The mass of unimodular lattices

The purpose of this paper is to show how to obtain the mass of a unimodular lattice from the point of view of the Bruhat-Tits theory. This is achieved by relating the local stabilizer of the lattice to a maximal parahoric subgroup of the special orthogonal group, and appealing to an explicit mass formula for parahoric subgroups developed by Gan, Hanke and Yu. Of course, the exact mass formula for positive defined unimodular lattices is well-known. Moreover, the exact formula for lattices of signature (1,n) (which give rise to hyperbolic orbifolds) was obtained by Ratcliffe and Tschantz, starting from the fundamental work of Siegel. Our approach works uniformly for the lattices of arbitrary signature (r,s) and hopefully gives a more conceptual way of deriving the above known results.Comment: 15 pages, to appear in J. Number Theor

Shock wave boundary layer interaction studied by high-speed schlieren

Shock wave boundary layer interactions at compression ramps have been examined by high-speed schlieren. A total of six ramps with angles ranging from 20 deg to 30 deg, the ramp angle effect on the SWBLI is thus studied. The present high-speed schlieren with a frame rate of 20 kHz generates a large ensemble of 9000 images, which secures the convergence of the statistics of the schlieren intensity. The rms of the schlieren intensity is of great interest, as it enables visualisation of the flow features that are not observable in the raw schlieren images, such as the corner separation/low momentum region, the spot of strong flow unsteadiness right after the shock wave and the location of the peak fluctuation over the ramp. Through the present systematic experimental investigation of SWBLI, the highspeed schlieren is demonstrated to be of great capability for SWBLI study

Transport of water in polysulphide elastomers

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Frequency-sweep examination for wave mode identification in multimodal ultrasonic guided wave signal

This article has been made available through the Brunel Open Access Publishing Fund.Ultrasonic guided waves can be used to assess and monitor long elements of a structure from a single position. The greatest challenges for any guided wave system are the plethora of wave modes arising from the geometry of the structural element which propagate with a range of frequency-dependent velocities and the interpretation of these combined signals reflected by discontinuities in the structural element. In this paper, a novel signal processing technique is presented using a combination of frequency-sweep measurement, sampling rate conversion, and Fourier transform. The technique is applied to synthesized and experimental data to identify different modes in complex ultrasonic guided wave signals. It is demonstrated throughout the paper that the technique also has the capability to derive the time of flight and group velocity dispersion curve of different wave modes in field inspections. © 2014 IEEE

Coexistence of superconductivity and antiferromagnetism in self-doped bilayer t-t'-J model

A self-doped bilayer t-t'-J model of an electron- and a hole-doped planes is studied by the slave-boson mean-field theory. A hopping integral between the differently doped planes, which are generated by a site potential, are renormalized by the electron-electron correlation. We find coexistent phases of antiferromagnetic (AFM) and superconducting orders, although the magnitudes of order parameters become more dissimilar in the bilayer away from half-filling. Fermi surfaces (FS's) with the AFM order show two pockets around the nodal and the anti-nodal regions. These results look like a composite of electron- and hole-doped FS's. In the nodal direction, the FS splitting is absent even in the bilayer system, since one band is flat due to the AFM order.Comment: 6 pages, 4 figure

Interlayer couplings and the coexistence of antiferromagnetic and d-wave pairing order in multilayer cuprates

A more extended low density region of coexisting uniform antiferromagnetism and d-wave superconductivity has been reported in multilayer cuprates, when compared to single or bilayer cuprates. This coexistence could be due to the enhanced screening of random potential modulations in inner layers or to the interlayer Heisenberg and Josephson couplings. A theoretical analysis using a renormalized mean field theory, favors the former explanation. The potential for an improved determination of the antiferromagnetic and superconducting order parameters in an ideal single layer from zero field NMR and infrared Josephson plasma resonances in multilayer cuprates is discussed.Comment: 6 pages, 2 figure

Biomass Utilization Allocation in Biofuel Production: Model and Application

Various biomass sources can potentially be used for biofuel production, and many of these same biomass sources also have other uses. This raises an important question about biomass utilization allocation. We demonstrate an economic principle for biomass allocation by examining the profitability of woody biomass utilization in a simple two-product case. We then develop a mixed-integer programming model for allocating multiple biomass resources in the production of different biofuels and bioproducts. Our model combines biomass utilization allocation with biofuel supply chain optimization. The model is applied to solving the forest biomass utilization allocation problem for East Texas in the southern United States. We find that besides biofuel prices, production scale and CO2 offset credits also significantly affect biomass utilization allocation. Our findings validate our integrative model approach to addressing biomass allocation and provide useful implications for enhancing the efficient utilization of forest biomass. Keywords: forest biomass, biofuel supply chain, greenhouse gas offset, mathematical programming, southern United States. Received 10 October 2010, Revised 20 July 2012, Accepted 24 October 2012