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inhomogeneous

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  • Differential equations classification In this video I introduce differential equations and discuss the various properties such as order linear homogeneous second order constant coefficients
  • Twinkle, Twinkle (by Science Groove) An explanation of T2* -- pronounced "tee two star" -- the time constant for the decay of a magnetic resonance signal in the XY plane. This song was written for the May 2002 meeting of the International Society for Magnetic Resonance in Medicine. Lyrics: Twinkle, twinkle, T2*; How I wonder what you are! XY signal soon decays; Why do the spins go out of phase? Twinkle, twinkle, T2*; Something pulls those spins apart. Spin-spin crosstalk sets T2, But by then T2* is through. A brief duration here is sealed By an inhomogeneous field. Twinkle, twinkle, T2*; Now I know just what you are!
  • Cosmic Reionization Visualization of the progress of reionization in a 1 Gpc/h volume. Ionized regions are blue and translucent, ionization fronts are red and white, and neutral regions are dark and opaque. A random sampling of 5 per cent (about 40000) of all the halos at z = 0 are shown in yellow. Reionization is still quite inhomogeneous on these large scales, with large regions ionizing long before others. Visualization by Marcelo Alvarez (Canadian institute for Theoretical Astrophysics), Ralf Kaehler and Tom Abel (Kavli Institute for Particle Astrophysics and Cosmology, SLAC National Accelerator Laboratory/Stanford University) For more information see cita.utoronto.ca~ www-group.slac.stanford.edu
  • Solution sets of linear equations Introduction to solution sets of linear equations, focusing on the relationship between homogeneous and inhomogeneous equations
  • Braking without ABS on inhomogeneous roadbed Doing some breaking without anti-lock braking system (ABS) on the Sachsenring, Free State of Saxony, Germany.
  • Stepped chute - Nappe flow inhomogeneous model for multiphase flow, and the ke model to represent the turbulence.
  • Damped, forced, harmonic oscillator Shows how to find the long-time asymptotics of the damped, forced, harmonic oscillator by solving a second-order, linear, inhomogeneous ode with constant coefficients.
  • Compressive Structured Light for Recovering Inhomogeneous Participating Media In this project, we propose a new method named compressive structured light for recovering inhomogeneous participating media. Whereas conventional structured light methods emit coded light patterns onto the surface of an opaque object to establish correspondence, compressive structured light projects patterns into a volume of participating medium to produce images which are integral measurements of the volume density along the line of sight. For a typical participating medium encountered in the real world, the integral nature of the acquired images enables the use of compressive sensing techniques that can recover the entire volume density from only a few measurements. This makes the acquisition process more efficient and enables reconstruction of dynamic volumetric phenomena. We show the effectiveness of our method with simulations as well as experiments on the volumetric recovery of multiple translucent layers, 3D point clouds etched in glass, and the dynamic process of milk drops dissolving in water. Project Page: www1.cs.columbia.edu
  • Montserrat Caballé Unmatched #18 Bis: Lucrezia Borgia (Lucrezia Borgia). "Tranquillo Ei Posa"; "Com'È Bello!" (Lucrezia Borgia); 1966. Still unbeatable; Montserrat Caballé has delivered one of her most exquisite singing in this role of Donizetti's Lucrezia Borgia. Having a perfect legato as she has, only a stupid could say she has no trills or not full low notes... Renée Fleming's mediocrity, vulgarity and inhomogeneous voice has nothing to do against Caballé. And the same goes for Gruberova and her absence of musicality, ludicrous style and brainless use of open low notes and flat middle notes (she shoul stick to coloratura roles). Finally, Maria Callas' attempt to sing this aria is shameful. Her voice is definitely ugly; well, opposite Caballé's, almost every singer voice is.
  • Lec 23 | MIT 3.320 Atomistic Computer Modeling of Materials Accelerated Molecular Dynamics, Kinetic Monte Carlo, and Inhomogeneous Spatial Coarse Graining View the complete course at: ocw.mit.edu License: Creative Commons BY-NC-SA More information at ocw.mit.edu More courses at ocw.mit.edu
  • Elastic yielding of entangled liquids Basic feature in polymer rheology could be inhomogeneous yielding as shown in this movie that shows the breakdown of an entangled polymer melt. For more, visit www3.uakron.edu This work is funded by NSF.
  • How to solve second order differential equations. Chris Tisdell UNSW Sydney A lecture on how to solve second order (inhomogeneous) differential equations. Plenty of examples are discussed and solved. The ideas are seen in university mathematics and have many applications to physics and engineering.
  • AlAsGaAs p-QW NW (001) HAADF STEM tilt series and 3D tomographic reconstruction of an inhomogeneous AlAs/GaAs multi p-QW nanowires (NWs)
  • PRIMA2009 Plenary Lecture 6: Linda Petzold (University of California Santa Barbara) Plenary Lecture from the 1st PRIMA Congress. Discrete stochastic simulation of spatially inhomogeneous biochemical systems, Linda Petzold, University of California Santa Barbara.
  • Particular solution for sin using complex exponentials Shows how to find a particular solution when the inhomogeneous term is a sine (or a cosine) using complex exponential functions.
  • A Formula for Particular Solutions Of Inhomogeneous Linear Ordinary Differential Equations of Third Order2 A Formula for Particular Solutions Of Inhomogeneous Linear Ordinary Differential Equations of Third Order As I have shown earlier in reference [6], a particular solution for inhomogeneous linear second order ordinary differential equations may be determined by the following short method. In this I have refrained from using the 's' notation, and all other shortcuts to impress the fact that the particular solution formula is not just for some 2nd order ODE's. And the formula is written, here, in a more compatible format. Please see reference [6] to view worked out examples, and my short table of 2nd order particular solutions video for even more, even more general ones. In the ***ysis of the 3rd order particular solution formula, the canvas becomes so full, even using the 's' notation, that it becomes indispensible - especially in video format. The ***ysis goes much the same, only with far more terms. The major differences are at the end, where the 2nd order formula is applied, and the relationship between the homogeneous and particular solutions in the variant of the reduction of order technique. Finally, a formula for third order ODE particular solutions may be written. Four worked out examples follow, followed by part of a general table-type one. My 4th order formula is on , now; and my arbitrary order formula is available on Kindle at . As always: All my books are available on Kindle in digital format at , and links to all my books may ...
  • Particular solution for a polynomial Shows how to find a particular solution when the inhomogeneous term is a polynomial function.
  • Coarse-graining of a virtual liver Coarse-graining of a virtual liver with the energy matching principle as described in: Numerical Coarsening of Inhomogeneous Linear Elastic Materials, ACM Transactions on Graphics (SIGGRAPH), 28(3), 2009. Lily Kharevych, Patrick Mullen, Houman Owhadi and Mathieu Desbrun www.acm.caltech.edu
  • Invisible Universe Presentation Invisible Universe International Conference Towards a new cosmological paradigm (june 29 - july3, 2009) The essential is invisible to our eye., astronomy and astrophysics and more in particular modern cosmology have shown that most of the universe is invisible to our eyes and to the most advanced observational devices. o "Observational Astrophysical Aspect of dark energy and dark matter" o "Experimental particle physics aspects of dark matter" o "Gravitation and cosmology (Quantum gravity - M-Theory and cosmology)" o "Inhomogeneous universes and backreaction" o "Dark energy as a new energy component" o "Dark matter candidates" o "Dark energy and Dark Matter as modified gravity" o "Theoretical and numerical aspects of cosmic structures and evolution"
  • Pastor Chui - All Isochrons Can Be Mixing Lines.flv This is a 12-minute sermon from science. It describes William Overn's paper on "Isochron Rock Dating is Fatally Flawed." Overn debated Darumple of the US Geologic Survey years ago. Overn points out there are two unknowns in one dating equation. No solution is possible without making assumptions. Adding more equations will only introduce more unknowns. Therefore, it is an unconvincing art. Both the initial concentrations of daughter and parents are not known. Therefore, assumptions must be made. When rocks formed from high temperatures, they will incorporate different amounts of different isotopes. Therefore, mixing cannot be ruled out. In fact, the mixing is either homogeneous or inhomogeneous. If the mixing is homogeneous, only a single point is obtained--no line is possible. If the mixing is inhomogeneous, a line may be obtained, but it has no significance of time, because it is an inhomogeneous mixing. Therefore, all isochron rock dating is fatally flawed.
  • Real-time Single Scattering Inside Inhomogeneous Materials D. Bernabei · F. Ganovelli · N. Pietroni · P.Cignoni · S. Pattanaik · R. Scopigno In this paper we propose a novel technique to perform real-time rendering of translucent inhomogeneous materials, one of the most well known problems of Computer Graphics. The developed technique is based on an adaptive volumetric point sampling, done in a preprocessing stage, which associates to each sample the optical depth for a predefined set of directions. This information is then used by a rendering algorithm that combines the objects surface rasterization with a ray tracing algorithm, implemented on the graphics processor, to compose the final image. This approach allows us to simulate light scattering phenomena for inhomogeneous isotropic materials in real time with an arbitrary number of light sources. We tested our algorithm by comparing the produced images with the result of ray tracing and showed that the technique is effective.
  • Lec 28 | MIT 18.03 Differential Equations, Spring 2006 Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters. View the complete course: ocw.mit.edu License: Creative Commons BY-NC-SA More information at ocw.mit.edu More courses at ocw.mit.edu
  • The Use of Nuclear Explosives To Disrupt or Divert Asteroids Google Tech Talks March 23, 2007 ABSTRACT Nuclear explosives are a mature technology with well-characterized effects. Proposed utilizations include a near asteroid burst to ablate surface material and nudge the body to a safer orbit, or a direct sub-surface burst to fragment the body. For this latter method, previous estimates suggest that for times as short as 1000 days, over 99.999% of the material is diverted, and no longer impacts the Earth, a huge mitigation factor. To better understand these possibilities, we have used a multidimensional radiation/hydrodynamics code to simulate sub-surface and above surface bursts on an inhomogeneous, 1 km diameter body with an average density of 2 g/cc....
  • Hubble's Cosmic Origins Spectrograph. Spectroscopes or spectrographs are absolutely essential in that toolbox of astronomical tools that are so important for research. They produce ugly pictures. But they are the nuts and bolts of physical science. They put the physics in astrophysics. If you look out across the universe today and you start seeing this inhomogeneous web-like structure with filaments, places where filaments come together, looks just like a big three-dimensional spider web, tracing all those filaments is the light of ordinary stars and galaxies. For more on this story, and others please visit us at For this story go to
  • Particular solution when the inhomogeneous term is a homogeneous solution To find the particular solution when the inhomogeneous term is a solution of the homogeneous equation, multiply by t.
  • Superconductor on Magnetic Rails Superconductor on Magnetic Rails When a superconductor enters the field of a permanent magnet, a current is induced to compensate the internal field and the magnet is repelled. In that way a superconductor can float over a magnet. When the field is increased, for instance by pressing the superconductor a little into the field, some flux lines will enter the superconductor at impurities and it is then held pinned at a certain distance from the magnet. When the field is homogenous in one direction, the superconductor is guided on a magnetic rail. This is tried out with a piece of YBCO yttrium barium copper oxide, a superconductor that becomes superconductive at 93K, a temperature that can be reached with cooling by liquid nitrogen (ln2) boiling at 77K. To stop the superconductor at the end of the rail, the field is made inhomogeneous at the end by turning the magnets. A superconductor does not hold its temperature for long just by its thermal capacity and with fading conductivity it slowly sinks down to the rails. To make it float longer, a housing out of a tea candle shell is formed around it and some drops of liquid nitrogen are added. The alternative to pinning the superconductor to the rails by pushing it in the superconductive state, is to adjust it in a short distance from the rails and to cool it below its transition temperature inside the magnetic field. When the superconductor is taken out from the field and pushed sideways over the tracks a periodic snapping to ...
  • Second-order, linear, inhomogeneous ode: exp How to solve the second-order, linear, inhomogeneous ode with constant coefficients and an exponential function inhomogeneous term.
  • Inhomogeneous 2nd order Differential Equations Please give me feedback. Hope it makes sense
  • Lec 13 | MIT 18.03 Differential Equations, Spring 2006 Finding Particular Sto Inhomogeneous ODE's: Operator and Solution Formulas Involving Exponentials. View the complete course: ocw.mit.edu License: Creative Commons BY-NC-SA More information at ocw.mit.edu More courses at ocw.mit.edu
  • Dispersion Of White Light Check us out at In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency. Media having such a property are termed dispersive media. Dispersion is sometimes called chromatic dispersion to emphasize its wavelength-dependent nature, or group-velocity dispersion (GVD) to emphasize the role of the group velocity. The most familiar example of dispersion is probably a rainbow, in which dispersion causes the spatial separation of a white light into components of different wavelengths (different colors). However, dispersion also has an effect in many other circumstances: for example, GVD causes pulses to spread in optical fibers, degrading signals over long distances; also, a cancellation between group-velocity dispersion and nonlinear effects leads to soliton waves. Dispersion is most often described for light waves, but it may occur for any kind of wave that interacts with a medium or passes through an inhomogeneous geometry (eg a waveguide), such as sound waves. There are generally two sources of dispersion: material dispersion and waveguide dispersion. Material dispersion comes from a frequency-dependent response of a material to waves. For example, material dispersion leads to undesired chromatic aberration in a lens or the separation of colors in a prism. Waveguide dispersion occurs when the speed of a wave in a waveguide (such as an optical ...
  • Homogeneous and Inhomogeneous 1st order Equations Hopefully will do 2nd order soon. homogeneous and inhomogeneous case for differential equations course
  • Lec 12 | MIT 18.03 Differential Equations, Spring 2006 Continuation: General Theory for Inhomogeneous ODE's. Stability Criteria for the Constant-coefficient ODE's. View the complete course: ocw.mit.edu License: Creative Commons BY-NC-SA More information at ocw.mit.edu More courses at ocw.mit.edu
  • Shear band or banding upon yielding in entangled polymers Polymeric liquids or molten plastics deform elastically before eventually flow. The yielding is seen here to lead to inhomogeneous cohesive breakup, based on a particle-tracking-velocimetric setup. For description of the method, see "A coherent description of nonlinear flow behavior of entangled polymers as related to processing and numerical simulations", SQ Wang, Macromol. Mater. Engr. 125, 15 (2007). Is this common in polymer rheology? Visit www3.uakron.edu The work is funded by NSF.
  • Coffeering Suppression of Coffee ring phenomena We developed a Electrowetting based nonintrusive method to suppress inhomogeneous distribution of solutes in an evaporating drop so called: coffee stain effect. This technology has various applications in improving combinatorial ***ysis, production of collloidal crystals and directed self assembly. "Suppressing the coffee stain effect: how to control colloidal self-assembly in evaporating drops using electrowetting", HBEral, D.Mampallil, F.Mugele Soft Matter, 2011, DOI:10.1039/C1SM05183K HBEral, DAMampallil, F.Mugele "A method for treating a liquid drop ", European patent application,No:10163000.2, 2010
  • Coronal Mass Ejection 2012 SOLAR STORM Our solar system is travelling at 11 million miles per hour in a spiral around the black hole at the center of our Milky Way Galaxy. The Solar System is entering an area of space that is high in energy and it will affect every single atom in the entire solar system. The sun is awakening to what NASA predicts as the largest once in a lifetime solar maximum! HOW THIS COULD CAUSE EARTHQUAKES: This information was channeled through me in an altered state of meditation.. The energy the sun gives off in a CME energizes Earth's magnetic fields, which temporarily alters the field and not just the outer edge of the magnetic band but the entire band, this is evident in Ampere's law in conjunction with Maxwell's equations, in which electrical charge changes the magnetic flux density per inhomogeneous electromagnetic wave. When electric charges oscillates or accelerates it creates a disturbance of the electromagnetic field. There is nothing in spatial dimension that stops the energy from traversing the entire magnetic band and displacing current, this is the norm as it is stated in Gauss's Law for Magnetism that magnetic field lines never begin nor end, forming either loops or extending to infinity, so there is no separation from disturbances at the outer edge of these loops. Its easier to directly observe visual interaction at the edge of our ionosphere but the energy is in fact circulating through those magnetic field lines. I want to illustrate that materials in earth's crust have ...
  • Feature-aware texturing We present a method for inhomogeneous 2D texture mapping guided by a feature mask, that preserves some regions of the image, such as foreground objects or other prominent parts. www.cs.nyu.edu
  • Cellular Automata with Global Control The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. This Demonstration implements an idea of Stephen Wolfram and others of a cellular automaton that chooses the rule to apply based on the global state of the automaton. The cellular automaton is thus temporally inhomogeneous. Here, you can specify two pos... Contributed by: Seth J. Chandler After work by: Stephen Wolfram, Jason Cawley, Todd Rowland and Alastair Hewitt
  • Power Series Solution for y"-2y'+y=x, y(0)=0, y'(0)=1 ODEs: Find the first four terms of the power series solution to the IVP y"-2y'+y=x, y(0)=0, y'(0)=1. To check our answer, we find the solution using the annihilator method and expand the exponential terms into power series.
  • VisBricks: Multiform Visualization of Large, Inhomogeneous Data Large volumes of real-world data often exhibit inhomogeneities: vertically in the form of correlated or independent dimensions, horizontally in the form of clustered or scattered data items. In essence, these inhomogeneities form the patterns in the data that researchers are trying to find and understand. Sophisticated statistical methods are available to do so, yet the visualization of their outcomes is mostly still done in a one-view-fits-all manner. In contrast, our novel visualization approach, VisBricks, acknowledges the inhomogeneity of the data and the need for different visualizations that suit the individual characteristics of the different data subsets. The overall visualization of the entire data set is patched together from smaller visualizations -- one VisBrick for each cluster in each group of interdependent dimensions. Whereas the total impression of all VisBricks together gives a comprehensive high-level overview of the different groups of data, each VisBrick independently shows details of the group of data it represents. State-of-the-art brushing and visual linking between all VisBricks furthermore allows comparing groupings and the distribution of data items among them. In this paper, we introduce the VisBricks visualization concept, discuss its design rationale and implementation, and demonstrate its usefulness by applying it to a use case from the field of biomedicine.
  • String Theory Multiverse - Sergei Dubovsky (SETI Talks) SETI Talks Archive: One of the most intriguing and controversial recent ideas in cosmology and string theory is that the Universe is highly inhomogeneous on the length scales much longer than its currently observable part, with many of the fundamental "constants" of Nature varying on the ultra-long length scales. Our location in this cosmic landscape is to a large extent determined by requiring that the local particle physics parameters should allow for life to develop. Dr. Dubovsky will review the origin of these ideas and explain how they can be supported by the near future observations of astrophysical black holes.
  • Variation of Parameters Solution of second order, linear, inhomogeneous differential equations using the method of variation of parameters. The example is Problem 88(b) for MAT2019 at UNSW
  • Magnetic Levitation Train Explanation: this is a museum model to demo how a magnetic levitation train works. It takes advantage of four design elements: (1) an inhomogeneous magnetic field that repels a diamagnetic plate so that it floats about 1 mm above the track, (2) the shape and size of the diamagnetic plate is optimized in a way so that, with the specific permanent magnet in use, the train is guided even at bends along the track without touching the surface, (3) a linear motor using a sensor coil and two drive coils to move the train model forward, (4) solar panels which convert solar energy into electrical energy. The track consists of three rows of neodymium platelets which are aligned in a way so that the two outer rows are inversely polarized to the middle row on which the train model moves. As a diamagnetic material a thin layer of pyrolytic graphite is used. Pyrolytic graphite is a material which is neither ferromagnetic nor paramagnetic so that the repulsive properties of diamagnetism become effective. The linear motor senses the slight disturbances in the magnetic field between the neodymium platelets of the track thanks to the sensor coil. It switches between the two drive coils to that the model train can move along. The little electricity which is needed for the linear motor to operate comes from the solar panels on top of the model train.