Status Updates Over Unreliable Multiaccess Channels

Applications like environmental sensing, and health and activity sensing, are supported by networks of devices (nodes) that send periodic packet transmissions over the wireless channel to a sink node. We look at simple abstractions that capture the following commonalities of such networks (a) the nodes send periodically sensed information that is temporal and must be delivered in a timely manner, (b) they share a multiple access channel and (c) channels between the nodes and the sink are unreliable (packets may be received in error) and differ in quality. We consider scheduled access and slotted ALOHA-like random access. Under scheduled access, nodes take turns and get feedback on whether a transmitted packet was received successfully by the sink. During its turn, a node may transmit more than once to counter channel uncertainty. For slotted ALOHA-like access, each node attempts transmission in every slot with a certain probability. For these access mechanisms we derive the age of information (AoI), which is a timeliness metric, and arrive at conditions that optimize AoI at the sink. We also analyze the case of symmetric updating, in which updates from different nodes must have the same AoI. We show that ALOHA-like access, while simple, leads to AoI that is worse by a factor of about 2e, in comparison to scheduled access

Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole

We derive an exact expression for the partition function of the Euclidean BTZ black hole. Using this, we show that for a black hole with large horizon area, the correction to the Bekenstein-Hawking entropy is $-3/2 log(Area)$, in agreement with that for the Schwarzschild black hole obtained in the canonical gravity formalism and also in a Lorentzian computation of BTZ black hole entropy. We find that the right expression for the logarithmic correction in the context of the BTZ black hole comes from the modular invariance associated with the toral boundary of the black hole.Comment: LaTeX, 10 pages, typos corrected, clarifications adde

Segregation by membrane rigidity in flowing binary suspensions of elastic capsules

Spatial segregation in the wall normal direction is investigated in suspensions containing a binary mixture of Neo-Hookean capsules subjected to pressure driven flow in a planar slit. The two components of the binary mixture have unequal membrane rigidities. The problem is studied numerically using an accelerated implementation of the boundary integral method. The effect of a variety of parameters was investigated, including the capillary number, rigidity ratio between the two species, volume fraction, confinement ratio, and the number fraction of the more floppy particle $X_f$ in the mixture. It was observed that in suspensions of pure species, the mean wall normal positions of the stiff and the floppy particles are comparable. In mixtures, however, the stiff particles were found to be increasingly displaced towards the walls with increasing $X_f$, while the floppy particles were found to increasingly accumulate near the centerline with decreasing $X_f$. The origins of this segregation is traced to the effect of the number fraction $X_f$ on the localization of the stiff and the floppy particles in the near wall region -- the probability of escape of a stiff particle from the near wall region to the interior is greatly reduced with increasing $X_f$, while the exact opposite trend is observed for a floppy particle with decreasing $X_f$. Simple model studies on heterogeneous pair collisions involving a stiff and a floppy particle mechanistically explain this observation. The key result in these studies is that the stiff particle experiences much larger cross-stream displacement in heterogeneous collisions than the floppy particle. A unified mechanism incorporating the wall-induced migration of deformable particles and the particle fluxes associated with heterogeneous and homogeneous pair collisions is presented.Comment: 19 Pages, 16 Figure

Spacetime Dependent Lagrangians and Weak-Strong Duality : Sine Gordon and Massive Thirring Models

The formalism of spacetime dependent lagrangians developed in Ref.1 is applied to the Sine Gordon and massive Thirring models.It is shown that the well-known equivalence of these models (in the context of weak-strong duality) can be understood in this approach from the same considerations as described in [1] for electromagnetic duality. A further new result is that all these can be naturally linked to the fact that the holographic principle has analogues at length scales much larger than quantum gravity. There is also the possibility of {\it noncommuting coodinates} residing on the boundaries. PACS: 11.15.-q: 11.10/EfComment: Latex, 16 pages, article shortened, references added, minor typos correcte

Mn(II), Fe(II), Co(II), Ni(II), Cu(II), Zn(II), Pd(II), Cd(II) & UO2(II) Chelates of Schiff Bases Derived from o-Aminobenzenesulphonic Acid & 2-Aminoethanesulphonic Acid & 2-Hydroxy-1-naphthaldehyde

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Black Hole Entropy from a Highly Excited Elementary String

Suggested correspondence between a black hole and a highly excited elementary string is explored. Black hole entropy is calculated by computing the density of states for an open excited string. We identify the square root of oscillator number of the excited string with Rindler energy of black hole to obtain an entropy formula which, not only agrees at the leading order with the Bekenstein-Hawking entropy, but also reproduces the logarithmic correction obtained for black hole entropy in the quantum geometry framework. This provides an additional supporting evidence for correspondence between black holes and strings.Comment: revtex, 4 page

First-Order Superfluid to Valence-Bond Solid Phase Transitions in Easy-Plane SU(\u3cem\u3eN\u3c/em\u3e) Magnets for Small \u3cem\u3eN\u3c/em\u3e

We consider the easy-plane limit of bipartite SU(N) Heisenberg Hamiltonians, which have a fundamental representation on one sublattice and the conjugate to fundamental on the other sublattice. For N = 2 the easy plane limit of the SU(2) Heisenberg model is the well-known quantum XY model of a lattice superfluid. We introduce a logical method to generalize the quantum XY model to arbitrary N, which keeps the Hamiltonian sign-free. We show that these quantum Hamiltonians have a world-line representation as the statistical mechanics of certain tightly packed loop models of N colors in which neighboring loops are disallowed from having the same color. In this loop representation we design an efficient Monte Carlo cluster algorithm for our model. We present extensive numerical results for these models on the two dimensional square lattice, where we find the nearest neighbor model has superfluid order for N ≤ 5 and valence-bond order for N \u3e 5. By introducing SU(N) easy-plane symmetric four-spin couplings we are able to tune across the superfluid-VBS phase boundary for all N ≤ 5. We present clear evidence that this quantum phase transition is first order for N = 2 and N = 5, suggesting that easy-plane deconfined criticality runs away generically to a first-order transition for small N