Half-Skyrmions and Spike-Vortex Solutions of Two-Component Nonlinear Schrodinger Systems

Recently, skyrmions with integer topological charges have been observed numerically but have not yet been shown rigorously on two-component systems of nonlinear Schrodinger equations (NLSE) describing a binary mixture of Bose-Einstein condensates. Besides, half-skyrmions characterized by half-integer topological charges can also be found in the nonlinear sigma model which is a model of the Bose-Einstein condensate of the Schwinger bosons. Here we prove rigorously the existence of half-skyrmions which may come from a new type of soliton solutions called spike-vortex solutions of two-component systems of NLSE on the entire plane. These spike-vortex solutions having spikes in one component and a vortex in the other component may form half-skyrmions. By Liapunov-Schmidt reduction process, we may find spike-vortex solutions of two-component systems of NLSE.Comment: to appear in J.Math.Phy

Stability of spikes in the shadow Gierer-Meinhardt system with Robin boundary conditions

We consider the shadow system of the Gierer-Meinhardt system in a smooth bounded domain RN,At=2A−A+,x, t>0, ||t=−||+Ardx, t>0 with the Robin boundary condition +aAA=0, x, where aA>0, the reaction rates (p,q,r,s) satisfy 1<p<()+, q>0, r>0, s0, 1<<+, the diffusion constant is chosen such that 1, and the time relaxation constant is such that 0. We rigorously prove the following results on the stability of one-spike solutions: (i) If r=2 and 1<p<1+4/N or if r=p+1 and 1<p<, then for aA>1 and sufficiently small the interior spike is stable. (ii) For N=1 if r=2 and 1<p3 or if r=p+1 and 1<p<, then for 0<aA<1 the near-boundary spike is stable. (iii) For N=1 if 3<p<5 and r=2, then there exist a0(0,1) and µ0>1 such that for a(a0,1) and µ=2q/(s+1)(p−1)(1,µ0) the near-boundary spike solution is unstable. This instability is not present for the Neumann boundary condition but only arises for the Robin boundary condition. Furthermore, we show that the corresponding eigenvalue is of order O(1) as 0. ©2007 American Institute of Physic

A nonlocal eigenvalue problem and the stability of spikes for reaction-diffusion systems with fractional reaction rates

We consider a nonlocal eigenvalue problem which arises in the study of stability of spike solutions for reaction-diffusion systems with fractional reaction rates such as the Sel'kov model, the Gray-Scott system, the hypercycle Eigen and Schuster, angiogenesis, and the generalized Gierer-Meinhardt system. We give some sufficient and explicit conditions for stability by studying the corresponding nonlocal eigenvalue problem in a new range of parameters

High glucose inhibits osteogenic differentiation through the BMP signaling pathway in bone mesenchymal stem cells in mice

Patients with diabetes tend to have an increased risk of osteoporosis that may be related to hyperglycemia. In vitro evidence has shown that high glucose can affect the proliferation and osteogenic differentiation of mesenchymal stem cells (MSCs). Tissue regeneration depends mainly on MSCs. However, the exact mechanisms involved in high glucose–induced bone loss remain unknown. In this study, we investigated the effects of high glucose on the proliferation and osteogenic differentiation of mice bone MSCs (BMSCs) and determined the specific mechanism of bone morphogenetic protein 2 (BMP-2) in the osteogenic differentiation of mice BMSCs in a high-glucose microenvironment. High glucose (< 25 mM) promoted cell growth but suppressed mineralization. The intracellular BMP-2 level in BMSCs cultured in a high-glucose microenvironment was significantly decreased and suppressed activation of the BMP signaling pathway. Consequently, expression of the osteogenic markers Runx2, alkaline phosphatase, and osteocalcin were decreased. Meanwhile, supplementation with ectogenic BMP-2 reversed the cell osteogenic differentiation and osteogenic marker down-regulation under high glucose. Our data indicate that BMP-2 plays an important role in regulating the osteogenic differentiation of BMSCs in a high-glucose microenvironment. Thus, it is possible that agents modifying this pathway could be used by BMSCs to promote bone regeneration in high-glucose microenvironments

iPTF13beo: The Double-Peaked Light Curve of a Type Ibn Supernova Discovered Shortly after Explosion

We present optical photometric and spectroscopic observations of the Type Ibn (SN 2006jc-like) supernova iPTF13beo. Detected by the intermediate Palomar Transient Factory ~3 hours after the estimated first light, iPTF13beo is the youngest and the most distant (~430 Mpc) Type Ibn event ever observed. The iPTF13beo light curve is consistent with light curves of other Type Ibn SNe and with light curves of fast Type Ic events, but with a slightly faster rise-time of two days. In addition, the iPTF13beo R-band light curve exhibits a double-peak structure separated by ~9 days, not observed before in any Type Ibn SN. A low-resolution spectrum taken during the iPTF13beo rising stage is featureless, while a late-time spectrum obtained during the declining stage exhibits narrow and intermediate-width He I and Si II features with FWHM ~ 2000-5000 km/s and is remarkably similar to the prototypical SN Ibn 2006jc spectrum. We suggest that our observations support a model of a massive star exploding in a dense He-rich circumstellar medium (CSM). A shock breakout in a CSM model requires an eruption releasing a total mass of ~0.1 Msun over a time scale of couple of weeks prior to the SN explosion.Comment: 8 pages, 5 figures, submitted to MNRA

Symbiotic Bright Solitary Wave Solutions of Coupled Nonlinear Schrodinger Equations

Conventionally, bright solitary wave solutions can be obtained in self-focusing nonlinear Schrodinger equations with attractive self-interaction. However, when self-interaction becomes repulsive, it seems impossible to have bright solitary wave solution. Here we show that there exists symbiotic bright solitary wave solution of coupled nonlinear Schrodinger equations with repulsive self-interaction but strongly attractive interspecies interaction. For such coupled nonlinear Schrodinger equations in two and three dimensional domains, we prove the existence of least energy solutions and study the location and configuration of symbiotic bright solitons. We use Nehari's manifold to construct least energy solutions and derive their asymptotic behaviors by some techniques of singular perturbation problems.Comment: to appear in Nonlinearit

Constraining Type Ia supernova models: SN 2011fe as a test case

The nearby supernova SN 2011fe can be observed in unprecedented detail. Therefore, it is an important test case for Type Ia supernova (SN Ia) models, which may bring us closer to understanding the physical nature of these objects. Here, we explore how available and expected future observations of SN 2011fe can be used to constrain SN Ia explosion scenarios. We base our discussion on three-dimensional simulations of a delayed detonation in a Chandrasekhar-mass white dwarf and of a violent merger of two white dwarfs-realizations of explosion models appropriate for two of the most widely-discussed progenitor channels that may give rise to SNe Ia. Although both models have their shortcomings in reproducing details of the early and near-maximum spectra of SN 2011fe obtained by the Nearby Supernova Factory (SNfactory), the overall match with the observations is reasonable. The level of agreement is slightly better for the merger, in particular around maximum, but a clear preference for one model over the other is still not justified. Observations at late epochs, however, hold promise for discriminating the explosion scenarios in a straightforward way, as a nucleosynthesis effect leads to differences in the 55Co production. SN 2011fe is close enough to be followed sufficiently long to study this effect.Comment: Accepted for publication in The Astrophysical Journal Letter

Expected resolution limits of x-ray free-electron laser single-particle imaging for realistic source and detector properties

The unprecedented intensity of x-ray free-electron laser sources has enabled single-particle x-ray diffraction imaging (SPI) of various biological specimens in both two-dimensional projection and three dimensions (3D). The potential of studying protein dynamics in their native conditions, without crystallization or chemical staining, has encouraged researchers to aim for increasingly higher resolutions with this technique. The currently achievable resolution of SPI is limited to the sub-10 nanometer range, mainly due to background effects, such as instrumental noise and parasitic scattering from the carrier gas used for sample delivery. Recent theoretical studies have quantified the effects of x-ray pulse parameters, as well as the required number of diffraction patterns to achieve a certain resolution, in a 3D reconstruction, although the effects of detector noise and the random particle orientation in each diffraction snapshot were not taken into account. In this work, we show these shortcomings and address limitations on achievable image resolution imposed by the adaptive gain integrating pixel detector noise

Classification and nondegeneracy of SU(n+1)SU(n+1) Toda system with singular sources

We consider the following Toda system \Delta u_i + \D \sum_{j = 1}^n a_{ij}e^{u_j} = 4\pi\gamma_{i}\delta_{0} \text{in}\mathbb R^2, \int_{\mathbb R^2}e^{u_i} dx -1$,$\delta_0$is Dirac measure at 0, and the coefficients$a_{ij}$form the standard tri-diagonal Cartan matrix. In this paper, (i) we completely classify the solutions and obtain the quantization result:$$\sum_{j=1}^n a_{ij}\int_{\R^2}e^{u_j} dx = 4\pi (2+\gamma_i+\gamma_{n+1-i}), \;\;\forall\; 1\leq i \leq n.$$This generalizes the classification result by Jost and Wang for$\gamma_i=0$,$\forall \;1\leq i\leq n$. (ii) We prove that if$\gamma_i+\gamma_{i+1}+...+\gamma_j \notin \mathbb Z$for all$1\leq i\leq j\leq n$, then any solution$u_i$ is \textit{radially symmetric} w.r.t. 0. (iii) We prove that the linearized equation at any solution is \textit{non-degenerate}. These are fundamental results in order to understand the bubbling behavior of the Toda system.Comment: 28 page

The link between SARS-CoV-2 related microglial reactivity and astrocyte pathology in the inferior olivary nucleus

The pathological involvement of the central nervous system in SARS-CoV2 (COVID-19) patients is established. The burden of pathology is most pronounced in the brain stem including the medulla oblongata. Hypoxic/ischemic damage is the most frequent neuropathologic abnormality. Other neuropathologic features include neuronophagia, microglial nodules, and hallmarks of neurodegenerative diseases: astrogliosis and microglial reactivity. It is still unknown if these pathologies are secondary to hypoxia versus a combination of inflammatory response combined with hypoxia. It is also unknown how astrocytes react to neuroinflammation in COVID-19, especially considering evidence supporting the neurotoxicity of certain astrocytic phenotypes. This study aims to define the link between astrocytic and microglial pathology in COVID-19 victims in the inferior olivary nucleus, which is one of the most severely affected brain regions in COVID-19, and establish whether COVID-19 pathology is driven by hypoxic damage. Here, we conducted neuropathologic assessments and multiplex-immunofluorescence studies on the medulla oblongata of 18 COVID-19, 10 pre-pandemic patients who died of acute respiratory distress syndrome (ARDS), and 7–8 control patients with no ARDS or COVID-19. The comparison of ARDS and COVID-19 allows us to identify whether the pathology in COVID-19 can be explained by hypoxia alone, which is common to both conditions. Our results showed increased olivary astrogliosis in ARDS and COVID-19. However, microglial density and microglial reactivity were increased only in COVID-19, in a region-specific manner. Also, olivary hilar astrocytes increased YKL-40 (CHI3L1) in COVID-19, but to a lesser extent than ARDS astrocytes. COVID-19 astrocytes also showed lower levels of Aquaporin-4 (AQP4), and Metallothionein-3 in subsets of COVID-19 brain regions. Cluster analysis on immunohistochemical attributes of astrocytes and microglia identified ARDS and COVID-19 clusters with correlations to clinical history and disease course. Our results indicate that olivary glial pathology and neuroinflammation in the COVID-19 cannot be explained solely by hypoxia and suggest that failure of astrocytes to upregulate the anti-inflammatory YKL-40 may contribute to the neuroinflammation. Notwithstanding the limitations of retrospective studies in establishing causality, our experimental design cannot adequately control for factors external to our design. Perturbative studies are needed to confirm the role of the above-described astrocytic phenotypes in neuroinflammation