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Topic: Lattice


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In the News (Thu 25 Apr 19)

  
  Crystal Lattice Structures
This page offers a concise index of common crystal lattice structures.
A graphical representation as well as useful information about the lattices can be obtained by clicking on the desired structure below.
Other sources of information about crystal lattices can be found at various sites around the Web.
rd.business.com /index.asp?epm=s.1&bdcq=lattice&bdcr=4&bdcu=http://cst-www.nrl.navy.mil/lattice/&bdct=20071111105551&bdcp=&partner=2662601&bdcs=nwuuid-2662601-6519CA6C-D26D-46A3-CB99-ABAE0B1F3565-ym   (207 words)

  
  eMedicine - Lattice Degeneration : Article by David Sarraf, MD
Lattice degeneration is characterized by oval or linear patches of atrophic retina with a reddish base and is variably located within the equatorial region of the fundus, typically inferotemporal.
Retinal detachments caused by lattice degeneration occur most commonly by a tractional tear at the cuff or posterior margin of the lattice lesion or less commonly by means of an atrophic hole within the zone of lattice.
Lattice degeneration complicated by tractional tears as the result of an acute, symptomatic posterior vitreous detachment represents a high-risk situation for future retinal detachment and is an urgent indication for laser retinopexy.
www.emedicine.com /oph/topic397.htm   (2042 words)

  
  Lattice (order) - Wikipedia, the free encyclopedia
Lattices constitute one of the most prominent representatives of a series of "lattice-like" structures which admit order-theoretic as well as algebraic descriptions, such as semilattices, Heyting algebras, and Boolean algebras.
The set of compact elements of an arithmetic complete lattice is a lattice with a least element, where the lattice operations are given by restricting the respective operations of the arithmetic lattice.
These conditions basically amount to saying that there is a functor from the category of sets and functions to the category of lattices and lattice homomorphisms which is left adjoint to the forgetful functor from lattices to their underlying sets.
en.wikipedia.org /wiki/Lattice_(order)   (2282 words)

  
 Lattice article - Lattice mathematical partially ordered supremum infimum Hasse diagrams - What-Means.com   (Site not responding. Last check: )
The elements of a lattice are regularly spaced, reminiscent of the intersection points of a lath lattice.
This concept is used in materials science, in which a lattice is a 3-dimensional array of regularly spaced points coinciding with the atom or molecule positions in a crystal.
It also occurs in computational physics, in which a lattice is an n-dimensional geometrical structure of sites, connected by bonds, which represent positions which may be occupied by atoms, molecules, electrons, spins, etc. For an article dealing with the formal representation of such structures see Lattice Geometries (http://www.hermetic.ch/compsci/lattgeom.htm).
www.what-means.com /encyclopedia/Lattice   (359 words)

  
 PlanetMath: complete lattice
A complete lattice is a nonempty poset in which every nonempty subset has a supremum and an infimum.
In particular, a complete lattice is a lattice.
This is version 1 of complete lattice, born on 2002-08-17.
planetmath.org /encyclopedia/CompleteLattice.html   (56 words)

  
 Lattice (order) - Encyclopedia.WorldSearch   (Site not responding. Last check: )
In mathematics, a lattice is a poset (i.e.
On the other hand, lattices can also be characterized as algebraic structures that satisfy certain identities.
This lattice has the empty set as least element, but it will only contain a greatest element if A itself is finite.
encyclopedia.worldsearch.com /meet.htm   (2298 words)

  
 Handbook of Ocular Disease Management - LATTICE DEGENERATION
Lattice degeneration occurs in eight to 11 percent of the general population.
In lattice degeneration alone, prophylactic treatment is not practical in that the risk of detachment is only 0.1 to 0.7 percent in the phakic eye.
Lattice degeneration both with and without atrophic holes is generally benign and does not require prophylactic treatment, as the complications of treatment are more severe than the natural history of the untreated condition.
www.revoptom.com /handbook/sect5e.htm   (552 words)

  
 Lattice_notes.html
Lattice, for computer-controlled electronics, is based on the just tuning theories of Tenney, Johnston, and others, which represent pitch as an n-dimensional discrete space, or lattice.
That is, xi is the coordinate of R on the n-dimensional lattice's ith axis.
Superp (for superparticular) generates a superparticular ratio of the form n/(n _ 1) where both n and n _ 1 are within the dimensionality of the lattice, and multiplies a point's frequency by this ratio, moving it the necessary distance along the necessary axes.
o-art.org /history/Computer/composers/Scholz/Lattice_notes.html   (1946 words)

  
 The Geometry Junkyard: Geometry of Numbers
Informally, a lattice is an infinite arrangement of points spaced with sufficient regularity that one can shift any point onto any other point by some symmetry of the arrangement.
More formally, a lattice can be defined as a discrete subgroup of a finite-dimensional vector space (the subgroup is often required not to lie within any subspace of the vector space, which can be expressed formally by saying that the quotient of the space by the lattice is compact).
Other types of lattices arise in crystallography and in sphere packing, where they are used to describe the locations of atoms or spheres.
www.ics.uci.edu /~eppstein/junkyard/lattice.html   (669 words)

  
 Lattice   (Site not responding. Last check: )
Lattice is to seek permission to build a liquefied natural gas import terminal at the Isle of Grain in the Medway, and hopes the site will be operational by the end of 2004.
Lattice is forming a £6m joint venture with RWE of Germany to provide transportation services to European gas traders and shippers.
Lattice is considering plans to build a large liquefied natural gas import terminal on the Isle of Grain in Kent, in preparation for the UK becoming a net importer of gas in about 2004.
www.ukbusinesspark.co.uk /latticea.htm   (232 words)

  
 Lead Free
Lattice is fully supportive of the various industry efforts throughout the world to phase out the use of lead and other undesirable elements from electronic equipment materials and manufacturing processes.
Lattice's goal is to develop all new products such that they reduce space, materials and power consumption for an equivalent electrical function.
Lattice lead free packages are qualified to Level 1, 3 or 4 moisture resistance depending on the package type with peak reflow temperatures of 260°C, 250°C or 245°C, consistent with IPC/JEDEC J-STD-020, Moisture/Reflow Sensitivity Classification for Nonhermetic Solid State Surface Mount Devices.
www.latticesemi.com /products/packaging/leadfree/index.cfm   (658 words)

  
 Wallpaper Groups: lattices
That's because in that case, the points in the lattice nearest any one point in the lattice are the vertices of a regular hexagon.
Lattices are special kinds of patterns, and their symmetry groups of five of these 17 groups.
Since a square is simultaneously a rectangle and a rhombus, square lattices have all the symmetries of both rectangular lattices and rhombic lattices.
www.clarku.edu /~djoyce/wallpaper/lattices.html   (864 words)

  
 Reciprocal Lattice
The relationship between the period and frequency is similar to that of the reciprocal and the direct lattice.
Therefore Fourier transformation is used in the studies of the real lattice to yield the reciprocal lattice in the same fashion as with the studies of any other periodic function, therefore the reciprocal space is also called Fourier space.
Because the rods are infinitely dense lattice points, the diffraction from a surface occurs continuously with changes in the direction and the magnitude of the incident wavevector as long as the wave is short enough to be diffracted.
www.chembio.uoguelph.ca /educmat/chm729/recip/vlad.htm   (1065 words)

  
 Lattice Corporate Profile   (Site not responding. Last check: )
Lattice is widely recognized as the first company to provide the C programming language on the IBM PC in 1982.
Lattice C remained the premier C Compiler on the PC platform for many years and Lattice C was ported to numerous other platforms including mainframes, mini computers, workstations, and non-IBM compatible PC’s.
Lattice was the first company to introduce a library of C routines to access and update dBASE database files, enabling C programmers to utilize data in dBASE files at a time when dBASE was a very popular programming language.
www.lattice.com /corp.htm   (600 words)

  
 Leech lattice - Wikipedia, the free encyclopedia
In mathematics, the Leech lattice is a lattice Λ in R
There are 23 orbits of them, and they correspond to the 23 Niemeier lattices other than the Leech lattice.
Conway showed that the Leech lattice is isometric to the Dynkin diagram of the reflection group of the 26-dimensional even Lorentzian unimodular lattice II
en.wikipedia.org /wiki/Leech_lattice   (413 words)

  
 Lattice Energy
The Lattice energy, U, is the amount of energy requried to separate a mole of the solid (s) into a gas (g) of its ions.
As defined, the lattice energy is positive, because energy is always required to separate the ions.
When methods to evaluate the energy of crystallization or lattice energy lead to reliable values, these values can be used in the Born-Hable cycle to evaluate other chemical properties, for example the electron affinity, which is really difficult to determine directly by experiment.
www.science.uwaterloo.ca /~cchieh/cact/applychem/lattice.html   (818 words)

  
 Index to Catalogue of Lattices
This data-base of lattices is a joint project of Gabriele Nebe, University of Ulm, nebe(AT)mathematik.uni-ulm.de, and Neil J. Sloane, AT&T Labs-Research, njas(AT)research.att.com.
The E_n lattices and their duals: E6, E6*, E7, E7a (a second version of E7), E7*, E8, E8 as a Hurwitzian lattice.
, a 5-modular lattice in the "+" genus.
www.research.att.com /~njas/lattices   (1893 words)

  
 The GIS Procedure : LATTICE Statement
The LATTICE statement defines the relationships between areas in a spatial database, that is, it defines which areas enclose other smaller areas (such as states enclose counties).
When a lattice hierarchy is defined, the area composite values for new points are assigned automatically as the points are added to the map.
A lattice definition also makes it possible to simultaneously assign attribute values to all points in a point layer by setting area attributes in the GIS Layer window.
www.sph.emory.edu /computing/unix/sas/sas8OnlineDoc/gis/z1028444.htm   (592 words)

  
 Lattice C   (Site not responding. Last check: )
Renn, SR and Lubensky, TC Abrikosov dislocation lattice in a...
Lattice C (according to its author, Lattice Corporation) was the first C compiler for the IBM PC, in 1982.
The compiler was subsequently repackaged by Microsoft under a distribution agreement as Microsoft C. In 1987 Lattice was bought by SAS Institute (not, as often alleged, by Microsoft).
www.wikiverse.org /lattice-c   (268 words)

  
 Bravais lattices
Cubic lattices are of interest since a large number of materials have a cubic lattice.
The three cubic Bravais lattices are the simple cubic lattice, the body centered cubic lattice and the face centered cubic lattice.
The face centered lattice equals the simple cubic lattice with the addition of a lattice point in the center of each of the six faces of each cube.
ece-www.colorado.edu /~bart/book/bravais.htm   (680 words)

  
 Lattice Geometries
The method of representation of lattice geometries described in this article was used in the software developed by the author to simulate the behavior of magnetic material by means of Ising and Potts spin models, as described in detail in his M.Phil.
The dimensionality of a lattice is the dimensionality of the Cartesian space used to define that lattice.
The "diamond" lattice, of dimensionality 3, is the geometry formed by carbon atoms in a diamond crystal.
www.hermetic.ch /compsci/lattgeom.htm   (1805 words)

  
 Lattice Semiconductor Acquires Vantis Corporation from AMD
Lattice products are sold worldwide through an extensive network of independent sales representatives and distributors, primarily to original equipment manufacturers ("OEMs") of communications, computing, industrial controls and military systems.
Lattice was founded in 1983 and is based in Hillsboro, Oregon.
Lattice Semiconductor, L (stylized) Lattice and isp, are either registered trademarks or trademarks of Lattice Semiconductor Corporation in the United States and/or other countries.
www.vantis.com /corporate/press/corporate/1999/pr042199.cfm   (891 words)

  
 Crystal Lattice Structures   (Site not responding. Last check: )
This lattice is "closest packed", because spheres of equal size occupy the maximum amount of space in this arrangment (74.05%); since this closest packing is based on a cubic array, it is called "cubic closest packing": CCP = FCC.
The Td cavities reside on a SC lattice which is half the dimension of the CCP lattice.
Zinc Blende lattices - The lattice of cations in zinc blende is a FCC lattice of the same dimension as the anion lattice, so the structure can be described as interpenetrating FCC lattices of the same unit cell dimension.
members.iworld.net /joo/physics/curri-sub/crystal/lattice.html   (1058 words)

  
 modular robotics: Lattice
Robots that use lattice reconfiguration are self-reconfigurable robots that rearrange their positions by moving from one position on a lattice to a neighboring position on the lattice, like LEGO(r) bricks that could rearrange themselves.
For example, in 2D, a lattice could be a rectilinear grid and the modules (usually all identical) move from one square to another.
The lattice structure makes planning the motions of when and where to move modules an interesting one from a computer science point of view as the space of possible motions is easy to represent in a computer.
www2.parc.com /spl/projects/modrobots/lattice   (349 words)

  
 Lattice Energy
An estimate of the strength of the bonds in an ionic compound can be obtained by measuring the lattice energy of the compound, which is the energy given off when oppositely charged ions in the gas phase come together to form a solid.
The lattice energy of NaCl, for example, is 787.3 kJ/mol, which is only slightly less than the energy given off when natural gas burns.
The lattice energy of a salt therefore gives a rough indication of the solubility of the salt in water because it reflects the energy needed to separate the positive and negative ions in a salt.
chemed.chem.purdue.edu /genchem/topicreview/bp/ch7/lattice.html   (430 words)

  
 Lattice MS-DOS & OS/2 C Development System   (Site not responding. Last check: )
Lattice C includes LASM, a blazing fast macro assembler that lets you performance tune your applications with assembly language modules.
In addition, Lattice C Compilers and Cross Compilers available for a wide range of operating systems on micros, minis, and mainframes give you have unmatched portability for the programs you create.
LMK Lattice Make Utility automates project management and guarantees that all the correct files are compiled with the correct options whenever changes are made in any of a complex application's modules.
www.lattice.com /otherdos.htm   (1856 words)

  
 Photonic lattice
The lattice, dubbed a photonic crystal (crystals have regularly repeating internal structures), now works in the infrared range (approximately 10-micron wavelengths).
The nearly leak-proof lattices form a cage that trap and guide approximately 95 percent of the light sent within them, as compared with approximately 30 percent for conventional waveguides, and they take only one-tenth to one-fifth the space to bend the light.
Gears that spin require spaces between parts; specifically, a silicon base is covered with an expendable coating in which a part can be etched, and then the expendable portion is removed by chemical and mechanical means, leaving the gear or axle unencumbered by surrounding material and thus able to spin freely [http://mems.sandia.gov/scripts/].
www.sandia.gov /media/photonic.htm   (1240 words)

  
 Ian's Shoelace Site - Lattice Lacing
Great for boots and sneakers with a wide gap, this method forms a neat woven lattice in the middle of the lacing.
Alternatively, feed the laces into the top two eyelets; this makes for a neater lattice, though the knot is then a little more difficult to tie.
Although Lattice Lacing works best on shoes with six pairs of eyelets, here's some simple diagrams for adapting it to work with different numbers of eyelet pairs.
www.fieggen.com /shoelace/latticelacing.htm   (660 words)

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