Effective dielectric response of nonlinear composites with external ac and dc electric field

The perturbation method is developed to investigate the effective nonlinear dielectric response of Kerr composites when the external ac and dc electric field is applied. Under the external ac and dc electric field E-app=E-a(1+sin omegat), the effective coupling nonlinear response can be induced by the cubic nonlinearity of Kerr nonlinear materials at the zero frequency, the finite basic frequency omega, the second and the third harmonics, 2omega and 3omega, and so on. As an example, we have investigated the cylindrical inclusions randomly embedded in a host and derived the formulas of the effective nonlinear dielectric response at harmonics in dilute limit. For a higher concentration of inclusions, we have proposed a nonlinear effective-medium approximation by introducing the general effective nonlinear response. With the relationships between the effective nonlinear response at harmonics and the general effective nonlinear response, we have derived a set of formulas of the effective nonlinear dielectric responses at harmonics for a larger volume fraction. (C) 2004 American Institute of Physics.

The Ontario and St. Lawrence Steamboat Company's hand-book for travelers to Niagara Falls, Montreal and Quebec, and through Lake Champlain to Saratoga Springs.

"Illustrated with maps, and numerous engravings from original sketches."

Buffalo, Brantford & Goderich Railway, County of Welland account book, 1853

The Buffalo and Brantford Railway Company was formed in 1850. The railway was renamed the Buffalo, Brantford & Goderich Railway in 1852 to reflect the plans to extend the line to Goderich. Financial problems led to a British group taking over the railway a few years later and the name was changed to the Buffalo & Lake Huron Railway. It was June 1858 before the line to Goderich was completed. Source: (http://brantford.library.on.ca/genealogy/railways.php#buffalo) March 8, 2010

Erie & Niagara Railway Collection, 1864-1884

William Alexander Thomson (1816-1878) was a promoter and developer of railway systems in western Ontario. He incorporated the Fort Erie Railroad Company in 1857, purchased the Erie and Ontario Railroad in 1863, and incorporated the Erie and Niagara Extension Railway Company in 1868 (later renamed the Canada Southern Railway). Thomson was also elected to the House of Commons for Welland in 1872, and re-elected in 1874. He was known for his support of public management of the currency and is seen as a pioneer advocate of government monetary policy. He was also an advocate of radical agrarian economic doctrine, believing that Canadian laws favoured mercantile interests over those of the producers of goods, and that this hindered national development.

Indenture of Release of All Existing Contracts and Agreements with Woodstock and Lake Erie Railway Co.

Indenture of release stating that all existing contracts and agreements made by the Woodstock and Lake Erie Railway Co. are cancelled. This release was between the executors of Samuel Zimmerman's will and the Woodstock and Lake Erie Railway Co. February 10, 1858.

Indenture between William and Ann Waters and William B. Winterbottom

Indenture of mortgage with dower between William and Ann Waters of Niagara to William B. Winterbottom of Niagara regarding the easterly half of Lot no. 265 in Niagara. This was recorded in the Register of Forms of Niagara on April 13, 1850, Book A, folios 207-208 - instrument no. 2093, April 1, 1850.

Mr. Woodward’s timetable regarding the suspension bridge to Toronto via the Great Western Railway and Port Dalhousie Railway

Mr. Woodward’s timetable regarding the suspension bridge to Toronto via the Great Western Railway and Port Dalhousie Railway (1 page, handwritten), Jan. 22, 1856

Port Dalhousie and the Thorold Railway pay roll for the months of October, November and December, 1854

Port Dalhousie and the Thorold Railway pay roll for services of engineering and contingencies furnished for the months of October, November and December, 1854.

Denver and Rio Grande Railway schedule

Denver and Rio Grande Railway schedule, 1881.

“Frisco Line” St. Louis and San Francisco Railway the direct line through St. Louis schedule

“Frisco Line” St. Louis and San Francisco Railway the direct line through St. Louis schedule, Jan. 9, 1882.