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

A causal Schwarzschild-de Sitter interior solution by gravitational decoupling

We employ the minimal geometric deformation approach to gravitational decoupling (MGD- decoupling) in order to build an exact anisotropic version of the Schwarzschild interior solution in a space-time with cosmological constant. Contrary to the well-known Schwarzschild interior, the matter density in the new solution is not uniform and possesses subluminal sound speed. It therefore satisfies all standard physical requirements for a candidate astrophysical object.Comment: 15 pages, 6 figure

The International Space Station as a Research Laboratory: A View to 2010 and Beyond

Assembly of International Space Station (ISS) is expected to be complete in 2010, with operations planned to continue through at least 2016. As we move nearer to assembly complete, replanning activities by NASA and ISS International Partners have been completed and the final complement of research facilities on ISS is becoming more certain. This paper will review pans for facilities in the US On-orbit Segment of ISS, including contributions from International Partners, to provide a vision of the research capabilities that will be available starting in 2010. At present, in addition to research capabilities in the Russian segment, the United States Destiny research module houses nine research facilities or racks. These facilities include five multi-purpose EXPRESS racks, two Human Research Facility (HRF) racks, the Microgravity Science Glovebox (MSG), and the Minus Eighty-degree Laboratory Freezer for ISS (MELFI), enabling a wide range of exploration-related applied as well as basic research. In the coming years, additional racks will be launched to augment this robust capability: Combustion Integrated Rack (CIR), Fluids Integrated Rack (FIR), Window Observation Rack Facility (WORF), Microgravity Science Research Rack (MSRR), Muscle Atrophy Research Exercise System (MARES), additional EXPRESS racks and possibly a second MELFI. In addition, EXPRESS Logistics Carriers (ELC) will provide attach points for external payloads. The European Space Agency s Columbus module will contain five research racks and provide four external attach sites. The research racks are Biolab, European Physiology Module (EPM), Fluid Science Lab (FSL), European Drawer System (EDS) and European Transport Carrier (ETC). The Japanese Kibo elements will initially support three research racks, Ryutai for fluid science, Saibo for cell science, and Kobairo for materials research, as well as 10 attachment sites for external payloads. As we look ahead to assembly complete, these new facilities represent a threefold increase from the current research laboratory infrastructure on ISS. In addition, the increase in resident crew size will increase from three to six in 2009, will provide the long-term capacity for completing research on board ISS. Transportation to and from ISS for crew and cargo will be provided by a fleet of vehicles from the United States, Russia, ESA and Japan, including accommodations for thermally-conditioned cargo. The completed ISS will have robust research accommodations to support the multidisciplinary research objective of scientists worldwide

Piecewise smooth systems near a co-dimension 2 discontinuity manifold: can one say what should happen?

We consider a piecewise smooth system in the neighborhood of a co-dimension 2 discontinuity manifold $\Sigma$. Within the class of Filippov solutions, if $\Sigma$ is attractive, one should expect solution trajectories to slide on $\Sigma$. It is well known, however, that the classical Filippov convexification methodology is ambiguous on $\Sigma$. The situation is further complicated by the possibility that, regardless of how sliding on $\Sigma$ is taking place, during sliding motion a trajectory encounters so-called generic first order exit points, where $\Sigma$ ceases to be attractive. In this work, we attempt to understand what behavior one should expect of a solution trajectory near $\Sigma$ when $\Sigma$ is attractive, what to expect when $\Sigma$ ceases to be attractive (at least, at generic exit points), and finally we also contrast and compare the behavior of some regularizations proposed in the literature. Through analysis and experiments we will confirm some known facts, and provide some important insight: (i) when $\Sigma$ is attractive, a solution trajectory indeed does remain near $\Sigma$, viz. sliding on $\Sigma$ is an appropriate idealization (of course, in general, one cannot predict which sliding vector field should be selected); (ii) when $\Sigma$ loses attractivity (at first order exit conditions), a typical solution trajectory leaves a neighborhood of $\Sigma$; (iii) there is no obvious way to regularize the system so that the regularized trajectory will remain near $\Sigma$ as long as $\Sigma$ is attractive, and so that it will be leaving (a neighborhood of) $\Sigma$ when $\Sigma$ looses attractivity. We reach the above conclusions by considering exclusively the given piecewise smooth system, without superimposing any assumption on what kind of dynamics near $\Sigma$ (or sliding motion on $\Sigma$) should have been taking place.Comment: 19 figure

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

Supersymmetric exact sequence, heat kernel and super KdV hierarchy

We introduce the free N=1 supersymmetric derivation ring and prove the existence of an exact sequence of supersymmetric rings and linear transformations. We apply necessary and sufficient conditions arising from this exact supersymmetric sequence to obtain the essential relations between conserved quantities, gradients and the N=1 super KdV hierarchy. We combine this algebraic approach with an analytic analysis of the super heat operator.We obtain the explicit expression for the Green's function of the super heat operator in terms of a series expansion and discuss its properties. The expansion is convergent under the assumption of bounded bosonic and fermionic potentials. We show that the asymptotic expansion when $t\to0^+$ of the Green's function for the super heat operator evaluated over its diagonal generates all the members of the N=1 super KdV hierarchy.Comment: 20 pages, to be published in JM

Polyphenols and Novel Insights Into Post-kidney Transplant Complications and Cardiovascular Disease:A Narrative Review

Kidney transplantation is the preferred treatment for end-stage kidney disease. It is, however, not devoid of complications. Delayed graft function related to ischemia-reperfusion injury (IRI), calcineurin inhibitor (CNI) nephrotoxicity, diabetes, and a particularly high-rate cardiovascular disease (CVD) risk, represent important complications following kidney transplantation. Oxidative stress and chronic low-grade inflammation are mechanisms of disease incompletely abrogated in stable kidney transplant recipient (KTR), contributing to the occurrence of these complications. Polyphenols, bioactive compounds with recognized antioxidant and anti-inflammatory properties have been strongly associated with prevention of CVD in the general population and have been shown to decrease IRI and antagonize CNI nephrotoxicity in animal experimental models, therefore they may have a role in prevention of complications in KTR. This narrative review aims to summarize and discuss current evidence on different polyphenols for prevention of complications, particularly prevention of CVD in KTR, pointing toward the need of further studies with potential clinical impact