Efficient Algorithms for Mixed Creative Telescoping

Creative telescoping is a powerful computer algebra paradigm -initiated by Doron Zeilberger in the 90's- for dealing with definite integrals and sums with parameters. We address the mixed continuous-discrete case, and focus on the integration of bivariate hypergeometric-hyperexponential terms. We design a new creative telescoping algorithm operating on this class of inputs, based on a Hermite-like reduction procedure. The new algorithm has two nice features: it is efficient and it delivers, for a suitable representation of the input, a minimal-order telescoper. Its analysis reveals tight bounds on the sizes of the telescoper it produces.Comment: To be published in the proceedings of ISSAC'1

Alien Registration- Dumont, Louis (Lewiston, Androscoggin County)

https://digitalmaine.com/alien_docs/29466/thumbnail.jp

Adding SALT to Coupled Microcavities: the making of active photonic molecule lasers

A large body of work has accumulated over the years in the study of the optical properties of single and coupled microcavities for a variety of applications, ranging from filters to sensors and lasers. The focus has been mostly on the geometry of individual resonators and/or on their combination in arrangements often referred to as photonic molecules (PMs). Our primary concern will be the lasing properties of PMs as ideal candidates for the fabrication of integrated microlasers, photonic molecule lasers. Whereas most calculations on PM lasers have been based on cold-cavity (passive) modes, i.e. quasi-bound states, a recently formulated steady-state ab initio laser theory (SALT) offers the possibility to take into account the spectral properties of the underlying gain transition, its position and linewidth, as well as incorporating an arbitrary pump profile. We will combine two theoretical approaches to characterize the lasing properties of PM lasers: for two-dimensional systems, the generalized Lorenz-Mie theory will obtain the resonant modes of the coupled molecules in an active medium described by SALT. Not only is then the theoretical description more complete, the use of an active medium provides additional parameters to control, engineer and harness the lasing properties of PM lasers for ultra-low threshold and directional single-mode emission.Comment: 16th International Conference on Transparent Optical Networks (2014

Optimization of integrated polarization filters

This study reports on the design of small footprint, integrated polarization filters based on engineered photonic lattices. Using a rods-in-air lattice as a basis for a TE filter and a holes-in-slab lattice for the analogous TM filter, we are able to maximize the degree of polarization of the output beams up to 98 % with a transmission efficiency greater than 75 %. The proposed designs allow not only for logical polarization filtering, but can also be tailored to output an arbitrary transverse beam profile. The lattice configurations are found using a recently proposed parallel tabu search algorithm for combinatorial optimization problems in integrated photonics

S and Q Matrices Reloaded: applications to open, inhomogeneous, and complex cavities

We present a versatile numerical algorithm for computing resonances of open dielectric cavities. The emphasis is on the generality of the system's configuration, i.e. the geometry of the (main) cavity (and possible inclusions) and the internal and external dielectric media (homogeneous and inhomogeneous). The method is based on a scattering formalism to obtain the position and width of the (quasi)-eigenmodes. The core of the method lies in the scattering S-matrix and its associated delay Q-matrix which contain all the relevant information of the corresponding scattering experiment. For instance, the electromagnetic near- and far-fields are readily extracted. The flexibility of the propagation method is displayed for a selected system.Comment: 15th International Conference on Transparent Optical Networks (2013

Ab initio investigation of lasing thresholds in photonic molecules

We investigate lasing thresholds in a representative photonic molecule composed of two coupled active cylinders of slightly different radii. Specifically, we use the recently formulated steady-state ab initio laser theory (SALT) to assess the effect of the underlying gain transition on lasing frequencies and thresholds. We find that the order in which modes lase can be modified by choosing suitable combinations of the gain center frequency and linewidth, a result that cannot be obtained using the conventional approach of quasi-bound modes. The impact of the gain transition center on the lasing frequencies, the frequency pulling effect, is also quantified

Il fait si noir [Música impresa]; Tu n'es qu'un employé; L'Étoile du marin; Petite Rose

Copia digital. Valladolid : Junta de Castilla y León. Consejería de Cultura y Turismo, 2012-201

Proteins at Interfaces: Conformational Behavior and Wear

Proteins at interfaces play a major role in biomaterials and lab-on-a-chip devices. Protein interactions with the surface change their conformations and therefore their ability to bind to their respective ligands. Another major area of interest surrounding biomaterials and lab-on-a-chip devices is the prediction and prevention of wear. Wear is the progressive loss of material from an object caused by contact and relative movement of the contacting solid, liquid, or gas. It is estimated that wear costs 1% of the gross domestic product (approximately $150 billion for the US). With the emergence of drug-releasing implants and lab-on-the-chip devices, wear has also become a major concern in bio- and nano- technology. In our laboratory, we use microtubules (filamentous proteins) gliding on kinesin motor proteins as transporters in biosensors. This system, known as the motility assay, is ideal for studying how the conformation of kinesins impacts the gliding of microtubules and therefore the performance of the biosensor. The proposed studies seek to show that kinesins' geometry changes with their grafting density following De Gennes' scaling laws for flexible polymers (Chapter 2 , published in Langmuir as E.L.P. Dumont, H. Belmas, and H. Hess, Observing the mushroom-to-brush transition for kinesin proteins, 2013, 29 (49), 15142-15145) and that microtubules experience molecular wear due to their repeated interactions with kinesins (Chapter 3, under review for Nature Nanotechnology as E.L.P. Dumont and H. Hess, Molecular wear of microtubules propelled by surface-adhered kinesins). These two results permit the prediction of the lifetime of biosensors using kinesin-propelled microtubules (Chapter 4, to be submitted to Nano Letters as Y. Jeune-Smith, E.L.P. Dumont and H. Hess, Wear and breakage combine to mechanically degrade kinesin-powered molecular shuttles). I also discuss the importance of mechanical fatigue for molecular machine design (Chapter 5, published as H. Hess and E.L.P. Dumont, Fatigue Failure and Molecular Machine Design, Small, 7, 1619-1623, 2011). Finally, and it is unrelated to the previous chapters, I developed Monte Carlo simulations for protein adsorption on polymer-coated surfaces (Chapter 6, to be submitted as E.L.P. Dumont, A.V. Guillaume, A. Gore, and H. Hess, Random Sequential Adsorption of proteins on polymer-covered surfaces: A simulation-based approach) and I explored a molecular model to explain the fracture of materials at low stresses (Chapter 7)