Unreferenced date March 2009 A velocity potential is used in fluid dynamics , when a fluid occupies a simply connected region and is irrotational . In such a case, math nabla times mathbf u 0, math where math mathbf u math denotes the flow velocity of the fluid. As a result, math mathbf u math can be represented as the gradient of a scalar field scalar function math Phi math math mathbf u nabla Phi math , math Phi math is known as a velocity potential for math mathbf u math . A velocity potential is not unique. If math a math is a constant then math Phi a math is also a velocity potential for math mathbf u math . Conversely, if math Psi math is a velocity potential for math mathbf u math then math Psi Phi b math for some constant math b math . In other words, velocity potentials are unique up to a constant.If value of satisfies Laplace equation ,it indicates case of fluid flow. Unlike a stream function , a velocity potential can exist in three dimensional flow. See also Hamiltonian fluid mechanics Potential flow DEFAULTSORT Velocity Potential Category Fluid dynamics Category Equations of fluid dynamics Fluiddynamics stub zh ... more details
Orphan date September 2008 Expressive potential is the degree to which a given MIDI controller music control interface input device enables a musician to control musical expression . An interface with low expressive potential enables control over a narrow range of musical expression, no matter how virtuoso virtuosic its player, whereas an interface with high expressive potential enables control over a wide range of musical expression. Expressive potential is independent of how that potential was, is, or will be realized in any given composition or performance. This independence allows the expressive potential of new musical instruments & interfaces to be compared and contrasted objectively with traditional musical instruments. The concept of expressive potential is closely related to the concept of affordance , i.e. all action possibilities latent in the environment, objectively measurable and independent of the individual s ability to recognize or realize them. One possible metric for expressive potential is the number of Degrees of freedom physics and chemistry degrees of freedom provided by the interface. The more degrees of freedom, the more independent expressive variables a musician can control independently during performance. The development of new interfaces to control musical expression is an active research area, supporting an annual conference, http nime.org New Interfaces for Musical Expression . Category Electronic music ... more details
membrane , the reversal potential also known as the Nernst potential of an ion is the membrane potential at which there is no net overall flow of that particular ion from one side of the membrane to the other. In the case of post synaptic neuron s, the reversal potential is the membrane potential ... ref In a single ion system, reversal potential is synonymous with equilibrium potential their numerical ... potential. Equilibrium refers to the fact that the net ion flux at a particular voltage is zero .... Reversal refers to the fact that a change of membrane potential on either side of the equilibrium potential reverses the overall direction of ion flux. ref name Purves The reversal potential is often called the Nernst potential , as it can be calculated from the Nernst equation . Ion channels conduct ... potential for that ion assuming the outside of the cell is at 0 volts . For example, the resting potential of most cells is close to the potassium K sup sup potassium ion reversal potential. This is because at resting potential, potassium conductance dominates. During a typical action potential ... number of sodium Na sup sup sodium ion channels, which brings the membrane potential close to the reversal potential of sodium. The relationship between the terms reversal potential and equilibrium potential only holds true for single ion systems. In multi ion systems, there are areas of the cell ... potential in the sense that membrane current reverses direction, it is not an equilibrium potential ... across the membrane. When a cell has significant permeabilities to more than one ion, the cell potential ... models The term driving force is related to equilibrium potential, and is likewise useful in understanding ... the actual membrane potential and an ion s equilibrium potential. It is defined by the following equation ... between the membrane potential and the ion s equilibrium potential i.e. V sub m sub E sub ... membrane potential, in the neuromuscular junction math EPC g ACh V m E rev , math where EPC is the end ... more details
Water potential is the potential energy of water per unit volume relative to pure water in reference conditions. Water potential quantifies the tendency of water to move from one area to another due to osmosis , gravity , mechanical pressure , or matrix effects such as surface tension . Water potential ... potential is typically expressed in potential energy per unit volume and very often is represented by the Greek letter math Psi math . Water potential integrates a variety of different potential ... systems, it is common for many potential factors to be important. For example, the addition of solutes to water lowers the water s potential makes it more negative , just as the increase in pressure increases its potential makes it more positive . If possible, water will move from an area of higher water potential to an area that has a lower water potential. One very common example is water ... potential of the solution flow proceeds until the difference in solute potential is balanced by another force, for example, pressure potential. Components of water potential Many different factors may affect the total water potential, and the sum of these potentials determines the overall water potential and the direction of water flow math Psi Psi 0 Psi pi Psi p Psi s Psi v Psi m math ref Taiz ... is the reference correction, math Psi pi math is the Solution solute potential, math Psi p math is the pressure component, math Psi s math is the gravity gravimetric component, math Psi v math is the potential due to humidity , and math Psi m math is the potential due to matrix effects e.g., fluid cohesion and surface tension. All of these factors are quantified as potential energies per unit volume ..., the reference condition is typically defined as pure water at the soil surface. Pressure Potential Pressure potential is based on mechanical pressure, and is an important component of the total water potential within plant cell biology cell s. Pressure potential increases as water enters a cell ... more details
Electromagnetism cTopic Electrostatics Distinguish Electric potential energy In classical electromagnetism , the electric potential a scalar physics scalar quantity denoted by , sub E sub or V and also called the electric field potential or the electrostatic potential at a point is equal to the electric potential energy measured in joule joules of a charged particle at that location divided by the electric charge charge measured in coulomb coulombs of the particle. The electric potential is independent ... potential can be calculated at a point in either a static time invariant electric field or in a dynamic ... volts . There is also a generalized electric scalar potential that is used in electrodynamics when time varying electromagnetic fields are present. This generalized electric potential cannot be simply interpreted as the ratio of potential energy to charge, however. Introduction Objects may possess ... mechanics explores the concepts such as Force physics force , energy , potential etc. in more detail. The electric potential or potential at a point in an electric field is defined as the work done in moving a unit positive charge from infinity to that point. Force and potential energy are directly related. As an object moves in the direction that the force accelerates it, its potential energy decreases. For example, the gravitational potential energy of a cannonball at the top of a hill is greater than at the base of the hill. As the object falls, that potential energy decreases and is translated to motion, or inertial kinetic energy. For certain forces, it is possible to define the potential of a field such that the potential energy of an object due to a field is dependent only on the position ... of time varying magnetic fields. The potential of an electric field is called the electric potential. The synonymous term electrostatic potential is also in common use. The electric potential and the magnetic vector potential together form a four vector , so that the two kinds of potential ... more details
Unreferenced date March 2007 Postsynaptic potentials are changes in the membrane potential of the postsynaptic terminal of a chemical synapse . Postsynaptic potentials are membrane potential graded potentials ... to enter or leave the cell. It is these ions that alter the membrane potential. Ions are subject ... potential Equilibrium potentials equilibrium potential , which is the state where the diffusion ... potential, there is no longer a net movement of ions. Two important equations that can determine membrane potential differences based on ion concentrations are the Nernst equation Nernst Equation and the Goldman Equation . Relation to action potentials Neurons have a resting potential of about 70mV ..., the membrane is said to be depolarization depolarized , as the potential comes closer to zero. This is an excitatory postsynaptic potential EPSP , as it brings the neuron s potential closer to its firing ... of negative charge, this moves the potential further from zero and is referred to as hyperpolarization . This is an inhibitory postsynaptic potential IPSP , as it changes the charge across the membrane .... EPSPs and IPSPs are transient changes in the membrane potential, and EPSPs resulting from transmitter ... large fluctuations in membrane potential. If the postsynaptic cell is sufficiently depolarized, an action potential will occur. Action potentials are not graded they are all or none responses. Termination ... is returned to its equilibrium potential. Algebraic summation Postsynaptic potentials are subject to summation ... two excitatory postsynaptic potentials, they combine so that the membrane potential is depolarized by the sum ... potentials, they can cancel out, or one can be stronger than the other, and the membrane potential ... receives an excitatory postsynaptic potential, and then the presynaptic neuron fires again, creating .... See also Action potential Electrophysiology Goldman equation Membrane potential Nernst equation Neuron Neurotransmission Postsynaptic Synapse End plate potential External links MeshName Postsynaptic ... more details
independent assessment of the method. ref Analysis of the potential of the Ecological Footprint ...?isoID 56 files DG Environment June 2008 Potential of the Ecological Footprint for monitoring environmental ...The ecological footprint is a measure of human demand on the Earth s ecosystems . It is a standardized measure of demand for natural capital that may be contrasted with the planet s Ecology ecological ... take to support humanity if everybody followed a given lifestyle. For 2007, humanity s total ecological footprint was estimated at 1.5 planet Earths in other words, humanity uses ecological services ... ecological footprint is widely used, ref United Nations Environment Programme UNEP reports. http ... ref Analysis Image Human welfare and ecological footprint.jpg thumb right 400px Ecological ... academic publication about the ecological footprint was by William Rees academic William Rees in 1992 ... October title Ecological footprints and appropriated carrying capacity what urban economics leaves out ... ref The ecological footprint concept and calculation method was developed as the PhD dissertation ..., from 1990 1994. ref Cite thesis degree PhD title Ecological Footprint and Appropriated Carrying ..., Vancouver. ref To make the idea more accessible, Rees came up with the term ecological footprint ..., February 17, 2008 ref In early 1996, Wackernagel and Rees published the book Our Ecological Footprint Reducing Human Impact on the Earth. ref name Wackernagel & Rees Ecological footprint analysis ... . Per capita ecological footprint EF , or ecological footprint analysis EFA , is a means of comparing ... , with the aim of altering personal behavior. Ecological footprints may be used to argue that many ... newsletter bv new data shows humanitys ecological debt compounding Living Planet Report 2008 outlines ... areas. ref name Wackernagel & Rees Wackernagel, Mathis & Rees, William 1996 Our Ecological Footprint New Society Press ref A number of NGO websites allow estimation of one s ecological footprint see Ecological ... more details
about a form of energy in physics the statistical method Potential energy statistics Classical mechanics Refimprove date June 2010 In physics , potential energy is the energy of a body or a system due ... potential energy was coined by the 19th century Scottish engineer and physicist William Rankine ... ref Overview Potential energy exists when a force acts upon an object that tends to restore it to a lower ... disappear. Instead, it is stored as potential energy. If the spring is released or the mass is dropped ... coaster. When the coaster climbs a hill it has potential energy. At the very top of the hill is its maximum potential energy. When the coaster speeds down the hill potential energy turns into kinetic. Kinetic energy is greatest at the bottom. The more formal definition is that potential energy ... position. There are various types of potential energy, each associated with a particular type of force. More specifically, every conservative force gives rise to potential energy. For example, the work of an Elasticity physics elastic force is called elastic potential energy work of the gravitational force is called gravitational potential energy work of the Coulomb force is called electric potential energy work of the strong nuclear force or weak nuclear force acting on the baryon charge physics charge is called nuclear potential energy work of intermolecular forces is called intermolecular potential energy. Chemical potential energy, such as the energy stored in fossil fuels , is the work ... of particles and the potential energy of their mutual positions. As a general rule, the work done by a conservative force F will be math ,W Delta U math where math Delta U math is the change in the potential energy associated with that particular force. Common notations for potential energy are U , V , and E sub p sub . Reference level The potential energy is a function of the state a system is in, and is defined .... Typically the potential energy of a system depends on the relative positions of its components ... more details
The potential density of a fluid parcel at pressure math P math is the density that the parcel would acquire if adiabatic process adiabatically brought to a reference pressure math P 0 math , often 1 bar unit bar 100 kilopascal kPa . Whereas density changes with changing pressure, potential density of a fluid parcel is conservation law conserved as the pressure experienced by the parcel changes provided no mixing with other parcels or net heat flux occurs . The concept is used in oceanography http oceanworld.tamu.edu resources ocng textbook contents.html and to a lesser extent atmospheric science . Potential density is a dynamically important property for static stability potential density must decrease upward. If it doesn t, a fluid parcel displaced upward finds itself lighter than its neighbors, and continues to move upward similarly, a fluid parcel displaced downward would be heavier than its neighbors. This is true even if the density of the fluid decreases upward. In stable conditions potential density decreasing upward motion along surfaces of constant potential density isopycnal s is energetically favored over flow across these surfaces diapycnal flow , so most of the motion ... rho theta math is used to denote potential density , with the reference pressure math P 0 math taken to be the pressure at the ocean surface. The corresponding potential density anomaly is denoted by math ... pressure to keep the definition of potential density dynamically meaningful. Reference pressures ... , say, the reference pressure 400 bar would be used, and the potential density anomaly symbol would be written math sigma 4 math . Potential density adjusts for the effect of Compressibility compression ... . The potential density would then be calculated as math rho theta rho P 0, theta,S 1,S 2,... math where math theta math is the potential temperature of the fluid parcel for the same reference pressure math P 0 math . See also Potential energy References cite book author John M. Wallace and Peter V ... more details
The relatively static membrane potential of quiescent cells is called the resting membrane potential or resting voltage , as opposed to the specific dynamic electrochemical phenomena called action potential and graded membrane potential . Apart from the latter two, which occur in Membrane potential excitable ... potential and dynamic voltage changes like action potential from biophysical point of view all ... ion channel s, ion transporter s, and exchangers. Conventionally, resting membrane potential can ... Any voltage is a difference in electric potential between two points for example, the separation .... The typical resting membrane potential of a cell arises from the separation of potassium ions ... relative permeability for potassium, the resulting membrane potential is almost always close to the potassium reversal potential . But in order for this process to occur, a concentration gradient ... membrane potential across an animal cell s cell membrane plasma membrane , potassium and sodium ... potential may be established by acidification of the inside of a membranous compartment such as the proton pump that generates membrane potential across synaptic vesicle membranes . Citation needed date January 2009 Electroneutrality In most quantitative treatments of membrane potential, such as the derivation ... charge excess in any side of the membrane. So, although there is an electric potential across ... involved in generating the resting potential below , that is, there is no actual measurable charge excess in either side. That occurs because the effect of charge on electrochemical potential is hugely ... change on electric potential. Generation of the resting potential Cell membranes are typically permeable ..., and others. To simplify the description of the ionic basis of the resting membrane potential, it is most ... to start. Image Membrane potential development.jpg thumb 400px A diagram showing the progression in the development of a membrane potential from a concentration gradient for potassium . span ... more details
The potential temperature of a Air parcel parcel of fluid at pressure math P math is the temperature ... math P 0 math , usually 1000 millibars. The potential temperature is denoted math theta math and, for air ... s equation. Contexts The concept of potential temperature applies to any stratified fluid. It is most ... in very deep ocean trenches and within the ocean mixed layer . When potential temperature is used instead, these apparently unstable conditions vanish. Comments Potential temperature is a more dynamically ... and warm as it descends on the other side but the potential temperature will not change in the absence ... to as dry adiabatic . Since parcels with the same potential temperature can be exchanged without work or heating being required, lines of constant potential temperature are natural flow pathways. Under almost all circumstances, potential temperature increases upwards in the atmosphere, unlike actual temperature which may increase or decrease. Potential temperature is conserved for all dry ... very close to being dry adiabatic . Potential temperature is a useful measure of the static stability of the unsaturated atmosphere. Under normal, stably stratified conditions, the potential temperature .... If the potential temperature decreases with height, math frac partial theta partial z 0 math ... of decreasing potential temperature with height are uncommon, except while vigorous convection is underway or during periods of strong insolation . Situations in which the equivalent potential temperature ... potential temperature is conserved under adiabatic or isentropic air motions, in steady, adiabatic flow lines or surfaces of constant potential temperature act as Streamlines, streaklines, and pathlines ... http weather.cod.edu analysis analysis.isentropic.html Potential temperature perturbations The atmospheric boundary layer ABL potential temperature perturbation is defined as the difference between the potential temperature of the ABL and the potential temperature of the free atmosphere above the ABL ... more details
about the general concept in the mathematical theory of vector fields the vector potential in electromagnetism Magnetic vector potential the vector potential in fluid mechanics Stream function In vector calculus , a vector potential is a vector field whose Curl mathematics curl is a given vector field. This is analogous to a scalar potential , which is a scalar field whose negative gradient is a given vector field. Formally, given a vector field v , a vector potential is a vector field A such that math mathbf v nabla times mathbf A . math If a vector field v admits a vector potential A , then from the equality math nabla cdot nabla times mathbf A 0 math divergence of the Curl mathematics curl is zero one obtains math nabla cdot mathbf v nabla cdot nabla times mathbf A 0, math which implies that v must be a solenoidal vector field . An interesting question is then if any solenoidal vector field admits a vector potential. The answer is yes, if the vector field satisfies certain conditions. fact date November 2011 Theorem Let math mathbf v mathbb R 3 to mathbb R 3 math be a solenoidal vector field which is twice smooth function continuously differentiable . Assume that v x decreases sufficiently fast as x . Define math mathbf A mathbf x frac 1 4 pi nabla times int mathbb R 3 frac mathbf v mathbf y left mathbf x mathbf y right , d mathbf y . math Then, A is a vector potential for v , that is, math nabla times mathbf A mathbf v . math A generalization of this theorem is the Helmholtz decomposition which states that any vector field can be decomposed as a sum of a solenoidal vector field and an irrotational vector field . Nonuniqueness The vector potential admitted by a solenoidal field is not unique. If A is a vector potential for v , then so is math mathbf A nabla m math where ... of vector analysis Magnetic potential Solenoid References Fundamentals of Engineering Electromagnetics by David K. Cheng, Addison Wesley, 1993. Category Fundamental physics concepts Category Potential ... more details
In mathematics , the Newtonian potential or Newton potential is an Operator mathematics operator in vector calculus that acts as the inverse to the negative Laplacian , on functions that are smooth and decay rapidly enough at infinity. As such, it is a fundamental object of study in potential theory ... case of three variables , where it served as the fundamental gravitational potential in Newton s law of universal gravitation . In modern potential theory, the Newtonian potential is instead thought of as an electrostatic potential . The Newtonian potential of a compact support compactly supported ... harv Evans 1998 and harv Gilbarg Trudinger 1983 . The Newtonian potential w of is a solution of the Poisson ... potential of a function is a partial inverse to the Laplace operator. The solution is not unique ... regular domains, and for suitably well behaved functions one first applies a Newtonian potential ... data. The Newtonian potential is defined more broadly as the convolution math Gamma mu x int mathbb ..., when the measure is positive measure positive , the Newtonian potential is subharmonic function ... R d f y ,dy. math In dimension d 3, this reduces to Newton s theorem that the potential ... sub , then the Newtonian potential of is referred to as a simple layer potential . Simple layer ... of electrostatics in the context of the electrostatic potential associated to a charge distribution ... to the study of the Neumann problem for the Laplace equation. See also Double layer potential Green s function Riesz potential Green s function for the three variable Laplace equation References ... isbn 3 540 41160 7 . springer id n n066580 title Newton potential first E.D. last Solomentsev springer id s s085260 title Simple layer potential first E.D. last Solomentsev springer id s s091400 title Surface potential first E.D. last Solomentsev Category Harmonic functions Category Isaac Newton Category Partial differential equations Category Potential theory Category Singular integrals pt Potencial ... more details
In anatomy , potential space refers to a space or cavity that can exist because two adjacent features that are not tightly adjoined, but does not appear during normal functioning. Examples subdural space vagina pericardial cavity costodiaphragmatic recess References Citations 1. cite book last Guyton first Arthur title Textbook of Medical Physiology publisher Elsevier Saunders location St. Louis year 2006 isbn 9780721602400 DEFAULTSORT Potential Space Category Anatomy Anatomy stub ... more details
Wikify date July 2011 The Buckingham potential is a formula that describes the Pauli repulsion energy and van der Waals energy math Phi 12 r math for the interaction of two atoms that are not directly bonded as a function of the interatomic distance math r math . math Phi 12 r A exp left Br right frac C r 6 math Here, math A math , math B math and math C math are constants. The two terms on the right hand side constitute a repulsion and an attraction, because they are positive and negative, respectively. Richard A. Buckingham proposed this, as a simplification of the Lennard Jones potential , in a theoretical study of the equation of state for gaseous helium, neon and argon ref R. A. Buckingham, The Classical Equation of State of Gaseous Helium, Neon and Argon , Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 168 pp. 264 283 1938 ref As explained in Buckingham s original paper and, e.g., in section 2.2.5 of Jensen s text ref name jensen F. Jensen, Introduction to Computational Chemistry , 2nd ed., Wiley, 2007, ref the repulsion is due to the interpenetration of the closed electron shells. There is therefore some justification for choosing the repulsive part of the potential as an exponential function. The Buckingham potential has been used extensively in simulations of molecular dynamics. Because the exponential term converges to a constant as math r math math 0 math , while the math r 6 math term diverges, the Buckingham potential turns over as math r math becomes small. This may be problematic when dealing with a structure with very short interatomic distances, as nuclear fusion can occur. ref name jensen References Reflist External links http www.sklogwiki.org SklogWiki index.php Buckingham potential Buckingham potential on http www.sklogwiki.org SklogWiki index.php Main Page SklogWiki Category Theoretical chemistry Category ... Category Potential ru ... more details
Unreferenced stub auto yes date December 2009 Ionic potential is the ratio of electric charge to the ionic radius radius of an ion . As such, the proportion measures the charge density at the surface of the ion usually the denser the charge, the stronger will be the ionic bond bond that the ion forms. The ionic potential gives the sense of how strongly or weakly the ion will be attracted, electrostatically, to ions of opposite charge and to what extent the ion will repel other ions of like charge. See also Surface charge Physical chemistry stub DEFAULTSORT Ionic Potential Category Ions Category Physical chemistry zh ... more details
Spike potentials are one of the action potential s, which occur in electrical activity of smooth muscle contraction in animals. These are true action potentials. Examples In the human gut they occur automatically when the resting membrane potential of the gastrointestinal smooth muscle becomes more positive than about 40 millivolts the normal resting membrane potential in the smooth muscle fibers of the gut is between 50 and 60 millivolts . The spike potentials last 10 to 40 times as long in gastrointestinal muscle as the action potentials in large nerve fibers , each gastrointestinal spike lasting as long as 10 to 20 milliseconds. ref guyton medical physiology 11th edition 2006, chapter 62, page 773 ref References Reflist Category Electrophysiology ... more details
the scalar potential of electromagnetism electric potential all other uses potential File Mass potential well increasing mass.gif thumb gravitational potential well of an increasing mass where math mathbf F nabla P math A scalar potential is a fundamental concept in vector analysis and physics the adjective scalar is frequently omitted if there is no danger of confusion with vector potential . The scalar potential is an example of a scalar field . Given a vector field F , the scalar potential ..., mathematicians may use a positive sign in front of the gradient to define the potential. ref See http www.math.umn.edu nykamp m2374 readings findpot for an example where the potential is defined without ... 5 author Louis Leithold page 1199 avoid using the term potential when solving for a function from its ... per unit length. In order for F to be described in terms of a scalar potential only, the following ... play a prominent role in many areas of physics and engineering. The gravity potential is the scalar potential associated with the gravity per unit mass, i.e., the acceleration due to the field, as a function of position. The gravity potential is the gravitational potential energy per unit mass. In electrostatics the electric potential is the scalar potential associated with the electric field , i.e., with the electrostatic force per unit Electric charge charge . The electric potential is in this case the electrostatic potential energy per unit charge. In fluid dynamics , irrotational lamellar field s have a scalar potential only in the special case when it is a Laplacian field . Certain aspects of the nuclear force can be described by a Yukawa potential . The potential play a prominent role ... mechanics . Further, the scalar potential is the fundamental quantity in quantum mechanics . Not every vector field has a scalar potential. Those that do are called conservative vector field conservative ... in terms of a scalar potential and corresponding vector potential . In electrodynamics the electromagnetic ... more details
File Diagram of zeta potential and slipping planeV2.svg thumb 300px Diagram showing the ionic concentration and potential difference as a function of distance from the charged surface of a particle suspended in a dispersion medium. Zeta potential is a scientific term for electrokinetic potential ref Definition of http goldbook.iupac.org E01968.html electrokinetic potential in IUPAC. Compendium of Chemical ... denoted using the Greek letter zeta , hence potential . From a theoretical viewpoint, zeta potential is electric potential in the interfacial double layer interfacial double layer DL at the location ... potential is the potential difference between the dispersion medium and the stationary layer of fluid ... potential is that its value can be related to the stability of colloidal dispersions e.g., a multivitamin syrup . The zeta potential indicates the degree of repulsion between adjacent, similarly ..., a high zeta potential will confer stability, i.e., the solution or dispersion will resist aggregation. When the potential is low, attraction exceeds repulsion and the dispersion will break and flocculate. So, colloids with high zeta potential negative or positive are electrically stabilized while colloids .... citation needed date November 2011 class wikitable Zeta potential mV Stability behavior of the colloid ... Moderate stability from 40 to 60 Good stability more than 61 Excellent stability Zeta potential ..., zeta potential is not equal to the Stern potential or electric surface potential in the double .... Nevertheless, zeta potential is often the only available path for characterization of double layer properties. Zeta potential should not be confused with electrode potential or electrochemical potential because electrochemical reactions are generally not involved in the development of zeta potential . Measurement of zeta potential Zeta potential is not measurable directly but it can be calculated ... for calculation of zeta potential. Electrokinetic phenomena main Electrokinetic phenomena Electrophoresis ... more details
Cleanup date July 2007 Statistical mechanics cTopic Thermodynamic potential Potentials The grand potential is a quantity used in statistical mechanics , especially for irreversible processes in Open system systems theory open system s. Grand potential is defined by math Phi G stackrel mathrm def U T S mu N math Where U is the energy , T is the temperature of the system, S is the entropy , is the chemical potential , and N is the number of particles in the system. The change in the grand potential is given by math d Phi G S dT N d mu P dV math Where P is pressure and V is volume . When the system is in thermodynamic equilibrium , sub G sub is a minimum. This can be seen by considering that d sub G sub is zero if the volume is fixed and the temperature and chemical potential have stopped evolving. For an ideal gas, math Phi G k B T ln Xi k B T Z 1 e beta mu math where is the grand partition function , k sub B sub is Boltzmann constant , Z sub 1 sub is the partition function statistical mechanics partition function for 1 particle and is equal to 1 k sub B sub T. Landau free energy Some authors refer to the Landau free energy or Landau potential as ref Lee, Joon Chang. 2002 book Thermal Physics Entropy and Free Energies ch. 5 . New Jersey World Scientific ref ref Reference on Landau potential is found in the book States of Matter by David Goodstein page 19 as math Omega F mu N , math where F is the Helmholtz free energy. For homogeneous systems, one obtains math Omega PV , math ref math Omega stackrel mathrm def F mu N U T S mu N math named after Russian physicist Lev Landau , which may be a synonym for the grand potential, depending on system stipulations. References Reflist See also Gibbs free energy Gibbs energy Helmholtz free energy Helmholtz energy External links http theory.ph.man.ac.uk judith stat therm node88.html Grand Potential Manchester University Category Thermodynamics de Gro kanonisches Potential ko he ja ru ... more details
Ecological region may refer to Ecoregion , a geographically defined area that is smaller than an ecozone and larger than an ecosystem A collection of ecological districts of New Zealand dab ... more details
In mathematics , the Riesz potential is a potential theory potential named after its discoverer, the Hungary Hungarian mathematician Marcel Riesz . In a sense, the Riesz potential defines an inverse for a power of the Laplace operator on Euclidean space. They generalize to several variables the Riemann Liouville integral s of one variable. If 0 &alpha n , then the Riesz potential I sub &alpha sub &fnof of a locally integrable function &fnof on R sup n sup is the function defined by NumBlk math I alpha f x frac 1 C alpha int mathbb R n frac f y x y n alpha , mathrm d y math EquationRef 1 where the constant is given by math C alpha pi n 2 2 alpha frac Gamma alpha 2 Gamma n alpha 2 . math This singular integral is well defined provided &fnof decays sufficiently rapidly at infinity, specifically if &fnof &isin Lp space L sup p sup R sup n sup with 1 p n &alpha . If p 1, then the rate of decay of &fnof and that of I sub &alpha sub &fnof are related in the form of an inequality the Hardy Littlewood Sobolev inequality math ... n . The Riesz potential can be defined more generally in a distribution mathematics weak sense ... function math K alpha x frac 1 C alpha frac 1 x n alpha . math The Riesz potential can therefore be defined whenever &fnof is a compactly supported distribution. In this connection, the Riesz potential ... in potential theory because I sub &alpha sub &mu is then a continuous subharmonic function off the support ... reveals that the Riesz potential is a Fourier multiplier . In fact, one has math widehat K alpha ... of functions, math lim alpha to 0 I alpha f x f x . math See also Bessel potential Fractional ... N. S. title Foundations of modern potential theory publisher Springer Verlag location Berlin, New ... Solomentsev first E.D. id R r082270 title Riesz potential citation first Elias last Stein authorlink ... Category Partial differential equations Category Potential theory Category Singular integrals ... more details
In physics , chemistry and biology , a potential gradient is the local derivative rate of change of the potential with respect to displacement, i.e. spatial derivative, or gradient. This quantity frequently occurs in equations of physical processes because it leads to some form of flux . In electrical engineering it refers specifically to electric potential gradient, which is equal to the electric field . Definition Elementary algebra calculus Fundamentally the expression for a potential gradient F in one dimension takes the form ref Essential Principles of Physics, P.M. Whelan, M.J. Hodgeson, 2nd ... is some type of potential , and x is displacement not distance , in the x direction. In the limit of infinitesimal ... differentials math F frac rm d phi rm d x , math In three dimensions, the resultant potential gradient is the sum of the potential gradients in each direction, in Cartesian coordinates math bold F bold ... , math bold F nabla phi , math Vector calculus The mathematical nature of a potential gradient arises ... problems, the scalar field is the potential, and the vector field is a force field, or flux current ... can be shown to be conservative, it is equal to the gradient in gravitational potential math mathbf g nabla Phi , math Notice the opposite signs between gravitational field and potential because as the potential gradient and field are opposite in direction, as the potential gradient increases, the gravitational ... field has identical properties to the gravitational field it is the gradient of the electric potential ... to the gradient in electric potential, a time dependent term must be added ref Introduction to Electrodynamics ... vector potential . Chemistry main Electrode potentials In an Electrochemistry Electrochemical ... , the Standard conditions for temperature and pressure standard electric potential difference is ref ... standard conditions . The potential gradient is relatively abrupt, since there is an almost definite boundary between the metal and solution, hence the term interface. Biology In biology , potential ... more details
Image GravityPotential.jpg thumb 300px Plot of a two dimensional slice of the gravitational potential ... of the body. In classical mechanics , the gravitational potential at a location is equal to the Work ... moves to that location from a reference location. It is analogous to the electric potential with mass playing the role of charge physics charge . By convention, the gravitational potential is defined ... potential is also known as the Newtonian potential and is fundamental in the study of potential theory . Potential energy The gravitational potential V is the potential energy U per unit mass math U m V math where m is the mass of the object. The potential energy is the negative of the work .... If the body has a mass of 1 unit, then the potential energy to be assigned to that body is equal to the gravitational potential. So the potential can be interpreted as the negative of the work done by the gravitational ... constant. In that case, the difference in potential energy from one height to another is to a good ... form The Scalar potentialpotential V at a distance x from a point particle point mass of mass M is math V frac GM x , math where G is the gravitational constant . The potential has units of energy ... of the gravitational potential. Because the potential has no angular components, its gradient is math ... square law math mathbf a frac GM x 2 . math The potential associated with a mass distribution ... n sub and have masses m sub 1 sub , ..., m sub n sub , then the potential of the distribution at the point ... measure dm on three dimensional Euclidean space R sup 3 sup , then the potential is the convolution ... , where dv r is the Euclidean volume element , then the gravitational potential is the volume integral ... is a potential function coming from a continuous mass distribution &rho r , then &rho can be recovered ... of distribution mathematics distribution s. As a consequence, the gravitational potential satisfies ... potential . Spherical symmetry A spherically symmetric mass distribution behaves to an observer ... more details
one source date October 2011 Reduction potential also known as redox potential , oxidation reduction potential , ORP or math E h math is a measure of the tendency of a chemical species to acquire electron s and thereby be redox reduced . Reduction potential is measured in volt s V , or millivolts mV . Each species has its own intrinsic reduction potential the more positive the potential, the greater ... solution s, the reduction potential is a measure of the tendency of the solution to either gain ... more positive reduction potential than the new species will have a tendency to gain electrons ... more negative reduction potential will have a tendency to lose electrons to the new species i.e. to be oxidized ... the reduction potential of an aqueous solution. Like pH, the reduction potential represents ... the Absolute electrode potential absolute potentials are difficult to accurately measure, reduction ... are determined by measuring the potential difference between an inert sensing electrode in contact ... standard of known potential. The standard hydrogen electrode SHE is the reference from which all standard redox potentials are determined and has been assigned an arbitrary half cell potential ... measurement of the reduction potential in aqueous solutions is relatively straightforward, many factors ... seldom correlate with calculated values. Nevertheless, reduction potential measurement has ... value e.g. process control and titration s . Standard reduction potential, math E 0 math see also Standard hydrogen electrode The standard reduction potential math E 0 math is measured under ... gas that is part of the reaction, and metal s in their pure state. The standard reduction potential ... given a potential of 0.00 volts. Historically, many countries, including the United States and Canada ... potential is quoted as measured against a different reference electrode than the one desired and it becomes necessary to convert to the desired reference potential. Alternatively, it may be necessary ... more details
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