Steady State Analysis and Heavy Traffic Limits for Regulated Markov Chains.

Consider a continuous time finite state irreducible Markov chain whose jump transitions are partitioned into one group that is regulated and the other group that is not. The regulated transitions are only allowed to occur if there is a token available. We collect the tokens in a buer and allow a regulated transition to occur simultaneously with the removal of a token from the buffer. New tokens are added to the buer at a constant Poisson rate but the regulated transitions will be blocked if they occur too quickly. We will apply matrix analysis to the joint distribution for the state of the Markov chain and the number of tokens in the buffer. We will give a simple stability condition for the joint process and show that its steady state distribution will have a matrix geometric distribution. Moreover, we obtain from our analysis a heavy traffic limit for this joint steady state distribution which has a product form structure. This Markov chain model and steady state analysis generalizes the work of many earlier papers on specific queueing systems such as Konheim and Reiser or Latouche and Neuts, but most significantly the work of Kogan and Puhalskii.Markov Chains, Matrix-Geometric Solution, Heavy-Traffic Limits, Product Form Solution, Tensor and Kronecker Products.

Increased Cycling Efficiency and Rate Capability of Copper-coated Silicon Anodes in Lithium-ion Batteries

Cycling efficiency and rate capability of porous copper-coated, amorphous silicon thin-film negative electrodes are compared to equivalent silicon thin-film electrodes in lithium-ion batteries. The presence of a copper layer coated on the active material plays a beneficial role in increasing the cycling efficiency and the rate capability of silicon thin-film electrodes. Between 3C and C/8 discharge rates, the available cell energy decreased by 8% and 18% for 40 nm copper-coated silicon and equivalent silicon thin-film electrodes, respectively. Copper-coated silicon thin-film electrodes also show higher cycling efficiency, resulting in lower capacity fade, than equivalent silicon thin-film electrodes. We believe that copper appears to act as a glue that binds the electrode together and prevents the electronic isolation of silicon particles, thereby decreasing capacity loss. Rate capability decreases significantly at higher copper-coating thicknesses as the silicon active-material is not accessed, suggesting that the thickness and porosity of the copper coating need to be optimized for enhanced capacity retention and rate capability in this system.Comment: 15 pages, 6 figure

Advanced turboprop vibratory characteristics

The assembly of SR5 advanced turboprop blades to develop a structural dynamic data base for swept props is reported. Steady state blade deformation under centrifugal loading and vibratory characteristics of the rotor assembly were measured. Vibration was induced through a system of piezoelectric crystals attached to the blades. Data reduction procedures are used to provide deformation, mode shape, and frequencies of the assembly at predetermined speeds

Observation of chaotic beats in a driven memristive Chua's circuit

In this paper, a time varying resistive circuit realising the action of an active three segment piecewise linear flux controlled memristor is proposed. Using this as the nonlinearity, a driven Chua's circuit is implemented. The phenomenon of chaotic beats in this circuit is observed for a suitable choice of parameters. The memristor acts as a chaotically time varying resistor (CTVR), switching between a less conductive OFF state and a more conductive ON state. This chaotic switching is governed by the dynamics of the driven Chua's circuit of which the memristor is an integral part. The occurrence of beats is essentially due to the interaction of the memristor aided self oscillations of the circuit and the external driving sinusoidal forcing. Upon slight tuning/detuning of the frequencies of the memristor switching and that of the external force, constructive and destructive interferences occur leading to revivals and collapses in amplitudes of the circuit variables, which we refer as chaotic beats. Numerical simulations and Multisim modelling as well as statistical analyses have been carried out to observe as well as to understand and verify the mechanism leading to chaotic beats.Comment: 30 pages, 16 figures; Submitted to IJB

Piezoelectric rotator for studying quantum effects in semiconductor nanostructures at high magnetic fields and low temperatures

We report the design and development of a piezoelectric sample rotation system, and its integration into an Oxford Instruments Kelvinox 100 dilution refrigerator, for orientation-dependent studies of quantum transport in semiconductor nanodevices at millikelvin temperatures in magnetic fields up to 10T. Our apparatus allows for continuous in situ rotation of a device through >100deg in two possible configurations. The first enables rotation of the field within the plane of the device, and the second allows the field to be rotated from in-plane to perpendicular to the device plane. An integrated angle sensor coupled with a closed-loop feedback system allows the device orientation to be known to within +/-0.03deg whilst maintaining the sample temperature below 100mK.Comment: 8 pages, 5 figure

Randomized Rounding for the Largest Simplex Problem

The maximum volume $j$-simplex problem asks to compute the $j$-dimensional simplex of maximum volume inside the convex hull of a given set of $n$ points in $\mathbb{Q}^d$. We give a deterministic approximation algorithm for this problem which achieves an approximation ratio of $e^{j/2 + o(j)}$. The problem is known to be $\mathrm{NP}$-hard to approximate within a factor of $c^{j}$ for some constant $c > 1$. Our algorithm also gives a factor $e^{j + o(j)}$ approximation for the problem of finding the principal $j\times j$ submatrix of a rank $d$ positive semidefinite matrix with the largest determinant. We achieve our approximation by rounding solutions to a generalization of the $D$-optimal design problem, or, equivalently, the dual of an appropriate smallest enclosing ellipsoid problem. Our arguments give a short and simple proof of a restricted invertibility principle for determinants