Discontinuity induced bifurcations of non-hyperbolic cycles in nonsmooth systems

We analyse three codimension-two bifurcations occurring in nonsmooth systems, when a non-hyperbolic cycle (fold, flip, and Neimark-Sacker cases, both in continuous- and discrete-time) interacts with one of the discontinuity boundaries characterising the system's dynamics. Rather than aiming at a complete unfolding of the three cases, which would require specific assumptions on both the class of nonsmooth system and the geometry of the involved boundary, we concentrate on the geometric features that are common to all scenarios. We show that, at a generic intersection between the smooth and discontinuity induced bifurcation curves, a third curve generically emanates tangentially to the former. This is the discontinuity induced bifurcation curve of the secondary invariant set (the other cycle, the double-period cycle, or the torus, respectively) involved in the smooth bifurcation. The result can be explained intuitively, but its validity is proven here rigorously under very general conditions. Three examples from different fields of science and engineering are also reported

Bifurcations of piecewise smooth flows:perspectives, methodologies and open problems

In this paper, the theory of bifurcations in piecewise smooth flows is critically surveyed. The focus is on results that hold in arbitrarily (but finitely) many dimensions, highlighting significant areas where a detailed understanding is presently lacking. The clearest results to date concern equilibria undergoing bifurcations at switching boundaries, and limit cycles undergoing grazing and sliding bifurcations. After discussing fundamental concepts, such as topological equivalence of two piecewise smooth systems, discontinuity-induced bifurcations are defined for equilibria and limit cycles. Conditions for equilibria to exist in n-dimensions are given, followed by the conditions under which they generically undergo codimension-one bifurcations. The extent of knowledge of their unfoldings is also summarized. Codimension-one bifurcations of limit cycles and boundary-intersection crossing are described together with techniques for their classification. Codimension-two bifurcations are discussed with suggestions for further study

Interplay between bending and stretching in carbon nanoribbons

We investigate the bending properties of carbon nanoribbons by combining continuum elasticity theory and tight-binding atomistic simulations. First, we develop a complete analysis of a given bended configuration through continuum mechanics. Then, we provide by tight-binding calculations the value of the bending rigidity in good agreement with recent literature. We discuss the emergence of a stretching field induced by the full atomic-scale relaxation of the nanoribbon architecture. We further prove that such an in-plane strain field can be decomposed into a first contribution due to the actual bending of the sheet and a second one due to edge effects.Comment: 5 pages, 6 figure

On the stability of the standard Riemann semigroup

We consider the dependence of the entropic solution of a hyperbolic system of conservation laws {ut + f(u)x = 0, u(0, \ub7) = u0 on the flux function f. We prove that the solution is Lipschitz continuous w.r.t, the C0 norm of the derivative of the perturbation of f. We apply this result to prove the convergence of the solution of the relativistic Euler equation to the classical limit

Understanding the determinants of stability and folding of small globular proteins from their energetics

The results of minimal model calculations suggest that the stability and the kinetic accessibility of the native state of small globular proteins are controlled by few "hot" sites. By mean of molecular dynamics simulations around the native conformation, which simulate the protein and the surrounding solvent at full--atom level, we generate an energetic map of the equilibrium state of the protein and simplify it with an Eigenvalue decomposition. The components of the Eigenvector associated with the lowest Eigenvalue indicate which are the "hot" sites responsible for the stability and for the fast folding of the protein. Comparison of these predictions with the results of mutatgenesis experiments, performed for five small proteins, provide an excellent agreement

Orbital dynamics of "smart dust" devices with solar radiation pressure and drag

This paper investigates how perturbations due to asymmetric solar radiation pressure, in the presence of Earth shadow, and atmospheric drag can be balanced to obtain long-lived Earth centred orbits for swarms of micro-scale 'smart dust' devices, without the use of active control. The secular variation of Keplerian elements is expressed analytically through an averaging technique. Families of solutions are then identified where Sun-synchronous apse-line precession is achieved passively to maintain asymmetric solar radiation pressure. The long-term orbit evolution is characterized by librational motion, progressively decaying due to the non-conservative effect of atmospheric drag. Long-lived orbits can then be designed through the interaction of energy gain from asymmetric solar radiation pressure and energy dissipation due to drag. In this way, the usual short drag lifetime of such high area-to-mass spacecraft can be greatly extended (and indeed selected). In addition, the effect of atmospheric drag can be exploited to ensure the rapid end-of-life decay of such devices, thus preventing long-lived orbit debris

Optical Spectroscopy of X-Mega targets in the Carina Nebula - VI. FO 15: a new O-Type double-lined eclipsing binary

We report the discovery of a new O-type double-lined spectroscopic binary with a short orbital period of 1.4 days. We find the primary component of this binary, FO 15, to have an approximate spectral type O5.5Vz, i.e. a Zero-Age-Main-Sequence star. The secondary appears to be of spectral type O9.5V. We have performed a numerical model fit to the public ASAS photometry, which shows that FO 15 is also an eclipsing binary. We find an orbital inclination of ~ 80 deg. From a simultaneous light-curve and radial velocity solution we find the masses and radii of the two components to be 30 +/- 1 and 16 +/- 1 solar masses and 7.5 +/- 0.5 and 5.3 +/- 0.5 solar radii. These radii, and hence also the luminosities, are smaller than those of normal O-type stars, but similar to recently born ZAMS O-type stars. The absolute magnitudes derived from our analysis locate FO 15 at the same distance as Eta Carinae. From Chandra and XMM X-ray images we also find that there are two close X-ray sources, one coincident with FO 15 and another one without optical counterpart. This latter seems to be a highly variable source, presumably due to a pre-main-sequence stellar neighbour of FO 15.Comment: 11 pages, 9 figures, 3 tables. Accepted for publication in MNRAS. Higher resolution version available at http://lilen.fcaglp.unlp.edu.ar/papers2006.htm