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186 relations: ACM SIGGRAPH, Adhémar Jean Claude Barré de Saint-Venant, Advection, Airfoil, Basis function, BBGKY hierarchy, Bending of plates, Biharmonic equation, Biot–Savart law, Body force, Boltzmann equation, Boundary value problem, Capillary action, Capillary surface, Cartesian coordinate system, Cauchy momentum equation, Central processing unit, Centripetal force, Chaos theory, Chapman–Enskog theory, Churchill–Bernstein equation, Classical mechanics, Claude-Louis Navier, Clay Mathematics Institute, Coandă effect, Colatitude, Computational fluid dynamics, Conceptual model, Conservation law, Conservation of mass, Conservative force, Conservative vector field, Constitutive equation, Continuity equation, Continuum (measurement), Continuum mechanics, Convection, Convection–diffusion equation, Coriolis force, Correlation function, Couette flow, Coulomb's law, Course of Theoretical Physics, Cubic function, Curl (mathematics), Cylindrical coordinate system, Derivation of the Navier–Stokes equations, Differential-algebraic system of equations, Diffusion, Diffusion equation, ..., Direct numerical simulation, Dissipative system, Divergence, Elliptic integral, Engineering, Equation of state, Eric W. Weisstein, Euclidean space, Euler equations (fluid dynamics), Existence theorem, Feynman diagram, Fictitious force, Flow conditioning, Flow velocity, Fluid dynamics, Fluid parcel, Froude number, Function (mathematics), Galilean invariance, Gifted (film), Gradient, Graph (discrete mathematics), Graph theory, Graphics processing unit, Gravity, Hagen–Poiseuille equation, Hagen–Poiseuille flow from the Navier–Stokes equations, Helmholtz decomposition, Homogeneous polynomial, Hooke's law, Hopf fibration, Hydraulic head, Hydraulics, Identity matrix, Implicit function, Incompressible flow, Inertia, Inertial frame of reference, Infinitesimal strain theory, Integro-differential equation, Inviscid flow, Isochoric process, Isotropy, Jacobian matrix and determinant, Jeffery–Hamel flow, Jos Stam, K–omega turbulence model, Knudsen number, Lamé parameters, Lamb vector, Laminar flow, Landau–Squire jet, Large eddy simulation, Linear elasticity, Linearity, Mach number, Magnetohydrodynamics, Material derivative, MathWorld, Maxwell's equations, McGraw-Hill Education, Millennium Prize Problems, Molecular dynamics, Mstislav Keldysh, Multiphase flow, Navier–Stokes equations, Navier–Stokes existence and smoothness, Newton's laws of motion, Newtonian fluid, No-slip condition, Non-dimensionalization and scaling of the Navier–Stokes equations, Nonlinear system, Nozzle, Ocean current, Ordinary differential equation, Orthogonal coordinates, Outer product, Oxford University Press, Partial differential equation, Particle, Perturbation theory, Physics, Polar coordinate system, Presses polytechniques et universitaires romandes, Pressure, Pressure-correction method, Probability distribution, Pseudorandomness, Pythagorean quadruple, Quantum field theory, Rayleigh–Bénard convection, Reynolds number, Reynolds transport theorem, Reynolds-averaged Navier–Stokes equations, Rotational symmetry, Scalar (mathematics), Scale analysis (mathematics), Science, Shear stress, Shear velocity, Shock wave, Sir George Stokes, 1st Baronet, Smoothness, Solenoidal vector field, Spalart–Allmaras turbulence model, Spherical coordinate system, Square root of 2, Stagnation point flow, Stochastic process, Stokes boundary layer, Stokes flow, Stokes stream function, Stokes' theorem, Stream function, Streamlines, streaklines, and pathlines, Stress (mechanics), Surface tension, Taylor–Green vortex, Temperature, Tensor calculus, Thermal conduction, Thermal hydraulics, Time, Trace (linear algebra), Transport coefficient, Turbulence, Turbulence kinetic energy, United States dollar, Vector Laplacian, Video game, Viscosity, Viscous liquid, Vlasov equation, Volume viscosity, Von Kármán swirling flow, Work (thermodynamics). Expand index (136 more) »
ACM SIGGRAPH
ACM SIGGRAPH is the international Association for Computing Machinery's Special Interest Group on Computer Graphics and Interactive Techniques based in New York.
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Adhémar Jean Claude Barré de Saint-Venant
Adhémar Jean Claude Barré de Saint-Venant (23 August 1797, Villiers-en-Bière, Seine-et-Marne – 6 January 1886, Saint-Ouen, Loir-et-Cher) was a mechanician and mathematician who contributed to early stress analysis and also developed the unsteady open channel flow shallow water equations, also known as the Saint-Venant equations that are a fundamental set of equations used in modern hydraulic engineering.
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Advection
In the field of physics, engineering, and earth sciences, advection is the transport of a substance by bulk motion.
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Airfoil
An airfoil (American English) or aerofoil (British English) is the shape of a wing, blade (of a propeller, rotor, or turbine), or sail (as seen in cross-section).
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Basis function
In mathematics, a basis function is an element of a particular basis for a function space.
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BBGKY hierarchy
In statistical physics, the BBGKY hierarchy (Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy, sometimes called Bogoliubov hierarchy) is a set of equations describing the dynamics of a system of a large number of interacting particles.
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Bending of plates
Bending of plates, or plate bending, refers to the deflection of a plate perpendicular to the plane of the plate under the action of external forces and moments.
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Biharmonic equation
In mathematics, the biharmonic equation is a fourth-order partial differential equation which arises in areas of continuum mechanics, including linear elasticity theory and the solution of Stokes flows.
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Biot–Savart law
In physics, specifically electromagnetism, the Biot–Savart law is an equation describing the magnetic field generated by a stationary electric current.
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Body force
A body force is a force that acts throughout the volume of a body.
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Boltzmann equation
The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium, devised by Ludwig Boltzmann in 1872.
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Boundary value problem
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions.
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Capillary action
Capillary action (sometimes capillarity, capillary motion, capillary effect, or wicking) is the ability of a liquid to flow in narrow spaces without the assistance of, or even in opposition to, external forces like gravity.
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Capillary surface
In fluid mechanics and mathematics, a capillary surface is a surface that represents the interface between two different fluids.
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Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
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Cauchy momentum equation
The Cauchy momentum equation is a vector partial differential equation put forth by Cauchy that describes the non-relativistic momentum transport in any continuum.
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Central processing unit
A central processing unit (CPU) is the electronic circuitry within a computer that carries out the instructions of a computer program by performing the basic arithmetic, logical, control and input/output (I/O) operations specified by the instructions.
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Centripetal force
A centripetal force (from Latin centrum, "center" and petere, "to seek") is a force that makes a body follow a curved path.
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Chaos theory
Chaos theory is a branch of mathematics focusing on the behavior of dynamical systems that are highly sensitive to initial conditions.
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Chapman–Enskog theory
Chapman–Enskog theory presents equations for dynamics of a multicomponent gas mixture in states close to local equilibrium.
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Churchill–Bernstein equation
In convective heat transfer, the Churchill–Bernstein equation is used to estimate the surface averaged Nusselt number for a cylinder in cross flow at various velocities.
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Classical mechanics
Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies.
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Claude-Louis Navier
Claude-Louis Navier (born Claude Louis Marie Henri Navier;; 10 February 1785 – 21 August 1836), was a French engineer and physicist who specialized in mechanics.
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Clay Mathematics Institute
The Clay Mathematics Institute (CMI) is a private, non-profit foundation, based in Peterborough, New Hampshire, United States.
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Coandă effect
The Coandă effect is the tendency of a fluid jet to stay attached to a convex surface.
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Colatitude
In spherical coordinates, colatitude is the complementary angle of the latitude, i.e. the difference between 90° and the latitude, where southern latitudes are denoted with a minus sign.
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Computational fluid dynamics
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to solve and analyze problems that involve fluid flows.
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Conceptual model
A conceptual model is a representation of a system, made of the composition of concepts which are used to help people know, understand, or simulate a subject the model represents.
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Conservation law
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time.
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Conservation of mass
The law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as system's mass cannot change, so quantity cannot be added nor removed.
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Conservative force
A conservative force is a force with the property that the total work done in moving a particle between two points is independent of the taken path.
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Conservative vector field
In vector calculus, a conservative vector field is a vector field that is the gradient of some function, known in this context as a scalar potential.
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Constitutive equation
In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and approximates the response of that material to external stimuli, usually as applied fields or forces.
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Continuity equation
A continuity equation in physics is an equation that describes the transport of some quantity.
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Continuum (measurement)
Continuum theories or models explain variation as involving gradual quantitative transitions without abrupt changes or discontinuities.
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Continuum mechanics
Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles.
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Convection
Convection is the heat transfer due to bulk movement of molecules within fluids such as gases and liquids, including molten rock (rheid).
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Convection–diffusion equation
The convection–diffusion equation is a combination of the diffusion and convection (advection) equations, and describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection.
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Coriolis force
In physics, the Coriolis force is an inertial force that acts on objects that are in motion relative to a rotating reference frame.
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Correlation function
A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables.
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Couette flow
In fluid dynamics, Couette flow is the flow of a viscous fluid in the space between two surfaces, one of which is moving tangentially relative to the other.
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Coulomb's law
Coulomb's law, or Coulomb's inverse-square law, is a law of physics for quantifying the amount of force with which stationary electrically charged particles repel or attract each other.
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Course of Theoretical Physics
The Course of Theoretical Physics is a ten-volume series of books covering theoretical physics that was initiated by Lev Landau and written in collaboration with his student Evgeny Lifshitz starting in the late 1930s.
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Cubic function
In algebra, a cubic function is a function of the form in which is nonzero.
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Curl (mathematics)
In vector calculus, the curl is a vector operator that describes the infinitesimal rotation of a vector field in three-dimensional Euclidean space.
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Cylindrical coordinate system
A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis, the direction from the axis relative to a chosen reference direction, and the distance from a chosen reference plane perpendicular to the axis.
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Derivation of the Navier–Stokes equations
The intent of this article is to highlight the important points of the derivation of the Navier–Stokes equations as well as its application and formulation for different families of fluids.
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Differential-algebraic system of equations
In mathematics, a differential-algebraic system of equations (DAEs) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a system.
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Diffusion
Diffusion is the net movement of molecules or atoms from a region of high concentration (or high chemical potential) to a region of low concentration (or low chemical potential) as a result of random motion of the molecules or atoms.
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Diffusion equation
The diffusion equation is a partial differential equation.
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Direct numerical simulation
A direct numerical simulation (DNS) is a simulation in computational fluid dynamics in which the Navier–Stokes equations are numerically solved without any turbulence model.
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Dissipative system
A dissipative system is a thermodynamically open system which is operating out of, and often far from, thermodynamic equilibrium in an environment with which it exchanges energy and matter.
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Divergence
In vector calculus, divergence is a vector operator that produces a scalar field, giving the quantity of a vector field's source at each point.
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Elliptic integral
In integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse.
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Engineering
Engineering is the creative application of science, mathematical methods, and empirical evidence to the innovation, design, construction, operation and maintenance of structures, machines, materials, devices, systems, processes, and organizations.
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Equation of state
In physics and thermodynamics, an equation of state is a thermodynamic equation relating state variables which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature (PVT), or internal energy.
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Eric W. Weisstein
Eric Wolfgang Weisstein (born March 18, 1969) is an encyclopedist who created and maintains MathWorld and Eric Weisstein's World of Science (ScienceWorld).
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Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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Euler equations (fluid dynamics)
In fluid dynamics, the Euler equations are a set of quasilinear hyperbolic equations governing adiabatic and inviscid flow.
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Existence theorem
In mathematics, an existence theorem is a theorem with a statement beginning 'there exist(s)..', or more generally 'for all,,...
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Feynman diagram
In theoretical physics, Feynman diagrams are pictorial representations of the mathematical expressions describing the behavior of subatomic particles.
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Fictitious force
A fictitious force (also called a pseudo force, d'Alembert force, or inertial force) is an apparent force that acts on all masses whose motion is described using a non-inertial frame of reference, such as a rotating reference frame.
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Flow conditioning
Flow conditioning ensures that the “real world” environment closely resembles the “laboratory” environment for proper performance of inferential flowmeters like orifice, turbine, coriolis, ultrasonic etc.
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Flow velocity
In continuum mechanics the macroscopic velocity, also flow velocity in fluid dynamics or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum.
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Fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids - liquids and gases.
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Fluid parcel
In fluid dynamics, within the framework of continuum mechanics, a fluid parcel is a very small amount of fluid, identifiable throughout its dynamic history while moving with the fluid flow.
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Froude number
In continuum mechanics, the Froude number is a dimensionless number defined as the ratio of the flow inertia to the external field (the latter in many applications simply due to gravity).
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Galilean invariance
Galilean invariance or Galilean relativity states that the laws of motion are the same in all inertial frames.
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Gifted (film)
Gifted is a 2017 American drama film directed by Marc Webb and written by Tom Flynn.
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Gradient
In mathematics, the gradient is a multi-variable generalization of the derivative.
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Graph (discrete mathematics)
In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
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Graph theory
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
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Graphics processing unit
A graphics processing unit (GPU) is a specialized electronic circuit designed to rapidly manipulate and alter memory to accelerate the creation of images in a frame buffer intended for output to a display device.
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Gravity
Gravity, or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or gravitate toward) one another.
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Hagen–Poiseuille equation
In nonideal fluid dynamics, the Hagen–Poiseuille equation, also known as the Hagen–Poiseuille law, Poiseuille law or Poiseuille equation, is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross section.
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Hagen–Poiseuille flow from the Navier–Stokes equations
In fluid dynamics, the derivation of the Hagen–Poiseuille flow from the Navier–Stokes equations shows how this flow is an exact solution to the Navier–Stokes equations.
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Helmholtz decomposition
In physics and mathematics, in the area of vector calculus, Helmholtz's theorem, also known as the fundamental theorem of vector calculus, states that any sufficiently smooth, rapidly decaying vector field in three dimensions can be resolved into the sum of an irrotational (curl-free) vector field and a solenoidal (divergence-free) vector field; this is known as the Helmholtz decomposition or Helmholtz representation.
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Homogeneous polynomial
In mathematics, a homogeneous polynomial is a polynomial whose nonzero terms all have the same degree.
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Hooke's law
Hooke's law is a principle of physics that states that the force needed to extend or compress a spring by some distance scales linearly with respect to that distance.
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Hopf fibration
In the mathematical field of differential topology, the Hopf fibration (also known as the Hopf bundle or Hopf map) describes a 3-sphere (a hypersphere in four-dimensional space) in terms of circles and an ordinary sphere.
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Hydraulic head
Hydraulic head or piezometric head is a specific measurement of liquid pressure above a geodetic datum.
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Hydraulics
Hydraulics (from Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids.
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Identity matrix
In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.
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Implicit function
In mathematics, an implicit equation is a relation of the form R(x_1,\ldots, x_n).
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Incompressible flow
In fluid mechanics or more generally continuum mechanics, incompressible flow (isochoric flow) refers to a flow in which the material density is constant within a fluid parcel—an infinitesimal volume that moves with the flow velocity.
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Inertia
Inertia is the resistance of any physical object to any change in its position and state of motion.
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Inertial frame of reference
An inertial frame of reference in classical physics and special relativity is a frame of reference in which a body with zero net force acting upon it is not accelerating; that is, such a body is at rest or it is moving at a constant speed in a straight line.
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Infinitesimal strain theory
In continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles are assumed to be much smaller (indeed, infinitesimally smaller) than any relevant dimension of the body; so that its geometry and the constitutive properties of the material (such as density and stiffness) at each point of space can be assumed to be unchanged by the deformation.
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Integro-differential equation
In mathematics, an integro-differential equation is an equation that involves both integrals and derivatives of a function.
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Inviscid flow
Inviscid flow is the flow of an inviscid fluid, in which the viscosity of the fluid is equal to zero.
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Isochoric process
An isochoric process, also called a constant-volume process, an isovolumetric process, or an isometric process, is a thermodynamic process during which the volume of the closed system undergoing such a process remains constant.
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Isotropy
Isotropy is uniformity in all orientations; it is derived from the Greek isos (ἴσος, "equal") and tropos (τρόπος, "way").
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Jacobian matrix and determinant
In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.
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Jeffery–Hamel flow
In fluid dynamics Jeffery–Hamel flow is a flow created by a converging or diverging channel with a source or sink of fluid volume at the point of intersection of the two plane walls.
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Jos Stam
Jos Stam (born 28 December 1965 in The Hague, Netherlands) is a researcher in the field of computer graphics, focusing on the simulation of natural physical phenomena for 3D-computer animation.
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K–omega turbulence model
In computational fluid dynamics, the k–omega (k–ω) turbulence model is a common two-equation turbulence model, that is used as a closure for the Reynolds-averaged Navier–Stokes equations (RANS equations).
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Knudsen number
The Knudsen number (Kn) is a dimensionless number defined as the ratio of the molecular mean free path length to a representative physical length scale.
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Lamé parameters
In continuum mechanics, the Lamé parameters (also called the Lamé coefficients, Lamé constants or Lamé moduli) are two material-dependent quantities denoted by λ and μ that arise in strain-stress relationships.
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Lamb vector
In fluid dynamics, Lamb vector is the cross product of vorticity vector and velocity vector of the flow field, named after the physicist Horace Lamb.
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Laminar flow
In fluid dynamics, laminar flow (or streamline flow) occurs when a fluid flows in parallel layers, with no disruption between the layers.
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Landau–Squire jet
In fluid dynamics, Landau–Squire jet or Submerged Landau jet describes a round submerged jet issued from a point source into an infinite fluid medium of the same kind.
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Large eddy simulation
Large eddy simulation (LES) is a mathematical model for turbulence used in computational fluid dynamics.
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Linear elasticity
Linear elasticity is the mathematical study of how solid objects deform and become internally stressed due to prescribed loading conditions.
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Linearity
Linearity is the property of a mathematical relationship or function which means that it can be graphically represented as a straight line.
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Mach number
In fluid dynamics, the Mach number (M or Ma) is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.
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Magnetohydrodynamics
Magnetohydrodynamics (MHD; also magneto-fluid dynamics or hydro­magnetics) is the study of the magnetic properties of electrically conducting fluids.
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Material derivative
In continuum mechanics, the material derivative describes the time rate of change of some physical quantity (like heat or momentum) of a material element that is subjected to a space-and-time-dependent macroscopic velocity field variations of that physical quantity.
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MathWorld
MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein.
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Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.
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McGraw-Hill Education
McGraw-Hill Education (MHE) is a learning science company and one of the "big three" educational publishers that provides customized educational content, software, and services for pre-K through postgraduate education.
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Millennium Prize Problems
The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000.
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Molecular dynamics
Molecular dynamics (MD) is a computer simulation method for studying the physical movements of atoms and molecules.
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Mstislav Keldysh
Mstislav Vsevolodovich Keldysh (Мстисла́в Все́володович Ке́лдыш; – 24 June 1978) was a Soviet scientist in the field of mathematics and mechanics, academician of the USSR Academy of Sciences (1946), President of the USSR Academy of Sciences (1961–1975), three times Hero of Socialist Labor (1956, 1961, 1971), fellow of the Royal Society of Edinburgh (1968).
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Multiphase flow
In fluid mechanics, multiphase flow is simultaneous flow of (a) materials with different states or phases (i.e. gas, liquid or solid), or (b) materials with different chemical properties but in the same state or phase (i.e. liquid-liquid systems such as oil droplets in water).
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Navier–Stokes equations
In physics, the Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous fluid substances.
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Navier–Stokes existence and smoothness
The Navier–Stokes existence and smoothness problem concerns the mathematical properties of solutions to the Navier–Stokes equations, one of the pillars of fluid mechanics (such as with turbulence).
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Newton's laws of motion
Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics.
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Newtonian fluid
In continuum mechanics, a Newtonian fluid is a fluid in which the viscous stresses arising from its flow, at every point, are linearly proportional to the local strain rate—the rate of change of its deformation over time.
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No-slip condition
In fluid dynamics, the no-slip condition for viscous fluids assumes that at a solid boundary, the fluid will have zero velocity relative to the boundary.
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Non-dimensionalization and scaling of the Navier–Stokes equations
In fluid mechanics, non-dimensionalization of the Navier–Stokes equations is the conversion of the Navier–Stokes equation to a nondimensional form.
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Nonlinear system
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input.
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Nozzle
A nozzle is a device designed to control the direction or characteristics of a fluid flow (especially to increase velocity) as it exits (or enters) an enclosed chamber or pipe.
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Ocean current
An ocean current is a seasonal directed movement of sea water generated by forces acting upon this mean flow, such as wind, the Coriolis effect, breaking waves, cabbing, temperature and salinity differences, while tides are caused by the gravitational pull of the Sun and Moon.
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Ordinary differential equation
In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.
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Orthogonal coordinates
In mathematics, orthogonal coordinates are defined as a set of d coordinates q.
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Outer product
In linear algebra, an outer product is the tensor product of two coordinate vectors, a special case of the Kronecker product of matrices.
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Oxford University Press
Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.
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Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
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Particle
In the physical sciences, a particle (or corpuscule in older texts) is a small localized object to which can be ascribed several physical or chemical properties such as volume, density or mass.
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Perturbation theory
Perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem.
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Physics
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
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Polar coordinate system
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.
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Presses polytechniques et universitaires romandes
The Presses polytechniques et universitaires romandes (PPUR, literally "Polytechnic and university press of French-speaking Switzerland") is a Swiss academic publishing house.
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Pressure
Pressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
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Pressure-correction method
Pressure-correction method is a class of methods used in computational fluid dynamics for numerically solving the Navier-Stokes equations normally for incompressible flows.
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Probability distribution
In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.
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Pseudorandomness
A pseudorandom process is a process that appears to be random but is not.
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Pythagorean quadruple
A Pythagorean quadruple is a tuple of integers,, and, such that.
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Quantum field theory
In theoretical physics, quantum field theory (QFT) is the theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics and quasiparticles in condensed matter physics.
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Rayleigh–Bénard convection
Rayleigh–Bénard convection is a type of natural convection, occurring in a plane horizontal layer of fluid heated from below, in which the fluid develops a regular pattern of convection cells known as Bénard cells.
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Reynolds number
The Reynolds number is an important dimensionless quantity in fluid mechanics used to help predict flow patterns in different fluid flow situations.
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Reynolds transport theorem
In differential calculus, the Reynolds transport theorem (also known as the Leibniz–Reynolds transport theorem), or in short Reynolds' theorem, is a three-dimensional generalization of the Leibniz integral rule which is also known as differentiation under the integral sign.
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Reynolds-averaged Navier–Stokes equations
The Reynolds-averaged Navier–Stokes equations (or RANS equations) are time-averaged equations of motion for fluid flow.
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Rotational symmetry
Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn.
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Scalar (mathematics)
A scalar is an element of a field which is used to define a vector space.
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Scale analysis (mathematics)
Scale analysis (or order-of-magnitude analysis) is a powerful tool used in the mathematical sciences for the simplification of equations with many terms.
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Science
R. P. Feynman, The Feynman Lectures on Physics, Vol.1, Chaps.1,2,&3.
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Shear stress
A shear stress, often denoted by (Greek: tau), is the component of stress coplanar with a material cross section.
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Shear velocity
Shear Velocity, also called friction velocity, is a form by which a shear stress may be re-written in units of velocity.
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Shock wave
In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance.
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Sir George Stokes, 1st Baronet
Sir George Gabriel Stokes, 1st Baronet, (13 August 1819 – 1 February 1903), was an Irish physicist and mathematician.
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Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
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Solenoidal vector field
In vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a '''transverse vector field''') is a vector field v with divergence zero at all points in the field.
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Spalart–Allmaras turbulence model
The Spalart–Allmaras model is a one-equation model that solves a modelled transport equation for the kinematic eddy turbulent viscosity.
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Spherical coordinate system
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane.
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Square root of 2
The square root of 2, or the (1/2)th power of 2, written in mathematics as or, is the positive algebraic number that, when multiplied by itself, gives the number 2.
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Stagnation point flow
Stagnation point flow represents a fluid flow in the immediate neighborhood of solid surface at which fluid approaching the surface divides into different streams or a counterflowing fluid streams encountered in experiments.
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Stochastic process
--> In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a collection of random variables.
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Stokes boundary layer
In fluid dynamics, the Stokes boundary layer, or oscillatory boundary layer, refers to the boundary layer close to a solid wall in oscillatory flow of a viscous fluid.
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Stokes flow
Stokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion,Kim, S. & Karrila, S. J. (2005) Microhydrodynamics: Principles and Selected Applications, Dover.
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Stokes stream function
In fluid dynamics, the Stokes stream function is used to describe the streamlines and flow velocity in a three-dimensional incompressible flow with axisymmetry.
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Stokes' theorem
In vector calculus, and more generally differential geometry, Stokes' theorem (also called the generalized Stokes theorem or the Stokes–Cartan theorem) is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus.
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Stream function
The stream function is defined for incompressible (divergence-free) flows in two dimensions – as well as in three dimensions with axisymmetry.
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Streamlines, streaklines, and pathlines
Streamlines, streaklines and pathlines are field lines in a fluid flow.
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Stress (mechanics)
In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material.
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Surface tension
Surface tension is the elastic tendency of a fluid surface which makes it acquire the least surface area possible.
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Taylor–Green vortex
In fluid dynamics, the Taylor–Green vortex is an unsteady flow of a decaying vortex, which has an exact closed form solution of the incompressible Navier–Stokes equations in Cartesian coordinates.
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Temperature
Temperature is a physical quantity expressing hot and cold.
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Tensor calculus
In mathematics, tensor calculus or tensor analysis is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime).
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Thermal conduction
Thermal conduction is the transfer of heat (internal energy) by microscopic collisions of particles and movement of electrons within a body.
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Thermal hydraulics
Thermal hydraulics (also called thermohydraulics) is the study of hydraulic flow in thermal fluids.
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Time
Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future.
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Trace (linear algebra)
In linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i.e., where aii denotes the entry on the ith row and ith column of A. The trace of a matrix is the sum of the (complex) eigenvalues, and it is invariant with respect to a change of basis.
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Transport coefficient
A Transport coefficient \gamma can be expressed via a Green-Kubo relation: where A is an observable occurring in a perturbed Hamiltonian, \langle \cdot \rangle is an ensemble average and the dot above the A denotes the time derivative.
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Turbulence
In fluid dynamics, turbulence or turbulent flow is any pattern of fluid motion characterized by chaotic changes in pressure and flow velocity.
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Turbulence kinetic energy
In fluid dynamics, turbulence kinetic energy (TKE) is the mean kinetic energy per unit mass associated with eddies in turbulent flow.
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United States dollar
The United States dollar (sign: $; code: USD; also abbreviated US$ and referred to as the dollar, U.S. dollar, or American dollar) is the official currency of the United States and its insular territories per the United States Constitution since 1792.
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Vector Laplacian
In mathematics and physics, the vector Laplace operator, denoted by \nabla^2, named after Pierre-Simon Laplace, is a differential operator defined over a vector field.
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Video game
A video game is an electronic game that involves interaction with a user interface to generate visual feedback on a video device such as a TV screen or computer monitor.
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Viscosity
The viscosity of a fluid is the measure of its resistance to gradual deformation by shear stress or tensile stress.
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Viscous liquid
In condensed matter physics and physical chemistry, the terms viscous liquid, supercooled liquid, and glassforming liquid are often used interchangeably to designate liquids that are at the same time highly viscous (see Viscosity of amorphous materials), can be or are supercooled, and able to form a glass.
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Vlasov equation
The Vlasov equation is a differential equation describing time evolution of the distribution function of plasma consisting of charged particles with long-range interaction, e.g. Coulomb.
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Volume viscosity
Volume viscosity (also called second coefficient of viscosity or dilatational viscosity or bulk viscosity) becomes important only for such effects where fluid compressibility is essential.
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Von Kármán swirling flow
Von Kármán swirling flow is a flow created by a uniformly rotating infinitely long plane disk, named after Theodore von Kármán who solved the problem in 1921.
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Work (thermodynamics)
In thermodynamics, work performed by a system is the energy transferred by the system to its surroundings, that is fully accounted for solely by macroscopic forces exerted on the system by factors external to it, that is to say, factors in its surroundings.
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References
[1] https://en.wikipedia.org/wiki/Navier–Stokes_equations
