Multiple time scales of fluvial processes — theory and applications

Fluvial processes comprise water flow, sediment transport and bed evolution, which normally feature distinct time scales. The time scales of sediment transport and bed deformation relative to the flow essentially measure how fast sediment transport adapts to capacity region in line with local flow scenario and the bed deforms in comparison with the flow, which literally dictates if a capacity based and/or decoupled model is justified. This paper synthesizes the recently developed multiscale theory for sediment-laden flows over erodible bed, with bed load and suspended load transport, respectively. It is unravelled that bed load transport can adapt to capacity sufficiently rapidly even under highly unsteady flows and thus a capacity model is mostly applicable, whereas a non-capacity model is critical for suspended sediment because of the lower rate of adaptation to capacity. Physically coupled modelling is critical for fluvial processes characterized by rapid bed variation. Applications are outlined on very active bed load sediment transported by flash floods and landslide dam break floods.     

Existence and joint continuity of local time of multi-parameter fractional Lévy processes

In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its local time.     

Mechanistic mathematical model of kinesin under time and space fluctuating loads

Kinesin-1 is a processive molecular motor that converts the energy from ATP hydrolysis and Brownian motion into directed movement. Single-molecule techniques have allowed the experimental characterization of single kinesins in vitro at a range of loads and ATP concentrations, and shown that each kinesin molecule moves processively along microtubules by alternately advancing each of its motor domains in a hand-over-hand fashion. Existing models of kinesin movement focus on time and space invariant loads, and hence are not well suited to describing transient dynamics. However, kinesin must undergo transient dynamics when external perturbations (e.g., interactions with other kinesin molecules) cause the load on each motor to change in time. We have developed a mechanistic model that describes, deterministically, the average motion of kinesin under time and space varying loads. The diffusion is modeled using a novel approach inspired by the classical closed form solution for the mean first-passage time. In the new approach, the potential in which the free motor domain diffuses is time varying and updated at each instant during the motion. The mechanistic model is able to predict experimental force-velocity data over a wide range of ATP concentrations (1 μM–10 mM). This mechanistic approach to modeling the mechanical behavior of the motor domains of kinesin allows rational and efficient characterization of the mechanochemical coupling, and provides predictions of kinesin with time-varying loads, which is critical for modeling coordinated transport involving several kinesin molecules.     

On fractional Euler–Lagrange and Hamilton equations and the fractional generalization of total time derivative

Fractional mechanics describe both conservative and nonconservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics, the equivalent Lagrangians play an important role because they admit the same Euler–Lagrange equations. By adding a total time derivative of a suitable function to a given classical Lagrangian or by multiplying with a constant, the Lagrangian we obtain are the same equations of motion. In this study, the fractional discrete Lagrangians which differs by a fractional derivative are analyzed within Riemann–Liouville fractional derivatives. As a consequence of applying this procedure, the classical results are reobtained as a special case. The fractional generalization of Faà di Bruno formula is used in order to obtain the concrete expression of the fractional Lagrangians which differs from a given fractional Lagrangian by adding a fractional derivative. The fractional Euler–Lagrange and Hamilton equations corresponding to the obtained fractional Lagrangians are investigated, and two examples are analyzed in detail.     

Simulation of bifurcation and escape—time diagrams of cascade—connected nonlinear systems for rubber strip transportation

Systems consisting of several cascade-connected transporters for rubber strip transportation are presented in this paper. In consideration of the systems structure and the fact that the technological parameters of rubber materials are time variant, one of the characteristics of these systems is the possibility of oscillations and chaos appearance. In this paper the conditions for appearance of oscillations and chaos in mentioned systems are analysed. The results are confirmed by simulation of bifurcation and escape-time diagrams.     

Adaptive synchronization of stochastic neural networks with mixed time delays and reaction–diffusion terms

In this paper, the problem of exponential synchronization is investigated for a class of stochastic perturbed chaotic neural networks with both mixed time delays and reaction?Cdiffusion terms. By employing Lyapunov?CKrasovskii functional and stochastic analysis approaches, an adaptive controller is designed to guarantee the exponential synchronization of proposed neural networks in the mean square. In particular, the mixed time delays in this paper synchronously consist of constant delay in the leakage term (i.e., ??leakage delay??), discrete time-varying delay and distributed time-varying delay which are more general than those discussed in the previous literature. Furthermore, our synchronization criteria are easily verified and do not need to solve any linear matrix inequality. Therefore, the results obtained in this paper generalize and improve those given in the previous literature. Finally, the extensive simulations are performed to show the effectiveness and feasibility of the obtained method.     

Viscoelastic melt rheology and time–temperature superposition of polycarbonate–multi-walled carbon nanotube nanocomposites

This work investigates the linear and non-linear viscoelastic melt rheology of four grades of polycarbonate melt compounded with 3 wt% Nanocyl NC7000 multi-walled carbon nanotubes and of the matching matrix polymers. Amplitude sweeps reveal an earlier onset of non-linearity and a strain overshoot in the nanocomposites. Mastercurves are constructed from isothermal frequency sweeps using vertical and horizontal shifting. Although all nanocomposites exhibit a second plateau at ～10⁵ Pa, the relaxation times estimated from the peak in loss tangent are not statistically different from those of pure melts estimated from cross-over frequencies: all relaxation timescales scale with molar mass in the same way, evidence that the relaxation of the polymer network is the dominant mechanism in both filled and unfilled materials. Non-linear rheology is also measured in large amplitude oscillatory shear. A comparison of the responses from frequency and amplitude sweep experiments reveals the importance of strain and temperature history on the response of such nanocomposites.     

Onset velocity of circulating fluidization and particle residence time distribution: A CFD–DEM study

Until now, the onset velocity of circulating fluidization in liquid–solid fluidized beds has been defined by the turning point of the time required to empty a bed of particles as a function of the superficial liquid velocity, and is reported to be only dependent on the liquid and particle properties. This study presents a new approach to calculate the onset velocity using CFD–DEM simulation of the particle residence time distribution (RTD). The onset velocity is identified from the intersection of the fitted lines of the particle mean residence time as a function of superficial liquid velocity. Our results are in reasonable agreement with experimental data. The simulation indicates that the onset velocity is influenced by the density and size of particles and weakly affected by riser height and diameter. A power-law function is proposed to correlate the mean particle residence time with the superficial liquid velocity. The collisional parameters have a minor effect on the mean residence time of particles and the onset velocity, but influence the particle RTD, showing some humps and trailing. The particle RTD is found to be related to the particle trajectories, which may indicate the complex flow structure and underlying mechanisms of the particle RTD.     

Rankine–Hugoniot conditions for fluids whose energy depends on space and time derivatives of density

By using the Hamilton principle of stationary action, we derive the governing equations and Rankine–Hugoniot conditions for continuous media where the specific energy depends on the space and time density derivatives. The governing system of equations is a time reversible dispersive system of conservation laws for the mass, momentum and energy. We obtain additional relations to the Rankine–Hugoniot conditions coming from the conservation laws and discuss the well-founded of shock wave discontinuities for dispersive systems.     

Pointwise-in-space stabilization and synchronization of a class of reaction–diffusion systems with mixed time delays via aperiodically impulsive control

Nonlinear Dynamics - This paper investigates the problems of pointwise-in-space stabilization and synchronization of semilinear reaction–diffusion systems with Dirichlet boundary conditions...     

Hopf bifurcation analysis of reaction–diffusion neural oscillator system with excitatory-to-inhibitory connection and time delay

The active control approach generally requires power input to suppress vibrations of structures, while the conventional passive manner often causes waste of energy after transferring vibrations of the primary structure to the auxiliary system. In this work, an innovative control strategy based on energy harvesting for efficiently suppressing the cross-flow-induced vibrations such as galloping is proposed. The novel design facilitates the harvester of not only alleviating the oscillation of the primary structure but also seizing the transferred vibrational energy. An analytical model for the coupled nonlinear dynamical system is established by utilizing the Euler–Lagrange principle and implementing the Galerkin discretization. The impacts of the electrical load resistance and tip mass of the energy harvester on the coupled frequency, damping, and the onset speed of instability of the coupled multi-mode system are investigated in details. The results show that there exists an optimal load resistance for each tip mass which maximizes the onset speed of galloping. For control purposes, it is found that there is a well-defined tip mass of the energy harvester at which the coupled system has the highest onset speed of instability, and hence, the bluff body has the lowest vibration amplitude for all considered load resistances. However, to efficiently harvest energy and control the bluff body, both the tip mass of the energy harvester and electrical load resistance can be accurately determined.     

Separating viscoelasticity and poroelasticity of gels with diferent length and time scales简

Viscoelasticity and poroelasticity commonly coexist as time-dependent behaviors in polymer gels. Engineering applications often require knowledge of both behaviors separated; however, few methods exist to decouple viscoelastic and poroelastic properties of gels. We propose a method capable of separating viscoelasticity and poroelasticity of gels in various mechanical tests. The viscoelastic char- acteristic time and the poroelastic diffusivity of a gel define an intrinsic material length scale of the gel. The experimen- tal setup gives a sample length scale, over which the solvent migrates in the gel. By setting the sample length to be much larger or smaller than the material length, the viscoelasticity and poroelasticity of the gel will dominate at different time scales in a test. Therefore, the viscoelastic and poroelastic properties of the gel can be probed separately at different time scales of the test. We further validate the method by finite-element models and stress-relaxation experiments.     

Effect of calcining temperature and time on the characteristics of Sb-doped SnO2 nanoparticles synthesized by the sol–gel method

Spherical Sb-doped SnO₂ (ATO) nanoparticles were synthesized by the sol–gel route, employing SnCl₄·5H₂O and SbCl₃ as precursors in an ethanol solution. The influences of the calcining temperature and calcining time on the crystallite size, crystallinity, lattice parameters, lattice distortion ratio and the resistivity of the ATO nanoparticles were synthetically investigated. The results suggested that the ATO nanoparticles were crystallized in a tetragonal cassiterite structure of SnO₂ with a highly (1 1 0)-plane-preferred orientation. The calcining temperature had a dominating effect on the crystallite size, crystallinity, lattice distortion ratios and resistivity of the ATO. As the calcining temperature increased, the average crystallite size increased, the crystallinity was promoted accompanied by a decrease in the lattice distortion ratio and a corresponding decrease in the resistivity of the ATO. X-ray diffraction (XRD) and Fourier transform infrared spectrophotometer (FTIR) analysis revealed that Sb ions could not entirely supplant the Sn ions in the SnO₂ lattice for a calcining time of less than 0.5 h, even at a calcining temperature of 1000 °C. The ATO nanoparticles calcined at 1000 °C for 3.0 h possessed the lowest resistivity of 10.18 Ω cm.     

On delay-dependent robust exponential stability of stochastic neural networks with mixed time delays and Markovian switching

This paper deals with the global exponential stability analysis problem for a general class of uncertain stochastic neural networks with mixed time delays and Markovian switching. The mixed time delays under consideration comprise both the discrete time-varying delays and the distributed time-delays. The main purpose of this paper is to establish easily verifiable conditions under which the delayed stochastic neural network is robustly exponentially stable in the mean square in the presence of parameters uncertainties, mixed time delays, and Markovian switching. By employing new Lyapunov–Krasovskii functionals and conducting stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the criteria for the robust exponential stability, which can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox. The criteria derived are dependent on both the discrete time delay and distributed time delay, and, are therefore, less conservative. A simple example is provided to demonstrate the effectiveness and applicability of the proposed testing criteria. This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, the National Natural Science Foundation of China under Grant 60774073, the Natural Science Foundation of Jiangsu Province of China under Grant BK2007075, the Natural Science Foundation of Jiangsu Education Committee of China under Grant 06KJD110206, the Scientific Innovation Fund of Yangzhou University of China under Grant 2006CXJ002, and the Alexander von Humboldt Foundation of Germany.     

Space–time focusing of acoustic waves on unknown scatterers

Consider a propagative medium, possibly inhomogeneous, containing some scatterers whose positions are unknown. Using an array of transmit–receive transducers, how can one generate a wave that would focus in space and time near one of the scatterers, that is, a wave whose energy would confine near the scatterer during a short time? The answer proposed in the present paper is based on the so-called DORT method (French acronym for: decomposition of the time reversal operator) which has led to numerous applications owing to the related space-focusing properties in the frequency domain, i.e., for time-harmonic waves. This method essentially consists in a singular value decomposition (SVD) of the scattering operator, that is, the operator which maps the input signals sent to the transducers to the measure of the scattered wave. By introducing a particular SVD related to the symmetry of the scattering operator, we show how to synchronize the time-harmonic signals derived from the DORT method to achieve space–time focusing. We consider the case of the scalar wave equation and we make use of an asymptotic model for small sound-soft scatterers, usually called the Foldy–Lax model. In this context, several mathematical and numerical arguments that support our idea are explored.     

Invariant analysis and exact solutions of nonlinear time fractional Sharma–Tasso–Olver equation by Lie group analysis

This paper is concerned with the time fractional Sharma–Tasso–Olver (FSTO) equation, Lie point symmetries of the FSTO equation with the Riemann–Liouville derivatives are considered. By using the Lie group analysis method, the invariance properties of the FSTO equation are investigated. In the sense of point symmetry, the vector fields of the FSTO equation are presented. And then, the symmetry reductions are provided. By making use of the obtained Lie point symmetries, it is shown that this equation can transform into a nonlinear ordinary differential equation of fractional order with the new independent variable ξ=xt ^?α/3. The derivative is an Erdélyi–Kober derivative depending on a parameter α. At last, by means of the sub-equation method, some exact and explicit solutions to the FSTO equation are given.     

Spatial evolution of Hindmarsh–Rose neural network with time delays

Nonlinear Dynamics - Spatial relations between neurons in the network with time delays play a crucial role in determining dynamics of the system. During the development of the nervous system,...     

Adaptive synchronization of time delay Hindmarsh–Rose neuron system via self-feedback

Synchronization of two mismatched time delay Hindmarsh?CRose neuron systems with self-feedback is investigated. Based on the Lyapunov stability theory and the adaptive control theory, a linear adaptive feedback controller and parameter estimation update law are proposed, and the sufficient conditions for synchronization of the two mismatched systems with chaotic bursting behavior are obtained. The correctness of the proposed methods is rigorously demonstrated. Finally, numerical simulations are employed to verify the effectiveness of the proposed scheme.     

Experimental flow pattern map,slippage and time–frequency representation of oil–water two-phase flow in horizontal small diameter pipes

We detect the flow structures of a horizontal oil–water two-phase flow in a 20 mm inner-diameter pipe using 8-channels radial mini-conductance probes. In particular, we present an experimental flow pattern map that includes 218 flow conditions and compare this map to the flow pattern transitional boundaries predicted by published models. In addition, using the Adaptive Optimal Kernel Time–Frequency Representation, we analyze the conductance fluctuating signals and characterize the flow pattern in terms of the total energy and dominant frequency. Based on the liquid holdup measurements using the quickly closing valve technology combined with three parallel-wire capacitance probes, we investigate the slip effect between the oil and water phases under various flow conditions. The results show that the flow structures greatly affect the slippage, and the slip ratio is sensitive to flow pattern variations.     

A predictor–corrector time integration algorithm for dynamic analysis of nonlinear systems

Nonlinear Dynamics - This paper presents a step-by-step time integration algorithm for efficiently solving second-order nonlinear dynamic problems. The method employs the rewriting of motion as two...