Hopf Bifurcations in a Watt Governor With a Spring

This paper pursues the study carried out by the authors in "Stability and Hopf bifurcation in a hexagonal governor system", focusing on the codimension one Hopf bifurcations in the hexagonal Watt governor differential system. Here are studied the codimension two, three and four Hopf bifurcations and the pertinent Lyapunov stability coefficients and bifurcation diagrams, ilustrating the number, types and positions of bifurcating small amplitude periodic orbits, are determined. As a consequence it is found an open region in the parameter space where two attracting periodic orbits coexist with an attracting equilibrium point.Comment: 30 pages and 7 figure

Mechanical oscillations in lasing microspheres

We investigate the feasibility of activating coherent mechanical oscillations in lasing microspheres by modulating the laser emission at a mechanical eigenfrequency. To this aim, 1.5% Nd3+:Barium-Titanium-Silicate microspheres with diameters around 50 {\mu}m were used as high quality factor (Q>10^6) whispering gallery mode lasing cavities. We have implemented a pump-and-probe technique in which the pump laser used to excite the Nd3+ ions is focused on a single microsphere with a microscope objective and a probe laser excites a specific optical mode with the evanescent field of a tapered fibre. The studied microspheres show monomode and multi-mode lasing action, which can be modulated in the best case up to 10 MHz. We have optically transduced thermally-activated mechanical eigenmodes appearing in the 50-70 MHz range, the frequency of which decreases with increasing the size of the microspheres. In a pump-and-probe configuration we observed modulation of the probe signal up to the maximum pump modulation frequency of our experimental setup, i.e., 20 MHz. This modulation decreases with frequency and is unrelated to lasing emission, pump scattering or thermal effects. We associate this effect to free-carrier-dispersion induced by multiphoton pump light absorption. On the other hand, we conclude that, in our current experimental conditions, it was not possible to resonantly excite the mechanical modes. Finally, we discuss on how to overcome these limitations by increasing the modulation frequency of the lasing emission and decreasing the frequency of the mechanical eigenmodes displaying a strong degree of optomechanical coupling.Comment: 17 pages, 5 figure

Group Strategyproof Pareto-Stable Marriage with Indifferences via the Generalized Assignment Game

We study the variant of the stable marriage problem in which the preferences of the agents are allowed to include indifferences. We present a mechanism for producing Pareto-stable matchings in stable marriage markets with indifferences that is group strategyproof for one side of the market. Our key technique involves modeling the stable marriage market as a generalized assignment game. We also show that our mechanism can be implemented efficiently. These results can be extended to the college admissions problem with indifferences

Stable schedule matching under revealed preference

Baiou and Balinski (Math. Oper. Res., 27 (2002) 485) studied schedule matching where one determines the partnerships that form and how much time they spend together, under the assumption that each agent has a ranking on all potential partners. Here we study schedule matching under more general preferences that extend the substitutable preferences in Roth (Econometrica 52 (1984) 47) by an extension of the revealed preference approach in Alkan (Econom. Theory 19 (2002) 737). We give a generalization of the GaleShapley algorithm and show that some familiar properties of ordinary stable matchings continue to hold. Our main result is that, when preferences satisfy an additional property called size monotonicity, stable matchings are a lattice under the joint preferences of all agents on each side and have other interesting structural properties

High frequency mechanical excitation of a silicon nanostring with piezoelectric aluminum nitride layers

A strong trend for quantum based technologies and applications follows the avenue of combining different platforms to exploit their complementary technological and functional advantages. Micro and nano-mechanical devices are particularly suitable for hybrid integration due to the easiness of fabrication at multi-scales and their pervasive coupling with electrons and photons. Here, we report on a nanomechanical technological platform where a silicon chip is combined with an aluminum nitride layer. Exploiting the AlN piezoelectricity, Surface Acoustic Waves are injected in the Si layer where the material has been localy patterned and etched to form a suspended nanostring. Characterizing the nanostring vertical displacement induced by the SAW, we found an external excitation peak efficiency in excess of 500 pm/V at 1 GHz mechanical frequency. Exploiting the long term expertise in silicon photonic and electronic devices as well as the SAW robustness and versatility, our technological platform represents a strong candidate for hybrid quantum systems

Defect analysis and alignment quantification of line arrays prepared by directed self-assembly of a block copolymer

Trabajo presentado al XXVIII Metrology, Inspection, and Process Control for Microlithography, celebrado en California (US) en 2014.Different linear patterns obtained from the directed self-assembly of the block copolymer (BCP) polystyrene-b-polyethylene oxide (PS-b-PEO) were analysed and compared. The hexagonal phase PS-b-PEO in a thin film exhibits linear pattern morphology, by conventional solvent annealing in an atmosphere saturated in chloroform. The surface energy of the silicon substrates was varied using surface functionalization of a self-assembly monolayer (SAM) and a polymer brush, chosen to investigate the influence of the surface energy on the self-assembly of the BCP. The linear patterns formed were analyzed with innovative image analysis software specifically developed in our laboratory to identify elements and defects of line arrays from block copolymer self-assembly. The technique starts by performing dimensional metrology to calculate the pitch size and estimate the linewidth of the lines. Secondly, the methodology allows identification and quantification of typical defects observable in BCP systems, such as turning points, disclination or branching points, break or lone points and end points. The defect density and the quantification of the alignment were estimated using our technique. The methodology presented here represents a step forward in dimensional metrology and defect analysis of BCP DSA systems and can be readily used to analyze other lithographic or non-lithographic patterns.The research leading to these results received funding from the European Union FP7 under the project LAMAND (grant agreement n° 245565), the Spanish MICIN under the project TAPHOR (contract nr. MAT2012-31392) and the Science Foundation Ireland under grant number 09/SIRG/I1615.Peer Reviewe

Tensile strain mapping in flat germanium membranes

Under the terms of the Creative Commons Attribution (CC BY) license to their work.-- et al.Scanning X-ray micro-diffraction has been used as a non-destructive probe of the local crystalline quality of a thin suspended germanium (Ge) membrane. A series of reciprocal space maps were obtained with ~4 μm spatial resolution, from which detailed information on the strain distribution, thickness, and crystalline tilt of the membrane was obtained. We are able to detect a systematic strain variation across the membranes, but show that this is negligible in the context of using the membranes as platforms for further growth. In addition, we show evidence that the interface and surface quality is improved by suspending the Ge.This work was carried out under the RCUK Basic Technology Programme supported by research Grant Nos. EP/F040784/1, EP/J001074/1, EP/L007010/1, by the European Community's Seventh Framework Programme (FP7/2007-2013) under Grant Agreement NANOFUNCTION No. 257375, by TAPHOR (MAT2012–31392), and by FP7 project MERGING (Grant No. 309150). This research used equipment funded by AWM and ERDF through the Science City Energy Efficiency project.Peer Reviewe

Comparison of Zn_{1-x}Mn_xTe/ZnTe multiple-quantum wells and quantum dots by below-bandgap photomodulated reflectivity

Large-area high density patterns of quantum dots with a diameter of 200 nm have been prepared from a series of four Zn_{0.93}Mn_{0.07}Te/ZnTe multiple quantum well structures of different well width (4 nm, 6 nm, 8 nm and 10 nm) by electron beam lithography followed by Ar+ ion beam etching. Below-bandgap photomodulated reflectivity spectra of the quantum dot samples and the parent heterostructures were then recorded at 10 K and the spectra were fitted to extract the linewidths and the energy positions of the excitonic transitions in each sample. The fitted results are compared to calculations of the transition energies in which the different strain states in the samples are taken into account. We show that the main effect of the nanofabrication process is a change in the strain state of the quantum dot samples compared to the parent heterostructures. The quantum dot pillars turn out to be freestanding, whereas the heterostructures are in a good approximation strained to the ZnTe lattice constant. The lateral size of the dots is such that extra confinement effects are not expected or observed.Comment: 23 pages, LaTeX2e (amsmath, epsfig), 7 EPS figure