga, Nobutomo

Recently, the fractional order PID (FO-PID) control, which is the extension of the PID control, has been focused on. Even though the FO-PID requires the high-order filter, it is difficult to realize the high-order filter due to the memory limitation of digital computer. For implementation of FO-PID, approximation of the fractional integrator and differentiator are required. Short memory principle (SMP) is one of the effective approximation methods. However, there is a disadvantage that the approximated filter with SMP cannot eliminate the steady-state error. For this problem, we introduce the distributed implementation of the integrator and the dynamic quantizer to make the efficient use of permissible memory. The objective of this study is to clarify how to implement the accurate FO-PID with limited memories. In this paper, we propose the implementation method of FO-PID with memory constraint using dynamic quantizer. And the trade off between approximation of fractional elements and quantized data size are examined so as to close to the ideal FO-PID responses. The effectiveness of proposed method is evaluated by numerical example and experiment in the temperature control of heat plate.

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.

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

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

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.

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.

Optimal fractional order PID design via Tabu Search based algorithm.

PubMed

Ateş, Abdullah; Yeroglu, Celaleddin

2016-01-01

This paper presents an optimization method based on the Tabu Search Algorithm (TSA) to design a Fractional-Order Proportional-Integral-Derivative (FOPID) controller. All parameter computations of the FOPID employ random initial conditions, using the proposed optimization method. Illustrative examples demonstrate the performance of the proposed FOPID controller design method. Copyright © 2015 ISA. Published by 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 .

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.

Active control strategy for synchronization and anti-synchronization of a fractional chaotic financial system

NASA Astrophysics Data System (ADS)

Huang, Chengdai; Cao, Jinde

2017-05-01

This paper is concerned with the issues of synchronization and anti-synchronization for fractional chaotic financial system with market confidence by taking advantage of active control approach. Some sufficient conditions are derived to guarantee the synchronization and anti-synchronization for the proposed fractional system. Moreover, the relationship between the order and synchronization(anti-synchronization) is demonstrated numerically. It reveals that synchronization(anti-synchronization) is faster as the order increases. Finally, two illustrative examples are exploited to verify the efficiency of the obtained theoretical results.

A robust fractional-order PID controller design based on active queue management for TCP network

NASA Astrophysics Data System (ADS)

Hamidian, Hamideh; Beheshti, Mohammad T. H.

2018-01-01

In this paper, a robust fractional-order controller is designed to control the congestion in transmission control protocol (TCP) networks with time-varying parameters. Fractional controllers can increase the stability and robustness. Regardless of advantages of fractional controllers, they are still not common in congestion control in TCP networks. The network parameters are time-varying, so the robust stability is important in congestion controller design. Therefore, we focused on the robust controller design. The fractional PID controller is developed based on active queue management (AQM). D-partition technique is used. The most important property of designed controller is the robustness to the time-varying parameters of the TCP network. The vertex quasi-polynomials of the closed-loop characteristic equation are obtained, and the stability boundaries are calculated for each vertex quasi-polynomial. The intersection of all stability regions is insensitive to network parameter variations, and results in robust stability of TCP/AQM system. NS-2 simulations show that the proposed algorithm provides a stable queue length. Moreover, simulations show smaller oscillations of the queue length and less packet drop probability for FPID compared to PI and PID controllers. We can conclude from NS-2 simulations that the average packet loss probability variations are negligible when the network parameters change.

A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors

NASA Astrophysics Data System (ADS)

Zou, Changfu; Zhang, Lei; Hu, Xiaosong; Wang, Zhenpo; Wik, Torsten; Pecht, Michael

2018-06-01

Electrochemical energy storage systems play an important role in diverse applications, such as electrified transportation and integration of renewable energy with the electrical grid. To facilitate model-based management for extracting full system potentials, proper mathematical models are imperative. Due to extra degrees of freedom brought by differentiation derivatives, fractional-order models may be able to better describe the dynamic behaviors of electrochemical systems. This paper provides a critical overview of fractional-order techniques for managing lithium-ion batteries, lead-acid batteries, and supercapacitors. Starting with the basic concepts and technical tools from fractional-order calculus, the modeling principles for these energy systems are presented by identifying disperse dynamic processes and using electrochemical impedance spectroscopy. Available battery/supercapacitor models are comprehensively reviewed, and the advantages of fractional types are discussed. Two case studies demonstrate the accuracy and computational efficiency of fractional-order models. These models offer 15-30% higher accuracy than their integer-order analogues, but have reasonable complexity. Consequently, fractional-order models can be good candidates for the development of advanced battery/supercapacitor management systems. Finally, the main technical challenges facing electrochemical energy storage system modeling, state estimation, and control in the fractional-order domain, as well as future research directions, are highlighted.

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

Adaptive neural output-feedback control for nonstrict-feedback time-delay fractional-order systems with output constraints and actuator nonlinearities.

PubMed

Zouari, Farouk; Ibeas, Asier; Boulkroune, Abdesselem; Cao, Jinde; Mehdi Arefi, Mohammad

2018-06-01

This study addresses the issue of the adaptive output tracking control for a category of uncertain nonstrict-feedback delayed incommensurate fractional-order systems in the presence of nonaffine structures, unmeasured pseudo-states, unknown control directions, unknown actuator nonlinearities and output constraints. Firstly, the mean value theorem and the Gaussian error function are introduced to eliminate the difficulties that arise from the nonaffine structures and the unknown actuator nonlinearities, respectively. Secondly, the immeasurable tracking error variables are suitably estimated by constructing a fractional-order linear observer. Thirdly, the neural network, the Razumikhin Lemma, the variable separation approach, and the smooth Nussbaum-type function are used to deal with the uncertain nonlinear dynamics, the unknown time-varying delays, the nonstrict feedback and the unknown control directions, respectively. Fourthly, asymmetric barrier Lyapunov functions are employed to overcome the violation of the output constraints and to tune online the parameters of the adaptive neural controller. Through rigorous analysis, it is proved that the boundedness of all variables in the closed-loop system and the semi global asymptotic tracking are ensured without transgression of the constraints. The principal contributions of this study can be summarized as follows: (1) based on Caputo's definitions and new lemmas, methods concerning the controllability, observability and stability analysis of integer-order systems are extended to fractional-order ones, (2) the output tracking objective for a relatively large class of uncertain systems is achieved with a simple controller and less tuning parameters. Finally, computer-simulation studies from the robotic field are given to demonstrate the effectiveness of the proposed controller. Copyright © 2018 Elsevier Ltd. All rights reserved.

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.

Sliding mode control for generalized robust synchronization of mismatched fractional order dynamical systems and its application to secure transmission of voice messages.

PubMed

Muthukumar, P; Balasubramaniam, P; Ratnavelu, K

2017-07-26

This paper proposes a generalized robust synchronization method for different dimensional fractional order dynamical systems with mismatched fractional derivatives in the presence of function uncertainty and external disturbance by a designing sliding mode controller. Based on the proposed theory of generalized robust synchronization criterion, a novel audio cryptosystem is proposed for sending or sharing voice messages secretly via insecure channel. Numerical examples are given to verify the potency of the proposed theories. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

O(t-α)-synchronization and Mittag-Leffler synchronization for the fractional-order memristive neural networks with delays and discontinuous neuron activations.

PubMed

Chen, Jiejie; Chen, Boshan; Zeng, Zhigang

2018-04-01

This paper investigates O(t -α )-synchronization and adaptive Mittag-Leffler synchronization for the fractional-order memristive neural networks with delays and discontinuous neuron activations. Firstly, based on the framework of Filippov solution and differential inclusion theory, using a Razumikhin-type method, some sufficient conditions ensuring the global O(t -α )-synchronization of considered networks are established via a linear-type discontinuous control. Next, a new fractional differential inequality is established and two new discontinuous adaptive controller is designed to achieve Mittag-Leffler synchronization between the drive system and the response systems using this inequality. Finally, two numerical simulations are given to show the effectiveness of the theoretical results. Our approach and theoretical results have a leading significance in the design of synchronized fractional-order memristive neural networks circuits involving discontinuous activations and time-varying delays. Copyright © 2018 Elsevier Ltd. All rights reserved.

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.

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.

Synchronization and anti-synchronization of a fractional order delayed memristor-based chaotic system using active control

NASA Astrophysics Data System (ADS)

Ding, Dawei; Qian, Xin; Wang, Nian; Liang, Dong

2018-05-01

In this paper, the issue of synchronization and anti-synchronization for fractional-delayed memristor-based chaotic system is studied by using active control strategy. Firstly, some explicit conditions are proposed to guarantee the synchronization and anti-synchronization of the proposed system. Secondly, the influence of order and time delay on the synchronization (anti-synchronization) is discussed. It reveals that synchronization (anti-synchronization) is faster as the order increases or the time delay decreases. Finally, some numerical simulations are presented to verify the validity of our theoretical analysis.

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.

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.

Mittag-Leffler synchronization of delayed fractional-order bidirectional associative memory neural networks with discontinuous activations: state feedback control and impulsive control schemes.

PubMed

Ding, Xiaoshuai; Cao, Jinde; Zhao, Xuan; Alsaadi, Fuad E

2017-08-01

This paper is concerned with the drive-response synchronization for a class of fractional-order bidirectional associative memory neural networks with time delays, as well as in the presence of discontinuous activation functions. The global existence of solution under the framework of Filippov for such networks is firstly obtained based on the fixed-point theorem for condensing map. Then the state feedback and impulsive controllers are, respectively, designed to ensure the Mittag-Leffler synchronization of these neural networks and two new synchronization criteria are obtained, which are expressed in terms of a fractional comparison principle and Razumikhin techniques. Numerical simulations are presented to validate the proposed methodologies.

Fractional order sliding-mode control based on parameters auto-tuning for velocity control of permanent magnet synchronous motor.

PubMed

Zhang, BiTao; Pi, YouGuo; Luo, Ying

2012-09-01

A fractional order sliding mode control (FROSMC) scheme based on parameters auto-tuning for the velocity control of permanent magnet synchronous motor (PMSM) is proposed in this paper. The control law of the proposed F(R)OSMC scheme is designed according to Lyapunov stability theorem. Based on the property of transferring energy with adjustable type in F(R)OSMC, this paper analyzes the chattering phenomenon in classic sliding mode control (SMC) is attenuated with F(R)OSMC system. A fuzzy logic inference scheme (FLIS) is utilized to obtain the gain of switching control. Simulations and experiments demonstrate that the proposed FROSMC not only achieve better control performance with smaller chatting than that with integer order sliding mode control, but also is robust to external load disturbance and parameter variations. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

Chaos in the fractional order logistic delay system: Circuit realization and synchronization

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

Baskonus, Haci Mehmet; Hammouch, Zakia; Mekkaoui, Toufik

2016-06-08

In this paper, we present a numerical study and a circuit design to prove existence of chaos in the fractional order Logistic delay system. In addition, we investigate an active control synchronization scheme in this system. Numerical and cicruit simulations show the effectiveness and feasibility of this method.

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.

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.

The Vertical Linear Fractional Initialization Problem

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

1999-01-01

This paper presents a solution to the initialization problem for a system of linear fractional-order differential equations. The scalar problem is considered first, and solutions are obtained both generally and for a specific initialization. Next the vector fractional order differential equation is considered. In this case, the solution is obtained in the form of matrix F-functions. Some control implications of the vector case are discussed. The suggested method of problem solution is shown via an example.

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.

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.

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.

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.

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.

Multi-objective LQR with optimum weight selection to design FOPID controllers for delayed fractional order processes.

PubMed

Das, Saptarshi; Pan, Indranil; Das, Shantanu

2015-09-01

An optimal trade-off design for fractional order (FO)-PID controller is proposed with a Linear Quadratic Regulator (LQR) based technique using two conflicting time domain objectives. A class of delayed FO systems with single non-integer order element, exhibiting both sluggish and oscillatory open loop responses, have been controlled here. The FO time delay processes are handled within a multi-objective optimization (MOO) formalism of LQR based FOPID design. A comparison is made between two contemporary approaches of stabilizing time-delay systems withinLQR. The MOO control design methodology yields the Pareto optimal trade-off solutions between the tracking performance and total variation (TV) of the control signal. Tuning rules are formed for the optimal LQR-FOPID controller parameters, using median of the non-dominated Pareto solutions to handle delayed FO processes. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

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.

The synchronisation of fractional-order hyperchaos compound system

NASA Astrophysics Data System (ADS)

Noghredani, Naeimadeen; Riahi, Aminreza; Pariz, Naser; Karimpour, Ali

2018-02-01

This paper presents a new compound synchronisation scheme among four hyperchaotic memristor system with incommensurate fractional-order derivatives. First a new controller was designed based on adaptive technique to minimise the errors and guarantee compound synchronisation of four fractional-order memristor chaotic systems. According to the suitability of compound synchronisation as a reliable solution for secure communication, we then examined the application of the proposed adaptive compound synchronisation scheme in the presence of noise for secure communication. In addition, the unpredictability and complexity of the drive systems enhance the security of secure communication. The corresponding theoretical analysis and results of simulation validated the effectiveness of the proposed synchronisation scheme using MATLAB.

Adaptive Synchronization of Fractional Order Complex-Variable Dynamical Networks via Pinning Control

NASA Astrophysics Data System (ADS)

Ding, Da-Wei; Yan, Jie; Wang, Nian; Liang, Dong

2017-09-01

In this paper, the synchronization of fractional order complex-variable dynamical networks is studied using an adaptive pinning control strategy based on close center degree. Some effective criteria for global synchronization of fractional order complex-variable dynamical networks are derived based on the Lyapunov stability theory. From the theoretical analysis, one concludes that under appropriate conditions, the complex-variable dynamical networks can realize the global synchronization by using the proper adaptive pinning control method. Meanwhile, we succeed in solving the problem about how much coupling strength should be applied to ensure the synchronization of the fractional order complex networks. Therefore, compared with the existing results, the synchronization method in this paper is more general and convenient. This result extends the synchronization condition of the real-variable dynamical networks to the complex-valued field, which makes our research more practical. Finally, two simulation examples show that the derived theoretical results are valid and the proposed adaptive pinning method is effective. Supported by National Natural Science Foundation of China under Grant No. 61201227, National Natural Science Foundation of China Guangdong Joint Fund under Grant No. U1201255, the Natural Science Foundation of Anhui Province under Grant No. 1208085MF93, 211 Innovation Team of Anhui University under Grant Nos. KJTD007A and KJTD001B, and also supported by Chinese Scholarship Council

Novel Numerical Methods for Optimal Control Problems Involving Fractional-Order Differential Equations

DTIC Science & Technology

2018-03-14

pricing, Appl. Math . Comp. Vol.305, 174-187 (2017) 5. W. Li, S. Wang, Pricing European options with proportional transaction costs and stochastic...for fractional differential equation. Numer. Math . Theor. Methods Appl. 5, 229–241, 2012. [23] Kilbas A.A. and Marzan, S.A., Cauchy problem for...numerical technique for solving fractional optimal control problems, Comput. Math . Appl., 62, Issue 3, 1055–1067, 2011. [26] Lotfi A., Yousefi SA., Dehghan M

Fuzzy fractional order sliding mode controller for nonlinear systems

NASA Astrophysics Data System (ADS)

Delavari, H.; Ghaderi, R.; Ranjbar, A.; Momani, S.

2010-04-01

In this paper, an intelligent robust fractional surface sliding mode control for a nonlinear system is studied. At first a sliding PD surface is designed and then, a fractional form of these networks PDα, is proposed. Fast reaching velocity into the switching hyperplane in the hitting phase and little chattering phenomena in the sliding phase is desired. To reduce the chattering phenomenon in sliding mode control (SMC), a fuzzy logic controller is used to replace the discontinuity in the signum function at the reaching phase in the sliding mode control. For the problem of determining and optimizing the parameters of fuzzy sliding mode controller (FSMC), genetic algorithm (GA) is used. Finally, the performance and the significance of the controlled system two case studies (robot manipulator and coupled tanks) are investigated under variation in system parameters and also in presence of an external disturbance. The simulation results signify performance of genetic-based fuzzy fractional sliding mode controller.

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.

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.

A review and evaluation of numerical tools for fractional calculus and fractional order controls

NASA Astrophysics Data System (ADS)

Li, Zhuo; Liu, Lu; Dehghan, Sina; Chen, YangQuan; Xue, Dingyü

2017-06-01

In recent years, as fractional calculus becomes more and more broadly used in research across different academic disciplines, there are increasing demands for the numerical tools for the computation of fractional integration/differentiation, and the simulation of fractional order systems. Time to time, being asked about which tool is suitable for a specific application, the authors decide to carry out this survey to present recapitulative information of the available tools in the literature, in hope of benefiting researchers with different academic backgrounds. With this motivation, the present article collects the scattered tools into a dashboard view, briefly introduces their usage and algorithms, evaluates the accuracy, compares the performance, and provides informative comments for selection.

Study of the fractional order proportional integral controller for the permanent magnet synchronous motor based on the differential evolution algorithm.

PubMed

Zheng, Weijia; Pi, Youguo

2016-07-01

A tuning method of the fractional order proportional integral speed controller for a permanent magnet synchronous motor is proposed in this paper. Taking the combination of the integral of time and absolute error and the phase margin as the optimization index, the robustness specification as the constraint condition, the differential evolution algorithm is applied to search the optimal controller parameters. The dynamic response performance and robustness of the obtained optimal controller are verified by motor speed-tracking experiments on the motor speed control platform. Experimental results show that the proposed tuning method can enable the obtained control system to achieve both the optimal dynamic response performance and the robustness to gain variations. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

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.

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 order fuzzy control of hybrid power system with renewable generation using chaotic PSO.

PubMed

Pan, Indranil; Das, Saptarshi

2016-05-01

This paper investigates the operation of a hybrid power system through a novel fuzzy control scheme. The hybrid power system employs various autonomous generation systems like wind turbine, solar photovoltaic, diesel engine, fuel-cell, aqua electrolyzer etc. Other energy storage devices like the battery, flywheel and ultra-capacitor are also present in the network. A novel fractional order (FO) fuzzy control scheme is employed and its parameters are tuned with a particle swarm optimization (PSO) algorithm augmented with two chaotic maps for achieving an improved performance. This FO fuzzy controller shows better performance over the classical PID, and the integer order fuzzy PID controller in both linear and nonlinear operating regimes. The FO fuzzy controller also shows stronger robustness properties against system parameter variation and rate constraint nonlinearity, than that with the other controller structures. The robustness is a highly desirable property in such a scenario since many components of the hybrid power system may be switched on/off or may run at lower/higher power output, at different time instants. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

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.

Leaderless consensus for the fractional-order nonlinear multi-agent systems under directed interaction topology

NASA Astrophysics Data System (ADS)

Bai, Jing; Wen, Guoguang; Rahmani, Ahmed

2018-04-01

Leaderless consensus for the fractional-order nonlinear multi-agent systems is investigated in this paper. At the first part, a control protocol is proposed to achieve leaderless consensus for the nonlinear single-integrator multi-agent systems. At the second part, based on sliding mode estimator, a control protocol is given to solve leaderless consensus for the the nonlinear single-integrator multi-agent systems. It shows that the control protocol can improve the systems' convergence speed. At the third part, a control protocol is designed to accomplish leaderless consensus for the nonlinear double-integrator multi-agent systems. To judge the systems' stability in this paper, two classic continuous Lyapunov candidate functions are chosen. Finally, several worked out examples under directed interaction topology are given to prove above results.

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.

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.

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.

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.

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.

Irradiance tailoring by fractional Fourier transform of a radial Gaussian beam array

NASA Astrophysics Data System (ADS)

Zhou, Pu; Wang, Xiaolin; Ma, Yanxing; Ma, Haotong; Liu, Zejin

2011-03-01

The fractional Fourier transform (FRFT) is applied to a radial Gaussian beam array. Analytical formula is derived for the irradiance distribution of coherent and incoherent radial Gaussian beam array in FRFT domain using Collins integral formula. It is revealed that the irradiance pattern can be tailored to be controllable dark-hollow, flat-topped and Gaussian beam pattern by changing of the fractional order of FRFT and the coherent state of the laser array.

Irradiance tailoring by fractional Fourier transform of a radial Gaussian beam array

NASA Astrophysics Data System (ADS)

Zhou, Pu; Wang, Xiaolin; Ma, Yanxing; Ma, Haotong; Liu, Zejin

2010-07-01

The fractional Fourier transform (FRFT) is applied to a radial Gaussian beam array. Analytical formula is derived for the irradiance distribution of coherent and incoherent radial Gaussian beam array in FRFT domain using Collins integral formula. It is revealed that the irradiance pattern can be tailored to be controllable dark-hollow, flat-topped and Gaussian beam pattern by changing of the fractional order of FRFT and the coherent state of the laser array.

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

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.

Finite-time robust control of uncertain fractional-order Hopfield neural networks via sliding mode control

NASA Astrophysics Data System (ADS)

Xi, Yangui; Yu, Yongguang; Zhang, Shuo; Hai, Xudong

2018-01-01

Not Available Project supported by the National Natural Science Foundation of China (Grant Nos. 11371049 and 61772063) and the Fundamental Research Funds for the Central Universities, China (Grant No. 2016JBM070).

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

Fractional-order active fault-tolerant force-position controller design for the legged robots using saturated actuator with unknown bias and gain degradation

NASA Astrophysics Data System (ADS)

Farid, Yousef; Majd, Vahid Johari; Ehsani-Seresht, Abbas

2018-05-01

In this paper, a novel fault accommodation strategy is proposed for the legged robots subject to the actuator faults including actuation bias and effective gain degradation as well as the actuator saturation. First, the combined dynamics of two coupled subsystems consisting of the dynamics of the legs subsystem and the body subsystem are developed. Then, the interaction of the robot with the environment is formulated as the contact force optimization problem with equality and inequality constraints. The desired force is obtained by a dynamic model. A robust super twisting fault estimator is proposed to precisely estimate the defective torque amplitude of the faulty actuator in finite time. Defining a novel fractional sliding surface, a fractional nonsingular terminal sliding mode control law is developed. Moreover, by introducing a suitable auxiliary system and using its state vector in the designed controller, the proposed fault-tolerant control (FTC) scheme guarantees the finite-time stability of the closed-loop control system. The robustness and finite-time convergence of the proposed control law is established using the Lyapunov stability theory. Finally, numerical simulations are performed on a quadruped robot to demonstrate the stable walking of the robot with and without actuator faults, and actuator saturation constraints, and the results are compared to results with an integer order fault-tolerant controller.

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.

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.

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

Fractional-order difference equations for physical lattices and some applications

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

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2015-10-15

Fractional-order operators for physical lattice models based on the Grünwald-Letnikov fractional differences are suggested. We use an approach based on the models of lattices with long-range particle interactions. The fractional-order operators of differentiation and integration on physical lattices are represented by kernels of lattice long-range interactions. In continuum limit, these discrete operators of non-integer orders give the fractional-order derivatives and integrals with respect to coordinates of the Grünwald-Letnikov types. As examples of the fractional-order difference equations for physical lattices, we give difference analogs of the fractional nonlocal Navier-Stokes equations and the fractional nonlocal Maxwell equations for lattices with long-range interactions.more » Continuum limits of these fractional-order difference equations are also suggested.« less

Boundedness of the solutions for certain classes of fractional differential equations with application to adaptive systems.

PubMed

Aguila-Camacho, Norelys; Duarte-Mermoud, Manuel A

2016-01-01

This paper presents the analysis of three classes of fractional differential equations appearing in the field of fractional adaptive systems, for the case when the fractional order is in the interval α ∈(0,1] and the Caputo definition for fractional derivatives is used. The boundedness of the solutions is proved for all three cases, and the convergence to zero of the mean value of one of the variables is also proved. Applications of the obtained results to fractional adaptive schemes in the context of identification and control problems are presented at the end of the paper, including numerical simulations which support the analytical results. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Symmetry classification of time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Naeem, I.; Khan, M. D.

2017-01-01

In this article, a new approach is proposed to construct the symmetry groups for a class of fractional differential equations which are expressed in the modified Riemann-Liouville fractional derivative. We perform a complete group classification of a nonlinear fractional diffusion equation which arises in fractals, acoustics, control theory, signal processing and many other applications. Introducing the suitable transformations, the fractional derivatives are converted to integer order derivatives and in consequence the nonlinear fractional diffusion equation transforms to a partial differential equation (PDE). Then the Lie symmetries are computed for resulting PDE and using inverse transformations, we derive the symmetries for fractional diffusion equation. All cases are discussed in detail and results for symmetry properties are compared for different values of α. This study provides a new way of computing symmetries for a class of fractional differential equations.

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.

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.

Wood species affect the degradation of crude oil in beach sand.

PubMed

Jandl, Gerald; Rodríguez Arranz, Alberto; Baum, Christel; Leinweber, Peter

2015-01-01

The addition of wood chips as a co-substrate can promote the degradation of oil in soil. Therefore, in the present study, the tree species-specific impact of wood chips of Scots pine (Pinus sylvestris L.), Norway spruce (Picea abies L.) and Western balsam poplar (Populus trichocarpa L.) on the degradation of crude oil was tested in beach sand in a 4-week incubation experiment. The CO2-C release increased in the order of control without wood chips < +spruce < +pine < +poplar. Initial and final hydrocarbon concentrations (C10 to C40), as indicators for the oil degradation, were determined with gas chromatography-flame ionization detection (GC-FID). The degradation increased for the light fraction (C10 to C22), the heavy fraction (C23 to C40) as well as the whole range (C10 to C40) in the order of control without wood chips (f(degrad.) = 23% vs. 0% vs. 12%) < +poplar (f(degrad.) = 49% vs. 19% vs. 36%) < +spruce (f(degrad.) = 55% vs. 34% vs. 46%) < +pine (f(degrad.) = 60% vs. 44% vs. 53%), whereas the heavy fraction was less degraded in comparison to the light fraction. It can be concluded, that the tree species-specific wood quality is a significant control of the impact on the degradation of hydrocarbons, and pine wood chips might be promising, possibly caused by their lower decomposability and lower substrate replacement than the other wood species.

Data-driven adaptive fractional order PI control for PMSM servo system with measurement noise and data dropouts.

PubMed

Xie, Yuanlong; Tang, Xiaoqi; Song, Bao; Zhou, Xiangdong; Guo, Yixuan

2018-04-01

In this paper, data-driven adaptive fractional order proportional integral (AFOPI) control is presented for permanent magnet synchronous motor (PMSM) servo system perturbed by measurement noise and data dropouts. The proposed method directly exploits the closed-loop process data for the AFOPI controller design under unknown noise distribution and data missing probability. Firstly, the proposed method constructs the AFOPI controller tuning problem as a parameter identification problem using the modified l p norm virtual reference feedback tuning (VRFT). Then, iteratively reweighted least squares is integrated into the l p norm VRFT to give a consistent compensation solution for the AFOPI controller. The measurement noise and data dropouts are estimated and eliminated by feedback compensation periodically, so that the AFOPI controller is updated online to accommodate the time-varying operating conditions. Moreover, the convergence and stability are guaranteed by mathematical analysis. Finally, the effectiveness of the proposed method is demonstrated both on simulations and experiments implemented on a practical PMSM servo system. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Formation of helical domain walls in the fractional quantum Hall regime as a step toward realization of high-order non-Abelian excitations

NASA Astrophysics Data System (ADS)

Wu, Tailung; Wan, Zhong; Kazakov, Aleksandr; Wang, Ying; Simion, George; Liang, Jingcheng; West, Kenneth W.; Baldwin, Kirk; Pfeiffer, Loren N.; Lyanda-Geller, Yuli; Rokhinson, Leonid P.

2018-06-01

We propose an experimentally feasible platform to realize parafermions (high-order non-Abelian excitations) based on spin transitions in the fractional quantum Hall effect regime. As a proof of concept we demonstrate a local control of the spin transition at a filling factor 2/3 and formation of a conducting fractional helical domain wall (fhDW) along a gate boundary. Coupled to an s -wave superconductor these fhDWs are expected to support parafermionic excitations. We present exact diagonalization numerical studies of fhDWs and show that they indeed possess electronic and magnetic structures needed for the formation of parafermions. A reconfigurable network of fhDWs will allow manipulation and braiding of parafermionic excitations in multigate devices.

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 novel continuous fractional sliding mode control

NASA Astrophysics Data System (ADS)

Muñoz-Vázquez, A. J.; Parra-Vega, V.; Sánchez-Orta, A.

2017-10-01

A new fractional-order controller is proposed, whose novelty is twofold: (i) it withstands a class of continuous but not necessarily differentiable disturbances as well as uncertainties and unmodelled dynamics, and (ii) based on a principle of dynamic memory resetting of the differintegral operator, it is enforced an invariant sliding mode in finite time. Both (i) and (ii) account for exponential convergence of tracking errors, where such principle is instrumental to demonstrate the closed-loop stability, robustness and a sustained sliding motion, as well as that high frequencies are filtered out from the control signal. The proposed methodology is illustrated with a representative simulation study.

Nonlinear fractional order proportion-integral-derivative active disturbance rejection control method design for hypersonic vehicle attitude control

NASA Astrophysics Data System (ADS)

Song, Jia; Wang, Lun; Cai, Guobiao; Qi, Xiaoqiang

2015-06-01

Near space hypersonic vehicle model is nonlinear, multivariable and couples in the reentry process, which are challenging for the controller design. In this paper, a nonlinear fractional order proportion integral derivative (NFOPIλDμ) active disturbance rejection control (ADRC) strategy based on a natural selection particle swarm (NSPSO) algorithm is proposed for the hypersonic vehicle flight control. The NFOPIλDμ ADRC method consists of a tracking-differentiator (TD), an NFOPIλDμ controller and an extended state observer (ESO). The NFOPIλDμ controller designed by combining an FOPIλDμ method and a nonlinear states error feedback control law (NLSEF) is to overcome concussion caused by the NLSEF and conversely compensate the insufficiency for relatively simple and rough signal processing caused by the FOPIλDμ method. The TD is applied to coordinate the contradiction between rapidity and overshoot. By attributing all uncertain factors to unknown disturbances, the ESO can achieve dynamic feedback compensation for these disturbances and thus reduce their effects. Simulation results show that the NFOPIλDμ ADRC method can make the hypersonic vehicle six-degree-of-freedom nonlinear model track desired nominal signals accurately and fast, has good stability, dynamic properties and strong robustness against external environmental disturbances.

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.

Mitigation of Subsynchronous Resonance with Fractional-order PI based UPFC controller

NASA Astrophysics Data System (ADS)

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

2017-02-01

Due to incorporation of series capacitor compensation in transmission line for stability improvement, subsynchronous oscillations are generated at turbine-generator shaft. These oscillations can damage the shaft system if these are not well suppressed. In order to damp out these oscillations, usually power system network should have sufficient damping and the increase of network damping is obtained by the injection of subsynchronous component of voltage and current into the line, which are extracted from the measured signal of the system. However, the effectiveness of damp out of these subsynchronous oscillations is possibly by incorporating UPFC in the transmission line network is of high interest and it should be further investigated. This research article proposes the mitigation of subsynchronous resonance (SSR) using fractional-order PI (FOPI) based unified power flow controller (UPFC). The robustness of the proposed controller is tested for 25%, 55% and 70% series compensation with a symmetrical fault (L-L-L fault). Further, Eigenvalue analysis and Fast Fourier Transform (FFT) analysis against operating point variations and uncertainties in the system are also examined. The IEEE first benchmark model is adopted for this study and the superiority of the FOPI based UPFC controller over PI based UPFC controller is discussed by comparing the results with various performance indices.

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

Generalized modeling of the fractional-order memcapacitor and its character analysis

NASA Astrophysics Data System (ADS)

Guo, Zhang; Si, Gangquan; Diao, Lijie; Jia, Lixin; Zhang, Yanbin

2018-06-01

Memcapacitor is a new type of memory device generalized from the memristor. This paper proposes a generalized fractional-order memcapacitor model by introducing the fractional calculus into the model. The generalized formulas are studied and the two fractional-order parameter α, β are introduced where α mostly affects the fractional calculus value of charge q within the generalized Ohm's law and β generalizes the state equation which simulates the physical mechanism of a memcapacitor into the fractional sense. This model will be reduced to the conventional memcapacitor as α = 1 , β = 0 and to the conventional memristor as α = 0 , β = 1 . Then the numerical analysis of the fractional-order memcapacitor is studied. And the characteristics and output behaviors of the fractional-order memcapacitor applied with sinusoidal charge are derived. The analysis results have shown that there are four basic v - q and v - i curve patterns when the fractional order α, β respectively equal to 0 or 1, moreover all v - q and v - i curves of the other fractional-order models are transition curves between the four basic patterns.

Comparison between fractionation and bioavailability of trace elements in rhizosphere and bulk soils.

PubMed

Wang, Zhongwen; Shan, Xiao-Quan; Zhang, Shuzhen

2002-03-01

Rhizosphere is a microbiosphere and has quite different chemical, physical and biological properties from bulk soils. A greenhouse experiment was performed to compare the difference of fractionation and bioavailability of trace elements Cr, Ni, Zn, Cu, Pb and Cd between rhizosphere soil and bulk soil. In the meantime, the influence of air-drying on the fractionation and bioavailability was also investigated by using wet soil sample as a control. Soils in a homemade rhizobox were divided into four zones: rhizosphere, near rhizosphere, near bulk soil and bulk soil zones, which was designated as S1, S2, S3 and S4. Elemental speciations were fractionated to water soluble, exchangeable and carbonate bound (B1), Fe-Mn oxide bound (B2), and organic and sulfide bound (B3) by a sequential extraction procedure. Speciation differences were observed for elements Cr, Ni, Zn, Cu, Pb and Cd between the rhizosphere and bulk soils, and between the air-dried and wet soils as well. The concentrations of all six heavy metals in fraction B1 followed the order of S2 > S3 > S1 > S4 and for B2, the order was S2 > S3 S4 > S1. For B3, the order was S1 > S3 S4 > S2, while for Cd the order was S2 > S3 approximately/= S4 > S1. The air-drying increased elemental concentration in fractions B1 and B2 by 20-50% and decreased in fraction B3 by about 20-100%. Correlation analysis also indicated that the bioavailability correlation coefficient of fraction B1 in rhizosphere wet soil to plants was better than that between either air-dried or nonrhizosphere soils. Therefore, application of rhizosphere wet soils should be recommended in the future study on the speciation analysis of trace elements in soils and bioavailability.

Fractional viscoelasticity in fractal and non-fractal media: Theory, experimental validation, and uncertainty analysis

NASA Astrophysics Data System (ADS)

Mashayekhi, Somayeh; Miles, Paul; Hussaini, M. Yousuff; Oates, William S.

2018-02-01

In this paper, fractional and non-fractional viscoelastic models for elastomeric materials are derived and analyzed in comparison to experimental results. The viscoelastic models are derived by expanding thermodynamic balance equations for both fractal and non-fractal media. The order of the fractional time derivative is shown to strongly affect the accuracy of the viscoelastic constitutive predictions. Model validation uses experimental data describing viscoelasticity of the dielectric elastomer Very High Bond (VHB) 4910. Since these materials are known for their broad applications in smart structures, it is important to characterize and accurately predict their behavior across a large range of time scales. Whereas integer order viscoelastic models can yield reasonable agreement with data, the model parameters often lack robustness in prediction at different deformation rates. Alternatively, fractional order models of viscoelasticity provide an alternative framework to more accurately quantify complex rate-dependent behavior. Prior research that has considered fractional order viscoelasticity lacks experimental validation and contains limited links between viscoelastic theory and fractional order derivatives. To address these issues, we use fractional order operators to experimentally validate fractional and non-fractional viscoelastic models in elastomeric solids using Bayesian uncertainty quantification. The fractional order model is found to be advantageous as predictions are significantly more accurate than integer order viscoelastic models for deformation rates spanning four orders of magnitude.

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.

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.

Membrane Capacitive Memory Alters Spiking in Neurons Described by the Fractional-Order Hodgkin-Huxley Model

PubMed Central

Weinberg, Seth H.

2015-01-01

Excitable cells and cell membranes are often modeled by the simple yet elegant parallel resistor-capacitor circuit. However, studies have shown that the passive properties of membranes may be more appropriately modeled with a non-ideal capacitor, in which the current-voltage relationship is given by a fractional-order derivative. Fractional-order membrane potential dynamics introduce capacitive memory effects, i.e., dynamics are influenced by a weighted sum of the membrane potential prior history. However, it is not clear to what extent fractional-order dynamics may alter the properties of active excitable cells. In this study, we investigate the spiking properties of the neuronal membrane patch, nerve axon, and neural networks described by the fractional-order Hodgkin-Huxley neuron model. We find that in the membrane patch model, as fractional-order decreases, i.e., a greater influence of membrane potential memory, peak sodium and potassium currents are altered, and spike frequency and amplitude are generally reduced. In the nerve axon, the velocity of spike propagation increases as fractional-order decreases, while in a neural network, electrical activity is more likely to cease for smaller fractional-order. Importantly, we demonstrate that the modulation of the peak ionic currents that occurs for reduced fractional-order alone fails to reproduce many of the key alterations in spiking properties, suggesting that membrane capacitive memory and fractional-order membrane potential dynamics are important and necessary to reproduce neuronal electrical activity. PMID:25970534

Closed form solutions of two time fractional nonlinear wave equations

NASA Astrophysics Data System (ADS)

Akbar, M. Ali; Ali, Norhashidah Hj. Mohd.; Roy, Ripan

2018-06-01

In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G‧ / G) -expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics.

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.

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…

Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models

NASA Astrophysics Data System (ADS)

Ahmed, E.; El-Sayed, A. M. A.; El-Saka, H. A. A.

2007-01-01

In this paper we are concerned with the fractional-order predator-prey model and the fractional-order rabies model. Existence and uniqueness of solutions are proved. The stability of equilibrium points are studied. Numerical solutions of these models are given. An example is given where the equilibrium point is a centre for the integer order system but locally asymptotically stable for its fractional-order counterpart.

Anaerobic digestion of organic fraction of municipal solid waste combining two pretreatment modalities, high temperature microwave and hydrogen peroxide.

PubMed

Shahriari, Haleh; Warith, Mostafa; Hamoda, Mohamed; Kennedy, Kevin J

2012-01-01

In order to enhance anaerobic digestion (AD) of the organic fraction of municipal solid waste (OFMSW), pretreatment combining two modalities, microwave (MW) heating in presence or absence of hydrogen peroxide (H(2)O(2)) were investigated. The main pretreatment variables affecting the characteristics of the OFMSW were temperature (T) via MW irradiation and supplemental water additions of 20% and 30% (SWA20 and SW30). Subsequently, the focus of this study was to evaluate mesophilic batch AD performance in terms of biogas production, as well as changes in the characteristics of the OFMSW post digestion. A high MW induced temperature range (115-175°C) was applied, using sealed vessels and a bench scale MW unit equipped with temperature and pressure controls. Biochemical methane potential (BMP) tests were conducted on the whole OFMSW as well as the liquid fractions. The whole OFMSW pretreated at 115°C and 145°C showed 4-7% improvement in biogas production over untreated OFMSW (control). When pretreated at 175°C, biogas production decreased due to formation of refractory compounds, inhibiting the digestion. For the liquid fraction of OFMSW, the effect of pretreatment on the cumulative biogas production (CBP) was more pronounced for SWA20 at 145°C, with a 26% increase in biogas production after 8days of digestion, compared to the control. When considering the increased substrate availability in the liquid fraction after MW pretreatment, a 78% improvement in biogas production vs. the control was achieved. Combining MW and H(2)O(2) modalities did not have a positive impact on OFMSW stabilization and enhanced biogas production. In general, all samples pretreated with H(2)O(2) displayed a long lag phase and the CBP was usually lower than MW irradiated only samples. First order rate constant was calculated. Copyright © 2011 Elsevier Ltd. All rights reserved.

Model-order reduction of lumped parameter systems via fractional calculus

NASA Astrophysics Data System (ADS)

Hollkamp, John P.; Sen, Mihir; Semperlotti, Fabio

2018-04-01

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach to the simulation of non-homogeneous systems dictates the use of numerical solutions and often imposes stringent compromises between accuracy and computational performance. Fractional calculus provides an alternative approach where complex dynamical systems can be modeled with compact fractional equations that not only can still guarantee analytical solutions, but can also enable high levels of order reduction without compromising on accuracy. Different approaches are explored in order to transform the integer order model into a reduced order fractional model able to match the dynamic response of the initial system. Analytical and numerical results show that, under certain conditions, an exact match is possible and the resulting fractional differential models have both a complex and frequency-dependent order of the differential operator. The implications of this type of approach for both model order reduction and model synthesis are discussed.

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

Fernandez-Gutierrez, Sulmer, E-mail: sulmer.a.fernandez.gutierrez@intel.com; Browning, Jim; Lin, Ming-Chieh

Phase-control of a magnetron is studied via simulation using a combination of a continuous current source and a modulated current source. The addressable, modulated current source is turned ON and OFF at the magnetron operating frequency in order to control the electron injection and the spoke phase. Prior simulation work using a 2D model of a Rising Sun magnetron showed that the use of 100% modulated current controlled the magnetron phase and allowed for dynamic phase control. In this work, the minimum fraction of modulated current source needed to achieve a phase control is studied. The current fractions (modulated versusmore » continuous) were varied from 10% modulated current to 100% modulated current to study the effects on phase control. Dynamic phase-control, stability, and start up time of the device were studied for all these cases showing that with 10% modulated current and 90% continuous current, a phase shift of 180° can be achieved demonstrating dynamic phase control.« less

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.

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.

Determination of bioactivity of chemical fractions of liquid wastes using freshwater and saltwater algae and crustaceans

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

Walsh, G.E.; Garnas, R.L.

1983-03-01

Complex wastes from industrial and municipal outfalls were fractionated chemically and tested for toxicity with freshwater and saltwater algae and crustaceans. The organic fraction of each waste was subfractionated into acid-, base-, and neutral-extractable portions, and the inorganic fraction was subfractionated into its anion and cation components. All wastes affected growth of the algae Skeletonema costatum (saltwater) and Monoraphidium capricornutum (freshwater) or survival of Mysidopsis bahia (saltwater) and Daphnia magna (freshwater). Usually, bioactivity was limited to one or two subfractions. In some cases, algal growth was stimulated by a fraction or subfraction, whereas stimulation was not detected in whole waste.more » It is suggested that fractionation must be done in order to estimate the full potential impact of complex wastes on aquatic systems. The method can also be used to identify toxic factors before application of cost-effective control technology.« less

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.

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

FAST TRACK COMMUNICATION: Magnetic exchange hardening in polycrystalline GdN thin films

NASA Astrophysics Data System (ADS)

Senapati, K.; Fix, T.; Vickers, M. E.; Blamire, M. G.; Barber, Z. H.

2010-08-01

We report the observation of intrinsic exchange hardening in polycrystalline GdN thin films grown at room temperature by magnetron sputtering. We find, in addition to the ferromagnetic phase, that a fraction of GdN crystallizes in a structural polymorphic form which orders antiferromagnetically. The relative fraction of these two phases was controlled by varying the relative abundance of reactive species in the sputtering plasma by means of the sputtering power and N2 partial pressure. An exchange bias of ~ 30 Oe was observed at 10 K. The exchange coupling between the ferromagnetic and the antiferromagnetic phases resulted in an order of magnitude enhancement in the coercive field in these films.

Spiking and bursting patterns of fractional-order Izhikevich model

NASA Astrophysics Data System (ADS)

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

2018-03-01

Bursting and spiking oscillations play major roles in processing and transmitting information in the brain through cortical neurons that respond differently to the same signal. These oscillations display complex dynamics that might be produced by using neuronal models and varying many model parameters. Recent studies have shown that models with fractional order can produce several types of history-dependent neuronal activities without the adjustment of several parameters. We studied the fractional-order Izhikevich model and analyzed different kinds of oscillations that emerge from the fractional dynamics. The model produces a wide range of neuronal spike responses, including regular spiking, fast spiking, intrinsic bursting, mixed mode oscillations, regular bursting and chattering, by adjusting only the fractional order. Both the active and silent phase of the burst increase when the fractional-order model further deviates from the classical model. For smaller fractional order, the model produces memory dependent spiking activity after the pulse signal turned off. This special spiking activity and other properties of the fractional-order model are caused by the memory trace that emerges from the fractional-order dynamics and integrates all the past activities of the neuron. On the network level, the response of the neuronal network shifts from random to scale-free spiking. Our results suggest that the complex dynamics of spiking and bursting can be the result of the long-term dependence and interaction of intracellular and extracellular ionic currents.

New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis.

PubMed

Ingo, Carson; Magin, Richard L; Parrish, Todd B

2014-11-01

Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establishing the utility of fractional order models, we apply entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation, in the form of the Mittag-Leffler function, gives an entropy minimum for the integer case of Gaussian diffusion and greater values of spectral entropy for non-integer values of the space and time derivatives. Furthermore, we consider kurtosis, defined as the normalized fourth moment, as another probabilistic description of the fractional time derivative. Finally, we demonstrate the implementation of anomalous diffusion, entropy and kurtosis measurements in diffusion weighted magnetic resonance imaging in the brain of a chronic ischemic stroke patient.

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.

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.

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.

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.

Calcium and strontium isotope fractionation in aqueous solutions as a function of temperature and reaction rate; I. Calcite

NASA Astrophysics Data System (ADS)

AlKhatib, Mahmoud; Eisenhauer, Anton

2017-07-01

In order to study Strontium (Sr) partitioning and isotope fractionation of Sr and Calcium (Ca) in calcite we performed precipitation (T) experiments decoupling temperature and precipitation rate (R∗). Calcite was precipitated at 12.5, 25.0 and 37.5 °C by diffusing NH3 and CO2 gases into aqueous solutions closely following the experimental setup of Lemarchand et al. (2004). The precipitation rate (R∗) for every sample was determined applying the initial rate method and from the specific surface area of almost all samples for each reaction. The order of reaction with respect to Ca2+ ions was determined to be one and independent of T. However, the order of reaction with respect to HCO3- changed from three to one as temperature increases from 12.5, 25 °C and 37.5 °C. Strontium incorporated into calcite (expressed as DSr = [Sr/Ca]calcite/[Sr/Ca]solution) was found to be R∗ and T dependent. As a function of increasing R∗ the Δ88/86Sr-values become more negative and as temperature increases the Δ88/86Sr values also increase at constant R∗. The DSr and Δ88/86Sr-values are correlated to a high degree and depend only on R∗ being independent of temperature, complexation and varying initial ratios. Latter observation may have important implications for the study of diagenesis, the paleo-sciences and the reconstruction of past environmental conditions. Calcium isotope fractionation (Δ44/40Ca) was also found to be R∗ and T dependent. For 12.5 and 25.0 °C we observe a general increase of the Δ44/40Ca values as a function of R∗ (Lemarchand et al. type behavior, Lemarchand et al. (2004)). Whereas at 37.5 °C a significant decreasing Δ44/40Ca is observed relative to increasing R∗ (Tang et al. type behavior, Tang et al. (2008)). In order to reconcile the discrepant observations we suggest that the temperature triggered change from a Ca2+-NH3-aquacomplex covalent controlled bonding to a Ca2+-H2O-aquacomplex van-der-Waals controlled bonding caused the change in sign of the R∗ - Δ44/40Ca slope due to the switch of an equilibrium type of isotope fractionation related to the covalent bonding during lower temperatures to a kinetic type of isotope fractionation at higher temperatures. This is supported by the observation that the Δ44/40Ca ratios tend to depend on the [Ca]:[DIC] ratio at 12.5 and 25 °C but is highly independent at 37.5 °C. Our observations imply the chemical fluid composition and temperature dependent complexation controls the amount and direction of Ca isotope fractionation in contrast to the Sr isotopes which do not show any change of its fractionation behavior as a function of complexation in the liquid phase.

Mixed H ∞ and Passive Projective Synchronization for Fractional Order Memristor-Based Neural Networks with Time-Delay and Parameter Uncertainty

NASA Astrophysics Data System (ADS)

Song, Xiao-Na; Song, Shuai; Tejado Balsera, Inés; Liu, Lei-Po

2017-10-01

This paper investigates the mixed H ∞ and passive projective synchronization problem for fractional-order (FO) memristor-based neural networks. Our aim is to design a controller such that, though the unavoidable phenomena of time-delay and parameter uncertainty are fully considered, the resulting closed-loop system is asymptotically stable with a mixed H ∞ and passive performance level. By combining active and adaptive control methods, a novel hybrid control strategy is designed, which can guarantee the robust stability of the closed-loop system and also ensure a mixed H ∞ and passive performance level. Via the application of FO Lyapunov stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequality techniques. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method. Supported by National Natural Science Foundation of China under Grant Nos. U1604146, U1404610, 61473115, 61203047, Science and Technology Research Project in Henan Province under Grant Nos. 152102210273, 162102410024, and Foundation for the University Technological Innovative Talents of Henan Province under Grant No. 18HASTIT019

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.

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.

Role of real-space micromotion for bosonic and fermionic Floquet fractional Chern insulators

NASA Astrophysics Data System (ADS)

Anisimovas, Egidijus; Žlabys, Giedrius; Anderson, Brandon M.; JuzeliÅ«nas, Gediminas; Eckardt, André

2015-06-01

Fractional Chern insulators are the proposed phases of matter mimicking the physics of fractional quantum Hall states on a lattice without an overall magnetic field. The notion of Floquet fractional Chern insulators refers to the potential possibilities to generate the underlying topological band structure by means of Floquet engineering. In these schemes, a highly controllable and strongly interacting system is periodically driven by an external force at a frequency such that double tunneling events during one forcing period become important and contribute to shaping the required effective energy bands. We show that in the described circumstances it is necessary to take into account also third order processes combining two tunneling events with interactions. Referring to the obtained contributions as micromotion-induced interactions, we find that those interactions tend to have a negative impact on the stability of fractional Chern insulating phases and discuss implications for future experiments.

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

Fractional-order in a macroeconomic dynamic model

NASA Astrophysics Data System (ADS)

David, S. A.; Quintino, D. D.; Soliani, J.

2013-10-01

In this paper, we applied the Riemann-Liouville approach in order to realize the numerical simulations to a set of equations that represent a fractional-order macroeconomic dynamic model. It is a generalization of a dynamic model recently reported in the literature. The aforementioned equations have been simulated for several cases involving integer and non-integer order analysis, with some different values to fractional order. The time histories and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the macroeconomic dynamic model proposed here involves the public sector deficit equation, which renders the model more realistic and complete when compared with the ones encountered in the literature. The results reveal that the fractional-order macroeconomic model can exhibit a real reasonable behavior to macroeconomics systems and might offer greater insights towards the understanding of these complex dynamic systems.

Fractionation of persistent organic pollutants in fish oil by high-performance liquid chromatography on a 2-(1-pyrenyl)ethyl silica column.

PubMed

Ortiz, X; Martí, R; Montaña, M J; Gasser, M; Margarit, L; Broto, F; Díaz-Ferrero, J

2010-09-01

The analysis of persistent organic pollutants in foodstuffs has become necessary for control of their levels in products for human and animal consumption. These analytical procedures usually require a fractionation step in order to separate the different families of pollutants to avoid interferences during the instrumental determination. In this study the separation was carried out on a 2-(1-pyrenyl)ethyl silica column, where analyte fractionation was based on differences in planarity and aromaticity. The fractionation of several types of persistent organic pollutants found in fish oil samples was studied; the pollutants included polychlorinated dibenzo-p-dioxins and dibenzofurans, polychlorinated biphenyls, polybrominated diphenyl ethers, and some organochlorine pesticides. Fractions were analyzed by high-resolution gas chromatography with electron-capture detection and high-resolution gas chromatography-high resolution mass spectroscopy. Finally, the whole method (including the purification, fractionation, and instrumental determination steps) was validated and successfully applied to the analysis of several samples of fish oil.

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.

Global synchronization in finite time for fractional-order neural networks with discontinuous activations and time delays.

PubMed

Peng, Xiao; Wu, Huaiqin; Song, Ka; Shi, Jiaxin

2017-10-01

This paper is concerned with the global Mittag-Leffler synchronization and the synchronization in finite time for fractional-order neural networks (FNNs) with discontinuous activations and time delays. Firstly, the properties with respect to Mittag-Leffler convergence and convergence in finite time, which play a critical role in the investigation of the global synchronization of FNNs, are developed, respectively. Secondly, the novel state-feedback controller, which includes time delays and discontinuous factors, is designed to realize the synchronization goal. By applying the fractional differential inclusion theory, inequality analysis technique and the proposed convergence properties, the sufficient conditions to achieve the global Mittag-Leffler synchronization and the synchronization in finite time are addressed in terms of linear matrix inequalities (LMIs). In addition, the upper bound of the setting time of the global synchronization in finite time is explicitly evaluated. Finally, two examples are given to demonstrate the validity of the proposed design method and theoretical results. Copyright © 2017 Elsevier Ltd. All rights reserved.

A new medical image segmentation model based on fractional order differentiation and level set

NASA Astrophysics Data System (ADS)

Chen, Bo; Huang, Shan; Xie, Feifei; Li, Lihong; Chen, Wensheng; Liang, Zhengrong

2018-03-01

Segmenting medical images is still a challenging task for both traditional local and global methods because the image intensity inhomogeneous. In this paper, two contributions are made: (i) on the one hand, a new hybrid model is proposed for medical image segmentation, which is built based on fractional order differentiation, level set description and curve evolution; and (ii) on the other hand, three popular definitions of Fourier-domain, Grünwald-Letnikov (G-L) and Riemann-Liouville (R-L) fractional order differentiation are investigated and compared through experimental results. Because of the merits of enhancing high frequency features of images and preserving low frequency features of images in a nonlinear manner by the fractional order differentiation definitions, one fractional order differentiation definition is used in our hybrid model to perform segmentation of inhomogeneous images. The proposed hybrid model also integrates fractional order differentiation, fractional order gradient magnitude and difference image information. The widely-used dice similarity coefficient metric is employed to evaluate quantitatively the segmentation results. Firstly, experimental results demonstrated that a slight difference exists among the three expressions of Fourier-domain, G-L, RL fractional order differentiation. This outcome supports our selection of one of the three definitions in our hybrid model. Secondly, further experiments were performed for comparison between our hybrid segmentation model and other existing segmentation models. A noticeable gain was seen by our hybrid model in segmenting intensity inhomogeneous images.

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.

Activation of tissue kallikrein-kininogen-kinin system in rabbit skin by a fraction isolated from Phoneutria nigriventer (armed spider) venom.

PubMed

Antunes, E; Marangoni, R A; Giglio, J R; Brain, S D; de Nucci, G

1993-11-01

Phoneutria nigriventer venom was fractionated by gel filtration followed by ion-exchange chromatography from which 16 fractions (I-XVI) were obtained and assayed in rabbit skin in order to identify those responsible for the increased vascular permeability observed with the whole venom. The fractions, and control mediators (tissue kallikrein, bradykinin and histamine) were intradermally injected in male New Zealand white rabbits. Local oedema formation was measured as the local accumulation of i.v. injected 125I-human serum albumin into skin sites. Fraction XIII was the only fraction assayed which significantly induced oedema formation. Fraction XIII-induced oedema was greatly reduced by either the protease inhibitor aprotinin or the bradykinin B2 receptor antagonist D-Arg,[Hyp3,Thi5,8D-Phe7]-Bk, whereas the plasma kallikrein inhibitor soybean trypsin inhibitor failed to significantly affect this oedematogenic response. The kininase II inhibitor captopril markedly potentiated fraction XIII-induced oedema. Our results indicate that the increased vascular permeability induced by fraction XIII is due to local generation of kinins in response to tissue (but not plasma) kallikrein-kinin system activation.

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.

Tuning rules for robust FOPID controllers based on multi-objective optimization with FOPDT models.

PubMed

Sánchez, Helem Sabina; Padula, Fabrizio; Visioli, Antonio; Vilanova, Ramon

2017-01-01

In this paper a set of optimally balanced tuning rules for fractional-order proportional-integral-derivative controllers is proposed. The control problem of minimizing at once the integrated absolute error for both the set-point and the load disturbance responses is addressed. The control problem is stated as a multi-objective optimization problem where a first-order-plus-dead-time process model subject to a robustness, maximum sensitivity based, constraint has been considered. A set of Pareto optimal solutions is obtained for different normalized dead times and then the optimal balance between the competing objectives is obtained by choosing the Nash solution among the Pareto-optimal ones. A curve fitting procedure has then been applied in order to generate suitable tuning rules. Several simulation results show the effectiveness of the proposed approach. Copyright © 2016. Published by Elsevier Ltd.

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.

Onset of fractional-order thermal convection in porous media

NASA Astrophysics Data System (ADS)

Karani, Hamid; Rashtbehesht, Majid; Huber, Christian; Magin, Richard L.

2017-12-01

The macroscopic description of buoyancy-driven thermal convection in porous media is governed by advection-diffusion processes, which in the presence of thermophysical heterogeneities fail to predict the onset of thermal convection and the average rate of heat transfer. This work extends the classical model of heat transfer in porous media by including a fractional-order advective-dispersive term to account for the role of thermophysical heterogeneities in shifting the thermal instability point. The proposed fractional-order model overcomes limitations of the common closure approaches for the thermal dispersion term by replacing the diffusive assumption with a fractional-order model. Through a linear stability analysis and Galerkin procedure, we derive an analytical formula for the critical Rayleigh number as a function of the fractional model parameters. The resulting critical Rayleigh number reduces to the classical value in the absence of thermophysical heterogeneities when solid and fluid phases have similar thermal conductivities. Numerical simulations of the coupled flow equation with the fractional-order energy model near the primary bifurcation point confirm our analytical results. Moreover, data from pore-scale simulations are used to examine the potential of the proposed fractional-order model in predicting the amount of heat transfer across the porous enclosure. The linear stability and numerical results show that, unlike the classical thermal advection-dispersion models, the fractional-order model captures the advance and delay in the onset of convection in porous media and provides correct scalings for the average heat transfer in a thermophysically heterogeneous medium.

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.

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.

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.

Extremely low order time-fractional differential equation and application in combustion process

NASA Astrophysics Data System (ADS)

Xu, Qinwu; Xu, Yufeng

2018-11-01

Fractional blow-up model, especially which is of very low order of fractional derivative, plays a significant role in combustion process. The order of time-fractional derivative in diffusion model essentially distinguishes the super-diffusion and sub-diffusion processes when it is relatively high or low accordingly. In this paper, the blow-up phenomenon and condition of its appearance are theoretically proved. The blow-up moment is estimated by using differential inequalities. To numerically study the behavior around blow-up point, a mixed numerical method based on adaptive finite difference on temporal direction and highly effective discontinuous Galerkin method on spatial direction is proposed. The time of blow-up is calculated accurately. In simulation, we analyze the dynamics of fractional blow-up model under different orders of fractional derivative. It is found that the lower the order, the earlier the blow-up comes, by fixing the other parameters in the model. Our results confirm the physical truth that a combustor for explosion cannot be too small.

Biologically important compounds in synfuels processes

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

Clark, B R; Ho, C; Griest, W H

1980-01-01

Crude products, by-products and wastes from synfuel processes contain a broad spectrum of chemical compounds - many of which are active in biological systems. Discerning which compound classes are most important is necessary in order to establish effective control over release or exposure. Polycyclic aromatic hydrocarbons (PAH), multialkylated PAH, primary aromatic amines and N-heterocyclic PAH are significant contributors to the overall mutagenic activities of a large number of materials examined. Ames test data show that the basic, primary aromatic amine fraction is the most active. PAHs, multialkylated PAHs and N-heterocyclic PAHs are all components of the neutral fraction. In nearlymore » all cases, the neutral fractions contribute the largest portion of the mutagenic activity, while the basic primary aromatic amine fractions have the highest specific activity. Neutral fractions are usually the largest (wt %) whereas the total basic fractions are small by comparison; thus, the overall greater contribution of the neutral fraction to the mutagenic activity of most samples. Biologically active constituents are isolated in preparative scale amounts from complex mixtures utilizing combinations of liquid-liquid extraction and various liquid chromatographic column-eluant combinations. Fractions are characterized using a combination of spectroscopic techniques and gas chromatography/mass spectrometry.« less

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.

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.

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.

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.

Numerical Simulation Analysis of High-precision Dispensing Needles for Solid-liquid Two-phase Grinding

NASA Astrophysics Data System (ADS)

Li, Junye; Hu, Jinglei; Wang, Binyu; Sheng, Liang; Zhang, Xinming

2018-03-01

In order to investigate the effect of abrasive flow polishing surface variable diameter pipe parts, with high precision dispensing needles as the research object, the numerical simulation of the process of polishing high precision dispensing needle was carried out. Analysis of different volume fraction conditions, the distribution of the dynamic pressure and the turbulence viscosity of the abrasive flow field in the high precision dispensing needle, through comparative analysis, the effectiveness of the abrasive grain polishing high precision dispensing needle was studied, controlling the volume fraction of silicon carbide can change the viscosity characteristics of the abrasive flow during the polishing process, so that the polishing quality of the abrasive grains can be controlled.

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.

H2 Ortho-to-para Conversion on Grains: A Route to Fast Deuterium Fractionation in Dense Cloud Cores?

NASA Astrophysics Data System (ADS)

Bovino, S.; Grassi, T.; Schleicher, D. R. G.; Caselli, P.

2017-11-01

Deuterium fractionation, I.e., the enhancement of deuterated species with respect to non-deuterated ones, is considered to be a reliable chemical clock of star-forming regions. This process is strongly affected by the ortho-to-para H2 ratio. In this Letter we explore the effect of the ortho-para (o-p) H2 conversion on grains on the deuteration timescale in fully-depleted dense cores, including the most relevant uncertainties that affect this complex process. We show that (I) the o-p H2 conversion on grains is not strongly influenced by the uncertainties on the conversion time and the sticking coefficient, and (II) that the process is controlled by the temperature and the residence time of ortho-H2 on the surface, I.e., by the binding energy. We find that for binding energies between 330 and 550 K, depending on the temperature, the o-p H2 conversion on grains can shorten the deuterium fractionation timescale by orders of magnitude, opening a new route for explaining the large observed deuteration fraction D frac in dense molecular cloud cores. Our results suggest that the star formation timescale, when estimated through the timescale to reach the observed deuteration fractions, might be shorter than previously proposed. However, more accurate measurements of the binding energy are needed in order to better assess the overall role of this process.

Fault-tolerant Control of a Cyber-physical System

NASA Astrophysics Data System (ADS)

Roxana, Rusu-Both; Eva-Henrietta, Dulf

2017-10-01

Cyber-physical systems represent a new emerging field in automatic control. The fault system is a key component, because modern, large scale processes must meet high standards of performance, reliability and safety. Fault propagation in large scale chemical processes can lead to loss of production, energy, raw materials and even environmental hazard. The present paper develops a multi-agent fault-tolerant control architecture using robust fractional order controllers for a (13C) cryogenic separation column cascade. The JADE (Java Agent DEvelopment Framework) platform was used to implement the multi-agent fault tolerant control system while the operational model of the process was implemented in Matlab/SIMULINK environment. MACSimJX (Multiagent Control Using Simulink with Jade Extension) toolbox was used to link the control system and the process model. In order to verify the performance and to prove the feasibility of the proposed control architecture several fault simulation scenarios were performed.

Left ventricular ejection fraction may not be useful as an end point of thrombolytic therapy comparative trials.

PubMed

Califf, R M; Harrelson-Woodlief, L; Topol, E J

1990-11-01

In the era of comparative and adjunctive trials in reperfusion therapy, the need to develop alternative end points for mortality reduction is clear. Left ventricular ejection fraction, which has been commonly used as a surrogate, is problematic due to missing values, technically inadequate studies, and lack of correlation with mortality results in controlled reperfusion trials performed to date. In this paper, we present a composite clinical end point that includes, in order, severity of adverse outcome death, hemorrhagic stroke, nonhemorrhagic stroke, poor ejection fraction (less than 30%), reinfarction, heart failure, and pulmonary edema. Such a composite index may be useful to detect true therapeutic benefit in reperfusion trials without necessitating greater than 20-30,000 patient enrollment.

Phosphorus content in three physical fractions of typical Chernozem

NASA Astrophysics Data System (ADS)

Kotelnikova, Anna; Egorova, Zoya; Sushkov, Nikolai; Matveeva, Natalia; Fastovets, Ilya; Rogova, Olga; Volkov, Dmitriy

2017-04-01

The widespread use of fertilizers makes it necessary to study not only the content but also the forms of occurrence of nutrients in soil, as well as the phase in which nutrients are transferred. These characteristics determine the availability of chemical elements for plants, but remain insufficiently studied. In this work we attempted to gain insight into the distribution of organo-mineral fractions in agriculturally used Chernozem from Voronezh (Russia) and the distribution of phosphorus - one of the most important nutrient elements - in this type of soil. We compared the distributions of phosphorus in physical fractions of the soil in 3 experimental groups: the control group (without fertilizers), the group fertilized with 1 dose of NPK, and the group fertilized with 2 doses of NPK. The soil was sampled during the period of treatment with fertilizers and during the period of aftereffect (4 years after the last application of fertilizers). In order to analyze organo-mineral fractions, we used size-density fractionation to separate the soil samples into three physical fractions: clay-associated fraction with particle size < 1μm (CF), light fraction with particle density < 2.0 g cm-3 (LF), and residual fraction > 2.0 g cm-3 (RF). Total phosphorus content (TPC) in the fractions was determined with Agilent 5100 ICP-AES spectrometer. To compare groups, simultaneous confidence intervals were computed from pooled variance estimators in ANOVA, and Fisher's LSD test was used. We showed that during the period of treatment with fertilizers LF increased proportionally to the dose of fertilizers, and a simultaneous reduction in RF was observed. During the period of aftereffect, the content of these fractions tended to the control value. The increase of LF may indicate increasing availability of nutrients, since this fraction is likely to participate in biological cycles. The analysis of TPC in fractions suggested that during the period of treatment with fertilizers most of phosphorus accumulates in CF. In the group with double dose of fertilizers TPC in CF was more than 1.5 times higher than in the control, while for LF the increase in TPC was not significant, and RF TPC was practically the same as in the control. Association of phosphorus predominantly with CF suggests that phosphorus was mainly adsorbed to the surface of clay particles rather than to organic components. Therefore, despite the increase in CF TPC as a consequence of treatment with fertilizers, the increase in availability of phosphorus is questionable. In the aftereffect period no significant differences in TPC were found. In conclusion, we showed that availability of fertilizers may be dependent on fractional composition of soil. Under our experimental conditions, phosphorus tended to bind predominantly to clay particles. However, in the aftereffect period, fractionation of TPC was similar to the control, indicating the need to further investigate the fate of phosphorus in soils.

Order - disorder transitions in granular sphere packings

NASA Astrophysics Data System (ADS)

Panaitescu, Andreea M.

Granular materials are ubiquitous in many industrial and natural processes, yet their complex behaviors characterized by unusual static and dynamic properties are still poorly understood. In this dissertation we investigate both the geometrical structure and the dynamical properties (the response to shear deformations, disorder-order transition and crystallization) of packings of mono-sized spheres as a function of the packing volume fraction. Different average packing fractions were obtained by submitting a dense granular material to periodic shear deformations and by epitaxy. Using advanced imaging techniques including the refractive index matched imaging (RIM) and X-ray computed tomography (CT) enables us to determine the three dimensional particles position inside the packing. From positions we obtain the Voronoi tessellation corresponding to the particles in the bulk and calculate the radial distribution and the bond-order metric. These two parameters are widely used to quantify the structure of the spherical particle systems. A granular packing undergoing periodic shear deformations is observed to slowly evolve towards crystallization and the packing fraction is correspondingly observed to increase smoothly from loose packing fraction, 0.59, well above the random close packing fraction, 0.637. Tracking the particles over several shear cycles allows us to obtain the probability distributions of particle displacements and the mean-square displacements and to compute the components of the diffusion tensor. We find that in a shear flow, the initial self-diffusion of the particles is anisotropic with diffusion greater in the flow direction compared with the velocity gradient direction which in turn is greater than in the vorticity direction. We further find that the granular matter under cyclic shear shows reversible as well as irreversible or plastic response for small enough strain amplitude. The appearance and the propagation of the crystalline order were studied using the orientational order metric. By following the evolution of the nucleating crystallites, we identified critical nuclei, determined their size and symmetry, and measured the average surface free energy. The structure of the nuclei was found to be random hexagonal close-packed, their average shape was non-spherical and they were oriented preferentially along the shear axis. When the packing volume fraction approaches a value close to the random close packing, crystallites with face centered cubic (fcc) order are observed with increasing probability, and ordered domains grow rapidly. A polycrystalline phase with domains of fcc and hcp order is obtained after hundreds of thousands of shear cycles. Depositing spheres on a substrate under the influence of gravity gives rise to a wide range of volume fractions and packing structures by simply controlling the nature of the substrate, the deposition rate and the energy of the particles. We analyzed the structures formed and investigate the development of the disordered phases as a function of the deposition rate. Furthermore, by comparing these structures with packings obtained by cyclic shear we showed that the structure of a granular packing depends strongly on the protocol used.

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.

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.

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.

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.

The role of control groups in mutagenicity studies: matching biological and statistical relevance.

PubMed

Hauschke, Dieter; Hothorn, Torsten; Schäfer, Juliane

2003-06-01

The statistical test of the conventional hypothesis of "no treatment effect" is commonly used in the evaluation of mutagenicity experiments. Failing to reject the hypothesis often leads to the conclusion in favour of safety. The major drawback of this indirect approach is that what is controlled by a prespecified level alpha is the probability of erroneously concluding hazard (producer risk). However, the primary concern of safety assessment is the control of the consumer risk, i.e. limiting the probability of erroneously concluding that a product is safe. In order to restrict this risk, safety has to be formulated as the alternative, and hazard, i.e. the opposite, has to be formulated as the hypothesis. The direct safety approach is examined for the case when the corresponding threshold value is expressed either as a fraction of the population mean for the negative control, or as a fraction of the difference between the positive and negative controls.

Minutes: Accredited Standards Committee on Acoustics, S1 U.S. Tag for ISO/TC43 Acoustics and IEC/TC29 Electroacoustics

DTIC Science & Technology

1991-05-02

international arena with respect to noise control technology and noise environmental quality In order to give you soma background into the work of the...14 a) A new working groug _S1/WG2Q Ground Impedance................ 14 b) Air Movement and Control Association. Inc. (AMCA...the Air Movement and Control Association (AMCA) on their inquiries concerning ANSI S1.11-1986 Specification for octave-band and fractional-octave-band

Global bifurcations in fractional-order chaotic systems with an extended generalized cell mapping method

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

Liu, Xiaojun; School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001; Hong, Ling, E-mail: hongling@mail.xjtu.edu.cn

Global bifurcations include sudden changes in chaotic sets due to crises. There are three types of crises defined by Grebogi et al. [Physica D 7, 181 (1983)]: boundary crisis, interior crisis, and metamorphosis. In this paper, by means of the extended generalized cell mapping (EGCM), boundary and interior crises of a fractional-order Duffing system are studied as one of the system parameters or the fractional derivative order is varied. It is found that a crisis can be generally defined as a collision between a chaotic basic set and a basic set, either periodic or chaotic, to cause a sudden discontinuousmore » change in chaotic sets. Here chaotic sets involve three different kinds: a chaotic attractor, a chaotic saddle on a fractal basin boundary, and a chaotic saddle in the interior of a basin and disjoint from the attractor. A boundary crisis results from the collision of a periodic (or chaotic) attractor with a chaotic (or regular) saddle in the fractal (or smooth) boundary. In such a case, the attractor, together with its basin of attraction, is suddenly destroyed as the control parameter passes through a critical value, leaving behind a chaotic saddle in the place of the original attractor and saddle after the crisis. An interior crisis happens when an unstable chaotic set in the basin of attraction collides with a periodic attractor, which causes the appearance of a new chaotic attractor, while the original attractor and the unstable chaotic set are converted to the part of the chaotic attractor after the crisis. These results further demonstrate that the EGCM is a powerful tool to reveal the mechanism of crises in fractional-order systems.« less

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.

(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.

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.

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.

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.

Finite-time stability and synchronization of memristor-based fractional-order fuzzy cellular neural networks

NASA Astrophysics Data System (ADS)

Zheng, Mingwen; Li, Lixiang; Peng, Haipeng; Xiao, Jinghua; Yang, Yixian; Zhang, Yanping; Zhao, Hui

2018-06-01

This paper mainly studies the finite-time stability and synchronization problems of memristor-based fractional-order fuzzy cellular neural network (MFFCNN). Firstly, we discuss the existence and uniqueness of the Filippov solution of the MFFCNN according to the Banach fixed point theorem and give a sufficient condition for the existence and uniqueness of the solution. Secondly, a sufficient condition to ensure the finite-time stability of the MFFCNN is obtained based on the definition of finite-time stability of the MFFCNN and Gronwall-Bellman inequality. Thirdly, by designing a simple linear feedback controller, the finite-time synchronization criterion for drive-response MFFCNN systems is derived according to the definition of finite-time synchronization. These sufficient conditions are easy to verify. Finally, two examples are given to show the effectiveness of the proposed results.

IONIC EFFECTS ON LIGNIFICATION AND PEROXIDASE IN TISSUE CULTURES

PubMed Central

Lipetz, Jacques; Garro, Anthony J.

1965-01-01

Crown-gall tumor tissue cultures release peroxidase into the medium in response to the concentration of specific ions in the medium. This release is not due to diffusion from cut surfaces or injured cells. Calcium, magnesium, and ammonium were, in that order, most effective in increasing peroxidase release. The enzyme was demonstrated cytochemically on the cell walls and in the cytoplasm. Cell wall fractions, exhaustively washed in buffer, still contained bound peroxidase. This bound peroxidase could be released by treating the wall fractions with certain divalent cations or ammonium. The order of effectiveness for removing the enzyme from the washed cell walls is: Ca++ ≈ Sr++ > Ba++ > Mg++ > NH4 +. These data support the thesis presented that specific ions can control the deposition of lignin on cell walls by affecting the peroxidase levels on these walls. PMID:19866650

Dispersant use as a response to oil spills: toxicological effects on fish cardiac performance.

PubMed

Milinkovitch, Thomas; Thomas-Guyon, Hélène; Lefrançois, Christel; Imbert, Nathalie

2013-04-01

Dispersant use is a controversial technique used to respond to oil spills in nearshore areas. In order to assess the toxicity of this technique, this study evaluated the cardiac toxicological effects on juvenile golden grey mullets Liza aurata exposed for 48 h to either dispersant alone, chemically dispersed oil, mechanically dispersed oil, the water-soluble fraction of oil or a control condition. Following exposure, the positive inotropic effects of adrenaline were assessed in order to evaluate a potential impairment on the cardiac performance. The results revealed an impairment of the positive inotropic effects of adrenaline for all the contaminants (single dispersant, dispersed and undispersed oil, water-soluble fraction of oil). This suggests that: (1) cardiac performance is a valuable parameter to study the physiopathological effects of dispersed oil; (2) dispersant application is likely to impair cardiac performance.

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.

Radiation effects on bovine taste bud membranes

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

Shatzman, A.R.; Mossman, K.L.

1982-11-01

In order to investigate the mechanisms of radiation-induced taste loss, the effects of radiation on preparations of enriched bovine taste bud membranes were studied. Taste buds containing circumvallate papilae, and surrounding control epithelial tissues devoid of taste buds, were obtained from steers and given radiation doses of 0-7000 cGy (rad). Tissue fractions were isolated into membrane-enriched and heterogeneous components using differential and sucrose gradient centrifugation of tissue homogenates. The yield of membranes, as measured by protein content in the buoyant membrane-enriched fractions, was reduced in quantity with increasing radiation dose. The relation between radiation dose and membrane quantity in membrane-enrichedmore » fractions could be fit by a simple exponential model with taste bud-derived membranes twice as radiosensitive as membranes from control epithelial tissue. Binding of sucrose, sodium, and acetate and fluoride stimulation of adenylate cyclase were nearly identical in both irradiated and nonirradiated intact membranes. Radiation had no effect on fractions of heterogeneous components. While it is not clear what changes are occurring in enriched taste cell membranes, damage to membranes may play an important role in the taste loss observed in patients following radiotherapy.« less

Fate and Distribution of Heavy Metals in Wastewater Irrigated Calcareous Soils

PubMed Central

Stietiya, Mohammed Hashem; Duqqah, Mohammad; Udeigwe, Theophilus; Zubi, Ruba; Ammari, Tarek

2014-01-01

Accumulation of heavy metals in Jordanian soils irrigated with treated wastewater threatens agricultural sustainability. This study was carried out to investigate the environmental fate of Zn, Ni, and Cd in calcareous soils irrigated with treated wastewater and to elucidate the impact of hydrous ferric oxide (HFO) amendment on metal redistribution among soil fractions. Results showed that sorption capacity for Zarqa River (ZR1) soil was higher than Wadi Dhuleil (WD1) soil for all metals. The order of sorption affinity for WD1 was in the decreasing order of Ni > Zn > Cd, consistent with electrostatic attraction and indication of weak association with soil constituents. Following metal addition, Zn and Ni were distributed among the carbonate and Fe/Mn oxide fractions, while Cd was distributed among the exchangeable and carbonate fractions in both soils. Amending soils with 3% HFO did not increase the concentration of metals associated with the Fe/Mn oxide fraction or impact metal redistribution. The study suggests that carbonates control the mobility and bioavailability of Zn, Ni, and Cd in these calcareous soils, even in presence of a strong adsorbent such as HFO. Thus, it can be inferred that in situ heavy metal remediation of these highly calcareous soils using iron oxide compounds could be ineffective. PMID:24723833

FRACTIONATING COLUMN PRODUCT COLLECTOR CONTROL

DOEpatents

Paxson, G.D. Jr.

1964-03-10

Means for detecting minute fluid products from a chemical separation column and for advancing a collector tube rack in order to automatically separate and collect successive fractionated products are described. A charge is imposed on the forming drops at the column orifice to create an electric field as the drop falls in the vicinity of a sensing plate. The field is detected by an electrometer tube coupled to the plate causing an output signal to actuate rotation of a collector turntable rack, thereby positioning new collectors under the orifice. The invention provides reliable automatic collection independent of drop size, rate of fall, or chemical composition. (AEC)

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.

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.

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.

Fractal Physiology and the Fractional Calculus: A Perspective

PubMed Central

West, Bruce J.

2010-01-01

This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process. Control of physiologic complexity is one of the goals of medicine, in particular, understanding and controlling physiological networks in order to ensure their proper operation. We emphasize the difference between homeostatic and allometric control mechanisms. Homeostatic control has a negative feedback character, which is both local and rapid. Allometric control, on the other hand, is a relatively new concept that takes into account long-time memory, correlations that are inverse power law in time, as well as long-range interactions in complex phenomena as manifest by inverse power-law distributions in the network variable. We hypothesize that allometric control maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can often be described using the fractional calculus to capture the dynamics of complex physiologic networks. PMID:21423355

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

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.

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.

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.

Characterization of pea (Pisum sativum) seed protein fractions.

PubMed

Rubio, Luis A; Pérez, Alicia; Ruiz, Raquel; Guzmán, M Ángeles; Aranda-Olmedo, Isabel; Clemente, Alfonso

2014-01-30

Legume seed proteins have to be chemically characterized in order to properly link their nutritional effects with their chemical structure. Vicilin and albumin fractions devoid of cross-contamination, as assessed by mass peptide fingerprinting analysis, were obtained from defatted pea (Pisum sativum cv. Bilbo) meal. The extracted protein fractions contained 56.7-67.7 g non-starch polysaccharides kg⁻¹. The vicilin fraction was higher than legumins in arginine, isoleucine, leucine, phenylalanine and lysine. The most abundant amino acids in the albumin fraction were aspartic acid, glutamic acid, lysine and arginine, and the amounts of methionine were more than double than those in legumins and vicilins. The pea albumin fraction showed a clear enrichment of protease inhibitory activity when compared with the seed meal. In vitro digestibility values for pea proteins were 0.63 ±  0.04, 0.88 ±  0.04 and 0.41 ±  0.23 for legumins, vicilins and albumins respectively. Vicilin and albumin fractions devoid of cross-contamination with other proteins were obtained from pea seed meal. The vicilin fraction also contained low amounts of soluble non-starch polysaccharides and was enriched in isoleucine, leucine, phenylalanine and lysine. In vitro digestibility values for pea proteins were similar or even numerically higher than those for control proteins. © 2013 Society of Chemical Industry.

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.

Simulation of hydrodynamics using large eddy simulation-second-order moment model in circulating fluidized beds

NASA Astrophysics Data System (ADS)

Juhui, Chen; Yanjia, Tang; Dan, Li; Pengfei, Xu; Huilin, Lu

2013-07-01

Flow behavior of gas and particles is predicted by the large eddy simulation of gas-second order moment of solid model (LES-SOM model) in the simulation of flow behavior in CFB. This study shows that the simulated solid volume fractions along height using a two-dimensional model are in agreement with experiments. The velocity, volume fraction and second-order moments of particles are computed. The second-order moments of clusters are calculated. The solid volume fraction, velocity and second order moments are compared at the three different model constants.

Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms

NASA Astrophysics Data System (ADS)

Yu, Yue; Perdikaris, Paris; Karniadakis, George Em

2016-10-01

We develop efficient numerical methods for fractional order PDEs, and employ them to investigate viscoelastic constitutive laws for arterial wall mechanics. Recent simulations using one-dimensional models [1] have indicated that fractional order models may offer a more powerful alternative for modeling the arterial wall response, exhibiting reduced sensitivity to parametric uncertainties compared with the integer-calculus-based models. Here, we study three-dimensional (3D) fractional PDEs that naturally model the continuous relaxation properties of soft tissue, and for the first time employ them to simulate flow structure interactions for patient-specific brain aneurysms. To deal with the high memory requirements and in order to accelerate the numerical evaluation of hereditary integrals, we employ a fast convolution method [2] that reduces the memory cost to O (log ⁡ (N)) and the computational complexity to O (Nlog ⁡ (N)). Furthermore, we combine the fast convolution with high-order backward differentiation to achieve third-order time integration accuracy. We confirm that in 3D viscoelastic simulations, the integer order models strongly depends on the relaxation parameters, while the fractional order models are less sensitive. As an application to long-time simulations in complex geometries, we also apply the method to modeling fluid-structure interaction of a 3D patient-specific compliant cerebral artery with an aneurysm. Taken together, our findings demonstrate that fractional calculus can be employed effectively in modeling complex behavior of materials in realistic 3D time-dependent problems if properly designed efficient algorithms are employed to overcome the extra memory requirements and computational complexity associated with the non-local character of fractional derivatives.

Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms

PubMed Central

Perdikaris, Paris; Karniadakis, George Em

2017-01-01

We develop efficient numerical methods for fractional order PDEs, and employ them to investigate viscoelastic constitutive laws for arterial wall mechanics. Recent simulations using one-dimensional models [1] have indicated that fractional order models may offer a more powerful alternative for modeling the arterial wall response, exhibiting reduced sensitivity to parametric uncertainties compared with the integer-calculus-based models. Here, we study three-dimensional (3D) fractional PDEs that naturally model the continuous relaxation properties of soft tissue, and for the first time employ them to simulate flow structure interactions for patient-specific brain aneurysms. To deal with the high memory requirements and in order to accelerate the numerical evaluation of hereditary integrals, we employ a fast convolution method [2] that reduces the memory cost to O(log(N)) and the computational complexity to O(N log(N)). Furthermore, we combine the fast convolution with high-order backward differentiation to achieve third-order time integration accuracy. We confirm that in 3D viscoelastic simulations, the integer order models strongly depends on the relaxation parameters, while the fractional order models are less sensitive. As an application to long-time simulations in complex geometries, we also apply the method to modeling fluid–structure interaction of a 3D patient-specific compliant cerebral artery with an aneurysm. Taken together, our findings demonstrate that fractional calculus can be employed effectively in modeling complex behavior of materials in realistic 3D time-dependent problems if properly designed efficient algorithms are employed to overcome the extra memory requirements and computational complexity associated with the non-local character of fractional derivatives. PMID:29104310

H{sub 2} Ortho-to-para Conversion on Grains: A Route to Fast Deuterium Fractionation in Dense Cloud Cores?

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

Bovino, S.; Grassi, T.; Schleicher, D. R. G.

Deuterium fractionation, i.e., the enhancement of deuterated species with respect to non-deuterated ones, is considered to be a reliable chemical clock of star-forming regions. This process is strongly affected by the ortho-to-para H{sub 2} ratio. In this Letter we explore the effect of the ortho–para (o–p) H{sub 2} conversion on grains on the deuteration timescale in fully-depleted dense cores, including the most relevant uncertainties that affect this complex process. We show that (i) the o–p H{sub 2} conversion on grains is not strongly influenced by the uncertainties on the conversion time and the sticking coefficient, and (ii) that the processmore » is controlled by the temperature and the residence time of ortho-H{sub 2} on the surface, i.e., by the binding energy. We find that for binding energies between 330 and 550 K, depending on the temperature, the o–p H{sub 2} conversion on grains can shorten the deuterium fractionation timescale by orders of magnitude, opening a new route for explaining the large observed deuteration fraction D {sub frac} in dense molecular cloud cores. Our results suggest that the star formation timescale, when estimated through the timescale to reach the observed deuteration fractions, might be shorter than previously proposed. However, more accurate measurements of the binding energy are needed in order to better assess the overall role of this process.« less

Impact of ultrafiltration and nanofiltration of an industrial fish protein hydrolysate on its bioactive properties.

PubMed

Picot, Laurent; Ravallec, Rozenn; Fouchereau-Péron, Martine; Vandanjon, Laurent; Jaouen, Pascal; Chaplain-Derouiniot, Maryse; Guérard, Fabienne; Chabeaud, Aurélie; Legal, Yves; Alvarez, Oscar Martinez; Bergé, Jean-Pascal; Piot, Jean-Marie; Batista, Irineu; Pires, Carla; Thorkelsson, Gudjon; Delannoy, Charles; Jakobsen, Greta; Johansson, Inez; Bourseau, Patrick

2010-08-30

Numerous studies have demonstrated that in vitro controlled enzymatic hydrolysis of fish and shellfish proteins leads to bioactive peptides. Ultrafiltration (UF) and/or nanofiltration (NF) can be used to refine hydrolysates and also to fractionate them in order to obtain a peptide population enriched in selected sizes. This study was designed to highlight the impact of controlled UF and NF on the stability of biological activities of an industrial fish protein hydrolysate (FPH) and to understand whether fractionation could improve its content in bioactive peptides. The starting fish protein hydrolysate exhibited a balanced amino acid composition, a reproducible molecular weight (MW) profile, and a low sodium chloride content, allowing the study of its biological activity. Successive fractionation on UF and NF membranes allowed concentration of peptides of selected sizes, without, however, carrying out sharp separations, some MW classes being found in several fractions. Peptides containing Pro, Hyp, Asp and Glu were concentrated in the UF and NF retentates compared to the unfractionated hydrolysate and UF permeate, respectively. Gastrin/cholecystokinin-like peptides were present in the starting FPH, UF and NF fractions, but fractionation did not increase their concentration. In contrast, quantification of calcitonin gene-related peptide (CGRP)-like peptides demonstrated an increase in CGRP-like activities in the UF permeate, relative to the starting FPH. The starting hydrolysate also showed a potent antioxidant and radical scavenging activity, and a moderate angiotensin-converting enzyme (ACE)-1 inhibitory activity, which were not increased by UF and NF fractionation. Fractionation of an FPH using membrane separation, with a molecular weight cut-off adapted to the peptide composition, may provide an effective means to concentrate CGRP-like peptides and peptides enriched in selected amino acids. The peptide size distribution observed after UF and NF fractionation demonstrates that it is misleading to characterize the fractions obtained by membrane filtration according to the MW cut-off of the membrane only, as is currently done in the literature. Copyright (c) 2010 Society of Chemical Industry.

[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.

Active vibration control of functionally graded beams with piezoelectric layers based on higher order shear deformation theory

NASA Astrophysics Data System (ADS)

Bendine, K.; Boukhoulda, F. B.; Nouari, M.; Satla, Z.

2016-12-01

This paper reports on a study of active vibration control of functionally graded beams with upper and lower surface-bonded piezoelectric layers. The model is based on higher-order shear deformation theory and implemented using the finite element method (FEM). The proprieties of the functionally graded beam (FGB) are graded along the thickness direction. The piezoelectric actuator provides a damping effect on the FGB by means of a velocity feedback control algorithm. A Matlab program has been developed for the FGB model and compared with ANSYS APDL. Using Newmark's method numerical solutions are obtained for the dynamic equations of FGB with piezoelectric layers. Numerical results show the effects of the constituent volume fraction and the influence the feedback control gain on the frequency and dynamic response of FGBs.

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 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.

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.

Fractional Fourier transform of Lorentz-Gauss vortex beams

NASA Astrophysics Data System (ADS)

Zhou, GuoQuan; Wang, XiaoGang; Chu, XiuXiang

2013-08-01

An analytical expression for a Lorentz-Gauss vortex beam passing through a fractional Fourier transform (FRFT) system is derived. The influences of the order of the FRFT and the topological charge on the normalized intensity distribution, the phase distribution, and the orbital angular momentum density of a Lorentz-Gauss vortex beam in the FRFT plane are examined. The order of the FRFT controls the beam spot size, the orientation of the beam spot, the spiral direction of the phase distribution, the spatial orientation of the two peaks in the orbital angular momentum density distribution, and the magnitude of the orbital angular momentum density. The increase of the topological charge not only results in the dark-hollow region becoming large, but also brings about detail changes in the beam profile. The spatial orientation of the two peaks in the orbital angular momentum density distribution and the phase distribution also depend on the topological charge.

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.

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).

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.

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.

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.

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

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.

Antibacterial activity of isolated phenolic compounds from cranberry (Vaccinium macrocarpon) against Escherichia coli.

PubMed

Rodríguez-Pérez, Celia; Quirantes-Piné, Rosa; Uberos, José; Jiménez-Sánchez, Cecilia; Peña, Alejandro; Segura-Carretero, Antonio

2016-03-01

Phenolic compounds from a cranberry extract were isolated in order to assess their contribution to the antibacterial activity against uropathogenic strains of Escherichia coli (UPEC). With this purpose, a total of 25 fractions from a cranberry extract were isolated using semipreparative high performance liquid chromatography (HPLC) and characterized based on the results obtained by reversed-phase HPLC coupled to mass spectrometry detection. Then, the effects on UPEC surface hydrophobicity and biofilm formation of the cranberry extract as well as the purest fractions (a total of 13) were tested. As expected, the whole extract presented a powerful antibacterial activity against UPEC while the selected fractions presented a different behavior. Myricetin and quercitrin significantly decreased (p < 0.05) E. coli biofilm formation compared with the control, while dihydroferulic acid glucuronide, procyanidin A dimer, quercetin glucoside, myricetin and prodelphinidin B led to a significant decrease of the surface hydrophobicity compared with the control. The results suggest that apart from proanthocyanidins, other compounds, mainly flavonoids, can act against E. coli biofilm formation and also modify UPEC surface hydrophobicity in vitro, one of the first steps of adhesion.

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

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.

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.)

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.

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…

Fractional-order information in the visual control of lateral locomotor interception.

PubMed

Bootsma, Reinoud J; Ledouit, Simon; Casanova, Remy; Zaal, Frank T J M

2016-04-01

Previous work on locomotor interception of a target moving in the transverse plane has suggested that interception is achieved by maintaining the target's bearing angle (often inadvertently confused and/or confounded with the target heading angle) at a constant value. However, dynamics-based model simulations testing the veracity of the underlying control strategy of nulling the rate of change in the bearing angle have been restricted to limited conditions of target motion, and only a few alternatives have been considered. Exploring a wide range of target motion characteristics with straight and curving ball trajectories in a virtual reality setting, we examined how soccer goalkeepers moved along the goal line to intercept long-range shots on goal, a situation in which interception is naturally constrained to movement along a single dimension. Analyses of the movement patterns suggested reliance on combinations of optical position and velocity for straight trajectories and optical velocity and acceleration for curving trajectories. As an alternative to combining such standard integer-order derivatives, we demonstrate with a simple dynamical model that nulling a single informational variable of a self-tuned fractional (rather than integer) order efficiently captures the timing and patterning of the observed interception behaviors. This new perspective could fundamentally change the conception of what perceptual systems may actually provide, both in humans and in other animals. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

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.

1,2,3,4,6 Penta-O-galloyl-β-d-glucose, a bioactivity guided isolated compound from Mangifera indica inhibits 11β-HSD-1 and ameliorates high fat diet-induced diabetes in C57BL/6 mice.

PubMed

Mohan, C G; Viswanatha, G L; Savinay, G; Rajendra, C E; Halemani, Praveen D

2013-03-15

Methanolic leaf extract of Mangifera indica (MEMI) was subjected to bioactivity guided fractionation in order to identify the active antidiabetic constituent. 32 fractions were evaluated for possible 11β-HSD-1 inhibition activity under in vitro conditions. The EA-7/8-9/10-4 fraction was evolved as a most potent fraction among all the fractions and it was identified as well known gallotannin compound 1,2,3,4,6 penta-O-galloyl-β-d-glucose (PGG) by spectral analysis. Based on these results the PGG was further evaluated in ex vivo 11β-HSD-1 inhibition assay and high fat diet (HFD)-induced diabetes in male C57BL/6 mice. Single dose (10, 25, 50 and 100mg/kg) of PGG and carbenoxolone (CBX) have dose dependently inhibited the 11β-HSD-1 activity in liver and adipose tissue. Furthermore, HFD appraisal to male C57BL/6 mice caused severe hyperglycemia, hypertriglyceridemia, elevated levels of plasma corticosterone and insulin, increased liver and white adipose mass with increase in body weight was observed compare to normal control. Also, oral glucose tolerance was significantly impaired compare to normal control. Interestingly, post-treatment with PGG for 21 days had alleviated the HFD-induced biochemical alterations and improved oral glucose tolerance compare to HFD-control. In conclusion, the PGG isolated from MEMI inhibits 11β-HSD-1 activity and ameliorates HFD-induced diabetes in male C57BL/6 mice. Copyright © 2013 Elsevier GmbH. All rights reserved.

Mg/Ca, Sr/Ca and Ca isotope ratios in benthonic foraminifers related to test structure, mineralogy and environmental controls

NASA Astrophysics Data System (ADS)

Gussone, Nikolaus; Filipsson, Helena L.; Kuhnert, Henning

2016-01-01

We analysed Mg/Ca, Sr/Ca and Ca isotope ratios of benthonic foraminifers from sediment core tops retrieved during several research cruises in the Atlantic Ocean, in order to improve the understanding of isotope fractionation and element partitioning resulting from biomineralisation processes and changes in ambient conditions. Species include foraminifers secreting tests composed of hyaline low magnesium calcite, porcelaneous high magnesium calcite as well as aragonite. Our results demonstrate systematic isotope fractionation and element partitioning patterns specific for these foraminiferal groups. Calcium isotope fractionation is similar in porcelaneous and hyaline calcite tests and both groups demonstrate the previously described anomaly with enrichment of heavy isotopes around 3-4 °C (Gussone and Filipsson, 2010). Calcium isotope ratios of the aragonitic species Hoeglundina elegans, on the other hand, are about 0.4‰ lighter compared to the calcitic species, which is in general agreement with stronger fractionation in inorganic aragonite compared to calcite. However, the low and strongly variable Sr content suggests additional processes during test formation, and we propose that transmembrane ion transport or a precursor phase to aragonite may be involved. Porcelaneous tests, composed of high Mg calcite, incorporate higher amounts of Sr compared to hyaline low Mg calcite, in agreement with inorganic calcite systematics, but also porcelaneous tests with reduced Mg/Ca show high Sr/Ca. While calcium isotopes, Sr/Ca and Mg/Ca in benthonic foraminifers primarily appear to fractionate and partition with a dominant inorganic control, δ44/40Ca temperature and growth rate dependencies of benthonic foraminifer tests favour a dominant contribution of light Ca by transmembrane transport relative to unfractionated seawater Ca to the calcifying fluid, thus controlling the formation of foraminiferal δ44/40Ca and Sr/Ca proxy signals.

Anaerobic digestion of organic fraction of municipal solid waste combining two pretreatment modalities, high temperature microwave and hydrogen peroxide

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

Shahriari, Haleh, E-mail: haleh.shahriari@gmail.com; Warith, Mostafa; Hamoda, Mohamed

2012-01-15

Highlights: Black-Right-Pointing-Pointer Microwave and H{sub 2}O{sub 2} pretreatment were studied to enhance anaerobic digestion of organic waste. Black-Right-Pointing-Pointer The whole waste pretreated at 115 Degree-Sign C or 145 Degree-Sign C had the highest biogas production. Black-Right-Pointing-Pointer Biogas production of the whole waste decreased at 175 Degree-Sign C due to formation of refractory compounds. Black-Right-Pointing-Pointer Pretreatment to 145 Degree-Sign C and 175 Degree-Sign C were the best when considering only the free liquid fraction. Black-Right-Pointing-Pointer H{sub 2}O{sub 2} pretreatment had a lag phase and the biogas production was not higher than MW pretreated samples. - Abstract: In order to enhance anaerobicmore » digestion (AD) of the organic fraction of municipal solid waste (OFMSW), pretreatment combining two modalities, microwave (MW) heating in presence or absence of hydrogen peroxide (H{sub 2}O{sub 2}) were investigated. The main pretreatment variables affecting the characteristics of the OFMSW were temperature (T) via MW irradiation and supplemental water additions of 20% and 30% (SWA20 and SW30). Subsequently, the focus of this study was to evaluate mesophilic batch AD performance in terms of biogas production, as well as changes in the characteristics of the OFMSW post digestion. A high MW induced temperature range (115-175 Degree-Sign C) was applied, using sealed vessels and a bench scale MW unit equipped with temperature and pressure controls. Biochemical methane potential (BMP) tests were conducted on the whole OFMSW as well as the liquid fractions. The whole OFMSW pretreated at 115 Degree-Sign C and 145 Degree-Sign C showed 4-7% improvement in biogas production over untreated OFMSW (control). When pretreated at 175 Degree-Sign C, biogas production decreased due to formation of refractory compounds, inhibiting the digestion. For the liquid fraction of OFMSW, the effect of pretreatment on the cumulative biogas production (CBP) was more pronounced for SWA20 at 145 Degree-Sign C, with a 26% increase in biogas production after 8 days of digestion, compared to the control. When considering the increased substrate availability in the liquid fraction after MW pretreatment, a 78% improvement in biogas production vs. the control was achieved. Combining MW and H{sub 2}O{sub 2} modalities did not have a positive impact on OFMSW stabilization and enhanced biogas production. In general, all samples pretreated with H{sub 2}O{sub 2} displayed a long lag phase and the CBP was usually lower than MW irradiated only samples. First order rate constant was calculated.« less

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

Dose-Fractionation Sensitivity of Prostate Cancer Deduced From Radiotherapy Outcomes of 5,969 Patients in Seven International Institutional Datasets: {alpha}/{beta} = 1.4 (0.9-2.2) Gy

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

Miralbell, Raymond, E-mail: Raymond.Miralbell@hcuge.ch; Institut Oncologic Teknon, Barcelona; Roberts, Stephen A.

2012-01-01

Purpose: There are reports of a high sensitivity of prostate cancer to radiotherapy dose fractionation, and this has prompted several trials of hypofractionation schedules. It remains unclear whether hypofractionation will provide a significant therapeutic benefit in the treatment of prostate cancer, and whether there are different fractionation sensitivities for different stages of disease. In order to address this, multiple primary datasets have been collected for analysis. Methods and Materials: Seven datasets were assembled from institutions worldwide. A total of 5969 patients were treated using external beams with or without androgen deprivation (AD). Standard fractionation (1.8-2.0 Gy per fraction) was usedmore » for 40% of the patients, and hypofractionation (2.5-6.7 Gy per fraction) for the remainder. The overall treatment time ranged from 1 to 8 weeks. Low-risk patients comprised 23% of the total, intermediate-risk 44%, and high-risk 33%. Direct analysis of the primary data for tumor control at 5 years was undertaken, using the Phoenix criterion of biochemical relapse-free survival, in order to calculate values in the linear-quadratic equation of k (natural log of the effective target cell number), {alpha} (dose-response slope using very low doses per fraction), and the ratio {alpha}/{beta} that characterizes dose-fractionation sensitivity. Results: There was no significant difference between the {alpha}/{beta} value for the three risk groups, and the value of {alpha}/{beta} for the pooled data was 1.4 (95% CI = 0.9-2.2) Gy. Androgen deprivation improved the bNED outcome index by about 5% for all risk groups, but did not affect the {alpha}/{beta} value. Conclusions: The overall {alpha}/{beta} value was consistently low, unaffected by AD deprivation, and lower than the appropriate values for late normal-tissue morbidity. Hence the fractionation sensitivity differential (tumor/normal tissue) favors the use of hypofractionated radiotherapy schedules for all risk groups, which is also very beneficial logistically in limited-resource settings.« less

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.

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.

Catch me if you can--the use of image guidance in the radiotherapy of an unusual case of esophageal cancer.

PubMed

Jensen, Alexandra D; Grehn, Christian; Nikoghosyan, Anna; Thieke, Christian; Krempien, Robert; Huber, Peter E; Debus, Jürgen; Münter, Marc W

2009-07-01

Despite maximum therapy the prognosis of esophageal carcinoma still remains extremely poor. New treatment strategies including improved radiation therapy techniques promise better outcome by improving local control through precise dose delivery due to higher conformality. A 62-year-old patient with locally advanced carcinoma of the gastroesophageal junction underwent definitive radiochemotherapy with intensity-modulated radiation therapy (IMRT). On positioning control with the in-room CT, the distal esophagus, and hence the tumor, was found to be highly mobile exhibiting changes in position of up to 4 cm from fraction to fraction. IMRT plans were created for various positions establishing a plan library to choose from as appropriate. CT scans were performed prior to each treatment fraction to clarify esophagus position in order to choose the adequate treatment plan. Image guidance was crucial in this unusual case of esophageal carcinoma. Without the information from position control CTs, the tumor would have received only about half the prescribed dose due to variations in position. For this specific case, in-room CT scans are probably superior to kilo- or megavoltage CTs due to the higher soft-tissue contrast enabling detection of positioning variation of the organ and offering the possibility to use the CT for treatment planning.

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.

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

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

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.

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.

[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.

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.

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.

Reduced-Order Structure-Preserving Model for Parallel-Connected Three-Phase Grid-Tied Inverters: Preprint

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

Johnson, Brian B; Purba, Victor; Jafarpour, Saber

Given that next-generation infrastructures will contain large numbers of grid-connected inverters and these interfaces will be satisfying a growing fraction of system load, it is imperative to analyze the impacts of power electronics on such systems. However, since each inverter model has a relatively large number of dynamic states, it would be impractical to execute 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 pointmore » of common coupling, and the control architecture for each inverter includes a current controller, a power controller, and a phase-locked loop for grid synchronization. We outline a structure-preserving reduced-order inverter model 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. That is, 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 an individual inverter in the paralleled system. Numerical simulations validate the reduced-order models.« less

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.

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.

Single-Event Upset Characterization of Common First- and Second-Order All-Digital Phase-Locked Loops

NASA Astrophysics Data System (ADS)

Chen, Y. P.; Massengill, L. W.; Kauppila, J. S.; Bhuva, B. L.; Holman, W. T.; Loveless, T. D.

2017-08-01

The single-event upset (SEU) vulnerability of common first- and second-order all-digital-phase-locked loops (ADPLLs) is investigated through field-programmable gate array-based fault injection experiments. SEUs in the highest order pole of the loop filter and fraction-based phase detectors (PDs) may result in the worst case error response, i.e., limit cycle errors, often requiring system restart. SEUs in integer-based linear PDs may result in loss-of-lock errors, while SEUs in bang-bang PDs only result in temporary-frequency errors. ADPLLs with the same frequency tuning range but fewer bits in the control word exhibit better overall SEU performance.

Superconducting quantum simulator for topological order and the toric code

NASA Astrophysics Data System (ADS)

Sameti, Mahdi; Potočnik, Anton; Browne, Dan E.; Wallraff, Andreas; Hartmann, Michael J.

2017-04-01

Topological order is now being established as a central criterion for characterizing and classifying ground states of condensed matter systems and complements categorizations based on symmetries. Fractional quantum Hall systems and quantum spin liquids are receiving substantial interest because of their intriguing quantum correlations, their exotic excitations, and prospects for protecting stored quantum information against errors. Here, we show that the Hamiltonian of the central model of this class of systems, the toric code, can be directly implemented as an analog quantum simulator in lattices of superconducting circuits. The four-body interactions, which lie at its heart, are in our concept realized via superconducting quantum interference devices (SQUIDs) that are driven by a suitably oscillating flux bias. All physical qubits and coupling SQUIDs can be individually controlled with high precision. Topologically ordered states can be prepared via an adiabatic ramp of the stabilizer interactions. Strings of qubit operators, including the stabilizers and correlations along noncontractible loops, can be read out via a capacitive coupling to read-out resonators. Moreover, the available single-qubit operations allow to create and propagate elementary excitations of the toric code and to verify their fractional statistics. The architecture we propose allows to implement a large variety of many-body interactions and thus provides a versatile analog quantum simulator for topological order and lattice gauge theories.

Novel microwave photonic fractional Hilbert transformer using a ring resonator-based optical all-pass filter.

PubMed

Zhuang, Leimeng; Khan, Muhammad Rezaul; Beeker, Willem; Leinse, Arne; Heideman, René; Roeloffzen, Chris

2012-11-19

We propose and demonstrate a novel wideband microwave photonic fractional Hilbert transformer implemented using a ring resonator-based optical all-pass filter. The full programmability of the ring resonator allows variable and arbitrary fractional order of the Hilbert transformer. The performance analysis in both frequency and time domain validates that the proposed implementation provides a good approximation to an ideal fractional Hilbert transformer. This is also experimentally verified by an electrical S₂₁ response characterization performed on a waveguide realization of a ring resonator. The waveguide-based structure allows the proposed Hilbert transformer to be integrated together with other building blocks on a photonic integrated circuit to create various system-level functionalities for on-chip microwave photonic signal processors. As an example, a circuit consisting of a splitter and a ring resonator has been realized which can perform on-chip phase control of microwave signals generated by means of optical heterodyning, and simultaneous generation of in-phase and quadrature microwave signals for a wide frequency range. For these functionalities, this simple and on-chip solution is considered to be practical, particularly when operating together with a dual-frequency laser. To our best knowledge, this is the first-time on-chip demonstration where ring resonators are employed to perform phase control functionalities for optical generation of microwave signals by means of optical heterodyning.

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.

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.

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.

Aqueous cholesteric liquid crystals using uncharged rodlike polypeptides. Polypeptide vesicles by conformation-specific assembly. Ordered chiral macroporous hybrid silica-polypeptide composites

NASA Astrophysics Data System (ADS)

Bellomo, Enrico Giuseppe

2005-07-01

Aqueous cholesteric liquid crystals using uncharged rodlike polypeptides . The aqueous, lyotropic liquid-crystalline phase behavior of an alpha helical polypeptide, has been studied using optical microscopy and X-ray scattering. Solutions of optically pure polypeptide were found to form cholesteric liquid crystals at volume fractions that decreased with increasing average chain length. At very high volume fractions, the formation of a hexagonal mesophase was observed. The pitch of the cholesteric phase could be varied by a mixture of enantiomeric samples, where the pitch increased as the mixture approached equimolar. The cholesteric phases could be untwisted, using either magnetic field or shear flow, into nematic phases, which relaxed into cholesterics upon removal of field or shear. We have found that the phase diagram of this polypeptide in aqueous solution parallels that of poly(gamma-benzyl glutamate) in organic solvents, thus providing a useful system for liquid-crystal applications requiring water as solvent. Polypeptide vesicles by conformation-specific assembly. We have found that block copolymers composed of polypeptide segments provide significant advantages in controlling both the function and supramolecular structure of bioinspired self-assemblies. Incorporation of the stable chain conformations found in proteins into block copolymers was found to provide an additional element of control, beyond amphiphilicity and composition that defines self-assembled architecture. The abundance of functionality present in amino acids, and the ease by which they can be incorporated into these materials, also provides a powerful mechanism to impart block copolypeptides with function. This combination of structure and function work synergistically to enable significant advantages in the preparation of therapeutic agents as well as provide insight into design of self-assemblies beginning to approach the complexity of natural structures such as virus capsids. Ordered chiral macroporous hybrid silica-polypeptide composites. The mineralization of organic templates has been investigated as an effective way to control the size and structure of inorganic frameworks. Hybrid structures incorporating polypeptide with silica have been prepared and characterized using X-ray scattering, TGA, SEM and TEM. The results support the interaction between silica and polymer to form ordered chiral macroporous structures that can be easily controlled by polymer molecular weight and volume fraction.

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.

LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays

NASA Astrophysics Data System (ADS)

Zhang, Hai; Ye, Renyu; Liu, Song; Cao, Jinde; Alsaedi, Ahmad; Li, Xiaodi

2018-02-01

This paper is concerned with the asymptotic stability of the Riemann-Liouville fractional-order neural networks with discrete and distributed delays. By constructing a suitable Lyapunov functional, two sufficient conditions are derived to ensure that the addressed neural network is asymptotically stable. The presented stability criteria are described in terms of the linear matrix inequalities. The advantage of the proposed method is that one may avoid calculating the fractional-order derivative of the Lyapunov functional. Finally, a numerical example is given to show the validity and feasibility of the theoretical results.

Numerical solution of distributed order fractional differential equations

NASA Astrophysics Data System (ADS)

Katsikadelis, John T.

2014-02-01

In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

Image compression-encryption algorithms by combining hyper-chaotic system with discrete fractional random transform

NASA Astrophysics Data System (ADS)

Gong, Lihua; Deng, Chengzhi; Pan, Shumin; Zhou, Nanrun

2018-07-01

Based on hyper-chaotic system and discrete fractional random transform, an image compression-encryption algorithm is designed. The original image is first transformed into a spectrum by the discrete cosine transform and the resulting spectrum is compressed according to the method of spectrum cutting. The random matrix of the discrete fractional random transform is controlled by a chaotic sequence originated from the high dimensional hyper-chaotic system. Then the compressed spectrum is encrypted by the discrete fractional random transform. The order of DFrRT and the parameters of the hyper-chaotic system are the main keys of this image compression and encryption algorithm. The proposed algorithm can compress and encrypt image signal, especially can encrypt multiple images once. To achieve the compression of multiple images, the images are transformed into spectra by the discrete cosine transform, and then the spectra are incised and spliced into a composite spectrum by Zigzag scanning. Simulation results demonstrate that the proposed image compression and encryption algorithm is of high security and good compression performance.

Spectral iterative method and convergence analysis for solving nonlinear fractional differential equation

NASA Astrophysics Data System (ADS)

Yarmohammadi, M.; Javadi, S.; Babolian, E.

2018-04-01

In this study a new spectral iterative method (SIM) based on fractional interpolation is presented for solving nonlinear fractional differential equations (FDEs) involving Caputo derivative. This method is equipped with a pre-algorithm to find the singularity index of solution of the problem. This pre-algorithm gives us a real parameter as the index of the fractional interpolation basis, for which the SIM achieves the highest order of convergence. In comparison with some recent results about the error estimates for fractional approximations, a more accurate convergence rate has been attained. We have also proposed the order of convergence for fractional interpolation error under the L2-norm. Finally, general error analysis of SIM has been considered. The numerical results clearly demonstrate the capability of the proposed method.

Distribution, diversity and abundance of bacterial laccase-like genes in different particle size fractions of sediments in a subtropical mangrove ecosystem.

PubMed

Luo, Ling; Zhou, Zhi-Chao; Gu, Ji-Dong

2015-10-01

This study investigated the diversity and abundance of bacterial lacasse-like genes in different particle size fractions, namely sand, silt, and clay of sediments in a subtropical mangrove ecosystem. Moreover, the effects of nutrient conditions on bacterial laccase-like communities as well as the correlation between nutrients and, both the abundance and diversity indices of laccase-like bacteria in particle size fractions were also studied. Compared to bulk sediments, Bacteroidetes, Caldithrix, Cyanobacteria and Chloroflexi were dominated in all 3 particle-size fractions of intertidal sediment (IZ), but Actinobacteria and Firmicutes were lost after the fractionation procedures used. The diversity index of IZ fractions decreased in the order of bulk > clay > silt > sand. In fractions of mangrove forest sediment (MG), Verrucomicrobia was found in silt, and both Actinobacteria and Bacteroidetes appeared in clay, but no new species were found in sand. The declining order of diversity index in MG fractions was clay > silt > sand > bulk. Furthermore, the abundance of lacasse-like bacteria varied with different particle-size fractions significantly (p < 0.05), and decreased in the order of sand > clay > silt in both IZ and MG fractions. Additionally, nutrient availability was found to significantly affect the diversity and community structure of laccase-like bacteria (p < 0.05), while the total organic carbon contents were positively related to the abundance of bacterial laccase-like genes in particle size fractions (p < 0.05). Therefore, this study further provides evidence that bacterial laccase plays a vital role in turnover of sediment organic matter and cycling of nutrients.

Design of an all-optical fractional-order differentiator with terahertz bandwidth based on a fiber Bragg grating in transmission.

PubMed

Liu, Xin; Shu, Xuewen

2017-08-20

All-optical fractional-order temporal differentiators with bandwidths reaching terahertz (THz) values are demonstrated with transmissive fiber Bragg gratings. Since the designed fractional-order differentiator is a minimum phase function, the reflective phase of the designed function can be chosen arbitrarily. As examples, we first design several 0.5th-order differentiators with bandwidths reaching the THz range for comparison. The reflective phases of the 0.5th-order differentiators are chosen to be linear phase, quadratic phase, cubic phase, and biquadratic phase, respectively. We find that both the maximum coupling coefficient and the spatial resolution of the designed grating increase when the reflective phase varies from quadratic function to cubic function to biquadratic function. Furthermore, when the reflective phase is chosen to be a quadratic function, the obtained grating coupling coefficient and period are more likely to be achieved in practice. Then we design fractional-order differentiators with different orders when the reflective phase is chosen to be a quadratic function. We see that when the designed order of the differentiator increases, the obtained maximum coupling coefficient also increases while the oscillation of the coupling coefficient decreases. Finally, we give the numerical performance of the designed 0.5th-order differentiator by showing its temporal response and calculating its cross-correlation coefficient.

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.

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.

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.

Solution to automatic generation control problem using firefly algorithm optimized I(λ)D(µ) controller.

PubMed

Debbarma, Sanjoy; Saikia, Lalit Chandra; Sinha, Nidul

2014-03-01

Present work focused on automatic generation control (AGC) of a three unequal area thermal systems considering reheat turbines and appropriate generation rate constraints (GRC). A fractional order (FO) controller named as I(λ)D(µ) controller based on crone approximation is proposed for the first time as an appropriate technique to solve the multi-area AGC problem in power systems. A recently developed metaheuristic algorithm known as firefly algorithm (FA) is used for the simultaneous optimization of the gains and other parameters such as order of integrator (λ) and differentiator (μ) of I(λ)D(µ) controller and governor speed regulation parameters (R). The dynamic responses corresponding to optimized I(λ)D(µ) controller gains, λ, μ, and R are compared with that of classical integer order (IO) controllers such as I, PI and PID controllers. Simulation results show that the proposed I(λ)D(µ) controller provides more improved dynamic responses and outperforms the IO based classical controllers. Further, sensitivity analysis confirms the robustness of the so optimized I(λ)D(µ) controller to wide changes in system loading conditions and size and position of SLP. Proposed controller is also found to have performed well as compared to IO based controllers when SLP takes place simultaneously in any two areas or all the areas. Robustness of the proposed I(λ)D(µ) controller is also tested against system parameter variations. © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Optimal distributed control of a diffuse interface model of tumor growth

NASA Astrophysics Data System (ADS)

Colli, Pierluigi; Gilardi, Gianni; Rocca, Elisabetta; Sprekels, Jürgen

2017-06-01

In this paper, a distributed optimal control problem is studied for a diffuse interface model of tumor growth which was proposed by Hawkins-Daruud et al in Hawkins-Daruud et al (2011 Int. J. Numer. Math. Biomed. Eng. 28 3-24). The model consists of a Cahn-Hilliard equation for the tumor cell fraction φ coupled to a reaction-diffusion equation for a function σ representing the nutrient-rich extracellular water volume fraction. The distributed control u monitors as a right-hand side of the equation for σ and can be interpreted as a nutrient supply or a medication, while the cost function, which is of standard tracking type, is meant to keep the tumor cell fraction under control during the evolution. We show that the control-to-state operator is Fréchet differentiable between appropriate Banach spaces and derive the first-order necessary optimality conditions in terms of a variational inequality involving the adjoint state variables. The financial support of the FP7-IDEAS-ERC-StG #256872 (EntroPhase) and of the project Fondazione Cariplo-Regione Lombardia MEGAsTAR ‘Matematica d’Eccellenza in biologia ed ingegneria come accelleratore di una nuona strateGia per l’ATtRattività dell’ateneo pavese’ is gratefully acknowledged. The paper also benefited from the support of the MIUR-PRIN Grant 2015PA5MP7 ‘Calculus of Variations’ for PC and GG, and the GNAMPA (Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica) for PC, GG and ER.

In vitro antiplasmodial activity and prophylactic potentials of extract and fractions of Trema orientalis (Linn.) stem bark.

PubMed

Olanlokun, John Oludele; David, Oluwole Moses; Afolayan, Anthony Jide

2017-08-15

Trema orientalis (T. orientalis Linn) has been used in the management of malaria in the western part of Nigeria and despite its application in ethnomedicine, there is dearth of scientific evidence to justify the acclaimed prophylactic antimalarial usage of the plant. The aim of this study is to assess the in vitro antiplasmodial cell-free assay and chemopreventive efficacy of the methanol extract of the stem bark of T. orientalis and its fractions as a prophylactic regimen for malaria prevention. Also, the antimicrobial activities of the extract and the fractions were investigated. Vacuum liquid chromatography was used to obtain dichloromethane, ethylacetate and methanol fractions from the methanol extract of T. orientalis. The fractions were tested for their prophylactic and cell-free antimalarial activity using murine models and β-hematin formation assay respectively. Disc diffusion method was used to determine the antibacterial activity of the extract and its fractions against both Gram-positive and Gram-negative bacteria. In the prophylactic experiment, dichloromethane (DCMF), methanol fraction (MF) and extract (ME) (in this order) showed significant chemopreventive effects against P. berghei invasion of the red blood cells when compared with both Sulfadoxine-Pyrimethamine (SP) and untreated controls. Results of the in vitro study showed that the DCMF had the highest effect in preventing the formation of β-hematin when compared with other fractions. The DCMF also had the highest percentage inhibition of β-hematin formation when compared with chloroquine. The extract and fractions showed a concentration dependent antibacterial activity. Methanol extract had a pronounced inhibitory effect on Enterobacter cloaca ATCC 13047 and Enterococcus faecalis ATCC 29212. Serratia mercescens ATCC 9986 and Pseudomonas aeruginosa ATCC 19582 were the most susceptible bacteria. The results obtained showed that both extract and fractions of T. orientalis possessed antiplasmodial and antimicrobial activity.

A componential view of children's difficulties in learning fractions.

PubMed

Gabriel, Florence; Coché, Frédéric; Szucs, Dénes; Carette, Vincent; Rey, Bernard; Content, Alain

2013-01-01

Fractions are well known to be difficult to learn. Various hypotheses have been proposed in order to explain those difficulties: fractions can denote different concepts; their understanding requires a conceptual reorganization with regard to natural numbers; and using fractions involves the articulation of conceptual knowledge with complex manipulation of procedures. In order to encompass the major aspects of knowledge about fractions, we propose to distinguish between conceptual and procedural knowledge. We designed a test aimed at assessing the main components of fraction knowledge. The test was carried out by fourth-, fifth- and sixth-graders from the French Community of Belgium. The results showed large differences between categories. Pupils seemed to master the part-whole concept, whereas numbers and operations posed problems. Moreover, pupils seemed to apply procedures they do not fully understand. Our results offer further directions to explain why fractions are amongst the most difficult mathematical topics in primary education. This study offers a number of recommendations on how to teach fractions.

A componential view of children's difficulties in learning fractions

PubMed Central

Gabriel, Florence; Coché, Frédéric; Szucs, Dénes; Carette, Vincent; Rey, Bernard; Content, Alain

2013-01-01

Fractions are well known to be difficult to learn. Various hypotheses have been proposed in order to explain those difficulties: fractions can denote different concepts; their understanding requires a conceptual reorganization with regard to natural numbers; and using fractions involves the articulation of conceptual knowledge with complex manipulation of procedures. In order to encompass the major aspects of knowledge about fractions, we propose to distinguish between conceptual and procedural knowledge. We designed a test aimed at assessing the main components of fraction knowledge. The test was carried out by fourth-, fifth- and sixth-graders from the French Community of Belgium. The results showed large differences between categories. Pupils seemed to master the part-whole concept, whereas numbers and operations posed problems. Moreover, pupils seemed to apply procedures they do not fully understand. Our results offer further directions to explain why fractions are amongst the most difficult mathematical topics in primary education. This study offers a number of recommendations on how to teach fractions. PMID:24133471

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.

Experimental identification of Ca isotopic fractionations in higher plants

NASA Astrophysics Data System (ADS)

Cobert, Florian; Schmitt, Anne-Désirée; Bourgeade, Pascale; Labolle, François; Badot, Pierre-Marie; Chabaux, François; Stille, Peter

2011-10-01

Hydroponic experiments have been performed in order to identify the co-occurring geochemical and biological processes affecting the Ca isotopic compositions within plants. To test the influence of the Ca concentration and pH of the nutritive solution on the Ca isotopic composition of the different plant organs, four experimental conditions were chosen combining two different Ca concentrations (5 and 60 ppm) and two pHs (4 and 6). The study was performed on rapid growing bean plants in order to have a complete growth cycle. Several organs (root, stem, leaf, reproductive) were sampled at two different growth stages (10 days and 6 weeks of culture) and prepared for Ca isotopic measurements. The results allow to identify three Ca isotopic fractionation levels. The first one takes place when Ca enters the lateral roots, during Ca adsorption on cation-exchange binding sites in the apoplasm. The second one takes place when Ca is bound to the polygalacturonic acids (pectins) of the middle lamella of the xylem cell wall. Finally, the last fractionation occurs in the reproductive organs, also caused by cation-exchange processes with pectins. However, the cell wall structures of these organs and/or number of available exchange sites seem to be different to those of the xylem wall. These three physico-chemical fractionation mechanisms allow to enrich the organs in the light 40Ca isotope. The amplitude of the Ca isotopic fractionation within plant organs is highly dependent on the composition of the nutritive solution: low pH (4) and Ca concentrations (5 ppm) have no effect on the biomass increase of the plants but induce smaller fractionation amplitudes compared to those obtained from other experimental conditions. Thus, Ca isotopic signatures of bean plants are controlled by the external nutritive medium. This study highlights the potential of Ca isotopes to be applied in plant physiology (to identify Ca uptake, circulation and storage mechanisms within plants) and in biogeochemistry (to identify Ca recycling, Ca content and pH evolutions in soil solutions through time).

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.

General solution of the Bagley-Torvik equation with fractional-order derivative

NASA Astrophysics Data System (ADS)

Wang, Z. H.; Wang, X.

2010-05-01

This paper investigates the general solution of the Bagley-Torvik equation with 1/2-order derivative or 3/2-order derivative. This fractional-order differential equation is changed into a sequential fractional-order differential equation (SFDE) with constant coefficients. Then the general solution of the SFDE is expressed as the linear combination of fundamental solutions that are in terms of α-exponential functions, a kind of functions that play the same role of the classical exponential function. Because the number of fundamental solutions of the SFDE is greater than 2, the general solution of the SFDE depends on more than two free (independent) constants. This paper shows that the general solution of the Bagley-Torvik equation involves actually two free constants only, and it can be determined fully by the initial displacement and initial velocity.

Long-term outcomes of late course accelerated hyper-fractionated radiotherapy for localized esophageal carcinoma in Mainland China: a meta-analysis.

PubMed

Zhang, Y W; Chen, L; Bai, Y; Zheng, X

2011-09-01

Published data on the long-term survival results of patients with localized esophageal carcinoma receiving late course accelerated hyper-fractionated radiotherapy (LCAF RT) versus conventional fractionated radiotherapy (CF RT) are inconclusive. In order to derive a more precise estimation of the both treatment-regimes, a meta-analysis based on systematic review of published articles was performed. A meta-analysis was performed using trials identified through Pubmed and Chinese national knowledge infrastructure. Results in 5-year survival and 5-year local control were collected from randomized trials comparing LCAF RT with CF RT. Review Manager (The Cochrane Collaboration, Oxford, England) and Stata software (Stata Corporation, College Station, TX, USA) were used for data management. A total of 11 trials were involved in this analysis with 572 cases and 567 controls. Our results showed that LCAF RT, compared with CF RT, significantly improved the 5-year survival (odds ratio [OR]= 2.93, 95% confidence interval [CI]: 2.15-4.00, P < 0.00001) and 5-year local control (OR = 3.96, 95% CI: 2.91-5.38, P < 0.00001). LCAF RT was more therapeutically beneficial than CF RT in the localized esophageal carcinoma. © 2011 Copyright the Authors. Journal compilation © 2011, Wiley Periodicals, Inc. and the International Society for Diseases of the Esophagus.

Generalized Functions for the Fractional Calculus

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

1999-01-01

Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q)[at(exp q)](1903a, 1903b, 1905), and the F-function F(sub q)[a,t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order differential equation and for the related initial value problem (Hartley and Lorenzo, 1999). This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the F-function. The R-function also returns itself on qth order differ-integration. An example application of the R-function is provided. A further generalization of the R-function, called the G-function brings in the effects of repeated and partially repeated fractional poles.

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.

Solution of a modified fractional diffusion equation

NASA Astrophysics Data System (ADS)

Langlands, T. A. M.

2006-07-01

Recently, a modified fractional diffusion equation has been proposed [I. Sokolov, J. Klafter, From diffusion to anomalous diffusion: a century after Einstein's brownian motion, Chaos 15 (2005) 026103; A.V. Chechkin, R. Gorenflo, I.M. Sokolov, V.Yu. Gonchar, Distributed order time fractional diffusion equation, Frac. Calc. Appl. Anal. 6 (3) (2003) 259279; I.M. Sokolov, A.V. Checkin, J. Klafter, Distributed-order fractional kinetics, Acta. Phys. Pol. B 35 (2004) 1323.] for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. In this letter we give the solution of the modified equation on an infinite domain. In contrast to the solution of the traditional fractional diffusion equation, the solution of the modified equation requires an infinite series of Fox functions instead of a single Fox function.

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 Systematic Review and Meta-Analysis of the Partitioning of Precipitation over Land

NASA Astrophysics Data System (ADS)

Padrón, Ryan S.; Gudmundsson, Lukas; Greve, Peter; Seneviratne, Sonia I.

2017-04-01

Long-term mean Precipitation (P) over land is partitioned into runoff (R) and evapotranspiration (ET). The aridity index, defined as the ratio between potential ET and P, constitutes the first order control of this partitioning (i.e. ET/P) within Budyko's framework. However, second order controls of ET/P can be significant, and their understanding remains a fundamental challenge. This study therefore introduces a new global observation-based dataset for the long-term mean partitioning of P into ET and R in approximately 2000 catchments, which is obtained from a systematic examination of 170 peer-reviewed studies. The new dataset serves as a basis to improve our understanding of these second order controls around the world. A list of 22 indicators of second order controls of ET/P are identified from the literature, and tested for significance using the new dataset. Results reveal that (i) climate type is a dominant control of ET/P, and additional controls vary with climatic region; (ii) climate characteristics and catchment slope dominate over other catchment controls—the phase shift between the seasonal cycle of P and potential ET appears as an important index across all climate types; (iii) despite the high attention that vegetation-related indices receive as controls of ET/P, they were found to be less important and not always significant; and (iv) the fraction of precipitation falling as snow is the most important second order control in regions with snow climate. The process-related insights from this study about the partitioning of P are a valuable asset for model development, watershed management, and the understanding of future water availability around the globe.

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.

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.

Global Mittag-Leffler stability analysis of fractional-order impulsive neural networks with one-side Lipschitz condition.

PubMed

Zhang, Xinxin; Niu, Peifeng; Ma, Yunpeng; Wei, Yanqiao; Li, Guoqiang

2017-10-01

This paper is concerned with the stability analysis issue of fractional-order impulsive neural networks. Under the one-side Lipschitz condition or the linear growth condition of activation function, the existence of solution is analyzed respectively. In addition, the existence, uniqueness and global Mittag-Leffler stability of equilibrium point of the fractional-order impulsive neural networks with one-side Lipschitz condition are investigated by the means of contraction mapping principle and Lyapunov direct method. Finally, an example with numerical simulation is given to illustrate the validity and feasibility of the proposed results. Copyright © 2017 Elsevier Ltd. All rights reserved.

Controls on old and new water contributions to stream flow at some nested catchments in Vermont, USA

USGS Publications Warehouse

Shanley, J.B.; Kendall, C.; Smith, T.E.; Wolock, D.M.; McDonnell, Jeffery J.

2002-01-01

Factors controlling the partitioning of old and new water contributions to stream flow were investigated for three events in four catchments (three of which were nested) at Sleepers River Research Watershed in Danville, Vermont. In the 1993 snowmelt period, two-component isotopic hydrograph separations showed that new water (meltwater) inputs to the stream ranged widely from 41 to 74%, and increased with catchment size (41 to 11 125 ha) (with one exception) and with open land cover (0-73%). Peak dissolved organic carbon concentrations and relative alkalinity dilution in stream water ranked in the same order among catchments as the new water fractions, suggesting that new water followed shallow flow paths. During the 1994 snowmelt, despite similar timing and magnitude of melt inputs, the new-water contribution to stream flow ranged only from 30 to 36% in the four catchments. We conclude that the uncommonly high and variable new water fractions in streamwater during the 1993 melt were caused by direct runoff of meltwater over frozen ground, which was prevalent in open land areas during the 1993 winter. In a high-intensity summer rainstorm in 1993, new water fractions were smaller relative to the 1993 snowmelt, ranging from 28 to 46%, but they ranked in the identical catchment order. Reconciliation of the contrasting patterns of new-old water partitioning in the three events appears to require an explanation that invokes multiple processes and effects, including: 1 topographically controlled increase in surface-saturated area with increasing catchment size; 2 direct runoff over frozen ground; 3 low infiltration in agriculturally compacted soils; 4 differences in soil transmissivity, which may be more relevant under dry antecedent conditions. These data highlight some of the difficulties faced by catchment hydrologists in formulating a theory of runoff generation at varying basin scales. Copyright ?? 2002 John Wiley and Sons, Ltd.

Controls on old and new water contributions to stream flow at some nested catchments in Vermont, USA

NASA Astrophysics Data System (ADS)

Shanley, James B.; Kendall, Carol; Smith, Thor E.; Wolock, David M.; McDonnell, Jeffrey J.

2002-02-01

Factors controlling the partitioning of old and new water contributions to stream flow were investigated for three events in four catchments (three of which were nested) at Sleepers River Research Watershed in Danville, Vermont. In the 1993 snowmelt period, two-component isotopic hydrograph separations showed that new water (meltwater) inputs to the stream ranged widely from 41 to 74%, and increased with catchment size (41 to 11 125 ha) (with one exception) and with open land cover (0-73%). Peak dissolved organic carbon concentrations and relative alkalinity dilution in stream water ranked in the same order among catchments as the new water fractions, suggesting that new water followed shallow flow paths. During the 1994 snowmelt, despite similar timing and magnitude of melt inputs, the new-water contribution to stream flow ranged only from 30 to 36% in the four catchments. We conclude that the uncommonly high and variable new water fractions in streamwater during the 1993 melt were caused by direct runoff of meltwater over frozen ground, which was prevalent in open land areas during the 1993 winter. In a high-intensity summer rainstorm in 1993, new water fractions were smaller relative to the 1993 snowmelt, ranging from 28 to 46%, but they ranked in the identical catchment order. Reconciliation of the contrasting patterns of new-old water partitioning in the three events appears to require an explanation that invokes multiple processes and effects, including: 1.topographically controlled increase in surface-saturated area with increasing catchment size;2.direct runoff over frozen ground;3.low infiltration in agriculturally compacted soils;4.differences in soil transmissivity, which may be more relevant under dry antecedent conditions. These data highlight some of the difficulties faced by catchment hydrologists in formulating a theory of runoff generation at varying basin scales.

Extracellular Enzyme Activity Profile in a Chemically Enhanced Water Accommodated Fraction of Surrogate Oil: Toward Understanding Microbial Activities After the Deepwater Horizon Oil Spill

PubMed Central

Kamalanathan, Manoj; Xu, Chen; Schwehr, Kathy; Bretherton, Laura; Beaver, Morgan; Doyle, Shawn M.; Genzer, Jennifer; Hillhouse, Jessica; Sylvan, Jason B.; Santschi, Peter; Quigg, Antonietta

2018-01-01

Extracellular enzymes and extracellular polymeric substances (EPS) play a key role in overall microbial activity, growth and survival in the ocean. EPS, being amphiphilic in nature, can act as biological surfactant in an oil spill situation. Extracellular enzymes help microbes to digest and utilize fractions of organic matter, including EPS, which can stimulate growth and enhance microbial activity. These natural processes might have been altered during the 2010 Deepwater Horizon oil spill due to the presence of hydrocarbon and dispersant. This study aims to investigate the role of bacterial extracellular enzymes during exposure to hydrocarbons and dispersant. Mesocosm studies were conducted using a water accommodated fraction of oil mixed with the chemical dispersant, Corexit (CEWAF) in seawater collected from two different locations in the Gulf of Mexico and corresponding controls (no additions). Activities of five extracellular enzymes typically found in the EPS secreted by the microbial community – α- and β-glucosidase, lipase, alkaline phosphatase, leucine amino-peptidase – were measured using fluorogenic substrates in three different layers of the mesocosm tanks (surface, water column and bottom). Enhanced EPS production and extracellular enzyme activities were observed in the CEWAF treatment compared to the Control. Higher bacterial and micro-aggregate counts were also observed in the CEWAF treatment compared to Controls. Bacterial genera in the order Alteromonadaceae were the most abundant bacterial 16S rRNA amplicons recovered. Genomes of Alteromonadaceae commonly have alkaline phosphatase and leucine aminopeptidase, therefore they may contribute significantly to the measured enzyme activities. Only Alteromonadaceae and Pseudomonadaceae among bacteria detected here have higher percentage of genes for lipase. Piscirickettsiaceae was abundant; genomes from this order commonly have genes for leucine aminopeptidase. Overall, this study provides insights into the alteration to the microbial processes such as EPS and extracellular enzyme production, and to the microbial community, when exposed to the mixture of oil and dispersant. PMID:29740422

Protective Effect of Ethyl Acetate Fraction of Stereospermum Suaveolens Against Hepatic Oxidative Stress in STZ Diabetic Rats.

PubMed

Balasubramanian, Thirumalaiswamy; Senthilkumar, G P; Karthikeyan, M; Chatterjee, Tapan Kumar

2013-07-01

Stereospermum suaveolens is a folk remedy for the treatment of diabetes and liver disorders in southern parts of India. In the present study, the protective effect of the ethyl acetate fraction of ethanol extract from S. suaveolens against hepatic oxidative stress was evaluated in streptozotocin (STZ)-induced diabetic rats for 14 days. The ethyl acetate fraction was administered orally to the STZ diabetic rats at the doses of 200 and 400 mg/kg. Blood glucose level was measured according to glucose oxidase method. In order to determine hepatoprotective activity, changes in the levels of serum biomarker enzymes such as aspartate transaminase (AST), alanine transaminase (ALT), and serum alkaline phosphatase (SALP) were assessed in the ethyl acetate fraction treated diabetic rats and were compared with the levels in diabetic control rats. In addition, the antioxidant activity of ethyl acetate fraction was evaluated using various hepatic parameters such as thiobarbituric acid reactive substances (TBARS), reduced glutathione (GSH), superoxide dismutase (SOD), and catalase (CAT). It was found that administration of ethyl acetate fraction (200 and 400 mg/kg) produced a significant (P < 0.001) fall in fasting blood glucose level, TBARS, bilirubin, AST, ALT, and SALP, while elevating the GSH levels, and SOD and CAT activities in diabetic rats. Histopathologic studies also revealed the protective effect of ethyl acetate fraction on the liver tissues of diabetic rats. It was concluded from this study that the ethyl acetate fraction from ethanol extract of S. suaveolens modulates the activity of enzymatic and nonenzymatic antioxidants and enhances the defense against hepatic oxidative stress in STZ-induced diabetic rats.

The impact of carbon sp{sup 2} fraction of reduced graphene oxide on the performance of reduced graphene oxide contacted organic transistors

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

Kang, Narae; Department of Physics, University of Central Florida, 12424 Research Parkway, Suite 400, Orlando, Florida 32826; Khondaker, Saiful I., E-mail: saiful@ucf.edu

2014-12-01

One of the major bottlenecks in fabricating high performance organic field effect transistors (OFETs) is a large interfacial contact barrier between metal electrodes and organic semiconductors (OSCs) which makes the charge injection inefficient. Recently, reduced graphene oxide (RGO) has been suggested as an alternative electrode material for OFETs. RGO has tunable electronic properties and its conductivity can be varied by several orders of magnitude by varying the carbon sp{sup 2} fraction. However, whether the sp{sup 2} fraction of RGO in the electrode affects the performance of the fabricated OFETs is yet to be investigated. In this study, we demonstrate thatmore » the performance of OFETs with pentacene as OSC and RGO as electrode can be continuously improved by increasing the carbon sp{sup 2} fraction of RGO. When compared to control palladium electrodes, the mobility of the OFETs shows an improvement of ∼200% for 61% sp{sup 2} fraction RGO, which further improves to ∼500% for 80% RGO electrode. Similar improvements were also observed in current on-off ratio, on-current, and transconductance. Our study suggests that, in addition to π-π interaction at RGO/pentacene interface, the tunable electronic properties of RGO electrode have a significant role in OFETs performance.« less

Generalized Lie symmetry approach for fractional order systems of differential equations. III

NASA Astrophysics Data System (ADS)

Singla, Komal; Gupta, R. K.

2017-06-01

The generalized Lie symmetry technique is proposed for the derivation of point symmetries for systems of fractional differential equations with an arbitrary number of independent as well as dependent variables. The efficiency of the method is illustrated by its application to three higher dimensional nonlinear systems of fractional order partial differential equations consisting of the (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov system, (3 + 1)-dimensional Burgers system, and (3 + 1)-dimensional Navier-Stokes equations. With the help of derived Lie point symmetries, the corresponding invariant solutions transform each of the considered systems into a system of lower-dimensional fractional partial differential equations.

Sequential CD34 cell fractionation by magnetophoresis in a magnetic dipole flow sorter.

PubMed

Schneider, Thomas; Karl, Stephan; Moore, Lee R; Chalmers, Jeffrey J; Williams, P Stephen; Zborowski, Maciej

2010-01-01

Cell separation and fractionation based on fluorescent and magnetic labeling procedures are common tools in contemporary research. These techniques rely on binding of fluorophores or magnetic particles conjugated to antibodies to target cells. Cell surface marker expression levels within cell populations vary with progression through the cell cycle. In an earlier work we showed the reproducible magnetic fractionation (single pass) of the Jurkat cell line based on the population distribution of CD45 surface marker expression. Here we present a study on magnetic fractionation of a stem and progenitor cell (SPC) population using the established acute myelogenous leukemia cell line KG-1a as a cell model. The cells express a CD34 cell surface marker associated with the hematopoietic progenitor cell activity and the progenitor cell lineage commitment. The CD34 expression level is approximately an order of magnitude lower than that of the CD45 marker, which required further improvements of the magnetic fractionation apparatus. The cells were immunomagnetically labeled using a sandwich of anti-CD34 antibody-phycoerythrin (PE) conjugate and anti-PE magnetic nanobead and fractionated into eight components using a continuous flow dipole magnetophoresis apparatus. The CD34 marker expression distribution between sorted fractions was measured by quantitative PE flow cytometry (using QuantiBRITE PE calibration beads), and it was shown to be correlated with the cell magnetophoretic mobility distribution. A flow outlet addressing scheme based on the concept of the transport lamina thickness was used to control cell distribution between the eight outlet ports. The fractional cell distributions showed good agreement with numerical simulations of the fractionation based on the cell magnetophoretic mobility distribution in the unsorted sample.

Use of the fractional Fourier transform in {pi}/2 converters of laser modes

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

Malyutin, A A

2004-02-28

The possibility of using the fractional Fourier transform (FrFT) in optical schemes for astigmatic {pi}/2 converters of Hermite-Gaussian modes to donut Laguerre-Gaussian modes is considered. Several schemes of converters based on the FrFT of the half-integer and irrational orders are presented. The lowest FrFT order than can be used in astigmatic mode converters is found. The properties of converters based on the fractional and ordinary Fourier transforms are compared. (laser beams)

Image encryption based on a delayed fractional-order chaotic logistic system

NASA Astrophysics Data System (ADS)

Wang, Zhen; Huang, Xia; Li, Ning; Song, Xiao-Na

2012-05-01

A new image encryption scheme is proposed based on a delayed fractional-order chaotic logistic system. In the process of generating a key stream, the time-varying delay and fractional derivative are embedded in the proposed scheme to improve the security. Such a scheme is described in detail with security analyses including correlation analysis, information entropy analysis, run statistic analysis, mean-variance gray value analysis, and key sensitivity analysis. Experimental results show that the newly proposed image encryption scheme possesses high security.

An accurate method for solving a class of fractional Sturm-Liouville eigenvalue problems

NASA Astrophysics Data System (ADS)

Kashkari, Bothayna S. H.; Syam, Muhammed I.

2018-06-01

This article is devoted to both theoretical and numerical study of the eigenvalues of nonsingular fractional second-order Sturm-Liouville problem. In this paper, we implement a fractional-order Legendre Tau method to approximate the eigenvalues. This method transforms the Sturm-Liouville problem to a sparse nonsingular linear system which is solved using the continuation method. Theoretical results for the considered problem are provided and proved. Numerical results are presented to show the efficiency of the proposed method.

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 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.

Malonyl-CoA decarboxylase (MCD) is differentially regulated in subcellular compartments by 5'AMP-activated protein kinase (AMPK). Studies using H9c2 cells overexpressing MCD and AMPK by adenoviral gene transfer technique.

PubMed

Sambandam, Nandakumar; Steinmetz, Michael; Chu, Angel; Altarejos, Judith Y; Dyck, Jason R B; Lopaschuk, Gary D

2004-07-01

Malonyl-CoA, a potent inhibitor of carnitine pamitoyl transferase-I (CPT-I), plays a pivotal role in fuel selection in cardiac muscle. Malonyl-CoA decarboxylase (MCD) catalyzes the degradation of malonyl-CoA, removes a potent allosteric inhibition on CPT-I and thereby increases fatty acid oxidation in the heart. Although MCD has several Ser/Thr phosphorylation sites, whether it is regulated by AMP-activated protein kinase (AMPK) has been controversial. We therefore overexpressed MCD (Ad.MCD) and constitutively active AMPK (Ad.CA-AMPK) in H9c2 cells, using an adenoviral gene delivery approach in order to examine if MCD is regulated by AMPK. Cells infected with Ad.CA-AMPK demonstrated a fourfold increase in AMPK activity as compared with control cells expressing green fluorescent protein (Ad.GFP). MCD activity increased 40- to 50-fold in Ad.MCD + Ad.GFP cells when compared with Ad.GFP control. Co-expressing AMPK with MCD further augmented MCD expression and activity in Ad.MCD + Ad.CA-AMPK cells compared with the Ad.MCD + Ad.GFP control. Subcellular fractionation further revealed that 54.7 kDa isoform of MCD expression was significantly higher in cytosolic fractions of Ad.MCD + Ad.CA-AMPK cells than of the Ad.MCD +Ad.GFP control. However, the MCD activities in cytosolic fractions were not different between the two groups. Interestingly, in the mitochondrial fractions, MCD activity significantly increased in Ad.MCD + Ad.CA-AMPK cells when compared with Ad.MCD + Ad.GFP cells. Using phosphoserine and phosphothreonine antibodies, no phosphorylation of MCD by AMPK was observed. The increase in MCD activity in mitochondria-rich fractions of Ad.MCD + Ad.CA-AMPK cells was accompanied by an increase in the level of the 50.7 kDa isoform of MCD protein in the mitochondria. This differential regulation of MCD expression and activity in the mitochondria by AMPK may potentially regulate malonyl-CoA levels at sites nearby CPT-I on the mitochondria.

Investigating the Energetic Ordering of Stable and Metastable TiO 2 Polymorphs Using DFT+ U and Hybrid Functionals

DOE PAGES

Curnan, Matthew T.; Kitchin, John R.

2015-08-12

Prediction of transition metal oxide BO 2 (B = Ti, V, etc.) polymorph energetic properties is critical to tunable material design and identifying thermodynamically accessible structures. Determining procedures capable of synthesizing particular polymorphs minimally requires prior knowledge of their relative energetic favorability. Information concerning TiO 2 polymorph relative energetic favorability has been ascertained from experimental research. In this study, the consistency of first-principles predictions and experimental results involving the relative energetic ordering of stable (rutile), metastable (anatase and brookite), and unstable (columbite) TiO 2 polymorphs is assessed via density functional theory (DFT). Considering the issues involving electron–electron interaction and chargemore » delocalization in TiO 2 calculations, relative energetic ordering predictions are evaluated over trends varying Ti Hubbard U 3d or exact exchange fraction parameter values. Energetic trends formed from varying U 3d predict experimentally consistent energetic ordering over U 3d intervals when using GGA-based functionals, regardless of pseudopotential selection. Given pertinent linear response calculated Hubbard U values, these results enable TiO 2 polymorph energetic ordering prediction. Here, the hybrid functional calculations involving rutile–anatase relative energetics, though demonstrating experimentally consistent energetic ordering over exact exchange fraction ranges, are not accompanied by predicted fractions, for a first-principles methodology capable of calculating exact exchange fractions precisely predicting TiO 2 polymorph energetic ordering is not available.« less

Time-fractional Cahn-Allen and time-fractional Klein-Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Yusuf, Abdullahi; Isa Aliyu, Aliyu; Baleanu, Dumitru

2018-03-01

This research analyzes the symmetry analysis, explicit solutions and convergence analysis to the time fractional Cahn-Allen (CA) and time-fractional Klein-Gordon (KG) equations with Riemann-Liouville (RL) derivative. The time fractional CA and time fractional KG are reduced to respective nonlinear ordinary differential equation of fractional order. We solve the reduced fractional ODEs using an explicit power series method. The convergence analysis for the obtained explicit solutions are investigated. Some figures for the obtained explicit solutions are also presented.

Novel control of gel fraction and enhancement of bonding strength for constructing 3D architecture of tissue engineering scaffold with alginate tubular fiber.

PubMed

Li, Yu; Liu, Yuanyuan; Li, Shuai; Liang, Gang; Jiang, Chen; Hu, Qingxi

2016-01-01

Alginate tubular fiber has been successfully prepared via coaxial fluid crosslink mode, which is potentially used for the construction of vascularized tissue engineering scaffolds (VTES). However, its elastic and smooth surface is negative for the adhesion of fibers. In this study, the gel fractions were controlled in a novel way of two-step crosslink process in order to meet the needs of each processing link. Based on such consideration, an appropriate formulation was selected to direct write single fiber, which ensured the tubular structure with enough gel portion as well as adhesion between fibers with the reserved sol. Finally, the integrity of the scaffolds had a further development within the 2nd crosslink bath process, which would help to solve the question of poor shear resistance for hydrogel scaffolds. Copyright © 2015 The Society for Biotechnology, Japan. Published by Elsevier B.V. All rights reserved.

Flexible body stability analysis of Space Shuttle ascent flight control system by using lambda matrix solution techniques

NASA Technical Reports Server (NTRS)

Bown, R. L.; Christofferson, A.; Lardas, M.; Flanders, H.

1980-01-01

A lambda matrix solution technique is being developed to perform an open loop frequency analysis of a high order dynamic system. The procedure evaluates the right and left latent vectors corresponding to the respective latent roots. The latent vectors are used to evaluate the partial fraction expansion formulation required to compute the flexible body open loop feedback gains for the Space Shuttle Digital Ascent Flight Control System. The algorithm is in the final stages of development and will be used to insure that the feedback gains meet the design specification.

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.

Extension of the root-locus method to a certain class of fractional-order systems.

PubMed

Merrikh-Bayat, Farshad; Afshar, Mahdi; Karimi-Ghartemani, Masoud

2009-01-01

In this paper, the well-known root-locus method is developed for the special subset of linear time-invariant systems commonly known as fractional-order systems. Transfer functions of these systems are rational functions with polynomials of rational powers of the Laplace variable s. Such systems are defined on a Riemann surface because of their multi-valued nature. A set of rules for plotting the root loci on the first Riemann sheet is presented. The important features of the classical root-locus method such as asymptotes, roots condition on the real axis and breakaway points are extended to the fractional case. It is also shown that the proposed method can assess the closed-loop stability of fractional-order systems in the presence of a varying gain in the loop. Moreover, the effect of perturbation on the root loci is discussed. Three illustrative examples are presented to confirm the effectiveness of the proposed algorithm.

A multi-domain spectral method for time-fractional differential equations

NASA Astrophysics Data System (ADS)

Chen, Feng; Xu, Qinwu; Hesthaven, Jan S.

2015-07-01

This paper proposes an approach for high-order time integration within a multi-domain setting for time-fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.

5 CFR 838.306 - Specifying type of annuity for application of formula, percentage or fraction.

Code of Federal Regulations, 2010 CFR

2010-01-01

... application of formula, percentage or fraction. 838.306 Section 838.306 Administrative Personnel OFFICE OF... for application of formula, percentage or fraction. (a) A court order directed at employee annuity that states the former spouse's share of employee annuity as a formula, percentage, or fraction is not...

29 CFR 4206.5 - Amount of credit in plans using the modified presumptive method.

Code of Federal Regulations, 2010 CFR

2010-07-01

... section, multiplied by the fractions described or determined under paragraph (c) of this section. When an... multiplied by the two fractions described in this paragraph in order to determine the amount of old liabilities that was previously assessed against the employer. (1) The first fraction is the fraction...

Fate of lignin, cutin and suberin in soil organic matter fractions - an incubation experiment

NASA Astrophysics Data System (ADS)

Mueller, Carsten W.; Mueller, Kevin E.; Freeman, Katherine H.; Ingrid, Kögel-Knabner

2010-05-01

The turnover of soil organic matter (SOM) is controlled by its chemical composition, its spatial accessibility and the association with the mineral phase. Separation of bulk soils by physical fractionation and subsequent chemical analysis of these fractions should give insights to how compositional differences in SOM drive turnover rates of different size-defined carbon pools. The main objective of this study was to elucidate the relative abundance and recalcitrance of lignin, cutin and suberin in aggregated bulk soils and SOM fractions in the course of SOM decomposition. Bulk soils and physically-separated size fractions (sand, silt and clay) of the Ah horizon of a forest soil (under Picea abies L.Karst) were parallel incubated over a period of one year. In order to differentiate between particulate OM (POM) and mineral-associated SOM the particle size fractions were additionally separated by density after the incubation experiment. We used solid-state 13C-CPMAS NMR spectroscopy and GC-MS (after copper oxide oxidation and solvent extraction) to analyze the composition of the incubated samples. The abundance and isotopic composition (including 13C and 14C) of the respired CO2 further enabled us to monitor the dynamics of SOM mineralization. This approach allowed for differentiating between C stabilization of soil fractions due to accessibility/aggregation and to biochemical recalcitrance at different scales of resolution (GC-MS, NMR). We found a relative enrichment of alkyl C and decreasing lignin contents in the order of sand < silt < clay by 13C-NMR spectroscopy and GC-MS within soils and fractions before the incubation, resulting in increased lipid to lignin ratios with decreasing particle size. An accumulation of aliphatic C compounds was especially found for the small silt and clay sized particulate OM (POM). For the fresh particulate OM (POM) of the sand fraction a clear decay of lignin was observed in the course of the incubation experiment, indicated by decreasing C/V and increasing ac/alV ratios. A relative decrease of aliphatic C in the incubated fractions compared to the incubated bulk soils showed the preferential mineralization of less recalcitrant C compounds that were spatially inaccessible in aggregates of the bulk soil. Differences in the abundance of lignin monomers, hydroxyl acids, n-alkanols and n-fatty acid methyl esters measured by GC MS before and after the incubation indicated selective degradation and preservation patterns at the molecular scale.

Infrared maritime target detection using the high order statistic filtering in fractional Fourier domain

NASA Astrophysics Data System (ADS)

Zhou, Anran; Xie, Weixin; Pei, Jihong

2018-06-01

Accurate detection of maritime targets in infrared imagery under various sea clutter conditions is always a challenging task. The fractional Fourier transform (FRFT) is the extension of the Fourier transform in the fractional order, and has richer spatial-frequency information. By combining it with the high order statistic filtering, a new ship detection method is proposed. First, the proper range of angle parameter is determined to make it easier for the ship components and background to be separated. Second, a new high order statistic curve (HOSC) at each fractional frequency point is designed. It is proved that maximal peak interval in HOSC reflects the target information, while the points outside the interval reflect the background. And the value of HOSC relative to the ship is much bigger than that to the sea clutter. Then, search the curve's maximal target peak interval and extract the interval by bandpass filtering in fractional Fourier domain. The value outside the peak interval of HOSC decreases rapidly to 0, so the background is effectively suppressed. Finally, the detection result is obtained by the double threshold segmenting and the target region selection method. The results show the proposed method is excellent for maritime targets detection with high clutters.

Parts and 'holes': gaps in rational number sense among children with vs. without mathematical learning disabilities.

PubMed

Mazzocco, Michèle M M; Devlin, Kathleen T

2008-09-01

Many middle-school students struggle with decimals and fractions, even if they do not have a mathematical learning disability (MLD). In the present longitudinal study, we examined whether children with MLD have weaker rational number knowledge than children whose difficulty with rational numbers occurs in the absence of MLD. We found that children with MLD failed to accurately name decimals, to correctly rank order decimals and/or fractions, and to identify equivalent ratios (e.g. 0.5 = 1/2); they also 'identified' incorrect equivalents (e.g. 0.05 = 0.50). Children with low math achievement but no MLD accurately named decimals and identified equivalent pairs, but failed to correctly rank order decimals and fractions. Thus failure to accurately name decimals was an indicator of MLD; but accurate naming was no guarantee of rational number knowledge - most children who failed to correctly rank order fractions and decimals tests passed the naming task. Most children who failed the ranking tests at 6th grade also failed at 8th grade. Our findings suggest that a simple task involving naming and rank ordering fractions and decimals may be a useful addition to in-class assessments used to determine children's learning of rational numbers.

Stereotactic radiosurgery vs. fractionated radiotherapy for tumor control in vestibular schwannoma patients: a systematic review.

PubMed

Persson, Oscar; Bartek, Jiri; Shalom, Netanel Ben; Wangerid, Theresa; Jakola, Asgeir Store; Förander, Petter

2017-06-01

Repeated controlled studies have revealed that stereotactic radiosurgery is better than microsurgery for patients with vestibular schwannoma (VS) <3 cm in need of intervention. In this systematic review we aimed to compare results from single-fraction stereotactic radiosurgery (SRS) to fractionated stereotactic radiotherapy (FSRT) for patients with VS. We systematically searched MEDLINE, Web of Science, Embase and Cochrane and screened relevant articles for references. Publications from 1995 through 2014 with a minimum of 50 adult (>18 years) patients with unilateral VS, followed for a median of >5 years, were eligible for inclusion. After screening titles and abstracts of the 1094 identified articles and systematically reviewing 98 of these articles, 19 were included. Patients with unilateral VS treated with radiosurgery were compared to patients treated with fractionated stereotactic radiotherapy. No randomized controlled trial (RCT) was identified. None of the identified controlled studies comparing SRS with FSRT were eligible according to the inclusion criteria. Nineteen case series on SRS (n = 17) and FSRT (n = 2) were included in the systematic review. Loss of tumor control necessitating a new VS-targeted intervention was found in an average of 5.0% of the patients treated with SRS and in 4.8% treated with FSRT. Mean deterioration ratio for patients with serviceable hearing before treatment was 49% for SRS and 45% for FSRT, respectively. The risk for facial nerve deterioration was 3.6% for SRS and 11.2% for FSRT and for trigeminal nerve deterioration 6.0% for SRS and 8.4% for FSRT. Since these results were obtained from case series, a regular meta-analysis was not attempted. SRS and FSRT are both noninvasive treatment alternatives for patients with VS with low rates of treatment failure in need of rescue therapy. In this selection of patients, the progression-free survival rates were on the order of 92-100% for both treatment options. There is a lack of high-quality studies comparing radiation therapy alternatives for patients with VS. Finally, 19 articles reported long-term tumor control after SRS, while only 2 articles reported long-term FSRT results, making effect estimates more uncertain for FSRT.

Interpreting the role of pH on stable isotopes in large benthic foraminifera

USGS Publications Warehouse

Robbins, Lisa L.; Knorr, P.O.; Wynn, J.G.; Hallock, P.; Harries, P.

2016-01-01

Large benthic foraminifera (LBF) are prolific producers of calcium carbonate sediments in shallow, tropical environments that are being influenced by ocean acidification (OA). Two LBF species, Amphistegina gibbosa (Order Rotaliida) with low-Mg calcite tests and Archaias angulatus (Order Miliolida) with high-Mg calcite tests, were studied to assess the effects of pH 7.6 on oxygen and carbon isotopic fractionation between test calcite and ambient seawater. The δ18O and δ13C values of terminal chambers and of whole adult tests of both species after 6 weeks were not significantly different between pH treatments of 8.0 and 7.6. However, tests of juveniles produced during the 6-week treatments showed significant differences between δ18O and δ13C values from control (pH 8.0) when compared with the treatment (pH 7.6) for both species. Although each individual's growth was photographed and measured, difficulty in distinguishing and manually extracting newly precipitated calcite from adult specimens likely confounded any differences in isotopic signals. However, juvenile specimens that resulted from asexual reproduction that occurred during the experiments did not contain old carbonate that could confound the new isotopic signals. These data reveal a potential bias in the design of OA experiments if only adults are used to investigate changes in test chemistries. Furthermore, the results reaffirm that different calcification mechanisms in these two foraminiferal orders control the fractionation of stable isotopes in the tests and will reflect decreasing pH in seawater somewhat differently. .

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.

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.

Non-standard radiotherapy fractionations delay the time to malignant transformation of low-grade gliomas.

PubMed

Henares-Molina, Araceli; Benzekry, Sebastien; Lara, Pedro C; García-Rojo, Marcial; Pérez-García, Víctor M; Martínez-González, Alicia

2017-01-01

Grade II gliomas are slowly growing primary brain tumors that affect mostly young patients. Cytotoxic therapies (radiotherapy and/or chemotherapy) are used initially only for patients having a bad prognosis. These therapies are planned following the "maximum dose in minimum time" principle, i. e. the same schedule used for high-grade brain tumors in spite of their very different behavior. These tumors transform after a variable time into high-grade gliomas, which significantly decreases the patient's life expectancy. In this paper we study mathematical models describing the growth of grade II gliomas in response to radiotherapy. We find that protracted metronomic fractionations, i.e. therapeutical schedules enlarging the time interval between low-dose radiotherapy fractions, may lead to a better tumor control without an increase in toxicity. Other non-standard fractionations such as protracted or hypoprotracted schemes may also be beneficial. The potential survival improvement depends on the tumor's proliferation rate and can be even of the order of years. A conservative metronomic scheme, still being a suboptimal treatment, delays the time to malignant progression by at least one year when compared to the standard scheme.

Sensory Characteristics and Volatile Components of Dry Dog Foods Manufactured with Sorghum Fractions.

PubMed

Donfrancesco, Brizio Di; Koppel, Kadri

2017-06-17

Descriptive sensory analysis and gas chromatography-mass spectrometry (GC-MS) with a modified headspace solid-phase microextraction (SPME) method was performed on three extruded dry dog food diets manufactured with different fractions of red sorghum and a control diet containing corn, brewer's rice, and wheat as a grain source in order to determine the effect of sorghum fractions on dry dog food sensory properties. The aroma compounds and flavor profiles of samples were similar with small differences, such as higher toasted aroma notes, and musty and dusty flavor in the mill-feed sample. A total of 37 compounds were tentatively identified and semi-quantified. Aldehydes were the major group present in the samples. The total volatile concentration was low, reflecting the mild aroma of the samples. Partial least squares regression was performed to identify correlations between sensory characteristics and detected aroma compounds. Possible relationships, such as hexanal and oxidized oil, and broth aromatics were identified. Volatile compounds were also associated with earthy, musty, and meaty aromas and flavor notes. This study showed that extruded dry dog foods manufactured with different red sorghum fractions had similar aroma, flavor, and volatile profiles.

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.

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.

Abundant closed form solutions of the conformable time fractional Sawada-Kotera-Ito equation using (G‧ / G) -expansion method

NASA Astrophysics Data System (ADS)

Al-Shawba, Altaf Abdulkarem; Gepreel, K. A.; Abdullah, F. A.; Azmi, A.

2018-06-01

In current study, we use the (G‧ / G) -expansion method to construct the closed form solutions of the seventh order time fractional Sawada-Kotera-Ito (TFSKI) equation based on conformable fractional derivative. As a result, trigonometric, hyperbolic and rational functions solutions with arbitrary constants are obtained. When the arbitrary constants are taken some special values, the periodic and soliton solutions are obtained from the travelling wave solutions. The obtained solutions are new and not found elsewhere. The effect of the fractional order on some of these solutions are represented graphically to illustrate the behavior of the exact solutions when the parameter take some special choose.

A fractional approach to the Fermi-Pasta-Ulam problem

NASA Astrophysics Data System (ADS)

Machado, J. A. T.

2013-09-01

This paper studies the Fermi-Pasta-Ulam problem having in mind the generalization provided by Fractional Calculus (FC). The study starts by addressing the classical formulation, based on the standard integer order differential calculus and evaluates the time and frequency responses. A first generalization to be investigated consists in the direct replacement of the springs by fractional elements of the dissipative type. It is observed that the responses settle rapidly and no relevant phenomena occur. A second approach consists of replacing the springs by a blend of energy extracting and energy inserting elements of symmetrical fractional order with amplitude modulated by quadratic terms. The numerical results reveal a response close to chaotic behaviour.

Photonic fractional Fourier transformer with a single dispersive device.

PubMed

Cuadrado-Laborde, C; Carrascosa, A; Díez, A; Cruz, J L; Andres, M V

2013-04-08

In this work we used the temporal analog of spatial Fresnel diffraction to design a temporal fractional Fourier transformer with a single dispersive device, in this way avoiding the use of quadratic phase modulators. We demonstrate that a single dispersive passive device inherently provides the fractional Fourier transform of an incident optical pulse. The relationships linking the fractional Fourier transform order and scaling factor with the dispersion parameters are derived. We first provide some numerical results in order to prove the validity of our proposal, using a fiber Bragg grating as the dispersive device. Next, we experimentally demonstrate the feasibility of this proposal by using a spool of a standard optical fiber as the dispersive device.

Building micro-soccer-balls with evaporating colloidal fakir drops

NASA Astrophysics Data System (ADS)

Gelderblom, Hanneke; Marín, Álvaro G.; Susarrey-Arce, Arturo; van Housselt, Arie; Lefferts, Leon; Gardeniers, Han; Lohse, Detlef; Snoeijer, Jacco H.

2013-11-01

Drop evaporation can be used to self-assemble particles into three-dimensional microstructures on a scale where direct manipulation is impossible. We present a unique method to create highly-ordered colloidal microstructures in which we can control the amount of particles and their packing fraction. To this end, we evaporate colloidal dispersion drops from a special type of superhydrophobic microstructured surface, on which the drop remains in Cassie-Baxter state during the entire evaporative process. The remainders of the drop consist of a massive spherical cluster of the microspheres, with diameters ranging from a few tens up to several hundreds of microns. We present scaling arguments to show how the final particle packing fraction of these balls depends on the drop evaporation dynamics, particle size, and number of particles in the system.

Meanings for Fraction as Number-Measure by Exploring the Number Line

ERIC Educational Resources Information Center

Psycharis, Giorgos; Latsi, Maria; Kynigos, Chronis

2009-01-01

This paper reports on a case-study design experiment in the domain of fraction as number-measure. We designed and implemented a set of exploratory tasks concerning comparison and ordering of fractions as well as operations with fractions. Two groups of 12-year-old students worked collaboratively using paper and pencil as well as a specially…

Bertrand's theorem and virial theorem in fractional classical mechanics

NASA Astrophysics Data System (ADS)

Yu, Rui-Yan; Wang, Towe

2017-09-01

Fractional classical mechanics is the classical counterpart of fractional quantum mechanics. The central force problem in this theory is investigated. Bertrand's theorem is generalized, and virial theorem is revisited, both in three spatial dimensions. In order to produce stable, closed, non-circular orbits, the inverse-square law and the Hooke's law should be modified in fractional classical mechanics.

Historical Analysis of Melt Pond Fraction on Arctic Sea Ice Through the Synthesis of High- and Medium- Resolution Optical Satellite Remote Sensing.

NASA Astrophysics Data System (ADS)

Wright, N.; Polashenski, C. M.

2017-12-01

Snow, ice, and melt ponds cover the surface of the Arctic Ocean in fractions that change throughout the seasons. These surfaces exert tremendous influence over the energy balance of the Arctic Ocean by controlling the absorption of solar radiation. Here we demonstrate the use of a newly released, open source, image classification algorithm designed to identify surface features in high resolution optical satellite imagery of sea ice. Through explicitly resolving individual features on the surface, the algorithm can determine the percentage of ice that is covered by melt ponds with a high degree of certainty. We then compare observations of melt pond fraction extracted from these images with an established method of estimating melt pond fraction from medium resolution satellite images (e.g. MODIS). Because high resolution satellite imagery does not provide the spatial footprint needed to examine the entire Arctic basin, we propose a method of synthesizing both high and medium resolution satellite imagery for an improved determination of melt pond fraction across whole Arctic. We assess the historical trends of melt pond fraction in the Arctic ocean, and address the question: Is pond coverage changing in response to changing ice conditions? Furthermore, we explore the image area that must be observed in order to get a locally representative sample (i.e. the aggregate scale), and show that it is possible to determine accurate estimates of melt pond fraction by observing sample areas significantly smaller than the typical footprint of high-resolution satellite imagery.

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.

Multiple positive solutions to a coupled systems of nonlinear fractional differential equations.

PubMed

Shah, Kamal; Khan, Rahmat Ali

2016-01-01

In this article, we study existence, uniqueness and nonexistence of positive solution to a highly nonlinear coupled system of fractional order differential equations. Necessary and sufficient conditions for the existence and uniqueness of positive solution are developed by using Perov's fixed point theorem for the considered problem. Further, we also established sufficient conditions for existence of multiplicity results for positive solutions. Also, we developed some conditions under which the considered coupled system of fractional order differential equations has no positive solution. Appropriate examples are also provided which demonstrate our results.

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

Comparison of hysteresis, thermomagnetic, and low-temperature magnetic properties of particle-size fractions from loess and paleosol samples in Central Asia and the Chinese Loess Plateau

NASA Astrophysics Data System (ADS)

Zan, Jinbo; Fang, Xiaomin; Yan, Maodu; Shen, Miaomiao

2018-05-01

Hysteresis, thermomagnetic and low-temperature magnetic experiments on particle-size fractioned samples from the Chinese Loess Plateau (CLP) can be used to better characterize the magnetic mineralogy and magnetic granulometry of Chinese loess/paleosols. However, a systematic study of the grain-size-dependent magnetic mineralogy of the Central Asian loess deposits has not been undertaken. In this paper, four size fractions of seventeen loess and paleosol samples from Central Asia and the CLP were subjected to aforementioned rock magnetic measurements. Our findings are as follows: (1) In Central Asia, the fractionated samples from loess and paleosol couplets exhibit no obvious differences in their magnetic mineralogy due to weak pedogenesis. (2) Thermomagnetic analyses suggest that the content of maghemite in the clay fraction of paleosols from the CLP is one or two orders of magnitude larger than that of the loess samples from the CLP and Central Asia. This result does not support the view that maghemite in the loess/palaeosol sequences of the CLP originated mainly from eolian sources. (3) Both hysteresis and low-temperature magnetic experiments demonstrate that detrital ferrimagnetic grains are mostly enriched in the 20-75 μm fraction of loess/paleosols from Central Asia and the CLP. The relative paucity of coarser magnetic grains in the > 75 μm fractions indicate that a positive correlation does not always exist between the magnetic concentration parameters and the sedimentological particle size in Chinese loess deposits. (4) The regional variations in the magnetic properties of the 20-75 μm fraction suggest that the supply of clastic sediments is the main control on the magnetic properties of loess deposits in Central Asia.

Protective Effect of Ethyl Acetate Fraction of Stereospermum Suaveolens Against Hepatic Oxidative Stress in STZ Diabetic Rats

PubMed Central

Balasubramanian, Thirumalaiswamy; Senthilkumar, G. P; Karthikeyan, M.; Chatterjee, Tapan Kumar

2013-01-01

Stereospermum suaveolens is a folk remedy for the treatment of diabetes and liver disorders in southern parts of India. In the present study, the protective effect of the ethyl acetate fraction of ethanol extract from S. suaveolens against hepatic oxidative stress was evaluated in streptozotocin (STZ)-induced diabetic rats for 14 days. The ethyl acetate fraction was administered orally to the STZ diabetic rats at the doses of 200 and 400 mg/kg. Blood glucose level was measured according to glucose oxidase method. In order to determine hepatoprotective activity, changes in the levels of serum biomarker enzymes such as aspartate transaminase (AST), alanine transaminase (ALT), and serum alkaline phosphatase (SALP) were assessed in the ethyl acetate fraction treated diabetic rats and were compared with the levels in diabetic control rats. In addition, the antioxidant activity of ethyl acetate fraction was evaluated using various hepatic parameters such as thiobarbituric acid reactive substances (TBARS), reduced glutathione (GSH), superoxide dismutase (SOD), and catalase (CAT). It was found that administration of ethyl acetate fraction (200 and 400 mg/kg) produced a significant (P < 0.001) fall in fasting blood glucose level, TBARS, bilirubin, AST, ALT, and SALP, while elevating the GSH levels, and SOD and CAT activities in diabetic rats. Histopathologic studies also revealed the protective effect of ethyl acetate fraction on the liver tissues of diabetic rats. It was concluded from this study that the ethyl acetate fraction from ethanol extract of S. suaveolens modulates the activity of enzymatic and nonenzymatic antioxidants and enhances the defense against hepatic oxidative stress in STZ-induced diabetic rats. PMID:24716175

Chemical profiling and cytotoxicity assay of bufadienolides in toad venom and toad skin.

PubMed

Meng, Qiong; Yau, Lee-Fong; Lu, Jing-Guang; Wu, Zhen-Zhen; Zhang, Bao-Xian; Wang, Jing-Rong; Jiang, Zhi-Hong

2016-07-01

Toad venom and toad skin have been widely used for treating various cancers in China. Bufadienolides are regarded as the main anticancer components of toad venom, but the difference on composition and anticancer activities of bufadienolides between toad venom and toad skin remains unclear. Fractions enriched with free and conjugated bufadienolides were prepared from toad venom and toad skin. Bufadienolides in each fraction were comprehensively profiled by using a versatile UHPLC-TOF-MS method. Relative contents of major bufadienolides were determined by using three bufogenins and one bufotoxin as marker compounds with validated UHPLC-TOF-MS method. Furthermore, cytotoxicity of the fractions was examined by MTT assay. Two fractions, i.e., bufogenin and bufotoxin fractions (TV-F and TV-C) were isolated from toad venom, and one bufotoxin fraction (TS-C) was isolated from toad skin. Totally 56 bufadienolides in these three fractions were identified, and 29 were quantified or semi-quantified. Bufotoxins were identified in both toad venom and toad skin, whereas bufogenins exist only in toad venom. Bufalin-3-conjugated bufotoxins are major components in toad venom, whereas cinobufotalin and cinobufagin-3-conjugated bufotoxins are main bufotoxins in toad skin. MTT assay revealed potent cytotoxicity of all the fractions in an order of TV-F>TV-C>TS-C. Our study represents the most comprehensive investigation on the chemical profiles of toad venom and toad skin from both qualitative and quantitative aspects. Eight bufotoxins were identified in toad skin responsible for the cytotoxicity for the first time. Our research provides valuable chemical evidence for the appropriate processing method, quality control and rational exploration of toad skin and toad venom for the development of anticancer medicines. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Alpine lakes preserve mineral dust signatures: Implications for long-range mineral dust transport and Last Glacial Maximum (LGM) tornado frequency in the United States

NASA Astrophysics Data System (ADS)

Bhattacharya, A.; Lora, J. M.; Pollen, A.; Vollmer, T.; Thomas, M.; Leithold, E. L.; Mitchell, J.; Tripati, A.

2016-12-01

The net amount of mineral dust accumulation in arid and semi-arid regions might not be entirely sourced locally or even regionally; in fact, new evidence suggests that there could be significant contributions from distal sources. The contribution from the distal sources needs to be identified, and accounted for, in order to accurately understand the meteorological and climatologic factors, both regional and global, that control mineral dust accumulation in arid and semi-arid regions. Most importantly, if identified, the two components of mineral dust accumulation- fine fraction (typically <4 microns) and coarse fraction (typically >25 microns)- could provide critical information about regional as well as global climate. There are large-scale climatological controls on the finer fraction of mineral dust, while the coarser fraction is related to intense invents (i.e., the occurrence of cyclones). However, studies attempting to separate these two size fractions in terrestrial archives have been limited. Here we separate the two size fractions using grain size analysis, and use trace element analysis in each size fraction to identify contributing source regions. We apply this technique to well-dated cores collected from three lakes that are distributed across the western, southwestern and Great Plains in the United States: Pear Lake in the Sierra Nevada Mountains (CA), Senator Beck Lake in the San Juan Mountains (CO), and North Lake (WY). These lakes are uniquely situated to monitor dust fluxes; previous studies have demonstrated that sedimentation in these lakes are dominated by mineral dust accumulation; there is also evidence of remotely and locally sourced dust in these lakes, and of textural differences between the two types of dust fractions. We compare our results with previously published data on dust from loess deposits in the United States, and isotopic modeling (LMDZ). We find evidence that the finer-grain size fraction in alpine lake cores could be of remote origin; work is underway to quantify this contribution. Most importantly, we find that during the Last Glacial Maximum (LGM) the Great Plains may not have witnessed an increase in the incidence of tornado frequency. Acknowledgements: James Sigman, Jacob Ashford, Jason Neff and Amato Evan

Some applications of the multi-dimensional fractional order for the Riemann-Liouville derivative

NASA Astrophysics Data System (ADS)

Ahmood, Wasan Ajeel; Kiliçman, Adem

2017-01-01

In this paper, the aim of this work is to study theorem for the one-dimensional space-time fractional deriative, generalize some function for the one-dimensional fractional by table represents the fractional Laplace transforms of some elementary functions to be valid for the multi-dimensional fractional Laplace transform and give the definition of the multi-dimensional fractional Laplace transform. This study includes that, dedicate the one-dimensional fractional Laplace transform for functions of only one independent variable and develop of the one-dimensional fractional Laplace transform to multi-dimensional fractional Laplace transform based on the modified Riemann-Liouville derivative.

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.

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

Order or chaos in Boolean gene networks depends on the mean fraction of canalizing functions

NASA Astrophysics Data System (ADS)

Karlsson, Fredrik; Hörnquist, Michael

2007-10-01

We explore the connection between order/chaos in Boolean networks and the naturally occurring fraction of canalizing functions in such systems. This fraction turns out to give a very clear indication of whether the system possesses ordered or chaotic dynamics, as measured by Derrida plots, and also the degree of order when we compare different networks with the same number of vertices and edges. By studying also a wide distribution of indegrees in a network, we show that the mean probability of canalizing functions is a more reliable indicator of the type of dynamics for a finite network than the classical result on stability relating the bias to the mean indegree. Finally, we compare by direct simulations two biologically derived networks with networks of similar sizes but with power-law and Poisson distributions of indegrees, respectively. The biologically motivated networks are not more ordered than the latter, and in one case the biological network is even chaotic while the others are not.

Origini Concettuali di Errori che si Riscontrano Nel Confrontare Numeri Decimali e Frazioni=Conceptual Sources of Difficulties Concerning the Ordering of Decimal Numbers and the Comparison of Fractions.

ERIC Educational Resources Information Center

Bonotto, C.

1993-01-01

Examined fifth-grade students' survey responses to investigate incorrect rules that derive from children's efforts to interpret decimals as integers or as fractions. Regarding fractions, difficulties arise because only the whole-part approach to fractions is presented in elementary school. (Author/MDH)

A study of fractional Schrödinger equation composed of Jumarie fractional derivative

NASA Astrophysics Data System (ADS)

Banerjee, Joydip; Ghosh, Uttam; Sarkar, Susmita; Das, Shantanu

2017-04-01

In this paper we have derived the fractional-order Schrödinger equation composed of Jumarie fractional derivative. The solution of this fractional-order Schrödinger equation is obtained in terms of Mittag-Leffler function with complex arguments, and fractional trigonometric functions. A few important properties of the fractional Schrödinger equation are then described for the case of particles in one-dimensional infinite potential well. One of the motivations for using fractional calculus in physical systems is that the space and time variables, which we often deal with, exhibit coarse-grained phenomena. This means infinitesimal quantities cannot be arbitrarily taken to zero - rather they are non-zero with a minimum spread. This type of non-zero spread arises in the microscopic to mesoscopic levels of system dynamics, which means that, if we denote x as the point in space and t as the point in time, then limit of the differentials d x (and d t) cannot be taken as zero. To take the concept of coarse graining into account, use the infinitesimal quantities as (Δ x) α (and (Δ t) α ) with 0 < α < 1; called as `fractional differentials'. For arbitrarily small Δ x and Δ t (tending towards zero), these `fractional' differentials are greater than Δ x (and Δ t), i.e. (Δ x) α > Δ x and (Δ t) α > Δ t. This way of defining the fractional differentials helps us to use fractional derivatives in the study of dynamic systems.

[Responses of accumulation-loss patterns for soil organic carbon and its fractions to tillage and water erosion in black soil area].

PubMed

Zhao, Peng Zhi; Chen, Xiang Wei; Wang, En Heng

2017-11-01

Tillage and water erosion have been recognized as the main factors causing degradation in soil organic carbon (SOC) pools of black soil. To further explore the response of SOC and its fractions to different driving forces of erosion (tillage and water), geostatistical methods were used to analyze spatial patterns of SOC and its three fractions at a typical sloping farmland based on tillage and water erosion rates calculated by local models. The results showed that tillage erosion and deposition rates changed according to the slope positions, decreasing in the order: upper-slope > lower-slope > middle-slope > toe-slope and toe-slope > lower-slope > middle-slope > upper-slope, respectively; while the order of water erosion rates decreased in the order: lower-slope > toe-slope > middle-slope > upper-slope. Tillage and water erosion cooperatively triggered intense soil loss in the lower-slope areas with steep slope gradient. Tillage erosion could affect C cycling through the whole slope at different levels, although the rate of tillage erosion (0.02-7.02 t·hm -2 ·a -1 ) was far less than that of water erosion (5.96-101.17 t·hm -2 ·a -1 ) in black soil area. However, water erosion only played a major role in controlling C dynamics in the runoff-concentrated lower slope area. Affected by water erosion and tillage erosion-deposition disturbance, the concentrations of SOC, particulate organic carbon and dissolved organic carbon in depositional areas were higher than in erosional areas, however, microbial biomass carbon showed an opposite trend. Tillage erosion dominated SOC dynamic by depleting particulate organic carbon.

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.

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.

The Redox Dynamics of Iron in a Seasonally Waterlogged Forest Soil (Chaux Forest, Eastern France) Traced with Rare Earth Element Distribution Patterns

NASA Astrophysics Data System (ADS)

Steinmann, M.; Floch, A. L.; Lucot, E.; Badot, P. M.

2014-12-01

The oxyhydroxides of iron are common soil minerals and known to control the availability of various major and trace elements essential for biogeochemical processes. We present a study from acidic natural forest soils, where reducing redox conditions due to seasonal waterlogging lead to the dissolution of Fe-oxyhydroxides, and to the release of Fe to soil water. In order to study in detail the mechanism of redox cycling of Fe, we used Rare Earth Element (REE) distribution patterns, because an earlier study has shown that they are a suitable tool to identify trace metal sources during soil reduction in wetland soils (Davranche et al., 2011). The REE patterns of soil leachates obtained with the modified 3-step BCR extraction scheme of Rauret et al., (1999) were compared with those of natural soil water. The adsorbed fractions (F1 leach), the reducible fraction of the deepest soil horizon H4 (F2 leach, 50-120 cm), and the oxidizable fractions of horizons H2 to H4 (F3 leachs, 24-120 cm) yielded REE patterns almost identical to soil water (see figure), showing that the REE and trace metal content of soil water was mainly derived from the F1 pool, and from the F2 and F3 pools of the clay mineral-rich deep soil horizons. In contrast, the F2 leach mobilized mainly Fe-oxyhydroxides associated with organic matter of the surface soil and yielded REE patterns significantly different from those of soil water. These results suggest that the trace metal content of soil water in hydromorphic soils is primarily controlled by the clay fraction of the deeper soil horizons and not by organic matter and related Fe-oxyhydroxides of the surface soil. Additional analyses are in progress in order to verify whether the REE and trace metals of the deeper soil horizons were directly derived from clay minerals or from associated Fe-oxyhydroxide coatings. Refs cited: Davranche et al. (2011), Chem. Geol. 284; Rauret et al. (1999), J. Environ. Monit. 1.

Exercise for Preventing Hospitalization and Readmission in Adults with Congestive Heart Failure.

PubMed

Aronow, Wilbert S; Shamliyan, Tatyana A

2018-05-04

We critically appraised all available evidence regarding exercise interventions for improving patient survival and reducing hospital admissions in adults with chronic heart failure (HF). We searched 4 databases up to April 2018 and graded the quality of evidence according to the Grading of Recommendations Assessment, Development and Evaluation (GRADE) working group approach. We reviewed 7 meta-analyses and the publications of 48 randomized, controlled trials (RCT). In HF with reduced ejection fraction, low-quality evidence suggests that exercise prevents all-cause hospitalizations (RR 0.77; 95% CI 0.63;0.93; 1328 patients in 15 RCTs) and hospitalizations due to HF (RR 0.57; 95% CI 0.37;0.88; 1073 patients in 13 RCTs) and improves quality of life (standardized mean difference [SMD] -0.37; 95% CI -0.60;-0.14; 1270 patients in 25 RCTs) but has no effect on mortality. In HF with preserved ejection fraction, low-quality evidence suggests that exercise improves peak oxygen uptake (mean difference [MD] 2.36; 95% CI 1.16;3.57; 171 patients in 3 RCTs) and quality of life (MD -4.65; 95% CI -8.46;-0.83; 203 patients in 4 RCTs). In patients after heart transplantation, low-quality evidence suggests that exercise improves peak oxygen uptake (SMD 0.68; 95% CI 0.43;0.93; 284 patients in 9 RCTs) but does not improve quality of life. In order to reduce hospitalization and improve quality of life for adults with HF and reduced ejection fraction, clinicians should recommend exercise interventions. For adults with HF and preserved ejection fraction and in those undergoing heart transplantation, clinicians may recommend exercise interventions in order to improve peak oxygen uptake.

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.

Malva sylvestris Inhibits Inflammatory Response in Oral Human Cells. An In Vitro Infection Model

PubMed Central

Benso, Bruna; Rosalen, Pedro Luiz; Alencar, Severino Matias; Murata, Ramiro Mendonça

2015-01-01

The aim of this study was to investigate the in vitro anti-inflammatory activity of Malva sylvestris extract (MSE) and fractions in a co-culture model of cells infected by Aggregatibacter actinomycetemcomitans. In addition, we evaluated the phytochemical content in the extract and fractions of M. sylvestris and demonstrated that polyphenols were the most frequent group in all samples studied. An in vitro dual-chamber model to mimic the periodontal structure was developed using a monolayer of epithelial keratinocytes (OBA-9) and a subepithelial layer of fibroblasts (HGF-1). The invasive periodontopathogen A. actinomycetemcomitans (D7S-1) was applied to migrate through the cell layers and induce the synthesis of immune factors and cytokines in the host cells. In an attempt to analyze the antimicrobial properties of MSE and fractions, a susceptibility test was carried out. The extract (MIC 175 μg/mL, MBC 500μg/mL) and chloroform fraction (MIC 150 μg/mL, MBC 250 μg/mL) were found to have inhibitory activity. The extract and all fractions were assessed using a cytotoxicity test and results showed that concentrations under 100 μg/mL did not significantly reduce cell viability compared to the control group (p > 0.05, viability > 90%). In order to analyze the inflammatory response, transcriptional factors and cytokines were quantified in the supernatant released from the cells. The chloroform fraction was the most effective in reducing the bacterial colonization (p< 0.05) and controlling inflammatory mediators, and promoted the down-regulation of genes including IL-1beta, IL-6, IL-10, CD14, PTGS, MMP-1 and FOS as well as the reduction of the IL-1beta, IL-6, IL-8 and GM-CSF protein levels (p< 0.05). Malva sylvestris and its chloroform fraction minimized the A. actinomycetemcomitans infection and inflammation processes in oral human cells by a putative pathway that involves important cytokines and receptors. Therefore, this natural product may be considered as a successful dual anti-inflammatory–antimicrobial candidate. PMID:26479870

Manufacture of fiber-epoxy test specimens: Including associated jigs and instrumentation

NASA Technical Reports Server (NTRS)

Mathur, S. B.; Felbeck, D. K.

1980-01-01

Experimental work on the manufacture and strength of graphite-epoxy composites is considered. The correct data and thus a true assessment of the strength properties based on a proper and scientifically modeled test specimen with engineered design, construction, and manufacture has led to claims of a very broad spread in optimized values. Such behavior is in the main due to inadequate control during manufacture of test specimen, improper curing, and uneven scatter in the fiber orientation. The graphite fibers are strong but brittle. Even with various epoxy matrices and volume fraction, the fracture toughness is still relatively low. Graphite-epoxy prepreg tape was investigated as a sandwich construction with intermittent interlaminar bonding between the laminates in order to produce high strength, high fracture toughness composites. The quality and control of manufacture of the multilaminate test specimen blanks was emphasized. The dimensions, orientation and cure must be meticulous in order to produce the desired mix.

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.

Well-posedness of the Einstein-Euler system in asymptotically flat spacetimes: The constraint equations

NASA Astrophysics Data System (ADS)

Brauer, Uwe; Karp, Lavi

This paper deals with the construction of initial data for the coupled Einstein-Euler system. We consider the condition where the energy density might vanish or tend to zero at infinity, and where the pressure is a fractional power of the energy density. In order to achieve our goals we use a type of weighted Sobolev space of fractional order. The common Lichnerowicz-York scaling method (Choquet-Bruhat and York, 1980 [9]; Cantor, 1979 [7]) for solving the constraint equations cannot be applied here directly. The basic problem is that the matter sources are scaled conformally and the fluid variables have to be recovered from the conformally transformed matter sources. This problem has been addressed, although in a different context, by Dain and Nagy (2002) [11]. We show that if the matter variables are restricted to a certain region, then the Einstein constraint equations have a unique solution in the weighted Sobolev spaces of fractional order. The regularity depends upon the fractional power of the equation of state.

Detrital Controls on Dissolved Organic Matter in Soils: A Field Experiment

NASA Astrophysics Data System (ADS)

Lajtha, K.; Crow, S.; Yano, Y.; Kaushal, S.; Sulzman, E.; Sollins, P.

2004-12-01

We established a long-term field study in an old growth coniferous forest at the H.J. Andrews Experimental Forest, OR, to address how detrital quality and quantity control soil organic matter accumulation and stabilization. The Detritus Input and Removal Treatments (DIRT) plots consist of treatments that double leaf litter, double woody debris inputs, exclude litter inputs, or remove root inputs via trenching. We measured changes in soil solution chemistry with depth, and conducted long-term incubations of bulk soils and soil density fractions from different treatments in order to elucidate effects of detrital inputs on the relative amounts and lability of different soil C pools. In the field, the effect of adding woody debris was to increase dissolved organic carbon (DOC) concentrations in O-horizon leachate and at 30 cm, but not at 100 cm, compared to control plots, suggesting increased rates of DOC retention with added woody debris. DOC concentrations decreased through the soil profile in all plots to a greater degree than did dissolved organic nitrogen (DON), most likely due to preferential sorption of high C:N hydrophobic dissolved organic matter (DOM) in upper horizons; %hydrophobic DOM decreased significantly with depth, and hydrophilic DOM had a much lower and narrower C:N ratio. Although laboratory extracts of different litter types showed differences in DOM chemistry, percent hydrophobic DOM did not differ among detrital treatments in the field, suggesting microbial equalization of DOM leachate in the field. In long-term laboratory incubations, light fraction material did not have higher rates of respiration than heavy fraction or bulk soils, suggesting that physical protection or N availability controls different turnover times of heavy fraction material, rather than differences in chemical lability. Soils from plots that had both above- and below-ground litter inputs excluded had significantly lower DOC loss rates, and a non-significant trend for lower respiration rates . Soils from plots with added wood had similar respiration and DOC loss rates as control soils, suggesting that the additional DOC sorption observed in the field in these soils was stabilized in the soil and not readily lost upon incubation.

Biogeochemical implications of labile phosphorus in forest soils determined by the Hedley fractionation procedure.

PubMed

Johnson, Arthur H; Frizano, Jaqueline; Vann, David R

2003-05-01

Forest ecologists and biogeochemists have used a variety of extraction techniques to assess labile vs. non-labile soil P pools in chronosequences, the balance between biological vs. geochemical control of P transformations across a wide range of soil orders, the role of plants with either N-fixing or mycorrhizal symbionts in controlling soil P fractions, and to make inferences about plant-available P. Currently, variants of the sequential extraction procedure developed by M. J. Hedley and co-workers afford the greatest discrimination among labile and non-labile organic and inorganic P pools. Results of recent studies that used this technique to evaluate P fractions in forest soils indicate the following: (1) in intact, highly weathered forest soils of the humid tropics, Hedley-labile P values are several times larger than extractable P values resulting from mildly acidic extracting solutions which were commonly used in the past 2 decades; (2) pools of Hedley-labile P are several times larger than the annual forest P requirement and P required from the soil annually in both temperate and tropical forests; (3) long-term trends in non-labile P pools during pedogenesis are adequately represented by the Walker and Syers' model of changes in P fractionation during soil development. However, to better represent trends in pools that can supply plant-available P across forest soils of different age and weathering status, the paradigm should be modified; and (4) across a wide range of tropical and temperate forest soils, organic matter content is an important determinant of Hedley-labile P.

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.

Lie symmetry analysis, exact solutions and conservation laws for the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa

2018-06-01

In this work, we investigate the Lie symmetry analysis, exact solutions and conservation laws (Cls) to the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGDK) equation with Riemann-Liouville (RL) derivative. The time fractional CDGDK is reduced to nonlinear ordinary differential equation (ODE) of fractional order. New exact traveling wave solutions for the time fractional CDGDK are obtained by fractional sub-equation method. In the reduced equation, the derivative is in Erdelyi-Kober (EK) sense. Ibragimov's nonlocal conservation method is applied to construct Cls for time fractional CDGDK.

Ruthenium(III) catalyzed oxidation of sugar alcohols by dichloroisocyanuric acid—A kinetic study

NASA Astrophysics Data System (ADS)

Lakshman Kumar, Y.; Venkata Nadh, R.; Radhakrishnamurti, P. S.

2016-02-01

Kinetics of ruthenium(III) catalyzed oxidation of biologically important sugar alcohols (myo-inositol, D-sorbitol, and D-mannitol) by dichloroisocyanuric acid was carried out in aqueous acetic acid—perchloric medium. The reactions were found to be first order in case of oxidant and ruthenium(III). Zero order was observed with the concentrations of sorbitol and mannitol whereas, a positive fractional order was found in the case of inositol concentration. An inverse fractional order was observed with perchloric acid in oxidation of three substrates. Arrhenius parameters were calculated and a plausible mechanism was proposed.

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.

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.

Robust H(∞) positional control of 2-DOF robotic arm driven by electro-hydraulic servo system.

PubMed

Guo, Qing; Yu, Tian; Jiang, Dan

2015-11-01

In this paper an H∞ positional feedback controller is developed to improve the robust performance under structural and parametric uncertainty disturbance in electro-hydraulic servo system (EHSS). The robust control model is described as the linear state-space equation by upper linear fractional transformation. According to the solution of H∞ sub-optimal control problem, the robust controller is designed and simplified to lower order linear model which is easily realized in EHSS. The simulation and experimental results can validate the robustness of this proposed method. The comparison result with PI control shows that the robust controller is suitable for this EHSS under the critical condition where the desired system bandwidth is higher and the external load of the hydraulic actuator is closed to its limited capability. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Probing Schrodinger equation with a continued fraction potential

NASA Astrophysics Data System (ADS)

Ahmed, Nasr; Alamri, Sultan Z.; Rassem, M.

2018-06-01

We suggest a new perturbed form of the quantum potential and investigate the possible solutions of Schrodinger equation. The new form can be written as a finite or infinite continued fraction. a comparison has been given between the continued fractional potential and the non-perturbed potential. We suggest the validity of this continued fractional quantum form in some quantum systems. As the order of the continued fraction increases the difference between the perturbed and the ordinary potentials decreases. The physically acceptable solutions critically depend on the values of the continued fraction coefficients αi .

The Concept of Fractional Number among Hearing-Impaired Students.

ERIC Educational Resources Information Center

Titus, Janet C.

This study investigated hearing-impaired students' understanding of the mathematical concept of fractional numbers, as measured by their ability to determine the order and equivalence of fractional numbers. Twenty-one students (ages 10-16) with hearing impairments were compared with 26 students with normal hearing. The study concluded that…

Nitrogen stabilization in organo-mineral fractions from soils with different land uses

NASA Astrophysics Data System (ADS)

Giannetta, Beatrice; Zaccone, Claudio; Rovira, Pere; Vischetti, Costantino; Plaza, César

2017-04-01

Understanding the processes that control quantity and quality of soil organic matter (SOM) interacting with mineral surfaces is of paramount importance. Although several physical fractionation methods have been proposed to date to obtain fractions that mirror SOM degree of stability and protection, a detailed quantification of stabilisation modes through which SOM bounds to the mineral matrix is still lacking. In this research we determined C and N distribution in several soils including coniferous and broadleaved forest soils, grassland soils, technosols and an agricultural soil amended with biochar at rates of 0 and 20 t/ha in a factorial combination with two types of organic amendment (municipal solid waste compost and sewage sludge). We performed a physical size fractionation by ultrasonic dispersion and wet sieving, splitting particles into four different size fractions: coarse sand (2000-200 µm diameter), fine sand (200-50 µm), coarse silt (50-20 µm) and fine silt plus clay (<20 µm). The fraction <20 µm, that includes organo-mineral complexes, was then subjected to the organo-mineral fractionation method (SOF) proposed by Lopez-Sangil and Rovira (2013), in order to define the importance of different stabilization modes. This method, in fact, allows resolving the nature of different bonds between mineral and organic components by the use of sequential extractions with chemical reagents (potassium sulphate, sodium tetraborate, sodium pyrophosphate, sodium hydroxide, sodium hydroxide after weak acid attack, sodium hydroxide after sodium dithionite pretreatment, and sodium hydroxide after hydrofluoric acid pretreatments). Elemental analysis (CHN) was then carried out on SOM pools isolated from different fractions. Preliminary data show that, for all land uses in general, and for grassland soils in particular, most of the total N is found in organo-mineral complexes (fraction <20 µm). The total N content of the size fractions, especially of the <20um fraction, was highly correlated with whole soil N content. Although a small N loss was observed during the fractionation procedure, especially in N-rich samples, and data analysis is still ongoing, these preliminary results could already represent a valuable insight into organic N stabilization by mineral matrix.

Hydroxybenzoic Acids Are Significant Contributors to the Antioxidant Effect of Borututu Bark, Cochlospermum angolensis Welw. ex Oliv.

PubMed Central

Abourashed, Ehab A.; Fu, Hao Wen

2017-01-01

Borututu (Cochlospermum angolensis) is an African tree whose bark has recently emerged as a herbal dietary supplement with claims for antioxidant activity. In order to substantiate the claimed activity of borututu supplements, we performed an activity-guided fractionation of the total extract utilizing a 1,1-diphenyl-2-picrylhydrazyl (DPPH) free radical scavenging assay. Subsequent flash and centrifugal chromatography resulted in the isolation of gallic acid (1) and protocatechuic acid (2) as the main antioxidant constituents. Two apocarotenoids and one flavonoid were also isolated from the chloroform fraction and were identified as cochloxanthin (3), dihydrocochloxanthin (4), and 7,4′-dimethyltaxifolin (5), respectively. A High-performance liquid chromatography (HPLC) method was also developed for fingerprinting borututu samples, with Compounds 1–4 suggested as chemical markers for quality control purposes. PMID:28134834

Changes in microbial biomass and P fractions in biogenic household waste compost amended with inorganic P fertilizers.

PubMed

Khan, Khalid Saifullah; Joergensen, Rainer Georg

2009-01-01

The present study was conducted to evaluate the changes in microbial biomass indices (C, N, and especially P) and in P fractions in compost amended with inorganic P fertilizers. In the non-amended control, the average contents of microbial biomass C, N, and P were 1744, 193, and 63 microg g(-1) compost, respectively. On average, 1.3% of total P was stored as microbial biomass P. The addition of KH(2)PO(4) and TSP (triple super phosphate) led to immediate significant increases in microbial biomass C, N, and P. Approximately, 4.6% of the added TSP and 5.8% of the added KH(2)PO(4) were incorporated on average into the microbial biomass throughout the incubation. Approximately, 4.7% of the 1mg and 5.8% of the 2mg addition rate were incorporated on average into the microbial biomass. In the amendment treatments, the average contents of microbial biomass C, N, and P declined by 44%, 64%, and 49%, respectively. Initially, the average size of the P fractions in the non-amended compost increased in the order (% of total P in brackets) resin P (0.7%)

Novel combination of photoactive species: photoresists formed from selectively esterified novolacs and polyfunctional photoactive compounds

NASA Astrophysics Data System (ADS)

Jeffries, Alfred T., III; Brzozowy, David J.; Naiini, Ahmad A.; Gallagher-Wetmore, Paula M.

1997-07-01

The addition of selected PACs to resists comprised of selectively esterified DNQ novolacs improves their performance in terms of side wall angle and resolution compared to resists whose photoactive component is composed of entirely selectively esterified DNQ novolacs. The performance gain is particularly evident for the resists with two selectively esterified fractions. A conventional 60/40 m-cresol/p-cresol novolac was synthesized and fractionated into five nearly equal weight fractions using supercritical fluids (SCF) fractionation technique. Resists were made from either a single esterified fraction [fraction Two, esterification level (EL), 42%] or dual esterified fractions (fractions Two and Four, EL 21% each), a selection of PACs and the remaining unesterified fractions. They were compared to a control containing only the corresponding esterified fraction(s). The PACs A and B were effective at increasing the resist profile angle for 0.50 (mu) features in the singly esterified novalacs in comparison to the control material and exhibited flat tops. The resolution and profiles of dual esterified fraction resists improved significantly when low levels of PACs were added to dual esterified fraction control resist. The comparison was made from 0.40 (mu) features. The resist made using PAC C is the best candidate for photospeed although its profile angle is less in comparison to PACs A and B.

Efficient algorithms for analyzing the singularly perturbed boundary value problems of fractional order

NASA Astrophysics Data System (ADS)

Sayevand, K.; Pichaghchi, K.

2018-04-01

In this paper, we were concerned with the description of the singularly perturbed boundary value problems in the scope of fractional calculus. We should mention that, one of the main methods used to solve these problems in classical calculus is the so-called matched asymptotic expansion method. However we shall note that, this was not achievable via the existing classical definitions of fractional derivative, because they do not obey the chain rule which one of the key elements of the matched asymptotic expansion method. In order to accommodate this method to fractional derivative, we employ a relatively new derivative so-called the local fractional derivative. Using the properties of local fractional derivative, we extend the matched asymptotic expansion method to the scope of fractional calculus and introduce a reliable new algorithm to develop approximate solutions of the singularly perturbed boundary value problems of fractional order. In the new method, the original problem is partitioned into inner and outer solution equations. The reduced equation is solved with suitable boundary conditions which provide the terminal boundary conditions for the boundary layer correction. The inner solution problem is next solved as a solvable boundary value problem. The width of the boundary layer is approximated using appropriate resemblance function. Some theoretical results are established and proved. Some illustrating examples are solved and the results are compared with those of matched asymptotic expansion method and homotopy analysis method to demonstrate the accuracy and efficiency of the method. It can be observed that, the proposed method approximates the exact solution very well not only in the boundary layer, but also away from the layer.

Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions

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

Han Yuecai; Hu Yaozhong; Song Jian, E-mail: jsong2@math.rutgers.edu

2013-04-15

We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter H>1/2). This maximum principle specifies a system of equations that the optimal control must satisfy (necessary condition for the optimal control). This system of equations consists of a backward stochastic differential equation driven by both fractional Brownian motions and the corresponding underlying standard Brownian motions. In addition to this backward equation, the maximum principle also involves the Malliavin derivatives. Our approach is to use conditioning and Malliavin calculus. To arrive at our maximum principle we need tomore » develop some new results of stochastic analysis of the controlled systems driven by fractional Brownian motions via fractional calculus. Our approach of conditioning and Malliavin calculus is also applied to classical system driven by standard Brownian motions while the controller has only partial information. As a straightforward consequence, the classical maximum principle is also deduced in this more natural and simpler way.« less

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.

Periodicity and positivity of a class of fractional differential equations.

PubMed

Ibrahim, Rabha W; Ahmad, M Z; Mohammed, M Jasim

2016-01-01

Fractional differential equations have been discussed in this study. We utilize the Riemann-Liouville fractional calculus to implement it within the generalization of the well known class of differential equations. The Rayleigh differential equation has been generalized of fractional second order. The existence of periodic and positive outcome is established in a new method. The solution is described in a fractional periodic Sobolev space. Positivity of outcomes is considered under certain requirements. We develop and extend some recent works. An example is constructed.

Fraction Intervention for Students with Mathematics Difficulties: Lessons Learned from Five Randomized Controlled Trials

ERIC Educational Resources Information Center

Fuchs, Lynn S.; Malone, Amelia S.; Schumacher, Robin F.; Namkung, Jessica; Wang, Amber

2017-01-01

In this article, the authors summarize results from 5 randomized controlled trials assessing the effects of intervention to improve the fraction performance of fourth-grade students at risk for difficulty in learning about fractions. The authors begin by explaining the importance of competence with fractions and why an instructional focus on…

Evaluation Lactogenic Activity of Ethyl Acetate Fraction of Torbangun (Coleus amboinicus L.) Leaves

NASA Astrophysics Data System (ADS)

Damanik, R. M.; Kustiyah, L.; Hanafi, M.; Iwansyah, A. C.

2017-12-01

This study aimed to assess the lactogenic property of ethyl acetate fraction of torbangun (Coleus amboinicus L.) leaves and to identify the compounds that responsibility as ‘milk booster’ using LC- MS approach. Lactagogue activity was evaluated in terms of quantity of milk produced from the rats treated with commercial milk booster (AF), ethyl acetate fraction of torbangun leaves (EA), water extraction of torbangun (AQ) and kaempferol (KP). The feed was given orally every two days and starting from Day 2 after giving birth until Day 28. The performance of milk production was measured along the experimental period by weight-suckle-weight method. The level of prolactin serum was determined by ELISA methods. Histopathological analysis of mammary gland, liver, intestines and kidney tissues was carried out. Moreover, in order to profiling and identification of compounds of ethyl acetate fraction, ultra-performance liquid chromatography quadrupole time of flight to electrospray ionization mass spectrometry (UPLC-QTOF-ESI-MS) in the positive-ion mode was performed. The ethyl acetate fraction of torbangun leaves (EA) was induced milk production about 17%, and AF 22% and KP 51% compared to the control group. Meanwhile, the EA was not significantly stimulate the synthesis of serum prolactin at Day 14 and Day 28 (p>0.05). Administration of EA did not cause any signs or symptoms of toxicity. In addition, a total of ten compounds was identified by UPLC-QTOF-ESI/MS in the ethyl acetate fraction of the leaves of C. amboinicus, mostly phenolic compounds, flavonols and some of their glycoside derivatives, such as: digiprolatone, and kaempferol-3-7-O-di-rhamnopyranoside. The present study reveals the ethyl acetate fraction of torbangun leaves and its bioactive compounds has the potency as a remedy for stimulating and improving milk production.

Effects of condensed tannin fractions of different molecular weights from a Leucaena leucocephala hybrid on in vitro methane production and rumen fermentation.

PubMed

Saminathan, Mookiah; Sieo, Chin Chin; Abdullah, Norhani; Wong, Clemente Michael Vui Ling; Ho, Yin Wan

2015-10-01

Molecular weights (MWs) and their chemical structures are the primary factors determining the influence of condensed tannins (CTs) on animal nutrition and methane (CH4 ) production in ruminants. In this study the MWs of five CT fractions from Leucaena leucocephala hybrid-Rendang (LLR) were determined and the CT fractions were investigated for their effects on CH4 production and rumen fermentation. The number-average molecular weight (Mn ) of fraction F1 (1265.8 Da), which was eluted first, was the highest, followed by those of fractions F2 (1028.6 Da), F3 (652.2 Da), F4 (562.2 Da) and F5 (469.6 Da). The total gas (mL g(-1) dry matter (DM)) and CH4 production decreased significantly (P < 0.05) with increasing MWs of the CT fractions, but there were no significant (P > 0.05) differences between the CT fractions and control on DM degradation. However, the in vitro N disappearance decreased significantly (P < 0.05) with the inclusion of CT fraction F1 (highest MW) compared with the control and other fractions (F2-F5). The inclusion of CT fraction F1 also significantly decreased (P < 0.05) total volatile fatty acid and acetic acid concentrations compared with the control. The acetic/propionic acid ratio was significantly decreased (P < 0.05) by fraction F1 but not by the control and other fractions (F2-F5). The CT fractions of different MWs from LLR could affect rumen fermentation and CH4 production, and the impact was more pronounced for the CT fraction with a higher MW. © 2014 Society of Chemical Industry.

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.

On stability of fixed points and chaos in fractional systems.

PubMed

Edelman, Mark

2018-02-01

In this paper, we propose a method to calculate asymptotically period two sinks and define the range of stability of fixed points for a variety of discrete fractional systems of the order 0<α<2. The method is tested on various forms of fractional generalizations of the standard and logistic maps. Based on our analysis, we make a conjecture that chaos is impossible in the corresponding continuous fractional systems.

29 CFR 4206.4 - Amount of credit in plans using the presumptive method.

Code of Federal Regulations, 2010 CFR

2010-07-01

... section, multiplied by the fractions described or determined under paragraph (c) of this section. When an... paragraph (b) are multiplied by the two fractions described in this paragraph in order to determine the amount of the old liabilities that was previously assessed against the employer. (1) The first fraction...

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.

Power flow controller with a fractionally rated back-to-back converter

DOEpatents

Divan, Deepakraj M.; Kandula, Rajendra Prasad; Prasai, Anish

2016-03-08

A power flow controller with a fractionally rated back-to-back (BTB) converter is provided. The power flow controller provide dynamic control of both active and reactive power of a power system. The power flow controller inserts a voltage with controllable magnitude and phase between two AC sources at the same frequency; thereby effecting control of active and reactive power flows between the two AC sources. A transformer may be augmented with a fractionally rated bi-directional Back to Back (BTB) converter. The fractionally rated BTB converter comprises a transformer side converter (TSC), a direct-current (DC) link, and a line side converter (LSC). By controlling the switches of the BTB converter, the effective phase angle between the two AC source voltages may be regulated, and the amplitude of the voltage inserted by the power flow controller may be adjusted with respect to the AC source voltages.

Thermodynamics of H-bonding in alcohols and water. The mobile order theory as opposed to the classical multicomponent order theories

NASA Astrophysics Data System (ADS)

Huyskens, P.; Kapuku, F.; Colemonts-Vandevyvere, C.

1990-09-01

In liquids the partners of H bonds constantly change. As a consequence the entities observed by IR spectroscopy are not the same as those considered for thermodynamic properties. For the latter, the H-bonds are shared by all the molecules. The thermodynamic "monomeric fraction", γ, the time fraction during which an alcohol molecule is vaporizable, is the square root of the spectroscopic monomeric fraction, and is the fraction of molecules which, during a time interval of 10 -14 s, have their hydroxylic proton and their lone pairs free. The classical thermodynamic treatments of Mecke and Prigogine consider the spectroscopic entities as real thermodynamic entities. Opposed to this, the mobile order theory considers all the formal molecules as equal but with a reduction of the entropy due to the fact that during a fraction 1-γ of the time, the OH proton follows a neighbouring oxygen atom on its journey through the liquid. Mobile order theory and classic multicomponent treatment lead, in binary mixtures of the associated substance A with the inert substance S, to expressions of the chemical potentials μ A and μ S that are fundamentally different. However, the differences become very important only when the molar volumes overlineVS and overlineVA differ by a factor larger than 2. As a consequence the equations of the classic theory can still fit the experimental vapour pressure data of mixtures of liquid alcohols and liquid alkanes. However, the solubilities of solid alkanes in water for which overlineVS > 3 overlineVA are only correctly predicted by the mobile order theory.

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.

Fraction Intervention for Students with Mathematics Difficulties: Lessons Learned from Five Randomized Control Trials

ERIC Educational Resources Information Center

Fuchs, Lynn S.; Malone, Amelia S.; Schumacher, Robin F.; Namkung, Jessica; Wang, Amber

2016-01-01

The purpose of this article was to summarize results from 5 randomized control trials assessing the effects of intervention to improve the fraction performance of 4th-grade students at-risk for difficulty in learning about fractions. We begin by explaining the importance of competence with fractions and why an instructional focus on fractions…

Exact solutions of fractional mBBM equation and coupled system of fractional Boussinesq-Burgers

NASA Astrophysics Data System (ADS)

Javeed, Shumaila; Saif, Summaya; Waheed, Asif; Baleanu, Dumitru

2018-06-01

The new exact solutions of nonlinear fractional partial differential equations (FPDEs) are established by adopting first integral method (FIM). The Riemann-Liouville (R-L) derivative and the local conformable derivative definitions are used to deal with the fractional order derivatives. The proposed method is applied to get exact solutions for space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation and coupled time-fractional Boussinesq-Burgers equation. The suggested technique is easily applicable and effectual which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs.

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

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.

Gap Reversal at Filling Factors 3 +1 /3 and 3 +1 /5 : Towards Novel Topological Order in the Fractional Quantum Hall Regime

NASA Astrophysics Data System (ADS)

Kleinbaum, Ethan; Kumar, Ashwani; Pfeiffer, L. N.; West, K. W.; Csáthy, G. A.

2015-02-01

In the region of the second Landau level several theories predict fractional quantum Hall states with novel topological order. We report the opening of an energy gap at the filling factor ν =3 +1 /3 , firmly establishing the ground state as a fractional quantum Hall state. This and other odd-denominator states unexpectedly break particle-hole symmetry. Specifically, we find that the relative magnitudes of the energy gaps of the ν =3 +1 /3 and 3 +1 /5 states from the upper spin branch are reversed when compared to the ν =2 +1 /3 and 2 +1 /5 counterpart states in the lower spin branch. Our findings raise the possibility that at least one of the former states is of an unusual topological order.

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.

Temperature response of permafrost soil carbon is attenuated by mineral protection.

PubMed

Gentsch, Norman; Wild, Birgit; Mikutta, Robert; Čapek, Petr; Diáková, Katka; Schrumpf, Marion; Turner, Stephanie; Minnich, Cynthia; Schaarschmidt, Frank; Shibistova, Olga; Schnecker, Jörg; Urich, Tim; Gittel, Antje; Šantrůčková, Hana; Bárta, Jiři; Lashchinskiy, Nikolay; Fuß, Roland; Richter, Andreas; Guggenberger, Georg

2018-05-18

Climate change in Arctic ecosystems fosters permafrost thaw and makes massive amounts of ancient soil organic carbon (OC) available to microbial breakdown. However, fractions of the organic matter (OM) may be protected from rapid decomposition by their association with minerals. Little is known about the effects of mineral-organic associations (MOA) on the microbial accessibility of OM in permafrost soils and it is not clear which factors control its temperature sensitivity. In order to investigate if and how permafrost soil OC turnover is affected by mineral controls, the heavy fraction (HF) representing mostly MOA was obtained by density fractionation from 27 permafrost soil profiles of the Siberian Arctic. In parallel laboratory incubations, the unfractionated soils (bulk) and their HF were comparatively incubated for 175 days at 5 and 15°C. The HF was equivalent to 70 ± 9% of the bulk CO 2 respiration as compared to a share of 63 ± 1% of bulk OC that was stored in the HF. Significant reduction of OC mineralization was found in all treatments with increasing OC content of the HF (HF-OC), clay-size minerals and Fe or Al oxyhydroxides. Temperature sensitivity (Q10) decreased with increasing soil depth from 2.4 to 1.4 in the bulk soil and from 2.9 to 1.5 in the HF. A concurrent increase in the metal-to-HF-OC ratios with soil depth suggests a stronger bonding of OM to minerals in the subsoil. There, the younger 14 C signature in CO 2 than that of the OC indicates a preferential decomposition of the more recent OM and the existence of a MOA fraction with limited access of OM to decomposers. These results indicate strong mineral controls on the decomposability of OM after permafrost thaw and on its temperature sensitivity. Thus, we here provide evidence that OM temperature sensitivity can be attenuated by MOA in permafrost soils. © 2018 John Wiley & Sons Ltd.

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.

Rate-induced solubility and suppression of the first-order phase transition in olivine LiFePO4.

PubMed

Zhang, Xiaoyu; van Hulzen, Martijn; Singh, Deepak P; Brownrigg, Alex; Wright, Jonathan P; van Dijk, Niels H; Wagemaker, Marnix

2014-05-14

The impact of ultrahigh (dis)charge rates on the phase transition mechanism in LiFePO4 Li-ion electrodes is revealed by in situ synchrotron diffraction. At high rates the solubility limits in both phases increase dramatically, causing a fraction of the electrode to bypass the first-order phase transition. The small transforming fraction demonstrates that nucleation rates are consequently not limiting the transformation rate. In combination with the small fraction of the electrode that transforms at high rates, this indicates that higher performances may be achieved by further optimizing the ionic/electronic transport in LiFePO4 electrodes.

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.

Dynamics and order-disorder transitions in bidisperse diblock copolymer blends

NASA Astrophysics Data System (ADS)

Wang, Yueqiang; Li, Xuan; Tang, Ping; Yang, Yuliang

2011-03-01

We employ the dynamic extension of self-consistent field theory (DSCFT) to study dynamics and order-disorder transitions (ODT) in AB diblock copolymer binary mixtures of two different monodisperse chain lengths by imitating the dynamic storage modulus G‧ corresponding to any given morphology in the oscillatory shear measurements. The different polydispersity index (PDI) is introduced by binary blending AB diblock copolymers with variations in chain lengths and chain number fractions. The simulation results show that the increase of polydispersity in the minority or symmetric block introduces a decrease in the segregation strength at the ODT, ( χN) ODT, whereas the increase of polydispersity in the majority block results in a decrease, then increase and final decrease again in ( χN) ODT. To the best of our knowledge, our DSCFT simulations, for the first time, predict an increase in ( χN) ODT with the PDI in the majority block, which produces the experimental results. The simulations by previous SCFT, which generally speaking, is capable of describing equilibrium morphologies, however, contradict the experimental data. The polydispersity acquired by properly tuning the chain lengths and number fractions of binary diblock copolymer blends should be a convenient and efficient way to control the microphase separation strength at the ODT.

The use of fractional orders in the determination of birefringence of highly dispersive materials by the channelled spectrum method

NASA Astrophysics Data System (ADS)

Nagarajan, K.; Shashidharan Nair, C. K.

2007-07-01

The channelled spectrum employing polarized light interference is a very convenient method for the study of dispersion of birefringence. However, while using this method, the absolute order of the polarized light interference fringes cannot be determined easily. Approximate methods are therefore used to estimate the order. One of the approximations is that the dispersion of birefringence across neighbouring integer order fringes is negligible. In this paper, we show how this approximation can cause errors. A modification is reported whereby the error in the determination of absolute fringe order can be reduced using fractional orders instead of integer orders. The theoretical background for this method supported with computer simulation is presented. An experimental arrangement implementing these modifications is described. This method uses a Constant Deviation Spectrometer (CDS) and a Soleil Babinet Compensator (SBC).

Crystallization of sheared hard spheres at 64.5% volume fraction

NASA Astrophysics Data System (ADS)

Swinney, H. L.; Rietz, F.; Schroeter, M.; Radin, C.

2017-11-01

A classic experiment by G.D. Scott Nature 188, 908, 1960) showed that pouring balls into a rigid container filled the volume to an upper limit of 64% of the container volume, which is well below the 74% volume fraction filled by spheres in a hexagonal close packed (HCP) or face center cubic (FCC) lattice. Subsequent experiments have confirmed a ``random closed packed'' (RCP) fraction of about 64%. However, the physics of the RCP limit has remained a mystery. Our experiment on a cubical box filled with 49400 weakly sheared glass spheres reveals a first order phase transition from a disordered to an ordered state at a volume fraction of 64.5%. The ordered state consists of crystallites of mixed FCC and HCP symmetry that coexist with the amorphous bulk. The transition is initiated by homogeneous nucleation: in the shearing process small crystallites with about ten or fewer spheres dissolve, while larger crystallites grow. A movie illustrates the crystallization process. German Academic Exchange Service (DAAD), German Research Foundation (DFG), NSF DMS, and R.A. Welch Foundation.

Generalized fractional diffusion equations for accelerating subdiffusion and truncated Lévy flights

NASA Astrophysics Data System (ADS)

Chechkin, A. V.; Gonchar, V. Yu.; Gorenflo, R.; Korabel, N.; Sokolov, I. M.

2008-08-01

Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by diffusion equations with fractional derivatives of distributed order. Such equations were introduced in A. V. Chechkin, R. Gorenflo, and I. Sokolov [Phys. Rev. E 66, 046129 (2002)] for the description of the processes getting more anomalous in the course of time (decelerating subdiffusion and accelerating superdiffusion). Here we discuss the properties of diffusion equations with fractional derivatives of the distributed order for the description of anomalous relaxation and diffusion phenomena getting less anomalous in the course of time, which we call, respectively, accelerating subdiffusion and decelerating superdiffusion. For the former process, by taking a relatively simple particular example with two fixed anomalous diffusion exponents we show that the proposed equation effectively describes the subdiffusion phenomenon with diffusion exponent varying in time. For the latter process we demonstrate by a particular example how the power-law truncated Lévy stable distribution evolves in time to the distribution with power-law asymptotics and Gaussian shape in the central part. The special case of two different orders is characteristic for the general situation in which the extreme orders dominate the asymptotics.

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

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

Generalized stochastic resonance for a fractional harmonic oscillator with bias-signal-modulated trichotomous noise

NASA Astrophysics Data System (ADS)

Lin, Lifeng; Wang, Huiqi; Huang, Xipei; Wen, Yongxian

2018-03-01

For a fractional linear oscillator subjected to both parametric excitation of trichotomous noise and external excitation of bias-signal-modulated trichotomous noise, the generalized stochastic resonance (GSR) phenomena are investigated in this paper in case the noises are cross-correlative. First, the generalized Shapiro-Loginov formula and generalized fractional Shapiro-Loginov formula are derived. Then, by using the generalized (fractional) Shapiro-Loginov formula and the Laplace transformation technique, the exact expression of the first-order moment of the system’s steady response is obtained. The numerical results show that the evolution of the output amplitude amplification is nonmonotonic with the frequency of periodic signal, the noise parameters, and the fractional order. The GSR phenomena, including single-peak GSR, double-peak GSR and triple-peak GSR, are observed in this system. In addition, the interplay of the multiplicative trichotomous noise, bias-signal-modulated trichotomous noise and memory can induce and diversify the stochastic multi-resonance (SMR) phenomena, and the two kinds of trichotomous noises play opposite roles on the GSR.

Exploring Effects of Multi-Touch Tabletop on Collaborative Fraction Learning and the Relationship of Learning Behavior and Interaction with Learning Achievement

ERIC Educational Resources Information Center

Hwang, Wu-Yuin; Shadiev, Rustam; Tseng, Chi-Wei; Huang, Yueh-Min

2015-01-01

This study designed a learning system to facilitate elementary school students' fraction learning. An experiment was carried out to investigate how the system, which runs on multi-touch tabletop versus tablet PC, affects fraction learning. Two groups, a control and experimental, were assigned. Control students have learned fraction by using tablet…

[Fractional exhaled nitric oxide in monitoring and therapeutic management of asthma].

PubMed

Melo, Bruno; Costa, Patrício; Afonso, Ariana; Machado, Vânia; Moreira, Carla; Gonçalves, Augusta; Gonçalves, Jean-Pierre

2014-01-01

Asthma is a chronic respiratory disease characterized by hyper-responsiveness and bronchial inflammation. The bronchial inflammation in these patients can be monitored by measuring the fractional exhaled nitric oxide. This study aims to determine fractional exhaled nitric oxide association with peak expiratory flow and with asthma control inferred by the Global Initiative for Asthma. Observational, analytical and cross-sectional study of children with asthma, 6-12 years-old, followed in the Outpatient Respiratory Pathology of Braga Hospital. Sociodemographic and clinical information were collected through a questionnaire. fractional exhaled nitric oxide and peak expiratory flow were determined by portable analyzer Niox Mino® and flow meter, respectively. The sample is constituted by 101 asthmatic children, 63 (62.4%) of males and 38 (37.6%) females. The mean age of participants in the sample is 9.18 (1.99) years. The logistic regression performed with the cutoff value obtained by ROC curve, revealed that fractional exhaled nitric oxide (b(FENO classes) = 0.85; χ(2)Wald (1) = 8.71; OR = 2.33; p = 0.003) has a statistical significant effect on the probability of changing level of asthma control. The odds ratio of going from "controlled" to "partly controlled/uncontrolled" is 2.33 per each level of fractional exhaled nitric oxide. The probability of an asthmatic children change their level of asthma control, from 'controlled' to 'partly controlled/uncontrolled', taking into account a change in their fractional exhaled nitric oxide level, increases 133%.

Isotopomers as a method for differentiating between bacterial and fungal production of nitrous oxide

NASA Astrophysics Data System (ADS)

Sutka, R. L.; Adams, G.; Ostrom, N.; Ostrom, P.

2007-12-01

In order to study the importance of fungi to nitrous oxide (N2O) production in the environment it is critical to have a non-intrusive method for differentiating between fungal and bacterial N2O production. Site preference (SP), the difference in d15N between the central and outer N atoms in N2O, has been used to differentiate between bacterial nitrification and denitrification. In this study we compare the SP, d15N and d18O of N2O produced by the two best-studied fungal denitrifiers, Fusarium oxysporum and Cylindrocarpon tonkinense, to data from our previous bacterial studies. Both d18O and SP values remained fairly constant during the course of nitrite reduction which likely reflects isotopic exchange with water in the case of d18O and conservative behavior in SP that has been observed previously (Sutka et al., 2006). We observed a wide range of fractionation factors for fungal denitrification, -74.7 to -6.6 ‰, and non-linear behavior indicating that fractionation was controlled by more than one step. We interpret the small degree of fractionation as reflecting fractionation during diffusion and the more negative values as being controlled by enzymatic fractionation. Data from this and our previous study of bacterial production (Sutka et al., 2006) reveals that N2O produced via nitrification by fungi can be differentiated from N2O produced by bacterial denitrification primarily on the basis of d18O. The site preference of N2O produced by F. oxysporum and C. tonkinense was 37.1 ± 2.5 ‰ and 36.9 ± 2.8 ‰, respectively. These results indicate that isotopomers can be used as a basis for differentiating bacterial and fungal denitrification. Our work further reveals the role that fungal and bacterial nitric oxide reductases have in determining site preference during N2O production.

Top-down and bottom-up lipidomic analysis of rabbit lipoproteins under different metabolic conditions using flow field-flow fractionation, nanoflow liquid chromatography and mass spectrometry.

PubMed

Byeon, Seul Kee; Kim, Jin Yong; Lee, Ju Yong; Chung, Bong Chul; Seo, Hong Seog; Moon, Myeong Hee

2015-07-31

This study demonstrated the performances of top-down and bottom-up approaches in lipidomic analysis of lipoproteins from rabbits raised under different metabolic conditions: healthy controls, carrageenan-induced inflammation, dehydration, high cholesterol (HC) diet, and highest cholesterol diet with inflammation (HCI). In the bottom-up approach, the high density lipoproteins (HDL) and the low density lipoproteins (LDL) were size-sorted and collected on a semi-preparative scale using a multiplexed hollow fiber flow field-flow fractionation (MxHF5), followed by nanoflow liquid chromatography-ESI-MS/MS (nLC-ESI-MS/MS) analysis of the lipids extracted from each lipoprotein fraction. In the top-down method, size-fractionated lipoproteins were directly infused to MS for quantitative analysis of targeted lipids using chip-type asymmetrical flow field-flow fractionation-electrospray ionization-tandem mass spectrometry (cAF4-ESI-MS/MS) in selected reaction monitoring (SRM) mode. The comprehensive bottom-up analysis yielded 122 and 104 lipids from HDL and LDL, respectively. Rabbits within the HC and HCI groups had lipid patterns that contrasted most substantially from those of controls, suggesting that HC diet significantly alters the lipid composition of lipoproteins. Among the identified lipids, 20 lipid species that exhibited large differences (>10-fold) were selected as targets for the top-down quantitative analysis in order to compare the results with those from the bottom-up method. Statistical comparison of the results from the two methods revealed that the results were not significantly different for most of the selected species, except for those species with only small differences in concentration between groups. The current study demonstrated that top-down lipid analysis using cAF4-ESI-MS/MS is a powerful high-speed analytical platform for targeted lipidomic analysis that does not require the extraction of lipids from blood samples. Copyright © 2015 Elsevier B.V. All rights reserved.

The spectrum of laser skin resurfacing: nonablative, fractional, and ablative laser resurfacing.

PubMed

Alexiades-Armenakas, Macrene R; Dover, Jeffrey S; Arndt, Kenneth A

2008-05-01

The drive to attain cosmetic facial enhancement with minimal risk and rapid recovery has inspired the field of nonsurgical skin rejuvenation. Laser resurfacing was introduced in the 1980s with continuous wave carbon dioxide (CO(2)) lasers; however, because of a high rate of side effects, including scarring, short-pulse, high-peak power, and rapidly scanned, focused-beam CO(2) lasers and normal-mode erbium-doped yttrium aluminium garnet lasers were developed, which remove skin in a precisely controlled manner. The prolonged 2-week recovery time and small but significant complication risk prompted the development of non-ablative and, more recently, fractional resurfacing in order to minimize risk and shorten recovery times. Nonablative resurfacing produces dermal thermal injury to improve rhytides and photodamage while preserving the epidermis. Fractional resurfacing thermally ablates microscopic columns of epidermal and dermal tissue in regularly spaced arrays over a fraction of the skin surface. This intermediate approach increases efficacy as compared to nonablative resurfacing, but with faster recovery as compared to ablative resurfacing. Neither nonablative nor fractional resurfacing produces results comparable to ablative laser skin resurfacing, but both have become much more popular than the latter because the risks of treatment are limited in the face of acceptable improvement. At the completion of this learning activity, participants should be familiar with the spectrum of lasers and light technologies available for skin resurfacing, published studies of safety and efficacy, indications, methodologies, side effects, complications, and management.

Rationale, conduct, and outcome using hypofractionated radiotherapy in prostate cancer

PubMed Central

Ritter, Mark

2008-01-01

Hypofractionated radiation therapy for prostate cancer has become of increasing interest with the recognition of a potential improvement in therapeutic ratio with treatments delivered in larger-sized fractions. In addition, the associated reduction in fraction number produces attractive cost and patient convenience advantages as well. A still limited but growing number of hypofractionation trials have reported acceptable short-term levels of toxicity and biochemical control, but most have insufficient follow-up to assure the long-term safety and efficacy of this approach. This situation will improve as many currently active trials mature, particularly several high value randomized trials. In contrast, extreme hypofractionation, with schedules delivering only on the order of 5 fractions, is truly in its infancy for prostate cancer, with extremely limited tolerance and efficacy information currently available. Several uncertainties in the radiobiology of hypofractionation mitigate for an organized, cautious investigational approach. The fractionation response (α/β ratio) of prostate cancers and, for that matter, late responding normal tissues, has yet to be rigorously defined. Additionally, the linear quadratic (LQ) model used in the design of hypofractionation schedules is subject to its own uncertainties, particularly with respect to the upper limit of fraction sizes for which it remains valid. Contemporary dose escalated radiation therapy is already highly effective, making it imperative that ongoing and future studies of hypofractionation be carried out in carefully designed, randomized clinical trials. Clinical validation permitting, the adaptation of hypofractionation as a standard of care could profoundly influence future management of localized prostate cancer. PMID:18725112

Dynamical property analysis of fractionally damped van der pol oscillator and its application

NASA Astrophysics Data System (ADS)

Zhong, Qiuhui; Zhang, Chunrui

2012-01-01

In this paper, the fractionally damped van der pol equation was studied. Firstly, the fractionally damped van der pol equation was transformed into a set of integer order equations. Then the Lyapunov exponents diagram was given. Secondly, it was transformed into a set of fractional integral equations and solved by a predictor-corrector method. The time domain diagrams and phase trajectory were used to describe the dynamic behavior. Finally, the fractionally damped van der pol equation was used to detect a weak signal.

Fractions: The New Frontier for Theories of Numerical Development

ERIC Educational Resources Information Center

Siegler, Robert S.; Fazio, Lisa K.; Bailey, Drew H.; Zhou, Xinlin

2013-01-01

Recent research on fractions has broadened and deepened theories of numerical development. Learning about fractions requires children to recognize that many properties of whole numbers are not true of numbers in general and also to recognize that the one property that unites all real numbers is that they possess magnitudes that can be ordered on…

Procedural and Conceptual Knowledge: Adults Reviewing Fractions

ERIC Educational Resources Information Center

Baker, William J.; Czarnocha, Bronislaw; Dias, Olen; Doyle, Kathleen; Kennis, James R.

2012-01-01

In the United States a majority of the students who enroll in community colleges require a review of secondary math before they are eligible for college level mathematics. In the pre-algebra course, that has a high drop-out rate, the most difficult topic for students is fractions. In order to better understand the fraction concept, Kieren…

Dietary unsaponifiable fraction of extra virgin olive oil supplementation attenuates lung injury and DNA damage of rats co-exposed to aluminum and acrylamide.

PubMed

Ghorbel, Imen; Chaâbane, Mariem; Boudawara, Ons; Kamoun, Naziha Grati; Boudawara, Tahia; Zeghal, Najiba

2016-10-01

Aluminum chloride (AlCl3) and acrylamide (ACR) are well known as environmental pollutants inducing oxidative stress. Our study investigated the effects of these contaminants and if the hydrophilic fraction of extra virgin olive oil was able to prevent lung oxidative stress and DNA damage. Animals were divided into four groups of six each: group 1, serving as controls, received distilled water; group 2 received in drinking water aluminum chloride (50 mg/ kg body weight) and by gavage acrylamide (20 mg/kg body weight); group 3 received both aluminum and acrylamide in the same way and the same dose as group 2 and hydrophilic fraction from olive oil (OOHF) (1 ml) by gavage; group 4 received only OOHF by gavage. Exposure of rats to both aluminum and acrylamide provoked oxidative stress in lung tissue based on biochemical parameters and histopathological alterations. In fact, we have observed an increase in malondialdehyde (MDA), H2O2, and advanced oxidation protein product (AOPP) and a decrease in reduced glutathione (GSH), non-protein thiols (NPSH), and vitamin C levels. Activities of catalase (CAT), glutathione peroxidase (GPx), and superoxide dismutase (SOD) were also decreased. Histopathological changes in lung tissue were noted like emphysema, vascular congestion, and infiltration of inflammatory cells. A random DNA degradation was observed on agarose gel in the lung of AlCl3 and acrylamide (ACR)-treated rats. Co-administration of OOHF to treated rats improved biochemical parameters to near control values and lung histoarchitecture. The smear formation of genomic DNA was reduced. The hydrophilic fraction of extra virgin olive oil might provide a basis for developing a new dietary supplementation strategy in order to prevent lung tissue damage.

Biodynamics of copper oxide nanoparticles and copper ions in an oligochaete - Part II: Subcellular distribution following sediment exposure

USGS Publications Warehouse

Thit, Amalie; Ramskov, Tina; Croteau, Marie-Noele; Selck, Henriette

2016-01-01

The use and likely incidental release of metal nanoparticles (NPs) is steadily increasing. Despite the increasing amount of published literature on metal NP toxicity in the aquatic environment, very little is known about the biological fate of NPs after sediment exposures. Here, we compare the bioavailability and subcellular distribution of copper oxide (CuO) NPs and aqueous Cu (Cu-Aq) in the sediment-dwelling worm Lumbriculus variegatus. Ten days (d) sediment exposure resulted in marginal Cu bioaccumulation in L. variegatus for both forms of Cu. Bioaccumulation was detected because isotopically enriched 65Cu was used as a tracer. Neither burrowing behavior or survival was affected by the exposure. Once incorporated into tissue, Cu loss was negligible over 10 d of elimination in clean sediment (Cu elimination rate constants were not different from zero). With the exception of day 10, differences in bioaccumulation and subcellular distribution between Cu forms were either not detectable or marginal. After 10 d of exposure to Cu-Aq, the accumulated Cu was primarily partitioned in the subcellular fraction containing metallothionein-like proteins (MTLP, ≈40%) and cellular debris (CD, ≈30%). Cu concentrations in these fractions were significantly higher than in controls. For worms exposed to CuO NPs for 10 d, most of the accumulated Cu was partitioned in the CD fraction (≈40%), which was the only subcellular fraction where the Cu concentration was significantly higher than for the control group. Our results indicate that L. variegatus handle the two Cu forms differently. However, longer-term exposures are suggested in order to clearly highlight differences in the subcellular distribution of these two Cu forms.

Optimization of the Technological Synthesis of Refractory Compounds

NASA Astrophysics Data System (ADS)

Gaidar, S. M.; Karelina, M. Yu.; Prikhod'ko, V. M.; Volkov, A. A.

2017-12-01

The results of experimental studies, which are related to the regulation of the fractional composition of refractory compounds by roll milling in using controlled roll opening and unbalanced peripheral speeds of rollers, are reported. The content of prepared fine, middle, and coarse fractions is within 50-80%; in this case, the milling time of synthesis products is less than the time of ball milling by an order of magnitude. The application of roll milling for refining the products of self-propagating high-temperature synthesis can be most efficient in using together with heat-generating reactor to solve the main problem of self-propagating synthesis (SHS), which is a problem for recent several decades (the problem is the creation of intense automated production of refractory compounds in using continuous manufacturing cycle within a energotechnological system with the recovery of a great quantity of heat released during SHS).

The post-Paleozoic chronology and mechanism of 13C depletion in primary marine organic matter

NASA Technical Reports Server (NTRS)

Popp, B. N.; Takigiku, R.; Hayes, J. M.; Louda, J. W.; Baker, E. W.

1989-01-01

Carbon-isotopic compositions of geoporphyrins have been measured from marine sediments of Mesozoic and Cenozoic age in order to elucidate the timing and extent of depletion of 13C in marine primary producers. These results indicate that the difference in isotopic composition of coeval marine carbonates and marine primary photosynthate was approximately 5 to 7 permil greater during the Mesozoic and early Cenozoic than at present. In contrast to the isotopic record of marine primary producers, isotopic compositions of terrestrial organic materials have remained approximately constant for this same interval of time. This difference in the isotopic records of marine and terrestrial organic matter is considered in terms of the mechanisms controlling the isotopic fractionation associated with photosynthetic fixation of carbon. We show that the decreased isotopic fractionation between marine carbonates and organic matter from the Early to mid-Cenozoic may record variations in the abundance of atmospheric CO2.

Influence of non-integer-order derivatives on unsteady unidirectional motions of an Oldroyd-B fluid with generalized boundary conditions

NASA Astrophysics Data System (ADS)

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

2018-03-01

The objective of this article is to study some unsteady Couette flows of an Oldroyd-B fluid with non-integer derivatives. The fluid fills an annular region of two infinite co-axial circular cylinders. Flows are due to the motion of the outer cylinder, that rotates about its axis with an arbitrary time-dependent velocity while the inner cylinder is held fixed. Closed form solutions of dimensionless velocity field and tangential tension are obtained by means of the finite Hankel transform and the theory of Laplace transform for fractional calculus. Several results in the literature including the rotational flows through an infinite cylinder can be obtained as limiting cases of our general solutions. Finally, the control of the fractional framework on the dynamics of fluid is analyzed by numerical simulations and graphical illustrations.

Schemes for efficient transmission of encoded video streams on high-speed networks

NASA Astrophysics Data System (ADS)

Ramanathan, Srinivas; Vin, Harrick M.; Rangan, P. Venkat

1994-04-01

In this paper, we argue that significant performance benefits can accrue if integrated networks implement application-specific mechanisms that account for the diversities in media compression schemes. Towards this end, we propose a simple, yet effective, strategy called Frame Induced Packet Discarding (FIPD), in which, upon detection of loss of a threshold number (determined by an application's video encoding scheme) of packets belonging to a video frame, the network attempts to discard all the remaining packets of that frame. In order to analytically quantify the performance of FIPD so as to obtain fractional frame losses that can be guaranteed to video channels, we develop a finite state, discrete time markov chain model of the FIPD strategy. The fractional frame loss thus computed can serve as the criterion for admission control at the network. Performance evaluations demonstrate the utility of the FIPD strategy.

Characterizing superconducting thin films using AC Magnetic Susceptibility

NASA Astrophysics Data System (ADS)

Mahoney, C. H.; Porzio, J.; Sullivan, M. C.

2014-03-01

We present our work on using ac magnetic susceptibility to determine the critical temperature of superconducting thin films. In ac magnetic susceptibility, the thin film is placed between two coils. One coil carries an ac signal, creating a varying external magnetic field. We measure the voltage induced in the pick-up coil on the opposite side of the sample and measure how the sample magnetization changes as the temperature changes. We will present our work to use ac susceptibility to determine critical temperature and superconducting volume fraction. Using our own analysis program, we are able to accurately locate the critical temperatures of the samples and determine the transition width. For the superconducting volume fraction, we etch samples in order to control the thicknesses of the sample and measure how much of the material grown on the surface is superconducting. Supported by NFS grant DMR-1305637.

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.

The binding of decomposition products of UDP-galactose to the microsomes and polyribosomes isolated from rat liver.

PubMed

Kopacz-Jodczyk, T; Gałasiński, W

1987-10-01

UDP-D-[U-14C]galactose is decomposed to [U-14C]galactose-1-phosphate and [U-14C]galactose by rat liver microsomal and crude polyribosomal fractions, under conditions commonly used to assay of glycosyltransferase activities. UDP-D-[U-14C]galactose, at neutral pH, is also chemically degraded to the [U-14C]galactose-1,2-cyclic phosphate. The 1,2-cyclic phosphate derivative of galactose also exists in the commercial UDP-D-[U-14C]galactose. It is a very important finding that products of the UDP-D-[U-14C]galactose decomposition are tightly, although nonenzymatically, bound to tested subcellular fractions and may create a false impression of protein glycosylation. The application of controls containing all radioactive substances present in suitable samples is recommended in order to avoid incorrect interpretations of the results.

Binding of decomposition products of UDP-galactose to the microsomes and polyribosomes isolated from rat liver

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

Kopacz-Jodczyk, T.; Galasinski, W.

1987-10-01

UDP-D-(U-/sup 14/C)galactose is decomposed to (U-/sup 14/C)galactose-1-phosphate and (U-/sup 14/C)galactose by rat liver microsomal and crude polyribosomal fractions, under conditions commonly used to assay of glycosyltransferase activities. UDP-D-(U-/sup 14/C)galactose, at neutral pH, is also chemically degraded to the (U-/sup 14/C)galactose-1,2-cyclic phosphate. The 1,2-cyclic phosphate derivative of galactose also exists in the commercial UDP-D-(U-/sup 14/C)galactose. It is a very important finding that products of the UDP-D-(U-/sup 14/C)galactose decomposition are tightly, although nonenzymatically, bound to tested subcellular fractions and may create a false impression of protein glycosylation. The application of controls containing all radioactive substances present in suitable samples is recommended inmore » order to avoid incorrect interpretations of the results.« less

Bethe lattice approach and relaxation dynamics study of spin-crossover materials

NASA Astrophysics Data System (ADS)

Oke, Toussaint Djidjoho; Hontinfinde, Félix; Boukheddaden, Kamel

2015-07-01

Dynamical properties of Prussian blue analogs and spin-crossover materials are investigated in the framework of a Blume-Emery-Griffiths (BEG) spin-1 model, where states ±1 and 0 represent the high-spin (HS) state and the low-spin state, respectively. The quadrupolar interaction depends on the temperature in the form . Magnetic interactions are controlled by a factor such that for (), magnetic ordering is not expected. The model is exactly solved using the Bethe lattice approach for the equilibrium properties. The results are closer to those calculated by numerical simulations with suitable Arrhenius-type transition rates. The study of relaxation processes of non-equilibrium HS states revealed one-step nonlinear sigmoidal relaxation curves of the HS fraction at low temperatures. We found that increasing the magnetic interactions leads to the appearance of a plateau in the thermal hysteresis as well as in the relaxation curves of the HS fraction at low temperature.

Identification of compounds in heavy fuel oil that are chronically toxic to rainbow trout embryos by effects-driven chemical fractionation.

PubMed

Adams, Julie; Bornstein, Jason M; Munno, Keenan; Hollebone, Bruce; King, Thomas; Brown, R Stephen; Hodson, Peter V

2014-04-01

The present study isolated and identified compounds in heavy fuel oil 7102 (HFO 7102) that are bioavailable and chronically toxic to rainbow trout embryos (Oncorhynchus mykiss). An effects-driven chemical fractionation combined the chemical separation of oil with toxicity testing and chemical analyses of each fraction to identify the major classes of compounds associated with embryo toxicity. Toxicity was assessed with 2 exposure methods, a high-energy chemical dispersion of oil in water, which included oil droplets in test solutions, and water accommodated fractions which were produced by oiled gravel desorption columns, and which did not contain visible oil droplets. Fractions of HFO with high concentrations of naphthalenes, alkanes, asphaltenes, and resins were nontoxic to embryos over the range of concentrations tested. In contrast, fractions enriched with 3- to 4-ringed alkyl polycyclic aromatic hydrocarbons (PAHs) were embryotoxic, consistent with published studies of crude oils and individual alkyl PAHs. The rank order of fraction toxicity did not vary between the exposure methods and was consistent with their PAH content; fractions with higher-molecular weight alkyl PAHs were the most toxic. Exposure of juvenile trout to most fractions of HFO induced higher activities of cytochrome P450 enzymes, with a rank order of potency that varied with exposure method and differed somewhat from that of embryotoxicity. Induction reflected the bioavailability of PAHs but did not accurately predict embryotoxicity. © 2013 SETAC.

Prefrontal vulnerabilities and whole brain connectivity in aging and depression.

PubMed

Lamar, Melissa; Charlton, Rebecca A; Ajilore, Olusola; Zhang, Aifeng; Yang, Shaolin; Barrick, Thomas R; Rhodes, Emma; Kumar, Anand

2013-07-01

Studies exploring the underpinnings of age-related neurodegeneration suggest fronto-limbic alterations that are increasingly vulnerable in the presence of disease including late life depression. Less work has assessed the impact of this specific vulnerability on widespread brain circuitry. Seventy-nine older adults (healthy controls=45; late life depression=34) completed translational tasks shown in non-human primates to rely on fronto-limbic networks involving dorsolateral (Self-Ordered Pointing Task) or orbitofrontal (Object Alternation Task) cortices. A sub-sample of participants also completed diffusion tensor imaging for white matter tract quantification (uncinate and cingulum bundle; n=58) and whole brain tract-based spatial statistics (n=62). Despite task associations to specific white matter tracts across both groups, only healthy controls demonstrated significant correlations between widespread tract integrity and cognition. Thus, increasing Object Alternation Task errors were associated with decreasing fractional anisotropy in the uncinate in late life depression; however, only in healthy controls was the uncinate incorporated into a larger network of white matter vulnerability associating fractional anisotropy with Object Alternation Task errors using whole brain tract-based spatial statistics. It appears that the whole brain impact of specific fronto-limbic vulnerabilities in aging may be eclipsed in the presence of disease-specific neuropathology like that seen in late life depression. Copyright © 2013 Elsevier Ltd. All rights reserved.

Finite-Time Stability for Fractional-Order Bidirectional Associative Memory Neural Networks with Time Delays

NASA Astrophysics Data System (ADS)

Xu, Chang-Jin; Li, Pei-Luan; Pang, Yi-Cheng

2017-02-01

This paper is concerned with fractional-order bidirectional associative memory (BAM) neural networks with time delays. Applying Laplace transform, the generalized Gronwall inequality and estimates of Mittag-Leffler functions, some sufficient conditions which ensure the finite-time stability of fractional-order bidirectional associative memory neural networks with time delays are obtained. Two examples with their simulations are given to illustrate the theoretical findings. Our results are new and complement previously known results. Supported by National Natural Science Foundation of China under Grant Nos.~61673008, 11261010, 11101126, Project of High-Level Innovative Talents of Guizhou Province ([2016]5651), Natural Science and Technology Foundation of Guizhou Province (J[2015]2025 and J[2015]2026), 125 Special Major Science and Technology of Department of Education of Guizhou Province ([2012]011) and Natural Science Foundation of the Education Department of Guizhou Province (KY[2015]482)

Fractional Order Two-Temperature Dual-Phase-Lag Thermoelasticity with Variable Thermal Conductivity

PubMed Central

Mallik, Sadek Hossain; Kanoria, M.

2014-01-01

A new theory of two-temperature generalized thermoelasticity is constructed in the context of a new consideration of dual-phase-lag heat conduction with fractional orders. The theory is then adopted to study thermoelastic interaction in an isotropic homogenous semi-infinite generalized thermoelastic solids with variable thermal conductivity whose boundary is subjected to thermal and mechanical loading. The basic equations of the problem have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by using a state space approach. The inversion of Laplace transforms is computed numerically using the method of Fourier series expansion technique. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. Some comparisons of the thermophysical quantities are shown in figures to study the effects of the variable thermal conductivity, temperature discrepancy, and the fractional order parameter. PMID:27419210

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.

Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions

NASA Astrophysics Data System (ADS)

Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em

2017-12-01

Starting with the asymptotic expansion of the error equation of the shifted Gr\\"{u}nwald--Letnikov formula, we derive a new modified weighted shifted Gr\\"{u}nwald--Letnikov (WSGL) formula by introducing appropriate correction terms. We then apply one special case of the modified WSGL formula to solve multi-term fractional ordinary and partial differential equations, and we prove the linear stability and second-order convergence for both smooth and non-smooth solutions. We show theoretically and numerically that numerical solutions up to certain accuracy can be obtained with only a few correction terms. Moreover, the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions. Numerical simulations verify the theoretical results and demonstrate that the new formula leads to better performance compared to other known numerical approximations with similar resolution.

Dissipativity and stability analysis of fractional-order complex-valued neural networks with time delay.

PubMed

Velmurugan, G; Rakkiyappan, R; Vembarasan, V; Cao, Jinde; Alsaedi, Ahmed

2017-02-01

As we know, the notion of dissipativity is an important dynamical property of neural networks. Thus, the analysis of dissipativity of neural networks with time delay is becoming more and more important in the research field. In this paper, the authors establish a class of fractional-order complex-valued neural networks (FCVNNs) with time delay, and intensively study the problem of dissipativity, as well as global asymptotic stability of the considered FCVNNs with time delay. Based on the fractional Halanay inequality and suitable Lyapunov functions, some new sufficient conditions are obtained that guarantee the dissipativity of FCVNNs with time delay. Moreover, some sufficient conditions are derived in order to ensure the global asymptotic stability of the addressed FCVNNs with time delay. Finally, two numerical simulations are posed to ensure that the attention of our main results are valuable. Copyright © 2016 Elsevier Ltd. All rights reserved.

A second-order unconstrained optimization method for canonical-ensemble density-functional methods

NASA Astrophysics Data System (ADS)

Nygaard, Cecilie R.; Olsen, Jeppe

2013-03-01

A second order converging method of ensemble optimization (SOEO) in the framework of Kohn-Sham Density-Functional Theory is presented, where the energy is minimized with respect to an ensemble density matrix. It is general in the sense that the number of fractionally occupied orbitals is not predefined, but rather it is optimized by the algorithm. SOEO is a second order Newton-Raphson method of optimization, where both the form of the orbitals and the occupation numbers are optimized simultaneously. To keep the occupation numbers between zero and two, a set of occupation angles is defined, from which the occupation numbers are expressed as trigonometric functions. The total number of electrons is controlled by a built-in second order restriction of the Newton-Raphson equations, which can be deactivated in the case of a grand-canonical ensemble (where the total number of electrons is allowed to change). To test the optimization method, dissociation curves for diatomic carbon are produced using different functionals for the exchange-correlation energy. These curves show that SOEO favors symmetry broken pure-state solutions when using functionals with exact exchange such as Hartree-Fock and Becke three-parameter Lee-Yang-Parr. This is explained by an unphysical contribution to the exact exchange energy from interactions between fractional occupations. For functionals without exact exchange, such as local density approximation or Becke Lee-Yang-Parr, ensemble solutions are favored at interatomic distances larger than the equilibrium distance. Calculations on the chromium dimer are also discussed. They show that SOEO is able to converge to ensemble solutions for systems that are more complicated than diatomic carbon.

Fraction distribution and risk assessment of heavy metals in waste clay sediment discharged through the phosphate beneficiation process in Jordan.

PubMed

Al-Hwaiti, Mohammad Salem; Brumsack, Hans Jurgen; Schnetger, Bernhard

2015-07-01

Heavy metal contamination of clay waste through the phosphate beneficiation process is a serious problem faced by scientists and regulators worldwide. Through the beneficiation process, heavy metals naturally present in the phosphate rocks became concentrated in the clay waste. This study evaluated the concentration of heavy metals and their fractions in the clay waste in order to assess the risk of environmental contamination. A five-step sequential extraction method, the risk assessment code (RAC), effects range low (ERL), effects range medium (ERM), the lowest effect level (LEL), the severe effect level (SEL), the redistribution index (U tf), the reduced partition index (I), residual partition index (I R), and the Nemerow multi-factor index (PC) were used to assess for clay waste contamination. Heavy metals were analyzed using high-resolution inductively coupled plasma mass spectrometry (HR-ICP-MS) and inductively coupled plasma optical emission spectroscopy (ICP-OES). Correlation analyses were carried out to better understand the relationships between the chemical characteristics and the contents of the different phase fractions. Concentrations of Cd and Cu confirmed that both were bound to the exchangeable fraction (F1) and the carbonate fraction (F2), presenting higher mobility, whereas Pb was most abundant in the Fe-Mn oxide fraction (F3) and organic matter fraction (F4). The residual fraction (F5) contained the highest concentrations (>60%) of As, Cr, Mo, V, and Zn, with lower mobility. Application of the RAC index showed that Cd and Cu should be considered a moderate risk, whereas As, Cr, Mo, Pb, and Zn presented a low risk. Cadmium and Cu contents in mobile fractions F1 and F2 were higher than ERL but lower than ERM. On the other hand, As, Pb, and Zn contents of mobile fractions F1 and F2 were lower than ERL and ERM guideline values. Moreover, total Pb concentrations in the clay waste were below the lowest effect level (LEL) threshold value period, Cr and Zn values in the clay waste were determined to have exceeded the severe effect level (SEL) limit values, whereas Cd and Cu level ranges between LEL and SEL indicate moderate contamination. I R values of heavy metals in the clay waste confirmed that Cd and Cu were bound to the exchangeable and carbonate fractions and presented higher mobility, whereas As, Cr, Mo, Pb, V, and Zn were bound to organic or residual fractions and consequently exhibit lower mobility. A Nemerow multi-factor index revealed that the mine site contains high levels of Cd, Cu, V, and Zn pollution. As and Cr were found at a moderate level of contamination, whereas Pb was present at a safe level of contamination. The order of the comprehensive contamination indices was Cd > Cu > Mo > Zn > V > Cr > As > Pb, indicating that the assessment of clay waste, especially with Cd and Cu, should be undertaken to control heavy metal contamination in adjacent urban and mine areas at the Eshidiya mines.

A new image encryption algorithm based on the fractional-order hyperchaotic Lorenz system

NASA Astrophysics Data System (ADS)

Wang, Zhen; Huang, Xia; Li, Yu-Xia; Song, Xiao-Na

2013-01-01

We propose a new image encryption algorithm on the basis of the fractional-order hyperchaotic Lorenz system. While in the process of generating a key stream, the system parameters and the derivative order are embedded in the proposed algorithm to enhance the security. Such an algorithm is detailed in terms of security analyses, including correlation analysis, information entropy analysis, run statistic analysis, mean-variance gray value analysis, and key sensitivity analysis. The experimental results demonstrate that the proposed image encryption scheme has the advantages of large key space and high security for practical image encryption.

Emotion recognition based on multiple order features using fractional Fourier transform

NASA Astrophysics Data System (ADS)

Ren, Bo; Liu, Deyin; Qi, Lin

2017-07-01

In order to deal with the insufficiency of recently algorithms based on Two Dimensions Fractional Fourier Transform (2D-FrFT), this paper proposes a multiple order features based method for emotion recognition. Most existing methods utilize the feature of single order or a couple of orders of 2D-FrFT. However, different orders of 2D-FrFT have different contributions on the feature extraction of emotion recognition. Combination of these features can enhance the performance of an emotion recognition system. The proposed approach obtains numerous features that extracted in different orders of 2D-FrFT in the directions of x-axis and y-axis, and uses the statistical magnitudes as the final feature vectors for recognition. The Support Vector Machine (SVM) is utilized for the classification and RML Emotion database and Cohn-Kanade (CK) database are used for the experiment. The experimental results demonstrate the effectiveness of the proposed method.

Blind third-order dispersion estimation based on fractional Fourier transformation for coherent optical communication

NASA Astrophysics Data System (ADS)

Yang, Lin; Guo, Peng; Yang, Aiying; Qiao, Yaojun

2018-02-01

In this paper, we propose a blind third-order dispersion estimation method based on fractional Fourier transformation (FrFT) in optical fiber communication system. By measuring the chromatic dispersion (CD) at different wavelengths, this method can estimation dispersion slope and further calculate the third-order dispersion. The simulation results demonstrate that the estimation error is less than 2 % in 28GBaud dual polarization quadrature phase-shift keying (DP-QPSK) and 28GBaud dual polarization 16 quadrature amplitude modulation (DP-16QAM) system. Through simulations, the proposed third-order dispersion estimation method is shown to be robust against nonlinear and amplified spontaneous emission (ASE) noise. In addition, to reduce the computational complexity, searching step with coarse and fine granularity is chosen to search optimal order of FrFT. The third-order dispersion estimation method based on FrFT can be used to monitor the third-order dispersion in optical fiber system.

Effective field theory approach to heavy quark fragmentation

DOE PAGES

Fickinger, Michael; Fleming, Sean; Kim, Chul; ...

2016-11-17

Using an approach based on Soft Collinear Effective Theory (SCET) and Heavy Quark Effective Theory (HQET) we determine the b-quark fragmentation function from electron-positron annihilation data at the Z-boson peak at next-to-next-to leading order with next-to-next-to leading log resummation of DGLAP logarithms, and next-to-next-to-next-to leading log resummation of endpoint logarithms. This analysis improves, by one order, the previous extraction of the b-quark fragmentation function. We find that while the addition of the next order in the calculation does not much shift the extracted form of the fragmentation function, it does reduce theoretical errors indicating that the expansion is converging. Usingmore » an approach based on effective field theory allows us to systematically control theoretical errors. Furthermore, while the fits of theory to data are generally good, the fits seem to be hinting that higher order correction from HQET may be needed to explain the b-quark fragmentation function at smaller values of momentum fraction.« less

Redistribution of fractions of zinc, cadmium, nickel, copper, and lead in contaminated calcareous soils treated with EDTA.

PubMed

Jalali, Mohsen; Khanlari, Zahra V

2007-11-01

Effect of ethylene diamine tetraacetic acid (EDTA) on the fractionation of zinc (Zn), cadmium (Cd), nickel (Ni), copper (Cu), and lead (Pb) in contaminated calcareous soils was investigated. Soil samples containing variable levels of contamination, from 105.9 to 5803 mg/kg Zn, from 2.2 to 1361 mg/kg Cd, from 31 to 64.0 mg/kg Ni, from 24 to 84 mg/kg Cu, and from 109 to 24,850 mg/kg Pb, were subjected to EDTA treatment at different dosages of 0, 1.0, and 2.0 g/kg. Metals in the incubated soils were fractionated after 5 months by a sequential extraction procedure, in which the metal fractions were experimentally defined as exchangeable (EXCH), carbonate (CARB), Mn oxide (MNO), Fe oxide (FEO), organic matter (OM), and residual (RES) fractions. In contaminated soils without EDTA addition, Zn, Ni, Cu, and Pb were predominately present in the RES fraction, up to 60.0%, 32.3%, 41.1%, and 36.8%, respectively. In general, with the EDTA addition, the EXCH and CARB fractions of these metals increased dramatically while the OM fraction decreased. The Zn, Ni, Cu, and Pb were distributed mostly in RES, OM, FEO, and CARB fractions in contaminated soils, but Cd was found predominately in the CARB, MNO, and RES fractions. The OM fraction decreased with increasing amounts of EDTA. In the contaminated soils, EDTA removed some Pb, Zn, Cu, and Ni from MNO, FEO, and OM fractions and redistributed them into CARB and EXCH fractions. Based on the relative percent in the EXCH and CARB fractions, the order of solubility was Cd > Pb > Ni > Cu > Zn for contaminated soils, before adding of EDTA, and after adding of EDTA, the order of solubility was Pb > Cd > Zn > Ni > Cu. The risk of groundwater contamination will increase after applying EDTA and it needed to be used very carefully.

Early Predictors of Middle School Fraction Knowledge

PubMed Central

Bailey, Drew H.; Siegler, Robert S.; Geary, David C.

2014-01-01

Recent findings that earlier fraction knowledge predicts later mathematics achievement raise the question of what predicts later fraction knowledge. Analyses of longitudinal data indicated that whole number magnitude knowledge in first grade predicted knowledge of fraction magnitudes in middle school, controlling for whole number arithmetic proficiency, domain general cognitive abilities, parental income and education, race, and gender. Similarly, knowledge of whole number arithmetic in first grade predicted knowledge of fraction arithmetic in middle school, controlling for whole number magnitude knowledge in first grade and the other control variables. In contrast, neither type of early whole number knowledge uniquely predicted middle school reading achievement. We discuss the implications of these findings for theories of numerical development and for improving mathematics learning. PMID:24576209

Optimal Control of Stochastic Systems Driven by Fractional Brownian Motions

DTIC Science & Technology

2014-10-09

problems for stochastic partial differential equations driven by fractional Brownian motions are explicitly solved. For the control of a continuous time...linear systems with Brownian motion or a discrete time linear system with a white Gaussian noise and costs 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 stochastic optimal control, fractional Brownian motion , stochastic

General covariance, topological quantum field theories and fractional statistics

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

Gamboa, J.

1992-01-20

Topological quantum field theories and fractional statistics are both defined in multiply connected manifolds. The authors study the relationship between both theories in 2 + 1 dimensions and the authors show that, due to the multiply-connected character of the manifold, the propagator for any quantum (field) theory always contains a first order pole that can be identified with a physical excitation with fractional spin. The article starts by reviewing the definition of general covariance in the Hamiltonian formalism, the gauge-fixing problem and the quantization following the lines of Batalin, Fradkin and Vilkovisky. The BRST-BFV quantization is reviewed in order tomore » understand the topological approach proposed here.« less

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.

Encryption and display of multiple-image information using computer-generated holography with modified GS iterative algorithm

NASA Astrophysics Data System (ADS)

Xiao, Dan; Li, Xiaowei; Liu, Su-Juan; Wang, Qiong-Hua

2018-03-01

In this paper, a new scheme of multiple-image encryption and display based on computer-generated holography (CGH) and maximum length cellular automata (MLCA) is presented. With the scheme, the computer-generated hologram, which has the information of the three primitive images, is generated by modified Gerchberg-Saxton (GS) iterative algorithm using three different fractional orders in fractional Fourier domain firstly. Then the hologram is encrypted using MLCA mask. The ciphertext can be decrypted combined with the fractional orders and the rules of MLCA. Numerical simulations and experimental display results have been carried out to verify the validity and feasibility of the proposed scheme.

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.

Reduced Order Models Via Continued Fractions Applied to Control Systems,

DTIC Science & Technology

1980-09-01

a simple * model of a nuclear reactor power generator [20, 21]. The heat generating process of a nuclear reactor is dependent upon the mechanism...called fission (a fragmentation of matter). The power generated by this process is directly related to the population of neutrons, n~t) and can be...150) 6(t ()n~t) - c(t) (151) where 6k(t) 6 kc(t)-an(t) (152) The variable 6k(t) is the input to the process and is given the name "reactivity". It is

Minimal complexity control law synthesis

NASA Technical Reports Server (NTRS)

Bernstein, Dennis S.; Haddad, Wassim M.; Nett, Carl N.

1989-01-01

A paradigm for control law design for modern engineering systems is proposed: Minimize control law complexity subject to the achievement of a specified accuracy in the face of a specified level of uncertainty. Correspondingly, the overall goal is to make progress towards the development of a control law design methodology which supports this paradigm. Researchers achieve this goal by developing a general theory of optimal constrained-structure dynamic output feedback compensation, where here constrained-structure means that the dynamic-structure (e.g., dynamic order, pole locations, zero locations, etc.) of the output feedback compensation is constrained in some way. By applying this theory in an innovative fashion, where here the indicated iteration occurs over the choice of the compensator dynamic-structure, the paradigm stated above can, in principle, be realized. The optimal constrained-structure dynamic output feedback problem is formulated in general terms. An elegant method for reducing optimal constrained-structure dynamic output feedback problems to optimal static output feedback problems is then developed. This reduction procedure makes use of star products, linear fractional transformations, and linear fractional decompositions, and yields as a byproduct a complete characterization of the class of optimal constrained-structure dynamic output feedback problems which can be reduced to optimal static output feedback problems. Issues such as operational/physical constraints, operating-point variations, and processor throughput/memory limitations are considered, and it is shown how anti-windup/bumpless transfer, gain-scheduling, and digital processor implementation can be facilitated by constraining the controller dynamic-structure in an appropriate fashion.

Unit Fractions in the Context of Proportionality: Supporting Students' Reasoning about the Inverse Order Relationship

ERIC Educational Resources Information Center

Cortina, Jose Luis; Visnovska, Jana; Zuniga, Claudia

2014-01-01

We analyze a classroom design experiment, conducted in a fourth grade classroom, that served to explore an instructional path in which the introduction of unit fractions and supporting proportional reasoning coincide. Central to this path is the use of means of support in which the objects that unit fractions quantify are not characterized as…

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.

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.

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.

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

Intake fraction of PM2.5 and NOX from vehicle emissions in Beijing based on personal exposure data

NASA Astrophysics Data System (ADS)

Du, Xuan; Wu, Ye; Fu, Lixin; Wang, Shuxiao; Zhang, Shaojun; Hao, Jiming

2012-09-01

The intake fraction (iF) is the portion of attributable population intake of a source emissions, and is used to link pollutant emissions and population exposure. This study is the first work that reported individual intake fraction of PM2.5 and NOX from vehicle emissions based on personal exposure data in China. We employed PM2.5 and NOX measurement data from 24-h personal exposure sampling and concentration monitoring in traffic environments in the urban area of Beijing to estimate the individual intake fraction (iFi). iFi distributions are presented in microenvironments (traffic, work, home) for adults and children. The individual results are used to calculate the intake fraction for the children group and the adults group in the urban area of Beijing. The iF of PM2.5 for the whole population of these two groups in Beijing is 153 per million, which is significantly higher than those estimates in the United States (1-50 per million) and Mexico (23-120 per million). The iF of NOX is 70 per million, among which the intake in the traffic micro-environment ranks first compared to the iF in the home and office due to a high accumulation of NOX concentration in vehicles. PM2.5 and NOX intake fraction values from vehicle emissions in this study are from at least several times to one order of magnitude higher than those from other industry sources in China. This strongly suggests the health risk from vehicle emissions is significantly higher. Therefore, to protect human health, especially for the large number of people living in the cities of China, controlling vehicle emissions should be the highest priority.

Low or High Fractionation Dose {beta}-Radiotherapy for Pterygium? A Randomized Clinical Trial

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

Viani, Gustavo Arruda, E-mail: gusviani@gmail.com; De Fendi, Ligia Issa; Fonseca, Ellen Carrara

2012-02-01

Purpose: Postoperative adjuvant treatment using {beta}-radiotherapy (RT) is a proven technique for reducing the recurrence of pterygium. A randomized trial was conducted to determine whether a low fractionation dose of 2 Gy within 10 fractions would provide local control similar to that after a high fractionation dose of 5 Gy within 7 fractions for surgically resected pterygium. Methods: A randomized trial was conducted in 200 patients (216 pterygia) between February 2006 and July 2007. Only patients with fresh pterygium resected using a bare sclera method and given RT within 3 days were included. Postoperative RT was delivered using a strontium-90more » eye applicator. The pterygia were randomly treated using either 5 Gy within 7 fractions (Group 1) or 2 Gy within 10 fractions (Group 2). The local control rate was calculated from the date of surgery. Results: Of the 216 pterygia included, 112 were allocated to Group 1 and 104 to Group 2. The 3-year local control rate for Groups 1 and 2 was 93.8% and 92.3%, respectively (p = .616). A statistically significant difference for cosmetic effect (p = .034), photophobia (p = .02), irritation (p = .001), and scleromalacia (p = .017) was noted in favor of Group 2. Conclusions: No better local control rate for postoperative pterygium was obtained using high-dose fractionation vs. low-dose fractionation. However, a low-dose fractionation schedule produced better cosmetic effects and resulted in fewer symptoms than high-dose fractionation. Moreover, pterygia can be safely treated in terms of local recurrence using RT schedules with a biologic effective dose of 24-52.5 Gy{sub 10.}.« 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.

Numerical simulation for solution of space-time fractional telegraphs equations with local fractional derivatives via HAFSTM

NASA Astrophysics Data System (ADS)

Pandey, Rishi Kumar; Mishra, Hradyesh Kumar

2017-11-01

In this paper, the semi-analytic numerical technique for the solution of time-space fractional telegraph equation is applied. This numerical technique is based on coupling of the homotopy analysis method and sumudu transform. It shows the clear advantage with mess methods like finite difference method and also with polynomial methods similar to perturbation and Adomian decomposition methods. It is easily transform the complex fractional order derivatives in simple time domain and interpret the results in same meaning.

The time-fractional radiative transport equation—Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion

NASA Astrophysics Data System (ADS)

Machida, Manabu

2017-01-01

We consider the radiative transport equation in which the time derivative is replaced by the Caputo derivative. Such fractional-order derivatives are related to anomalous transport and anomalous diffusion. In this paper we describe how the time-fractional radiative transport equation is obtained from continuous-time random walk and see how the equation is related to the time-fractional diffusion equation in the asymptotic limit. Then we solve the equation with Legendre-polynomial expansion.

Oscillation of a class of fractional differential equations with damping term.

PubMed

Qin, Huizeng; Zheng, Bin

2013-01-01

We investigate the oscillation of a class of fractional differential equations with damping term. Based on a certain variable transformation, the fractional differential equations are converted into another differential equations of integer order with respect to the new variable. Then, using Riccati transformation, inequality, and integration average technique, some new oscillatory criteria for the equations are established. As for applications, oscillation for two certain fractional differential equations with damping term is investigated by the use of the presented results.

Spatial Distribution, Chemical Fraction and Fuzzy Comprehensive Risk Assessment of Heavy Metals in Surface Sediments from the Honghu Lake, China

PubMed Central

Xiao, Minsi; Zhang, Jingdong; Liu, Chaoyang; Qiu, Zhenzhen; Cai, Ying

2018-01-01

Spatial concentrations and chemical fractions of heavy metals (Cr, Cu, Pb, Zn and Cd) in 16 sampling sites from the Honghu Lake were investigated using an atomic absorption spectrophotometer and optimized BCR (the European Community Bureau of Reference) three-stage extraction procedure. Compared with the corresponding probable effect levels (PELs), adverse biological effects of the studied five sediment metals decreased in the sequence of Cr > Cu > Zn > Pb > Cd. Geo-accumulation index (Igeo) values for Cr, Cu, Pb and Zn in each sampling site were at un-contamination level, while the values for Cd varied from un-contamination level to moderate contamination level. Spatially, the enrichment degree of Cd in lower part of the South Lake, the west part of the North Lake and the outlet were higher than the other parts of Honghu Lake. For metal chemical fractions, the proportions of the acid-extractable fraction of five metal contents were in the descending order: Cd, Cu, Zn, Pb and Cr. Cd had the highest bioaccessibility. Being the above indexes focused always on heavy metals’ total content or chemical fraction in deterministic assessment system, which may confuse decision makers, the fuzzy comprehensive risk assessment method was established based on PEI (Potential ecological risk index), RAC (Risk assessment code) and fuzzy theory. Average comprehensive risks of heavy metals in sediments revealed the following orders: Cd (considerable risk) > Cu (moderate risk) > Zn (low risk) > Pb > Cr. Thus, Cd and Cu were determined as the pollutants of most concern. The central part of South Honghu Lake (S4, S5, S6, S9, S12 and S14), east part of the North Honghu Lake (S1) and outlet of outlet of the Honghu Lake (S10) were recommended as the priority control areas. Specifically, it is necessary to pay more attention to S1, S4, S5, S6, S9 and S16 when decision making for their calculated membership values (probabilities) of adjacent risk levels quite close. PMID:29373483

Highly Concentrated Nebular Noble Gases in Porous Nanocarbon Separates from the Saratov (L4) Meteorite

NASA Astrophysics Data System (ADS)

Amari, Sachiko; Matsuda, Jun-ichi; Stroud, Rhonda M.; Chisholm, Matthew F.

2013-11-01

The majority of heavy noble gases (Ar, Kr, and Xe) in primitive meteorites are stored in a poorly understood phase called Q. Although Q is thought to be carbonaceous, the full identity of the phase has remained elusive for almost four decades. In order to better characterize phase Q and, in turn, the early solar nebula, we separated carbon-rich fractions from the Saratov (L4) meteorite. We chose this meteorite because Q is most resistant in thermal alteration among carbonaceous noble gas carriers in meteorites and we hoped that, in this highly metamorphosed meteorite, Q would be present but not diamond: these two phases are very difficult to separate from each other. One of the fractions, AJ, has the highest 132Xe concentration of 2.1 × 10-6 cm3 STP g-1, exceeding any Q-rich fractions that have yet been analyzed. Transmission electron microscopy studies of the fraction AJ and a less Q-rich fraction AI indicate that they both are primarily porous carbon that consists of domains with short-range graphene orders, with variable packing in three dimensions, but no long-range graphitic order. The relative abundance of Xe and C atoms (6:109) in the separates indicates that individual noble gas atoms are associated with only a minor component of the porous carbon, possibly one or more specific arrangements of the nanoparticulate graphene.

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.

Compact drilling and sample system

NASA Technical Reports Server (NTRS)

Gillis-Smith, Greg R.; Petercsak, Doug

1998-01-01

The Compact Drilling and Sample System (CDSS) was developed to drill into terrestrial, cometary, and asteroid material in a cryogenic, vacuum environment in order to acquire subsurface samples. Although drills were used by the Apollo astronauts some 20 years ago, this drill is a fraction of the mass and power and operates completely autonomously, able to drill, acquire, transport, dock, and release sample containers in science instruments. The CDSS has incorporated into its control system the ability to gather science data about the material being drilled by measuring drilling rate per force applied and torque. This drill will be able to optimize rotation and thrust in order to achieve the highest drilling rate possible in any given sample. The drill can be commanded to drill at a specified force, so that force imparted on the rover or lander is limited. This paper will discuss the cryo dc brush motors, carbide gears, cryogenic lubrication, quick-release interchangeable sampling drill bits, percussion drilling and the control system developed to achieve autonomous, cryogenic, vacuum, lightweight drilling.

Method and apparatus for recirculation with control of synchrotron radiation

DOEpatents

Douglas, David R.; Tennant, Christopher

2016-08-02

A method for controlling beam quality degradation from ISR and CSR and stabilizing the microbunching instability (.mu.BI) in a high brightness electron beam. The method includes providing a super-periodic second order achromat line with each super period being individually linearly achromatic and isochronous, setting individual superperiod tunes to rational fractions of an integer (such as 4.sup.th or 6.sup.th integers), setting individual bend angles to be as small as practical to reduce driving terms due to dispersion and dispersive angle, and setting bend radii as large enough to suppress ISR but not negatively affect the radial dependence of CSR. The method includes setting the structure of the individual superperiods to minimize bend plane beam envelope values in the dipoles to reduce betatron response to a CSR event at a dispersed location, increasing beam angular divergence, and creating dispersion nodes in the dipoles to similarly reduce response to CSR events, and limit R.sub.56 modulation in order to mitigate .mu.BI.

On the singular perturbations for fractional differential equation.

PubMed

Atangana, Abdon

2014-01-01

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

Analytical solutions for the motion of a charged particle in electric and magnetic fields via non-singular fractional derivatives

NASA Astrophysics Data System (ADS)

Morales-Delgado, V. F.; Gómez-Aguilar, J. F.; Taneco-Hernandez, M. A.

2017-12-01

In this work we propose fractional differential equations for the motion of a charged particle in electric, magnetic and electromagnetic fields. Exact solutions are obtained for the fractional differential equations by employing the Laplace transform method. The temporal fractional differential equations are considered in the Caputo-Fabrizio-Caputo and Atangana-Baleanu-Caputo sense. Application examples consider constant, ramp and harmonic fields. In addition, we present numerical results for different values of the fractional order. In all cases, when α = 1, we recover the standard electrodynamics.

Distribution of selected heavy metals in sediments of the Agueda river (Central Portugal).

PubMed

dos Reis, Anabela Ribeiro; Parker, Andrew; Carter, Joy; Ferreira, Martim Portugal

2005-01-01

The state of river water deterioration in the Agueda hydrographic basin, mostly in the western part, partly reflects the high rate of housing and industrial development in this area in recent years. The streams have acted as a sink for organic and inorganic loads from several origins: domestic and industrial sewage and agricultural waste. The contents of the heavy metals Cr, Cd, Ni, Cu, Pb, and Zn were studied by sequential chemical extraction of the principal geochemical phases of streambed sediments, in the <63 microm fraction, in order to assess their potential availability to the environment, investigating the metal concentrations, assemblages, and trends. The granulometric and mineralogical characteristics of this sediment fraction were also studied. This study revealed clear pollution by Cr, Cd, Ni, Cu, Zn, and Pb, as a result from both natural and anthropogenic origins. The chemical transport of metals appears to be essentially by the following geochemical phases, in decreasing order of significance: (exchangeable + carbonates) > (organics) > (Mn and Fe oxides and hydroxides). The (exchangeable + carbonate) phase plays an important part in the fixation of Cu, Ni, Zn, and Cd. The organic phase is important in the fixation of Cr, Pb, and also Cu and Ni. Analyzing the metal contents in the residual fraction, we conclude that Zn and Cd are the most mobile, and Cr and Pb are less mobile than Cu and Ni. The proximity of the pollutant sources and the timing of the influx of contaminated material control the distribution of the contaminant-related sediments locally and on the network scale.

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.

Long-Term Effect of Crop Rotation and Fertilisation on Bioavailability and Fractionation of Copper in Soil on the Loess Plateau in Northwest China

PubMed Central

Zang, Yifei; Wei, Xiaorong; Hao, Mingde

2015-01-01

The bioavailability and fractionation of Cu reflect its deliverability in soil. Little research has investigated Cu supply to crops in soil under long-term rotation and fertilisation on the Loess Plateau. A field experiment was conducted in randomized complete block design to determine the bioavailability and distribution of Cu fractions in a Heilu soil (Calcaric Regosol) after 18 years of rotation and fertilisation. The experiment started in 1984, including five cropping systems (fallow control, alfalfa cropping, maize cropping, winter wheat cropping, and grain-legume rotation of pea/winter wheat/winter wheat + millet) and five fertiliser treatments (unfertilised control, N, P, N + P, and N + P + manure). Soil samples were collected in 2002 for chemical analysis. Available Cu was assessed by diethylene triamine pentaacetic acid (DTPA) extraction, and Cu was fractionated by sequential extraction. Results showed that DTPA-Cu was lower in cropping systems compared with fallow control. Application of fertilisers resulted in no remarkable changes in DTPA-Cu compared with unfertilised control. Correlation and path analyses revealed that soil pH and CaCO3 directly affected Cu bioavailability, whereas available P indirectly affected Cu bioavailability. The concentrations of Cu fractions (carbonate and Fe/Al oxides) in the plough layer were lower in cropping systems, while the values in the plough sole were higher under grain-legume rotation relative to fallow control. Manure with NP fertiliser increased Cu fractions bound to organic matter and minerals in the plough layer, and its effects in the plough sole varied with cropping systems. The direct sources (organic-matter-bound fraction and carbonate-bound fraction) of available Cu contributed much to Cu bioavailability. The mineral-bound fraction of Cu acted as an indicator of Cu supply potential in the soil. PMID:26694965

Long-Term Effect of Crop Rotation and Fertilisation on Bioavailability and Fractionation of Copper in Soil on the Loess Plateau in Northwest China.

PubMed

Zang, Yifei; Wei, Xiaorong; Hao, Mingde

2015-01-01

The bioavailability and fractionation of Cu reflect its deliverability in soil. Little research has investigated Cu supply to crops in soil under long-term rotation and fertilisation on the Loess Plateau. A field experiment was conducted in randomized complete block design to determine the bioavailability and distribution of Cu fractions in a Heilu soil (Calcaric Regosol) after 18 years of rotation and fertilisation. The experiment started in 1984, including five cropping systems (fallow control, alfalfa cropping, maize cropping, winter wheat cropping, and grain-legume rotation of pea/winter wheat/winter wheat + millet) and five fertiliser treatments (unfertilised control, N, P, N + P, and N + P + manure). Soil samples were collected in 2002 for chemical analysis. Available Cu was assessed by diethylene triamine pentaacetic acid (DTPA) extraction, and Cu was fractionated by sequential extraction. Results showed that DTPA-Cu was lower in cropping systems compared with fallow control. Application of fertilisers resulted in no remarkable changes in DTPA-Cu compared with unfertilised control. Correlation and path analyses revealed that soil pH and CaCO3 directly affected Cu bioavailability, whereas available P indirectly affected Cu bioavailability. The concentrations of Cu fractions (carbonate and Fe/Al oxides) in the plough layer were lower in cropping systems, while the values in the plough sole were higher under grain-legume rotation relative to fallow control. Manure with NP fertiliser increased Cu fractions bound to organic matter and minerals in the plough layer, and its effects in the plough sole varied with cropping systems. The direct sources (organic-matter-bound fraction and carbonate-bound fraction) of available Cu contributed much to Cu bioavailability. The mineral-bound fraction of Cu acted as an indicator of Cu supply potential in the soil.

THE SERUM PROTEIN FRACTIONS IN THYMOQUINONE TREATED RATS.

PubMed

A, Güllü; S, Dede

2016-01-01

TQ has been used as treatment and preventive agent for many diseases over the years. The goal of this study was to investigate the effects of TQ supplement on fractions of serum proteins. Fourteen male Wistar-Albino rats (200-250 g weight) were used as material for two groups; (control (C) and thymoquinone (TQ) respectively. Each group contained seven rats. The control group had only corn oil, while the TQ group was dissolved in corn oil. 30 mg/kg/day were given by oral gavage for four weeks. The serum protein fractions were identified using cellulose acetate technique. The total protein level and albumin, α-1, α-2 fractions and A/G ratio have showed no difference between groups (p>0.05). β-globulin fractions of TQ group were higher than control's (p<0.05). In addition, it was observed that the γ-globulin levels of TQ group were lower than that of the control group's (p<0.05). From the results, it was observed that the changes of these fractions may have originated from elevation or decline synthesis, or activities of containing proteins.