The formation of singularities in two-dimensional magnetohydrodynamic flow is investigated by direct numerical simulation. It is shown that two-dimensional magnetohydrodynamic turbulence is not as singular as three-dimensional hydrodynamic turbulence (in the sense that it has a less highly excited small-scale structure) but that it is more singular than two-dimensional hydrodynamic turbulence.

An envelope equation is derived which describes the radial evolution of a radiation beam propagating through a plasma. The radiation envelope equation contains a defocusing term due to diffraction spreading and a focusing term due to relativistic oscillations of the plasma electrons. The case of a constant density background plasma is analyzed in detail and an expression for a critical laser power is derived. For powers exceeding the critical power, the radiation envelope oscillates and does not diffract. Under certain conditions the radiation beam propagates through the plasma with a constant radius envelope.

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Enumeration of circulating tumor cells (CTCs) from cancer patient blood is an established diagnostic assay used to evaluate patient status as a singleplex test. However, in the coming age of personalized medicine, multiplex analysis of patient CTCs, including proteomic and genomic techniques, will have to be integrated with CTC isolation platform technologies. Advancements in microfabrication have demonstrated that CTCs can be isolated and analyzed using microfluidic lab-on-a-chip devices. However, to date, most microfluidic devices are either still in the development phase, not applicable to all clinical tests, or are not commercially available. To overcome these discrepancies, we describe an all-in-one device for the isolation and multiplexing of clinically applicable CTC assays. Microfilters present an ideal lab-on-a-chip platform for analysis of CTCs as non-toxic and inert materials allow for a multitude of tests from cell growth through clinical staining techniques, all without background interference. Lithographically fabricated microfilters, can be made with high porosity, precise pore dimensions, arrayed pore distribution, and optimized for CTC size-based isolation. In this study we describe microfilter use in isolation and in situ analysis of CTCs using multiple sequential techniques including culture, FISH, histopathological analysis, H&E staining, photobleaching and re-staining. Further, as a proof of principle, we then describe the ability to quantitatively release patient derived CTCS from the microfilters for potential use in downstream genomic/proteomic analysis.

include, among other things, continuous frequency tunability, very high power of operatbios asid hiigh efficiency. Vic free electron laamr ;s charmeterized by a pump field; foi example., a spatially periodic magnetic filrd, which scatters from o, relativistic electron bkatn. The scattered radiation has a wavelength much smaller thaai the pump wavelength depending on the electron (Continued) DD ASTRACT (Continued),beoz energy. We present & general self-conulsteAt non-linear theory of the free electron lawe promess. The non4invar formulation of'the temporal steady state free electron laser problem results in -st of coupled differential Oquatirns govairiiip the spatWa ovolution of the ampl itudes and wavelength lrnf the radiation~ad space charge f&r1Ida These 1!quations are readily solved numerialy since the amnpltude and wavelength vtry on a Mpatla Scale which is comparable to a growth length of the output radiation. A itunaber of nuinerical/analytical illustrations are presenetd ranging from the optical to the stibmillllmter wavelunitth regime. Our non incear formulation in the linear regime is compared with lknsar theory and agrement is found to he excellent.. Analytical expressions for the saturated of ficiency and radiation amplitude ate als Shown to be in very good agreement with our non-linear numerical soiutiana. Efficiency curves are obtained for both the optical and submindimoter FEL examples with fixed magnetic: pump parameters. We show that these intrinsic efficiencie can be greatly enhanced by appropriately contouring the magnetic pump period~ciii the case of the optical FEL, the theoretical W4nge pals efficiency can be peter than 20% by'ã ppropriately decreasing the pump period and increasing th, pump magnetic field.