3,519 research outputs found

    Ground state solution of Bose-Einstein condensate by directly minimizing the energy functional

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    In this paper, we propose a new numerical method to compute the ground state solution of trapped interacting Bose-Einstein condensation (BEC) at zero or very low temperature by directly minimizing the energy functional via finite element approximation. As preparatory steps we begin with the 3d Gross-Pitaevskii equation (GPE), scale it to get a three-parameter model and show how to reduce it to 2d and 1d GPEs. The ground state solution is formulated by minimizing the energy functional under a constraint, which is discretized by the finite element method. The finite element approximation for 1d, 2d with radial symmetry and 3d with spherical symmetry and cylindrical symmetry are presented in detail and approximate ground state solutions, which are used as initial guess in our practical numerical computation of the minimization problem, of the GPE in two extreme regimes: very weak interactions and strong repulsive interactions are provided. Numerical results in 1d, 2d with radial symmetry and 3d with spherical symmetry and cylindrical symmetry for atoms ranging up to millions in the condensation are reported to demonstrate the novel numerical method. Furthermore, comparisons between the ground state solutions and their Thomas-Fermi approximations are also reported. Extension of the numerical method to compute the excited states of GPE is also presented.Comment: 33 pages, 22 figure

    Highly Scalable, Closed-Loop Synthesis of Drug-Loaded, Layer-by-Layer Nanoparticles

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    Layer-by-layer (LbL) self-assembly is a versatile technique from which multi­component and stimuli-responsive nanoscale drug-carriers can be constructed. Despite the benefits of LbL assembly, the conventional synthetic approach for fabricating LbL nanoparticles requires numerous purification steps that limit scale, yield, efficiency, and potential for clinical translation. In this report, a generalizable method for increasing throughput with LbL assembly is described by using highly scalable, closed-loop diafiltration to manage intermediate purification steps. This method facilitates highly controlled fabrication of diverse nanoscale LbL formulations smaller than 150 nm composed from solid-polymer, mesoporous silica, and liposomal vesicles. The technique allows for the deposition of a broad range of polyelectrolytes that included native polysaccharides, linear polypeptides, and synthetic polymers. The cytotoxicity, shelf life, and long-term storage of LbL nanoparticles produced using this approach are explored. It is found that LbL coated systems can be reliably and rapidly produced: specifically, LbL-modified liposomes could be lyophilized, stored at room temperature, and reconstituted without compromising drug encapsulation or particle stability, thereby facilitating large scale applications. Overall, this report describes an accessible approach that significantly improves the throughput of nanoscale LbL drug-carriers that show low toxicity and are amenable to clinically relevant storage conditions.National Institutes of Health (U.S.) (Grant 1F32EB017614–02)Swiss National Science Foundation (Postdoctoral Fellowship

    Metallicities, dust and molecular content of a QSO-Damped Lyman-{\alpha} system reaching log N (H i) = 22: An analog to GRB-DLAs

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    We present the elemental abundance and H2 content measurements of a Damped Lyman-{\alpha} (DLA) system with an extremely large H i column density, log N(H i) (cm-2) = 22.0+/-0.10, at zabs = 3.287 towards the QSO SDSS J 081634+144612. We measure column densities of H2, C i, C i^*, Zn ii, Fe ii, Cr ii, Ni ii and Si ii from a high signal-to-noise and high spectral resolution VLT-UVES spectrum. The overall metallicity of the system is [Zn/H] = -1.10 +/- 0.10 relative to solar. Two molecular hydrogen absorption components are seen at z = 3.28667 and 3.28742 (a velocity separation of \approx 52 km s-1) in rotational levels up to J = 3. We derive a total H2 column density of log N(H2) (cm-2) = 18.66 and a mean molecular fraction of f = 2N(H2)/[2N(H2) + N(H i)] = 10-3.04+/-0.37, typical of known H2-bearing DLA systems. From the observed abundance ratios we conclude that dust is present in the Interstellar Medium (ISM) of this galaxy, with a enhanced abundance in the H2-bearing clouds. However, the total amount of dust along the line of sight is not large and does not produce any significant reddening of the background QSO. The physical conditions in the H2-bearing clouds are constrained directly from the column densities of H2 in different rotational levels, C i and C i^* . The kinetic temperature is found to be T = 75 K and the particle density lies in the range nH = 50-80 cm-3 . The neutral hydrogen column density of this DLA is similar to the mean H i column density of DLAs observed at the redshift of {\gamma}-ray bursts (GRBs). We explore the relationship between GRB-DLAs and high column density end of QSO-DLAs finding that the properties (metallicity and depletion) of DLAs with log N(H i) > 21.5 in the two populations do not appear to be significantly different

    A Cross-Correlation Analysis of Mg II Absorption Line Systems and Luminous Red Galaxies from the SDSS DR5

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    We analyze the cross-correlation of 2,705 unambiguously intervening Mg II (2796,2803A) quasar absorption line systems with 1,495,604 luminous red galaxies (LRGs) from the Fifth Data Release of the Sloan Digital Sky Survey within the redshift range 0.36<=z<=0.8. We confirm with high precision a previously reported weak anti-correlation of equivalent width and dark matter halo mass, measuring the average masses to be log M_h(M_[solar]h^-1)=11.29 [+0.36,-0.62] and log M_h(M_[solar]h^-1)=12.70 [+0.53,-1.16] for systems with W[2796A]>=1.4A and 0.8A<=W[2796A]<1.4A, respectively. Additionally, we investigate the significance of a number of potential sources of bias inherent in absorber-LRG cross-correlation measurements, including absorber velocity distributions and the weak lensing of background quasars, which we determine is capable of producing a 20-30% bias in angular cross-correlation measurements on scales less than 2'. We measure the Mg II - LRG cross-correlation for 719 absorption systems with v<60,000 km s^-1 in the quasar rest frame and find that these associated absorbers typically reside in dark matter haloes that are ~10-100 times more massive than those hosting unambiguously intervening Mg II absorbers. Furthermore, we find evidence for evolution of the redshift number density, dN/dz, with 2-sigma significance for the strongest (W>2.0A) absorbers in the DR5 sample. This width-dependent dN/dz evolution does not significantly affect the recovered equivalent width-halo mass anti-correlation and adds to existing evidence that the strongest Mg II absorption systems are correlated with an evolving population of field galaxies at z<0.8, while the non-evolving dN/dz of the weakest absorbers more closely resembles that of the LRG population.Comment: 21 pages, 19 figures; Published in Astrophysical Journa

    The most metal-poor damped Ly alpha system at z<3: constraints on early nucleosynthesis

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    To constrain the conditions for very early nucleosynthesis in the Universe we compare the chemical enrichment pattern of an extremely metal-poor damped Lyman alpha (DLA) absorber with predictions from recent explosive nucleosynthesis model calculations. For this, we have analyzed chemical abundances in the DLA system at z_abs=2.6183 toward the quasar Q0913+072 (z_em=2.785) using public UVES/VLT high spectral resolution data. The total neutral hydrogen column density in this absorber is logN(HI)=20.36. Accurate column densities are derived for CII, NI, OI, AlII, SiII, and FeII. Upper limits are given for FeIII and NiII. With [C/H]=-2.83, [N/H]=-3.84, and [O/H]=-2.47, this system represents one of the most metal-poor DLA systems investigated so far. It offers the unique opportunity to measure accurate CNO abundances in a protogalactic structure at high redshift. Given the very low overall abundance level and the observed abundance pattern, the data suggest that the chemical evolution of this DLA system is dominated by one or at most a few stellar generations. With reference to numerical model calculations, the chemical abundances in the DLA system are consistent with an enrichment from a single starburst of a zero-metallicity population of massive stars (10-50 M_sun) exploding as core-collapse Supernovae (SNe), i.e., the classical Type II Supernovae (SNeII), and possibly as hyper-energetic (E>10^51erg) core-collapse Supernovae, so-called Hypernovae (HNe), as well. In contrast, models using non-zero metallicity progenitors or other explosion mechanisms, such as pair-instability Supernovae (PISNe) or Type Ia Supernovae (SNeIa), do not match the observed abundance pattern.Comment: 9 pages, 4 figures, accepted for publication in Astronomy and Astrophysic
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