Determination of fractional energy loss of waves in nearshore waters using an improved high-order Boussinesq-type model

Fractional energy losses of waves due to wave breaking when passing over a submerged bar are studied systematically using a modified numerical code that is based on the high-order Boussinesq-type equations. The model is first tested by the additional experimental data, and the model's capability of simulating the wave transformation over both gentle slope and steep slope is demonstrated. Then, the model's breaking index is replaced and tested. The new breaking index, which is optimized from the several breaking indices, is not sensitive to the spatial grid length and includes the bottom slopes. Numerical tests show that the modified model with the new breaking index is more stable and efficient for the shallow-water wave breaking. Finally, the modified model is used to study the fractional energy losses for the regular waves propagating and breaking over a submerged bar. Our results have revealed that how the nonlinearity and the dispersion of the incident waves as well as the dimensionless bar height (normalized by water depth) dominate the fractional energy losses. It is also found that the bar slope (limited to gentle slopes that less than 1:10) and the dimensionless bar length (normalized by incident wave length) have negligible effects on the fractional energy losses.

Kernel-based local order estimation of nonlinear nonparametric systems

We consider the local order estimation of nonlinear autoregressive systems with exogenous inputs (NARX), which may have different local dimensions at different points. By minimizing the kernel-based local information criterion introduced in this paper, the strongly consistent estimates for the local orders of the NARX system at points of interest are obtained. The modification of the criterion and a simple procedure of searching the minimum of the criterion, are also discussed. The theoretical results derived here are tested by simulation examples.

Nanofibers fabricated using triaxial electrospinning as zero order drug delivery systems

A new strategy for creating functional trilayer nanofibers through triaxial electrospinning is demonstrated. Ethyl cellulose (EC) was used as the filament-forming matrix in the outer, middle, and inner working solutions and was combined with varied contents of the model active ingredient ketoprofen (KET) in the three fluids. Triaxial electrospinning was successfully carried out to generate medicated nanofibers. The resultant nanofibers had diameters of 0.74 ± 0.06 μm, linear morphologies, smooth surfaces, and clear trilayer nanostructures. The KET concentration in each layer gradually increased from the outer to the inner layer. In vitro dissolution tests demonstrated that the nanofibers could provide linear release of KET over 20 h. The protocol reported in this study thus provides a facile approach to creating functional nanofibers with sophisticated structural features.

Optimal controllers with complex order derivatives

This paper studies the optimization of complex-order algorithms for the discrete-time control of linear and nonlinear systems. The fundamentals of fractional systems and genetic algorithms are introduced. Based on these concepts, complexorder control schemes and their implementation are evaluated in the perspective of evolutionary optimization. The results demonstrate not only that complex-order derivatives constitute a valuable alternative for deriving control algorithms, but also the feasibility of the adopted optimization strategy.

Multidimensional scaling analysis of fractional systems

This paper investigates the use of multidimensional scaling in the evaluation of fractional system. Several algorithms are analysed based on the time response of the closed loop system under the action of a reference step input signal. Two alternative performance indices, based on the time and frequency domains, are tested. The numerical experiments demonstrate the feasibility of the proposed visualization method.

Complex order biped rhythms

Animal locomotion is a complex process, involving the central pattern generators (neural networks, located in the spinal cord, that produce rhythmic patterns), the brainstem command systems, the steering and posture control systems and the top layer structures that decide which motor primitive is activated at a given time. Pinto and Golubitsky studied an integer CPG model for legs rhythms in bipeds. It is a four-coupled identical oscillators' network with dihedral symmetry. This paper considers a new complex order central pattern generator (CPG) model for locomotion in bipeds. A complex derivative Dα±jβ, with α, β ∈ ℜ+, j = √-1, is a generalization of the concept of an integer derivative, where α = 1, β = 0. Parameter regions where periodic solutions, identified with legs' rhythms in bipeds, occur, are analyzed. Also observed is the variation of the amplitude and period of periodic solutions with the complex order derivative.

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.

Fractional State Space Analysis of Economy Systems

This paper examines modern economic growth according to the multidimensional scaling (MDS) method and state space portrait (SSP) analysis. Electing GDP per capita as the main indicator for economic growth and prosperity, the long-run perspective from 1870 to 2010 identifies the main similarities among 34 world partners’ modern economic growth and exemplifies the historical waving mechanics of the largest world economy, the USA. MDS reveals two main clusters among the European countries and their old offshore territories, and SSP identifies the Great Depression as a mild challenge to the American global performance, when compared to the Second World War and the 2008 crisis.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Visualizing control systems performance: A fractional perspective

This article presents a novel method for visualizing the control systems behavior. The proposed scheme uses the tools of fractional calculus and computes the signals propagating within the system structure as a time/frequency-space wave. Linear and nonlinear closed-loop control systems are analyzed, for both the time and frequency responses, under the action of a reference step input signal. Several nonlinearities, namely, Coulomb friction and backlash, are also tested. The numerical experiments demonstrate the feasibility of the proposed methodology as a visualization tool and motivate its extension for other systems and classes of nonlinearities.

An LMI approach to H∞ synchronization of second-order neutral master-slave systems

The H∞ synchronization problem of the master and slave structure of a second-order neutral master-slave systems with time-varying delays is presented in this paper. Delay-dependent sufficient conditions for the design of a delayed output-feedback control are given by Lyapunov-Krasovskii method in terms of a linear matrix inequality (LMI). A controller, which guarantees H∞ synchronization of the master and slave structure using some free weighting matrices, is then developed. A numerical example has been given to show the effectiveness of the method

Second-order Møller-Plesset perturbation theory without basis set superposition error : II : open-shell systems

The basis set superposition error-free second-order MØller-Plesset perturbation theory of intermolecular interactions was studied. The difficulties of the counterpoise (CP) correction in open-shell systems were also discussed. The calculations were performed by a program which was used for testing the new variants of the theory. It was shown that the CP correction for the diabatic surfaces should be preferred to the adiabatic ones

Stable reduced-order models for discrete-time systems

The Routh-stability method is employed to reduce the order of discrete-time system transfer functions. It is shown that the Routh approximant is well suited to reduce both the denominator and the numerator polynomials, although alternative methods, such as PadÃ�Â(c)-Markov approximation, are also used to fit the model numerator coefficients.