Orphan date February 2009 Expert subject physics date November 2008 Thermodynamic length is a Riemannian metric defined on a manifold of thermodynamic state s. Clarify date November 2008 Category Thermodynamics Physics stub ... more details
NOTOC For the measurement of an ammunition cartridge Overall length Image LOA LWL.svg thumb right 300px LOA Length Overall & LWL Waterline Length Image Ship length measurements.png thumb right 300px Detailed hull dimensions Length overall , often abbreviated as LOA , o a , o.a. or oa refers to the maximum length of a vessel from the two points on the hull measured perpendicular to the waterline. Length overall is commonly used to indicate maximum length of a vessel. LOA is the most commonly used way of expressing the size of a boat, and is also used for calculating the cost of a marina Berth moorings berth ref cite web url http www.mosquitocreekmarina.com moorage.html title Boat Moorage publisher Mosquito Creek Marina accessdate 2009 07 13 ref for example, 2.50 per metre LOA . As said, LOA often means length of the hull. ref cite web url http www.westlawn.edu student center definitions.asp title Definitions of Boat, Yacht, Small Craft, and Related Terms publisher Westlawn Institute of Marine ... http books.google.com ?id 9 7ycOuv6a4C&pg PA64&dq LOA length overall LOD donald title Dictionary ... ?id QgMRudqoLGQC&pg PR19&dq length overall unambiguously tons gross last Sch uffelen first ... publisher Wilh. Wilhelmsen ASA accessdate 2009 07 18 ref Sparred length , Total length including bowsprit , Mooring length and LOA including bowsprit are other expressions that might indicate the full length of a sailing ship. LOH In ISO 8666 for small boats, cited by a product description, ref ... International page 4 format PDF ref there is a definition of LOH, length of hull, ref cite ... 2009 07 18 ref that measures shorter than LOA. LWL Another measure of length is LWL loaded waterline length which is more useful in assessing a vessel s performance. In some cases particularly old yacht s or vessels with bowsprit s LWL can be considerably shorter than LOA. See also Overall length ... of Historic Vessels The National Register of Historic Vessels Length between perpendiculars References ... more details
For the measurement of a ship s lengthlength overall The overall length of an ammunition Cartridge firearms cartridge is a measurement from the base of the brass Shell projectile shell Casing ammunition casing to the tip of the bullet , seated into the brass casing. ref name COTW2009 cite book title Cartridges of the World A Complete and Illustrated Reference for Over 1500 Cartridges first Frank C. last Barnes coauthors Holt Bodinson, Layne Simpson edition 12 page 157 publisher Gun Digest Books year 2009 isbn 9780896899360 ref Handloaded cartridges and commercially available cartridges for firearm s are normally created with a maximum length standardized by the Sporting Arms and Ammunition Manufacturers Institute SAAMI . A cartridge s overall length may be shorter than the maximum standard, equal to the standard, or sometimes even longer. The maximum overall length is dictated by the need to fit into a box magazine of standard manufacture. For example, the .223 Remington cartridge, when loaded for use in the AR 15 rifle or the military s M16 rifle M 16 rifle , has to fit into the removable box magazine for that rifle. This dictates that the cartridge s maximum overall length be no greater than 2.260 . However, for competition purposes during off hand and slow fire prone match stages, the .223 Remington is loaded one cartridge at a time into the rifle s receiver. This allows for the cartridge to be longer than the standardized 2.260 SAAMI maximum overall length. These cartridges can be safely loaded to a length that has the ogive portion of the bullet just touching the rifle s lands. Many competitive shooters will make these cartridges 0.005 less than the truly maximum allowable overall length, for the sake of safety. ref name ABC cite book title The ABCs of Reloading The Definitive Guide for Novice to Expert first Rodney last James edition 9 page 127 publisher Krause Publications year 2011 isbn 9781440213960 ref It is desirable for these single loaded cartridges to have ... more details
Refimprove date December 2009 The Kuhn length is a theoretical treatment, developed by Werner Kuhn , in which a real polymer chain is considered as a collection of math N math Kuhn segments each with a Kuhn length math b math . Each Kuhn segment can be thought of as if they are freely jointed with each other. ref Flory, P.J. 1953 Principles of Polymer Chemistry , Cornell Univ. Press, ISBN 0 8014 0134 8 ref ref Flory, P.J. 1969 Statistical Mechanics of Chain Molecules , Wiley, ISBN 0 470 26495 0 reissued 1989, ISBN 1 56990 019 1 ref ref Rubinstein, M., Colby, R. H. 2003 Polymer Physics , Oxford University Press, ISBN 0 19 852059 X ref Each segment in a freely jointed chain can randomly orient in any direction without the influence of any forces, independent of the directions taken by other segments. Thus the real chain consisting of math n math bonds and with fixed bond angles and bond lengths is replaced by an equivalent chain with math N math connected Kuhn segments that can orient in any random direction. The length of a fully stretched chain or the contour length is math L Nb math for the Kuhn segment chain. In the simplest treatment, such a chain follows the random walk model, where each step taken in a random direction is independent of the directions taken in the previous steps, forming a random coil . The average end to end distance for a chain satisfying the random walk model is math R 2 Nb 2 math . Since the space occupied by a segment in the polymer chain cannot be taken ... homopolymer chain consists of the same repeat units with bond length math l math and bond angle ... cos textstyle phi , math is the average cosine of the dihedral angle. Also the fully stretched length ... length math b math can be obtained. File Molecule 1.jpg thumb Bond angle For worm like chain semiflexible chain , Kuhn length equals two times the persistence length ref Gert R. Strobl 2007 The physics ... ref . References Reflist DEFAULTSORT Kuhn Length Category Polymer chemistry Category Polymer physics ... more details
Determining the length of an irregular arc segment is also called rectification of a curve . Historically ... to calculate the length of each linear segment using the Pythagorean theorem in Euclidean space, for example , the total length of the approximation can be found by summation summing ... arbitrarily small . For some curves there is a smallest number L that is an upper bound on the length ... and the curve is defined to have arc length L . Finding arc lengths by integrating See also Differential geometry of curves Length and natural parametrization l1 Differential geometry of curves Consider ... dx math its derivative with respect to x are continuous function continuous on a , b . The length ... arc length between t a and t b is math s int a b sqrt X t 2 Y t 2 , dt. math This is more clearly ... in polar coordinate system polar coordinates by math r f theta math then the arc length is given ... even simple curves, there are no Solution in closed form closed form solutions of arc length and numerical integration is necessary. Curves with closed form solution for arc length include the catenary ... line mathematics straight line . The lack of closed form solution for the arc length of an Ellipse ... t sup 5 sup , x t sup 3 sup In order to approximate the arc length of the curve, it is split into many ... that its length element of the arc length will be the differential mathematics differential ds . We ... length from x a to x b of the graph of the function . For example, the curve in this figure is defined by math begin cases y t 5, x t 3. end cases math Subsequently, the arc length integral for values ... computational approximations, we can obtain a very accurate but still approximate arc length of 2.905 ... a rectifiable curve given by a function f x . To approximate the arc length S along f between ... exists. The length of any given hypotenuse is given by the Pythagorean Theorem math sqrt Delta x ... right 2 , Delta x i math As the length math Delta x math of these segments decreases, the approximation ... more details
Unreferenced date December 2009 Line and length in cricket refers to the direction and point of bouncing on the pitch cricket pitch of a delivery cricket delivery . The two concepts are frequently discussed together. Line The line of a cricket delivery is the direction of its trajectory measured in the Horizontal plane horizontal axis. More simply, it is a measure of how far to the left or right the ball is travelling, compared to a line drawn straight down the pitch. It is usually referred to in terms of the directions Fielding cricket Off and leg side fields off away in front of the batsman and leg side leg in towards or behind the batsman , rather than left and right, however. Line controls how much room the batsman has to play various shots, and sometimes dictates what shot he must play. A line directed at the wicket , for example, must be defended with the bat, as failing to hit the ball will result in the batsman being dismissal cricket out bowled , whilst a batsman blocking the ball ... since been outlawed. See Bodyline for full details. Length File Length cricket .svg thumb right 325px A diagram showing the relative positions of short, good and full lengths The length of a delivery ... bouncing closer to the bowler , long or full bouncing nearer the batsman , or a good length an optimal length, somewhere in between . The length of a ball controls how high the ball rises from the pitch ... horizontally in its flight, also making it easier for the batsman to hit. A good length ball is a compromise ..., but not so far that he can react easily to hit it. For quick bowlers the good length ball ... three to four metres before the batsman. Though the optimal length will vary according to the state .... A bowler can use variation in length to upset the rhythm of a batsman. A typical sequence would be a series .... If the batsman does not react to the change in length quickly enough, he can be left with his ... being hit, and may intimidate him into uncertainty about the next few balls. DEFAULTSORT Line And Length ... more details
A cable length or cable s length is a nautical Units of measurement unit of measure equal to one tenth of a nautical mile or 100 fathoms , or sometimes 120 fathoms. The unit is named after the length of a ship s anchor cable in the age of sail . The definition varies International frac 10 nautical mile , or 185.2 metre m Imperial units Imperial Admiralty frac 10 Nautical mile Admiralty mile convert 185.2 m ft lk on , or 101 fathom s The traditional British fathom varied from 5 feet to 7 feet in the Merchant Navy . United States customary units U.S. customary US Navy 120 fathoms 720 feet, 219.456 m References citation author Fenna, Donald year 2002 contribution cable, cable length, cable s length title A Dictionary of Weights, Measures, and Units location Oxford publisher University Press isbn 0198605226 . Also fathom , from the same work. citation url http web.archive.org web 20080707042523 http www.royal navy.mod.uk server show nav.3807 content title Navy Slang Cable Curry publisher Royal Navy accessdate February 2011 . See also Conversion of units Category Units of length Category Nautical terms be x old cs Kabel jednotka de Kabell nge et Kaabeltau el es Cable unidad de longitud fr Encablure he hr Kabel mjera lv Kabe tauva mk nl Kabellengte ja no Kabellengde nn Kabellengd pl Kabel jednostka ru fi Kaapelinmitta sv Kabell ngd tr Gomina uk ... more details
The Richard Tolman Tolman length math delta math also known as Tolman s delta measures the extent by which the surface tension of a small liquid drop deviates from its planar value. It is conveniently defined in terms of an expansion in math 1 R math , with math R R e math the equimolar radius of the liquid drop, of the pressure difference across the droplet s surface center math Delta p frac 2 sigma R left 1 frac delta R ldots right math 1 center In this expression, math Delta p p l p v math is the pressure difference between the bulk pressure of the liquid inside and the pressure of the vapour outside, and math sigma math is the surface tension of the planar interface , i.e. the interface with zero curvature math R infty math . The Tolman length math delta math is thus defined as the leading order correction in an expansion in math 1 R math . Another way to define the tolman length is to consider the radius dependence of the surface tension, math sigma R math . To leading order in math 1 R math one has center math sigma R sigma left 1 frac 2 delta R ldots right math 2 center Here math ... length is defined as a coefficient in an expansion in math 1 R math and therefore does not depend on R. Furthermore, the Tolman length can be related to the radius of spontaneous curvature when ... center math delta sigma frac 2k R 0 math center Any result for the Tolman length therefore gives information about the radius of spontaneous curvature, math R 0 math . If the Tolman length is known ... length implies a negative math R 0 math and a preferred curvature towards the vapour phase. Apart from being related to the radius of spontaneous curvature, the Tolman length can also be linked to the surface ... of tension. Using the Gibbs adsorption equation , Tolman himself showed that the Tolman length can ... Gibbs Gibbs yields the value of the Tolman length center math delta lim R s rightarrow infty R e ... making the magnitude of the Tolman length in the order of nanometers. References R.C. Tolman, J ... more details
No footnotes date January 2010 In physics , the attenuation length or absorption length is the distance math lambda math into a material when the probability has dropped to math 1 e math that a Elementary particle particle has not been Absorption electromagnetic radiation absorbed . Alternatively, if there is a beam of particles incident on the material, the attenuation length is the distance where the intensity physics intensity of the beam has dropped to math 1 e math , or about 63 of the particles have been stopped. Mathematically, the probability of finding a particle at depth x into the material is calculated by Beer Lambert law math P x e x lambda , math . In general math lambda math is material dependent. See also Beer s Law Mean free path Attenuation coefficient Attenuation electromagnetic radiation Radiation length References S. Eidelman et al. Particle Data Group , Review of particle physics , Phys. Lett. B 592 2004 http pdg.lbl.gov http www.ct.infn.it rivel Glossario node2.html External links http henke.lbl.gov optical constants atten2.html Category Particle physics Category Experimental particle physics particle stub de Absorptionsl nge it Lunghezza di attenuazione ... more details
In mathematics , especially in the area of algebra known as group theory , the Fitting length or nilpotent length measures how far a solvable group is from being nilpotent group nilpotent . The concept is named after Hans Fitting , due to his investigations of nilpotent normal subgroups . Definition A Fitting chain or Fitting series or visible anchor nilpotent series for a group mathematics group is a subnormal series with nilpotent group nilpotent quotient group quotients . In other words, a finite sequence of subgroup s including both the whole group and the trivial group, such that each is a normal subgroup of the previous one, and such that the quotients of successive terms are nilpotent groups. The Fitting length or nilpotent length of a group mathematics group is defined to be the smallest possible length of a Fitting chain, if one exists. Upper and lower Fitting series Just as the upper central series and lower central series are extremal among central series , there are analogous series extremal among nilpotent series. For a finite group H , the Fitting subgroup Fit H is the maximal normal nilpotent subgroup, while the minimal subgroup such that the quotient by it is nilpotent is sub sub H , the intersection of the finite lower central series , which is called the nilpotent residual . These correspond to the center and the commutator subgroup for upper and lower central ... series, at each step taking the minimal possible subgroup. Examples A group has Fitting length ... Fitting length 2. The tetrahedral group symmetric group on four points has Fitting length 3. The symmetric ... product of n copies of the symmetric group on three points has Fitting length 2 n . Properties ... sup i sup G , and F sub i sub G H sub n i sub . For a solvable group, the length of the lower Fitting series is equal to length of the upper Fitting series, and this common length is the Fitting length ... length first Alexandre last Turull note the typos, Fitting height versus Fitting length springer ... more details
In physics , length contraction according to Hendrik Lorentz is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any non zero velocity relative to that observer ... , the length is 99.9 of the length at rest at a speed of 42,300,000 m s 95 million mph, .141c , the length is still 99 . As the magnitude of the velocity approaches the speed of light, the effect ... where math L 0 math is the proper length the length of the object in its rest frame , math L math is the length ... in relative movement, the length of the object is measured by subtracting the simultaneously ... would observe the length of the object in the direction of motion as very near zero. History Main History of special relativity Length contraction was postulated by George Francis FitzGerald 1889 and Hendrik ... the hypothesis of the stationary aether Lorentz ether theory Length contraction Lorentz ... as of electromagnetic origin, and length contraction appeared to be a direct consequence of this model ... a dynamical explanation for length contraction. But this model was subject to the same problem as the original hypotheses Length contraction and the non electromagnetic forces were only invented ... that length contraction was no dynamical effect in the aether, but rather a kinematic effect due ... meaning of all relativistic effects in spacetime . So length contraction is not of Kinetics physics ... and the observed object is zero, then the proper length math L 0 math of the object can simply be determined ... was passing by at the same time . It s clear that distance AB is equal to length math L math ... distant than those of A and C. Thus the definition of simultaneity is crucial for measuring the length ... . As the result of this transformation see Derivation , the proper length remains unchanged and always denotes the greatest length of an object, yet the length of the same object as measured in another inertial frame is shorter than the proper length. This contraction only occurs in the line of motion ... more details
Mergeto Jeans instability date May 2009 Jeans length is the critical radius of a cloud typically a cloud of interstellar dust where thermal energy, which causes the cloud to expand, is counteracted by gravity, which causes the cloud to collapse. It is named after the British astronomer Sir James Jeans , who concerned himself with the stability of spherical nebula in the early 1900s. ref cite journal jstor 90845 title The Stability of a Spherical Nebula year 1902 journal Philosophical Transactions of the Royal Society of London ref The formula for Jeans Length is math lambda J sqrt frac 15k B T 4 pi G mu rho math where math k B math is Boltzmann s constant , math T math is the temperature of the cloud, math r math is the radius of the cloud, math mu math is the mass per particle in the cloud, math G math is the Gravitational Constant and math rho math is the cloud s mass density i.e. the cloud s mass divided by the cloud s volume . http scienceworld.wolfram.com physics JeansLength.html Perhaps the easiest way to conceptualize Jeans Length is in terms of a close approximation, in which we discard the factors math 15 math and math 4 pi math and in which we rephrase math rho math as math frac M r 3 math . The formula for Jeans Length then becomes math lambda J approx sqrt frac k B Tr 3 GM mu math It is then immediately obvious that math lambda J r math when math k B T frac GM mu r math i.e. the cloud s radius is the Jeans Length when thermal energy per particle equals gravitational work per particle. At this critical length the cloud neither expands nor contracts. It is only when thermal energy is not equal to gravitational work that the cloud either expands and cools or contracts and warms, a process that continues until equilibrium is reached. Jeans Length as oscillation wavelength The Jeans Length is the oscillation wavelength below which stable oscillations rather than gravitational collapse will occur. math lambda J frac 2 pi k J c s left frac pi G rho right 1 2 math ... more details
length for side slip defined by Pacejka is higher than the relaxation length determined from the steady state side force. accessdate 2010 10 31 ref The relaxation length assotiated with camber thrust has been found to be nearly zero. ref name Cossalter Importance A tire s relaxation length controls ... of Technology pages 16 quote the relaxation length plays an important role in the shimmy phenomenon ... more details
refimprove date December 2011 In telecommunications , electrical length is the length of a transmission medium or antenna electronics antenna element expressed as the number of wavelength s of the Signalling telecommunication signal propagating in the medium. Electromagnetic waves propagate more slowly in a medium than in free space, so a wave in a medium will have a larger number of waves than a wave of the same frequency propagating over the same distance in free space. Alternatively put, the distance ..., hence the transmission medium is said to have an electrical length greater than its physical length. The electrical length is most commonly expressed in units of the wavelength, , which is related ... v f math A length may be stated as 2 or 3 or 0.5 etc. It is also sometimes expressed in radian s or degree angle degrees . A length of can be converted to radians by math theta 2 pi nu , math ... space, and the electrical length approximately 1.5 times the physical length. Antennas Many antenna ... length be equal to a multiple of a half wavelength, 2, while for a monopole antenna it is a multiple of a quarter wavelength, 4. The electrical length of an antenna element is, in general, different from its physical length. For example, increasing the diameter of the conductor, or the presence ... length. Antennas which are the wrong length to be resonant, or which must operate at a different ... 1037C ref An antenna which is shorter than its resonant length has capacitive reactance . The capacitance ... its resonant length has inductive reactance , and can be electrically shortened by adding a loading ... of a suitable electronic device, without changing the physical length of the aerial, in such a way ... wavelength. Thus an aerial with a length corresponding to the eighth of the radiated wavelength can ... than about one half wave length of the frequency at which the antenna operates. These antennas may operate ... Dec 7, 1937 DEFAULTSORT Electrical Length Category Telecommunications Category Antennas de Elektrische ... more details
length of a collection of curve s math Gamma math is a conformal invariant of math Gamma ... length of math Gamma math is equal to the extremal length of the image of math Gamma math under math f math . For this reason, the extremal length is a useful tool in the study of conformal mappings. Extremal length can also be useful in dimensions greater than two, but the following deals primarily with the two dimensional setting. Definition of extremal length To define extremal length ... gamma math we let math L rho gamma int gamma rho , dz math denote the math rho math length of math gamma math , where math dz math denotes the Euclidean distance Euclidean element of length. It is possible ... the measure of every subinterval math J subset I math is the length of the restriction of math ... integral math int I rho gamma t ,d mathrm length gamma t math , where math mathrm length gamma t math is the length of the restriction of math gamma math to math s in I s le t math . Also set math ... int D rho 2 ,dx ,dy, math and the extremal length of math Gamma math is math EL Gamma sup rho frac ... length of the collection of curves in math D math with one endpoint in one set and the other endpoint in the other set. Examples In this section the extremal length is calculated in several examples. The first three of these examples are actually useful in applications of extremal length. Extremal ... math R 0,w times 0,h math . Let math Gamma math be the set of all finite length curves math gamma ... gamma math has finite length. We will now prove that in this case math EL Gamma w h math First .... As the proof shows, the extremal length of math Gamma math is the same as the extremal length ... length of the family of curves math Gamma , math that connect the bottom edge of math ... length, and a similar duality property occurs in the context of the next subsection. Observe ... 1 math and math C 2 math which is the extremal length of the collection math Gamma math of curves math ... more details
In physics, the radiation length is a characteristic of a material, related to the energy loss of high energy, electromagnetic interacting elementary particle particles with it. Definition High energy electrons 10 MeV predominantly lose energy in matter by bremsstrahlung , and high energy photons by SubatomicParticle Antielectron SubatomicParticle Electron pair production. The characteristic amount of matter traversed for these related interactions is called the radiation length math X sub 0 sub , usually measured in g cm sup 2 sup . It is both the mean distance over which a high energy electron loses all but math frac 1 e mathematical constant e of its energy by bremsstrahlung, and frac 7 9 of the mean free path for pair production by a high energy photon. It is also the appropriate scale length for describing high energy electromagnetic cascades. The radiation length for a given material consisting of a single type of nuclei can be approximated by the following expression ref cite book last Eidelman first S. title Review of Particle Physics ref math X 0 frac 716.4 cdot A Z Z 1 ln frac 287 sqrt Z mathrm g cdot mathrm cm 2 frac 1432.8 cdot A Z Z 1 11.319 ln Z mathrm g cdot mathrm cm 2 math , where math Z is the atomic number and math A is mass number of the nucleus. For electrons at lower energies below few tens of MeV s , the energy loss by ionization is predominant. While this definition may also be used for other electromagnetic interacting particles beyond lepton s and photons, the presence of the stronger strong interaction hadronic and Nuclear force nuclear interaction makes it a far less interesting characterisation of the material the nuclear collision length and nuclear interaction length are more relevant. Comprehensive tables for radiation lengths and other properties of materials are available from http pdg.lbl.gov AtomicNuclearProperties See also Mean free path Attenuation length Attenuation coefficient Attenuation Range particle radiation Stopping power ... more details
Length constant is a constant used in neurobiology signified by the Greek letter lambda &lambda . The longer a length constant is, the bigger the effect a potential either an action potential or a current injected at the site will have along the cell. A long length constant can result in spatial summation , or the algebraic summation of one potential with other potentials from other areas of the cell. In an action potential or in a passive spread of signal in a neuron , the constant &lambda is math lambda sqrt frac r m r i r o math where r sub m sub is the resistance across the membrane, r sub i sub is the resistance inside the membrane, and r sub o sub is the resistance outside the membrane. In calculation, the effects of r sub o sub are negligible, so the equation becomes math lambda sqrt frac r m r i math The resistance across the membrane is a function of the number of open ion channels and the resistance inside the membrane is generally a function of the diameter of the axon . A large diameter is related to a lower r sub i sub . The length constant is used to describe the rise of potential difference across the membrane math V x V max 1 e x lambda math The fall of voltage is described by math V x V max e x lambda math Where voltage is typically in millivolts, x is distance in millimeters, and &lambda is in millimeters. V sub max sub is defined as the maximum voltage attained in the action potential, where math V max r m I math where r sub m sub is the resistance across the membrane and I is the current flow. Setting for x &lambda for the rise of voltage sets V x equal to .63 V sub max sub . This means that the length constant is the distance at which 63 of V sub max sub has been reached during the rise of voltage. Setting for x &lambda for the fall of voltage sets V x equal to .37 V sub max sub , meaning that the length constant is the distance at which 37 of V sub ... in this way, it can be seen that the length constant increases with increasing radius of the neuron ... more details
s is related to the Rayleigh length by ref name Siegman1986 math Theta mathrm div 2 frac w 0 z R . math ... Depth of field References reflist http www.rp photonics.com rayleigh length.html Rayleigh length ... more details
The Bjerrum length after Danish chemist Niels Bjerrum 1879 1958 ref http www.rsc.org delivery ArticleLinking DisplayArticleForFree.cfm?doi TF959550X001&JournalCode TF ref is the separation at which the electrostatic interaction between two elementary charge s is comparable in magnitude to the thermal energy scale, math k B T math , where math k B math is the Boltzmann constant and math T math is the Absolute temperature absolute temperature in Kelvin . This length scale arises naturally in discussions of electrostatic, electrodynamic and electrokinetic phenomena in electrolytes, polyelectrolyte and colloidal dispersions. ref cite book last1 Russel first1 William B. first2 D. A. last2 Saville first3 William R. last3 Schowalter title Colloidal Dispersions publisher Cambridge University Press location New York year 1989 ref In SI units standard units , the Bjerrum length is given by math lambda B frac e 2 4 pi varepsilon 0 varepsilon r k B T , math where math e math is the elementary charge , math varepsilon r math is the relative dielectric constant of the medium and math varepsilon 0 math is the vacuum permittivity . For water at room temperature math T 300 math K , math varepsilon r approx 80 math , so that math lambda B approx 0.7 math nm. In Gaussian units , math 4 pi varepsilon 0 1 math and the Bjerrum length has the simpler form math lambda B frac e 2 varepsilon r k B T . math References Reflist Category physical chemistry de Bjerrum L nge fa ... more details
Orphan date January 2011 The transport length in a strongly diffusing medium noted l is the length over which the direction of propagation of the photon is randomized. It is related to the mean free path l by the relation ref A. Ishimaru, Wave Propagation and Scattering in Random Media, Academic Press, New York, 1978. ref math l frac l 1 g math with g the asymmetry coefficient. math g cos theta math or averaging of the scattering angle over a high number of scattering events. g can be evaluated with the Mie theory . br If g 0, l l . A single scattering is already isotropic. br If g 1, l infinite. A single scattering doesn t deviate the photons. Then the scattering never gets isotropic. This length is useful for renormalizing a non isotropic scattering problem into an isotropic one in order to use classical diffusion laws Fick law and Brownian motion . The transport length might be measured by transmission experiments of backscattering experiments. ref Talanta, Volume 50, Issue 2, 13 September 1999, Pages 445 456 ref ref P. Snabre, A. Arhaliass, Anisotropic scattering of light in random media. Incoherent backscattered spot light, Appl. Optics 37 18 1998 211 225. ref gallery Image figure mean free path.png Mean free path simple scheme gallery References references External links http www.formulaction.com tech mls gb.html Illustrated description movies of multiple light scattering and application to colloid stability Category Optics Category Colloids ... more details
Cleanup date April 2008 Refimprove date February 2008 In aviation , the flight length is defined as the time airborne during a flight. class infobox bordered style width 25em text align left font size 95 Short haul flight 3 hours Medium haul flight 3 to 6 hours Long haul flight 6 hours Domestic A short haul domestic flight is commonly categorized into being no longer than convert 500 mi abbr on 1.5 hours in length, meaning that all domestic flights within a country such as the United Kingdom are short haul. In addition to this criterion, the destination airport must be in the same country as the departure airport. Domestic flights can vary greatly in length due to some countries being larger than others. Short haul flights A short haul flight is defined by Thomas Cook Airlines as a flight under 3 hours in length. ref cite book title How to Survive a Long Haul Flight last Eaves first Matthew authorlink coauthors year 2008 publisher Mandival location London isbn 9780955984402 ref Image Southwest Airlines Boeing 737 7H4 N231WN.jpg right thumb Boeing 737 7H4, a typical short haul aircraft A short haul flight was defined by Cathay Pacific as flights between Hong Kong and Tokyo or Korea as well as between New York and Vancouver . ref http www.cathaypacific.com cpa en HK manageyourtrip travelextras extralegroomseat Safety ref A short haul flight is defined by the UK Treasury as a flight under 2000 miles in distance. In the United Kingdom , HM Treasury levy Air Passenger Duty on all flights, according to banding by distance. Medium haul flight A medium haul flight is a flight between ... long distances, typically beyond six and a half hours in length, ref http www.thomascookairlines.co.uk ... route to minimise flight length. For long haul flights, the most direct route is a great circle around ... route . The great circle distance between airports may therefore give an approximation of flight length ... calculator DEFAULTSORT Flight Length Category Civil aviation de Flugstrecke fr Vol long courrier pt ... more details
orphan date December 2009 The Krogh Length , math lambda K math , is the distance between capillaries at which nutrients diffuse to based on cellular consumption of the nutrients ref Fournier, R. L. Basic Transport Phenomena in Biomedical Engineering 1st edn Taylor & Francis, London, 1999 . ref ref http www.nature.com nmat journal v6 n11 abs nmat2022.html Choi et al. Microfluidic scaffolds for tissue engineering. Nature Materials 2007 vol. 6 pp. 908 915 ref . It can be described as math lambda K sqrt D s c o R math where math D s math is the diffusion constant of the solute in the substrate, math c o math is the concentration in the channel, and math R math is the consumption by the cells. Units are in terms of length . References references See also August Krogh Biomedical engineering Capillaries Diffusion Biot number Peclet number Category Cardiovascular physiology Category Biomedical engineering ... more details
The scattering length in quantum mechanics describes low energy scattering . It is defined as the following low energy limit mathematics limit , math lim k to 0 k cot delta k frac 1 a , math where math a math is the scattering length, math k math is the wave number , and math delta k math is the s wave phase shift . The elastic Cross section physics cross section , math sigma e math , at low energies is determined solely by the scattering length, math lim k to 0 sigma e 4 pi a 2 . math General concept When a slow particle scatters off a short ranged scatterer e.g. an impurity in a solid or a heavy particle it cannot resolve the structure of the object since its de Broglie wavelength is very long. The idea is that then it should not be important what precise Scalar potential potential math V r math one scatters off, but only how the potential looks at long length scales. The formal way to solve this problem is to do a partial wave expansion somewhat analogous to the multipole expansion in Classical electromagnetism classical electrodynamics , where one expands in the angular momentum components of the outgoing wave. At very low energy the incoming particle does not see any structure, therefore to lowest order one has only a spherical symmetric outgoing wave, the so called s wave scattering angular momentum math l 0 math . At higher energies one also needs to consider p and d wave math l 1,2 math scattering and so on. The concept behind describing low energy properties in terms ... the s wave i.e. angular momentum math l 0 math scattering length for a given potential we look ... length is defined as the scattering length . For our potential we have therefore math a r 0 math , in other words the scattering length for a hard sphere is just the radius. Alternatively one could say that an arbitrary potential with s wave scattering length math a s math has the same low energy scattering properties as a hard sphere of radius math a s math . To relate the scattering length ... more details
In plasma physics , the Debye length also called Debye radius , named after the Dutch physicist and physical ... words, the Debye length is the distance over which significant charge separation can occur. A Debye sphere is a volume whose radius is the Debye length, in which there is a sphere of influence, and outside of which charges are screened. The notion of Debye length plays an important role in plasma physics , electrolytes and colloids DLVO theory . Physical origin The Debye length arises naturally in the thermodynamic ... has the units of an inverse length squared and by dimensional analysis leads to the definition of the characteristic length scale math lambda D left frac varepsilon r varepsilon 0 , k B T sum j 1 N n j 0 , q j 2 right 1 2 math that commonly is referred to as the Debye H ckel length. As the only characteristic length scale in the Debye H ckel equation, math lambda D math sets the scale for variations ... to the Debye H ckel length in the same way, regardless of the sign of their charges. The Debye H ckel length may be expressed in terms of the Bjerrum length math lambda B math as math lambda D ... length may reach macroscopic values, such as in the magnetosphere, solar wind, interstellar medium ... td td Magnetic field br B T td td Debye length br sub D sub m td tr tr align center td bgcolor eeeeee ... in cosmic plasmas has not been generally recognized. Debye length in a plasma In a plasma, the background medium may be treated as the vacuum math varepsilon r 1 math , and the Debye length ... D sub is the Debye length, sub 0 sub is the permittivity of free space , k sub B sub is the Boltzmann ... Principles of plasma diagnostics ISBN 0 521 38583 0 ref Debye length in an electrolyte In an electrolyte or a colloids colloidal dispersion , the Debye length ref Russel, W.B., Saville, D.A. and Schowalter ... length of the medium. For water at room temperature, sub B sub 0.7 nm. At room temperature ... in molar concentration molar M or mol L Debye length in silicon The Debye length has become increasingly ... more details
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