Stability of abstract thermoelastic systems with inertial terms

A statistical theory for the construction of the equations of viscous displacement in a porous medium is considered. This yields a continuum theory for immiscible displacement which can be applied to either a homogeneous or inhomogeneous porous medium. The relative motions of the fluid are considered in terms of the motion of surfaces of constant saturation which are smoothed surfaces at the macroscopic scale considered. The boundary conditions and initial conditions at the injection boundary are considered as well as the boundary conditions and breakthrough conditions at the recovery boundary and the side boundary conditions. The inertial terms are included in the equations and shown to be of importance in describing these initial conditions and the breakthrough conditions.

Download Full-text

Finite-time stabilization of complex-valued neural networks with proportional delays and inertial terms: A non-separation approach

Neural Networks ◽

10.1016/j.neunet.2022.01.005 ◽

2022 ◽

Author(s):

Changqing Long ◽

Guodong Zhang ◽

Zhigang Zeng ◽

Junhao Hu

Keyword(s):

Neural Networks ◽

Finite Time ◽

Proportional Delays ◽

Finite Time Stabilization ◽

Inertial Terms ◽

Complex Valued

Download Full-text

Parametric Resonances of a Cantilevered Pipe Conveying Fluid: A Nonlinear Analysis

Volume 3A: 15th Biennial Conference on Mechanical Vibration and Noise — Vibration of Nonlinear, Random, and Time-Varying Systems ◽

10.1115/detc1995-0272 ◽

1995 ◽

Author(s):

C. Semler ◽

M. P. Païdoussis

Keyword(s):

Flow Velocity ◽

Standard Form ◽

Harmonic Component ◽

Harmonic Balance Method ◽

Pipe Conveying Fluid ◽

Mean Flow ◽

Incremental Harmonic Balance Method ◽

Inertial Terms ◽

The Stability ◽

Conveying Fluid

Abstract This paper deals with the nonlinear dynamics and the stability of cantilevered pipes conveying fluid, where the fluid has a harmonic component of flow velocity, assumed to be small, superposed on a constant mean value. The mean flow velocity is near the critical value for which the pipe becomes unstable by flutter through a Hopf bifurcation. The partial differential equation is transformed into a set of ordinary differential equations (ODEs) using the Galerkin method. The equations of motion contain nonlinear inertial terms, and hence cannot be put into standard form for numerical integration. Various approaches are adopted to tackle the problem: (a) a perturbation method via which the nonlinear inertial terms are removed by finding an equivalent term using the linear equation; the system is then put into first-order form and integrated using a Runge-Kutta scheme; (b) a finite difference method based on Houbolt’s scheme, which leads to a set of nonlinear algebraic equations that is solved with a Newton-Raphson approach; (c) the stability boundaries are obtained using an incremental harmonic balance method as proposed by S.L. Lau. Using the three methods, the dynamics of the pipe conveying fluid is investigated in detail. For example, the effects of (i) the forcing frequency, (ii) the perturbation amplitude, and (iii) the flow velocity are considered. Particular attention is paid to the effects of the nonlinear terms. These results are compared with experiments undertaken in our laboratory, utilizing elastomer pipes conveying water. The pulsating component of the flow is generated by a plunger pump, and the motions are monitored by a noncontacting optical follower system. It is shown, both numerically and experimentally, that periodic and quasiperiodic oscillations can exist, depending on the parameters.

Download Full-text

Mass Nature of Heat and Its Applications I: Motion of Thermomass Fluid and General Heat Conduction Law

2010 14th International Heat Transfer Conference, Volume 3 ◽

10.1115/ihtc14-22505 ◽

2010 ◽

Author(s):

Zeng-Yuan Guo ◽

Bing-Yang Cao

Keyword(s):

Heat Flux ◽

Heat Conduction ◽

Gas Flow ◽

Short Pulse ◽

Rest Mass ◽

Inertial Force ◽

High Heat Flux ◽

Phase Lag ◽

Energy Relation ◽

Inertial Terms

The concept of thermomass is defined as the equivalent mass of thermal energy according to the Einstein’s mass-energy relation. Hence, the phonon gas in dielectrics can be regarded a weighty, compressible fluid. Heat conduction in the medium, where the rest mass lattices or molecules acts the porous framework, resembles the gas flow through the porous medium. Newton mechanics has been applied to establish the equation of state and the equation of motion for the phonon gas as in fluid mechanics, since the drift velocity of a phonon gas is normally much less than the speed of light. The momentum equation of the thermomass gas, including the driving, inertial and resistant forces, is a damped wave equation, which is in fact the general conduction law. This is because it reduces to the CV (Cattaneo-Vernotte) model or the single phase-lag model as the heat flux related inertial terms are neglected, and reduces to Fourier’s heat conduction law as all inertial terms are neglected. Therefore, the underlying physics of Fourier’s heat conduction law is the balance between the driving force and the resistant force of the heat motion, and Fourier’s law will break down when the inertial force is comparable to the resistant force, for instance, in the case of ultra-short pulse laser heating or heat conduction in carbon nanotubes at ultra-high heat flux.

Download Full-text

Inertial Mann-Type Algorithm for a Nonexpansive Mapping to Solve Monotone Inclusion and Image Restoration Problems

Symmetry ◽

10.3390/sym12050750 ◽

2020 ◽

Vol 12 (5) ◽

pp. 750

Author(s):

Natthaphon Artsawang ◽

Kasamsuk Ungchittrakool

Keyword(s):

Fixed Point ◽

Nonexpansive Mapping ◽

Image Restoration ◽

Zero Point ◽

Monotone Operators ◽

Fixed Point Problem ◽

Point Problem ◽

Type Method ◽

Type Algorithm ◽

Inertial Terms

In this article, we establish a new Mann-type method combining both inertial terms and errors to find a fixed point of a nonexpansive mapping in a Hilbert space. We show strong convergence of the iterate under some appropriate assumptions in order to find a solution to an investigative fixed point problem. For the virtue of the main theorem, it can be applied to an approximately zero point of the sum of three monotone operators. We compare the convergent performance of our proposed method, the Mann-type algorithm without both inertial terms and errors, and the Halpern-type algorithm in convex minimization problem with the constraint of a non-zero asymmetric linear transformation. Finally, we illustrate the functionality of the algorithm through numerical experiments addressing image restoration problems.

Download Full-text

Double Hopf bifurcation in a four-neuron delayed system with inertial terms

Nonlinear Dynamics ◽

10.1007/s11071-015-2291-y ◽

2015 ◽

Vol 82 (4) ◽

pp. 1969-1978 ◽

Cited By ~ 2

Author(s):

JuHong Ge ◽

Jian Xu

Keyword(s):

Hopf Bifurcation ◽

Double Hopf Bifurcation ◽

Delayed System ◽

Inertial Terms

Download Full-text

Comparative Analyses between The Zero-Inertia and Fully Dynamic Models of the Shallow Waters Equations for Unsteady Overland Flow Propagation

10.20944/preprints201711.0130.v1 ◽

2017 ◽

Author(s):

Costanza Aricò ◽

Carmelo Nasello

Keyword(s):

Overland Flow ◽

Dynamic Models ◽

Numerical Models ◽

Nonlinear Partial Differential Equations ◽

Computational Effort ◽

Point Of View ◽

Shallow Waters ◽

Hyperbolic Model ◽

Flow Routing ◽

Inertial Terms

The shallow water equations are widely applied for the simulation of flow routing in rivers and floodplains, as well as for flood inundation mapping. From a mathematical point of view, they are a hyperbolic system of nonlinear partial differential equations, whose numerical integration is sometimes computationally burdensome. For this reason, the interest of many researchers has been focused on the study of simplified forms of the original set of equations, which requires less computational effort. One of the most commonly applied simplifications consists in neglecting the inertial terms, which changes the hyperbolic model to a parabolic one. The effects of such a choice on the outputs of the simulations of flooding events are controversial and an important topic of debate. In the present paper, two numerical models, recently proposed for the solution of the complete and zero-inertia forms of the shallow waters equations, are applied to several unsteady flow routing scenarios. We simulate synthetic and laboratory studies, starting from very simple geometries and moving towards complex topographies. Analyzing the role of the terms in the momentum equations, we try to understand the effect, on the computed results, of neglecting the inertial terms in the zero-inertia formulation. We analyze the computational costs.

Download Full-text