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47-647: The town was founded by the Searle family of Surrey, England, of which the elder brother, Richard (originally a labourer), emigrated to South Africa under a government-sponsored scheme in 1845. He arrived in Great Brak River to work for the Central Road Board in 1850. Richard's brother, Charles, and sister-in-law, Pamela, are credited with founding the village in 1859. The Searle family went on to become toll keepers (toll houses were operated by private contractors during

94-714: A chase of one or two miles I lost it in the windings of the channel. Such, in the month of August 1834, was my first chance interview with that singular and beautiful phenomenon which I have called the Wave of Translation. Scott Russell spent some time making practical and theoretical investigations of these waves. He built wave tanks at his home and noticed some key properties: Scott Russell's experimental work seemed at odds with Isaac Newton 's and Daniel Bernoulli 's theories of hydrodynamics . George Biddell Airy and George Gabriel Stokes had difficulty accepting Scott Russell's experimental observations because they could not be explained by

141-548: A collision with other solitons. So solitary waves on a water surface are near -solitons, but not exactly – after the interaction of two (colliding or overtaking) solitary waves, they have changed a bit in amplitude and an oscillatory residual is left behind. Solitons are also studied in quantum mechanics, thanks to the fact that they could provide a new foundation of it through de Broglie 's unfinished program, known as "Double solution theory" or "Nonlinear wave mechanics". This theory, developed by de Broglie in 1927 and revived in

188-509: A more detailed description. Many exactly solvable models have soliton solutions, including the Korteweg–de Vries equation , the nonlinear Schrödinger equation , the coupled nonlinear Schrödinger equation, and the sine-Gordon equation . The soliton solutions are typically obtained by means of the inverse scattering transform , and owe their stability to the integrability of the field equations. The mathematical theory of these equations

235-433: A plain in the direction of the prevailing wind. Barchans and mega-barchans may coalesce into ridges that extend for hundreds of kilometers. Dune collisions and changes in wind direction spawn new barchans from the horns of the old ones and govern the size distribution of a given field. As barchan dunes migrate, smaller dunes outpace larger dunes, catching-up the rear of the larger dune and eventually appear to punch through

282-747: A solution in one homotopy class to another. The solutions are truly distinct, and maintain their integrity, even in the face of extremely powerful forces. Examples of topological solitons include the screw dislocation in a crystalline lattice , the Dirac string and the magnetic monopole in electromagnetism , the Skyrmion and the Wess–Zumino–Witten model in quantum field theory , the magnetic skyrmion in condensed matter physics, and cosmic strings and domain walls in cosmology . In 1834, John Scott Russell describes his wave of translation . The discovery

329-402: A source in the form of a Dirac-delta function at the origin. As a consequence it displays a singularity in this point (although the electric field is everywhere regular). In some physical contexts (for instance string theory) this feature can be important, which motivated the introduction of a special name for this class of solitons. On the other hand, when gravity is added (i.e. when considering

376-581: A topologically stable soliton solution of a field theory with conserved baryon number. The bound state of two solitons is known as a bion , or in systems where the bound state periodically oscillates, a breather . The interference-type forces between solitons could be used in making bions. However, these forces are very sensitive to their relative phases. Alternatively, the bound state of solitons could be formed by dressing atoms with highly excited Rydberg levels. The resulting self-generated potential profile features an inner attractive soft-core supporting

423-484: A very common landform in sandy deserts all over the world and are arc-shaped, markedly asymmetrical in cross section, with a gentle slope facing toward the wind sand ridge, comprising well-sorted sand . This type of dune possesses two "horns" that face downwind, with the steeper slope known as the slip face, facing away from the wind, downwind, at the angle of repose of the sand in question, approximately 30–35 degrees for medium-fine dry sand. The upwind side

470-517: Is 15 km away at George International Airport to the east. Barchan A barchan or barkhan dune (from Kazakh бархан [bɑɾˈχɑn] ) is a crescent -shaped dune . The term was introduced in 1881 by Russian naturalist Alexander von Middendorf , based on their occurrence in Turkestan and other inland desert regions. Barchans face the wind , appearing convex and are produced by wind action predominantly from one direction. They are

517-469: Is a broad and very active field of mathematical research. Some types of tidal bore , a wave phenomenon of a few rivers including the River Severn , are 'undular': a wavefront followed by a train of solitons. Other solitons occur as the undersea internal waves , initiated by seabed topography , that propagate on the oceanic pycnocline . Atmospheric solitons also exist, such as the morning glory cloud of

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564-401: Is bounded by the hilly coastal plain in the north and by an approximately 30 m high bush-covered dune ridge to the south. The dunes east of the mouth form a bluff about 50-60 m high consisting of 20 m basal dune rock, probably of Tertiary age, overlaid by a partly vegetated field of transverse barchan sand dunes. The Hersham residential area has been developed in this area. Although Great Brak

611-472: Is described here in Scott Russell's own words: I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat suddenly stopped – not so the mass of water in the channel which it had put in motion; it accumulated round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming

658-531: Is linked to the mainland by a single lane bridge. Other highlights in Great Brak River include a local history museum, historic buildings built between 1852 and the mid-1930s, the Wolwedans Dam , and a restored power station dating back to the early 1900s. The 4-star Botlierskop Private Game Reserve is the biggest commercial attraction in the Great Brak area, along with several small shops and restaurants located in

705-474: Is now known as the Korteweg–de Vries equation , including solitary wave and periodic cnoidal wave solutions. In 1965 Norman Zabusky of Bell Labs and Martin Kruskal of Princeton University first demonstrated soliton behavior in media subject to the Korteweg–de Vries equation (KdV equation) in a computational investigation using a finite difference approach. They also showed how this behavior explained

752-561: Is packed by the wind, and stands at about 15 degrees. Barchans may be 9–30 m (30–98 ft) high and 370 m (1,210 ft) wide at the base measured perpendicular to the wind. Simple barchan dunes may appear as larger, compound barchan or megabarchan dunes, which can gradually migrate with the wind as a result of erosion on the windward side and deposition on the leeward side, at a rate of migration ranging from about one meter to 100 meters per year. Barchans usually occur as groups of isolated dunes and may form chains that extend across

799-554: Is part of the greater Mosselbay municipality it is also a town in its own right. Great Brak churches include The Searles Memorial, St. John's Anglican Church, VGK, New Apostolic Church, Old Apostolic Church, United Congregational Church, NG Church and the Kingdom Hall of the Jehovah's Witnesses. Today, Great Brak River is chiefly a holiday destination, with beaches and the lagoon providing the major attractions. The island residential area

846-480: Is stable against decay to the "trivial solution". Soliton stability is due to topological constraints, rather than integrability of the field equations. The constraints arise almost always because the differential equations must obey a set of boundary conditions , and the boundary has a nontrivial homotopy group , preserved by the differential equations. Thus, the differential equation solutions can be classified into homotopy classes . No continuous transformation maps

893-518: The Born–Infeld model . The name appears to have been coined by G. W. Gibbons in order to distinguish this solution from the conventional soliton, understood as a regular , finite-energy (and usually stable) solution of a differential equation describing some physical system. The word regular means a smooth solution carrying no sources at all. However, the solution of the Born–Infeld model still carries

940-496: The Gordon–Haus (GH) jitter . The GH jitter requires sophisticated, expensive compensatory solutions that ultimately makes dense wavelength-division multiplexing (DWDM) soliton transmission in the field unattractive, compared to the conventional non-return-to-zero/return-to-zero paradigm. Further, the likely future adoption of the more spectrally efficient phase-shift-keyed/QAM formats makes soliton transmission even less viable, due to

987-453: The Gulf of Carpentaria , where pressure solitons traveling in a temperature inversion layer produce vast linear roll clouds . The recent and not widely accepted soliton model in neuroscience proposes to explain the signal conduction within neurons as pressure solitons. A topological soliton , also called a topological defect, is any solution of a set of partial differential equations that

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1034-525: The Union Canal in Scotland. He reproduced the phenomenon in a wave tank and named it the " Wave of Translation ". The term soliton was coined by Zabusky and Kruskal to describe localized, strongly stable propagating solutions to the Korteweg–de Vries equation , which models waves of the type seen by Russell. The name was meant to characterize the solitary nature of the waves, with the 'on' suffix recalling

1081-432: The ' light bullets ' of nonlinear optics are often called solitons despite losing energy during interaction). Dispersion and nonlinearity can interact to produce permanent and localized wave forms. Consider a pulse of light traveling in glass. This pulse can be thought of as consisting of light of several different frequencies. Since glass shows dispersion, these different frequencies travel at different speeds and

1128-546: The 1800s), and would establish shopping, accommodation, shoe-making and timber businesses in the village. The Great Brak River and its tributaries rises on the slopes of the Engelsberg and Jonkersberg (Varing River) in the Outeniqua Mountain Range 25 km in a straight line from the Great Brak River mouth. The catchment is relatively long and narrow being about 25 km long and reaching a maximum of about 8 km wide. Much of

1175-424: The 1950s, is the natural continuation of his ideas developed between 1923 and 1926, which extended the wave–particle duality introduced by Albert Einstein for the light quanta , to all the particles of matter. The observation of accelerating surface gravity water wave soliton using an external hydrodynamic linear potential was demonstrated in 2019. This experiment also demonstrated the ability to excite and measure

1222-414: The 3D self-trapped soliton, an intermediate repulsive shell (barrier) preventing solitons’ fusion, and an outer attractive layer (well) used for completing the bound state resulting in giant stable soliton molecules. In this scheme, the distance and size of the individual solitons in the molecule can be controlled dynamically with the laser adjustment. In field theory bion usually refers to the solution of

1269-714: The Gordon–Mollenauer effect. Consequently, the long-haul fiberoptic transmission soliton has remained a laboratory curiosity. Solitons may occur in proteins and DNA. Solitons are related to the low-frequency collective motion in proteins and DNA . A recently developed model in neuroscience proposes that signals, in the form of density waves, are conducted within neurons in the form of solitons. Solitons can be described as almost lossless energy transfer in biomolecular chains or lattices as wave-like propagations of coupled conformational and electronic disturbances. Solitons can occur in materials, such as ferroelectrics , in

1316-623: The domains, influencing the direction of the soliton network propagation. Nonidealities such as disruptions to the soliton network and surface impurities can influence soliton propagation as well. Domain walls can meet at nodes and get effectively pinned, forming triangular domains, which have been readily observed in various ferroelectric twisted bilayer systems. In addition, closed loops of domain walls enclosing multiple polarization domains can inhibit soliton propagation and thus, switching of polarizations across it. Also, domain walls can propagate and meet at wrinkles and surface inhomogeneities within

1363-480: The existing water wave theories. Additional observations were reported by Henry Bazin in 1862 after experiments carried out in the canal de Bourgogne in France. Their contemporaries spent some time attempting to extend the theory but it would take until the 1870s before Joseph Boussinesq and Lord Rayleigh published a theoretical treatment and solutions. In 1895 Diederik Korteweg and Gustav de Vries provided what

1410-439: The form of a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued its course along the channel apparently without change of form or diminution of speed. I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles an hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height. Its height gradually diminished, and after

1457-542: The form of domain walls. Ferroelectric materials exhibit spontaneous polarization, or electric dipoles, which are coupled to configurations of the material structure. Domains of oppositely poled polarizations can be present within a single material as the structural configurations corresponding to opposing polarizations are equally favorable with no presence of external forces. The domain boundaries, or “walls”, that separate these local structural configurations are regions of lattice dislocations . The domain walls can propagate as

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1504-403: The large dune to appear on the other side. The process appears superficially similar to waves of light, sound, or water that pass directly through each other, but the detailed mechanism is very different. The dunes emulate soliton behavior, but unlike solitons, which flow through a medium leaving it undisturbed (similar to waves passing through water), the sand particles themselves are moved. When

1551-422: The lattice. It has been observed that soliton or domain wall propagation across a moderate length of the sample (order of nanometers to micrometers) can be initiated with applied stress from an AFM tip on a fixed region. The soliton propagation carries the mechanical perturbation with little loss in energy across the material, which enables domain switching in a domino-like fashion. It has also been observed that

1598-409: The medium. (Dispersive effects are a property of certain systems where the speed of a wave depends on its frequency.) Solitons were subsequently found to provide stable solutions of a wide class of weakly nonlinear dispersive partial differential equations describing physical systems. The soliton phenomenon was first described in 1834 by John Scott Russell (1808–1882) who observed a solitary wave in

1645-575: The phases of ballistic solitons. Much experimentation has been done using solitons in fiber optics applications. Solitons in a fiber optic system are described by the Manakov equations . Solitons' inherent stability make long-distance transmission possible without the use of repeaters , and could potentially double transmission capacity as well. The above impressive experiments have not translated to actual commercial soliton system deployments however, in either terrestrial or submarine systems, chiefly due to

1692-541: The polarizations, and thus, the local structural configurations can switch within a domain with applied forces such as electric bias or mechanical stress. Consequently, the domain walls can be described as solitons, discrete regions of dislocations that are able to slip or propagate and maintain their shape in width and length.   In recent literature, ferroelectricity has been observed in twisted bilayers of van der Waal materials such as molybdenum disulfide and graphene . The moiré superlattice that arises from

1739-503: The puzzling earlier work of Fermi, Pasta, Ulam, and Tsingou . In 1967, Gardner, Greene, Kruskal and Miura discovered an inverse scattering transform enabling analytical solution of the KdV equation. The work of Peter Lax on Lax pairs and the Lax equation has since extended this to solution of many related soliton-generating systems. Solitons are, by definition, unaltered in shape and speed by

1786-438: The relative twist angle between the van der Waal monolayers generates regions of different stacking orders of the atoms within the layers. These regions exhibit inversion symmetry breaking structural configurations that enable ferroelectricity at the interface of these monolayers. The domain walls that separate these regions are composed of partial dislocations where different types of stresses, and thus, strains are experienced by

1833-515: The river drains an elevated coastal platform or platform or plateau 150-300 m above sea level. Below the Wolwedans dam the river enters a gorge which takes the form of a V which is indicative of a non-glacial valley. Between the village of Great Brak and the Garden Route Freeway (N2 Highway) and other bridges the river enters the lagoon basin (estuary) about 1 km long and 0.5 km wide. The basin

1880-428: The seabed. Soliton In mathematics and physics , a soliton is a nonlinear, self-reinforcing, localized wave packet that is strongly stable , in that it preserves its shape while propagating freely, at constant velocity, and recovers it even after collisions with other such localized wave packets. Its remarkable stability can be traced to a balanced cancellation of nonlinear and dispersive effects in

1927-451: The shape of the pulse therefore changes over time. However, also the nonlinear Kerr effect occurs; the refractive index of a material at a given frequency depends on the light's amplitude or strength. If the pulse has just the right shape, the Kerr effect exactly cancels the dispersion effect and the pulse's shape does not change over time. Thus, the pulse is a soliton. See soliton (optics) for

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1974-519: The smaller dune catches up the larger dune, the winds begin to deposit sand on the rear dune while blowing sand off the front dune without replenishing it. Eventually, the rear dune has assumed dimensions similar to the former front dune which has now become a smaller, faster moving dune that pulls away with the wind. Barchan dunes have been observed on Mars , where the thin atmosphere produces winds strong enough to move sand and dust. Marine barchan dunes appear underwater as sands shift their way across

2021-585: The town center. The 250 year old shoe factory of Bolton Footwear, originally started by the Searl family, is still in operation today in Groot Brak River and is one of the primary employers in the town. The town can easily be reached by vehicle using the N2 national highway that runs through the town. Great Brak River is halfway on the N2 between Mossel Bay to the west and George to the east. The nearest commercial airport

2068-402: The type of dislocations found at the walls can affect propagation parameters such as direction. For instance, STM measurements showed four types of strains of varying degrees of shear, compression, and tension at domain walls depending on the type of localized stacking order in twisted bilayer graphene. Different slip directions of the walls are achieved with different types of strains found at

2115-469: The usage for particles such as electrons , baryons or hadrons , reflecting their observed particle-like behaviour. A single, consensus definition of a soliton is difficult to find. Drazin & Johnson (1989 , p. 15) ascribe three properties to solitons: More formal definitions exist, but they require substantial mathematics. Moreover, some scientists use the term soliton for phenomena that do not quite have these three properties (for instance,

2162-532: The van der Waal layers, which can act as obstacles obstructing the propagation. In magnets, there also exist different types of solitons and other nonlinear waves. These magnetic solitons are an exact solution of classical nonlinear differential equations — magnetic equations, e.g. the Landau–Lifshitz equation , continuum Heisenberg model , Ishimori equation , nonlinear Schrödinger equation and others. Atomic nuclei may exhibit solitonic behavior. Here

2209-410: The whole nuclear wave function is predicted to exist as a soliton under certain conditions of temperature and energy. Such conditions are suggested to exist in the cores of some stars in which the nuclei would not react but pass through each other unchanged, retaining their soliton waves through a collision between nuclei. The Skyrme Model is a model of nuclei in which each nucleus is considered to be

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