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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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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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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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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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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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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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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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The Elastic Dielectric Response of Elastomers Filled with Liquid Inclusions: From Fundamentals to Governing Equations
Over the past decade, soft solids containing electro-and magneto-active liquid—as opposed to solid—inclusions have emerged as a new class of smart...
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New ideas on governing equations of fluid dynamics
Classical fluid kinematics or Cauchy-Stokes decomposition mistreated vorticity as fluid rotation and mixed flow stretching with shearing. Classical...
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One-Dimensional Governing Equations and Finite Element Formulation
Chapter 1 suggests that the three-dimensional displacements on the midline of a cross-sectional wall can be expressed as products of the generalized...
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Governing Equations for Different Solution Schemes
This chapter enumerates various types of governing equations in terms of displacements, displacement functions, or stress functions. These equations...
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Basics of Single Phase Convection Heat Transfer and Governing Equations
As explained in Chap. 2, convection is one of the modes of heat transfer.
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Well-posedness of the governing equations for a quasi-linear viscoelastic model with pressure-dependent moduli in which both stress and strain appear linearly
The response of a body described by a quasi-linear viscoelastic constitutive relation, whose material moduli depend on the mechanical pressure (that...
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Fundamental Governing Equations
In this chapter, the conservation equations for mass and momentum are derived to describe the flow of Newtonian fluids. Subsequently, the basic...
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Derivation of Governing Equations by Using Vector Approach and Comparison of Analytical Solutions of Post-buckling Behaviors of Transverse Functionally Graded Shear Deformable Beam Theories
In this study, the post-buckling behavior of a transverse functionally graded beam is investigated. Euler–Bernoulli beam theory (EBT) and shear...
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Governing Equations and Thermodynamics of Compressible Flows
Before delving into the topic of gas dynamics, it is assumed that the reader has a solid foundation in mathematics (especially calculus) as well as a...
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Physics-Informed Neural Network for Solution of Nonlinear Differential Equations
In the recent years, machine learning techniques, notably deep learning, have emerged as vital tools in diverse arenas ranging from image recognition...
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Accurate, Real-Time Replication of Governing Equations of Physical Systems with Transpose CNNs — for Industry 4.0 and Digital Twins
The Universal Approximation Theorem provides the theoretical basis for perceptron-like architectures to represent the functionality of complicated...
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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)...