Conformal Maps to Multiply-Slit Domains and Applications

By exploiting conformal maps to vertically slit regions in the complex plane, a recently developed rational spectral method [Tee and Trefethen, 2006] is able to solve PDEs with interior layer-like behaviour using significantly fewer collocation points than traditional spectral methods. The conformal maps are chosen to 'enlarge the region of analyticity' in the solution: an idea which can be extended to other numerical methods based upon global polynomial interpolation. Here we show how such maps can be rapidly computed in both periodic and nonperiodic geometries, and apply them to some challenging differential equations

Low temperature vortex liquid states induced by quantum fluctuations in the quasi two dimensional organic superconductor kappa-(BEDT-TTF)_{2} Cu(NCS)_{2}

We report the transport properties in the vortex liquid states induced by quantum fluctuations at low temperature in the layered organic superconductor kappa-(BEDT-TTF)_{2} Cu(NCS)_{2}. A steep drop of the resistivity observed below about 1 K separates the liquid state into two regions. In the low resistance state at lower temperature, a finite resistivity with weak temperature dependence persists down to 100 mK at least. The finite resistivity in the vortex state at T ~= 0 K indicates the realization of quantum vortex liquid assisted by the strong quantum fluctuations instead of the thermal one. A possible origin for separating these liquid states is a remnant vortex melting line at the original position, which is obscured and suppressed by the quantum fluctuations. A non-linear behavior of the in-plane resistivity appears at large current density in only the low resistance state, but not in another vortex liquid state at higher temperature, where the thermal fluctuations are dominant. The transport properties in the low resistance state are well understood in the vortex slush concept with a short-range order of vortices. Thus the low resistance state below 1 K is considered to be a novel quantum vortex slush state.Comment: 7 pages, 5 figure

Equations for predicting airborne cleanliness in non-unidirectional airflow cleanrooms

Equations are derived in this paper for predicting the airborne concentration of particles and microbe-carrying particles in non-unidirectional airflow cleanrooms during manufacturing. The equations are obtained for a variety of ventilation systems with different configurations for mixing fresh and recirculated air, air filter placements, and number and efficiency of air filters. The variables in the equations are air supply rate, airborne dispersion rate of contamination from machinery and people, surface deposition of particles from air, particle concentration in fresh makeup air, proportion of make-up air, and air filter efficiencies. The equations are amenable to relatively simple modification for the study of different cleanroom ventilation systems. The use of these equations to investigate the effect of different configurations of ventilation systems and the relative importance of the equation variables on airborne concentrations will be reported in a further paper

A rational spectral collocation method with adaptively transformed Chebyshev grid points

A spectral collocation method based on rational interpolants and adaptive grid points is presented. The rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed Chebyshev points. The locations of the grid points are adapted to singularities of the underlying solution, and the locations of these singularities are approximated by the locations of poles of Chebyshev-Padé approximants. Numerical experiments on two time-dependent problems, one with finite time blow-up and one with a moving front, indicate that the method far outperforms the standard Chebyshev spectral collocation method for problems whose solutions have singularities in the complex plan close to [-1,1]

Logic-controlled occlusive cuff system

An occlusive cuff system comprises a pressure cuff and a source of regulated compressed gas feeding the cuff through an electrically operated fill valve. An electrically operated vent valve vents the cuff to the ambient pressure. The fill valve is normally closed and the vent valve is normally open. In response to an external start signal, a logic network opens the fill valve and closes the vent valve, thereby starting the pressurization cycle and a timer. A pressure transducer continuously monitors the pressure in the cuff. When the transducer's output equals a selected reference voltage, a comparator causes the logic network to close the fill valve. The timer, after a selected time delay, opens the vent valve to the ambient pressure, thereby ending the pressurization cycle

Calculation of airborne cleanliness and air supply rate for non-unidirectional airflow cleanrooms

Equations have been recently derived by Whyte, Lenegan and Eaton for calculating the airborne concentration of particles and microbe-carrying particles in non-unidirectional airflow cleanrooms. These equations cover a variety of ventilation systems, and contain the variables of air supply rate, airborne dispersion rate of contamination from machinery and people, surface deposition of particles from the air, concentration of contamination in fresh make-up air, proportion of fresh air, and air filter efficiencies. The relative importance of these variables is investigated in this present research paper, with particular regard to the removal efficiency, location, and number of air filters. It was shown that air filters were important in ensuring low levels of contamination in cleanrooms but the types of filters specified in current cleanroom designs were very effective in ensuring a minimal contribution to the cleanroom’s airborne contamination especially when a secondary filter is used in addition to a primary and terminal filter. The most important determinants of airborne contamination were the air supply rate and the dispersion rate of contamination within the cleanroom, with a lesser effect from deposition of airborne particles onto cleanroom surfaces. The information gathered confirmed the usefulness of the equation previously used by Whyte, Whyte, Eaton and Lenegan to calculate the air supply rate required for a specified concentration of airborne contamination