The compositional construction of Markov processes II

In an earlier paper we introduced a notion of Markov automaton, together with parallel operations which permit the compositional description of Markov processes. We illustrated by showing how to describe a system of n dining philosophers, and we observed that Perron-Frobenius theory yields a proof that the probability of reaching deadlock tends to one as the number of steps goes to infinity. In this paper we add sequential operations to the algebra (and the necessary structure to support them). The extra operations permit the description of hierarchical systems, and ones with evolving geometry

Gravitational waves from hyperbolic encounters

The emission of gravitational waves from a system of massive objects interacting on hyperbolic orbits is studied in the quadrupole approximation. Analytic expressions are derived for the gravitational radiation luminosity, the total energy output and the gravitational radiation amplitude. An estimation of the expected number of events towards different targets (i.e. globular clusters and the center of the Galaxy) is also given. In particular, for a dense stellar cluster at the galactic center, a rate up to one event per year is obtained.Comment: 6 pages, 2 figure

Risk-based system to control safety level of flooded passenger ships

Predicting the consequences of flooding is a key issue that may help the ship master of a large passenger ship to make rational decisions in emergency situations. To this end, the Delphi Emergency Decision Support System (Delphi EDSS) has been designed and is under implementation to continuously assess ship's state of survivability. Analyses are performed by means of a time-domain simulation program, where transient stages of flooding are investigated and stored off-line for all the potential damage scenarios. The Delphi EDSS evaluates the ship risk level including the most important aspects related to safety state while establishing the time-to-capsize which is of primary concern for the safe evacuation of the damaged ship. The methodology is based on a scientific approach, setting an overall platform for rational assessment of non-survivability risk. Determination of the global risk level and its components requires solution of a multicriterial problem, where the level of importance of each criterion contributing to determination of a global risk index is combined with fuzzified contributors to risk calculated at lower levels

Anomalous resilient to decoherence macroscopic quantum superpositions generated by universally covariant optimal quantum cloning

We show that the quantum states generated by universal optimal quantum cloning of a single photon represent an universal set of quantum superpositions resilient to decoherence. We adopt Bures distance as a tool to investigate the persistence ofquantum coherence of these quantum states. According to this analysis, the process of universal cloning realizes a class of quantum superpositions that exhibits a covariance property in lossy configuration over the complete set of polarization states in the Bloch sphere.Comment: 8 pages, 6 figure

Magnetic Control of Transmission and Helicity of Nano-Structured Optical Beams in Magnetoplasmonic Vortex Lenses

We theoretically investigate the generation of far-field propagating optical beams with a desired orbital angular momentum by using an archetypical magnetoplasmonic tip surrounded by a gold spiral slit. The use of a magnetic material can lead to important implications once magneto-optical activity is activated through the application of an external magnetic field. The physical model and the numerical study presented here introduce the concept of magnetically tunable plasmonic vortex lens, namely a magnetoplasmonic vortex lens, which ensures a tunable selectivity in the polarization state of the generated nanostructured beam. The presented system provides a promising platform for a localized excitation of plasmonic vortices followed by their beaming in the far-field with an active modulation of both light's transmittance and helicity

Time-dependent Nonlinear Optical Susceptibility of an Out-of-Equilibrium Soft Material

We investigate the time-dependent nonlinear optical absorption of a clay dispersion (Laponite) in organic dye (Rhodamine B) water solution displaying liquid-arrested state transition. Specifically, we determine the characteristic time $\tau_D$ of the nonlinear susceptibility build-up due as to the Soret effect. By comparing $\tau_D$ with the relaxation time provided by standard dynamic light scattering measurements we report on the decoupling of the two collective diffusion times at the two very different length scales during the aging of the out-of-equilibrium system. With this demonstration experiment we also show the potentiality of nonlinear optics measurements in the study of the late stage of arrest in soft materials

Why haven't loose globular clusters collapsed yet?

We report on the discovery of a surprising observed correlation between the slope of the low-mass stellar global mass function (GMF) of globular clusters (GCs) and their central concentration parameter c=log(r_t/r_c), i.e. the logarithmic ratio of tidal and core radii. This result is based on the analysis of a sample of twenty Galactic GCs with solid GMF measurements from deep HST or VLT data. All the high-concentration clusters in the sample have a steep GMF, most likely reflecting their initial mass function. Conversely, low-concentration clusters tend to have a flatter GMF implying that they have lost many stars via evaporation or tidal stripping. No GCs are found with a flat GMF and high central concentration. This finding appears counter-intuitive, since the same two-body relaxation mechanism that causes stars to evaporate and the cluster to eventually dissolve should also lead to higher central density and possibly core-collapse. Therefore, more concentrated clusters should have lost proportionately more stars and have a shallower GMF than low concentration clusters, contrary to what is observed. It is possible that severely depleted GCs have also undergone core collapse and have already recovered a normal radial density profile. It is, however, more likely that GCs with a flat GMF have a much denser and smaller core than suggested by their surface brightness profile and may well be undergoing collapse at present. In either case, we may have so far seriously underestimated the number of post core-collapse clusters and many may be lurking in the Milky Way.Comment: Four pages, one figure, accepted for publication in ApJ Letter