Benito Amilcare Andrea Mussolini was an Italian politician and journalist, the leader of the National Fascist Party. He ruled Italy as Prime Minister from 1922 to 1943. Known as Il Duce, Mussolini was the founder of Italian Fascism. In 1912, Mussolini had been a leading member of the National Directorate of the Italian Socialist Party, but was expelled from the PSI for advocating military intervention in World War I, in opposition to the party's stance on neutrality. Mussolini served in the Royal Italian Army during the war until he was wounded and discharged in 1917. Mussolini denounced the PSI, his views now centering on nationalism instead of socialism and founded the fascist movement which came to oppose egalitarianism and class conflict, instead advocating "revolutionary nationalism" transcending class lines. Following the March on Rome in October 1922, Mussolini became the youngest Prime Minister in Italian history until the appointment of Matteo Renzi in February 2014. After removing all political opposition through his secret police and outlawing labor strikes and his followers consolidated their power through a series of laws that transformed the nation into a one-party dictatorship.
Within five years, Mussolini had established dictatorial authority by both legal and extraordinary means and aspired to create a totalitarian state. In 1929, Mussolini signed the Lateran Treaty with the Vatican, ending decades of struggle between the Italian state and the Papacy, recognized the independence of Vatican City. After the Abyssinia Crisis of 1935–1936, Mussolini invaded Ethiopia in the Second Italo–Ethiopian War; the invasion was condemned by the Western powers and was answered with economic sanctions against Italy. Relations between Germany and Italy improved due to Hitler's support of the invasion. In 1936, Mussolini surrendered Austria to the German sphere of influence, signed the treaty of cooperation with Germany and proclaimed the creation of a Rome–Berlin Axis. From 1936 through 1939, Mussolini provided huge amounts of military support to Franco's forces in the Spanish Civil War; this active intervention further distanced Italy from Britain. Mussolini had sought to delay a major war in Europe, but Germany invaded Poland on 1 September 1939, resulting in declarations of war by France and the UK and the start of World War II.
On 10 June 1940—with the Fall of France imminent—Italy entered the war on the side of Germany, though Mussolini was aware that Italy did not have the military capacity and resources to carry out a long war with the British Empire. He believed that after the imminent French armistice, Italy could gain territorial concessions from France, he could concentrate his forces on a major offensive in North Africa, where British and Commonwealth forces were outnumbered by Italian forces. However, the British government refused to accept proposals for a peace that would involve accepting Axis victories in Eastern and Western Europe. In October 1940, Mussolini sent Italian forces into Greece; the invasion failed and the following Greek counter-offensive pushed the Italians back to occupied Albania. The Greek debacle and simultaneous defeats against the British in North Africa reduced Italy to dependence on Germany. Beginning in June 1941, Mussolini sent Italian forces to participate in the invasion of the Soviet Union, Italy declared war on the United States in December.
In 1943, Italy suffered one disaster after another: by February the Red Army had destroyed the Italian Army in Russia. As a consequence, early on 25 July, the Grand Council of Fascism passed a motion of no confidence for Mussolini. After the king agreed the armistice with the allies, on 12 September 1943 Mussolini was rescued from captivity in the Gran Sasso raid by German paratroopers and Waffen-SS commandos led by Major Otto-Harald Mors. Adolf Hitler, after meeting with the rescued former dictator put Mussolini in charge of a puppet regime in northern Italy, the Italian Social Republic, informally known as the Salò Republic. In late April 1945, in the wake of near total defeat and his mistress Clara Petacci attempted to flee to Switzerland, but both were captured by Italian communist partisans and summarily executed by firing squad on 28 April 1945 near Lake Como, his body was taken to Milan, where it was hung upside down at a service station to publicly confirm his demise. Mussolini was born on 29 July 1883 in Dovia di Predappio, a small town in the province of Forlì in Romagna.
During the Fascist era, Predappio was dubbed "Duce's town" and Forlì was called "Duce's city", with pilgrims going to Predappio and Forlì to see the birthplace of Mussolini. Benito Mussolini's father, Alessandro Mussolini, was a blacksmith and a socialist, while his mother, was a devout Catholic schoolteacher. Owing to his father's political leanings, Mussolini was named Benito after liberal Mexican president Benito Juárez, while his middle names Andrea and Amilcare were from Italian socialists Andrea Costa and Amilcare Cipriani. Benito was the eldest of his parents' three children, his siblings Arnaldo and Edvige fol
University College London
University College London, which has operated under the official name of UCL since 2005, is a public research university located in London, United Kingdom. It is a constituent college of the federal University of London, is the third largest university in the United Kingdom by total enrolment, the largest by postgraduate enrolment. Established in 1826 as London University by founders inspired by the radical ideas of Jeremy Bentham, UCL was the first university institution to be established in London, the first in England to be secular and to admit students regardless of their religion. UCL makes the contested claims of being the third-oldest university in England and the first to admit women. In 1836 UCL became one of the two founding colleges of the University of London, granted a royal charter in the same year, it has grown through mergers, including with the Institute of Neurology, the Royal Free Hospital Medical School, the Eastman Dental Institute, the School of Slavonic and East European Studies, the School of Pharmacy and the Institute of Education.
UCL has its main campus in the Bloomsbury area of central London, with a number of institutes and teaching hospitals elsewhere in central London and satellite campuses in Queen Elizabeth Olympic Park in Stratford, east London and in Doha, Qatar. UCL is organised into 11 constituent faculties, within which there are over 100 departments and research centres. UCL operates several culturally significant museums and manages collections in a wide range of fields, including the Petrie Museum of Egyptian Archaeology and the Grant Museum of Zoology and Comparative Anatomy, administers the annual Orwell Prize in political writing. In 2017/18, UCL had around 41,500 students and 15,100 staff and had a total group income of £1.45 billion, of which £476.3 million was from research grants and contracts. In the most recent Research Excellence Framework rankings for research power, UCL was the top-rated university in the UK as calculated by Times Higher Education, second as calculated by The Guardian/Research Fortnight.
UCL had the 9th highest average entry tariff in the UK for students starting in 2016. UCL is ranked from tenth to twentieth in the four major international rankings, from eighth to eleventh in the national league tables. UCL is a member of numerous academic organisations, including the Russell Group and the League of European Research Universities, is part of UCL Partners, the world's largest academic health science centre, the "golden triangle" of research-intensive English universities. UCL alumni include the'Father of the Nation' of each of India and Mauritius, the founders of Ghana, modern Japan and Nigeria, the inventor of the telephone, one of the co-discoverers of the structure of DNA. UCL academics discovered five of the occurring noble gases, discovered hormones, invented the vacuum tube, made several foundational advances in modern statistics; as of 2018, 33 Nobel Prize winners and 3 Fields medalists have been affiliated with UCL as alumni, faculty or researchers. UCL was founded on 11 February 1826 under the name London University, as an alternative to the Anglican universities of Oxford and Cambridge.
London University's first Warden was Leonard Horner, the first scientist to head a British university. Despite the held belief that the philosopher Jeremy Bentham was the founder of UCL, his direct involvement was limited to the purchase of share No. 633, at a cost of £100 paid in nine instalments between December 1826 and January 1830. In 1828 he did nominate a friend to sit on the council, in 1827 attempted to have his disciple John Bowring appointed as the first professor of English or History, but on both occasions his candidates were unsuccessful; this suggests that while his ideas may have been influential, he himself was less so. However, Bentham is today regarded as the "spiritual father" of UCL, as his radical ideas on education and society were the inspiration to the institution's founders the Scotsmen James Mill and Henry Brougham. In 1827, the Chair of Political Economy at London University was created, with John Ramsay McCulloch as the first incumbent, establishing one of the first departments of economics in England.
In 1828 the university became the first in England to offer English as a subject and the teaching of Classics and medicine began. In 1830, London University founded the London University School, which would become University College School. In 1833, the university appointed Alexander Maconochie, Secretary to the Royal Geographical Society, as the first professor of geography in the UK. In 1834, University College Hospital opened as a teaching hospital for the university's medical school. In 1836, London University was incorporated by royal charter under the name University College, London. On the same day, the University of London was created by royal charter as a degree-awarding examining board for students from affiliated schools and colleges, with University College and King's College, London being named in the charter as the first two affiliates; the Slade School of Fine Art was founded as part of University College in 1871, following a bequest from Felix Slade. In 1878, the University of London gained a supplemental charter making it the first British university to be allowed to award degrees to women.
The same year, UCL admitted women to the faculties of Arts and Law and of Science, although women remained barred from the faculties of Engineering and of Medicine. While UCL claims to have been the first university in England
La Concha Renaissance San Juan Resort
La Concha Renaissance San Juan Resort is a historic luxury resort located at the Condado oceanfront within the district of Santurce in San Juan, Puerto Rico. The hotel was first opened in 1958 during the Tropical Modernism Movement; the building was designed by Miguel Ferrer, of the firm Toro Ferrer Architects. Another part of the complex, the seashell-inspired building for the restaurant La Perla, was designed by architect Mario Salvadori. La Concha Resort incorporates tropical climate features such as cross-ventilation, natural illumination, open lobbies and seamless transitions between inside and outside spaces, with details relevant to Island traditions: an interior patio, blinds, a mirador encompassing both the sea and the city and the use of water throughout as a leitmotif; the protective concrete element in the façade, called brise-soleil in French or “quiebrasol” in Spanish, is an architectural element used by famed architect Le Corbusier. The purpose of the “quiebrasol” is to filter the sun’s rays towards the interior corridors.
In 1973, the La Concha was united with the adjacent Condado Beach Hotel into one hotel, known as the Hyatt Puerto Rico. In 1976, the complex was taken over by Hilton International and renamed the Condado Beach La Concha Convention Center, with a huge convention wing built between the two existing hotel structures; the complex was taken over by Carnival Cruise Line and renamed the Condado Beach Trio, before closing in 1995. The government-owned properties sat vacant for years, were severed in 2004, the convention center between them was demolished to build a public park; the La Concha reopened in December 2007, managed by Renaissance Hotels as La Concha Renaissance San Juan Resort, after a $220 million renovation. In the summer of 2010, the hotel opened a $100 million addition called The Suites Tower which features an atrium style building with one and two bedroom suites, architectural lighting, amenities; the hotel's Casino del Mar is located on the street level of the new tower. List of hotels in Puerto Rico Media related to La Concha Resort at Wikimedia Commons Official website
World War II
World War II known as the Second World War, was a global war that lasted from 1939 to 1945. The vast majority of the world's countries—including all the great powers—eventually formed two opposing military alliances: the Allies and the Axis. A state of total war emerged, directly involving more than 100 million people from over 30 countries; the major participants threw their entire economic and scientific capabilities behind the war effort, blurring the distinction between civilian and military resources. World War II was the deadliest conflict in human history, marked by 50 to 85 million fatalities, most of whom were civilians in the Soviet Union and China, it included massacres, the genocide of the Holocaust, strategic bombing, premeditated death from starvation and disease, the only use of nuclear weapons in war. Japan, which aimed to dominate Asia and the Pacific, was at war with China by 1937, though neither side had declared war on the other. World War II is said to have begun on 1 September 1939, with the invasion of Poland by Germany and subsequent declarations of war on Germany by France and the United Kingdom.
From late 1939 to early 1941, in a series of campaigns and treaties, Germany conquered or controlled much of continental Europe, formed the Axis alliance with Italy and Japan. Under the Molotov–Ribbentrop Pact of August 1939, Germany and the Soviet Union partitioned and annexed territories of their European neighbours, Finland and the Baltic states. Following the onset of campaigns in North Africa and East Africa, the fall of France in mid 1940, the war continued between the European Axis powers and the British Empire. War in the Balkans, the aerial Battle of Britain, the Blitz, the long Battle of the Atlantic followed. On 22 June 1941, the European Axis powers launched an invasion of the Soviet Union, opening the largest land theatre of war in history; this Eastern Front trapped most crucially the German Wehrmacht, into a war of attrition. In December 1941, Japan launched a surprise attack on the United States as well as European colonies in the Pacific. Following an immediate U. S. declaration of war against Japan, supported by one from Great Britain, the European Axis powers declared war on the U.
S. in solidarity with their Japanese ally. Rapid Japanese conquests over much of the Western Pacific ensued, perceived by many in Asia as liberation from Western dominance and resulting in the support of several armies from defeated territories; the Axis advance in the Pacific halted in 1942. Key setbacks in 1943, which included a series of German defeats on the Eastern Front, the Allied invasions of Sicily and Italy, Allied victories in the Pacific, cost the Axis its initiative and forced it into strategic retreat on all fronts. In 1944, the Western Allies invaded German-occupied France, while the Soviet Union regained its territorial losses and turned toward Germany and its allies. During 1944 and 1945 the Japanese suffered major reverses in mainland Asia in Central China, South China and Burma, while the Allies crippled the Japanese Navy and captured key Western Pacific islands; the war in Europe concluded with an invasion of Germany by the Western Allies and the Soviet Union, culminating in the capture of Berlin by Soviet troops, the suicide of Adolf Hitler and the German unconditional surrender on 8 May 1945.
Following the Potsdam Declaration by the Allies on 26 July 1945 and the refusal of Japan to surrender under its terms, the United States dropped atomic bombs on the Japanese cities of Hiroshima and Nagasaki on 6 and 9 August respectively. With an invasion of the Japanese archipelago imminent, the possibility of additional atomic bombings, the Soviet entry into the war against Japan and its invasion of Manchuria, Japan announced its intention to surrender on 15 August 1945, cementing total victory in Asia for the Allies. Tribunals were set up by fiat by the Allies and war crimes trials were conducted in the wake of the war both against the Germans and the Japanese. World War II changed the political social structure of the globe; the United Nations was established to foster international co-operation and prevent future conflicts. The Soviet Union and United States emerged as rival superpowers, setting the stage for the nearly half-century long Cold War. In the wake of European devastation, the influence of its great powers waned, triggering the decolonisation of Africa and Asia.
Most countries whose industries had been damaged moved towards economic expansion. Political integration in Europe, emerged as an effort to end pre-war enmities and create a common identity; the start of the war in Europe is held to be 1 September 1939, beginning with the German invasion of Poland. The dates for the beginning of war in the Pacific include the start of the Second Sino-Japanese War on 7 July 1937, or the Japanese invasion of Manchuria on 19 September 1931. Others follow the British historian A. J. P. Taylor, who held that the Sino-Japanese War and war in Europe and its colonies occurred and the two wars merged in 1941; this article uses the conventional dating. Other starting dates sometimes used for World War II include the Italian invasion of Abyssinia on 3 October 1935; the British historian Antony Beevor views the beginning of World War II as the Battles of Khalkhin Gol fought between Japan and the fo
Italian racial laws
The Italian racial laws were a set of laws promulgated by Fascist Italy from 1938 to 1943 to enforce racial discrimination in Italy, directed against the Italian Jews and the native inhabitants of the colonies. The first and most important of the leggi razziali was the Regio Decreto 17 Novembre 1938 Nr. 1728. It restricted civil rights of Jews, banned their books and excluded Jews from public office and higher education. Additional laws stripped Jews of their assets, restricted travel and provided for their confinement in internal exile, as was done for political prisoners; the promulgation of the racial laws was preceded by a long press campaign and by publication of the "Manifesto of Race" earlier in 1938, a purportedly-scientific report by fascist scientists and supporters that asserted racial principles, including the superiority of Europeans over other races. The final decision about the law was made during the meeting of the Gran Consiglio del Fascismo, which took place on the night between 6 and 7 October 1938 in Rome, Palazzo Venezia.
Not all Fascists supported discrimination: while the pro-German, anti-Jewish Roberto Farinacci and Giovanni Preziosi pushed for them, Italo Balbo opposed the laws. The laws prohibited Jews from having any professional position and prohibited sexual relations and marriages between Italians and Jews and Africans. Fascist Italy publicized a publication titled "Manifesto of the Racial Scientists" which included a mixture of biological racism and history. After the fall of Benito Mussolini on July 25, 1943, the Badoglio government suppressed the laws, they remained in force and were made more severe in the territories ruled by the Italian Social Republic until the end of the war. Leading Fascists such as Dino Grandi and Italo Balbo opposed the racial laws, they were unpopular with most ordinary Italians. Most Jews in Italy were either ancient Italian Jews that practiced the Italian rite and had been living in Italy since Ancient Roman times. In any case, Jews in Italy, in general, had assimilated into Italian society and had contributed to Italian culture over the course of two millennia.
Most Italians were not acquainted with Jews, Italian society was unaccustomed to the kind of anti-Semitism, common and thrived for centuries in German-speaking countries and other parts of northern and eastern Europe, where Jews had a greater presence and lived in large numbers for a long period of time. No racial laws were promulgated in Fascist Italy prior to 1938; the racial laws were introduced at the same time as Fascist Italy began to ally itself with Nazi Germany and mere months before Fascist Italy would form the Pact of Steel military alliance with Nazi Germany. William Shirer in The Rise and Fall of the Third Reich suggests that Mussolini enacted the laws to appease his powerful German allies, rather than to satisfy any genuine anti-Semitic sentiment among the Italian people. Indeed, prior to 1938 and the Pact of Steel alliance and many notable Italian fascists had been critical of Nordicism, biological racism, anti-Semitism the virulent and violent anti-Semitism and biological racism found in Nazi Germany.
Many early supporters of Italian fascism, including Mussolini's mistress, the writer and socialite Margherita Sarfatti, had in fact been middle class or upper middle class Italian Jews. Nordicism and biological racism were considered incompatible with the early Italian fascist philosophy. In 1929, Mussolini noted that Italian Jews had been a demographically small yet culturally integral part of Italian society since Ancient Rome, his views on Italian Jews were consistent with his early Mediterraneanist viewpoint, which suggested that all Mediterranean cultures, including the Jewish culture, shared a common bond. He further argued that Italian Jews had become "Italians" or natives to Italy after such a long period on the peninsula. However, Mussolini's views on race were contradictory and quick to change when necessary, as Fascist Italy became subordinate to Nazi Germany's interests, Mussolini began adopting racial theories borrowed from or based on Nazi Germany's racial policies, leading to the introduction of the anti-Semitic racial laws.
Historian Federico Chabod argued that the introduction of the Nordicist-influenced racial laws was a large factor in the decrease of public support among Italians for Fascist Italy, many Italians viewed the racial laws as an obvious imposition or intrusion of Nazi German values into Italian cultures and a sign that Mussolini and Fascist Italy's power was collapsing under Nazi German influence. De Felice, Renzo. Storia degli ebrei italiani sotto il fascismo. Turin: Einaudi. ISBN 8806172794. Burgio, Nel nome della razza. Il razzismo nella storia d'Italia, Il Mulino, Bologna,ISBN 88-15-07200-4 Centro Furio Jesi, La menzogna della razza. Documenti e imma
Manhattan referred to locally as the City, is the most densely populated of the five boroughs of New York City and its economic and administrative center, cultural identifier, historical birthplace. The borough is coextensive with New York County, one of the original counties of the U. S. state of New York. The borough consists of Manhattan Island, bounded by the Hudson and Harlem rivers. S. mainland, physically connected to the Bronx and separated from the rest of Manhattan by the Harlem River. Manhattan Island is divided into three informally bounded components, each aligned with the borough's long axis: Lower and Upper Manhattan. Manhattan has been described as the cultural, financial and entertainment capital of the world, the borough hosts the United Nations Headquarters. Anchored by Wall Street in the Financial District of Lower Manhattan, New York City has been called both the most economically powerful city and the leading financial center of the world, Manhattan is home to the world's two largest stock exchanges by total market capitalization: the New York Stock Exchange and NASDAQ.
Many multinational media conglomerates are based in Manhattan, the borough has been the setting for numerous books and television shows. Manhattan real estate has since become among the most expensive in the world, with the value of Manhattan Island, including real estate, estimated to exceed US$3 trillion in 2013. Manhattan traces its origins to a trading post founded by colonists from the Dutch Republic in 1624 on Lower Manhattan. Manhattan is documented to have been purchased by Dutch colonists from Native Americans in 1626 for 60 guilders, which equals $1038 in current terms; the territory and its surroundings came under English control in 1664 and were renamed New York after King Charles II of England granted the lands to his brother, the Duke of York. New York, based in present-day Manhattan, served as the capital of the United States from 1785 until 1790; the Statue of Liberty greeted millions of immigrants as they came to the Americas by ship in the late 19th and early 20th centuries and is a world symbol of the United States and its ideals of liberty and peace.
Manhattan became a borough during the consolidation of New York City in 1898. New York County is the United States' second-smallest county by land area, is the most densely populated U. S. county. It is one of the most densely populated areas in the world, with a census-estimated 2017 population of 1,664,727 living in a land area of 22.83 square miles, or 72,918 residents per square mile, higher than the density of any individual U. S. city. On business days, the influx of commuters increases this number to over 3.9 million, or more than 170,000 people per square mile. Manhattan has the third-largest population of New York City's five boroughs, after Brooklyn and Queens, is the smallest borough in terms of land area. Manhattan Island is informally divided into three areas, each aligned with its long axis: Lower and Upper Manhattan. Many districts and landmarks in Manhattan are well known, as New York City received a record 62.8 million tourists in 2017, Manhattan hosts three of the world's 10 most-visited tourist attractions in 2013: Times Square, Central Park, Grand Central Terminal.
The borough hosts many prominent bridges, such as the Brooklyn Bridge. Chinatown incorporates the highest concentration of Chinese people in the Western Hemisphere, the Stonewall Inn in Greenwich Village, part of the Stonewall National Monument, is considered the birthplace of the modern gay rights movement; the City of New York was founded at the southern tip of Manhattan, the borough houses New York City Hall, the seat of the city's government. Numerous colleges and universities are located in Manhattan, including Columbia University, New York University, Cornell Tech, Weill Cornell Medical College, Rockefeller University, which have been ranked among the top 40 in the world; the name Manhattan derives from the Munsee dialect of the Lenape language'manaháhtaan'. The Lenape word has been translated as "the place where we get bows" or "place for gathering the bows". According to a Munsee tradition recorded in the 19th century, the island was named so for a grove of hickory trees at the lower end, considered ideal for the making of bows.
It was first recorded in writing as Manna-hata, in the 1609 logbook of Robert Juet, an officer on Henry Hudson's yacht Halve Maen. A 1610 map depicts the name as Manna-hata, twice, on both the west and east sides of the Mauritius River. Alternative folk etymologies include "island of many hills", "the island where we all became intoxicated" and "island", as well as a phrase descriptive of the whirlpool at Hell Gate; the area, now Manhattan was long inhabited by the Lenape Native Americans. In 1524, Florentine explorer Giovanni da Verrazzano – sailing in service of King Francis I of France – became the first documented European to visit the area that would become New York City, he entered the tidal strait now known as The Narrows and named the land around Upper New York
Photoelasticity describes changes in the optical properties of a material under mechanical deformation. It is a property of all dielectric media and is used to experimentally determine the stress distribution in a material, where it gives a picture of stress distributions around discontinuities in materials. Photoelastic experiments are an important tool for determining critical stress points in a material, are used for determining stress concentration in irregular geometries; the photoelastic phenomenon was first discovered by the Scottish physicist David Brewster. Experimental frameworks were developed at the beginning of the twentieth century with the works of E. G. Coker and L. N. G. Filon of University of London, their book Treatise on Photoelasticity, published in 1930 by Cambridge Press, became a standard text on the subject. Between 1930 and 1940, many other books appeared on the subject, including books in Russian and French. At the same time, much development occurred in the field – great improvements were achieved in technique, the equipment was simplified.
With refinements in the technology, photoelastic experiments were extended to determining three-dimensional states of stress. In parallel to developments in experimental technique, the first phenomenological description of photoelasticity was given in 1890 by Friedrich Pockels, however this was proved inadequate a century by Nelson & Lax as the description by Pockels only considered the effect of mechanical strain on the optical properties of the material. With the advent of the digital polariscope – made possible by light-emitting diodes – continuous monitoring of structures under load became possible; this led to the development of dynamic photoelasticity, which has contributed to the study of complex phenomena such as fracture of materials. Photoelasticity has been used for a variety of stress analyses and for routine use in design before the advent of numerical methods, such as for instance finite elements or boundary elements. Digitization of polariscopy enables fast image acquisition and data processing, which allows its industrial applications to control quality of manufacturing process for materials such as glass and polymer.
Dentistry utilizes photoelasticity to analyze strain in denture materials. Photoelasticity can be used to investigate the localized stress state within masonry or in proximity of a rigid line inclusion embedded in an elastic medium. In the former case, the problem is nonlinear due to the contacts between bricks, while in the latter case the elastic solution is singular, so that numerical methods may fail to provide correct results; these can be obtained through photoelastic techniques. Dynamic photoelasticity integrated with high-speed photography is utilized to investigate fracture behavior in materials. Another important application of the photoelasticity experiments is to study the stress field around bi-material notches. Bi-material notches exist in many engineering application like welded or adhesively bonded structures For a linear dielectric material the change in the inverse permittivity tensor Δ i j with respect to the deformation is described by Δ i j = P i j k l ∂ k u l where P i j k l is the fourth-rank photoelasticity tensor, u l is the linear displacement from equilibrium, ∂ l denotes denotes differentiation with respect to the Cartesian coordinate x l.
For isotropic materials, this definition simplifies to Δ i j = p i j k l s k l where p i j k l is the symmetric part of the photoelastic tensor, s k l is the linear strain. The antisymmetric part of P i j k l is known as the roto-optic tensor. From either definition, it is clear that deformations to the body may induce optical anisotropy, which can cause an otherwise optically isotropic material to exhibit birefringence. Although the symmetric photoelastic tensor is most defined with respect to mechanical strain, it is possible to express photoelasticity in terms of the mechanical stress; the experimental procedure relies on the property of birefringence, as exhibited by certain transparent materials. Birefringence is a phenomenon in which a ray of light passing through a given material experiences two refractive indices; the property of birefringence is observed in many optical crystals. Upon the application of stresses, photoelastic materials exhibit the property of birefringence, the magnitude of the