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Melting, or fusion, is a physical process that results in the phase transition of a substance from a solid to a liquid. This occurs when the internal energy of the solid increases by the application of heat or pressure, which increases the substance's temperature to the melting point. At the melting point, the ordering of ions or molecules in the solid breaks down to a less ordered state, the solid melts to become a liquid. Substances in the molten state have reduced viscosity as the temperature increases. An exception to this principle is the element sulfur, whose viscosity increases in the range of 160 °C to 180 °C due to polymerization; some organic compounds melt through states of partial order between solid and liquid. From a thermodynamics point of view, at the melting point the change in Gibbs free energy ∆G of the substances is zero, but there are non-zero changes in the enthalpy and the entropy, known as the enthalpy of fusion and the entropy of fusion. Melting is therefore classified as a first-order phase transition.

Melting occurs when the Gibbs free energy of the liquid becomes lower than the solid for that material. The temperature at which this occurs is dependent on the ambient pressure. Low-temperature helium is the only known exception to the general rule. Helium-3 has a negative enthalpy of fusion at temperatures below 0.3 K. Helium-4 has a slightly negative enthalpy of fusion below 0.8 K. This means that, at appropriate constant pressures, heat must be removed from these substances in order to melt them. Among the theoretical criteria for melting, the Lindemann and Born criteria are those most used as a basis to analyse the melting conditions; the Lindemann criterion states that melting occurs because of vibrational instability, e.g. crystals melt when the average amplitude of thermal vibrations of atoms is high compared with interatomic distances, e.g. <δu2>1/2 > δLRs, where δu is the atomic displacement, the Lindemann parameter δL ≈ 0.20...0.25 and Rs is one-half of the inter-atomic distance. The Lindemann melting criterion is supported by experimental data both for crystalline materials and for glass-liquid transitions in amorphous materials.

The Born criterion is based on a rigidity catastrophe caused by the vanishing elastic shear modulus, i.e. when the crystal no longer has sufficient rigidity to mechanically withstand the load. Under a standard set of conditions, the melting point of a substance is a characteristic property; the melting point is equal to the freezing point. However, under created conditions, supercooling or superheating past the melting or freezing point can occur. Water on a clean glass surface will supercool several degrees below the freezing point without freezing. Fine emulsions of pure water have been cooled to −38 degrees Celsius without nucleation to form ice. Nucleation occurs due to fluctuations in the properties of the material. If the material is kept still there is nothing to trigger this change, supercooling may occur. Thermodynamically, the supercooled liquid is in the metastable state with respect to the crystalline phase, it is to crystallize suddenly. Glasses are amorphous solids which are fabricated when the molten material cools rapidly to below its glass transition temperature, without sufficient time for a regular crystal lattice to form.

Solids are characterised by a high degree of connectivity between their molecules, fluids have lower connectivity of their structural blocks. Melting of a solid material can be considered as a percolation via broken connections between particles e.g. connecting bonds. In this approach melting of an amorphous material occurs when the broken bonds form a percolation cluster with Tg dependent on quasi-equilibrium thermodynamic parameters of bonds e.g. on enthalpy and entropy of formation of bonds in a given system at given conditions: T g = H d S d + R ln ⁡, where fc is the percolation threshold and R is the universal gas constant. Although Hd and Sd are not true equilibrium thermodynamic parameters and can depend on the cooling rate of a melt they can be found from available experimental data on viscosity of amorphous materials. Below its melting point, quasi-liquid films can be observed on crystalline surfaces; the thickness of the film is temperature dependent. This effect is common for all crystalline materials.

Pre-melting shows its effects in e.g. frost heave, the growth of snowflakes and, taking grain boundary interfaces into account, maybe in the movement of glaciers. In genetics, melting DNA means to separate the double-stranded DNA into two single strands by heating or the use of chemical agents, cf. polymerase chain reaction. List of chemical elements providing melting points Phase diagram Zone melting The dictionary definition of melting at Wiktionary

The Gate of Calais

The Gate of Calais or O, the Roast Beef of Old England is a 1748 painting by William Hogarth, reproduced as a print from an engraving the next year. Hogarth produced the painting directly after his return from France, where he had been arrested as a spy while sketching in Calais; the scene depicts a side of beef being transported from the harbour to an English tavern in the port, while a group of undernourished, ragged French soldiers and a fat friar look on hungrily. Hogarth painted himself in the left corner with a "soldier's hand upon my shoulder." In July 1748, Hogarth took a trip to Paris, taking advantage of the armistice which preceded the signing of the Treaty of Aix-la-Chapelle in October that year. He travelled with some artist friends, including Thomas Hudson and Alexander Van Aken, Francis Hayman, Henry Cheere. George Vertue reports that the group split up on the return journey, with Hogarth and Hayman making their way to Calais to catch the boat to England and the others continuing their tour to Flanders and the Netherlands.

While waiting in Calais, Hogarth decided to sketch the gate of the port and drawbridge which were still adorned with the English arms. His sketching of the fortifications aroused suspicion, he was arrested and taken before the governor. Most accounts relate. Horace Walpole elaborates the account, reporting that Hogarth was forced to demonstrate his abilities by producing sketches and caricatures as demanded by the French, "particularly a scene of the shore, with an immense piece of beef landing for the Lion d'Argent, the English inn at Calais, several hungry friars following it." At any rate, Hogarth was returned to England by the next boat. According to Hogarth's autobiographical notes, he started on the painting as soon as he arrived home from Calais; the painting was completed followed by an engraving early the next year. The painting takes a viewpoint under an archway in the main outer wall of Calais; the scene within centres around a sirloin of beef destined for the English tavern, the Lion d'Argent, carried by a chef who stands out in his bright white apron and cap.

The French soldiers, dressed in rags and forced to eat their watery soupe maigre, gather round licking their lips. Two soldiers in sabots can be seen carrying a cauldron of the grey unappetising soup; the Franciscan friar who greedily rubs his finger in the fat of the beef joint, is thought to be based on Hogarth's friend John Pine. In the foreground, a Highlander, an exile from the Jacobite rising of 1745, sits slumped against the wall, his strength sapped by the poor French fare – a raw onion and a crust of bread. Hogarth is seen sketching to the left in the background, but the tip of the halberd and hand of the soldier who will arrest him are just appearing round the corner behind him. There are strong references to the celebration of Eucharist in the picture. Through the gates, under the sign of a dove a Roman Catholic mass is being celebrated. In the foreground, but still aligned with those in the background under the cross of the gate, the principal characters worship the beef; the man carrying it bows under the weight appearing to offer it up to the friar on bended knee.

Above the scene in front of the gate, the dove of peace is replaced by the crow. In the foreground fishwives superstitiously worship the face of a ray, the Jacobite clasps his hand together in prayer. Hogarth's antipathy to the French had been apparent in his art since Noon in his Four Times of the Day series, painted in 1736; the March to Finchley, which he painted in 1749/50, provides a companion theme to The Gate of Calais: it depicts a fictional gathering of robust English guardsman who are to march north to defend London against the invasion of Bonnie Prince Charlie's Jacobites in 1745. Further anti-French sentiment is apparent in his two Invasion engravings, published in 1756, in Beer Street, where Rev. James Townley's accompanying verses stress the superiority of the English; the Gate of Calais' secondary title, O, the Roast Beef of Old England, is a reference to the popular patriotic ballad'The Roast Beef of Old England' from Henry Fielding's The Grub-Street Opera, which told of how the food "ennobled our brains and enriched our blood" and laughed at "all-vapouring France"".

The painting was bought by the 1st Earl of Charlemont sometime after the 1761 Society of Artists' Exhibition at which it was displayed, by which time England had been at war with France again for 5 years. Ian Pears believes that by showing The Gates of Calais at the exhibition, Hogarth was challenging the patriotic spirit of the British by asking them to pay as much for a work by an Englishman as they would for a work by a continental painter; the painting was acquired by the 1st Duke of Westminster at an auction at Christie's in 1891. The print, produced from an engraving, completed in part by Charles Mosley, was published on 6 March 1749. Entitled "O The Roast Beef of Old England", it was priced at 5 shillings and advertised as: A print design'd and engrav'd by MR HOGARTH, representing a PRODIGY which appear'd before the Gate of CALAIS. O the Roast-beef of Old England, &c. To be had at the Golden Head in Leicester-Square, at the Print Shops; the main difference between the painting and the engraving is the crow on top of the gate, which is

List of Australian treaties

This is a list of active treaties that the Government of Australia has entered into since the federation of Australia in 1901. The Australian Department of Foreign Affairs and Trade, in conjunction with the Australasian Legal Information Institute, has published an online Australian Treaties Database from where this list is obtained and updated. No substantial treaty has been entered into between the government of Australia and the Indigenous people of Australia; as of 2017 Australia is the only Commonwealth country. Some prior treaties exist in pockets, such as Batman's Treaty, but these are not substantial government treaties, i.e. treaties between the Government of the day and the traditional custodians of the land. Main article: List of Australian bilateral treaties List of Australian bilateral treaties on extradition and criminal matters List of Australian bilateral treaties on postal services and money orders List of Australian bilateral treaties on commerce and arbitration List of Australian bilateral treaties on intellectual property List of Australian multilateral treaties Primary source of information, further reading: Australian Treaties Library, Australasian Legal Information Institute DFAT – Treaty making process

Associative property

In mathematics, the associative property is a property of some binary operations. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs. Within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed; that is, rearranging the parentheses in such an expression will not change its value. Consider the following equations: + 4 = 2 + = 9 2 × = × 4 = 24. Though the parentheses were rearranged on each line, the values of the expressions were not altered. Since this holds true when performing addition and multiplication on any real numbers, it can be said that "addition and multiplication of real numbers are associative operations". Associativity is not the same as commutativity, which addresses whether or not the order of two operands changes the result. For example, the order does not matter in the multiplication of real numbers, that is, a × b = b × a, so we say that the multiplication of real numbers is a commutative operation.

Associative operations are abundant in mathematics. However, many important and interesting operations are non-associative. In contrast to the theoretical properties of real numbers, the addition of floating point numbers in computer science is not associative, the choice of how to associate an expression can have a significant effect on rounding error. Formally, a binary operation ∗ on a set S is called associative if it satisfies the associative law: ∗ z = x ∗ for all x, y, z in S. Here, ∗ is used to replace the symbol of the operation, which may be any symbol, the absence of symbol as for multiplication. Z = x = xyz for all x, y, z in S; the associative law can be expressed in functional notation thus: f = f. If a binary operation is associative, repeated application of the operation produces the same result regardless of how valid pairs of parentheses are inserted in the expression; this is called the generalized associative law. For instance, a product of four elements may be written, without changing the order of the factors, in five possible ways: d d a a If the product operation is associative, the generalized associative law says that all these formulas will yield the same result.

So unless the formula with omitted parentheses has a different meaning, the parentheses can be considered unnecessary and "the" product can be written unambiguously as a b c d. As the number of elements increases, the number of possible ways to insert parentheses grows but they remain unnecessary for disambiguation. An example where this does not work is the logical biconditional ↔, it is associative, thus A ↔ is equivalent to ↔ C, but A ↔ B ↔ C most means, not equivalent. Some examples of associative operations include the following; the concatenation of the three strings "hello", " ", "world" can be computed by concatenating the first two strings and appending the third string, or by joining the second and third string and concatenating the first string with the result. The two methods produce the same result. In arithmetic and multiplication of real numbers are associative.

144th Indiana Infantry Regiment

The 144th Indiana Infantry Regiment was an infantry regiment from Indiana that served in the Union Army between March 6 and August 5, 1865, during the American Civil War. The regiment was organized at Indianapolis, with a strength of 1,036 men and mustered in on March 6, 1865; the 144th was composed of companies raised in the 2nd district and it left Indiana for Harper's Ferry, West Virginia, on March 9. The regiment was attached to the 1st Brigade, 1st Provisional Division, Army of the Shenandoah. Duty was performed at Halltown and Charleston, West Virginia, prior to serving in Winchester, Stevenson's Depot and Opequon Creek, Virginia until early August; the regiment was mustered out on August 5, 1865. During its service the regiment incurred forty-six fatalities, another nineteen deserted and one unaccounted for. List of Indiana Civil War regiments Dyer, Frederick H.. A Compendium of the War of the Rebellion. New York and London. Thomas Yoseloff, Publisher. LCCN 59-12963. Holloway, William R.. Civil War Regiments From Indiana. Pensacola, Florida. ISBN 1-9321-5731-X. Terrell, W. H. H.. The Report of the Adjutant General of the State of Indiana. Containing Rosters for the Years 1861–1865, Volume 7. Indianapolis, Indiana. Samuel M. Douglass, State Printer

Ginés Jesús Hernández

Sergio María Ginés Jesús Hernández y Martínez, known by his religious name as Sergio María and by his papal name as Gregory XVIII, is the former pope of the Palmarian Catholic Church. Hernández was in office from 2011 until his 2016 resignation. Hernández fell in love, lost his faith and left the church, he has subsequently reconciled with the Catholic Church. Hernández is a former member of the Spanish Military. Hernández is a Carlist. Between 2005 and 2011, Hernández served as church secretary of state under pope Manuel Corral. After Corral's death, Hernández succeeded Corral, on 16 July 2011, as pope at El Palmar de Troya and adopted the papal name Gregory XVIII. Hernández nominated his successor Joseph Odermatt from Switzerland. According to Professor Magnus Lundberg, of the University of Uppsala, Hernández resigned from his papacy on 22 April 2016 for marrying Nieves Trivedi, was succeeded on 23 April 2016 by Odermatt who took Peter III as his papal name. Conclavism Antipope