151 research outputs found

    Distributed Slicing in Dynamic Systems

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    Peer to peer (P2P) systems are moving from application specific architectures to a generic service oriented design philosophy. This raises interesting problems in connection with providing useful P2P middleware services capable of dealing with resource assignment and management in a large-scale, heterogeneous and unreliable environment. The slicing service, has been proposed to allow for an automatic partitioning of P2P networks into groups (slices) that represent a controllable amount of some resource and that are also relatively homogeneous with respect to that resource. In this paper we propose two gossip-based algorithms to solve the distributed slicing problem. The first algorithm speeds up an existing algorithm sorting a set of uniform random numbers. The second algorithm statistically approximates the rank of nodes in the ordering. The scalability, efficiency and resilience to dynamics of both algorithms rely on their gossip-based models. These algorithms are proved viable theoretically and experimentally

    A Superstabilizing log(n)\log(n)-Approximation Algorithm for Dynamic Steiner Trees

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    In this paper we design and prove correct a fully dynamic distributed algorithm for maintaining an approximate Steiner tree that connects via a minimum-weight spanning tree a subset of nodes of a network (referred as Steiner members or Steiner group) . Steiner trees are good candidates to efficiently implement communication primitives such as publish/subscribe or multicast, essential building blocks for the new emergent networks (e.g. P2P, sensor or adhoc networks). The cost of the solution returned by our algorithm is at most logS\log |S| times the cost of an optimal solution, where SS is the group of members. Our algorithm improves over existing solutions in several ways. First, it tolerates the dynamism of both the group members and the network. Next, our algorithm is self-stabilizing, that is, it copes with nodes memory corruption. Last but not least, our algorithm is \emph{superstabilizing}. That is, while converging to a correct configuration (i.e., a Steiner tree) after a modification of the network, it keeps offering the Steiner tree service during the stabilization time to all members that have not been affected by this modification

    Quenched crystal field disorder and magnetic liquid ground states in Tb2Sn2-xTixO7

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    Solid-solutions of the "soft" quantum spin ice pyrochlore magnets Tb2B2O7 with B=Ti and Sn display a novel magnetic ground state in the presence of strong B-site disorder, characterized by a low susceptibility and strong spin fluctuations to temperatures below 0.1 K. These materials have been studied using ac-susceptibility and muSR techniques to very low temperatures, and time-of-flight inelastic neutron scattering techniques to 1.5 K. Remarkably, neutron spectroscopy of the Tb3+ crystal field levels appropriate to at high B-site mixing (0.5 < x < 1.5 in Tb2Sn2-xTixO7) reveal that the doublet ground and first excited states present as continua in energy, while transitions to singlet excited states at higher energies simply interpolate between those of the end members of the solid solution. The resulting ground state suggests an extreme version of a random-anisotropy magnet, with many local moments and anisotropies, depending on the precise local configuration of the six B sites neighboring each magnetic Tb3+ ion.Comment: 6 pages, 6 figure

    Spin dynamics and disorder effects in the S=1/2 kagome Heisenberg spin liquid phase of kapellasite

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    We report 35^{35}Cl NMR, ESR, μ\muSR and specific heat measurements on the S=1/2S=1/2 frustrated kagom\'e magnet kapellasite, α\alpha-Cu3_3Zn(OH)6_6Cl2_2, where a gapless spin liquid phase is stabilized by a set of competing exchange interactions. Our measurements confirm the ferromagnetic character of the nearest-neighbour exchange interaction J1J_1 and give an energy scale for the competing interactions J10|J| \sim 10 K. The study of the temperature-dependent ESR lineshift reveals a moderate symmetric exchange anisotropy term DD, with D/J3|D/J|\sim 3%. These findings validate a posteriori the use of the J1J2JdJ_1 - J_2 - J_d Heisenberg model to describe the magnetic properties of kapellasite [Bernu et al., Phys. Rev. B 87, 155107 (2013)]. We further confirm that the main deviation from this model is the severe random depletion of the magnetic kagom\'e lattice by 27%, due to Cu/Zn site mixing, and specifically address the effect of this disorder by 35^{35}Cl NMR, performed on an oriented polycrystalline sample. Surprisingly, while being very sensitive to local structural deformations, our NMR measurements demonstrate that the system remains homogeneous with a unique spin susceptibility at high temperature, despite a variety of magnetic environments. Unconventional spin dynamics is further revealed by NMR and μ\muSR in the low-TT, correlated, spin liquid regime, where a broad distribution of spin-lattice relaxation times is observed. We ascribe this to the presence of local low-energy modes.Comment: 15 pages, 11 figures. To appear in Phys. Rev.

    Gapped and gapless short range ordered magnetic states with (12,12,12)(\frac{1}{2},\frac{1}{2},\frac{1}{2}) wavevectors in the pyrochlore magnet Tb2+x_{2+x}Ti2x_{2-x}O7+δ_{7+\delta}

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    Recent low temperature heat capacity (CP_P) measurements on polycrystalline samples of the pyrochlore antiferromagnet Tb2+x_{2+x}Ti2x_{2-x}O7+δ_{7+\delta} have shown a strong sensitivity to the precise Tb concentration xx, with a large anomaly exhibited for x0.005x \sim 0.005 at TC0.5T_C \sim 0.5 K and no such anomaly and corresponding phase transition for x0x \le 0. We have grown single crystal samples of Tb2+x_{2+x}Ti2x_{2-x}O7+δ_{7+\delta}, with approximate composition x=0.001,+0.0042x=-0.001, +0.0042, and +0.0147+0.0147, where the x=0.0042x=0.0042 single crystal exhibits a large CP_P anomaly at TCT_C=0.45 K, but neither the x=0.001x=-0.001 nor the x=+0.0147x=+0.0147 single crystals display any such anomaly. We present new time-of-flight neutron scattering measurements on the x=0.001x=-0.001 and the x=+0.0147x=+0.0147 samples which show strong (12,12,12)\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right) quasi-Bragg peaks at low temperatures characteristic of short range antiferromagnetic spin ice (AFSI) order at zero magnetic field but only under field-cooled conditions, as was previously observed in our x=0.0042x = 0.0042 single crystal. These results show that the strong (12,12,12)\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right) quasi-Bragg peaks and gapped AFSI state at low temperatures under field cooled conditions are robust features of Tb2_2Ti2_2O7_7, and are not correlated with the presence or absence of the CP_P anomaly and phase transition at low temperatures. Further, these results show that the ordered state giving rise to the CP_P anomaly is confined to 0x0.010 \leq x \leq 0.01 for Tb2+x_{2+x}Ti2x_{2-x}O7+δ_{7+\delta}, and is not obviously connected with conventional order of magnetic dipole degrees of freedom.Comment: 7 pages, 3 figure
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