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57-549: Iverian Mountain or Iberian Mountain is a 344-meter (1129 feet) high hill in New Athos , Abkhazia , Georgia . There are ruins of the ancient capital of Abkhazia, Anakopia , on the mountain top. On the mountain northern slope New Athos Cave is located. From the top of Iverian Mountain a scenic view of the Black Sea coast from Bichvinta Cape  [ ru ] to Sukhumi opens. This Georgia location article

114-581: A topographical prominence requirement, typically 100 feet (30.5 m) or 500 feet (152.4 m). In practice, mountains in Scotland are frequently referred to as "hills" no matter what their height, as reflected in names such as the Cuillin Hills and the Torridon Hills . In Wales, the distinction is more a term of land use and appearance and has nothing to do with height. For a while,

171-418: A body with no net movement of matter. An example of a process where both bulk motion and diffusion occur is human breathing. First, there is a "bulk flow" process. The lungs are located in the thoracic cavity , which expands as the first step in external respiration. This expansion leads to an increase in volume of the alveoli in the lungs, which causes a decrease in pressure in the alveoli. This creates

228-489: A formalism similar to Fourier's law for heat conduction (1822) and Ohm's law for electric current (1827). Robert Boyle demonstrated diffusion in solids in the 17th century by penetration of zinc into a copper coin. Nevertheless, diffusion in solids was not systematically studied until the second part of the 19th century. William Chandler Roberts-Austen , the well-known British metallurgist and former assistant of Thomas Graham studied systematically solid state diffusion on

285-436: A hill). The rounded peaks of hills results from the diffusive movement of soil and regolith covering the hill, a process known as downhill creep . Various names may be used to describe types of hills, based on appearance and method of formation. Many such names originated in one geographical region to describe a type of hill formation particular to that region, though the names are often adopted by geologists and used in

342-548: A limit of 2,000 feet (610 m) and Whittow states "Some authorities regard eminences above 600 m (1,969 ft) as mountains, those below being referred to as hills." Today, a mountain is usually defined in the UK and Ireland as any summit at least 2,000 feet or 610 meters high, while the UK government's Countryside and Rights of Way Act 2000 defined mountainous areas (for the purposes of open access legislation) as areas above 600 meters (1,969 feet). Some definitions include

399-530: A liquid medium and just large enough to be visible under an optical microscope exhibit a rapid and continually irregular motion of particles known as Brownian movement. The theory of the Brownian motion and the atomistic backgrounds of diffusion were developed by Albert Einstein . The concept of diffusion is typically applied to any subject matter involving random walks in ensembles of individuals. In chemistry and materials science , diffusion also refers to

456-536: A much smaller force entrenched on the hill top. Battles for the possession of high ground have often resulted in heavy casualties to both sides, such as the 1969 Battle of Hamburger Hill during the Vietnam War , the Battle of Stalingrad and Battle of Peleliu during World War II , and the 1969 Kargil War between India and Pakistan. The Great Wall of China is an enduring example of hilltop fortification. It

513-524: A physical and atomistic one, by considering the random walk of the diffusing particles . In the phenomenological approach, diffusion is the movement of a substance from a region of high concentration to a region of low concentration without bulk motion . According to Fick's laws, the diffusion flux is proportional to the negative gradient of concentrations. It goes from regions of higher concentration to regions of lower concentration. Sometime later, various generalizations of Fick's laws were developed in

570-441: A pressure gradient between the air outside the body at relatively high pressure and the alveoli at relatively low pressure. The air moves down the pressure gradient through the airways of the lungs and into the alveoli until the pressure of the air and that in the alveoli are equal, that is, the movement of air by bulk flow stops once there is no longer a pressure gradient. Second, there is a "diffusion" process. The air arriving in

627-454: A wider geographical context. These include: Many settlements were originally built on hills, either to avoid floods (particularly if they were near a large body of water), for defense (since they offer a good view of the surrounding land and require would-be attackers to fight uphill), or to avoid densely forested areas. For example, Ancient Rome was built on seven hills , helping to protect it from invaders. Some settlements, particularly in

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684-562: Is In case the diffusion coefficient is independent of x {\displaystyle x} , Fick's second law can be simplified to where Δ {\displaystyle \Delta } is the Laplace operator , Fick's law describes diffusion of an admixture in a medium. The concentration of this admixture should be small and the gradient of this concentration should be also small. The driving force of diffusion in Fick's law

741-479: Is where ( J , ν ) {\displaystyle (\mathbf {J} ,{\boldsymbol {\nu }})} is the inner product and o ( ⋯ ) {\displaystyle o(\cdots )} is the little-o notation . If we use the notation of vector area Δ S = ν Δ S {\displaystyle \Delta \mathbf {S} ={\boldsymbol {\nu }}\,\Delta S} then The dimension of

798-418: Is a net movement of oxygen molecules down the concentration gradient. In astronomy , atomic diffusion is used to model the stellar atmospheres of chemically peculiar stars . Diffusion of the elements is critical in understanding the surface composition of degenerate white dwarf stars and their evolution over time. In the scope of time, diffusion in solids was used long before the theory of diffusion

855-414: Is a stub . You can help Misplaced Pages by expanding it . This Abkhazia location article is a stub . You can help Misplaced Pages by expanding it . Hill A hill is a landform that extends above the surrounding terrain. It often has a distinct summit , and is usually applied to peaks which are above elevation compared to the relative landmass, though not as prominent as mountains . Hills fall under

912-545: Is a small hill. Other words include knoll and (in Scotland, Northern Ireland and northern England) its variant, knowe. Artificial hills may be referred to by a variety of technical names, including mound and tumulus . Hills may form through geomorphic phenomena : faulting , erosion of larger landforms such as mountains and movement and deposition of sediment by glaciers (notably moraines and drumlins or by erosion exposing solid rock which then weathers down into

969-536: Is a vector J {\displaystyle \mathbf {J} } representing the quantity and direction of transfer. Given a small area Δ S {\displaystyle \Delta S} with normal ν {\displaystyle {\boldsymbol {\nu }}} , the transfer of a physical quantity N {\displaystyle N} through the area Δ S {\displaystyle \Delta S} per time Δ t {\displaystyle \Delta t}

1026-423: Is called a normal diffusion (or Fickian diffusion); Otherwise, it is called an anomalous diffusion (or non-Fickian diffusion). When talking about the extent of diffusion, two length scales are used in two different scenarios: "Bulk flow" is the movement/flow of an entire body due to a pressure gradient (for example, water coming out of a tap). "Diffusion" is the gradual movement/dispersion of concentration within

1083-437: Is comparable to or smaller than the mean free path of the molecule diffusing through the pore. Under this condition, the collision with the pore walls becomes gradually more likely and the diffusivity is lower. Finally there is configurational diffusion, which happens if the molecules have comparable size to that of the pore. Under this condition, the diffusivity is much lower compared to molecular diffusion and small differences in

1140-436: Is intensity of any local source of this quantity (for example, the rate of a chemical reaction). For the diffusion equation, the no-flux boundary conditions can be formulated as ( J ( x ) , ν ( x ) ) = 0 {\displaystyle (\mathbf {J} (x),{\boldsymbol {\nu }}(x))=0} on the boundary, where ν {\displaystyle {\boldsymbol {\nu }}}

1197-564: Is popular in hilly areas such as the English Peak District and the Scottish Highlands . Many hills are categorized according to relative height or other criteria and feature on lists named after mountaineers, such as Munros (Scotland) and Wainwrights (England). Specific activities such as " peak bagging " (or "Munro bagging") involve climbing hills on these lists with the aim of eventually climbing every hill on

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1254-412: Is the j {\displaystyle j} th thermodynamic force and L i j {\displaystyle L_{ij}} is Onsager's matrix of kinetic transport coefficients . The thermodynamic forces for the transport processes were introduced by Onsager as the space gradients of the derivatives of the entropy density s {\displaystyle s} (he used

1311-528: Is the antigradient of concentration, − ∇ n {\displaystyle -\nabla n} . In 1931, Lars Onsager included the multicomponent transport processes in the general context of linear non-equilibrium thermodynamics. For multi-component transport, where J i {\displaystyle \mathbf {J} _{i}} is the flux of the i {\displaystyle i} th physical quantity (component), X j {\displaystyle X_{j}}

1368-421: Is the change in the value of a quantity; for example, concentration, pressure , or temperature with the change in another variable, usually distance . A change in concentration over a distance is called a concentration gradient , a change in pressure over a distance is called a pressure gradient , and a change in temperature over a distance is called a temperature gradient . The word diffusion derives from

1425-434: Is the normal to the boundary at point x {\displaystyle x} . Fick's first law: The diffusion flux, J {\displaystyle \mathbf {J} } , is proportional to the negative gradient of spatial concentration, n ( x , t ) {\displaystyle n(x,t)} : where D is the diffusion coefficient . The corresponding diffusion equation (Fick's second law)

1482-458: Is universally recognized that atomic defects are necessary to mediate diffusion in crystals. Henry Eyring , with co-authors, applied his theory of absolute reaction rates to Frenkel's quasichemical model of diffusion. The analogy between reaction kinetics and diffusion leads to various nonlinear versions of Fick's law. Each model of diffusion expresses the diffusion flux with the use of concentrations, densities and their derivatives. Flux

1539-460: Is widely used in many fields, including physics ( particle diffusion ), chemistry , biology , sociology , economics , statistics , data science , and finance (diffusion of people, ideas, data and price values). The central idea of diffusion, however, is common to all of these: a substance or collection undergoing diffusion spreads out from a point or location at which there is a higher concentration of that substance or collection. A gradient

1596-457: The i {\displaystyle i} th component. The corresponding driving forces are the space vectors where T is the absolute temperature and μ i {\displaystyle \mu _{i}} is the chemical potential of the i {\displaystyle i} th component. It should be stressed that the separate diffusion equations describe the mixing or mass transport without bulk motion. Therefore,

1653-495: The Latin word, diffundere , which means "to spread out". A distinguishing feature of diffusion is that it depends on particle random walk , and results in mixing or mass transport without requiring directed bulk motion. Bulk motion, or bulk flow, is the characteristic of advection . The term convection is used to describe the combination of both transport phenomena . If a diffusion process can be described by Fick's laws , it

1710-472: The kinetic coefficients L i j {\displaystyle L_{ij}} should be symmetric ( Onsager reciprocal relations ) and positive definite ( for the entropy growth ). The transport equations are Here, all the indexes i , j , k = 0, 1, 2, ... are related to the internal energy (0) and various components. The expression in the square brackets is the matrix D i k {\displaystyle D_{ik}} of

1767-596: The 1775 Battle of Bunker Hill (which was actually fought on Breed's Hill ) in the American War of Independence ; and Cemetery Hill and Culp's Hill in the 1863 Battle of Gettysburg , the turning point of the American Civil War . The Battle of San Juan Hill in the 1898 Spanish–American War won the Americans control of Santiago de Cuba but only after suffering from heavy casualties inflicted by

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1824-528: The Middle East, are located on artificial hills consisting of debris (particularly mudbricks ) that has accumulated over many generations. Such a location is known as a " tell ". In Northern Europe , many ancient monuments are sited in heaps. Some of these are defensive structures (such as the hillforts of the Iron Age ), but others appear to have hardly any significance. In Britain, many churches at

1881-460: The US defined a mountain as being 1,000 feet (304.8 m) or more tall. Any similar landform lower than this height was considered a hill. The United States Geological Survey , however, has concluded that these terms do not in fact have technical definitions in the US. The Great Soviet Encyclopedia defined "hill" as an upland with a relative height of up to 200 m (660 ft). A hillock

1938-401: The alveoli has a higher concentration of oxygen than the "stale" air in the alveoli. The increase in oxygen concentration creates a concentration gradient for oxygen between the air in the alveoli and the blood in the capillaries that surround the alveoli. Oxygen then moves by diffusion, down the concentration gradient, into the blood. The other consequence of the air arriving in alveoli is that

1995-474: The category of slope landforms . The distinction between a hill and a mountain is unclear and largely subjective, but a hill is universally considered to be not as tall, or as steep as a mountain. Geographers historically regarded mountains as hills greater than 1,000 feet (304.8 meters) above sea level . In contrast, hillwalkers have tended to regard mountains as peaks 2,000 feet (610 m) above sea level. The Oxford English Dictionary also suggests

2052-413: The cell (against the concentration gradient). Because there are more oxygen molecules outside the cell, the probability that oxygen molecules will enter the cell is higher than the probability that oxygen molecules will leave the cell. Therefore, the "net" movement of oxygen molecules (the difference between the number of molecules either entering or leaving the cell) is into the cell. In other words, there

2109-418: The city's fog and civil engineering projects today famous as tourist attractions such as the cable cars and Lombard Street . Hills provide important advantages to an army that controls their heights, giving them an elevated view and firing position and forcing an opposing army to charge uphill to attack a fort or other position. They may also conceal forces behind them, allowing a force to lie in wait on

2166-433: The coefficient of diffusion for CO 2 in the air. The error rate is less than 5%. In 1855, Adolf Fick , the 26-year-old anatomy demonstrator from Zürich, proposed his law of diffusion . He used Graham's research, stating his goal as "the development of a fundamental law, for the operation of diffusion in a single element of space". He asserted a deep analogy between diffusion and conduction of heat or electricity, creating

2223-410: The concentration of carbon dioxide in the alveoli decreases. This creates a concentration gradient for carbon dioxide to diffuse from the blood into the alveoli, as fresh air has a very low concentration of carbon dioxide compared to the blood in the body. Third, there is another "bulk flow" process. The pumping action of the heart then transports the blood around the body. As the left ventricle of

2280-510: The crest of a hill, using that crest for cover, and firing on unsuspecting attackers as they broach the hilltop. As a result, conventional military strategies often demand possession of high ground. Because of their strategic and tactical values, hills have been the site of many notable battles, such as the Battle of Alesia in 52 BC and the first recorded military conflict in Scotland, the Battle of Mons Graupius in AD 83. Modern era conflicts include

2337-595: The diffusion ( i , k  > 0), thermodiffusion ( i  > 0, k  = 0 or k  > 0, i  = 0) and thermal conductivity ( i = k = 0 ) coefficients. Under isothermal conditions T  = constant. The relevant thermodynamic potential is the free energy (or the free entropy ). The thermodynamic driving forces for the isothermal diffusion are antigradients of chemical potentials, − ( 1 / T ) ∇ μ j {\displaystyle -(1/T)\,\nabla \mu _{j}} , and

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2394-397: The diffusion flux is [flux] = [quantity]/([time]·[area]). The diffusing physical quantity N {\displaystyle N} may be the number of particles, mass, energy, electric charge, or any other scalar extensive quantity . For its density, n {\displaystyle n} , the diffusion equation has the form where W {\displaystyle W}

2451-428: The example of gold in lead in 1896. : "... My long connection with Graham's researches made it almost a duty to attempt to extend his work on liquid diffusion to metals." In 1858, Rudolf Clausius introduced the concept of the mean free path . In the same year, James Clerk Maxwell developed the first atomistic theory of transport processes in gases. The modern atomistic theory of diffusion and Brownian motion

2508-443: The frame of thermodynamics and non-equilibrium thermodynamics . From the atomistic point of view , diffusion is considered as a result of the random walk of the diffusing particles. In molecular diffusion , the moving molecules in a gas, liquid, or solid are self-propelled by kinetic energy. Random walk of small particles in suspension in a fluid was discovered in 1827 by Robert Brown , who found that minute particle suspended in

2565-421: The heart contracts, the volume decreases, which increases the pressure in the ventricle. This creates a pressure gradient between the heart and the capillaries, and blood moves through blood vessels by bulk flow down the pressure gradient. There are two ways to introduce the notion of diffusion : either a phenomenological approach starting with Fick's laws of diffusion and their mathematical consequences, or

2622-430: The kinetic diameter of the molecule cause large differences in diffusivity . Biologists often use the terms "net movement" or "net diffusion" to describe the movement of ions or molecules by diffusion. For example, oxygen can diffuse through cell membranes so long as there is a higher concentration of oxygen outside the cell. However, because the movement of molecules is random, occasionally oxygen molecules move out of

2679-584: The liquid and solid lead. Yakov Frenkel (sometimes, Jakov/Jacob Frenkel) proposed, and elaborated in 1926, the idea of diffusion in crystals through local defects (vacancies and interstitial atoms). He concluded, the diffusion process in condensed matter is an ensemble of elementary jumps and quasichemical interactions of particles and defects. He introduced several mechanisms of diffusion and found rate constants from experimental data. Sometime later, Carl Wagner and Walter H. Schottky developed Frenkel's ideas about mechanisms of diffusion further. Presently, it

2736-540: The list. Cooper's Hill Cheese-Rolling and Wake is an annual event in the West Country of England which involves rolling a wheel of cheese down a hill. Contestants stand at the top and chase the wheel of cheese to the bottom. The winner, the one who catches the cheese, gets to keep the wheel of cheese as a prize. Cross country running courses may include hills which can add diversity and challenge to those courses. Diffusion The concept of diffusion

2793-451: The main phenomenon was described by him in 1831–1833: "...gases of different nature, when brought into contact, do not arrange themselves according to their density, the heaviest undermost, and the lighter uppermost, but they spontaneously diffuse, mutually and equally, through each other, and so remain in the intimate state of mixture for any length of time." The measurements of Graham contributed to James Clerk Maxwell deriving, in 1867,

2850-401: The matrix of diffusion coefficients is ( i,k  > 0). There is intrinsic arbitrariness in the definition of the thermodynamic forces and kinetic coefficients because they are not measurable separately and only their combinations ∑ j L i j X j {\textstyle \sum _{j}L_{ij}X_{j}} can be measured. For example, in

2907-415: The movement of fluid molecules in porous solids. Different types of diffusion are distinguished in porous solids. Molecular diffusion occurs when the collision with another molecule is more likely than the collision with the pore walls. Under such conditions, the diffusivity is similar to that in a non-confined space and is proportional to the mean free path. Knudsen diffusion occurs when the pore diameter

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2964-407: The term "force" in quotation marks or "driving force"): where n i {\displaystyle n_{i}} are the "thermodynamic coordinates". For the heat and mass transfer one can take n 0 = u {\displaystyle n_{0}=u} (the density of internal energy) and n i {\displaystyle n_{i}} is the concentration of

3021-444: The terms with variation of the total pressure are neglected. It is possible for diffusion of small admixtures and for small gradients. For the linear Onsager equations, we must take the thermodynamic forces in the linear approximation near equilibrium: where the derivatives of s {\displaystyle s} are calculated at equilibrium n ∗ {\displaystyle n^{*}} . The matrix of

3078-500: The tops of hills are thought to have been built on the sites of earlier pagan holy places. The Washington National Cathedral in Washington, D.C. has followed this tradition and was built on the highest hill in that city. Some cities' hills are culturally significant in their foundation, defense, and history. In addition to Rome, hills have played a prominent role in the history of San Francisco , with its hills being central to

3135-469: Was built on hilltops to help defend against invaders from the north, such as Mongols . Hillwalking is a British English term for a form of hiking which involves the ascent of hills. The activity is usually distinguished from mountaineering as it does not involve ropes or technically difficult rock climbing , although the terms mountain and hill are often used interchangeably in Britain. Hillwalking

3192-500: Was created. For example, Pliny the Elder had previously described the cementation process , which produces steel from the element iron (Fe) through carbon diffusion. Another example is well known for many centuries, the diffusion of colors of stained glass or earthenware and Chinese ceramics . In modern science, the first systematic experimental study of diffusion was performed by Thomas Graham . He studied diffusion in gases, and

3249-554: Was developed by Albert Einstein , Marian Smoluchowski and Jean-Baptiste Perrin . Ludwig Boltzmann , in the development of the atomistic backgrounds of the macroscopic transport processes , introduced the Boltzmann equation , which has served mathematics and physics with a source of transport process ideas and concerns for more than 140 years. In 1920–1921, George de Hevesy measured self-diffusion using radioisotopes . He studied self-diffusion of radioactive isotopes of lead in

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