scholarly journals Shear Flow in Cylindrical Open Channel Under Precession

2021 ◽  
Author(s):  
Hajar Alshoufi
Keyword(s):  
Open Channel ◽  
Kdv Equation ◽  
Linear Part ◽  
Time Discretization ◽  
Forced Oscillations ◽  
Wave Form ◽  
Stream Velocity ◽  
Nonlinear Part ◽  
Sommerfeld Equation ◽  
Specific Impact

The study of forced oscillations in open cylindrical channel under precession is extended to include the shear effect, that is induced by inertial waves in such systems. The linear part of the problem led to two equations for stability one for the viscous part similar to Orr-Sommerfeld equation and one for the inviscid part similar to Rayleigh equation, the second was solved and discussed depending on the stream function observation. The linear part also led to relationship that connects between the stream velocity and the disturbance one is derived in a form similar to Burns conditions for open flows under normal conditions. Experimentally measuring the horizontal velocity distribution with depth showed that this distribution is sinusoidal one. Burns condition was solved based on this assumption. The nonlinear part of the problem led to a new version of Koteweg De-Vries (KdV) equation that is solved numerically by applying the leapfrog method for time discretization, Fourier transformation for the space one, and the trapezoidal rule for solving the integrals with depth, the results showed that the shear has no specific impact on the wave form which is similar to the classical results obtained by the theories under normal conditions.

scholarly journals Stability under Galerkin truncation of A-stable Runge–Kutta discretizations in time

2014 ◽  
Vol 144 (3) ◽  
pp. 603-636 ◽  
Author(s):  
Marcel Oliver ◽  
Claudia Wulff
Keyword(s):  
Spatial Resolution ◽  
Truncation Error ◽  
Evolution Equations ◽  
Linear Part ◽  
Time Discretization ◽  
Time Step ◽  
Nonlinear Part ◽  
Scale Of Hilbert Spaces ◽  
Galerkin Truncation ◽  
Runge Kutta

We consider semilinear evolution equations for which the linear part is normal and generates a strongly continuous semigroup, and the nonlinear part is sufficiently smooth on a scale of Hilbert spaces. We approximate their semi-flow by an implicit A-stable Runge–Kutta discretization in time and a spectral Galerkin truncation in space. We show regularity of the Galerkin-truncated semi-flow and its time discretization on open sets of initial values with bounds that are uniform in the spatial resolution and the initial value. We also prove convergence of the space-time discretization without any condition that couples the time step to the spatial resolution. We then estimate the Galerkin truncation error for the semi-flow of the evolution equation, its Runge–Kutta discretization and their respective derivatives, showing how the order of the Galerkin truncation error depends on the smoothness of the initial data. Our results apply, in particular, to the semilinear wave equation and to the nonlinear Schrodinger equation.

scholarly journals An implicit–explicit time discretization scheme for second-order semilinear wave equations with application to dynamic boundary conditions

2021 ◽  
Vol 147 (4) ◽  
pp. 869-899
Author(s):  
Marlis Hochbruck ◽  
Jan Leibold
Keyword(s):  
Wave Equations ◽  
Linear Part ◽  
Time Integration ◽  
Time Discretization ◽  
Second Order ◽  
Time Step ◽  
Element Discretization ◽  
Linear System Of Equations ◽  
A Priori Error Estimate ◽  
Nonlinear Part

AbstractWe construct and analyze a second-order implicit–explicit (IMEX) scheme for the time integration of semilinear second-order wave equations. The scheme treats the stiff linear part of the problem implicitly and the nonlinear part explicitly. This makes the scheme unconditionally stable and at the same time very efficient, since it only requires the solution of one linear system of equations per time step. For the combination of the IMEX scheme with a general, abstract, nonconforming space discretization we prove a full discretization error bound. We then apply the method to a nonconforming finite element discretization of an acoustic wave equation with a kinetic boundary condition. This yields a fully discrete scheme and a corresponding a-priori error estimate.

Forecasting of Summer Monsoon Rainfall over Gangetic West Bengal, India Utilising Intrinsic Mode Functions, Linear and Neural Regression

2020 ◽  
Vol 12 (1) ◽  
pp. 60-69 ◽  
Author(s):  
Pijush Basak
Keyword(s):  
Neural Network ◽  
West Bengal ◽  
Monsoon Rainfall ◽  
Linear Part ◽  
Intrinsic Mode Functions ◽  
Quasi Biennial Oscillation ◽  
Nonlinear Part ◽  
South West ◽  
South West Monsoon ◽  
West Monsoon

The South West Monsoon rainfall data of the meteorological subdivision number 6 of India enclosing Gangetic West Bengal is shown to be decomposable into eight empirical time series, namely Intrinsic Mode Functions. This leads one to identify the first empirical mode as a nonlinear part and the remaining modes as the linear part of the data. The nonlinear part is modeled with the technique Neural Network based Generalized Regression Neural Network model technique whereas the linear part is sensibly modeled through simple regression method. The different Intrinsic modes as verified are well connected with relevant atmospheric features, namely, El Nino, Quasi-biennial Oscillation, Sunspot cycle and others. It is observed that the proposed model explains around 75% of inter annual variability (IAV) of the rainfall series of Gangetic West Bengal. The model is efficient in statistical forecasting of South West Monsoon rainfall in the region as verified from independent part of the real data. The statistical forecasts of SWM rainfall for GWB for the years 2012 and 2013 are108.71 cm and 126.21 cm respectively, where as corresponding to the actual rainfall of 93.19 cm 115.20 cm respectively which are within one standard deviation of mean rainfall.

Hybrid Neural Network Models of Six-Axis Force Sensor

2012 ◽  
Vol 591-593 ◽  
pp. 1450-1456
Author(s):  
Sheng Lai Chen ◽  
Jian Zhong Hong
Keyword(s):  
Neural Network ◽  
Linear Part ◽  
Network Models ◽  
Mapping Function ◽  
Force Sensor ◽  
Measuring System ◽  
Data Simulation ◽  
Neural Network Models ◽  
Nonlinear Part ◽  
Force Signal

A method of analyzing the Six-axis force measuring system by hybrid modeling is introduced in this paper. The mapping function of signal voltage output, which is input vectors of the Neural Network (NN) model, and measuring force signal, which is output vectors of the NN model, is represented as two parts. The determined linear part obtains the main principle and the the information of transfer matrix. The undetermined nonlinear part are estimated by neural network. The problems about nonlinear error and coupling are solved. The accuracy and feasibility of the method are displayed by the result of experiment data simulation.

scholarly journals Surface Structure and Nanomechanical Properties of Shewanella putrefaciens Bacteria at Two pH values (4 and 10) Determined by Atomic Force Microscopy

2005 ◽  
Vol 187 (11) ◽  
pp. 3864-3868 ◽  
Author(s):  
Fabien Gaboriaud ◽  
Sidney Bailet ◽  
Etienne Dague ◽  
Frédéric Jorand
Keyword(s):  
Atomic Force Microscopy ◽  
A Priori ◽  
Linear Part ◽  
Shewanella Putrefaciens ◽  
Nonlinear Part ◽  
Force Microscopy ◽  
Nanomechanical Properties ◽  
Ph Values ◽  
Atomic Force ◽  
Force Curves

ABSTRACT The nanomechanical properties of gram-negative bacteria (Shewanella putrefaciens) were investigated in situ in aqueous solutions at two pH values, specifically, 4 and 10, by atomic force microscopy (AFM). For both pH values, the approach force curves exhibited subsequent nonlinear and linear regimens that were related to the progressive indentation of the AFM tip in the bacterial cell wall, including a priori polymeric fringe (nonlinear part), while the linear part was ascribed to compression of the plasma membrane. These results indicate the dynamic of surface ultrastructure in response to changes in pH, leading to variations in nanomechanical properties, such as the Young's modulus and the bacterial spring constant.

S-synchronization Structural Identifiability and Identification of Nonlinear Dynamic Systems

2020 ◽  
Vol 21 (6) ◽  
pp. 323-336
Author(s):  
N. N. Karabutov
Keyword(s):  
Nonlinear System ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Structural Parameters ◽  
Linear Part ◽  
Structural Identification ◽  
Nonlinear Dynamic Systems ◽  
Necessary Condition ◽  
Structural Identifiability ◽  
Nonlinear Part

An approach to the structural identifiability analysis of nonlinear dynamic systems under uncertainty is proposed. We have shown that S-synchronization is the necessary condition for the structural identifiability of a nonlinear system. Conditions are obtained for the design of a model which identifies the nonlinear part of the system. The method is proposed for the obtaining of a set which contains the information on the nonlinear part. A class of geometric frameworks which reflect the state of the system nonlinear part is introduced. Geometrical frameworks are defined on the synthesized set. The conditions are given for the structural indistinguishability of geometric frameworks on the set of S-synchronizing inputs. Local identifiability conditions are obtained for the nonlinear part. We are shown that a non-synchronizing input gives an insignificant geometric framework. This leads to a structural non-identifiability of the system nonlinear part. The method is proposed for the estimation of the structural identifiability the nonlinear part of the system. Conditions for parametric identifiability of the system linear part are obtained. We show that the structural identifiability is the basis for the structural identification of the system. The hierarchical immersion method is proposed for the estimation of nonlinear system structural parameters. The method is used for the structural identification of a system with Bouc-Wen hysteresis.

A generalized finite-time analytical approach for the synchronization of chaotic and hyperchaotic systems

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Muhammad Haris ◽  
Muhammad Shafiq ◽  
Adyda Ibrahim ◽  
Masnita Misiran
Keyword(s):  
Finite Time ◽  
Chaotic Systems ◽  
Closed Loop ◽  
Time Synchronization ◽  
Linear Part ◽  
Content Type ◽  
Nonlinear Part ◽  
Analytical Stability ◽  
Chaotic Signals ◽  
The Stability

PurposeThe purpose of this paper is to develop some interesting results in the field of chaotic synchronization with a new finite-time controller to reduce the time of convergence.Design/methodology/approachThis article proposes a finite-time controller for the synchronization of hyper(chaotic) systems in a given time. The chaotic systems are perturbed by the model uncertainties and external disturbances. The designed controller achieves finite-time synchronization convergence to the steady-state error without oscillation and elimination of the nonlinear terms from the closed-loop system. The finite-time synchronization convergence reduces the hacking duration and recovers the embedded message in chaotic signals within a given preassigned limited time. The free oscillation convergence keeps the energy consumption low and alleviates failure chances of the actuator. The proposed finite-time controller is a combination of linear and nonlinear parts. The linear part keeps the stability of the closed-loop, the nonlinear part increases the rate of convergence to the origin. A generalized form of analytical stability proof is derived for the synchronization of chaotic and hyper-chaotic systems. The simulation results provide the validation of the accomplish synchronization for the Lu chaotic and hyper-chaotic systems.FindingsThe designed controller not only reduces the time of convergence without oscillation of the trajectories which can run the system for a given time domain.Originality/valueThis work is originally written by the author.

scholarly journals A Simple Attitude Control of Quadrotor Helicopter Based on Ziegler-Nichols Rules for Tuning PD Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
ZeFang He ◽  
Long Zhao
Keyword(s):  
Linear System ◽  
Attitude Control ◽  
Feedback Linearization ◽  
Linear Part ◽  
The Other ◽  
Pd Controller ◽  
Control Effect ◽  
Nonlinear Part ◽  
Nonlinear Controllers ◽  
Attitude Controller

An attitude control strategy based on Ziegler-Nichols rules for tuning PD (proportional-derivative) parameters of quadrotor helicopters is presented to solve the problem that quadrotor tends to be instable. This problem is caused by the narrow definition domain of attitude angles of quadrotor helicopters. The proposed controller is nonlinear and consists of a linear part and a nonlinear part. The linear part is a PD controller with PD parameters tuned by Ziegler-Nichols rules and acts on the quadrotor decoupled linear system after feedback linearization; the nonlinear part is a feedback linearization item which converts a nonlinear system into a linear system. It can be seen from the simulation results that the attitude controller proposed in this paper is highly robust, and its control effect is better than the other two nonlinear controllers. The nonlinear parts of the other two nonlinear controllers are the same as the attitude controller proposed in this paper. The linear part involves a PID (proportional-integral-derivative) controller with the PID controller parameters tuned by Ziegler-Nichols rules and a PD controller with the PD controller parameters tuned by GA (genetic algorithms). Moreover, this attitude controller is simple and easy to implement.

GLOBAL SYNCHRONIZATION OF A CLASS OF CHAOTIC SYSTEMS WITH A SCALAR TRANSMITTED SIGNAL

2004 ◽  
Vol 14 (04) ◽  
pp. 1431-1437 ◽  
Author(s):  
JUNGUO LU ◽  
YUGENG XI ◽  
XIAOFAN WANG
Keyword(s):  
Chaotic Systems ◽  
Linear Part ◽  
Feedback Gain ◽  
Chaotic Oscillator ◽  
Hyperchaotic System ◽  
State Variables ◽  
Error Feedback ◽  
Global Synchronization ◽  
Nonlinear Part ◽  
Output Error

This letter proposes a new global synchronization theorem for a class of chaotic systems. Specially, in the synchronization theorem neither the linear part nor the nonlinear part of the chaotic system requires the special structure indicated in [Wang & Wang, 1998]. We take a linear combination of the original system state variables as the scale-driving signal. We prove that the global synchronization can be attained through the simple linear output error feedback. The linear output error feedback gain is a function of a free parameter. We use Chua's chaotic oscillator and Saito's hyperchaotic system to illustrate the applicability of our synchronization scheme and discuss the issues concerning robustness.

New results for a Lasota–Wazewska model

2019 ◽  
Vol 12 (02) ◽  
pp. 1950019 ◽  
Author(s):  
Farouk Chérif ◽  
Mohsen Miraoui
Keyword(s):  
Periodic Solutions ◽  
Linear Part ◽  
Periodic Oscillation ◽  
Mixed Delays ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Nonlinear Part ◽  
Pseudo Almost Periodic Solutions ◽  
Pseudo Almost Periodic Functions ◽  
Pseudo Almost Periodic

In nature there is no phenomenon that is purely periodic, and this gives the idea to consider the measure pseudo almost periodic oscillation. In this paper, by employing a suitable fixed point theorem, the properties of the measure pseudo almost periodic functions and differential inequality, we investigate the existence and uniqueness of the measure pseudo almost periodic solutions for some models of Lasota–Wazewska equation with measure pseudo almost periodic coefficients and mixed delays. We suppose that the linear part has almost periodic and the nonlinear part is assumed to be measure pseudo almost periodic. Moreover, the global attractivity and the exponential stability of the measure pseudo almost periodic solutions are also considered for the system. As application, an illustrative numerical example is given to demonstrate the effectiveness of the obtained results.

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