Third order trace formula

In J. Funct. Anal. 257 (2009) 1092-1132, Dykema and Skripka showed the existence of higher order spectral shift functions when the unperturbed self-adjoint operator is bounded and the perturbation is Hilbert-Schmidt. In this article, we give a different proof for the existence of spectral shift function for the third order when the unperturbed operator is self-adjoint (bounded or unbounded, but bounded below).

Higher-order analysis of crack-tip fields in power-law hardening materials

In this paper, we present an exact higher-order asymptotic analysis on the near-crack-tip fields in elastic-plastic materials under plane strain, Mode I. A four- or five-term asymptotic series of the solutions is derived. It is found that when 1.6 < n less-than-or-equal-to 2.8 (here, n is the hardening exponent), the elastic effect enters the third-order stress field; but when 2.8< n less-than-or-equal-to 3.7 this effect turns to enter the fourth-order field, with the fifth-order field independent. Moreover, if n>3.7, the elasticity only affects the fields whose order is higher than 4. In this case, the fourth-order field remains independent. Our investigation also shows that as long as n is larger than 1.6, the third-order field is always not independent, whose amplitude coefficient K3 depends either on K1 or on both K1 and K2 (K1 and K2 arc the amplitude coefficients of the first- and second-order fields, respectively). Firmly, good agreement is found between our results and O'Dowd and Shih's numerical ones[8] by comparison.

Ghost imaging with thermal light by third-order correlation

Ghost imaging with classical incoherent light by third-order correlation is investigated. We discuss the similarities and the differences between ghost imaging by third-order correlation and by second-order correlation, and analyze the effect from each correlation part of the third-order correlation function on the imaging process. It is shown that the third-order correlated imaging includes richer correlated imaging effects than the second-order correlated one, while the imaging information originates mainly from the correlation of the intensity fluctuations between the test detector and each reference detector, as does ghost imaging by second-order correlation.

Super-resolution scanning laser microscopy with a third-order optical nonlinear thin film

In a configuration of optical far-field scanning microscopy, super-resolution achieved by inserting a third-order optical nonlinear thin film is demonstrated and analyzed in terms of the frequency response function. Without the thin film the microscopy is diffraction limited; thus, subwavelength features cannot be resolved. With the nonlinear thin film inserted, the resolution is dramatically improved and thus the microscopy resolves features significantly smaller than the smallest spacing allowed by the diffraction limit. A theoretical model is established and the device is analyzed for the frequency response function. The results show that the frequency response function exceeds the cutoff spatial frequency of the microscopy defined by the laser wavelength and the numerical aperture of the convergent lens. The main contribution to the improvement of the cutoff spatial frequency is from the phase change induced by the complex transmission of the nonlinear thin film. Experimental results are presented and are shown to be consistent with the results of theoretical simulations.

The coupling of St. John, US Virgin Islands Marine Protected Areas based on reef fish habitat affinities and movements across management boundaries [Poster]

NOAA's Biogeograpy Branch, the National Park Service (NPS), US Geological Survey, and the University of the Virgin Islands (UVI) are using acoustice telemetry to quantify spatial patterns and habitat affinities of reef fishes in the US Virgin Islands (USVI). The objective of the study is to define the movements of reef fishes among habitats within and between the Virgin Islands Coral Reef Nationla Monument (VICRNM), adjacent to Virgin Islands National Park (VIIS), and USVI Territorial waters. In order to better understand species habitat utilization patterns and movement of fishes among management regimes and areas open to fishing around St. John, we deployed an array of hydroacoutstic receivers and acoustically tagged reef fishes. A total of 150 fishes, representing 18 species and 10 families were acoustically tagged along the south shore of St. John from July 2006 to June 2008. Thirty six receivers with a detection range of approximately 300m each were deployed in shallow nearshore bays and across the shelf to depths of approximately 30m. Receivers were located within reefs and adjacent to reefs in seagrass, algal beds, or sand habitats. Example results include the movement of lane snappers and blue striped grunts that demonstrated diel movement from reef habitats during daytime hours to offshore seagrass beds at night. Fish associated with reefs that did not have adjacent seagrass beds made more extensive movements than those fishes associated with reefs that had adjacent seagrass habitats. The array comprised of both nearshore and cross shelf location of receives provides information on fine to broad scale fish movement patterns across habitats and among management units to examine the strength of ecological connectivity between management areas and habitats. For more information go to: http://ccma.nos.noaa.gov/ecosystems/ coralreef/acoustic_tracking.html

Acoustic tracking of reef fishes to elucidate habitat utilization patterns and residence times inside and outside marine protected areas around the island of St. John, USVI

This technical memorandum describes a developing project under the direction of NOAA’s Biogeography Branch in consultation with the National Park Service and US Geological Survey to understand and quantify spatial patterns and habitat affinities of reef fishes in the US Virgin Islands. The purpose of this report is to describe and disseminate the initial results from the project and to share information on the location of acoustic receivers and species electronic tag ID codes. The Virgin Islands Coral Reef National Monument (VICRNM), adjacent to Virgin Islands National Park (VIIS), was established by Executive Order in 2000, but resources within the monument are poorly documented and the degree of connectivity to VIIS is unknown. Whereas, VICRNM was established with full protection from resource exploitation, VIIS has incurred resource harvest by fishers since 1956 as allowed in its enabling legislation. Large changes in local reef communities have occurred over the past several decades, in part due to overexploitation. In order to better understand the habitat utilization patterns and movement of fishes among management regimes and areas open to fishing around St, John, an array of hydroacoustic receivers was deployed while a variety of reef fish species were acoustically tagged. In July 2006, nine receivers with a detection range of ca. 350 m were deployed in Lameshur Bay on the south shore of St. John, within VIIS. Receivers were located adjacent to reefs and in seagrass beds, inshore and offshore of these reefs. It was found that lane snappers and bluestriped grunts showed diel movement from reef habitats during daytime hours to offshore seagrass bed at night. Timing of migrations was highly predictable and coincided with changes in sunrise and sunset over the course of the year. Fish associated with reefs that did not have adjacent seagrass beds made more extensive movements than those fishes associated with reefs that had adjacent seagrass habitats. In April 2007, 21 additional receivers were deployed along much of the south shore of St. John (ca. 20 km of shoreline). This current array will address broader-scale movement among management units and examine the potential benefits of the VICRNM to provide adult “spillover” into VIIS and adjacent harvested areas. The results from this work will aid in defining fine to moderate spatial scales of reef fish habitat affinities and in designing and evaluating marine protected areas.

Interaction between the intrinsic second- and third-order optical fields in an Al0.53Ga0.47N/GaN heterostructure

We present an experimental demonstration of the interaction between the intrinsic second- and third-order optical fields in an Al0.53Ga0.47N/GaN heterostructure. The sample was deposited by metal-organic chemical vapor deposition on (0001) sapphire. The nonlinear optical coefficients of the sample, which were measured with a Mach-Zehnder interferometer system, quadratically increase with the applied modulating voltage, indicating the existence of the third-order optical field. The third-order signal was then detected by the Z-scan method and we calculated the built-in dc field on the AlGaN/GaN interface to confirm the strong interaction between the intrinsic second- and third-order optical fields. (c) 2008 American Institute of Physics.

Tellurium enhanced non-resonant third-order optical nonlinearity in a germano-silicate optical fiber

碲掺杂的高非线性石英光纤

Third-order Stokes wave solutions for interfacial internal waves in a three-layer density-stratified fluid

Interfacial internal waves in a three-layer density-stratified fluid are investigated using a singular method, and third-order asymptotic solutions of the velocity potentials and third-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory. as expected, the third-order solutions describe the third-order nonlinear modification and the third-order nonlinear interactions between the interfacial waves. The wave velocity depends on not only the wave number and the depth of each layer but also on the wave amplitude.

Rotary Club of St. Catharines fonds, 1973-1985, n.d.

The first Rotary Club was created in February 1905, by Chicago lawyer Paul P. Harris. Harris envisioned a club which would bring members of the business community closer together. As his vision grew more members were acquired. In order to accommodate everyone, meetings were held at each of the member’s place of business; hence the name Rotary Club was adopted. A wagon wheel was chosen as an appropriate symbol to denote the club; which today has become the cogwheel. By the close of its first year the club had thirty members. Slowly Rotary Clubs began emerging across the country and by 1910 they had become International by moving North to Canada. By 1921 Rotary representation was present in every Continent and in 1922 the name Rotary International had been approved. The Rotary Club of St. Catharines came into existence on May 19, 1921 under the Charter President Canon Bill Broughall. The Club’s beginnings were humble with only twenty-five members; however, by their seventy-fifth anniversary the club had grown to one hundred and forty-four. The Rotary Club of St. Catharines is a non-profit charity, prescribing to the motto Service above Self. This motto is demonstrated through the Clubs numerous contributions to society both locally and internationally. The Club raises funds, supports exchange programs, and participates in community service work. Some of the organizations which have benefited from the Clubs donations; include, Easter Seals, the Niagara Peninsula Children’s Centre, and the Youth Exchange Program.

Letter to Dexter Deverardo, clerk of Fonthill from the Welland Canal Office of St. Catharines

Letter to Dexter Deverardo, clerk of Fonthill from the Welland Canal Office of St. Catharines in order to see that the work is done in a satisfactory manner. This letter is signed in pencil by S.D. Woodruff (4 pages, handwritten), Jan. 8, 1855.

Third order nonlinear optical studies in europium naphthalocyanine using degenerate four wave mixing and Z-scan

Third order nonlinear susceptibility χ(3) and second hyperpolarizability (γ) of a bis-naphthalocyanine viz. europium naphthalocyanines, Eu(Nc)2, were measured in dimethyl formamide solution using degenerate four wave mixing at 532 nm under nanosecond pulse excitation. Effective nonlinear absorption coefficient, βeff and imaginary part of nonlinear susceptibility, Im(χ(3)) were obtained using open aperture /Z-scan technique at the same wavelength. Optical limiting property of the sample was also investigated. The role of excited state absorption in deciding the nonlinear properties of this material is discussed.

Boundary value problems for third-order linear PDEs in time-dependent domains

We present the extension of a methodology to solve moving boundary value problems from the second-order case to the case of the third-order linear evolution PDE qt + qxxx = 0. This extension is the crucial step needed to generalize this methodology to PDEs of arbitrary order. The methodology is based on the derivation of inversion formulae for a class of integral transforms that generalize the Fourier transform and on the analysis of the global relation associated with the PDE. The study of this relation and its inversion using the appropriate generalized transform are the main elements of the proof of our results.

Fractional order modeling of large three-dimensional RC networks

An incidence matrix analysis is used to model a three-dimensional network consisting of resistive and capacitive elements distributed across several interconnected layers. A systematic methodology for deriving a descriptor representation of the network with random allocation of the resistors and capacitors is proposed. Using a transformation of the descriptor representation into standard state-space form, amplitude and phase admittance responses of three-dimensional random RC networks are obtained. Such networks display an emergent behavior with a characteristic Jonscher-like response over a wide range of frequencies. A model approximation study of these networks is performed to infer the admittance response using integral and fractional order models. It was found that a fractional order model with only seven parameters can accurately describe the responses of networks composed of more than 70 nodes and 200 branches with 100 resistors and 100 capacitors. The proposed analysis can be used to model charge migration in amorphous materials, which may be associated to specific macroscopic or microscopic scale fractal geometrical structures in composites displaying a viscoelastic electromechanical response, as well as to model the collective responses of processes governed by random events described using statistical mechanics.