Bifurcations of the normal modes of the Ne?Br2 complex

We study the classical dynamics of the rare gas-dihalogen Ne?Br₂ complex in its ground electronic state. By considering the dihalogen bond frozen at its equilibrium distance, the system has two degrees of freedom and its potential energy surface presents linear and T-shape isomers. We find the nonlinear normal modes of both isomers that determine the phase space structure of the system. By means of surfaces of section and applying the numerical continuation of families of periodic orbits, we detect and identify the different bifurcations suffered by the normal modes as a function of the system energy. Finally, using the Orthogonal Fast Lyapunov Indicator (OFLI), we study the evolution of the fraction of the phase space volume occupied by regular motions.     

Phase-space Lagrangian dynamics of incompressible thermofluids

Phase-space Lagrangian dynamics in ideal fluids (i.e., continua) is usually related to the so-called ideal tracer particles. The latter, which can in principle be permitted to have arbitrary initial velocities, are understood as particles of infinitesimal size which do not produce significant perturbations of the fluid and do not interact among themselves. An unsolved theoretical problem is the correct definition of their dynamics in ideal fluids. The issue is relevant in order to exhibit the connection between fluid dynamics and the classical dynamical system, underlying a prescribed fluid system, which uniquely generates its time-evolution.The goal of this paper is to show that the tracer-particle dynamics can be exactly established for an arbitrary incompressible fluid uniquely based on the construction of an inverse kinetic theory (IKT) [M. Tessarotto, M. Ellero, Bull. Am. Phys. Soc. 45 (9) (2000) 40; M. Tessarotto, M. Ellero, AIP Conf. Proc. 762 (2005) 108. RGD24, Italy, July 10-16, 2004; M. Ellero, M. Tessarotto, Physica A 355 (2005) 233; M. Tessarotto, M. Ellero, Physica A 373 (2007) 142, arXiv: physics/0602140; M. Tessarotto, M. Ellero, in: M.S. Ivanov, A.K. Rebrov (Eds.), Proc. 25th RGD, International Symposium on Rarefied gas Dynamics, St. Petersburg, Russia, July 21-28, 2006, Novosibirsk Publ. House of the Siberian Branch of the Russian Academy of Sciences, 2007, p. 1001, arXiv:physics/0611113; M. Tessarotto, C. Cremaschini, Strong solutions of the incompressible Navier-Stokes equations in external domains: Local existence and uniqueness, arXiv:0809.5164v1 [math-ph], 2008]. As an example, the case of an incompressible Newtonian thermofluid is considered here.     

Field emission measured from nanostructured germanium and silicon thin films

We have prepared nanostructured thin films of germanium and silicon. The films were grown by an ion beam sputtering technique followed by a rapid annealing step using an electron beam annealer. The annealing temperature is a comparatively low 500 °C, resulting in well defined nano-islands on the film surface. Electron field emission has been measured from the surfaces under high vacuum. The threshold electric field value for significant current flow was measured as 2.5 V μm⁻¹ for a silicon thin film which is comparable to other silicon technologies. A value of 0.5 V μm⁻¹ for a germanium thin film represents an order of magnitude improvement for related germanium nanostructured systems.     

Discussion on Perturbation to Weak Noether Symmetry and Adiabatic Invariants for Lagrange Systems

We study a new symmetric perturbation, i.e. weakly Noether symmetric perturbation （WNSP）. The criterion and definition of WNSP and Noether symmetric perturbation （NSP） are given. A theorem between WNSP and adiabatic invariants is established. It is concluded that WNSP is different from NSP, the sufficient condition when WNSP is NSP can be presented, and the former is broader. We apply our results to the planar Kepler problem.     

Prediction and Refinement of High-Order Virial Coefficients for a Hard-Sphere System

The n^th virialcoefficient for a hard-sphere system is expressed as the sum of n^2 and a remainder. When n ≥ 3, the remainders of the viriaJs can be accurately expressed with Pade-type functions of n. The maximum deviations are only 0.039-0.053%, which are much better than the existing approaches. By using the predicted virials, the compressibility factors of the hard-sphere system can be predicted very accurately in the whole stable fluid region, and those in the metastable fluid region can also be well predicted up to a packing fraction of 0.545. The simulated B7 and Bl0 are found to be inconsistent with the other known virials, and thus they are refined to be 53.2467 and 105.042, respectively.     

Tunable optical limiting of gold nanorod thin films

Permalloy (Py) films were deposited on Si(111) or Corning 0211 glass substrates. There were two deposition temperatures: T _s=room temperature (RT) and T _s=270°C. The film thickness (t _f) ranges from 10 to 130 nm. The crystal structure properties of the films were studied by X-ray diffraction and transmission electron microscopy. Mechanical properties (including Young’s modulus E _f and hardness H _f) of each film were measured by the nanoindentation (NI) technique. E _f of the Py/Si(111) films was checked again by the laser induced surface acoustic wave (LA-SAW) technique. It was found that the NI technique is best suited for the measurements of E _f and H _f, but only when the sample belongs to the (soft film)/(soft substrate) system, such as the Py/glass film. For the (soft film)/(hard substrate) system, such as the Py/Si(111) film, the NI technique often provides higher values of E _f and H _f than expected. The anomalous phenomenon, associated with the NI technique may be related to the anisotropic crystal structures in the Py films on different kinds of substrates. From this study, we conclude that [E _f of Py/Si(111)]>[E _f of Py/glass] and [H _f of Py/Si(111)]>[H _f of Py/glass]. The good mechanical properties of the Py/Si(111) film make it a better candidate for recording head applications.     

Characterization, global analysis and integrability of a family of Poisson structures

An n-dimensional solution family of the Jacobi equations is characterized and investigated, including the global determination of its main features: the Casimir invariants, the construction of the Darboux canonical form and the proof of integrability for the related Poisson systems. Examples are given and include novel Poisson formulations.     

Lagrangian approach for analysis of radiation pressure induced parametric instability in micro-resonators

We introduce a new scheme for determining radiation pressure coupling to microresonator devices. It is shown that for the input pump powers there exists a threshold value for instability behavior. Radiation pressure can couple mechanical modes of a cavity to it's optical modes, leading to parametric oscillation instability. Here we present an approximate analysis of such nonlinear effect with Hamilton's least action principle. Our Lagrangian includes no interaction term, but interaction between optical and mechanical modes has been taken into account through integration limit.     

Numerical tests of a new molecule-dependent momentum transport equation

It is shown that a new incompressible fluid equation is obtained by inclusion of a new dimensionless coupling parameter in the momentum transport equation derived in [L. Jirkovsky, L. Bo-ot, Momentum transport equation for the fluids using projection-perturbation formalism and onset of turbulence, Physica A 352 (2005) 241-251] from the Boltzmann kinetic equation where the Boltzmann collision integral includes inelastic interactions of quantum origin among the particles of the fluid. Numerical results from the equation for the plane and circular Poiseuille flows are consistent with the observations. The numerical tests also manifest a difference in the onset of turbulence between the flat plates and the circular pipe flow systems. Although all obtained velocity profiles are flattened at the center-a feature of turbulence-the results demonstrate greater stability of the velocity profiles in the circular pipe flow.     

Classical probability waves

Probability waves in the configuration space are associated with coherent solutions of the classical Liouville or Fokker-Planck equations. Distributions localized in the momentum space provide action waves, described by the probability density and the generating function of the Hamilton-Jacobi theory. It is shown that by introducing a minimum distance in the coordinate space, the action distributions aquire the phase-space dispersion specific to the quantum objects. At finite temperature, probability density waves propagating with the sound velocity can arise as nonstationary solutions of the classical Fokker-Planck equation. The results suggest that in a system of quantum Brownian particles, a transition from complex to real probability waves could be observed.