Towards a minimal order distributed observer for linear systems

In this paper we consider the distributed estimation problem for continuous-time linear time-invariant (LTI) systems. A single linear plant is observed by a network of local observers. Each local observer in the network has access to only part of the output of the observed system, but can also receive information on the state estimates of its neigbours. Each local observer should in this way generate an estimate of the plant state. In this paper we study the problem of existence of a reduced order distributed observer. We show that if the observed system is observable and the network graph is a strongly connected directed graph, then a distributed observer exists with state space dimension equal to $Nn - \sum_{i =1}^N p_i$, where $N$ is the number of network nodes, $n$ is the state space dimension of the observed plant, and $p_i$ is the rank of the output matrix of the observed output received by the $i$th local observer. In the case of a single observer, this result specializes to the well-known minimal order observer in classical observer design.Comment: 12 pages, 1 figur

Online Algorithms for Geographical Load Balancing

It has recently been proposed that Internet energy costs, both monetary and environmental, can be reduced by exploiting temporal variations and shifting processing to data centers located in regions where energy currently has low cost. Lightly loaded data centers can then turn off surplus servers. This paper studies online algorithms for determining the number of servers to leave on in each data center, and then uses these algorithms to study the environmental potential of geographical load balancing (GLB). A commonly suggested algorithm for this setting is “receding horizon control” (RHC), which computes the provisioning for the current time by optimizing over a window of predicted future loads. We show that RHC performs well in a homogeneous setting, in which all servers can serve all jobs equally well; however, we also prove that differences in propagation delays, servers, and electricity prices can cause RHC perform badly, So, we introduce variants of RHC that are guaranteed to perform as well in the face of such heterogeneity. These algorithms are then used to study the feasibility of powering a continent-wide set of data centers mostly by renewable sources, and to understand what portfolio of renewable energy is most effective

Universal quantized spin-Hall conductance fluctuation in graphene

We report a theoretical investigation of quantized spin-Hall conductance fluctuation of graphene devices in the diffusive regime. Two graphene models that exhibit quantized spin-Hall effect (QSHE) are analyzed. Model-I is with unitary symmetry under an external magnetic field $B\ne 0$ but with zero spin-orbit interaction, $t_{SO}=0$. Model-II is with symplectic symmetry where B=0 but $t_{SO} \ne 0$. Extensive numerical calculations indicate that the two models have exactly the same universal QSHE conductance fluctuation value $0.285 e/4\pi$ regardless of the symmetry. Qualitatively different from the conventional charge and spin universal conductance distributions, in the presence of edge states the spin-Hall conductance shows an one-sided log-normal distribution rather than a Gaussian distribution. Our results strongly suggest that the quantized spin-Hall conductance fluctuation belongs to a new universality class

Enhanced temperature uniformity by tetrahedral laser heating

emperature profile on a spherical sample that is heated by laser beams in various geometries while processed in vacuum is analyzed. Sample heating by one or four laser beams was considered. An analytical expression was derived for directional sample heating cases. It suggests an enhanced temperature uniformity over the samples when heated with four diffuse laser beams arranged in a tetrahedral geometry. This was experimentally verified by heating a spherical stainless steel sample by laser beams. Both the calculated and experimentally determined temperature variations over the sample suggest that use of diffuse four beams arranged in tetrahedral geometry would be effective in reducing temperature variation to within 1 K. The enhancement in the temperature uniformity for four diffuse beams arranged in a tetrahedral geometry by a factor of 50 over a single focused beam is promising to accurately measure of thermophysical properties. This drastic improvement in temperature uniformity might even enable atomic diffusion measurements in the undercooled liquid states of the bulk glass forming alloys since Marangoni and gravity driven convection will be substantially reduced

Quantum Anomalous Hall Effect in Graphene Proximity Coupled to an Antiferromagnetic Insulator

We propose realizing the quantum anomalous Hall effect by proximity coupling graphene to an antiferromagnetic insulator that provides both broken time-reversal symmetry and spin-orbit coupling. We illustrate our idea by performing ab initio calculations for graphene adsorbed on the (111) surface of BiFeO3. In this case, we find that the proximity-induced exchange field in graphene is about 70 meV, and that a topologically nontrivial band gap is opened by Rashba spin-orbit coupling. The size of the gap depends on the separation between the graphene and the thin film substrate, which can be tuned experimentally by applying external pressure.Comment: 5pages, 5 figure

A variant transfer matrix method suitable for transport through multi-probe systems

We have developed a variant transfer matrix method that is suitable for transport through multi-probe systems. Using this method, we have numerically studied the quantum spin Hall effect (QSHE) on 2D graphene with both intrinsic (Vso) and Rashba (Vr) spin-orbit (SO) couplings. The integer QSHE arises in the presence of intrinsic SO interaction and is gradually destroyed by the Rashba SO interaction and disorder fluctuation. We have numerically determined the phase boundaries separating integer QSHE and spin Hall liquid. We have found that when Vso> 0.2t with t the hopping constant the energy gap needed for the integer QSHE is the largest satisfying |E|<t. For smaller Vso the energy gap decreases linearly. In the presence of Rashba SO interaction or disorders, the energy gap diminishes. With Rashba SO interaction the integer QSHE is robust at the largest energy within the energy gap while at the smallest energy within the energy gap the integer QSHE is insensitive to the disorder