Efficient split eld FDTD analysis of third-order nonlinear materials in two-dimensionally periodic media

In this work the split-field finite-difference time-domain method (SF-FDTD) has been extended for the analysis of two-dimensionally periodic structures with third-order nonlinear media. The accuracy of the method is verified by comparisons with the nonlinear Fourier Modal Method (FMM). Once the formalism has been validated, examples of one- and two-dimensional nonlinear gratings are analysed. Regarding the 2D case, the shifting in resonant waveguides is corroborated. Here, not only the scalar Kerr effect is considered, the tensorial nature of the third-order nonlinear susceptibility is also included. The consideration of nonlinear materials in this kind of devices permits to design tunable devices such as variable band filters. However, the third-order nonlinear susceptibility is usually small and high intensities are needed in order to trigger the nonlinear effect. Here, a one-dimensional CBG is analysed in both linear and nonlinear regime and the shifting of the resonance peaks in both TE and TM are achieved numerically. The application of a numerical method based on the finite- difference time-domain method permits to analyse this issue from the time domain, thus bistability curves are also computed by means of the numerical method. These curves show how the nonlinear effect modifies the properties of the structure as a function of variable input pump field. When taking the nonlinear behaviour into account, the estimation of the electric field components becomes more challenging. In this paper, we present a set of acceleration strategies based on parallel software and hardware solutions.

Unfolding Operator Method for Thin Domains with a Locally Periodic Highly Oscillatory Boundary

We analyze the behavior of solutions of the Poisson equation with homogeneous Neumann boundary conditions in a two-dimensional thin domain which presents locally periodic oscillations at the boundary. The oscillations are such that both the amplitude and period of the oscillations may vary in space. We obtain the homogenized limit problem and a corrector result by extending the unfolding operator method to the case of locally periodic media.

Periodic emission of droplets from an oscillating electrified meniscus of a low-viscosity, highly conductive liquid

The generation of identical droplets of controllable size in the micrometer range is a problem of much interest owing to the numerous technological applications of such droplets. This work reports an investigation of the regime of periodic emission of droplets from an electrified oscillating meniscus of a liquid of low viscosity and high electrical conductivity attached to the end of a capillary tube, which may be used to produce droplets more than ten times smaller than the diameter of the tube. To attain this periodic microdripping regime, termed axial spray mode II by Juraschek and Röllgen [R. Juraschek and F. W. Röllgen, Int. J. Mass Spectrom. 177, 1 (1998)], liquid is continuously supplied through the tube at a given constant flow rate, while a dc voltage is applied between the tube and a nearby counter electrode. The resulting electric field induces a stress at the surface of the liquid that stretches the meniscus until, in certain ranges of voltage and flow rate, it develops a ligament that eventually detaches, forming a single droplet, in a process that repeats itself periodically. While it is being stretched, the ligament develops a conical tip that emits ultrafine droplets, but the total mass emitted is practically contained in the main droplet. In the parametrical domain studied, we find that the process depends on two main dimensionless parameters, the flow rate nondimensionalized with the diameter of the tube and the capillary time, q, and the electric Bond number BE, which is a nondimensional measure of the square of the applied voltage. The meniscus oscillation frequency made nondimensional with the capillary time, f, is of order unity for very small flow rates and tends to decrease as the inverse of the square root of q for larger values of this parameter. The product of the meniscus mean volume times the oscillation frequency is nearly constant. The characteristic length and width of the liquid ligament immediately before its detachment approximately scale as powers of the flow rate and depend only weakly on the applied voltage. The diameter of the main droplets nondimensionalized with the diameter of the tube satisfies dd≈(6/π)1/3(q/f)1/3, from mass conservation, while the electric charge of these droplets is about 1/4 of the Rayleigh charge. At the minimum flow rate compatible with the periodic regimen, the dimensionless diameter of the droplets is smaller than one-tenth, which presents a way to use electrohydrodynamic atomization to generate droplets of highly conducting liquids in the micron-size range, in marked contrast with the cone-jet electrospray whose typical droplet size is in the nanometric regime for these liquids. In contrast with other microdripping regimes where the mass is emitted upon the periodic formation of a narrow capillary jet, the present regime gives one single droplet per oscillation, except for the almost massless fine aerosol emitted in the form of an electrospray.

Report on the Status of Findings and Recommendations from the City of Bertram’s Periodic Examination Report dated August 27, 2014 for the period August 1, 2015 through July 31, 2016

Report on the Status of Findings and Recommendations from the City of Bertram’s Periodic Examination Report dated August 27, 2014 for the period August 1, 2015 through July 31, 2016

Report on the Status of Findings and Recommendations from the City of Olin’s Periodic Examination Report dated November 17, 2014 for the period June 1, 2015 through April 30, 2016

Report on the Status of Findings and Recommendations from the City of Olin’s Periodic Examination Report dated November 17, 2014 for the period June 1, 2015 through April 30, 2016

Report on the Status of Findings and Recommendations from the City of Kelley’s Periodic Examination Report dated December 11, 2014 for the period April 1, 2015 through March 31, 2016

Report on the Status of Findings and Recommendations from the City of Kelley’s Periodic Examination Report dated December 11, 2014 for the period April 1, 2015 through March 31, 2016

Report on the Status of Findings and Recommendations from the City of Low Moor’s Periodic Examination Report dated November 13, 2014 for the period November 1, 2015 through July 31, 2016

Report on the Status of Findings and Recommendations from the City of Low Moor’s Periodic Examination Report dated November 13, 2014 for the period November 1, 2015 through July 31, 2016

Report on the Status of Findings and Recommendations on the City of Randalia’s Periodic Examination Report dated March 25, 2015

Report on the Status of Findings and Recommendations on the City of Randalia’s Periodic Examination Report dated March 25, 2015

Report on the Status of Findings and Recommendations from the City of Gilman’s Periodic Examination Report dated October 10, 2014 for the period June 1, 2015 through February 29, 2016

Report on the Status of Findings and Recommendations from the City of Gilman’s Periodic Examination Report dated October 10, 2014 for the period June 1, 2015 through February 29, 2016

Report on the Status of Findings and Recommendations on the City of Kimballton’s Periodic Examination Report dated August 11, 2014 for the period December 1, 2015 through May 31, 2016

Report on the Status of Findings and Recommendations on the City of Kimballton’s Periodic Examination Report dated August 11, 2014 for the period December 1, 2015 through May 31, 2016

Report on the Status of Findings and Recommendations from the City of Harper’s Periodic Examination Report dated December 15, 2014 for the period December 1, 2015 through May 31, 2016

Report on the Status of Findings and Recommendations from the City of Harper’s Periodic Examination Report dated December 15, 2014 for the period December 1, 2015 through May 31, 2016

Report on the Status of Findings and Recommendations on the City of Derby’s Periodic Examination Report dated August 27, 2014 for the period April 1, 2015 through March 31, 2016

Report on the Status of Findings and Recommendations on the City of Derby’s Periodic Examination Report dated August 27, 2014 for the period April 1, 2015 through March 31, 2016

Convergence time to equilibrium distributions of autonomous and periodic non-autonomous graphs

We present some estimates of the time of convergence to the equilibrium distribution in autonomous and periodic non-autonomous graphs, with ergodic stochastic adjacency matrices, using the eigenvalues of these matrices. On this way we generalize previous results from several authors, that only considered reversible matrices.

Acoustic Propagation over Periodic and Quasi-Period Rough Surfaces Proceedings

Numerical techniques such as the Boundary Element Method, Finite Element Method and Finite Difference Time Domain have been used widely to investigate plane and curved wave-front scattering by rough surfaces. For certain shapes of roughness elements (cylinders, semi-cylinders and ellipsoids) there are semi-analytical alternatives. Here, we present a theory for multiple scattering by cylinders on a hard surface to investigate effects due to different roughness shape, the effects of vacancies and variation of roughness element size on the excess attenuation due to a periodically rough surfaces.