Preliminary tests of an advanced high-temperature combustion system

A combustion system has been developed to operate efficiently and with good durability at inlet pressures to 4.05 MPa (40 atm), inlet air temperatures to 900 K, and exhaust gas temperatures to 2480 K. A preliminary investigation of this system was conducted at inlet pressures to 0.94 MPa (9 atm), a nominal inlet air temperature of 560 K, and exhaust gas temperatures to 2135 K. A maximum combustion efficiency of 98.5 percent was attained at a fuel-air ratio of 0.033; the combustion efficiency decreased to about 90 percent as the fuel-air ratio was increased to 0.058. An average liner metal temperature of 915 K, 355 kelvins greater than the nominal inlet air temperature, was reached with an average exhaust gas temperature of 2090 K. The maximum local metal temperature at this condition was about 565 kelvins above the nominal inlet air temperature and decreased to 505 kelvins above with increasing combustor pressure. Tests to determine the isothermal total pressure loss of the combustor showed a liner loss of 1.1 percent and a system loss of 6.5 percent

Infinite-cluster geometry in central-force networks

We show that the infinite percolating cluster (with density P_inf) of central-force networks is composed of: a fractal stress-bearing backbone (Pb) and; rigid but unstressed ``dangling ends'' which occupy a finite volume-fraction of the lattice (Pd). Near the rigidity threshold pc, there is then a first-order transition in P_inf = Pd + Pb, while Pb is second-order with exponent Beta'. A new mean field theory shows Beta'(mf)=1/2, while simulations of triangular lattices give Beta'_tr = 0.255 +/- 0.03.Comment: 6 pages, 4 figures, uses epsfig. Accepted for publication in Physical Review Letter

Floppy modes and the free energy: Rigidity and connectivity percolation on Bethe Lattices

We show that negative of the number of floppy modes behaves as a free energy for both connectivity and rigidity percolation, and we illustrate this result using Bethe lattices. The rigidity transition on Bethe lattices is found to be first order at a bond concentration close to that predicted by Maxwell constraint counting. We calculate the probability of a bond being on the infinite cluster and also on the overconstrained part of the infinite cluster, and show how a specific heat can be defined as the second derivative of the free energy. We demonstrate that the Bethe lattice solution is equivalent to that of the random bond model, where points are joined randomly (with equal probability at all length scales) to have a given coordination, and then subsequently bonds are randomly removed.Comment: RevTeX 11 pages + epsfig embedded figures. Submitted to Phys. Rev.

Statics and dynamics of domain patterns in hexagonal-orthorhombic ferroelastics

We study the statics and the dynamics of domain patterns in proper hexagonal-orthorhombic ferroelastics; these patterns are of particular interest because they provide a rare physical realization of disclinations in crystals. Both our static and dynamical theories are based entirely on classical, nonlinear elasticity theory; we use the minimal theory consistent with stability, symmetry and ability to explain qualitatively the observed patterns. After scaling, the only parameters of the static theory are a temperature variable and a stiffness variable. For moderate to large stiffness, our static results show nested stars, unnested stars, fans and other nodes, triangular and trapezoidal regions of trapped hexagonal phase, etc observed in electron microscopy of Ta4N and Mg-Cd alloys, and also in lead orthovanadate (which is trigonal-monoclinic); we even find imperfections in some nodes, like those observed. For small stiffness, we find patterns like those observed in the mineral Mg-cordierite. Our dynamical studies of growth and relaxation show the formation of these static patterns, and also transitory structures such as 12-armed bursts, streamers and striations which are also seen experimentally. The major aspects of the growth-relaxation process are quite unlike those in systems with conventional order parameters, for it is inherently nonlocal; for example, the changes from one snapshot to the next are not predictable by inspection.Comment: 9 pages, 3 figures (1 b&w, 2 colour); animations may be viewed at http://huron.physics.utoronto.ca/~curnoe/sim.htm

Rapid state purification protocols for a Cooper pair box

We propose techniques for implementing two different rapid state purification schemes, within the constraints present in a superconducting charge qubit system. Both schemes use a continuous measurement of charge (z) measurements, and seek to minimize the time required to purify the conditional state. Our methods are designed to make the purification process relatively insensitive to rotations about the x-axis, due to the Josephson tunnelling Hamiltonian. The first proposed method, based on the scheme of Jacobs [Phys. Rev. A 67, 030301(R) (2003)] uses the measurement results to control bias (z) pulses so as to rotate the Bloch vector onto the x-axis of the Bloch sphere. The second proposed method, based on the scheme of Wiseman and Ralph [New J. Phys. 8, 90 (2006)] uses a simple feedback protocol which tightly rotates the Bloch vector about an axis almost parallel with the measurement axis. We compare the performance of these and other techniques by a number of different measures.Comment: 14 pages, 14 figures. v2: Revised version after referee comments. Accepted for publication by Physical Review

Conditional control of quantum beats in a cavity QED system

We probe a ground-state superposition that produces a quantum beat in the intensity correlation of a two-mode cavity QED system. We mix drive with scattered light from an atomic beam traversing the cavity, and effectively measure the interference between the drive and the light from the atom. When a photon escapes the cavity, and upon detection, it triggers our feedback which modulates the drive at the same beat frequency but opposite phase for a given time window. This results in a partial interruption of the beat oscillation in the correlation function, that then returns to oscillate.Comment: 9 pages, 5 figures, XVII Reuni\'on Iberoamericana de \'Optica, X Encuentro de \'Optica, L\'aseres y Aplicaciones (RIAO-OPTILAS-2010

Simulation of the Performance of the IISc Chemical Kinetics Shock Tube

This report presents the results of an investigation of the performance of the Chemical Kinetics Shock tube at the Indian Institute of Science. The one-dimensional Lagrangian code L1d of Jacobs (1998) has been used to simulate the tube at several operating conditions. The conditions have different shock tube filling pressures, resulting in different shock speeds and different tube lengths, resulting in different dwell times. The simulations have been performed both with and without viscous effects simulated in the tubes. At the lowest shock tube filling pressure condition, the shock tube operates in an overtailored mode and it is undertailored at the higher filling pressure conditions. The results show that viscous effects, which lead to attenuation of the primary shock and heat loss from the test gas to the tube walls, result in an increasing p5 pressure during the test time. The viscous effects are more dominant at the condition with the lowest filling pressure (highest primary shock speed). A simulation run for 50 ms after diaphragm rupture or the configuration with a long driver tube shows that the test gas is periodically re-compressed by reflections of waves along the driver and shock tubes. The recompressions become sequentially weaker and thus the test gas temperature and pressure are never raised to as high levels as for the primary compression

On coalgebras with internal moves

In the first part of the paper we recall the coalgebraic approach to handling the so-called invisible transitions that appear in different state-based systems semantics. We claim that these transitions are always part of the unit of a certain monad. Hence, coalgebras with internal moves are exactly coalgebras over a monadic type. The rest of the paper is devoted to supporting our claim by studying two important behavioural equivalences for state-based systems with internal moves, namely: weak bisimulation and trace semantics. We continue our research on weak bisimulations for coalgebras over order enriched monads. The key notions used in this paper and proposed by us in our previous work are the notions of an order saturation monad and a saturator. A saturator operator can be intuitively understood as a reflexive, transitive closure operator. There are two approaches towards defining saturators for coalgebras with internal moves. Here, we give necessary conditions for them to yield the same notion of weak bisimulation. Finally, we propose a definition of trace semantics for coalgebras with silent moves via a uniform fixed point operator. We compare strong and weak bisimilation together with trace semantics for coalgebras with internal steps.Comment: Article: 23 pages, Appendix: 3 page