Generation of oblique dark solitons in supersonic flow of Bose-Einstein condensate past an obstacle

Nonlinear and dispersive properties of Bose-Einstein condensate (BEC) provide a possibility of formation of various nonlinear structures such as vortices and bright and dark solitons (see, e.g., [1]). Yet another type of nonlinear wave patterns has been observed in a series of experiments on the BEC flow past macroscopic obstacles [2]. In [3] these structures have been associated with spatial dispersive shock waves. Spatial dispersive shock waves represent dispersive analogs of the the well-known viscous spatial shocks (oblique jumps of compression) occurring in supersonic flows of compressible fluids past obstacles. In a viscous fluid, the shock can be represented as a narrow region within which strong dissipation processes take place and the thermodynamic parameters of the flow undergo sharp change. On the contrary, if viscosity is negligibly small compared with dispersion effects, the shock discontinuity resolves into an expanding in space oscillatory structure which transforms gradually, as the distance from the obstacle increases, into a \fan" of stationary solitons. If the obstacle is small enough, then such a \fan" reduces to a single spatial dark soliton [4]. Here we shall present the theory of these new structures in BEC

Interaction of oblique dark solitons in two-dimensional supersonic nonlinear Schr\"odinger flow

We investigate the collision of two oblique dark solitons in the two dimensional supersonic nonlinear Schr\"odinger flow past two impenetrable obstacles. We numerically show that this collision is very similar to the dark soliton collisions in the one dimensional case. We observe that it is practically elastic and we measure the shifts of the solitons positions after their interaction

Recent Drifts in pH-Sensitive Reverse Osmosis

Preparation of some smart PAm-ZTS pH-responsive membranes, via reactions between ZTS and PAm under different conditions, was conducted for testing pressure-driven reverse osmosis membranes (PDROMs) in active rejection of Ce4+, Pr3+, Sm3+, Gd3+, Dy3+, and Ho3+ ionic lanthanide species in their 3+ and 4+ states. Recent theoretical models to designate the membrane operations were mathematically itemized, after selective characterization of the PDROMs. The pH scale response of the membrane was confirmed using static adsorption and hydraulic pervasion result estimations. The flux across the PAm-ZTS membrane decreased with the lowering pH value, with drastic decreases between pH 4 and 7, and was both reversible and durable with pH shifts between ~3 and ~8. At lower pH 3, the individual pores were in a closed-state due to the prolonged structure of the amide chains on the porous surfaces. In contrast, at pH 8, the higher pH value, the membrane pores were in an open-state format, because of the collapsed structures of the amide chains. This grants a clear possible approach for manufacturing some pH-responsive composite membranes and inspires further design for their stimuli-responsive actions by incorporating molecularly designed macromolecules, synthesized by controlled polymerization

Improved Resolution of Magnetic Resonance Microscopy in Examination of Skin Tumors

Magnetic resonance imaging has become increasingly important for visualization and tissue differentiation of internal organs. Because of limited resolution, investigation of skin has been of little diagnostic value so far. We combined a homogeneous magnetic field of 9.4 T, as used in magnetic resonance spectroscopy, with gradient fields of 11.7 G/cm and an imaging unit to obtain a voxel resolution of 40 × 40 × 300 μm3. With this magnetic resonance microscopy unit, we studied normal skin, 12 nevocellular nevi, 20 basal cell carcinomas, 8 melanomas, and 8 seborrheic keratoses after excision in vitro. The specimens were visualized in spin-echo images. The proton relaxation times T1 and T2 were determined for the different skin layers and tumor tissues. Interpretation of the spin-echo images was based on comparison with the correlating histology. Epidermis, dermis, subcutaneous tissue, and hair follicle complexes could be distinguished. Stratum corneum and hairs emitted no signal. All tumors presented as distinct, signal-rich, homogeneous structures within the dark, signal-poor dermis. Their shape corresponded to their outline in the histologic sections. Buds of superficial basal cell carcinomas could be resolved. The proton relaxation times T1 and T2 were significantly different among all skin layers and tumors. Our results demonstrate that with sufficient resolution, differentiation of skin tumors is possible using magnetic resonance imaging