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46 relations: Advection, Baker's map, Batchelor scale, Cambridge University Press, Chaos theory, Comptes rendus de l'Académie des Sciences, Conservation of mass, Contour advection, Convection–diffusion equation, Diffusion, Dynamical system, Ergodicity, Exponential growth, Flow tracer, Flow velocity, Fluid, Fluid dynamics, Fluid mechanics, Fractal, Fractal dimension, French Academy of Sciences, Gradient, Hassan Aref, Inviscid flow, Jacobian matrix and determinant, Journal of Fluid Mechanics, Koch snowflake, Lagrangian and Eulerian specification of the flow field, Liquid, Lyapunov exponent, Michel Hénon, Mixing (physics), Navier–Stokes equations, Ordinary differential equation, Poincaré map, Principal component analysis, Shear stress, Simple shear, Stagnation point, Stream function, Streamlines, streaklines, and pathlines, Taylor series, Trajectory (fluid mechanics), Uncertainty exponent, Velocity, Vladimir Arnold.
Advection
In the field of physics, engineering, and earth sciences, advection is the transport of a substance by bulk motion.
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Baker's map
In dynamical systems theory, the baker's map is a chaotic map from the unit square into itself.
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Batchelor scale
The Batchelor Scale, determined by George Batchelor (1954), describes the size of a droplet of scalar that will diffuse in the same time it takes the energy in an eddy of size η to dissipate.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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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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Comptes rendus de l'Académie des Sciences
Comptes rendus de l'Académie des Sciences (English: Proceedings of the Academy of sciences), or simply Comptes rendus, is a French scientific journal which has been published since 1666.
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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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Contour advection
Contour advection is a Lagrangian method of simulating the evolution of one or more contours or isolines of a tracer as it is stirred by a moving fluid.
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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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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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Dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.
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Ergodicity
In probability theory, an ergodic dynamical system is one that, broadly speaking, has the same behavior averaged over time as averaged over the space of all the system's states in its phase space.
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Exponential growth
Exponential growth is exhibited when the rate of change—the change per instant or unit of time—of the value of a mathematical function is proportional to the function's current value, resulting in its value at any time being an exponential function of time, i.e., a function in which the time value is the exponent.
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Flow tracer
A flow tracer is any fluid property used to track flow.
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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
In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress.
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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 mechanics
Fluid mechanics is a branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them.
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Fractal
In mathematics, a fractal is an abstract object used to describe and simulate naturally occurring objects.
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Fractal dimension
In mathematics, more specifically in fractal geometry, a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is measured.
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French Academy of Sciences
The French Academy of Sciences (French: Académie des sciences) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research.
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Gradient
In mathematics, the gradient is a multi-variable generalization of the derivative.
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Hassan Aref
Hassan Aref (28 September 1950 – 9 September 2011) was the Reynolds Metals Professor in the Department of at Virginia Tech, and the Niels Bohr Visiting Professor at the Technical University of Denmark.
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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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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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Journal of Fluid Mechanics
The Journal of Fluid Mechanics is a peer-reviewed scientific journal in the field of fluid mechanics.
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Koch snowflake
The Koch snowflake (also known as the Koch curve, Koch star, or Koch island) is a mathematical curve and one of the earliest fractal curves to have been described.
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Lagrangian and Eulerian specification of the flow field
In classical field theory the Lagrangian specification of the field is a way of looking at fluid motion where the observer follows an individual fluid parcel as it moves through space and time.
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Liquid
A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure.
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Lyapunov exponent
In mathematics the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectories.
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Michel Hénon
Michel Hénon (1931 in Paris – 7 April 2013 in Nice) was a French mathematician and astronomer.
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Mixing (physics)
In physics, a dynamical system is said to be mixing if the phase space of the system becomes strongly intertwined, according to at least one of several mathematical definitions.
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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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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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Poincaré map
In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower-dimensional subspace, called the Poincaré section, transversal to the flow of the system.
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Principal component analysis
Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components.
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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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Simple shear
Simple shear is a deformation in which parallel planes in a material remain parallel and maintain a constant distance, while translating relative to each other.
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Stagnation point
In fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is zero.
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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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Taylor series
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.
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Trajectory (fluid mechanics)
In fluid mechanics, meteorology and oceanography, a trajectory traces the motion of a single point, often called a parcel, in the flow.
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Uncertainty exponent
In mathematics, the uncertainty exponent is a method of measuring the fractal dimension of a basin boundary.
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Velocity
The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time.
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Vladimir Arnold
Vladimir Igorevich Arnold (alternative spelling Arnol'd, Влади́мир И́горевич Арно́льд, 12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician.
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Chaotic Advection, Chaotic transport.
References
[1] https://en.wikipedia.org/wiki/Chaotic_mixing
