185 research outputs found
Linear stability of magnetohydrodynamic flow in a perfectly conducting rectangular duct
We analyse numerically the linear stability of a liquid metal flow in a
rectangular duct with perfectly electrically conducting walls subject to a
uniform transverse magnetic field. A non-standard three dimensional vector
stream function/vorticity formulation is used with Chebyshev collocation method
to solve the eigenvalue problem for small-amplitude perturbations. A relatively
weak magnetic field is found to render the flow linearly unstable as two weak
jets appear close to the centre of the duct at the Hartmann number Ha \approx
9.6. In a sufficiently strong magnetic field, the instability following the
jets becomes confined in the layers of characteristic thickness \delta \sim
Ha^{-1/2} located at the walls parallel to the magnetic field. In this case the
instability is determined by \delta, which results in both the critical
Reynolds and wavenumbers numbers scaling as \sim \delta^{-1}. Instability modes
can have one of the four different symmetry combinations along and across the
magnetic field. The most unstable is a pair of modes with an even distribution
of vorticity along the magnetic field. These two modes represent strongly
non-uniform vortices aligned with the magnetic field, which rotate either in
the same or opposite senses across the magnetic field. The former enhance while
the latter weaken one another provided that the magnetic field is not too
strong or the walls parallel to the field are not too far apart. In a strong
magnetic field, when the vortices at the opposite walls are well separated by
the core flow, the critical Reynolds and wavenumbers for both of these
instability modes are the same: Re_c \approx 642Ha^{1/2}+8.9x10^3Ha^{-1/2} and
k_c \approx 0.477Ha^{1/2}. The other pair of modes, which differs from the
previous one by an odd distribution of vorticity along the magnetic field, is
more stable with approximately four times higher critical Reynolds number.Comment: 16 pages, 8 figures, revised version, to appear in J. Fluid Mec
Prismatic cohomology and de Rham-Witt forms
For any prism we construct a canonical map . This map is necessary for existence of a
canonical base change comparison between prismatic cohomology and de Rham-Witt
forms. We construct a canonical map from prismatic cohomology to de Rham-Witt
forms and prove that it is an isomorphism in the perfect case. Using this we
get an explicit description of the prismatic cohomology for a polynomial
algebra over .Comment: 22 page
The Design, modeling and simulation of switching fabrics: For an ATM network switch
The requirements of today\u27s telecommunication systems to support high bandwidth and added flexibility brought about the expansion of (Asynchronous Transfer Mode) ATM as a new method of high-speed data transmission. Various analytical and simulation methods may be used to estimate the performance of ATM switches. Analytical methods considerably limit the range of parameters to be evaluated due to extensive formulae used and time consuming iterations. They are not as effective for large networks because of excessive computations that do not scale linearly with network size. One the other hand, simulation-based methods allow determining a bigger range of performance parameters in a shorter amount of time even for large networks. A simulation model, however, is more elaborate in terms of implementation. Instead of using formulae to obtain results, it has to operate software or hardware modules requiring a certain amount of effort to create. In this work simulation is accomplished by utilizing the ATM library - an object oriented software tool, which uses software chips for building ATM switches. The distinguishing feature of this approach is cut-through routing realized on the bit level abstraction treating ATM protocol data units, called cells, as groups of 424 bits. The arrival events of cells to the system are not instantaneous contrary to commonly used methods of simulation that consider cells as instant messages. The simulation was run for basic multistage interconnection network types with varying source arrival rate and buffer sizes producing a set of graphs of cell delays, throughput, cell loss probability, and queue sizes. The techniques of rearranging and sorting were considered in the simulation. The results indicate that better performance is always achieved by bringing additional stages of elements to the switching system
Recommended from our members
Experimental model of the interfacial instability in aluminium reduction cells
A solution has been found to the long-standing problem of experimental modelling of the interfacial instability in aluminium reduction cells. The idea is to replace the electrolyte overlaying molten aluminium with a mesh of thin rods supplying current down directly into the liquid metal layer. This eliminates electrolysis altogether and all the problems associated with it, such as high temperature, chemical aggressiveness of media, products of electrolysis, the necessity for electrolyte renewal, high power demands, etc. The result is a room temperature, versatile laboratory model which simulates Sele-type, rolling pad interfacial instability. Our new, safe laboratory model enables detailed experimental investigations to test the existing theoretical models for the first time
- …