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Beam divergence

In electromagnetics in optics, beam divergence is an angular measure of the increase in beam diameter or radius with distance from the optical aperture or antenna aperture from which the beam emerges. The term is relevant only in the "far field", away from any focus of the beam. Speaking, the far field can commence physically close to the radiating aperture, depending on aperture diameter and the operating wavelength. Beam divergence is used to characterize electromagnetic beams in the optical regime, for cases in which the aperture from which the beam emerges is large with respect to the wavelength. However, it is used in the radio frequency band for cases in which the antenna is large relative to a wavelength. Beam divergence refers to a beam of circular cross section, but not so. A beam may, for example, have an elliptical cross section, in which case the orientation of the beam divergence must be specified, for example with respect to the major or minor axis of the elliptical cross section.

The divergence of a beam can be calculated if one knows the beam diameter at two separate points far from any focus, the distance between these points. The beam divergence, Θ, is given by Θ = 2 arctan ⁡. If a collimated beam is focused with a lens, the diameter D m of the beam in the rear focal plane of the lens is related to the divergence of the initial beam by Θ = D m f, where f is the focal length of the lens. Note that this measurement is valid only when the beam size is measured at the rear focal plane of the lens, i.e. where the focus would lie for a collimated beam, not at the actual focus of the beam, which would occur behind the rear focal plane for a divergent beam. Like all electromagnetic beams, lasers are subject to divergence, measured in milliradians or degrees. For many applications, a lower-divergence beam is preferable. Neglecting divergence due to poor beam quality, the divergence of a laser beam is proportional to its wavelength and inversely proportional to the diameter of the beam at its narrowest point.

For example, an ultraviolet laser that emits at a wavelength of 308 nm will have a lower divergence than an infrared laser at 808 nm, if both have the same minimum beam diameter. The divergence of good-quality laser beams is modeled using the mathematics of Gaussian beams. Gaussian laser beams are said to be diffraction limited when their radial beam divergence θ = Θ / 2 is close to the minimum possible value, given by θ = λ π w, where λ is the laser wavelength and w is the radius of the beam at its narrowest point, called the "beam waist"; this type of beam divergence is observed from optimized laser cavities. Information on the diffraction-limited divergence of a coherent beam is inherently given by the N-slit interferometric equation. Laser beam profiler Laser linewidth Laser divergence calculator Interactive beam divergence graph

Diffusionless transformation

A diffusionless transformation is a phase change that occurs without the long-range diffusion of atoms but rather by some form of cooperative, homogeneous movement of many atoms that results in a change in crystal structure. These movements are small less than the interatomic distances, the atoms maintain their relative relationships; the ordered movement of large numbers of atoms lead some to refer to these as military transformations in contrast to civilian diffusion-based phase changes. The most encountered transformation of this type is the martensitic transformation which, while being the most studied, is only one subset of non-diffusional transformations; the martensitic transformation in steel represents the most economically significant example of this category of phase transformations but an increasing number of alternatives, such as shape memory alloys, are becoming more important as well. When a structural change occurs by the coordinated movement of atoms relative to their neighbors the change is termed displacive transformation.

This covers a broad range of transformations and so further classifications have been developed. The first distinction can be drawn between transformations dominated by lattice-distortive strains and those where shuffles are of greater importance. Homogeneous lattice-distortive strains known as Bain strains, are strains that transform one Bravais lattice into a different one; this can be represented by a strain matrix S which transforms one vector, y, into a new vector, x: y = S x This is homogeneous as straight lines are transformed to new straight lines. Examples of such transformations include a cubic lattice increasing in size on all three axes or shearing into a monoclinic structure. Shuffles, as the name suggests, involve the small movement of atoms within the unit cell; as a result, pure shuffles do not result in a shape change of the unit cell - only its symmetry and structure. Phase transformations result in the creation of an interface between the transformed and parent material; the energy required to generate this new interface will depend on its nature - how well the two structures fit together.

An additional energy term occurs if the transformation includes a shape change since, if the new phase is constrained by the surrounding material, this may give rise to elastic or plastic deformation and hence a strain energy term. The ratio of these interfacial and strain energy terms has a notable effect on the kinetics of the transformation and the morphology of the new phase. Thus, shuffle transformations, where distortions are small, are dominated by interfacial energies and can be usefully separated from lattice-distortive transformations where the strain energy tends to have a greater effect. A subclassification of lattice-distortive displacements can be made by considering the dilational and shear components of the distortion. In transformations dominated by the shear component, it is possible to find a line in the new phase, undistorted from the parent phase while all lines are distorted when the dilation is predominant. Shear dominated transformations can be further classified according to the magnitude of the strain energies involved compared to the innate vibrations of the atoms in the lattice and hence whether the strain energies have a notable influence on the kinetics of the transformation and the morphology of the resulting phase.

If the strain energy is a significant factor the transformations are dubbed martensitic and if it is not the transformation is referred to as quasi-martensitic. The difference between austenite and martensite is, in some ways, quite small: while the unit cell of austenite is, on average, a perfect cube, the transformation to martensite distorts this cube by interstitial carbon atoms that do not have time to diffuse out during displacive transformation; the unit cell becomes longer in one dimension and shorter in the other two. The mathematical description of the two structures is quite different, for reasons of symmetry, but the chemical bonding remains similar. Unlike cementite, which has bonding reminiscent of ceramic materials, the hardness of martensite is difficult to explain in chemical terms; the explanation hinges on the crystal's subtle change in dimension. A microscopic crystallite is millions of unit cells long. Since all of these units face the same direction, distortions of a fraction of a percent become magnified into a major mismatch between neighboring materials.

The mismatch is sorted out by the creation of myriad crystal defects, in a process reminiscent of work hardening. As in work-hardened steel, these defects prevent atoms from sliding past one another in an organized fashion, causing the material to become harder. Shape memory alloys have surprising mechanical properties, that were explained by an analogy to martensite. Unlike the iron-carbon system, alloys in the nickel-titanium system can be chosen that make the "martensitic" phase thermodynamically stable. In addition to displacive transformation and diffusive transformation, a new phase transformation that involves displasive sublattice transition and atomic diffusion was discovered using a high-pressure x-ray diffraction system; the new transformation mechanism has been christened a pseudomartensitic transformation. Christian, J. W. Theory of Transformations in Metals and Alloys, Pergamon Press Khachaturyan, A. G. Theory of Structural Transformations in Solids, Dover Publications, NY Green, D.

J.. V.. Transformation Toughening of Ceramics. Boca Raton: CRC Press. ISBN 0-8493-6594-5. Extensive resources from Cambridge University The cubic-to-te

Clay Condrey

Clayton Lee Condrey is an American former professional baseball relief pitcher, who played in Major League Baseball for the San Diego Padres and Philadelphia Phillies. Condrey featured five pitches: a sinker, curveball, a four-seam fastball; the right-handed pitcher played at McNeese State University. The New York Yankees selected Condrey in the 94th round, with selection No. 1,730 of the 1996 Major League Baseball draft out of Angelina Junior College. Condrey would sign with the San Diego Padres in 1998, he was signed by then-Padres scout Theo Epstein. Condrey pitched with the San Diego Padres in the 2002 and 2003 seasons before he moved to the Phillies in the offseason. In the Padres organization as a starter, Clay started 43 games between the Triple-A Portland Beavers and the major leagues, giving up 118 earned runs in 257.1 innings. Condrey pitched his entire 2004 season for the Triple-A Scranton/Wilkes-Barre Red Barons of the International League, where he led the team in starts and innings pitched, compiling an ERA of 5.50.

His 2005 campaign dropped in appearances, where he appeared in only 24 starts, but he subsequently lowered his ERA to 4.15. After being converted to relief, he was off to a strong start in 2006 as well, allowing only 3 earned runs in eight appearances, but was called up to the Phillies in May. Condrey began the 2007 season on the Phillies' active roster, but on April 14, 2007, Condrey was designated for assignment by the Phillies to make room on the roster for starting pitcher Freddy García, on the DL since the end of spring training. Condrey would be designated for assignment three other times, up until August 3, 2007, when he was recalled from Triple-A Ottawa for his fifth stint of the season with the Phillies. Condrey was included on the postseason roster for the National League East Champion Phillies in 2007 and appeared in Game 2 of the NLDS against the Colorado Rockies. In 2008, Condrey pitched well in middle-relief. In accordance with one of the oddities of the baseball rulebook, he earned a save in a 12–2 Phillies victory over the Nationals on May 21 by pitching three innings in relief of Jamie Moyer and not surrendering the lead, though he entered the game with the Phillies leading by twelve runs.

Philadelphia won its second straight NL East title in 2008, Condrey was again part of the postseason roster. He appeared in Game 3 of the NLDS against the Milwaukee Brewers and Game 3 of the NLCS against the Los Angeles Dodgers. Condrey would get a World Series ring. Though still part of the active roster, Condrey did not appear in any World Series games. Condrey went 6-2 with one save and a 3.00 ERA in 45 appearances for the Phillies in 2009, but was not included on the postseason roster as Philadelphia returned to the World Series before falling to the Yankees in six games. On December 12, 2009, Condrey became a free agent. On January 6, 2010, Condrey signed a one-year deal with the Minnesota Twins, but experienced some elbow discomfort at the beginning of the season and did not pitch after 2010. Career statistics and player information from MLB, or ESPN, or Baseball-Reference, or Fangraphs, or Baseball-Reference, or Retrosheet

English Dresden

The English Dresden is a famous diamond found at the Bagagem mines in Minas Gerais in Brazil, in 1857 at about the same time as the celebrated Star of the South. It was a part separated by cleavage from a larger mass, in the rough weighed 119.5 carats. What became of the remaining portion is unknown, though Mr. Dresden suggests that it may have either been destroyed when taking it from the rock, or may have remained behind in its former itacolumite matrix; the English Dresden was acquired in Rio de Janeiro by Edward Dresden. He sent it to London for valuation, and had it cut by Costers of Amsterdam, who had earned a good reputation for the way they had cut the renowned diamond the Koh-i Nur for the British Royal Family. One of their experts, Mr. Voorsanger, cut it into a drop-form brilliant. By chance, Dresden was able to compare it to the Koh-i Noor, he relates, "I matched my drop with the'Koh-i-Noor' at Garrard's one day, to the surprise of all present, the latter's color turned yellowish, a proof how white my diamond must be."

But despite having remarkable clarity and excellent color, it was hard to find a buyer for it. It was offered to no avail. A London dealer was offered a half share in it at the low price of £12,500, but he declined. In 1863, an Indian Maharajah and an English cotton merchant traveled from India, the Maharajah was unable to afford the price asked: £40,000; the merchant, was captivated by the gem, expressed a desire to acquire it himself, though he lacked the means to do so. As luck would have it, within a year of expressing this desire, the American Civil War stopped supplies of cotton from the southern states, the commodity soared in value; the War in America finished and cotton prices again sunk, placing the merchant in an embarrassing financial position. The pressure led to his untimely unexpected demise, his estate had to besettled, his executors were in the fortunate position of being able to sell on the celebrated "Durban Drop", to cover the £40,000. This time the diamond was purchased by Malhār Rāo, the Gaekwad of the princely state of Baroda, in India.

In 1880, the Gaekwad had the diamond set in a necklace along with its sister stone the Star of the South, which he had purchased. In 1948, the necklace was altered and more diamonds were added. Sita Devi, the Gaekwad's Maharani was photographed wearing it at her husband's birthday party; the diamond is named after its first owner, but it was styled the "English Dresden" to distinguish it from a number of other famous diamonds with the same name: the Dresden Green, the Dresden White and the Dresden Yellow, which were kept in the German city of Dresden. It is known as the "Dresden Drop" or the "Star of Dresden". List of diamonds

Paul Walfish

Paul Gerald Walfish, was a Canadian endocrinologist "whose research in the area of thyroid physiology and pathology has contributed to improved health care in Canada for newborn infants". Born in Toronto, Walfish graduated from the University of Toronto in 1958 and specialized in internal medicine. After receiving a McLaughlin Foundation Fellowship, he spent a year studying endocrinology at Harvard Medical School, he joined the University of Toronto's Department of Medicine as a teacher, becoming a professor in 1982. Walfish has worked at Mount Sinai Hospital since 1964 as a clinician, he helped pioneer techniques of early thyroid cancer detection using fine-needle biopsies and ultrasounds. Walfish died from leukemia on 28 July 2018, aged 83. In 1990, Walfish was made a Member of the Order of Canada. In 2007, he was made a Member of the Order of Ontario in recognition for being a "leader in the international thyroidology community". In 1983, he received an Award of Merit from the City of Toronto.

In 1987, he was made a Fellow of the Royal Society of Medicine, England. He was awarded the 125th Anniversary of the Confederation of Canada Medal and the Queen Elizabeth II Golden Jubilee Medal. In 2004, he was the first Canadian to receive the American Thyroid Association's Paul Starr Award for outstanding contributions in clinical thyroidology. In 2007, he was awarded the Canadian Medical Association's Medal of Service "for advancing the art and science of treating thyroid diseases worldwide and raising the standards of medical practice in Canada"

Oflag XXI-C

Oflag XXI-C was a German Army World War II prisoner-of-war camp for officers located in Warthegau, a western province of Poland, incorporated into the German Reich in 1939. It held Norwegian officers arrested in 1942 and 1943. Most soldiers and officers had been released after the end of the Norwegian campaign, but as resistance activities increased, the officers were rearrested and sent to POW camps; the camp was established in June 1942 near Schokken 30 km north of Poznań, in what had been Oflag XXI-A, opened in September 1940 as a camp for Polish officers. In March 1943 it was moved to Schildberg 29 km south of Ostrów, taking over buildings used as a camp for wounded and sick British non-commissioned officers and designated Stalag XXI-A; this camp was unique in that it comprised several buildings in the centre of the small town, from which the remaining Polish inhabitants had been removed. These buildings were surrounded by barbed-wire fences. In 1944 the Norwegian officers were located. There was a sub-camp, designated Oflag XXI-C/Z established at Grune bei Lissa, between September 1943 and January 1945.

In January 1945 the officers were marched out westward arriving at Oflag III-A in Luckenwalde, south of Berlin. On 21 April 1945 the Red Army liberated the camp. On 5 May 1945 the Norwegians were transported east to a camp near Lignica in Silesia travelled for several days by train to Hamburg and Aarhus, Denmark arriving in Oslo on 28 May 1945. A Norwegian POW Museum was established in 1996 within the regional museum in the town-hall of Ostrzeszów. List of prisoner-of-war camps in Germany Occupation of Norway by Nazi Germany