Generalized Rayleigh and Jacobi processes and exceptional orthogonal polynomials

We present four types of infinitely many exactly solvable Fokker-Planck equations, which are related to the newly discovered exceptional orthogonal polynomials. They represent the deformed versions of the Rayleigh process and the Jacobi process.Comment: 17 pages, 4 figure

Analysis and design of integration formulas for a random integrand

Analysis of integration formulas and procedure for designing optimal integration formul

Micro heat exchanger by using MEMS impinging jets

A micro impinging-jet heat exchanger is presented here. Heat transfer is studied for single jet, slot arrays and jet arrays. In order to facilitate micro heat transfer measurements with these devices, a MEMS sensor chip, which has an 8 x 8 temperature-sensor array on one side, and an integrated heater on the other side has been designed and fabricated. This sensor chip allows 2-D surface temperature measurement with various jets impinging on it. It is found that micro impinging jets can be highly efficient when compared to existing macro impinging-jet microelectronics packages such as IBM 4381. For example, using a single nozzle jet (500-μm diameter driven by 5 psig pressure), the sensor chip (2 x 2 cm^2) temperature can be cooled down from 70 to 33°C. The cooling becomes more efficient when nozzle arrays (4x5 over 1 cm^2 area) are used under the same driving pressure. Interestingly, although higher driving pressure gives better cooling (lower surface temperature), the cooling efficiency, defined as h/0.5pv^2, is actually higher for lower driving pressure

A suspended microchannel with integrated temperature sensors for high-pressure flow studies

A freestanding microchannel, with integrated temperature sensors, has been developed for high-pressure flow studies. These microchannels are approximately 20μm x 2μm x 4400μm, and are suspended above 80 μm deep cavities, bulk micromachined using BrF3 dry etch. The calibration of the lightly boron-doped thermistor-type sensors shows that the resistance sensitivity of these integrated sensors is parabolic with respect to temperature and linear with respect to pressure. Volumetric flow rates of N2 in the microchannel were measured at inlet pressures up to 578 psig. The discrepancy between the data and theory results from the flow acceleration in a channel, the non-parabolic velocity profile, and the bulging of the channel. Bulging effects were evaluated by using incompressible water flow measurements, which also measures 1.045x10^-3N-s/m^2 for the viscosity of DI water. The temperature data from sensors on the channel shows the heating of the channel due to the friction generated by the high-pressure flow inside

Spin-glass-like state in GdCu: role of phase separation and magnetic frustration

We report investigations on the ground state magnetic properties of intermetallic compound GdCu through dc magnetization measurements. GdCu undergoes first order martensitic type structural transition over a wide temperature window of coexisting phases. The high temperature cubic and the low temperature orthorhombic phases have different magnetic character and they show antiferromagnetic and helimagnetic orderings below 145 K and 45 K respectively. We observe clear signature of a glassy magnetic phase below the helimagnetic ordering temperature, which is marked by thermomagnetic irreversibility, aging and memory effects. The glassy magnetic phase in GdCu is found to be rather intriguing with its origin lies in the interfacial frustration due to distinct magnetic character of the coexisting phases.Comment: Physical Review B 83, 134427 (2011