Narrow Results

In this paper, the dynamics modeling and vibration suppression analysis of a nonsmooth system with coupled parallel combined damping NES system is carried out. First, the mechanical and mathematical models of the system are established, and the functional expressions of the nonsmooth terms are given. Second, the damping effect of the parallel combined damping NES under impulsive excitation is analyzed, and the damping effect of the parallel connection under different excitation intensities is analyzed by using the comparison of time response and energy change, as well as the influence of the NES parameters on the vibration suppression situation of the system. Finally, the vibration-damping effect exerted by the parallel combined damping NES under random excitation is analyzed, and the influence of the NES parameters is analyzed on the basis of the probability densities of displacement and energy. The results of the study show that the parallel connection provides better damping performance than a single connection, both under impulsive excitation and under random excitation, and that the optimal value of the system mass ratio is not 0.1 under this connection; it is also found that, under both forms of excitation, the parameter values of the NES are not taken to be larger, the better the damping effect suffered by the main system, but that there exists an appropriate range of values. This study is an important theoretical guide for the engineering application of multi-degree-of-freedom NES.

The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be nonnegative and the integral of them over an entire hypersurface should be equal to one. To satisfy these requirements in a covariant manner, the foliation of space–time must be such that each integral curve of the current crosses each hypersurface of the foliation once and only once. In some cases, it is necessary to use hypersurfaces that are not spacelike everywhere. The generalization to the many-particle case is also possible.

Under the condition of strong electron–LO–phonon coupling in a RbCl quantum pseudodot (QPD) with an applied magnetic field (MF), the eigenenergies and the eigenfunctions of the ground and the first excited states (GFES) are obtained by using a variational method of the Pekar type (VMPT). A single qubit can be realized in this two-level quantum system. The electron’s probability density oscillates in the RbCl QPD with a certain period of $T_0=7.933$ fs when the electron is in the superposition state of the GFES. The results indicate that due to the presence of the asymmetrical structure in the z direction of the RbCl QPD, the electron’s probability density shows double-peak configuration, whereas there is only peak if the confinement is a symmetric structure in the x and y directions of the RbCl QPD. The oscillating period is an increasing function of the cyclotron frequency and the polaron radius, whereas it is a decreasing one of the chemical potential of the two-dimensional electron gas and the zero point of the pseudoharmonic potential (PP).

We study some of the most commonly used mutual information estimators, based on histograms of fixed or adaptive bin size, k-nearest neighbors and kernels and focus on optimal selection of their free parameters. We examine the consistency of the estimators (convergence to a stable value with the increase of time series length) and the degree of deviation among the estimators. The optimization of parameters is assessed by quantifying the deviation of the estimated mutual information from its true or asymptotic value as a function of the free parameter. Moreover, some commonly used criteria for parameter selection are evaluated for each estimator. The comparative study is based on Monte Carlo simulations on time series from several linear and nonlinear systems of different lengths and noise levels. The results show that the k-nearest neighbor is the most stable and less affected by the method-specific parameter. A data adaptive criterion for optimal binning is suggested for linear systems but it is found to be rather conservative for nonlinear systems. It turns out that the binning and kernel estimators give the least deviation in identifying the lag of the first minimum of mutual information from nonlinear systems, and are stable in the presence of noise.

In this paper, some properties of the chaotic propagating pulse wave in a ring of six-coupled bistable oscillators are investigated. When coupling factor α becomes large beyond a certain critical value, the standing pulse wave converts to a propagating pulse wave. Further, as α is increased, the propagating pulse wave behaves chaotically. We find some interesting properties of the chaotic propagating pulse wave such as random change of propagating direction and stepwise change of pulse position with respect to time. In particular, we notice that the shape of probability density of one-direction propagation time and distance is similar to that of Logistic map.

In this paper, we introduce a dynamical model for the time evolution of probability density functions incorporating uncertainty in the parameters. The uncertainty follows stochastic processes, thereby defining a new class of stochastic processes with values in the space of probability densities. The purpose is to quantify uncertainty that can be used for probabilistic forecasting. Starting from a set of traded prices of equity indices, we do some empirical studies. We apply our dynamic probabilistic forecasting to option pricing, where our proposed notion of model uncertainty reduces to uncertainty on future volatility. A distribution of option prices follows, reflecting the uncertainty on the distribution of the underlying prices. We associate measures of model uncertainty of prices in the sense of Cont.

We study the motion of overdamped Brownian particles in a periodic potential with a temporally oscillating amplitude. First we investigate diffusive motion in the untitled potential. Furthermore, if a constant force is applied, the oscillating potential induces a synchronized motion. The deterministic dynamics becomes in resonance with the potential oscillations. This dynamics gives rise to a transport with extremely low dispersion. We distinguish slow and fast oscillatory driving and give analytical expressions for the mean velocity and effective diffusion.

In this paper, a stochastic SEIQ model with nonlinear incidence rate is proposed. The existence and uniqueness of global positive solution of the stochastic model are proved. Then, by constructing some Lyapunov functions, we derive a sufficient condition for the ergodic stationary distribution when $R_0^s$ is greater than one. By solving a four-dimensional Fokker–Planck equation, we get the exact expression of log-normal probability density function of stationary distribution for the stochastic model. Sufficient condition for the extinction of the exposed and infected population is also provided. Finally, numerical simulations are presented to verify the above theoretical results.

We investigate the eigenenergies and the eigenfunctions of the ground and the first excited states of an electron, which is strongly coupled to LO-phonon in an asymmetric quantum dot (QD) by using variational method of Pekar type. The present system may be used as a two-level qubit. When the electron is in the superposition state of the ground and the first excited states, the probability density of the electron oscillates in the QD with a certain period. It is found that the oscillation period is an increasing function of the transverse and the longitudinal effective confinement lengths of the QD, whereas it is a decreasing one of the electron–phonon coupling strength.

Tracking variations of neuronal membrane potential in response to multiple synaptic inputs remains an important open field of investigation since information about neural network behavior and higher brain functions can be inferred from such studies. Much experimental work has been done, with recent advances in multi-electrode recordings and imaging technology giving exciting results. However, experiments have also raised questions of compatibility with available theoretical models. Here we show how methods of modern infinite dimensional analysis allow closed form expressions for important quantities rich in information such as the conditional probability density (cpd). In particular, we use a Feynman integral approach where fluctuations in the dynamical variable are parametrized with Hida white noise variables. The stochastic process described then gives variations in time of the relative membrane potential defined as the difference between the neuron membrane and firing threshold potentials. We obtain the cpd for several forms of current modulation coefficients reflecting the flow of synaptic currents, and which are analogous to drift coefficients in the configuration space Fokker-Planck equation. In particular, we consider cases of voltage and time dependence for current modulation for periodic and non-periodic oscillatory current modulation described by sinusoidal and Bessel functions.

A limitation of most whole cell models to date is the assumption that intracellular Ca²⁺ channels are globally coupled by a continuously stirred bulk cytosolic [Ca²⁺], when in fact open intracellular Ca²⁺ channels experience elevated domain [Ca²⁺]. Such heterogeneous local [Ca²⁺] can be modeled using a 2N+2-compartment model that includes bulk cytosolic and luminal [Ca²⁺] and 2N compartments representing cytosolic and luminal Ca²⁺ domains associated with N stochastically gating intracellular channels. We have introduced an alternative whole cell model formulation that solves a system of advection-reaction equations for the probability density of cytosolic and luminal domain [Ca²⁺] jointly distributed with channel state. This probability density formulation and an associated moment closure approach have been used to create computationally efficient models of local control of Ca²⁺-induced Ca²⁺ release in ventricular cardiac myocytes.

The application of the method for choosing a distribution law in relation to a family of two-sided power distributions for further use in metrological applications is considered. An efficiency of the method is assessed by statistical modeling based on the Monte Carlo method. Comparison is made with the maximum likelihood method when estimating a single parameter of distribution law (power). For the considered family of distributions, the coverage factor and coverage interval are estimated.