A detonation stability formulation for arbitrary equations of state and multi-step reaction mechanisms

A general normal-mode linear stability formulation of steady planar detonation waves is presented that is valid both for an arbitrary equation of state and for multi-step, multi-species chemical kinetics. The general formulation can be used for many purposes, including an examination of gaseous detonation stability with complex reaction kinetics in which the individual reacting species have variable thermochemical properties. In the present paper, we consider two cases that could not be obtained by previous one-step chemistry, polytropic gas formulations: the first concerns the effect of a difference in heat capacities between product and fuel species, as well as a possible mole change, in a single-step irreversible reaction. The second examines the effects of exothermic or endothermic heat release/absorption in the chain-initiation stage of a model three-step reaction.     

Natural boundaries and rational approximants

The use of rational approximants to simulate the natural boundary of a function is examined. Determination of the poles of the approximants illustrates the enormous power of the MATHEMATICA computer package.     

Time-dependent electron thermal flux inhibition in direct-drive laser implosions

We simulate direct-drive CH target implosions with square laser pulses by a one-dimensional Fokker-Planck solver combined with a hydrodynamic code, and compare the results with those simulated by the flux-limited Spitzer-H?rm model. We find that the electron thermal flux inhibition is time dependent, resulting in longer density scale length, larger laser absorption, and smaller growth of Rayleigh-Taylor instability. The time of peak neutron production calculated from Fokker-Planck simulations agrees with experiments for both 1-ns and 400-ps pulses.     

Local distinguishability of multipartite orthogonal quantum states

We consider one copy of a quantum system prepared in one of two orthogonal pure states, entangled or otherwise, and distributed between any number of parties. We demonstrate that it is possible to identify which of these two states the system is in by means of local operations and classical communication alone. The protocol we outline is both completely reliable and completely general; it will correctly distinguish any two orthogonal states 100% of the time.     

Identification of a set of genes showing regionally enriched expression in the mouse brain

Background

We have recorded responses from single neurons in murine visual cortex to determine the effectiveness of the input from the two murine cone photoreceptor mechanisms and whether there is any unique selectivity for cone inputs at this higher region of the visual system that would support the possibility of colour vision in mice. Each eye was stimulated by diffuse light, either 370 (strong stimulus for the ultra-violet (UV) cone opsin) or 505 nm (exclusively stimulating the middle wavelength sensitive (M) cone opsin), obtained from light emitting diodes (LEDs) in the presence of a strong adapting light that suppressed the responses of rods.

Results

Single cells responded to these diffuse stimuli in all areas of striate cortex. Two types of responsive cells were encountered. One type (135/323 – 42%) had little to no spontaneous activity and responded at either the on and/or the off phase of the light stimulus with a few impulses often of relatively large amplitude. A second type (166/323 – 51%) had spontaneous activity and responded tonically to light stimuli with impulses often of small amplitude. Most of the cells responded similarly to both spectral stimuli. A few (18/323 – 6%) responded strongly or exclusively to one or the other spectral stimulus and rarely in a spectrally opponent manner.

Conclusion

Most cells in murine striate cortex receive excitatory inputs from both UV- and M-cones. A small fraction shows either strong selectivity for one or the other cone mechanism and occasionally cone opponent responses. Cells that could underlie chromatic contrast detection are present but extremely rare in murine striate cortex.     

Unsolvable Problems About Small Cancellation and Word Hyperbolic Groups

We apply a construction of Rips to show that a number of algorithmicproblems concerning certain small cancellation groups and, inparticular, word hyperbolic groups, are recursively unsolvable.Given any integer k > 2, there is no algorithm to determinewhether or not any small cancellation group can be generatedby either two elements or more than k elements. There is a smallcancellation group E such that there is no algorithm to determinewhether or not any finitely generated subgroup of E is all ofE, or is finitely presented, or has a finitely generated secondintegral homology group.     

New methods for determining the thermal activation energies of light sensitive traps

Two methods have been developed for determining the thermal activation energies of light sensitive traps in systems with either one or two trap types and a single type of recombination centre. No assumptions about the kinetic order are needed for the methods to be successful, although the two- trap case requires sufficient difference in trap activation energies. There is potential to apply the methods to more complex systems, and the theory is readily transferred to the traps used in ESR.     

Shock-induced ignition of thermally sensitive explosives

The process of planar detonation ignition, induced by a constant-velocitypiston or equivalently by a shock reflected from a stationarywall, is investigated using high-resolution one-dimensionalnumerical simulations. The standard one-step model with Arrheniuskinetics, which models thermally sensitive explosives, is employed.Emphasis is on comparing and contrasting the results of thefinite activation temperature simulations with high activationtemperature asymptotic predictions and previous simulations.During the induction phase, it is shown that the asymptoticresults give qualitatively good predictions. However, for parametersrepresentative of gaseous explosives, subsequent to thermalrunaway at the piston and the formation of a reaction wave,the high activation temperature asymptotic theory is qualitativelyincorrect for moderately high activation temperatures. It isshown that the results are very sensitive to the value of theactivation temperature, especially the distance from the pistonat which a secondary shock forms and the degree of unsteadinessin the reaction wave which moves away from the piston. The dependenceof the ignition evolution on the other parameters (initial shockMach number, heat of reaction and polytropic index) is alsoinvestigated. It is shown that qualitative predictions regardingthe dependence of the ignition evolution on each of the parameterscan be elucidated from finite activation temperature homogeneousexplosion calculations together with the high activation temperatureasymptotic shock ignition results. It is found that for sufficientlystrong initiating shocks the ignition evolution is qualitativelydifferent from cases studied previously in that no secondaryshock forms. For a high polytropic index, corresponding to asimple equation of state model for condensed phase explosives,the results are in much better qualitative agreement with theasymptotic theory.