orphan date June 2010 Refers to the gradient created in the nephron s of the kidney s, between the tubules and the interstitial fluid surrounding them. It is created by the solutes urea and salt exiting and reentering the tubules at different sections of the nephron. The selective permeability of the tubules is a major factor in this process. Tissue osmolarity increases from Cortex anatomy cortex outer layar of a nephron , to inner renal medulla middle layer of a nephron . Category Renal physiology ... more details
In mathematical morphology and digital image processing , a morphological gradient is the difference between the dilation morphology dilation and the erosion morphology erosion of a given image. It is an image where each pixel value typically non negative indicates the contrast intensity in the close neighborhood of that pixel. It is useful for edge detection and Segmentation image processing segmentation applications. Mathematical definition and types Let math f E mapsto R math be a grayscale image, mapping points from a Euclidean space or discrete grid E such as R sup 2 sup or Z sup 2 sup into the real line. Let math b x math be a grayscale structuring element . Usually, b is symmetry symmetric and has short support , e.g., math b x left begin array ll 0,& x leq 1, infty,& mbox otherwise end array right. math . Then, the morphological gradient of f is given by math G f f oplus b f ominus b math , where math oplus math and math ominus math denote the dilation and the erosion, respectively. An internal gradient is given by math G i f f f ominus b math , and an external gradient is given by math G e f f oplus b f math . The internal and external gradients are thinner than the gradient, but the gradient peaks are located on the edges, whereas the internal and external ones are located at each side of the edges. Notice that math G i G e G math . If math b 0 geq 0 math , then all the three gradients have non negative values at all pixels. References cite id serra82 Image Analysis and Mathematical Morphology by Jean Serra, ISBN 0126372403 1982 cite Image Analysis and Mathematical Morphology, Volume 2 Theoretical Advances by Jean Serra, ISBN 0 12 637241 1 1988 An Introduction to Morphological Image Processing by Edward R. Dougherty, ISBN 0 8194 0845 X 1992 External links http cmm.ensmp.fr beucher publi morph grad.pdf Morphological gradients , Centre de Morphologie Math matique, cole des Mines de Paris Category Mathematical morphology Category Digital geometry compu graphics ... more details
In differential geometry , the four gradient is the four vector generalization of the gradient . Definition The covariant components compactly written in index notation are ref The Cambridge Handbook of Physics Formulas, G. Woan, Cambridge University Press, 2010, ISBN 978 0 521 57507 2 ref math dfrac partial partial x alpha left frac 1 c frac partial partial t , nabla right partial alpha , alpha math The comma in the last part above math , alpha math implies the partial differentiation with respect to math x alpha math . This is not the same as a semi colon, used for the covariant derivative . The contravariant components are ref The Cambridge Handbook of Physics Formulas, G. Woan, Cambridge University Press, 2010, ISBN 978 0 521 57507 2 ref math partial alpha g alpha beta partial beta left frac 1 c frac partial partial t , nabla right math where g sup sup is the Metric tensor general relativity metric tensor , which here has been chosen for flat spacetime with the metric signature , , , . Alternative symbols to math partial alpha math is math Box math or D . Usage The square of D is the four Laplacian , which is called the d Alembert operator math D cdot D partial alpha partial alpha frac 1 c 2 frac partial 2 partial t 2 nabla 2 math . As it is the dot product of two four vectors, the d Alembertian is a Lorentz invariant scalar. Occasionally, in analogy with the 3 dimensional notation, the symbols math Box math and math Box 2 math are used for the 4 gradient and d Alembertian respectively. More commonly however, the symbol math Box math is reserved for the d Alembertian. Derivation In 3 dimensions, the gradient operator maps a scalar field to a vector field such that the line integral between any two points in the vector field is equal to the difference between the scalar ... of the gradient to four dimensions should be math partial alpha left frac partial partial t , nabla ... gives the correct definition of four gradient math partial alpha left frac 1 c frac partial partial ... more details
Engineering Hay says The ruling grade may be defined as the maximum gradient over which a tonnage ... gradient on the division. Momentum grades, pusher grades, or those that must regularly be doubled ... compensate for this, the gradient should be a little less steep the sharper the curve is the necessary ... is analogous to compensation for curvature and requires the gradient in the tunnel and for some ... compensation for gradient is not a simple equation, but is rather a trial and error process. Since ... on the first Cascade Tunnel , too little compensation for tunnel gradient was made. It is worthwhile .... The lines approaching the first cascade tunnel had a ruling gradient of 2.2 1 in 45.5 , while the tunnel itself had a gradient of 1.7 1 in 58.8 facing eastbound trains. This gradient appears to be chosen .... Even though the ruling gradient in the tunnel was slightly less than that on the tracks on either ... say 1 in 400 or 0.25 , with a very steep section in the open air on the western approaches. The gradient .... Strictly speaking, the level gradient should continue for a suitable distance beyond the portal ... minimum smoke. The tunnel should have a slight gradient to facilitate drainage of water. Open ... gradient, a better solution would have been to have a level tunnel from New Tye West to Cascade Tunnel Station West , with a 2.6 mile stretch of say 4 gradient 1 in 25 on the western approaches from ..., this tunnel was on a steep gradient, indeed the ruling grade of 1 in 33, which caused problems with the smoke ... have a relatively gentle gradient of 1 in 90 1.11 . However, the frequent gaps between the tunnels ... conditions as the gradient of 1 in 200 0.5 Percent sign in the tunnel was not sufficiently reduced ... Dividing Range . It is not known how winds would affect the fume issue. Curve and Gradient Books ... more details
Gradient analysis is an empirical analytical method used in plant community ecology to relate the abundances of various species in a plant community to various environmental gradients by Ordination statistics ordination or by Weighted mean weighted averaging . These gradients are usually Variable mathematics variables that are important in plant species distributions, and include temperature, water availability, light, and soil nutrients, or their closely correlated surrogates. References Mike Palmer, http ordination.okstate.edu Ordination Methods for Ecologists Botany Department of Oklahoma State University. Retrieved 15 August 2010. ecology stub modelling ecosystems expanded other Category Community ecology ... more details
multiple issues orphan May 2010 unreferenced May 2010 notability May 2010 A redox gradient is the biogeochemical sorting of reductant s and oxidants according to redox potential , with the most reducing conditions at depth, having its origin in the depletion of oxygen and the successive depletion of reactants with depth. They form in Stratification water stratified environments where oxygen does not penetrate deeper than the immediate surface environment. Examples include waterlogged soil s, marine pelagic and hemipelagic sediments, and, most notably, the Black Sea . Category Chemical reactions Category Chemical nomenclature Category Coordination chemistry ... more details
calculus cTopic Vector calculus The gradient theorem , also known as the fundamental theorem of calculus for line integrals , says that a line integral through a gradient field any irrotational vector field conservative vector field can be expressed as the gradient of a scalar field can be evaluated by evaluating the original scalar field at the endpoints of the curve math phi left mathbf q right phi left mathbf p right int gamma mathbf p , mathbf q nabla phi mathbf r cdot d mathbf r . math It is a generalization of the fundamental theorem of calculus to any curve in a plane or space generally n dimensional rather than just the real line, and it is also a special case of the more general Stokes Theorem . The gradient theorem implies that line integrals through irrotational vector fields are Conservative vector field Path independence path independent . In physics this theorem is one of the ways of defining a Conservative force conservative force . By placing math phi math as potential, math nabla phi math is a conservative field . Work done by conservative forces does not depend on the path followed by the object, but only the end points, as the above equation shows. Proof If math phi math is a differentiable function differentiable function from some connected space connected subset of math mathbb R n math to math mathbb R math , and if math mathbf r math is a continuous function continuous function from some connected subset of math mathbb R math to math mathbb R n math , then by the the multivariate chain rule The chain rule in higher dimensions chain rule , math frac d dt phi mathbf r t nabla phi mathbf r t cdot mathbf r t , math where math cdot math is the usual dot product . Therefore, if math mathbf r math parametrization parametrizes the continuous curve math gamma math with endpoints math mathbf p math and math mathbf q math orientability oriented in the direction ... teoremo fa fr Th or me du gradient it Teorema del gradiente ... more details
as geothermal energy . The geothermal gradient has been used for space heating and bathing since ... gradient varies with location and is typically measured by determining the bottom open hole temperature ... In areas of Holocene Tectonic uplift uplift and erosion Fig. 1 the initial gradient will be higher than .... If the gradient of the stabilized regime is projected above the inflection point to its intersect ... and Deposition sediment deposition Fig. 2 the initial gradient will be lower than the average until ..., M the thermal conductivity of the rocks there, and g the measured geothermal gradient. A representative ... Hence, using the global average geothermal conducting gradient of 0.02 K m we get that q 0.06 W m . This estimate ... gradient with periods varying from daily to tens of thousands of years and an amplitude which decreases ... a constant geothermal gradient throughout the Earth s surface. ref name Stacey If that rate of temperature ... S waves . The temperature gradient dramatically decreases with depth for two reasons. First ... by advection , or material transport. Thus, the geothermal gradient within the bulk of Earth s mantle is of the order of 0.3 kelvin per kilometer, and is determined by the adiabatic gradient associated ..., 2005 Refend Geophysics navbox Geothermal power DEFAULTSORT Geothermal Gradient Category Geological ... an Gradient cheotermico ca Gradient geot rmic da Geotermi de Geothermische Tiefenstufe es Gradiente geot rmico fr Gradient g othermique hr Geotermalni gradijent id Panas bumi it Gradiente geotermico hu Geotermikus gradiens nl Geotherm ja no Geotermi pl Gradient geotermiczny pt Gradiente ... more details
Gradient enhanced NMR is a method for obtaining high resolution nuclear magnetic resonance spectra without the need for phase cycling . Pulsed field gradientGradient methodology is used extensively for two purposes, either rephasing selection or dephasing elimination of a particular magnetization transfer pathway. It includes the application of magnetic field gradient pulses to select specific coherence physics s. By using actively shielded gradients, a Pulsed field gradientgradient pulse is applied during the evolution period of the selected coherence to dephase the transverse magnetization and another gradient pulse refocuses the desired coherences remaining during the acquisition period. Advantages Significant reduction in measuring time Reduced T1 artifacts Elimination of phase cycling and difference methods Possibility for three and four quantum editing The ability to detect resonances at the same chemical shift as a strong solvent resonance Drawbacks A need for field frequency lock blanking during long runs. Examples Selection of transverse magnetization I sub x sub , S sub x sub , I sub y sub etc. gradient 180 x gradient Suppression of transverse magnetization I sub x sub , S sub x sub , I sub y sub etc. gradient 180 x gradient References Ralph E. Hurd, Gradient Enhanced Spectroscopy, Journal of magnetic resonance. 87, 422 428 1990 Category Nuclear magnetic resonance ... more details
Unreferenced date November 2006 A pulsed field gradient is a short, timed pulse with spatial dependent field intensity. Any gradient is identified by four characteristics axis, strength, shape and duration. Pulsed field gradient PFG techniques are key to magnetic resonance imaging , magnetic resonance imaging Magnetic resonance spectrosopy spatially selective spectroscopy and studies of diffusion via NMR. PFG techniques are widely used as an alternative to phase cycling in modern NMR spectroscopy. Common field gradients in NMR The effect of a uniform magnetic field gradient in the z direction on spin I, is considered to be a rotation around z axis by an angle sub I sub Gz where G is the gradient magnitude and sub I sub is the gyromagnetic ratio of spin I. It introduces a phase factor to the magnetizations z, sub I sub zG The time duration is of order ms. See also Gradient enhanced NMR spectroscopy DEFAULTSORT Pulsed Field Gradient Category Nuclear magnetic resonance Physics stub ... more details
div style float right border solid 10px white Test sample values div The Alveolar arterial gradient A a gradient , is a measure of the difference between the alveoli alveolar concentration of oxygen and the artery ..., Pt. 1 work accessdate 2008 11 14 ref Equation The equation for calculating the A a gradient is math Aa Gradient P AO 2 P aO 2 math ref name urlAlveolar arterial Gradient cite web url http www users.med.cornell.edu spon picu calc aagrad.htm title Alveolar arterial Gradient work accessdate 2008 11 14 ... in arterial blood br In its expanded form, the A a gradient can be calculated by math Aa Gradient ... version of the equation is math Aa Gradient left 150 frac 5 4 P CO 2 right P aO 2 math Values and meaning The A a gradient is useful in determining the source of hypoxemia . The measurement helps isolate ... else in the body . A normal A a gradient for a young adult non smoker breathing air, is between 5 10 mmHg. Normally, the A a gradient increases with age. For every decade a person has lived, their A a gradient is expected to increase by 1 mmHg. As a quick calculation, a normal A a gradient is less than the patient s age divided by 4 4. Thus, a 40 year old should have an A a gradient less than 14. An abnormally increased A a gradient suggests a defect in diffusion , V Q ventilation perfusion ... 7311 3 ref Because A a gradient is approximated as 150 5 4 P sub CO2 sub Pa sub O2 sub , the direct .... Therefore the A a gradient essentially demonstrates a high respiratory effort low arterial P sub CO2 sub relative to the achieved level of oxygenation arterial P sub O2 sub . A high A a gradient .... If lack of oxygenation is proportional to low respiratory effort, then the A a gradient is not increased a healthy person who hypoventilates would have hypoxia, but a normal A a gradient. At an extreme, high CO2 levels from hypoventilation can mask an existing high A a gradient. This mathematical artifact makes A a gradient more clinically useful in the setting of hyperventilation. Mechanical ... more details
In differential topology , a mathematical discipline, and more specifically in Morse theory , a gradient like vector field is a generalization of gradient vector field . The primary motivation is as a technical tool in the construction of Morse function s, to show that one can construct a function whose critical points are at distinct levels. One first constructs a Morse function, then uses gradient like vector fields to move around the critical points, yielding a different Morse function. Definition Given a Morse function f on a manifold M, a gradient like vector field X for the function f is, informally away from critical points, X points in the same direction as the gradient of f, and near a critical point in the neighborhood of a critical point , it equals the gradient of f, when f is written in standard form given in the Morse lemma s. Formally ref http books.google.com books?id TtKyqozvgIwC&pg PA63 p. 63 ref away from critical points, math X cdot f 0, math around every critical point there is a neighborhood on which f is given as in the Morse lemmas math f x f b x 1 2 cdots x alpha 2 x alpha 1 2 cdots x n 2 math and on which X equals the gradient of f. Dynamical system The associated dynamical system of a gradient like vector field, a gradient like dynamical system , is a special case of a Morse Smale system . References reflist refbegin An introduction to Morse theory, Yukio Matsumoto, 2002, Section 2.3 Gradient like vector fields, http books.google.com books?id TtKyqozvgIwC&pg PA56 p. 56 69 http hilbertthm90.wordpress.com 2009 09 25 gradient like vector fields exist Gradient Like Vector Fields Exist , September 25, 2009 refend Category Morse theory Category Differential topology differential geometry stub topology stub ... more details
Context date October 2009 Immobilized pH gradient IPG gel s are the acrylamide gel matrix Polymerization co polymerized with the pH gradient, which result in completely stable gradients except the most alkaline 12 pH values. The immobilized pH gradient is obtained by the continuous change in the ratio of Immobilines . An Immobiline is a weak acid or Base chemistry base defined by its pK value. ref Barnes et al., Electrophoresis in Practice A Guide to theory and Practice. Page 44. VCH Publishers Inc, 1993 USA ref This alternative method eliminates the problems of gradient instability and poor sample loading capacity associated with carrier ampholyte pH gradient. ref Wilkins et al., Proteome Research New Frontiers in Functional Genomics. Page 14. Springer, 1997 Germany ref Commercial precast IPG gels are available. References references Category Acid base chemistry ... more details
Gradient pattern analysis GPA ref name rosa2000 Rosa, R.R., Pontes, J., Christov, C.I., Ramos, F.M., Rodrigues Neto, C., Rempel, E.L., Walgraef, D. Physica A 283 , 156 2000 . ref is a geometric computing method for characterizing symmetry breaking of an ensemble of asymmetric vectors regularly distributed in a square lattice. Usually, the lattice of vectors represent the first order gradient of a scalar field, here an M x M square amplitude matrix mathematics matrix . An important property of the gradient representation is the following A given M x M matrix where all amplitudes are different results in an M x M gradient lattice containing math N V M 2 math asymmetric vectors. As each vector can be characterized by its norm and phase, variations in the math M 2 math amplitudes can modify the respective math M 2 math gradient pattern. The original concept of GPA was introduced by Rosa, Sharma and Valdivia in 1999 ref name Rosa99 Rosa, R.R. Sharma, A.S.and Valdivia, J.A. Int. J. Mod. Phys. C , 10 , 147 1999 , doi 10.1142 S0129183199000103 . ref . Usually GPA is applied for spatio temporal pattern analysis in physics and environmental sciences operating on time series and digital images ... gradient asymmetries computing the so called gradient asymmetry coefficient , that has been ... C N V math is valid for any gradient square lattice. As the asymmetry coefficient is very sensitive to small changes in the phase and modulus of each gradient vector, it can distinguish complex variability ... but depends solely on the local symmetry properties of the correspondent gradient pattern ... called gradient moments can be calculated from the gradient lattice. ref name rosa03 Rosa, R.R. Campos ... lattice, the gradient moments have the basic property of being globally invariant for rotation and modulation . The primary research on gradient lattices applied to characterize weak turbulence ... is called Gradient spectral analysis GSA , usually applied to short time series analysis. ref ... more details
Gradient well formedness is a problem that arises in the analysis of data in generative linguistics , in which a linguistic entity is neither completely grammatical nor completely ungrammatical. A native speaker may judge a word, phrase or pronunciation as not quite right or almost there, rather than dismissing it as completely unacceptable or fully accepting it as well formed. Thus, the acceptability of the given entity lies on a Image gradientgradient between well formedness and ill formedness. Some Linguist generative linguists think that ill formedness might be strictly additive, thus trying to figure out universal grammar universal constraints by acquiring scalar grammaticality judgements from Informant linguistics informants . Generally, however, gradient well formedness is considered an unsolved problems in linguistics unsolved problem in generative linguistics . See also Constituent linguistics Grammaticality List of linguistic example sentences References citation last Albright first Adam month January year 2007 title Gradient phonological acceptability as a grammatical effect url http www.mit.edu albright papers Albright GrammaticalGradience.pdf accessdate 2009 04 11 citation last Featherston first Sam year 2004 title Judgements in syntax Why they are good, how they can be better url http www.sfb441.uni tuebingen.de sam papers DGfS04.handout.pdf accessdate 2008 04 09 citation last Hayes first Bruce P. month August year 1997 title Gradient Well Formedness in Optimality Theory url http www.linguistics.ucla.edu people hayes gradient.pdf accessdate 2006 09 20 ling stub Category Generative linguistics Category Unsolved problems in linguistics ... more details
The Loss of Strength Gradient LSG was devised by Kenneth Boulding in 1962. He argued that the amount of a nation s military power that could be brought to bear in any part of the world depended on geographic distance. The Loss of Strength Gradient demonstrated, in graphical form, that the further away the target of aggression the less strength that could be made available. It also showed how this loss of strength could be ameliorated by the use of forward positions. ref Kenneth Boulding, Conflict and Defense, New York Harper, 1962 , p. 262. ref Boulding went on to support the idea of a decline in the Loss of Strength Gradient. He used two lines of attack. One of these was that transport was becoming easier. Another was that combatants had achieved sufficient capacity to defeat the opponent through strategic air and missile power. Boulding said that there had been a military revolution in the 20th century, the significance of which was a very substantial diminution in the cost of transportation of organized violence of all kinds, especially of organized armed forces and an enormous increase in the range of the deadly projectile. ref Kenneth Boulding, The Meaning of the 20th Century The Great Transition, London George Allen & Unwin, 1965 , p. 87. ref There is support for the continued importance of the Loss of Strength Gradient such that where it is reduced in significance it is of only temporary nature. Transport is said not to be becoming permanently easier while air power is said not to be permanently replacing need for forward deployed ground forces. ref K. Webb, The Continued Importance of Geographic Distance and Boulding s Loss of Strength Gradient , Comparative Strategy, Volume 26 Issue 4, 2007, pp. 295 310. ref See also Strategic depth Defence in depth Culminating point Military power projection References Reflist mil stub DEFAULTSORT Loss Of Strength Gradient Category Military doctrines Category Military logistics Category Military geography ... more details
Multiple issues unreferenced February 2010 wikify February 2011 orphan January 2011 Pore pressure gradient is a dimensional Petrophysics petrophysical term used by drilling engineer s during the design of drilling programs for drilling constructing Oil well oil and gas wells into the earth. It is the pressure gradient inside the pore space of the rock column from the surface of the ground down to total depth TD , as compared to the pressure gradient of seawater in deep water. Whereas in pure math , the gradient of a scalar function expressed by the math notation grad f may not have physical units associated with it in drilling engineering the pore pressure gradient is usually expressed in API type International Association of Drilling Contractors IADC physical units of measurement, namely psi per foot. In the well known formula P 0.052 mud weight total vertical depth taught in almost all petroleum engineering courses worldwide, the mud weight MW is expressed in pounds per U.S. gallon, and the total vertical depth TVD is expressed in feet, and 0.052 is a conversion constant that can be derived by dimensional analysis later. This is pretty lazy considering math mathrm 1 psi ft frac 1 ft 12 in times frac 1 lb in 2 1 psi times frac 231 in 3 1 US Gal 19.25000000 lb gal math It would be more accurate to divide by 19.25. clarify date February 2010 Therefore, for a column of fresh water of 8.33 pounds per gallon lb U.S. gal standing still hydrostatically in a 41,000 foot vertical cased wellbore from top to bottom vertical hole , the pressure gradient would be grad P pressure gradient 0.052 8.33 0.433 psi ft and the hydrostatic bottom hole pressure BHP is then BHP grad P TVD 0.43316 41,000 17,759 psi However, the pore pressure is usually much greater than a column of fresh water ... open hole interval at 41,000 feet with a pore pressure gradient of 19 lb U.S. gal, the BHP ... ref ref tags which will then appear here automatically Reflist DEFAULTSORT Pore Pressure Gradient Category ... more details
In acoustics , the sound speed gradient is the rate of change of the speed of sound with distance, for example with depth in the ocean , ref name NTRP 1 02 cite book title Navy Supplement to the DOD Dictionary of Military and Associated Terms month August year 2006 publisher United States Navy Department Of The Navy url https www.nwdc.navy.mil Documents NTRP 1 02.pdf id NTRP 1 02 ref or height in the Earth s atmosphere . A sound speed gradient leads to refraction of sound wavefront s in the direction of lower sound speed, causing the sound rays to follow a curved path. The Radius of curvature mathematics radius of curvature of the sound path is inversely proportional to the gradient. ref cite book title Noise Control chapter 10. Outdoor sound propagation series ME 458 Engineering Noise Control year 2000 first J. S. last Lamancusa url http www.mne.psu.edu lamancusa me458 10 osp.pdf publisher Penn State University location State College, PA format pdf pages 10.6 10.7 ref When the sun warms the Earth s surface, there is a negative temperature gradient in atmosphere. The speed of sound decreases with decreasing temperature, so this also creates a negative sound speed gradient. ref name Ahnert cite book title Sound Reinforcement Engineering first Wolfgang last Ahnert coauthors Steffen, Frank publisher Taylor and Francis place London year 1999 pages 40 isbn 0415238706 ref The sound wave front travels faster near the ground, so the sound is refraction refracted upward, away from listeners on the ground, creating an acoustic shadow at some distance from the source. ref cite book last Everest first F. title The Master Handbook of Acoustics publisher McGraw Hill location New York year ..., or in the morning over water, when the sound speed gradient is positive. In this case, sound ... acoustics. However, when there is a zero sound speed gradient, values of sound speed have the same ... Reflist See also SOFAR channel Wind gradient science stub hydroacoustics Category Acoustics ... more details
In numerical optimization , the nonlinear conjugate gradient method generalizes the conjugate gradient method to nonlinear optimization . For a quadratic function math displaystyle f x math math displaystyle f x Ax b 2 math The minimum of math f math is obtained when the gradient is 0 math nabla x f 2 A top Ax b 0 math . Whereas linear conjugate gradient seeks a solution to the linear equation math displaystyle A top Ax A top b math , the nonlinear conjugate gradient method is generally used to find the local minimum of a nonlinear function using its gradient math nabla x f math alone. It works when the function is approximately quadratic near the minimum, which is the case when the function is twice differentiable at the minimum. Given a function math displaystyle f x math of math N math variables to minimize, its gradient math nabla x f math indicates the direction of maximum increase. One simply starts in the opposite steepest descent direction math Delta x 0 nabla x f x 0 math with an adjustable step length math displaystyle alpha math and performs a line search in this direction until it reaches the minimum of math displaystyle f math math displaystyle alpha 0 arg min alpha f x 0 alpha Delta x 0 math , math displaystyle x 1 x 0 alpha 0 Delta x 0 math After this first iteration in the steepest direction math displaystyle Delta x 0 math , the following steps constitute one iteration ... conjugate gradient method but have been obtained with line searches. The conjugate gradient method ... gradient iteration as Newton like methods require computing the Hessian matrix of second derivatives in addition to the gradient. Quasi Newton methods also require more memory to operate see also the limited ... An Introduction to the Conjugate Gradient Method Without the Agonizing Pain by Jonathan ... , chapter 10, section 6 Conjugate Gradient Methods in Multidimensions William H. Press Editor ... Press 2nd edition 1992 . Category Optimization algorithms and methods Category Gradient methods ... more details
The pressure gradient force is not actually a force but the acceleration of air due to pressure difference a force per unit mass . It is usually responsible for accelerating a parcel of air from a high atmospheric pressure region to a low pressure region, resulting in wind . In meteorology, pressure gradient force refers to the horizontal movement of air according to the equation math frac F x m frac 1 rho frac dp dx frac F y m frac 1 rho frac dp dy frac F z m frac 1 rho frac dp dz math The term math F m math is equal to the acceleration math dv dt math because this is an expression of Newton s law math F ma math . math dp dx math is the component of the pressure gradient along the x axis. math rho math is the mass density and math 1 rho math shows that as the mass density increases, the acceleration due to the pressure gradient becomes smaller. The pressure gradient force acts at right angles to isobar meteorology isobar s in the direction from high to low pressure. The greater the pressure difference over a given horizontal distance, the greater the force and hence the stronger the wind. The pressure gradient force, however, is not the only force that acts on a moving parcel of air &mdash if it were, then low and high pressure regions would eventually disappear. Other forces acting on a horizontally moving parcel of air include surface friction , coriolis force , centrifugal force fictitious centrifugal force . In large scale atmospheric flows, the coriolis force generally balances the pressure gradient force, producing winds blowing largely along the isobars however, near the surface the friction term is also important, generally giving a resulting net wind direction diagonal to the isobars with a component blowing towards the low pressure center . References Roland B. Stull 2000 Meteorology for Scientists and Engineers , Second Edition, Ed. Brooks Cole, ISBN 0 534 37214 7. Category Fluid dynamics Category Atmospheric dynamics climate stub ca For a b rica de Gradientkraft ... more details
Test sample values align right The serum ascites albumin gradient or gap SAAG is a calculation used in medicine to help determine the cause of ascites . ref name pmid18334692 cite journal author Wong CL, Holroyd Leduc J, Thorpe KE, Straus SE title Does this patient have bacterial peritonitis or portal hypertension? How do I perform a paracentesis and analyze the results? journal JAMA volume 299 issue 10 pages 1166 78 year 2008 month March pmid 18334692 doi 10.1001 jama.299.10.1166 url http jama.ama assn.org cgi pmidlookup?view long&pmid 18334692 ref The SAAG may be a better discriminant than the older method of classifying ascites fluid as a transudate versus exudate . ref name pmid1616215 cite journal author Runyon BA, Montano AA, Akriviadis EA, Antillon MR, Irving MA, McHutchison JG title The serum ascites albumin gradient is superior to the exudate transudate concept in the differential diagnosis of ascites journal Annals of Internal Medicine volume 117 issue 3 pages 215 20 year 1992 month August pmid 1616215 doi url ref The formula is as follows SAAG albumin concentration of Blood serum serum albumin concentration of ascitic fluid . Ideally, the two values should be measured at the same time. The reason for the value measurement is simple, using Starling s forces as a guide. If you think about it, when you have a small gap i.e. 1.1 then fluid wants to equilibrate due to oncotic pressures being similar. In conditions where there is a high gradient ie, 1.1 , the fluid SHOULD stay in the circulation because of the serum oncotic pressure trying to maintain it. Despite this desire, the ascites will still accumulate secondary to the hydrostatic pressure ie Budd Chiari, Heart Failure or Cirrhosis pushing the fluid into the abdomen. Differential High gradient A high gradient 1.1 g dL indicates the ascites is due to portal hypertension with 97 accuracy. ref name pmid1616215 ... Low gradient A low gradient 1.1 g dL indicates ascites not associated with increased portal pressure ... more details
as alternating gradient focusing an idea pioneered on this accelerator References cite book title Inward ... National Laboratory Alternating Gradient Synchrotron web page neutrino detectors Category Particle physics facilities Category Brookhaven National Laboratory particle stub de Alternating Gradient ... more details
Nanotech Nanomat Gradient Multi Layer GML Nanomaterials nano film is an assembly of Quantum Dot layers with a built in gradient of nanoparticle size, composition or density. Properties of such nanostructure are finding its applications in design of solar cell s ref http ieeexplore.ieee.org xpl freeabs all.jsp?arnumber 5411731 Energy transfer between quantum dots of different sizes for quantum dot solar cells ref ref http www.freepatentsonline.com y2008 0142075.html Nanophotovoltaic Device with Improved Quantum Efficiency ref ref http www.freepatentsonline.com y2009 0255580.html Quantum dot solar cell with quantum dot bandgap gradients ref and energy storage devices ref http www.freepatentsonline.com y2010 0183919.html Quantum dot ultracapacitor and electron battery ref . The GML nano structure can be embedded in the organic material polymer , or can include Quantum Dots made of two or more types of material. Image GMLnanofilm.png thumb center 300px Schema of Gradient Multi Layer GML nanofilm Photovoltaic applications The GML nanofilm only 100 nanometers thick can absorb the entire Sun spectrum 0.3 2.0 eV . At the same time, gradient of the quantum dots size can create a gradient of the electro chemical potential, acting as an equivalent of built in electric field inside a nanofilm. This enhances transport of electron s and Electron hole holes , and improves Quantum efficiency of a solar cell internal quantum efficiency IQE and photocurrent . Manufacturing The industrial manufacturing of GML nanofilms represents a challenge. Traditional methods of building nanostructured materials like spin coating can t form GML nanostructures, while more effective methods like Atomic Layer Deposition ALD or Langmuir Blodget microchemical method. ref http www.freepatentsonline.com y2008 0108122.html Microchemical nanofactories ref are expensive. The cost efficient alternative for manufacturing ... Reflist colwidth 30em External links http www.nanotech now.com news.cgi?story id 40310 Gradient ... more details
Image Grin lens.png frame right A gradient index lens with a parabolic variation of refractive index n with radial distance x . The lens focuses light in the same way as a conventional lens. Gradient index ... spherical lenses. Gradient index lenses may have a refraction gradient that is spherical, axial, or radial. In nature The Lens anatomy lens of the eye is the most obvious example of gradient index optics ... et al. , 2006 . Another example of gradient index optics in nature is the common mirage of a pool ... cool air above it. The variation in temperature and thus density of the air causes a gradient in its refractive index, causing it to increase with height. This index gradient causes refraction ... light at varying intensities in order to give a refractive gradient. Ion exchange Hensler, 1975 Glass .... Thus the sample obtains a gradient material structure and a corresponding gradient of the refractive ... to give a varying gradient. History Wikify section date July 2011 In 1854, J C Maxwell suggested ... cylinder with a refractive index gradient that varied symmetrically with the radial distance from ... applications. Theory An inhomogeneous gradient index lens possesses a refractive index whose change ... the change in arc length for a spherical gradient, to each physical dimension math alt L integral .... The refractive index gradient of GRIN lenses can be mathematically modelled according to the method of production used. For example, GRIN lenses made from a radial gradient index material, such as SELFOC ... Wesley, ISBN 0 201 11609 X. Hensler J R, Method of Producing a Refractive Index Gradient in Glass ... Gradient, U.S. Patent 3,904,268 9 Sept. 1975 . Luneberg R K, 1964 . Mathematical Theory of Optics ... W 1978 . Gradient Index Optics . New York Academic Press. Maxwell, J.C. 1854 . Cambridge and Dublin Math. J. 8, 188 Mohr R K, Wilder J A, Macedo P B, and Gupta P K, in Digest of Topical Meeting on Gradient ... Index Gradient, U.S. Patent 3,718,383 Feb. 1973 . Shirk J.S, Sandrock M, Scribner D, Fleet E, Stroman ... more details
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