Dissipative and generative fractional electric elements in modeling $${\varvec{RC}}$$ RC and $${\varvec{RL}}$$ RL circuits

Nonlinear Dynamics - Two types of constitutive equations consisting of instantaneous and power type hereditary contributions are proposed in order to model generalized capacitor (inductor). The...     

Tailoring the electrochemical charge storage properties of carbonaceous support by redox properties of heteropoly acids: where does the synergy come from?

Journal of Solid State Electrochemistry - The synergistic effects between two Keggin-type heteropoly acids (HPAs) and carbon surface were examined and elucidated. An improved high rate capability...     

A semi-analytical solution for electric double layers near an elliptical cylinder

A theoretical analysis on the electric double layer formed near the surface of an infinite cylinder with an elliptical cross section and a prescribed electric potential in an ionic conductor was performed using the linearized Gouy–Chapman theory. A semi-analytical solution in terms of the Mathieu functions was obtained. The distributions of the electric potential, cations, anions, and electric field were calculated. The effects of various physical and geometric parameters were examined. The fields vary rapidly near the elliptical boundary and are nearly uniform at far field. Electric field concentrations were found at the ends of the semi-major and semi-minor axes of the ellipse. These concentrations are sensitive to the physical and geometric parameters.     

Energy harvesting in a Mathieu–van der Pol–Duffing MEMS device using time delay

This paper investigates quasi-periodic vibration-based energy harvesting in a delayed nonlinear MEMS device consisting of a delayed Mathieu–van der Pol–Duffing type oscillator coupled to a delayed piezoelectric coupling mechanism. We use the multiple scales method to approximate the quasi-periodic response and the related power output near the principal parametric resonance. The effect of time delay on the energy harvesting performance is studied. It is shown that for appropriate combination of time delay parameters, there exists an optimum range of excitation frequency beyond the resonance where quasi-periodic vibration-based energy harvesting is maximum. Numerical simulations are performed to confirm the analytical predictions.     

On Lie symmetries and soliton solutions of $$$$-dimensional Bogoyavlenskii equations

The present article is devoted to find some invariant solutions of the \((2+1)\)-dimensional Bogoyavlenskii equations using similarity transformations method. The system describes \((2+1)\)-dimensional interaction of a Riemann wave propagating along y-axis with a long wave along x-axis. All possible vector fields, commutative relations and symmetry reductions are obtained by using invariance property of Lie group. Meanwhile, the method reduces the number of independent variables by one, which leads to the reduction of Bogoyavlenskii equations into a system of ordinary differential equations. The system so obtained is solved under some parametric restrictions and provides invariant solutions. The derived solutions are much efficient to explain the several physical properties depending upon various existing arbitrary constants and functions. Moreover, some of them are more general than previously established results (Peng and Shen in Pramana 67:449–456, 2006; Malik et al. in Comput Math Appl 64:2850–2859, 2012; Zahran and Khater in Appl Math Model 40:1769–1775, 2016; Zayed and Al-Nowehy in Opt Quant Electron 49(359):1–23, 2017). In order to provide rich physical structures, the solutions are supplemented by numerical simulation, which yield some positons, negatons, kinks, wavefront, multisoliton and asymptotic nature.     

Limit Cycles of Piecewise Smooth Differential Equations on Two Dimensional Torus

In this paper we study the limit cycles of some classes of piecewise smooth vector fields defined in the two dimensional torus. The piecewise smooth vector fields that we consider are composed by linear, Ricatti with constant coefficients and perturbations of these one, which are given in (3). Considering these piecewise smooth vector fields we characterize the global dynamics, studying the upper bound of number of limit cycles, the existence of non-trivial recurrence and a continuum of periodic orbits. We also present a family of piecewise smooth vector fields that posses a finite number of fold points and, for this family we prove that for any 2k number of limit cycles there exists a piecewise smooth vector fields in this family that presents k number of limit cycles and prove that some classes of piecewise smooth vector fields presents a non-trivial recurrence or a continuum of periodic orbits.     

Turbulent Flame Speeds of Premixed Supersonic Flame Kernels

It is unclear whether turbulent flame speed scalings established in low speed regimes are applicable to supersonic flames. To investigate this question, the canonical flame kernel is investigated in a scramjet-like channel having a one degree wall divergence. The growth, shape and internal kernel dynamics are investigated. Results are presented for three Mach numbers, four equivalence ratios, and three turbulence generators. Schlieren photography provides flame images for growth rate statistics and particle image velocimetry (PIV) provides turbulence statistics and investigation of internal kernel dynamics. Supersonic flame kernels are self-propagating and respond to the equivalence ratio in a fashion that is similar to low speed flames. However, supersonic flame kernels have features that are not present in subsonic flame kernels. Baroclinicity, resulting from pressure-density misalignment, creates a reacting vortex ring structure. Further, the mean kernel shape has a Mach number dependence and the vortex ring enhances the turbulent flame speed through entrainment of reactants and augmented flame surface growth. Hence, the previously established (low speed) flame speed scalings are inappropriate for supersonic flame kernels. Drawing motivation from vortex ring literature, the ring propagation velocity is used as the characteristic velocity and a new flame speed scaling is proposed.     

Experimental study on flow control of the turbulent boundary layer with micro-bubbles

The effect of micro-bubbles on the turbulent boundary layer in the channel flow with Reynolds numbers (Re) ranging from \(0.87\times 10 ^{5}\) to \(1.23\times 10^{5}\) is experimentally studied by using particle image velocimetry (PIV) measurements. The micro-bubbles are produced by water electrolysis. The velocity profiles, Reynolds stress and instantaneous structures of the boundary layer, with and without micro-bubbles, are measured and analyzed. The presence of micro-bubbles changes the streamwise mean velocity of the fluid and increases the wall shear stress. The results show that micro-bubbles have two effects, buoyancy and extrusion, which dominate the flow behavior of the mixed fluid in the turbulent boundary layer. The buoyancy effect leads to upward motion that drives the fluid motion in the same direction and, therefore, enhances the turbulence intense of the boundary layer. While for the extrusion effect, the presence of accumulated micro-bubbles pushes the flow structures in the turbulent boundary layer away from the near-wall region. The interaction between these two effects causes the vorticity structures and turbulence activity to be in the region far away from the wall. The buoyancy effect is dominant when the Re is relatively small, while the extrusion effect plays a more important role when Re rises.     

The essence of neuronal activity from the consistency of two different neuron models

Based on the H–H equation, this study has proposed the calculation and analysis of energy expenditure for a single neuron which is activated at sup-threshold and subthreshold, as well as the criterion of the energy expenditure of neurons activated sup-threshold and subthreshold, which was the maximum power of a sodium ion pump. Results of the study showed that not only the electrophysiological activities of neurons were strictly restricted by the energy levels in the brain, but also the activities of neurons also had dual nature, meaning that subthreshold neurons were mainly with energy expenditure, while sup-threshold neurons were with both energy absorption and energy expenditure. These new findings were compared with the novel neuro-biophysical models that we have published last year, uncovering that the two models were essentially equivalent.     

Theoretical analysis for the mechanical behavior caused by an electromagnetic cycle in ITER $$\hbox {Nb}_{3}\hbox {Sn}$$ cable-in-conduit conductors

The central solenoid (CS) is one of the key components of the International Thermonuclear Experimental Reactor (ITER) tokamak and which is often considered as the heart of this fusion reactor. This solenoid will be built by using \(\hbox {Nb}_{3}\hbox {Sn}\) cable-in-conduit conductors (CICC), capable of generating a 13 T magnetic field. In order to assess the performance of the \(\hbox {Nb}_{3}\hbox {Sn}\) CICC in nearly the ITER condition, many short samples have been evaluated at the SULTAN test facility (the background magnetic field is of 10.85 T with the uniform length of 400 mm at 1% homogeneity) in Centre de Recherches en Physique des Plasma (CRPP). It is found that the samples with pseudo-long twist pitch (including baseline specimens) show a significant degradation in the current-sharing temperature (Tcs), while the qualification tests of all short twist pitch (STP) samples, which show no degradation versus electromagnetic cycling, even exhibits an increase of Tcs. This behavior was perfectly reproduced in the coil experiments at the central solenoid model coil (CSMC) facility last year. In this paper, the complex structure of the \(\hbox {Nb}_{3}\hbox {Sn}\) CICC would be simplified into a wire rope consisting of six petals and a cooling spiral. An analytical formula for the Tcs behavior as a function of the axial strain of the cable is presented. Based on this, the effects of twist pitch, axial and transverse stiffness, thermal mismatch, cycling number, magnetic distribution, etc., on the axial strain are discussed systematically. The calculated Tcs behavior with cycle number show consistency with the previous experimental results qualitatively and quantitatively. Lastly, we focus on the relationship between Tcs and axial strain of the cable, and we conclude that the Tcs behavior caused by electromagnetic cycles is determined by the cable axial strain. Once the cable is in a compression situation, this compression strain and its accumulation would lead to the Tcs degradation. The experimental observation of the Tcs enhancement in the CS STP samples should be considered as a contribution of the shorter length of the high field zone in SULTAN and CSMC devices, as well as the tight cable structure.