NLSEmagic: Nonlinear Schr\"odinger Equation Multidimensional Matlab-based GPU-accelerated Integrators using Compact High-order Schemes

We present a simple to use, yet powerful code package called NLSEmagic to numerically integrate the nonlinear Schr\"odinger equation in one, two, and three dimensions. NLSEmagic is a high-order finite-difference code package which utilizes graphic processing unit (GPU) parallel architectures. The codes running on the GPU are many times faster than their serial counterparts, and are much cheaper to run than on standard parallel clusters. The codes are developed with usability and portability in mind, and therefore are written to interface with MATLAB utilizing custom GPU-enabled C codes with the MEX-compiler interface. The packages are freely distributed, including user manuals and set-up files.Comment: 37 pages, 13 figure

The Open Flux Problem

The heliospheric magnetic field is of pivotal importance in solar and space physics. The field is rooted in the Sun's photosphere, where it has been observed for many years. Global maps of the solar magnetic field based on full-disk magnetograms are commonly used as boundary conditions for coronal and solar wind models. Two primary observational constraints on the models are (1) the open field regions in the model should approximately correspond to coronal holes (CHs) observed in emission and (2) the magnitude of the open magnetic flux in the model should match that inferred from in situ spacecraft measurements. In this study, we calculate both magnetohydrodynamic and potential field source surface solutions using 14 different magnetic maps produced from five different types of observatory magnetograms, for the time period surrounding 2010 July. We have found that for all of the model/map combinations, models that have CH areas close to observations underestimate the interplanetary magnetic flux, or, conversely, for models to match the interplanetary flux, the modeled open field regions are larger than CHs observed in EUV emission. In an alternative approach, we estimate the open magnetic flux entirely from solar observations by combining automatically detected CHs for Carrington rotation 2098 with observatory synoptic magnetic maps. This approach also underestimates the interplanetary magnetic flux. Our results imply that either typical observatory maps underestimate the Sun's magnetic flux, or a significant portion of the open magnetic flux is not rooted in regions that are obviously dark in EUV and X-ray emission

Azimuthal Modulational Instability of Vortices in the Nonlinear Schr\"odinger Equation

We study the azimuthal modulational instability of vortices with different topological charges, in the focusing two-dimensional nonlinear Schr{\"o}dinger (NLS) equation. The method of studying the stability relies on freezing the radial direction in the Lagrangian functional of the NLS in order to form a quasi-one-dimensional azimuthal equation of motion, and then applying a stability analysis in Fourier space of the azimuthal modes. We formulate predictions of growth rates of individual modes and find that vortices are unstable below a critical azimuthal wave number. Steady state vortex solutions are found by first using a variational approach to obtain an asymptotic analytical ansatz, and then using it as an initial condition to a numerical optimization routine. The stability analysis predictions are corroborated by direct numerical simulations of the NLS. We briefly show how to extend the method to encompass nonlocal nonlinearities that tend to stabilize solutions.Comment: 8 pages, 6 figures, in press for Optics Communication

Vascular Remodeling in Health and Disease

The term vascular remodeling is commonly used to define the structural changes in blood vessel geometry that occur in response to long-term physiologic alterations in blood flow or in response to vessel wall injury brought about by trauma or underlying cardiovascular diseases.1, 2, 3, 4 The process of remodeling, which begins as an adaptive response to long-term hemodynamic alterations such as elevated shear stress or increased intravascular pressure, may eventually become maladaptive, leading to impaired vascular function. The vascular endothelium, owing to its location lining the lumen of blood vessels, plays a pivotal role in regulation of all aspects of vascular function and homeostasis.5 Thus, not surprisingly, endothelial dysfunction has been recognized as the harbinger of all major cardiovascular diseases such as hypertension, atherosclerosis, and diabetes.6, 7, 8 The endothelium elaborates a variety of substances that influence vascular tone and protect the vessel wall against inflammatory cell adhesion, thrombus formation, and vascular cell proliferation.8, 9, 10 Among the primary biologic mediators emanating from the endothelium is nitric oxide (NO) and the arachidonic acid metabolite prostacyclin [prostaglandin I2 (PGI2)], which exert powerful vasodilatory, antiadhesive, and antiproliferative effects in the vessel wall

Effect of dual growth factor delivery on chondrogenic differentiation of rabbit marrow mesenchymal stem cells encapsulated in injectable hydrogel composites.

Contains fulltext : 80847.pdf (publisher's version ) (Open Access)An injectable hydrogel composite consisting of oligo(poly(ethylene glycol)fumarate) (OPF) and gelatin microparticles has been developed as a novel carrier system for cells and growth factors. Rabbit marrow mesenchymal stem cells (MSCs) and gelatin microparticles (MPs) loaded with insulin-like growth factor-1 (IGF-1), transforming growth factor-beta1 (TGF-beta1), or a combination of both growth factors were mixed with OPF, a poly(ethylene glycol)-diacrylate crosslinker and the radical initiators ammonium persulfate and N,N,N',N'-tetramethylethylenediamine, and then crosslinked at 37 degrees C for 8 min to form hydrogel composites. Hydrogel composites encapsulating rabbit marrow MSCs and blank MPs served as controls. At day 14, confocal fluorescent images of OPF hydrogels showed a strong aggregation of rabbit marrow MSCs when encapsulated with IGF-1-loaded MPs with or without TGF-beta1-loaded MPs. Quantitative RT-PCR results showed that rabbit marrow MSCs encapsulated with MPs loaded with TGF-beta1 or both TGF-beta1 and IGF-1 had a significant increase in the expression of chondrocyte-specific genes such as collagen type II and aggrecan at day 14 as compared with the control group. Specifically, samples with both TGF-beta1-loaded MPs and IGF-1-loaded MPs exhibited a 121 +/- 20-fold increase of type II collagen gene expression and a 71 +/- 24-fold increase of aggrecan gene expression after 14 days of in vitro culture as compared with controls at day 0. These results suggest that hydrogel composites based on OPF and gelatin microparticles have great potential as carriers for MSCs and multiple growth factors for cartilage tissue engineering applications

Quasimonochromatic x-ray source using photoabsorption-edge transition radiation

By designing transition radiators to emit x-rays at the foil material's K-, L-, or M-shell photoabsorption edge, the x-ray spectrum is narrowed. The source is quasimonochromatic, directional, and intense and uses an electron beam whose energy is considerably lower than that needed for synchrotron sources. Depending on the selection of foil material, the radiation can be produced wherever there is a photoabsorption edge. In this paper we report the results of the measurement of the x-ray spectrum from a transition radiator composed of 10 foils of 2-um titanium and exposed to low-current, 90.2-MeV electrons, The measured band of emission was from 3.2 5o 5 keV. In addition, a measurement was performed of the total power from a transition radiator composed of 18 foils of 2.o-um copper exposed to a high-average-current electron beam of 40 uA and at energies of 135, 172, and 200 MeV. The maximum measured power was 4.0 mW. The calculated band of emission was from 4 to 9 keV.National Science Foundation of the Small Business Innovative Research (SBIR) program, Grant no. PHY-8460914; Department of Energy SBIR program, Grant No. DE-FG03-90ER80872; Canadian Natural Science and Engineering Research Council and the Naval Postgraduate SchoolThis investigation was supported by a Special Research Opportunity Grant from the U.S. Office of Naval Research, Department of the Navy and by the Foundation Research Program of the Naval Postgraduate School (Monterey, Ca.)Approved for public release; distribution is unlimited