The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

Hakeperävaunun aerodynamiikan parantaminen

Raskaankaluston ajoneuvojen aerodynaaminen kehitys on kulkenut väärään suuntaan jo vuosisadan verran ja niiden muodon määräävä tekijä on kuljetustilan maksimointi ja toi-minnallisuus. Lähiaikoina on astumassa EU:ssa uusi direktiivi voimaan, joka sallii lisämas-san käyttämisen aerodynaamisiin lisäosiin. Työn tarkoituksena on tutkia mahdollisuuksia parantaa hakeperävaunun aerodynamiikkaa yksinkertaisilla lisäosilla. Työ on rajattu koskemaan perävaununetuosaan, -sivuosaan ja -pohjaan. Lisäksi rajoitteita asettaa Suomenlainsäädäntö ja EU:n direktiivit. Työssä perehdytään ilmanvastusvoiman syntymekanismeihin raskaankaluston ajoneuvojen kannalta ja käydään läpi merkittävimmät vaikuttavat tekijät ilmanvastusvoimiin sekä kuorma-auton perävaunun eri muotojen ja osien vaikutus. Perävaunuun asetettavien il-manohjaimien vaikutukset ja toiminta selvitetään. Avainasemassa hakeperävaunun aerodynamiikan parantamisessa on ilmavirtauksen estä-minen perävaunun alle sekä etupuolelta. Lisäksi virtausten muuttamien perävaunun takana on hyödyllistä. Merkittävimmät hyödyt saadaan niistä ratkaisuista, jotka estävät ilman virtausta perävau-nun alle sekä renkaisiin. Näitä ratkaisuja olivat sivuhelmat ja pohjan sekä renkaiden kote-lointi. Lisäksi ilmavirtauksen estäminen perävaunun edestä tuotti merkittävää hyötyä. Levy perävaunun välissä tai koko välin peittämällä saadaan aikaan huomattavaa vähenemistä ilmanvastuksessa.

Viimeisimmän finanssikriisin vaikutukset Helsingin Pörssin kulutuspalveluita tuottaviin yrityksiin

Tämän kandidaatintutkielman tarkoituksena on analysoida miten vuonna 2008 alkanut finanssikriisi ja sen aiheuttama taloudellinen epävarmuus ovat vaikuttaneet Nasdaq OMX Helsingin pörssiin listattujen kulutuspalveluita tuottavien yritysten suorituskykyyn. Näiden yritysten suorituskykyä analysoitiin tarkemmin tarkastelemalla kannattavuuden, maksuvalmiuden ja vakavaraisuuden tunnuslukuja aikavälillä 2008-2014. Tutkimuksen tavoitteena oli selvittää, minkälaisia muutoksia suorituskyvyn suhteen tutkitulla aikavälillä oli tapahtunut kulutuspalveluita tuottavien yritysten keskuudessa. Muutoksia analysoitiin sekä kokonaisuutena että yrityskohtaisesti. Lisäksi tutkittiin, miten kulutuspalveluryhmän sisäiset toimialat olivat selviytyneet finanssikriisistä. Käsiteltävää yritysryhmää analysoitiin tunnuslukuanalyysiä hyödyntäen. Saatujen tulosten mukaan finanssikriisillä ei ollut suurta vaikutusta käsiteltävien yritysten maksuvalmiuteen tai vakavaraisuuteen. Kannattavuuden tunnusluvut sen sijaan heikkenivät merkittävästi koko ryhmän osalta finanssikriisin vaikutuksesta. Yrityskohtaiset erot olivat tutkimuksessa melko suuria. Etenkin mediayhtiöiden tunnusluvut heikkenivät merkittävästi tutkitulla aikavälillä. Mediayhtiöiden huonoon suoriutumiseen liittyy finanssikriisin lisäksi muitakin tekijöitä. Median digitalisoituminen on aiheuttanut useille yrityksille ongelmia liiketoiminnan kannattavuuden ylläpitämisessä. Monet tutkituista yrityksistä ovat kuitenkin pystyneet kääntämään liiketoimintansa kannattavampaan suuntaan vuoden 2013 jälkeen. Johtopäätöksenä voidaankin vetää, että viimeisin finanssikriisi oli vaikutuksiltaan merkittävä ja pitkäkestoinen.

New Brock Centre

The Brock centre was later renamed Alphie's Trough after Alfred, the horse given to General Brock by Sir James Craig.

John Marchese

John Marchese was an arts student and was the first Manager of the Brock Student Pub operated out of Alfie's Trough which was our first student center paid for by the students and built in 1969. It had its grand opening in 1970.

Project Summary Cover

The cover of the project summary pamphlet for Alphies Trough.

Project Summary Back

The project summary for Alphies Trough.

Tower's North Facet

This view is from behind the tower along the escarpment. The photograph would have been taken near Alphie's Trough, north of the tower, facing southwards. A portion of the Thistle Complex is visible.

Microfacies analysis of the lower paleocene beda formation in Western Concession 59 and Block 59F, Sirte Basin, Libya /

The rock sequence of the Tertiary Beda Formation of S. W. concession 59 and 59F block in Sirte Basin of Libya has been subdivided into twelve platformal carbonate microfacies. These microfacies are dominated by muddy carbonates, such as skeletal mudstones, wackestones, and packstones with dolomites and anhydrite. Rock textures, faunal assemblages and sedimentary structures suggest shallow, clear, warm waters and low to moderate energy conditions within the depositional shelf environment. The Beda Formation represents a shallowing-upward sequence typical of lagoonal and tidal flat environments marked at the top by sabkha and brackish-water sediments. Microfossils include benthonic foraminifera, such as miliolids, Nummulites, - oerculina and other smaller benthonics, in addition to dasycladacean algae, ostracods, molluscs, echinoderms, bryozoans and charophytes. Fecal pellets and pelloids, along with the biotic allochems, contributed greatly to the composition of the various microfacies. Dolomite, where present, is finely crystalline and an early replacement product. Anhydrite occurs as nodular, chickenwire and massive textures indicating supratidal sabkha deposition. Compaction, micr it i zat ion , dolomit izat ion , recrystallization, cementation, and dissolution resulted in alteration and obliteration of primary sedimentary structures of the Beda Formation microfacies. The study area is located in the Gerad Trough which developed as a NE-SW trending extensional graben. The Gerad trough was characterized by deep-shallow water conditions throughout the deposition of the Beda Formation sediments. The study area is marked by several horsts and grabens; as a result of extent ional tectonism. The area was tectonically active throughout the Tertiary period. Primary porosity is intergranular and intragranular, and secondary processes are characterized by dissolution, intercrystalline, fracture and fenestral features. Diagenesis, through solution leaching and dolomitization, contributed greatly to porosity development. Reservoir traps of the Beda Formation are characterized by normal fault blocks and the general reservoir characteristics/properties appear to be facies controlled.

Custom House Niagara forms, 1833

In 1833 William Clarke, the collector of customs at Niagara, completed and signed four forms for the movement of goods between Niagara and York, and Niagara and Brantford. The forms were issued to the firm of Lewis & Gray, James Armstrong, J.A. Wilks, and William Blackely. The goods being transported included scythes, corn brooms, hide whips, sacks, snuff, shovels, spades and two apple trees.

Gilbert McMicken document, n.d.

Gilbert McMicken emigrated to Upper Canada in 1832 and settled in Chippawa. In 1835 he was married to Ann Theresa Duff. In 1837 the family moved to Queenston where he was directly involved in the Kingston-Queenston trade endeavours begun by Robert Hamilton. He had a variety of interests, including a partnership with James Hamilton, son of Robert Hamilton. He was also a collector of customs in Queenston and operated the Niagara Suspension Bridge Bank for a time. He entered politics and represented Niagara as well as becoming mayor of Clifton, now part of Niagara Falls, Ont., in 1856. McMicken went on to have an illustrious career, serving as land agent and leader of Canada’s first undercover agency. McMicken moved to Manitoba and was active in business and politics. He died in Winnipeg in 1891. Source: Dictionary of Canadian Biography – Gilbert McMicken website (March 22, 2010)

Scholfield-Galbraith family fonds, 1865-1924

The Scholfield and Galbraith families of Dunnville, Ont. were related by marriage. Thomas Jefferson Galbraith (1842-1921) worked as a collector of canal tolls at Port Maitland, a landing waiter and searcher and an acting preventive officer in Customs. He was married to Jane Ann [Jennie] Montieth and they had five children, Margaret, Minnie Montieth, Genevieve Marion, Edith Stuart and Thomas Percy Galbraith. Genevieve Marion Galbraith was married to Harry E. Scholfield, son of Frederick Scholfield (d.1908) and Georginna Galer (d. 1888), a dry goods merchant in Dunnville. Some extent records belong to a William Scholfield who operated a mill in Dunnville. Included are records related to land lease, mortgage and bargain and sale agreements between Scholfield and various individuals, including Richard Kirkpatrick, William Kohler, Alvin Drake, Robert Ban[u]d, Henry Beckett, Sr., Samuel Waltho, Nehemiah Niece.

Lt. Col. John Clark Papers, 1838-1851 [photocopy]

Lt. Col. John Clark (1787-1862) was born in Kingston, Upper Canada. In 1801 Clark became a private in the 1st regiment of the Lincoln Militia, serving under Ralfe Clench. By June 1812 he was promoted to lieutenant by Maj. Gen. Sir Isaac Brock. During the War of 1812 he served as lieutenant and adjutant for the Lincoln Militia flank company on the Niagara frontier under Col. William Claus, and was present at the surrender of the enemy at the battle of Queenston Heights. By 1838 the Lincoln Militia was being re-organized and Lt. Col John Clark was requested to lead the 5th Regiment, made up of men from both Grantham and Louth townships in Lincoln County. He served in this capacity until his retirement in 1851?. Around this same time Clark bought from William May Jr. a house in Grantham Township. He was to call his home Walnut Dale Farm. John Clark also served as the customs collector for Port Dalhousie, and as a secretary in the Welland Canal Company. One hundred years later efforts by a local heritage group to save John Clark’s home failed, when the house was hit by arsonists. By this time the house had become known as the May-Clark-Seiler House. See RG 195 Anne Taylor Fonds for more information regarding the efforts of the heritage group to save this home. Clark died in 1862 at the age of 79 years and is buried in Victoria Lawn Cemetery. John Clark’s daughter Catherine (mentioned in the diary portion of the papers) was married to William Morgan Eccles.

Irish John Willson United Empire Loyalist Family Fonds

John Willson first came to Upper Canada along with his friend Nathaniel Pettit in the late 1700s. They both moved with their families from New Jersey where they had both been imprisioned for not siding with the rebels and maintaining Loyalist allegiences. Pettit arrived with his four daughters, leaving his son behind. Willson came with his wife and nine children. Willson received 1200 acres of land as well as 200 per child. He settled at the corner of Dorchester road and Thorold Stone Road, where he and his family did very well for themselves. Willson as well as his son Thomas ran ox-teams on the portage. His son John became the proprietor of the Exchange hotel at Niagara, and Charles operated at the Pavilion hotel at Falls View. Shortly after his arrival in Upper Canada John Willson changed his name to “Irish” John Willson, as there were 5 other “John Willsons” which appeared on the Loyalists lists. Irish John drowned in the Niagara River in 1798, and his family continued to thrive in Niagara after his death. His second son Thomas Willson, married Abigail Pettit, daughter of his Father’s friend Nathaniel. Thomas was awarded 250 acres of land as a Loyalist and 200 for Abigail, as she was the daughter of a loyalist. He became a blacksmith and also operated ox-teams along the portage. He was Assessor for Stamford Township for 1800, 1807, 1820 and 1829. During the years 1808, 1822, 1825, 1826 and 1831 he was a tax collector and overseer of Statute of Labour. Thomas and Abigail Willson had nine children together. Francis Bond Head Willson of Beaverdams (mentioned throughout the collection) was a great grandson of Thomas and Abigail. Thomas and his wife are both buried beside the Lundy’s Lane United Church. *for more information on the remaining Willson family please refer to box #1, folders 1-3. * Genealogical information from a paper prepared by Pearl Wilson and given before the Lundy’s Lane Historical Society, May 1945, by Hazel Culp Ferris. Box 1 Folder 1.