Jerk Influence Coefficients,via Screw Theory,of Closed Chains

In this paper a novel method for determining the kinematic influence coefficients up to the jerk analysis of closed chains with multiple degrees of freedom by means of screw theory, also known as motor algebra, is introduced. A closed chain is obtained by rigidly attaching the end-effector of a serial chain to the base link. This condition ensures that the velocity, acceleration, and jerk, both angular and of any point fixed to the end-effector are zero. Afterwards, a comparison between the kinematic equations of motion, up to the jerk analysis, obtained by traditional methods with those obtained by means of screw theory reveals the corresponding influence coefficients associated to the generalized coordinates employed to represent the motion of the closed chain. Finally, a numerical example is provided. Sommario. In questo lavoro viene proposto un nuovo metodo per la determinazione dei coefficienti che consentono di sviluppare l'analisi cinematica (jerk incluso) di catene chiuse a molti gradi di liberta' per mezzo della screw theory o algebra dei moti spaziali. La catena chiusa e' ottenuta attaccando rigidamente l'end-effector di una catena seriale al membro di base. Questa condizione assicura che velocita' accelerazione e jerk, sia nel moto angolare che per ciascun punto solidale con l'end-effector siano nulli. Un confronto tra le equazioni cinematiche del moto, inclusa l'analisi del jerk, ottenute con metodi tradizionali e quelle ottenute dalla screw theory, mostra i corrispondenti coefficienti di influenza associati alle coordinate generalizzate impiegate per descrivere il moto della catena chiusa. Un esempio numerico conclude il lavoro.     

Rate of Convergence in Homogenization of Parabolic PDEs

We consider the solutions to /tu ⁽ⁿ⁾=a ⁽ⁿ⁾(x)u ⁽ⁿ⁾ where {a ⁽ⁿ⁾(x)} _n=1,2,... are random fields satisfying a well-mixing condition (which is different to the usual strong mixing condition). In this paper we estimate the rate of convergence of u ⁽ⁿ⁾ to the solution of a heat equation. Since our equation is of simple form, we get quite strong result which covers the previous homogenization results obtained on this equation.     

Electrodynamics of the vortex lattice in untwinned YBaCuO by complex impedance measurements

We report complex impedance measurements in an untwinned YBaCuO crystal. Our broad frequency range covers both the quasi static response and the resistive response of the vortex lattice. It allow us to characterize the irreversibility line without the need of any frequency dependent pinning parameters. We confirm the validity of the two modes model of vortex dynamic, and extract both the surface critical current and the flux flow resistivity around the first order transition T_m. This latter is identified by the abrupt loss of pinning and by an unexpected step of (T) at T_m. Received 22 November 2002 / Received in final form 17 February 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: alain.pautrat@ismra.fr RID="b" ID="b"UMR 6508 associée au CNRS     

Phase transformations in highly excited clusters

In this communication we analyze the behavior of excited drops that undergo fragmentation. We focus our attention on two scenarios: in the first one the system is free to expand, while in the second one it is confined inside a spherical volume. It is shown that the caloric curve of free expanding systems does not display a vapor branch. In the case of constrained ones, they behave as undergoing a first order phase transition at low densities while as a second order one at high densities. The transition from liquid-like to vapor-like behavior is signaled both by the caloric curves and thermal response functions.     

Cooling efficiency in collisions between Pd and He,Ne, Ar and Kr

The cooling of the metal cluster Pd₁₃ in an atmosphere of rare gas has been studied by means of computer simulation. By simulation, the average energy transfer in collisions between one cluster and one gas atom has been obtained. Emphasis has been placed on conditions when the temperatures of the colliding species are almost equal. All modes of motion, inclusive the translation, must be considered in order to obtain vanishing energy transfer at equilibrium. A simulation scheme is presented by which the energy transfer is zero to the cluster when the gas and the cluster temperatures are equal. At equilibrium the energy transfer does however not vanish for all impact parameters. In the collisions with Pd₁₃, the cluster is heated by collisions with a small impact parameter but equally cooled by collisions with a large impact parameter. Argon and krypton are found to cool Pd₁₃ equally efficiently while neon and helium are less efficient cooling agents. Received 28 September 2001 / Received in final form 8 August 2002 Published online 12 November 2002 RID="a" ID="a"e-mail: JanW@phc.gu.se     

Non-adiabatic transitions at a continuum edge

We consider interaction of a single level with a broad, tending to semi-infinite continuum. In an example of two exactly solvable problems, we show that for time dependent quantum systems the probability of the irreversible transition from a discrete level to a continuum is strongly inhibited or even completely suppressed by the presence of a discrete adiabatic level near the continuum edge. Received 10 October 2002 Published online 4 March 2003 RID="a" ID="a"e-mail: Alain.Sarfati@lac.u-psud.fr     

Experimental determination of spin-rotation and spin-spin magnetic interactions in by nuclear spin conversion

When a gas sample of ¹³CH₃F is prepared with a population of isomers (ortho and para forms) far from the equilibrium given by nuclear spin statistics, it relaxes towards this equilibrium with an exponential decay rate. This phenomenon called nuclear spin conversion is mainly governed by intramolecular spin-spin and spin-rotation interactions. In the quantum relaxation model [P.L. Chapovsky, Phys. Rev. A 43, 3624 (1991)], two pairs of ortho-para levels (J = 9, K = 3; J' = 11, K' = 1) and (J = 20, K = 3; J' = 21, K' = 1) are principally responsible for the conversion. The levels of the second pair are coupled by both spin-spin and spin-rotation interactions. The application of an electric field (up to 10 kV/cm) induces a crossing of the Stark components of this pair, which is observed for the first time. A specific experimental set-up based on an electric field of alternating triangular shape is used, which allows the determination of the strength of both interactions via the measurement of the spin conversion decay rates. This work yields the first experimental value for the electronic contribution to the spin-rotation interaction in ¹³CH₃F. Received 23 May 2002 / Received in final form 18 September 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: Patrice.Cacciani@univ-lille1.fr     

Analysis of Queueing Systems with Synchronous Single Vacation for Some Servers

We study a multi-server M/M/c type queue with a single vacation policy for some idle servers. In this queueing system, if at a service completion instant, any d (d c) servers become idle, these d servers will take one and only one vacation together. During the vacation of d servers, the other c–d servers do not take vacation even if they are idle. Using a quasi-birth-and-death process and the matrix analytic method, we obtain the stationary distribution of the system. Conditional stochastic decomposition properties have been established for the waiting time and the queue length given that all servers are busy.     

Borel stay-in-a-set games

Consider an n-person stochastic game with Borel state space S, compact metric action sets A ₁,A ₂,,A _n , and law of motion q such that the integral under q of every bounded Borel measurable function depends measurably on the initial state x and continuously on the actions (a ₁,a ₂,,a _n ) of the players. If the payoff to each player i is 1 or 0 according to whether or not the stochastic process of states stays forever in a given Borel set G _i , then there is an -equilibrium for every >0. AMS (1991) subject classification: 60G40, 91A60, 60E15, 46A55.