The quantum dynamics of a mesoscopic driven RLC circuit consisting of a linear inductor, a linear resistor and a nonlinear capacitor

The nonlinear capacitor that obeys of a cubic polynomial voltage–charge relation (usually a power series in charge) is introduced. The quantum theory for a mesoscopic electric circuit with charge discreteness is investigated, and the Hamiltonian of a quantum mesoscopic electrical circuit comprised by a linear inductor, a linear resistor and a nonlinear capacitor under the influence of a time-dependent external source is expressed. Using the numerical solution approaches, a good analytic approximate solution for the quantum cubic Duffing equation is found. Based on this, the persistent current is obtained antically. The energy spectrum of such nonlinear electrical circuit has been found. The dependency of the persistent current and spectral property equations to linear and nonlinear parameters is discussed by the numerical simulations method, and the quantum dynamical behavior of these parameters is studied.

About the features of the least squares method with linearization when determining nonlinear parameters of functional dependencies

The features of approximation of empirical data by functional dependence with nonlinear parameters using the two-stage least squares method are considered in this paper. A method of simplified parameter estimation by constructing a new expression that depends on the parameters in a linear way is described. To obtain the final solution, the least squares estimation of the main dependence linearized in terms of parameters is performed. The influence of various forms of noise imposed on the theoretical dependence on the approximations is modeled.

Morphometry of cellular behavior of coelomocytes from starfish Asterias amurensis

A comprehensive statistical analysis using a wide range of linear and non-linear morphological parameters enabled identification of the main stages in the in vitro dynamics of cell behavior of immune cells of the marine invertebrate Asterias amurensis (Echinodermata, Asteroidea). Three stages may be distinguished in the cell behavior, which are characterized by the differences in complexity of the cell boundary microsculpture as well as by the size and asymmetry of the cell and convex hull of the cell. The first stage (5 min after placing cells onto a substrate) is characterized by more complex cell morphology and an increase in the process number and spreading area. The second stage (15 min) is characterized by simplification of cell morphology, retraction of some processes, and rounding of cells upon continued cell spreading. At the third stage (60 min), new large processes with rounded contours emerge due to partial retraction of the flattened cell surface. Each stage is characterized by statistically significant differences in several linear and nonlinear parameters of the external morphology for all cell types.

Optical solitons for the Kaup–Newell equation by collective variables method

In this work, we present a collective variable (CV) approach to establish dispersive solitary wave solutions for the Kaup–Newell Equation (KNE). The full CV theory has been utilized to enunciate the soliton molecules through its ground-laying parameters including the power of each pulse, phase and center-of-mass. Additionally, the dynamics of an ultra short pulse has been analyzed by using CV. This work may be utilized for various dynamics of solitons as well as the influence the amplitude, temporal position, frequency, phase and chirp on the solitons’ nonlinear parameters. Moreover, the numerical simulations have been designed by means of appropriate parameter values to explain more on the obtained results.

Application of nonlinear analysis for the assessment of gait in patients with Parkinson’s disease

BACKGROUND: Gait can be affected by diseases such as Parkinson’s disease (PD), which lead to alterations like shuffle gait or loss of balance. PD diagnosis is based on subjective measures to generate a score using the Unified Parkinson’s Disease Rating Scale (UPDRS). To improve clinical assessment accuracy, gait analysis can utilise linear and nonlinear methods. A nonlinear method called the Lyapunov exponent (LE) is being used to identify chaos in dynamic systems. This article presents an application of LE for diagnosing PD. OBJECTIVE: The objectives were to use the largest Lyapunov exponents (LaLyEx), sample entropy (SampEn) and root mean square (RMS) to assess the gait of subjects diagnosed with PD; to verify the applicability of these parameters to distinguish between people with PD and healthy controls (CO); and to differentiate subjects within the PD group according to the UPDRS assessment. METHODS: The subjects were divided into the CO group (n= 12) and the PD group (n= 14). The PD group was also divided according to the UPDRS score: UPDRS 0 (n= 7) and UPDRS 1 (n= 7). Kinematic data of lower limbs were measured using inertial measurement units (IMU) and nonlinear parameters (LaLyEx, SampEn and RMS) were calculated. RESULTS: There were significant differences between the CO and PD groups for RMS, SampEn and the LaLyEx. After dividing the PD group according to the UPDRS score, there were significant differences in LaLyEx and RMS. CONCLUSIONS: The selected parameters can be used to distinguish people with PD from CO subjects, and separate people with PD according to the UPDRS score.

An Efficient Algorithm for Ill-Conditioned Separable Nonlinear Least Squares

For separable nonlinear least squares models, a variable projection algorithm based on matrix factorization is studied, and the ill-conditioning of the model parameters is considered in the specific solution process of the model. When the linear parameters are estimated, the Tikhonov regularization method is used to solve the ill-conditioned problems. When the nonlinear parameters are estimated, the QR decomposition, Gram–Schmidt orthogonalization decomposition, and SVD are applied in the Jacobian matrix. These methods are then compared with the method in which the variables are not separated. Numerical experiments are performed using RBF neural network data, and the experimental results are analyzed in terms of both qualitative and quantitative indicators. The results show that the proposed algorithms are effective and robust.

Polarizabilities and Rydberg States in the Presence of a Debye Potential

Polarizabilities and hyperpolarizabilities, α1, β1, γ1, α2, β2, γ2, α3, β3, γ3, δ and ε of hydrogenic systems have been calculated in the presence of a Debye–Huckel potential, using pseudostates for the S, P, D and F states. All of these converge very quickly as the number of terms in the pseudostates is increased and are essentially independent of the nonlinear parameters. All the results are in good agreement with the results obtained for hydrogenic systems obtained by Drachman. The effective potential seen by the outer electron is −α1/x4 + (6β1 − α2)/x6 + higher-order terms, where x is the distance from the outer electron to the nucleus. The exchange and electron–electron correlations are unimportant because the outer electron is far away from the nucleus. This implies that the conventional variational calculations are not necessary. The results agree well with the results of Drachman for the screening parameter equal to zero in the Debye–Huckel potential. We can calculate the energies of Rydberg states by using the polarizabilities and hyperpolarizabilities in the presence of Debye potential seen by the outer electron when the atoms are embedded in a plasma. Most calculations are carried out in the absence of the Debye–Huckel potential. However, it is not possible to carry out experiments when there is a complete absence of plasma at a particular electron temperature and density. The present calculations of polarizabilities and hyperpolarizabilities will provide accurate results for Rydberg states when the measurements for such states are carried out.

Mechanical systems of precise robots with vibrodrives, the vibrating mass of the exciting force of which performs impacts into deformable support and direction of the exciting force coincides with the line of relative motion of the system

Manipulator consisting from one sided self stopping mechanism and two masses which interact through an elastic – dissipative member is investigated. The drive of the manipulator is the generator of mechanical vibrations. With such elements the system is nonlinear. A separate case is investigated when static positions of equilibrium of both masses are located in one point. Because of this spectrums of eigenfrequencies are linear and infinite. All those facts mean that the operation of the manipulator is optimal. Fast development of robots gives rise to the investigations of increasing intensity creating various types of robots especially in the area of high precision. Mechanical systems of robot must perform laws and trajectories of motion, positioning in space with highest possible precision as well as ensure dynamicity of highest possible stability. Those aims are achieved in the presented paper by creating a structure of the best design, based on vibroimpacts as well as by choosing corresponding nonlinear parameters of the system. The investigation is performed by analytical – numerical method. The obtained results enable to create mechanical systems for precise robots.