870 micron continuum observations of the bubble-shaped nebula Gum 31

We are presenting here a study of the cold dust in the infrared ring nebula Gum 31. We aim at deriving the physical properties of the molecular gas and dust associated with the nebula, and investigating its correlation with the star formation in the region, that was probably triggered by the expansion of the ionization front. We use 870 micron data obtained with LABOCA to map the dust emission. The obtained LABOCA image was compared to archival IR,radio continuum, and optical images. The 870 micron emission follows the 8 micron (Spitzer), 250 micron, and 500 micron (Herschel) emission distributions showing the classical morphology of a spherical shell. We use the 870 micron and 250 micron images to identify 60 dust clumps in the collected layers of molecular gas using the Gaussclumps algorithm. The clumps have effective deconvolved radii between 0.16 pc and 1.35 pc, masses between 70 Mo and 2800 Mo, and volume densities between 1.1x10^3 cm^-3 and 2.04x10^5 cm^-3. The total mass of the clumps is 37600 Mo. The dust temperature of the clumps is in the range from 21 K to 32 K, while inside the HII region reaches ~ 40 K. The clump mass distribution is well-fitted by a power law dN/dlog(M/Mo) proportional to M^(-alpha), with alpha=0.93+/-0.28. The slope differs from those obtained for the stellar IMF in the solar neighborhood, suggesting that the clumps are not direct progenitors of single stars/protostars. The mass-radius relationship for the 41 clumps detected in the 870 microns emission shows that only 37% of them lie in or above the high-mass star formation threshold, most of them having candidate YSOs projected inside. A comparison of the dynamical age of the HII region with the fragmentation time, allowed us to conclude that the collect and collapse mechanism may be important for the star formation at the edge of Gum 31, although other processes may also be acting.Comment: 15 pages, 10 figures. Accepted for publication in A&

Linear theory and violent relaxation in long-range systems: a test case

In this article, several aspects of the dynamics of a toy model for longrange Hamiltonian systems are tackled focusing on linearly unstable unmagnetized (i.e. force-free) cold equilibria states of the Hamiltonian Mean Field (HMF). For special cases, exact finite-N linear growth rates have been exhibited, including, in some spatially inhomogeneous case, finite-N corrections. A random matrix approach is then proposed to estimate the finite-N growth rate for some random initial states. Within the continuous, $N \rightarrow \infty$, approach, the growth rates are finally derived without restricting to spatially homogeneous cases. All the numerical simulations show a very good agreement with the different theoretical predictions. Then, these linear results are used to discuss the large-time nonlinear evolution. A simple criterion is proposed to measure the ability of the system to undergo a violent relaxation that transports it in the vicinity of the equilibrium state within some linear e-folding times

Characterization of the initial filamentation of a relativistic electron beam passing through a plasma

The linear instability that induces a relativistic electron beam passing through a return plasma current to filament transversely is often related to some filamentation mode with wave vector normal to the beam or confused with Weibel modes. We show that these modes may not be relevant in this matter and identify the most unstable mode on the two-stream/filamentation branch as the main trigger for filamentation. This sets both the characteristic transverse and longitudinal filamentation scales in the non-resistive initial stage.Comment: 4 page, 3 figures, to appear in PR

Phase transition in the collisionless regime for wave-particle interaction

Gibbs statistical mechanics is derived for the Hamiltonian system coupling self-consistently a wave to N particles. This identifies Landau damping with a regime where a second order phase transition occurs. For nonequilibrium initial data with warm particles, a critical initial wave intensity is found: above it, thermodynamics predicts a finite wave amplitude in the limit of infinite N; below it, the equilibrium amplitude vanishes. Simulations support these predictions providing new insight on the long-time nonlinear fate of the wave due to Landau damping in plasmas.Comment: 12 pages (RevTeX), 2 figures (PostScript

Scaling laws for the largest Lyapunov exponent in long-range systems: A random matrix approach

We investigate the laws that rule the behavior of the largest Lyapunov exponent (LLE) in many particle systems with long range interactions. We consider as a representative system the so-called Hamiltonian alpha-XY model where the adjustable parameter alpha controls the range of the interactions of N ferromagnetic spins in a lattice of dimension d. In previous work the dependence of the LLE with the system size N, for sufficiently high energies, was established through numerical simulations. In the thermodynamic limit, the LLE becomes constant for alpha greater than d whereas it decays as an inverse power law of N for alpha smaller than d. A recent theoretical calculation based on Pettini's geometrization of the dynamics is consistent with these numerical results (M.-C. Firpo and S. Ruffo, cond-mat/0108158). Here we show that the scaling behavior can also be explained by a random matrix approach, in which the tangent mappings that define the Lyapunov exponents are modeled by random simplectic matrices drawn from a suitable ensemble.Comment: 5 pages, no figure

Topological aspects of geometrical signatures of phase transitions

Certain geometric properties of submanifolds of configuration space are numerically investigated for classical lattice phi^4 models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the two-dimensional case, when a phase transition is present. The observed phenomenology strongly supports, though in an indirect way, a recently proposed topological conjecture about a topology change of the configuration space submanifolds as counterpart of a phase transition.Comment: REVTEX file, 4 pages, 5 figure

Increased flexibility in lab-on-chip design with a polymer patchwork approach

Nanofluidic structures are often the key element of many lab-on-chips for biomedical and environmental applications. The demand for these devices to be able to perform increasingly complex tasks triggers a request for increasing the performance of the fabrication methods. Soft lithography and poly(dimethylsiloxane) (PDMS) have since long been the basic ingredients for producing low-cost, biocompatible and flexible devices, replicating nanostructured masters. However, when the desired functionalities require the fabrication of shallow channels, the \u201croof collapse\u201d phenomenon, that can occur when sealing the replica, can impair the device functionalities. In this study, we demonstrate that a \u201cfocused drop-casting\u201d of h-PDMS (hard PDMS) on nanostructured regions, provides the necessary stiffness to avoid roof collapse, without increasing the probability of deep cracks formation, a drawback that shows up in the peel-off step, when h-PDMS is used all over the device area. With this new approach, we efficiently fabricate working devices with reproducible sub-100 nm structures. We verify the absence of roof collapse and deep cracks by optical microscopy and, in order to assess the advantages that are introduced by the proposed technique, the acquired images are compared with those of cracked devices, whose top layer, of h-PDMS, and with those of collapsed devices, made of standard PDMS. The geometry of the critical regions is studied by atomic force microscopy of their resin casts. The electrical resistance of the nanochannels is measured and shown to be compatible with the estimates that can be obtained from the geometry. The simplicity of the method and its reliability make it suitable for increasing the fabrication yield and reducing the costs of nanofluidic polymeric lab-on-chips

Topological origin of the phase transition in a mean-field model

We argue that the phase transition in the mean-field XY model is related to a particular change in the topology of its configuration space. The nature of this topological transition can be discussed on the basis of elementary Morse theory using the potential energy per particle V as a Morse function. The value of V where such a topological transition occurs equals the thermodynamic value of V at the phase transition and the number of (Morse) critical points grows very fast with the number of particles N. Furthermore, as in statistical mechanics, also in topology the way the thermodynamic limit is taken is crucial.Comment: REVTeX, 5 pages, with 1 eps figure included. Some changes in the text. To appear in Physical Review Letter

Nanofabrication strategies for influencing biomolecule behavior

In recent years, nanofabrication techniques have shown themselves to have the most promising potential for innovative research on crucial biomolecules for life sciences, such as DNA and RNA. Two main examples are: Firstly, large-scale nanostructuring, effective for engineering innovative biosensors; and secondly, nanopores, intensively exploited for developing fast and inexpensive technologies for DNA sequencing, a major research challenge in the field of biomedicine. In addition to nanopores, nanoslits and nanochannels allow interesting functionalities for the study, processing and sorting of DNA. For example, when a long DNA chain is forced to enter a nanochannel, it stretches, thus acquiring a conformation which allows its genetic information to be optically read. Herein, we have focused on various geometry-based strategies, involving short and long channels, as well as funnels and a series of pit nanostructures, integrated into polymeric lab-on-a-chip models. We have implemented these miniaturized systems in order to study, at single molecule level, the typical conformations of DNA chains in various nano-confinement conditions whilst also observing the dynamic behavior of the long strands in crossing structures with different cross sections. In fact, by taking advantage of polydimethylsiloxane's elasticity, we have developed a strategy for modulating the translocation dynamics of single molecules crossing a nanochannel. Lastly, we have investigated on important applications for life and material sciences of the recent innovative tool which counts and recognizes nanoparticles through a new simultaneous optical and electrical sensing method

Emergence of a non trivial fluctuating phase in the XY model on regular networks

We study an XY-rotor model on regular one dimensional lattices by varying the number of neighbours. The parameter $2\ge\gamma\ge1$ is defined. $\gamma=2$ corresponds to mean field and $\gamma=1$ to nearest neighbours coupling. We find that for $\gamma<1.5$ the system does not exhibit a phase transition, while for $\gamma > 1.5$ the mean field second order transition is recovered. For the critical value $\gamma=\gamma_c=1.5$, the systems can be in a non trivial fluctuating phase for whichthe magnetisation shows important fluctuations in a given temperature range, implying an infinite susceptibility. For all values of $\gamma$ the magnetisation is computed analytically in the low temperatures range and the magnetised versus non-magnetised state which depends on the value of $\gamma$ is recovered, confirming the critical value $\gamma_{c}=1.5$