Helmholtz's theorems. In fluid mechanics, Helmholtz's theorems, named after Hermann von Helmholtz, describe the three-dimensional motion of fluid in the vicinity of vortex filaments. These theorems apply to inviscid flows and flows where the influence of viscous forces are small and can be ignored. Helmholtz’s three theorems are as follows:Helmholtz’s first theorem: The strength of a vortex filament is constant along its length. Helmholtz’s second theorem: A vortex filament cannot end in a fluid; it must extend to the boundaries of the fluid or form a closed path. Helmholtz’s third theorem: In the absence of rotational external forces, a fluid that is initially irrotational remains irrotational. Helmholtz’s theorems apply to inviscid flows. Alternative expressions of the three theorems are as follows: 1. Helmholtz’s theorems have application in understanding: Starting vortex Horseshoe vortex Wingtip vortices.
Helmholtz’s theorems are now generally proven with reference to Kelvin's circulation theorem. Notes Helmholtz theorem. Helmholtz theorem (classical mechanics) The Helmholtz theorem of classical mechanics reads as follows: Let is the kinetic energy and is a "U-shaped" potential energy profile which depends on a parameter . Let denote the time average. Let Then The thesis of this theorem of classical mechanics reads exactly as the heat theorem of thermodynamics.
Is given by time average of the kinetic energy, and the entropy ). Helmholtz, H., von (1884a). Helmholtz's theorems. AlterNet - Photos du journal. Obama is picking his targets in Iraq and Syria while missing the point. “We are now living in what we might as well admit is the Age of Iraq,” New York Times op-ed columnist David Brooks recently wrote. There, in the Land of the Two Rivers, he continued, the United States confronts the “core problem” of our era — “the interaction between failing secular governance and radical Islam.”
Brooks is wrong. For starters, he misconstrues the core problem — which is a global conflict pitting tradition against modernity. Traditionalists, especially numerous in but not confined to the Islamic world, cling to the conviction that human existence should be God-centered human order. Proponents of modernity, taking their cues from secularized Western elites, strongly prefer an order that favors individual autonomy and marginalizes God. Not God first, but we first — our own aspirations, desires and ambitions. This conflict did not originate in nor does it emanate from Iraq. The effort failed abysmally. All the military power in the world won’t solve those problems. Closed-form expression. Problems are said to be tractable if they can be solved in terms of a closed-form expression.
Example: roots of polynomials is closed-form since its solutions can be expressed in terms of elementary functions: Similarly solutions of cubic and quartic (third and fourth degree) equations can be expressed using arithmetic, square roots, and cube roots, or alternatively using arithmetic and trigonometric functions. However, there are quintic equations without closed-form solutions using elementary functions, such as x5 − x + 1 = 0. An area of study in mathematics referred to broadly as Galois theory involves proving that no closed-form expression exists in certain contexts, based on the central example of closed-form solutions to polynomials. Closed-form vs. analytical expressions Dealing with non-closed-form expressions Transformation into closed-form expressions The expression: Differential Galois theory whose antiderivative is (up to constants) the error function:
HTML URL Encoding Reference. Harmonic function. This article is about harmonic functions in mathematics. For harmonic function in music, see diatonic functionality. everywhere on U. This is usually written as or Examples Examples of harmonic functions of two variables are: The real and imaginary part of any holomorphic functionThe function ; this is a special case of the example above, as , and is a holomorphic function.The function defined on (e.g. the electric potential due to a line charge, and the gravity potential due to a long cylindrical mass) Examples of harmonic functions of three variables are given in the table below with Finally, examples of harmonic functions of n variables are: The constant, linear and affine functions on all of Rn (for example, the electric potential between the plates of a capacitor, and the gravity potential of a slab)The function on for n > 2. Remarks If f is a harmonic function on U, then all partial derivatives of f are also harmonic functions on U. .
Properties of harmonic functions with. HIM: Description. Hausdorff Trimester Program May 5 - August 22, 2014 Organizers: Herbert Koch, Daniel Tataru, Christoph Thiele Harmonic analysis and partial differential equations have been closely interlinked areas in recent decades, with ideas flowing back and forth and stimulating progress in both areas. This program will bring together researchers in these two fields, some who have worked in both fields and some who have specialized in one field but are interested in learning more about the other.
Four workshops will take place: Confirmed senior participants: Pascal Auscher, Jonathan Bennett, Michael Christ, Guy David, Jean-Marc Delort, Ciprian Demeter, Benjamin Dodson, Thomas Duyckaerts, Patrick Gerard, Sebastian Herr, Steven Hofmann, Tuomas Hytönen, Alexandru Ionescu, Rowan Killip, Joachim Krieger, Michael T. Harmonic Analysis and Partial Differential Equations | Clay Mathematics Institute. Rodrigues' formula. Statement Rodrigues stated his formula for Legendre polynomials A similar formula holds for many other sequences of orthogonal functions arising from Sturm-Liouville equations, and these are also called the Rodrigues formula for that case, especially when the resulting sequence is polynomial. References Electric potential. The electric potential at a point is equal to the electric potential energy (measured in joules) of any charged particle at that location divided by the charge (measured in coulombs) of the particle.
Since the charge of the test particle has been divided out, the electric potential is a "property" related only to the electric field itself and not the test particle. The electric potential can be calculated at a point in either a static (time-invariant) electric field or in a dynamic (varying with time) electric field at a specific time, and has the units of joules per coulomb (J C–1), or volts (V). There is also a generalized electric scalar potential that is used in electrodynamics when time-varying electromagnetic fields are present. This generalized electric potential cannot be simply interpreted as the ratio of potential energy to charge, however. Introduction Force and potential energy are directly related.
In electrostatics Electric potential due to a point charge Gauge fixing. Although the unphysical axes in the space of detailed configurations are a fundamental property of the physical model, there is no special set of directions "perpendicular" to them. Hence there is an enormous amount of freedom involved in taking a "cross section" representing each physical configuration by a particular detailed configuration (or even a weighted distribution of them).
Judicious gauge fixing can simplify calculations immensely, but becomes progressively harder as the physical model becomes more realistic; its application to quantum field theory is fraught with complications related to renormalization, especially when the computation is continued to higher orders. Historically, the search for logically consistent and computationally tractable gauge fixing procedures, and efforts to demonstrate their equivalence in the face of a bewildering variety of technical difficulties, has been a major driver of mathematical physics from the late nineteenth century to the present. .
Coulomb's law. Coulomb's law, or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. The law was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism. It is analogous to Isaac Newton's inverse-square law of universal gravitation. Coulomb's law can be used to derive Gauss's law, and vice versa. The law has been tested heavily, and all observations have upheld the law's principle.
History Charles Augustin de Coulomb Early investigators of the 18th century who suspected that the electrical force diminished with distance as the force of gravity did (i.e., as the inverse square of the distance) included Daniel Bernoulli and Alessandro Volta, both of whom measured the force between plates of a capacitor, and Franz Aepinus who supposed the inverse-square law in 1758. The law Coulomb's law states that: and respectively, where to ).
By. Electric potential energy. Electric potential energy, or electrostatic potential energy, is a potential energy (measured in joules) that results from conservative Coulomb forces and is associated with the configuration of a particular set of point charges within a defined system. An object may have electric potential energy by virtue of two key elements: its own electric charge and its relative position to other electrically charged objects.
The term "electric potential energy" is used to describe the potential energy in systems with time-variant electric fields, while the term "electrostatic potential energy" is used to describe the potential energy in systems with time-invariant electric fields. Definition The electrostatic potential energy can be defined in terms of the electric field or in terms of the electric potential. Where E is the electrostatic field and ds is the displacement vector in a curve from the reference position rref to the final position r. where Units Notes References Magnet link linux. What are your must haves for your Linux machine? : linux4noobs. Data Encryption. GNU Privacy Guard. MagnetUri - Public rTorrent Community Wiki.
1. Introduction To learn all about magnet links, read the Wikipedia article. Magnet URIs are implemented in the stable version 0.8.9, and can be loaded from a watch directory via special bencoded files (note that the unstable 0.9.0 has a bug regarding loading these files). At the time of this writing, rTorrent is able to get torrent files via DHT, but does not distribute them itself. And yes, "getting them via DHT" implies that you need to activate DHT for magnets to do anything at all. Copy the magnet link to the clipboard, press Backspace or Enter in rTorrent, then simply paste the link into the prompt and press Enter again. 3.
An already working installation of PyroScope is assumed here, so the mktor command is available. Update PyroScope to the latest SVN head revision (beyond r1746). Then set mktor as the magnet: URI handler Firefox Linux: Open about:config in a Firefox tab. 4. 4.1. Make the script executable chmod 0755 magnet.sh Run the script with a magnet URI: . 4.2. 5. PyroScope - Public rTorrent Community Wiki. QuickStartGuide - pyroscope - How to get started - installation and first steps. - Python Torrent Tools. InstallReleaseVersion - pyroscope - How to get started - installation and first steps. - Python Torrent Tools. Use InstallFromSource, the release version is out of date ➽ If you want to update your already installed software, go to the MigrationGuide instead! For a working installation, you have to meet these requirements first: Python 2.5 or a higher 2.x version (2.6 is recommended); go to if you're on an OS that doesn't have Python out of the box. for rtcontrol and rtxmlrpc, an existing rTorrent installation, with the xmlrpc option compiled in and the scgi_local or scgi_port command added to your ~/.rtorrent.rc.
Using rTorrent 0.9.2, 0.8.9 or 0.8.6 is recommended — PyroScope should work together with older versions though, up to a point. On Debian, Ubuntu, and other Debian-derived distributions, do this: sudo apt-get install python-setuptoolssudo easy_install --prefix /usr/local pyrocore After that, the CommandLineTools should be immediately available in your shell prompt. Debian, Ubuntu, and other Debian-derived distributions Arch Linux Other Linux variants and Mac OSX. rTorrent. "libTorrent" redirects here. It is not to be confused with libtorrent. Technical details rTorrent packages are available for various Linux distributions and Unix-like systems, and it will compile and run on nearly every POSIX-compliant operating system, such as FreeBSD and OS X. rTorrent uses ncurses and is suitable for use with screen; it uses commands such as Carriage return to load a torrent, after which ^S can be used to start a torrent (where ^ is shorthand for Ctrl key), backspace can be used to automatically start a torrent once it is loaded, making a subsequent issue of ^S unnecessary, ^K for stop, and ^D for pause, or if already paused or stopped, ^D again to delete the torrent. It supports saving of sessions and allows the user to add and remove torrents.
It also supports partial downloading of multi-file torrents. rTorrent can be controlled via XML-RPC over SCGI. ruTorrent is a popular Web-based interface. See also Comparison of BitTorrent clients References Displacement current. In electromagnetism, displacement current is a quantity appearing in Maxwell's equations that is defined in terms of the rate of change of electric displacement field. Displacement current has the units of electric current density, and it has an associated magnetic field just as actual currents do.
However it is not an electric current of moving charges, but a time-varying electric field. In materials, there is also a contribution from the slight motion of charges bound in atoms, dielectric polarization. The idea was conceived by James Clerk Maxwell in his 1861 paper On Physical Lines of Force, Part III in connection with the displacement of electric particles in a dielectric medium. Maxwell added displacement current to the electric current term in Ampère's Circuital Law. Explanation The electric displacement field is defined as: where: ε0 is the permittivity of free space E is the electric field intensity The modern justification of displacement current is explained below. where and. Legendre's equation. Generating function. Sturm–Liouville theory. Bessel function. Integrating factor. Python+-2.6.4-i486.pet - puppy-development - Complete Python PyGobject PyGtk PySqlite2 set to NOT compile bytecode files - Puppy Linux Development Tree.
Sha1sum. Magnetic potential. Kernel -- from Wolfram MathWorld. Induced Electric Field. Magnetic potential. Faraday's law of induction. Faraday's law of induction. Aharonov–Bohm effect. Covariant formulation of classical electromagnetism. Maxwell's equations. THE DISPLACEMENT CURRENT AND MAXWELLS EQUATIONS. A Dynamical Theory of the Electromagnetic Field.