Anchored burning bijections on finite and infinite graphs

Let $G$ be an infinite graph such that each tree in the wired uniform spanning forest on $G$ has one end almost surely. On such graphs $G$, we give a family of continuous, measure preserving, almost one-to-one mappings from the wired spanning forest on $G$ to recurrent sandpiles on $G$, that we call anchored burning bijections. In the special case of $\mathbb{Z}^d$, $d \ge 2$, we show how the anchored bijection, combined with Wilson's stacks of arrows construction, as well as other known results on spanning trees, yields a power law upper bound on the rate of convergence to the sandpile measure along any exhaustion of $\mathbb{Z}^d$. We discuss some open problems related to these findings.Comment: 26 pages; 1 EPS figure. Minor alterations made after comments from refere

Logarithmic current fluctuations in non-equilibrium quantum spin chains

We study zero-temperature quantum spin chains which are characterized by a non-vanishing current. For the XX model starting from the initial state |... + + + - - - ...> we derive an exact expression for the variance of the total spin current. We show that asymptotically the variance exhibits an anomalously slow logarithmic growth; we also extract the sub-leading constant term. We then argue that the logarithmic growth remains valid for the XXZ model in the critical region.Comment: 9 pages, 4 figures, minor alteration

TCP over High Speed Variable Capacity Links: A Simulation Study for Bandwidth Allocation

New optical network technologies provide opportunities for fast, controllable bandwidth management. These technologies can now explicitly provide resources to data paths, creating demand driven bandwidth reservation across networks where an applications bandwidth needs can be meet almost exactly. Dynamic synchronous Transfer Mode (DTM) is a gigabit network technology that provides channels with dynamically adjustable capacity. TCP is a reliable end-to-end transport protocol that adapts its rate to the available capacity. Both TCP and the DTM bandwidth can react to changes in the network load, creating a complex system with inter-dependent feedback mechanisms. The contribution of this work is an assessment of a bandwidth allocation scheme for TCP flows on variable capacity technologies. We have created a simulation environment using ns-2 and our results indicate that the allocation of bandwidth maximises TCP throughput for most flows, thus saving valuable capacity when compared to a scheme such as link over-provisioning. We highlight one situation where the allocation scheme might have some deficiencies against the static reservation of resources, and describe its causes. This type of situation warrants further investigation to understand how the algorithm can be modified to achieve performance similar to that of the fixed bandwidth case

Testing the Elliott-Yafet spin-relaxation mechanism in KC8; a model system of biased graphene

Temperature dependent electron spin resonance (ESR) measurements are reported on stage 1 potassium doped graphite, a model system of biased graphene. The ESR linewidth is nearly isotropic and although the g-factor has a sizeable anisotropy, its majority is shown to arise due to macroscopic magnetization. Albeit the homogeneous ESR linewidth shows an unusual, non-linear temperature dependence, it appears to be proportional to the resistivity which is a quadratic function of the temperature. These observations suggests the validity of the Elliott-Yafet relaxation mechanism in KC8 and allows to place KC8 on the empirical Beuneu-Monod plot among ordinary elemental metals.Comment: 6 pages, 4 figures, submitted to Phys. Rev.