Thermodynamics of Vortices in the Plane

The thermodynamics of vortices in the critically coupled abelian Higgs model, defined on the plane, are investigated by placing $N$ vortices in a region of the plane with periodic boundary conditions: a torus. It is noted that the moduli space for $N$ vortices, which is the same as that of $N$ indistinguishable points on a torus, fibrates into a $CP_{N-1}$ bundle over the Jacobi manifold of the torus. The volume of the moduli space is a product of the area of the base of this bundle and the volume of the fibre. These two values are determined by considering two 2-surfaces in the bundle corresponding to a rigid motion of a vortex configuration, and a motion around a fixed centre of mass. The partition function for the vortices is proportional to the volume of the moduli space, and the equation of state for the vortices is $P(A-4\pi N)=NT$ in the thermodynamic limit, where $P$ is the pressure, $A$ the area of the region of the plane occupied by the vortices, and $T$ the temperature. There is no phase transition.Comment: 17 pages, DAMTP 93-3

Strategic Analyses of the National River Linking Project (NRLP) of India, Series 1. India’s water future: scenarios and issues

River basinsEnvironmental flowsDevelopment projectsWater requirementsIrrigated farmingWater demandFood demandGroundwater irrigationIrrigation efficiencyWater harvestingSupplemental irrigationWater productivityWater conservationDrip irrigationSprinkler irrigationRainfed farmingAgricultural policy

Patient-specific 3D Printed Liver Models for Pre-operative Planning and Improved Patient Adherence

Project Background: 3D anatomical relationships in the liver are not always visually accessible for surgeons performing resections even with advanced imaging options. Firm understanding of these relationships is essential for timely procedures, which can improve patient outcomes and lower hospital expenses. Patient-specific 3D modeling has existed for some time, though it is costly. New cost-effective techniques have surfaced which may yield opportunities for more effective preoperative planning in liver surgery and improved patient adherence. Methods: Digital patient-specific 3D reconstruction of a liver was completed by interpolating data from MRI scans using 3D Slicer, a segmenting program. The liver model was processed and 3D printed as a shell to be used as a mold. The liver shell, associated vasculature, and tumor were printed using polylactic acid (PLA) filament on an Ultimaker S5 3D printer. Transparent silicone was used as a cast, giving the model a solid form yet still allowing examination of the inside contents. Results: One completed liver model was used in pre-surgical consultation of a patient with hepatocellular carcinoma undergoing liver resection and during the surgical procedure as a guide for the surgical team. A follow-up survey concerning qualitative aspects of the model administered to the surgical team suggested high accuracy of the model compared to the anatomy observed during the procedure. Conclusion: Cost-effective techniques in producing patient specific 3D anatomical models appears not only feasible, but highly effective in improving communication between the surgical team during the procedure and also between the surgeon and the patient during pre-surgical consultation. Future research may be conducted concerning the model’s visual clarity as well as impact on patient adherence post-op

Energy relaxation of an excited electron gas in quantum wires: many-body electron LO-phonon coupling

We theoretically study energy relaxation via LO-phonon emission in an excited one-dimensional electron gas confined in a GaAs quantum wire structure. We find that the inclusion of phonon renormalization effects in the theory extends the LO-phonon dominated loss regime down to substantially lower temperatures. We show that a simple plasmon-pole approximation works well for this problem, and discuss implications of our results for low temperature electron heating experiments in quantum wires.Comment: 10 pages, RevTex, 4 figures included. Also available at http://www-cmg.physics.umd.edu/~lzheng