scholarly journals Резонансный отклик масштабно-инвариантных функций случайного процесса с турбулентным спектром

2021 ◽  
Vol 47 (13) ◽  
pp. 36
Author(s):  
В.П. Коверда ◽  
В.Н. Скоков
Keyword(s):  
Critical State ◽  
Nonlinear Differential Equations ◽  
Random Processes ◽  
Resonant Response ◽  
Scale Invariant ◽  
Invariant Functions ◽  
Turbulent Spectrum ◽  
Large Fluctuations ◽  
Harmonic Action ◽  
The Stability

Scale-invariant random processes with large fluctuations are modeled by a system of two stochastic nonlinear differential equations describing interacting phase transitions. It is shown that under the action of white noise, a critical state arises, characterized by a turbulent spectrum and a scale-invariant distribution function. The critical state corresponds to the maximum entropy, which indicates the stability of the process. An external harmonic action on a random process with a turbulent spectrum gives rise to a resonant response of scale-invariant functions.

Random filters which preserve the stability of random inputs

1988 ◽  
Vol 20 (2) ◽  
pp. 275-294 ◽  
Author(s):  
Stamatis Cambanis
Keyword(s):  
Transfer Function ◽  
Moving Average ◽  
Random Processes ◽  
Time Shift ◽  
Linear Filter ◽  
Random Inputs ◽  
The Stability ◽  
Non Gaussian ◽  
Random Gain

A stationary stable random processes goes through an independently distributed random linear filter. It is shown that when the input is Gaussian or harmonizable stable, then the output is also stable provided the filter&s transfer function has non-random gain. In contrast, when the input is a non-Gaussian stable moving average, then the output is stable provided the filter&s randomness is due only to a random global sign and time shift.

On the Stability of the Linearly Related Modes of Certain Nonlinear Two-Degree-of-Freedom Systems

1961 ◽  
Vol 28 (1) ◽  
pp. 71-77 ◽  
Author(s):  
C. P. Atkinson
Keyword(s):  
Nonlinear Differential Equations ◽  
Mass Ratio ◽  
Positive Mass ◽  
Fourth Degree ◽  
Real Roots ◽  
General Stability ◽  
The Stability ◽  
The Masses ◽  
Spring Constants ◽  
Two Degree Of Freedom

This paper presents a method for analyzing a pair of coupled nonlinear differential equations of the Duffing type in order to determine whether linearly related modal oscillations of the system are possible. The system has two masses, a coupling spring and two anchor springs. For the systems studied, the anchor springs are symmetric but the masses are not. The method requires the solution of a polynomial of fourth degree which reduces to a quadratic because of the symmetric springs. The roots are a function of the spring constants. When a particular set of spring constants is chosen, roots can be found which are then used to set the necessary mass ratio for linear modal oscillations. Limits on the ranges of spring-constant ratios for real roots and positive-mass ratios are given. A general stability analysis is presented with expressions for the stability in terms of the spring constants and masses. Two specific examples are given.

Bifurcation and stability analysis of stagnation points for an asymmetric peristaltic transport

2020 ◽  
Vol 98 (2) ◽  
pp. 172-182 ◽  
Author(s):  
Kaleem Ullah ◽  
Nasir Ali
Keyword(s):  
Flow Field ◽  
Amplitude Ratio ◽  
Nonlinear Differential Equations ◽  
Global Bifurcation ◽  
Flow Region ◽  
Peristaltic Transport ◽  
Trapping Region ◽  
Long Wavelength ◽  
Stagnation Points ◽  
The Stability

This paper investigates the streamline topologies and stability of stagnation points and their bifurcations for an asymmetric peristaltic flow. The asymmetry of channel is due to the propagation of peristaltic waves with different phases and amplitudes on the flexible channel walls. An exact analytic solution of the flow problem subject to the constraints of low Reynolds number and long wavelength is obtained in wave frame of reference moving with wave velocity. A system of nonlinear differential equations is established to locate and classify the stagnation points in the flow domain. Different flow situations, manifested in the flow field, are categorized as: backward flow, trapping, and augmented flow. The transition from one situation to the other corresponds to bifurcation, which is explored graphically through local and global bifurcation diagrams. This analysis discloses the stability status of stagnation points and ranges of involved parameters in which various flow conditions appear in the flow field. It is concluded that the trapping in an asymmetric peristaltic transport can be reduced by increasing the phase difference of the channel walls. It is also found that the augmented flow region shrinks and the trapping region expands by increasing the amplitude ratio of the channel walls.

scholarly journals RgCop-A regularized copula based method for gene selection in single cell rna-seq data

2021 ◽  
Vol 17 (10) ◽  
pp. e1009464
Author(s):  
Snehalika Lall ◽  
Sumanta Ray ◽  
Sanghamitra Bandyopadhyay
Keyword(s):  
Single Cell ◽  
Gene Selection ◽  
Real Life ◽  
Classification Performance ◽  
Rna Seq ◽  
Scale Invariant ◽  
Dependence Measure ◽  
Highly Expressed Genes ◽  
The Stability ◽  
Downstream Analysis

Gene selection in unannotated large single cell RNA sequencing (scRNA-seq) data is important and crucial step in the preliminary step of downstream analysis. The existing approaches are primarily based on high variation (highly variable genes) or significant high expression (highly expressed genes) failed to provide stable and predictive feature set due to technical noise present in the data. Here, we propose RgCop, a novel regularized copula based method for gene selection from large single cell RNA-seq data. RgCop utilizes copula correlation (Ccor), a robust equitable dependence measure that captures multivariate dependency among a set of genes in single cell expression data. We raise an objective function by adding a l1 regularization term with Ccor to penalizes the redundant co-efficient of features/genes, resulting non-redundant effective features/genes set. Results show a significant improvement in the clustering/classification performance of real life scRNA-seq data over the other state-of-the-art. RgCop performs extremely well in capturing dependence among the features of noisy data due to the scale invariant property of copula, thereby improving the stability of the method. Moreover, the differentially expressed (DE) genes identified from the clusters of scRNA-seq data are found to provide an accurate annotation of cells. Finally, the features/genes obtained from RgCop can able to annotate the unknown cells with high accuracy.

scholarly journals Modified Variational Iteration Algorithm-II: Convergence and Applications to Diffusion Models

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Hijaz Ahmad ◽  
Tufail A. Khan ◽  
Predrag S. Stanimirović ◽  
Yu-Ming Chu ◽  
Imtiaz Ahmad
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Nonlinear Models ◽  
Nonlinear Differential Equations ◽  
Variational Iteration Method ◽  
Iteration Algorithm ◽  
Compact Finite Difference Method ◽  
Variational Iteration ◽  
Linear And Nonlinear ◽  
The Stability

Variational iteration method has been extensively employed to deal with linear and nonlinear differential equations of integer and fractional order. The key property of the technique is its ability and flexibility to investigate linear and nonlinear models conveniently and accurately. The current study presents an improved algorithm to the variational iteration algorithm-II (VIA-II) for the numerical treatment of diffusion as well as convection-diffusion equations. This newly introduced modification is termed as the modified variational iteration algorithm-II (MVIA-II). The convergence of the MVIA-II is studied in the case of solving nonlinear equations. The main advantage of the MVIA-II improvement is an auxiliary parameter which makes sure a fast convergence of the standard VIA-II iteration algorithm. In order to verify the stability, accuracy, and computational speed of the method, the obtained solutions are compared numerically and graphically with the exact ones as well as with the results obtained by the previously proposed compact finite difference method and second kind Chebyshev wavelets. The comparison revealed that the modified version yields accurate results, converges rapidly, and offers better robustness in comparison with other methods used in the literature. Moreover, the basic idea depicted in this study is relied upon the possibility of the MVIA-II being utilized to handle nonlinear differential equations that arise in different fields of physical and biological sciences. A strong motivation for such applications is the fact that any discretization, transformation, or any assumptions are not required for this proposed algorithm in finding appropriate numerical solutions.

Explicit Expressions for Buckling Analysis of Thin-Walled Beams Under Combined Loads with Laterally-Fixed Ends and Application to Stability Analysis of Saw Blades

2020 ◽  
pp. 2150032
Author(s):  
Van Binh Phung ◽  
Ngoc Doan Tran ◽  
Viet Duc Nguyen ◽  
V. S. Prokopov ◽  
Hoang Minh Dang
Keyword(s):  
Critical State ◽  
Bending Moment ◽  
Critical Issue ◽  
Eccentric Load ◽  
Concentrated Load ◽  
Combined Loads ◽  
Distributed Load ◽  
Thin Walled ◽  
The Stability ◽  
2D And 3D

This paper studies the critical issue of thin-walled beams with laterally fixed ends. The method for defining the formulae of twist moment for the beams subjected to combined loads was elucidated. Based on this, the governing differential equations of the beam were developed. The procedure for determining the critical state of the beam by the energy method was presented. With this procedure, the critical state of the beam concerned under three types of loadings such as axial force [Formula: see text], bending moment [Formula: see text] and distributed load [Formula: see text] (or concentrated load [Formula: see text]) was examined deliberately. The outcomes were presented in explicit closed-form, which can be illustrated in 2D and 3D graphs. Also, the analytical solution obtained was in agreement with the numerical one obtained by the commercial software NX Nastran. Furthermore, the analytical solutions were applied straightforwardly to explore the stability and design optimization of the tooth-blade for the new frame-type saw machine under an eccentric load. The result can also be promisingly used to study problems of thin-walled beams with laterally fixed ends subjected to other types of loads.

Paper 28. Yawing of a Ship Steered by an Automatic Pilot in Rough Seas

1972 ◽  
Vol 14 (7) ◽  
pp. 207-210
Author(s):  
A. Sh. Afremoff ◽  
E. P. Nikolaev
Keyword(s):  
Transfer Function ◽  
Angular Velocity ◽  
Random Processes ◽  
Mean Square ◽  
Sea State ◽  
Following Seas ◽  
The Stability ◽  
Stationary Random Processes ◽  
Rudder Angle ◽  
Automatic Pilot

This paper is concerned with the non-linear characteristics of an auto-pilot in improving the stability of ships in following seas. The theory is developed for optimizing the auto-pilot, accounting for the non-linearities introduced by limitations on rudder angle and rudder angular velocity. The yaw and rudder angles are assumed to be stationary random processes, and the Wiener–Hopf integral is used to obtain the transfer function relating them in a system of waves, hence yielding the optimum rudder behaviour. For given auto-pilot characteristics, it is shown how root-mean-square yaw angles may be estimated for a ship in a given course in a known sea state.

Robust Active Chatter Control in Milling Processes With Variable Pitch Cutters

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
Tao Huang ◽  
Lijun Zhu ◽  
Shengli Du ◽  
Zhiyong Chen ◽  
Han Ding
Keyword(s):  
Nonlinear Differential Equations ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Linear Matrix ◽  
Variable Pitch ◽  
Stability Lobe ◽  
Milling Operations ◽  
Controller Gain ◽  
Chatter Control ◽  
The Stability

Milling chatters caused by the regenerative effect is one of the major limitations in increasing the machining efficiency and accuracy of milling operations. This paper studies robust active chatter control for milling processes with variable pitch cutters whose dynamics are governed by multidelay nonlinear differential equations. We propose a state feedback controller based on linear matrix inequality (LMI) approach that can enlarge multiple stability domains in the stability lobe diagram (SLD) while the controller gain is minimized. Numerical simulations of active magnetic bearing systems demonstrate the effectiveness of the proposed method.

Nonlinear Oscillation of a Rotor-AMB System With Time Varying Stiffness and Multi-External Excitations

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
M. Kamel ◽  
H. S. Bauomy
Keyword(s):  
Steady State ◽  
Order Approximation ◽  
Nonlinear Differential Equations ◽  
Steady State Solution ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Multiple Time ◽  
Time Varying ◽  
The Stability ◽  
Amb System

The rotor-active magnetic bearing system subjected to a periodically time-varying stiffness having quadratic and cubic nonlinearities is studied and solved. The multiple time scale technique is applied to solve the nonlinear differential equations governing the system up to the second order approximation. All possible resonance cases are deduced at this approximation and some of them are confirmed by applying the Rung–Kutta method. The main attention is focused on the stability of the steady-state solution near the simultaneous principal resonance and the effects of different parameters on the steady-state response. A comparison is made with the available published work.

Sign in / Sign up

Export Citation Format

Share Document