Optimal mapping of joint faults into healthy joint velocity space for fault-tolerant redundant manipulators

redundant manipulator

Managing sustainable rural water supply in EthiopiaLength: pp.103-112

Water supplyModelsEnergyAppropriate technology

Packing odd TT-joins with at most two terminals

Take a graph $G$, an edge subset $\Sigma\subseteq E(G)$, and a set of terminals $T\subseteq V(G)$ where $|T|$ is even. The triple $(G,\Sigma,T)$ is called a signed graft. A $T$-join is odd if it contains an odd number of edges from $\Sigma$. Let $\nu$ be the maximum number of edge-disjoint odd $T$-joins. A signature is a set of the form $\Sigma\triangle \delta(U)$ where $U\subseteq V(G)$ and $|U\cap T)$ is even. Let $\tau$ be the minimum cardinality a $T$-cut or a signature can achieve. Then $\nu\leq \tau$ and we say that $(G,\Sigma,T)$ packs if equality holds here. We prove that $(G,\Sigma,T)$ packs if the signed graft is Eulerian and it excludes two special non-packing minors. Our result confirms the Cycling Conjecture for the class of clutters of odd $T$-joins with at most two terminals. Corollaries of this result include, the characterizations of weakly and evenly bipartite graphs, packing two-commodity paths, packing $T$-joins with at most four terminals, and a new result on covering edges with cuts.Comment: extended abstract appeared in IPCO 2014 (under the different title "the cycling property for the clutter of odd st-walks"

Improving the optomechanical entanglement and cooling by photothermal force

Cooling and Entanglement in optomechanical systems coupled through radiation pressure and photothermal force is studied. To develop the photothermal model, we derive an expression for deformation constant of the force. Exploiting linearized quantum Langevin equations we investigate dynamics of such systems. According to our analysis, in addition to separate action of radiation pressure and photothermal force, their cross correlation effect plays an important role in dynamics of the system. We also achieve an exact relation for the phonon number of the mechanical resonator in such systems, and then we derive an analytical expression for it at weak coupling limit. At strong coupling regime, we show that utilizing the photothermal pressure makes the ground state cooling more approachable. The effect of photothermal force on the optomechanical entanglement is investigated in detail. According to our exact numerical and approximate analytical studies, even though the photothermal force is naturally a dissipative force, it can improve the optomechanical entanglement both quantitatively and qualitatively.Comment: 13 pages, 5 figure

Entangling the motion of two optically trapped objects via time-modulated driving fields

We study entanglement of the motional degrees of freedom of two tethered and optically trapped microdisks inside a single cavity. By properly choosing the position of the trapped objects in the optical cavity and driving proper modes of the cavity it is possible to equip the system with linear and quadratic optomechanical couplings. We show that a parametric coupling between the fundamental vibrational modes of two tethered mircodiscs can be generated via a time modulated input laser. For a proper choice of the modulation frequency, this mechanism can drive the motion of the microdisks into an inseparable state in the long time limit via a two-mode squeezing process. We numerically confirm the performance of our scheme for current technology and briefly discuss an experimental setup which can be employed for detecting this entanglement by employing the quadratic coupling. We also comment on the perspectives for generating such entanglement between the oscillations of optically levitated nanospheres.Comment: 9 pages, 3 figure