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From the Lattice Boltzmann Equation to Fluid Governing Equations
In this chapter, we derive the fluid governing equationsFluid governing equation (the continuityFluid governing equationmass conservation and...
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Prototype One-Dimensional Boundary-Value Problem (BVP): Governing Differential Equation and Variational Formulations with Examples
In this chapter we introduce the prototype one-dimensional BVP and present the corresponding Principle of Minimum Potential Energy that will serve as...
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The Navier–Stokes Equation
The governing equation of viscous flow is the Navier–StokesNavier-Stokes (N–S) equationN–S equation.
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Simplification of Governing Equation for Fluid Flow Between Two Concentric Cylinders
The fluid film journal bearing has two parts, i.e., journal/shaft and the bearing. At stop position, journal is at rest on the bearing’s inner...
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Discovering governing equation from data for multi-stable energy harvester under white noise
It is sometimes difficult to model the stochastic differential equations for strongly nonlinear multi-stable vibration energy harvesters, especially...
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Discovering differential governing equations of hysteresis dynamic systems by data-driven sparse regression method
Hysteresis phenomenon widely exists in various metamaterials and smart actuators. Governing equations can describe and predict the static/dynamic...
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Determining Equations Governing Multibody Dynamic Systems Through Joint Kinematics and Kinematic Chain Effects in Closed-Form Mechanisms
In this study, the governing equations of dynamic systems were derived using a novel method that integrated the kinematic properties of joints and...
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Governing Equations
This chapter presents the equations framing the tip streaming phenomenon. These equations provide the theoretical framework to analyze the...
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GOVERNING EQUATIONS FOR ONE-DIMENSIONAL FLOW
Three conservation laws - mass, momentum, and energy - are used to describe open-channel flows. Two flow variables, such as the flow depth and...
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Sensitivity analysis of parameters governing the iceberg draft through neural network-based models
Precise estimation of the iceberg draft may significantly reduce the collision risk of deep keel icebergs with the offshore facilities comprising the...
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Bifurcation analysis, chaotic behaviors, sensitivity analysis, and soliton solutions of a generalized Schrödinger equation
The main goal of the present study is to conduct a deeper investigation into a generalized Schrödinger equation describing the propagation of optical...
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Wave Equation
The wave equation can support two initial conditions and two boundary conditions because of second derivatives with respect to space and time that...
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Development of governing equations for mixing shocks in two-phase flows
An important phenomenon in the gas–liquid two-phase mixtures is a sudden change in the flow that may lead to transition of the flow regime from...
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Basic Equation of Seepage Flow
According to the classical Darcy law, the relationship between the seepage flow velocity and the pressure gradient of horizontal flow is linear. If...
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Dynamic Surface Sliding Mode Fault-Tolerant Control for the Hydro-turbine Governing System with Input Delay
PurposeAiming at the problems of the strong nonlinearity, multivariable strong coupling and uncertainty parameters in the nonlinear hydro-turbine...
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An efficient and explicit local image inpainting method using the Allen–Cahn equation
Image inpainting is the process of restoring damaged areas in an image using information available from neighboring regions. In this paper, we...
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Validity of Methods for Analytically Solving the Governing Equation of Smoke Filling in Enclosures with Floor Leaks and Growing Fires
The main objective of this paper is to evaluate the validity of the existing methods for analytically solving the governing equation of smoke filling...
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Introduction and Governing Equations
The differential equations governing the transport of mass, momentum and energy (or other scalars) in a flowing fluid are derived from the...
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The Governing Equations of a Simple Fluid
In this Chapter we derive formally the fundamental equatxsions describing the transport of mass, momentum, and energy of a one component, single...
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Scaling laws governing the elastic properties of 3D graphenes
In this study, we comprehensively investigated the scaling law for elastic properties of three-dimensional honeycomb-like graphenes (3D graphenes)...