What is stokesian dynamics?
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To correctly simulate the rheology of concentrated suspensions at high shear rates requires the inclusion of hydrodynamic forces between particles. The computation of such interactions is very intensive, and it presents a significant challenge: to produce algorithms that enable a study of systems with large numbers of particles. The work of Brady and coworkers in the early eighties [1] showed the way forward to such a goal. The technique, Stokesian Dynamics presents a formalism for studying such systems. We first write down the Langevin equation for a colloidal particle within a hydrodynamic medium:\n\nFH + FC + FB = M · dU/dt\n\nHere, F represents forces acting on an individual particle: Hydrodynamic, Colloidal (charge repulsion/attraction for example) and Brownian forces. M is the mass of the particle, and U its velocity.Within a colloidal system, the time scales of interest dictate that inertia may be neglected. Thus the right hand side of above equation can be neglected. We also work with the assumption that the fluid obeys the Stokes equations, i.e. we are within a low Reynolds number regime. Thus the hydrodynamic forces can be considered linear in the velocities, therefore FH = R·U, where R is a resistance tensor, the elements of which describe the hydrodynamic interactions between individual particles. To simulate colloid particles, we need to determine the particles velocities at each time step, thus the above equation becomes:\n\nU = -R-1 · (FC + FB)\n\nThus solving for U requires the inversion of the resistance matrix R. This typically restricts the size of the systems that one can study to less than 100 particles. In order to simulate systems on a larger scale, Ball and Melrose [2] have proposed an approximation that is applicable to colloids at high concentrations in shear flow. They argue that at such concentrations, where the typical interparticle spacing is small, the near-field terms in the resistance matrix (which are given by lubrication theory) will dominate in shear flow. Thus R can be made sparse; this greatly increases computational efficiency. The method is now typically of O(N2) compared to O(N3) for the full matrix, making the study of larger systems feasible (typically as much as 4,000 particles). Even though the resistance tensor is sparse and consists of near-field terms, the inversion of such a matrix results in a many-bodied far-field mobility tensor. Ref. [2] gives full details on the technique, in particular how to correctly handle the correlated Brownian forces through use of a 2nd order difference scheme. The code has been implemented and validated. It has a suite of colloid interactions, including charge, depletion, and polymer coats. Particles may interact with just squeeze lubrication or with full modes of shear and rotation. Nearest neighbours are identified through the construction of a Delaunay mesh which is co-moving with the particle centres. Sample results from using this algorthim are given in the Colloid Rheology section of this site.\n\nReferences\n\nBrady, J. F. and G. Bossis, "The rheology of concentrated suspensions of spheres in simple shear flow by numerical simulation," J. Fluid Mech, 155, 105-129 (1985) \nBall, R. C. and J. R. Melrose, "A simulation technique for many spheres in quasi-static motion under frame-invariant pair drag and Brownian forces," Physica A, 247, 444-472 (1997)
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Ott, Edward (2002). Chaos in Dynamical Systems. Cambridge University Press New, York. ISBN 0521010845. \nGutzwiller, Martin (1990). Chaos in Classical and Quantum Mechanics. Springer-Verlag New York, LLC. ISBN 0387971734. \nMoon, Francis (1990). Chaotic and Fractal Dynamics. Springer-Verlag New York, LLC. ISBN 0471545716. \nTufillaro, Abbott, Reilly (1992). An experimental approach to nonlinear dynamics and chaos. Addison-Wesley New York. ISBN 0201554410. \nGollub, J. P.; Baker, G. L. (1996). Chaotic dynamics. Cambridge University Press. ISBN 0521476852. \nBaker, G. L. (1996). Chaos, Scattering and Statistical Mechanics. Cambridge University Press. ISBN 0521395119. \nAlligood, K. T. (1997). Chaos: an introduction to dynamical systems. Springer-Verlag New York, LLC. ISBN 0387946772. \nKiel, L. Douglas; Elliott, Euel W. (1997). Chaos Theory in the Social Sciences. Perseus Publishing. ISBN 0472084720. \nStrogatz, Steven (2000). Nonlinear Dynamics and Chaos. Perseus Publishing. ISBN 0738204536. \nSprott, Julien Clinton (2003). Chaos and Time-Series Analysis. Oxford University Press. ISBN 0198508409. \nHoover, William Graham (1999,2001). Time Reversibility, Computer Simulation, and Chaos. World Scientific. ISBN 981-02-4073-2. \n Beauty of Fractals, by H.-O. Peitgen and P.H. Richter \nChance and Chaos, by David Ruelle \nComputers, Pattern, Chaos, and Beauty, by Clifford A. Pickover \nFractals, by Hans Lauwerier \nFractals Everywhere, by Michael Barnsley \nOrder Out of Chaos, by Ilya Prigogine and Isabelle Stengers \nChaos and Life, by Richard J Bird \nDoes God Play Dice?, by Ian Stewart \nThe Science of Fractal Images, by Heinz-Otto Peitgen and Dietmar Saupe, Eds. \nExplaining Chaos, by Peter Smith \nChaos: Making a New Science, New York: Penguin, by James Gleick \nComplexity, by M. Mitchell Waldrop \nChaos, Fractals and Self-organisation, by Arvind Kumar \nChaotic Evolution and Strange Attractors, by David Ruelle \nSync: The emerging science of spontaneous order, by Steven Strogatz \nThe Essence of Chaos, by Edward Lorenz \nDeep Simplicity, by John Gribbin \nThe Road To Chaos, by Yoshisuke Ueda \nThe Chaos Avant-Garde: Memoirs of the Early Days of Chaos Theory, Edited by Ralph H. Abraham and Yoshisuke Ueda
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ok...\n\ntry this...do a little research on Newtonian versus non-Newtonian fluids. (see link)  There are several types of fluids (this is a very important topic in Chemical Engineering, so don't be worried if you don't understand all of the mathematics on this link).\n\nSet up a web/video camera above a bowl containing one of each type of fluid in the table. Make sure you have a ruler or some other scale in view of your shot. Then take turns dropping:\n1) Large marble\n2) Small marble\n3) Pencil\n4) die (singular of dice)\n\nwhile you photograph the results.  Discuss General shape differences of the waves generated by the objects.  And discuss wavelength differences (measured using the ruler in your shot and freeze frames of the video) between the different types of fluids.  \n\nThis project will yield some cool photographs and a demonstration will act as an awesome visual aid as well.\n\nHope this is what you were looking for. If not, or if you need any additional information, feel free to contact me. Good luck.
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fluids - convection is due to the movement of molecules
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Biot-Savart Law. Look it up.
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You shake it. You can describe it mathematically with a step function.
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Try this:\n\nStructure and Interpretation of Classical Mechanics\nhttp://mitpress.mit.edu/SICM/\nbook-Z-H-20.html#%_chap_2
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Orbits of planets\n\nBending of light\n\nParabolic trajectories\n\nTides\n\nRiver flow\n\netc\n\netc\n\netc
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good link below\n\nhttp://en.wikipedia.org/wiki/Kinetic_theory
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The physical science and technology of the static and dynamic behavior of fluids.
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Previous answerer had it correct.  Falling-ball viscometers are based on Stokes' Law.  See sources below for a complete description.
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An especially significant property of chaotic systems is great sensitivity to initial conditions.  Move the tiniest amount in x,y in Mandelbrot and you have a radically different outcome.
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Curl, divergence, gradient.
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In the cup stationery is static.  Goes down your throat follows dynamics.  Due to some reason, if acts like a laxative, then it is real fluid dynamics.\nVR
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Surely you know the foumla for Re?\n\nRe=(density*velocity*length)/viscosity\n\nRe=(1000*1*25*10^-3)/1014*10^-3\n\nRe=24.655 (3dp)\n\nI think you've got yourself a laminar flow.
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Modelling actions of natural dacay.\n\nAmortization.  The interest on a loan is calculated on the remaining balance.\n\nFluid dynamics.  The fluid pressure in a silo is a log function of how full it is.  As the level drops, the pressure drops logarithmically.\n\nElectronics.  The time constants of capacitors and inductors\nare logarithmic.\n\nThe list goes on...
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Dynamic Choropleth Maps are a data visualization tool for spatial analyses.