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Magnetotactic bacteria (MTB) can rapidly relocate to optimal habitats by magnetotaxis, and play an important role in iron biogeochemical cycling. This study aimed to evaluate the contribution of the external magnetostatic field to the diversity of MTB in freshwater sediments from Yangtze River (Changjiang River, CJ), Chagan Lake (CGH) and Zhalong Wetland (ZL). The magnetic field intensity was tightly associated with the community richness of MTB in CJ, whereas it was closely related to the diversity of MTB in CGH and ZL (p < 0.05), elucidating a significant variation in the community composition of MTB. Magnetic exposure time appeared more significant correlation with community richness than diversity for MTB in CJ and CGH (p < 0.05), while an opposite relationship existed in ZL (p < 0.01). Herbaspirillum (93.81–96.48 %) dominated in the sediments of these surfacewatesr regardless of waterbody types, while it shifted to Magnetospirillum in ZL under 100 Gs magnetic field. The network connectivity and stability of MTB deteriorate with the increase of magnetic field intensity. Functional analysis showed that the Two-component system and ABC transporter system of MTB obviously responded to magnetic field intensity and exposure time. Our findings will pave the way to understanding the response mechanism of MTB community in freshwater sediments to the external magnetostatic field. [Display omitted] • MTB widely exist in Changjiang River (CJ), Chagan Lake (CGH) and Zhalong Wetland (ZL) of China. • Dominant Herbaspirillum and Magnetospira occur all sediment samples. • Magnetic field intensity and exposure time both affect MTB diversity and richness. • Network connectivity and stability of MTB deteriorate as magnetic field intensity. • Metabolic function and ABC transporter system visibly respond to magnetic field. [ABSTRACT FROM AUTHOR]

In this paper, we study the steady flows to the compressible Euler-Poisson system for semiconductors with the nonzero angular velocity in a radially symmetric way in an annulus. The main purpose here is to elucidate the effect of the angular velocity in the structure of the steady flows. We show the well-posedness of all kinds of types of radially symmetric spiral flows including radial subsonic/supersonic/transonic flows, and further give a specific classification of the flow patterns under the assumption of various boundary conditions at the inner and the outer circle. Additionally, different from the purely radial case, the uniqueness of radial subsonic flow can not be obtained due to the nonlocal effect caused by the angular velocity, consequently we prove the uniqueness of the radial subsonic solution in the case without the semiconductor effect or with a small current assumption. Moreover, some new patterns of spiral flows with or without shock are observed, such as a smooth transonic flow and a supersonic-supersonic shock flow for a large relaxation time parameter. [ABSTRACT FROM AUTHOR]

For unipolar hydrodynamic model of semiconductor device represented by Euler-Poisson equations, when the doping profile is supersonic, and the boundary data are in subsonic region and supersonic region separately, the system possesses the shock transonic steady-states and the smooth transonic steady-states. In this paper we study the nonlinear structural stability and the linear dynamic instability of these steady transonic solutions. For any relaxation time: 0 < τ ≤ + ∞ , by means of elaborate singularity analysis, we first investigate the structural stability of the C 1 -smooth transonic steady-states, once the perturbations of the initial data and the doping profiles are small enough. We note that, when the C 1 -smooth transonic steady-states pass through the sonic line, they produce singularities for the system, and cause some essential difficulty in the proof of structural stability. Moreover, when the relaxation time is large enough τ ≫ 1 , under the condition that the electric field is positive at the shock location, we prove that the transonic shock steady-states are structurally stable with respect to small perturbations of the supersonic doping profile. Furthermore, we show the linearly dynamic instability for these transonic shock steady-states provided that the electric field is suitable negative. The proofs for the structural stability results are based on singularity analysis, a monotonicity argument on the shock position and the downstream density, and the stability analysis of supersonic and subsonic solutions. The linear dynamic instability of the steady transonic shock for Euler-Poisson equations can be transformed to the ill-posedness of a free boundary problem for the Klein-Gordon equation. By using a nontrivial transformation and the shooting method, we prove that the linearized problem has a transonic shock solution with exponential growths. These results enrich and develop the existing studies. [ABSTRACT FROM AUTHOR]

In this paper, we study the well-posedness, ill-posedness and uniqueness of the stationary 3-D radial solution to the bipolar isothermal hydrodynamic model for semiconductors. The density of electron is imposed with sonic boundary and interiorly subsonic case and the density of hole is fully subsonic case. It is difficult to estimate the upper and lower bounds of the holes due to the coupling of electrons and holes and the degeneracy of electrons at the boundary. Thus, we use the topological degree method to prove the well-posedness of solution. We prove the ill-posedness of subsonic solution under some conditions by direct mathematical analysis and contradiction method. The ill-posedness property shows significant difference to the unipolar model. Another highlight of this paper is the application of specific energy method to obtain the uniqueness of solution in two cases. One case is the relaxation time τ = ∞ , namely, the pure Euler-Poisson case; the other case is j τ ≪ 1 , which means that, when the current flow is sufficiently small and the relaxation time is sufficiently large both can satisfy. [ABSTRACT FROM AUTHOR]

As shown in [17,18] , for the hydrodynamic model of semiconductors represented by Euler-Poisson equations with sonic boundary and subsonic/supersonic doping profile, the structure of stationary solutions are very complicated. It may possess various solutions like subsonic/supersonic/transonic flows. In this paper, we consider a more challenging case where the doping profile is transonic, which is categorized into two types: subsonic-dominated and supersonic-dominated. In the subsonic-dominated case, we show that the system has a unique interior subsonic solution, at least one interior supersonic solution and infinitely many transonic solutions under the suitable assumptions. However, the difference with the case of subsonic doping profile is that the interior subsonic solution and interior supersonic solution may not exist in special cases when the relaxation time is small. In the supersonic-dominated case, the non-existence and existence of all types of solutions are also obtained. The approach adopted is the technical compactness analysis combining the Green's function method. Here, the results obtained perfectly develop the existing studies. [ABSTRACT FROM AUTHOR]

The initial boundary value problem for the compressible barotropic Navier–Stokes equations is investigated in the case that the initial density has a jump discontinuity across an interior closed curve in two-dimensional bounded domain. If the initial data is a small perturbation of the constant state and the interior closed curve is near a circle inside the domain, the global existence and large time behavior of the piecewise strong solution is shown, in particular, the jump of the fluid density across the convecting curve decays exponentially in time. [ABSTRACT FROM AUTHOR]