Two-cell stochastic model of the Schlögl reaction with small diffusional coupling

We study a stochastic theory of the two-cell model of the Schlögl reaction beyond the bistability threshold. We restrict ourselves to the case of a small diffusional coupling, where inhomogeneous steady states occur, and where a nucleationlike behavior is expected. Our analysis agrees with the deterministic analysis in the thermodynamic limit, and permits to calculate the long time evolution of the probability distribution function. We compare our results with a recent Monte Carlo simulation of this problem.     

Melnikov theoretic methods for characterizing the dynamics of the bistable piezoelectric inertial generator in complex spectral environments

Piezoelectric energy harvesters exploiting strong mechanical nonlinearities exhibit intrinsic suitability for one of several modern challenges in vibratory energy harvesting: consistent kinetic performance in the presence of broadband environmental excitation. In particular, the bistable piezoelectric generator has been prolifically examined. However, most of the relevant literature relies on numerical simulation of specific experimental realizations to demonstrate superior performance. Due to the complexities and lack of analytical solutions for such designs, streamlined methods for parameter optimization,potential well shaping, optimal electromechanical coupling considerations, and other design methodologies are thus inhibited. To facilitate future innovation and research, this paper employs techniques from chaotic dynamical systems theory to provide a simplified analytical framework such that deeper insight into the performance of the bistable piezoelectric inertial generator may be obtained. Specifically, Melnikov theory is investigated to provide metrics for which homoclinic bifurcation may occur in the presence of harmonic, multi-frequency, and broadband excitation. The analysis maintains full consideration of the electromechanical coupling and electrical impedance effects and predicts that for range of dimensionless electrical impedance values, the threshold for chaotic motion and other high-energy solutions is significantly influenced.     

Monte Carlo calculation of the mean work required to drive a bistable system

The mean work required to drive a bistable system from one equilibrium state to another is calculated by using a Langevin simulation combined with Monte Carlo sampling. The resulting work depends not only on the proposal form but also on the temperature, because the particle subjected to thermal fluctuation passes over the barrier during a finite time. This shows that the mean work of a periodic signal done on a particle in a double-well potential is a non-monotonic function of the temperature when the energetic barrier is encountered. By applying this to information erasure in a Brownian computer, it is discovered that the work dissipated into the environment for 1-bit information erasure from two states to a single state can be minimized at a finite temperature.     

Shear-flow suppression of hotspot growth

We consider the role of fluid shear in maintaining anomalous “hotspot” solutions reported for a chaotically stirred bistable chemical reaction model [S.M. Cox, Persistent localized states for a chaotically mixed bistable reaction, Phys. Rev. E 74 (2006) 056206]. In the well-mixed regime, the chemical concentration is governed by a single autonomous ordinary differential equation with two stable equilibria. Whether the reaction goes to extinction or to an excited state depends on whether the initial concentration lies below or above some unstable threshold. By contrast, when the concentration varies spatially, and the chemical is stirred, the interplay between advection, diffusion and reaction is much more complicated, and the fate of the reaction depends sensitively on the initial conditions. It has previously been shown that, if the stirring is temporally periodic, a localised hotspot may form, and so the system never becomes fully extinct, nor fully excited. In this work, we first demonstrate that hotspots are in some sense generic, in that they are easily found by trial and error, by choosing reaction parameter values between those giving rise to global extinct and excited states. We also show that hotspots may be associated with hyperbolic, elliptic or even parabolic orbits associated with the underlying stirring. We observe that fluid shear is an important mechanism in localising a hotspot, and derive a reduced ordinary differential equation model which can predict the fate of a chemical stripe in a shear flow accurately.     

Nonlinear phenomena of left-handed nonlinear split-ring resonators

We theoretically analyze a two-dimensional periodic structure consisting of period nonlinear split-ring resonators (SRRs) with varactor diode. The diode is loaded into the slit of the SRRs. Then, we demonstrate nonlinear phenomena of left-handed nonlinear SRRs. This paper introduces nonlinear SRRs based on left-handed (LH) media and simulates self-tuning mechanisms, bistable effects in the microwave frequency range. In addition, with the increase of input power, the nonlinear response of the SRRs becomes multi-valued, paving a way for creating bistable tunable metamaterials.     

位置反馈型双稳态电磁阀的研制

针对双稳态电磁阀启/闭不可靠和运行不稳定两个关键技术问题,提出了在双稳态电磁阀的基本结构上,安装一个位置传感器,同时采用非固定脉宽驱动;方案还设计了具有自动纠错功能的驱动电路。实验结果证明:该方法实现了最佳效率驱动,彻底解决了双稳态电磁阀启/闭不可靠和运行不稳定等问题。     

Existence and stability of traveling waves in periodic media governed by a bistable nonlinearity

We prove the existence of multidimensional traveling wave solutions of the bistable reaction-diffusion equation with periodic coefficients under the condition that these coefficients are close to constants. In the case of one space dimension, we prove their asymptotic stability.     

Unfolding pathway and its identifiability in heterogeneous chains of bistable units

We investigate the behavior of a chain of bistable units with an heterogeneous distribution of energy jumps between the folded and unfolded states. For homogeneous chains, loaded by soft or hard devices, all units at each switching occurrence have the same probability to unfold and it is therefore impossible to identify an unfolding pathway. Conversely, the heterogeneity represents a quenched disorder from the statistical mechanics point of view, and is able to break the symmetry eventually generating an unfolding pathway. We prove that the most probable pathway is realized by arranging the energy jumps in ascending order. Hence, the mechanics of this system is able to implement a statistical sorting procedure. We quantitatively evaluate the identifiability of the obtained unfolding pathway in terms of the variance of the heterogeneous energy jumps and the temperature. This concept is applied to both deterministic and random distributions of energy jumps within the chain.