Motion of a classical charged particle

The Lorentz-Dirac equation is not an unavoidable consequence of solely linear and angular momenta conservation for a point charge. It also requires an additional assumption concerning the elementary character of the charge. We here use a less restrictive elementarity assumption for a spinless charge and derive a system of conservation equations that are not properly the equation of motion because, as it contains an extra scalar variable, the future evolution of the charge is not determined. We show that a supplementary constitutive relation can be added so that the motion is determined and free from the troubles that are customary in the Lorentz-Dirac equation, i.e., preacceleration and runaways.

Estimating the motion of an underwater robot from a monocular image sequence

When underwater vehicles perform navigation close to the ocean floor, computer vision techniques can be applied to obtain quite accurate motion estimates. The most crucial step in the vision-based estimation of the vehicle motion consists on detecting matchings between image pairs. Here we propose the extensive use of texture analysis as a tool to ameliorate the correspondence problem in underwater images. Once a robust set of correspondences has been found, the three-dimensional motion of the vehicle can be computed with respect to the bed of the sea. Finally, motion estimates allow the construction of a map that could aid to the navigation of the robot

Brownian motion of spiral waves driven by spatiotemporal structured noise

Spiral chemical waves subjected to a spatiotemporal random excitability are experimentally and numerically investigated in relation to the light-sensitive Belousov-Zhabotinsky reaction. Brownian motion is identified and characterized by an effective diffusion coefficient which shows a rather complex dependence on the time and length scales of the noise relative to those of the spiral. A kinematically based model is proposed whose results are in good qualitative agreement with experiments and numerics.

Plasma-enhanced chemical vapor deposition of boron nitride thin films from B2H6-H2-NH3 and B2H6-N2 gas mixtures

Highly transparent and stoichiometric boron nitride (BN) films were deposited on both electrodes (anode and cathode) of a radio-frequency parallel-plate plasma reactor by the glow discharge decomposition of two gas mixtures: B2H6-H2-NH3 and B2H6-N2. The chemical, optical, and structural properties of the films, as well as their stability under long exposition to humid atmosphere, were analyzed by x-ray photoelectron, infrared, and Raman spectroscopies; scanning and transmission electron microscopies; and optical transmittance spectrophotometry. It was found that the BN films grown on the anode using the B2H6-H2-NH3 mixture were smooth, dense, adhered well to substrates, and had a textured hexagonal structure with the basal planes perpendicular to the film surface. These films were chemically stable to moisture, even after an exposition period of two years. In contrast, the films grown on the anode from the B2H6-N2 mixture showed tensile stress failure and were very unstable in the presence of moisture. However, the films grown on the cathode from B2H6-H2-NH3 gases suffered from compressive stress failure on exposure to air; whereas with B2H6-N2 gases, adherent and stable cathodic BN films were obtained with the same crystallographic texture as anodic films prepared from the B2H6-H2-NH3 mixture. These results are discussed in terms of the origin of film stress, the effects of ion bombardment on the growing films, and the surface chemical effects of hydrogen atoms present in the gas discharge.

Holography, thermodynamics and fluctuations of charged AdS black holes

rg model with A3 potential. The holographically dual field theories provide the description of the microscopic degrees of freedom which underlie all of the thermodynamics, as can be seen by examining the form of the microscopic fluctuations.

Brownian motion of multidimensional systems in nonpotential velocity-dependent fields of force

We study the Brownian motion in velocity-dependent fields of force. Our main result is a Smoluchowski equation valid for moderate to high damping constants. We derive that equation by perturbative solution of the Langevin equation and using functional derivative techniques.

Noise-induced Brownian motion of spiral waves

We study the erratic displacement of spiral waves forced to move in a medium with random spatiotemporal excitability. Analytical work and numerical simulations are performed in relation to a kinematic scheme, assumed to describe the autowave dynamics for weakly excitable systems. Under such an approach, the Brownian character of this motion is proved and the corresponding dispersion coefficient is evaluated. This quantity shows a nontrivial dependence on the temporal and spatial correlation parameters of the external fluctuations. In particular, a resonantlike behavior is neatly evidenced in terms of the noise correlation time for the particular situation of spatially uniform fluctuations. Actually, this case turns out to be, to a large extent, exactly solvable, whereas a pair of dispersion mechanisms are discussed qualitatively and quantitatively to explain the results for the more general scenario of spatiotemporal disorder.

Reconfigurable Architecture To Estimate The Motion Of An Underwater Vehicle

This work proposes a parallel architecture for a motion estimation algorithm. It is well known that image processing requires a huge amount of computation, mainly at low level processing where the algorithms are dealing with a great numbers of data-pixel. One of the solutions to estimate motions involves detection of the correspondences between two images. Due to its regular processing scheme, parallel implementation of correspondence problem can be an adequate approach to reduce the computation time. This work introduces parallel and real-time implementation of such low-level tasks to be carried out from the moment that the current image is acquired by the camera until the pairs of point-matchings are detected

Cooperative motion of intrinsic and actuated semiflexible swimmers

We examine the phenomenon of hydrodynamic-induced cooperativity for pairs of flagellated micro-organism swimmers, of which spermatozoa cells are an example. We consider semiflexible swimmers, where inextensible filaments are driven by an internal intrinsic force and torque-free mechanism (intrinsic swimmers). The velocity gain for swimming cooperatively, which depends on both the geometry and the driving, develops as a result of the near-field coupling of bending and hydrodynamic stresses. We identify the regimes where hydrodynamic cooperativity is advantageous and quantify the change in efficiency. When the filaments' axes are parallel, hydrodynamic interaction induces a directional instability that causes semiflexible swimmers that profit from swimming together to move apart from each other. Biologically, this implies that flagella need to select different synchronized collective states and to compensate for directional instabilities (e.g., by binding) in order to profit from swimming together. By analyzing the cooperative motion of pairs of externally actuated filaments, we assess the impact that stress distribution along the filaments has on their collective displacements.

On the many-time formulation of classical particle dynamics

Starting from the standard one-time dynamics of n nonrelativistic particles, the n-time equations of motion are inferred, and a variational principle is formulated. A suitable generalization of the classical LieKnig theorem is demonstrated, which allows the determination of all the associated presymplectic structures. The conditions under which the action of an invariance group is canonical are studied, and a corresponding Noether theorem is deduced. A formulation of the theory in terms of n first-class constraints is recovered by means of coisotropic imbeddings. The proposed approach also provides for a better understanding of the relativistic particle dynamics, since it shows that the different roles of the physical positions and the canonical variables is not peculiar to special relativity, but rather to any n-time approach: indeed a nonrelativistic no-interaction theorem is deduced.

Charged-particle interaction with liquids: Ripplon excitations

We calculate the ripplon field contribution to the self-energy of an electron exterior to a liquid for planar and spherical geometries. We compare the full dielectric calculation of the electron-liquid interaction with the simpler alternative method consisting of integrating the electron-atom static-induced-dipolar potential through the whole liquid volume. We obtain good agreement between both methods for a nonpolar liquid such as 4He but differences up to 40% for a polar liquid such as water. We study the conditions under which the ripplon contribution to the self-energy is a perturbation. For an electron moving parallel to a planar liquid surface, we calculate the ripplon contribution to its stopping power. For this dynamical case, we conclude that the alternative method is a good approximation even for polar liquids.

Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.

Algebraic decay of velocity fluctuations near a wall

Computer simulations of the dynamics of a colloidal particle suspended in a fluid confined by an interface show that the asymptotic decay of the velocity correlation functions is algebraic. The exponents of the long-time tails depend on the direction of motion of the particle relative to the surface, as well as on the specific nature of the boundary conditions. In particular, we find that for the angular velocity correlation function, the decay in the presence of a slip surface is faster than the one corresponding to a stick one. An intuitive picture is introduced to explain the various long-time tails, and the simulations are compared with theoretical expressions where available.

Rate of convergence of a particle method to the solution of the Mc Kean-Vlasov's equation

This paper studies the rate of convergence of an appropriatediscretization scheme of the solution of the Mc Kean-Vlasovequation introduced by Bossy and Talay. More specifically,we consider approximations of the distribution and of thedensity of the solution of the stochastic differentialequation associated to the Mc Kean - Vlasov equation. Thescheme adopted here is a mixed one: Euler/weakly interactingparticle system. If $n$ is the number of weakly interactingparticles and $h$ is the uniform step in the timediscretization, we prove that the rate of convergence of thedistribution functions of the approximating sequence in the $L^1(\Omega\times \Bbb R)$ norm and in the sup norm is of theorder of $\frac 1{\sqrt n} + h $, while for the densities is ofthe order $ h +\frac 1 {\sqrt {nh}}$. This result is obtainedby carefully employing techniques of Malliavin Calculus.