Global well-posedness for a slightly supercritical surface quasi-geostrophic equation

We use a nonlocal maximum principle to prove the global existence of smooth solutions for a slightly supercritical surface quasi-geostrophic equation. By this we mean that the velocity field $u$ is obtained from the active scalar $\theta$ by a Fourier multiplier with symbol $i k^\perp |k|^{-1} m(k|)$, where $m$ is a smooth increasing function that grows slower than $\log \log |k|$ as $|k|\rightarrow \infty$.Comment: 11 pages, second version with slightly stronger resul

Vortex axisymmetrization, inviscid damping, and vorticity depletion in the linearized 2D Euler equations

Coherent vortices are often observed to persist for long times in turbulent 2D flows even at very high Reynolds numbers and are observed in experiments and computer simulations to potentially be asymptotically stable in a weak sense for the 2D Euler equations. We consider the incompressible 2D Euler equations linearized around a radially symmetric, strictly monotone decreasing vorticity distribution. For sufficiently regular data, we prove the inviscid damping of the θ-dependent radial and angular velocity fields with the optimal rates ∥ur(t)∥≲⟨t⟩−1 and ∥∥uθ(t)∥∥≲⟨t⟩−2 in the appropriate radially weighted L2 spaces. We moreover prove that the vorticity weakly converges back to radial symmetry as t→∞, a phenomenon known as vortex axisymmetrization in the physics literature, and characterize the dynamics in higher Sobolev spaces. Furthermore, we prove that the θ-dependent angular Fourier modes in the vorticity are ejected from the origin as t→∞, resulting in faster inviscid damping rates than those possible with passive scalar evolution. This non-local effect is called vorticity depletion. Our work appears to be the first to find vorticity depletion relevant for the dynamics of vortices

Revival of the side-to-side approach for distal coronary anastomosis

Side-to-side anastomosis was employed by just ten proportional stitches while performing distal anastomosis during coronary artery surgery. This technique is simple and quick. Here this simple technique is described in detail and the postoperative status of grafted conduits is reported

On the supercritically diffusive magneto-geostrophic equations

We address the well-posedness theory for the magento-geostrophic equation, namely an active scalar equation in which the divergence-free drift velocity is one derivative more singular than the active scalar. In the presence of supercritical fractional diffusion given by (-\Delta)^\gamma, where 0<\gamma<1, we discover that for \gamma>1/2 the equations are locally well-posed, while for \gamma<1/2 they are ill-posed, in the sense that there is no Lipschitz solution map. The main reason for the striking loss of regularity when \gamma goes below 1/2 is that the constitutive law used to obtain the velocity from the active scalar is given by an unbounded Fourier multiplier which is both even and anisotropic. Lastly, we note that the anisotropy of the constitutive law for the velocity may be explored in order to obtain an improvement in the regularity of the solutions when the initial data and the force have thin Fourier support, i.e. they are supported on a plane in frequency space. In particular, for such well-prepared data one may prove the local existence and uniqueness of solutions for all values of \gamma \in (0,1).Comment: 24 page

On the analyticity and Gevrey class regularity up to the boundary for the Euler Equations

We consider the Euler equations in a three-dimensional Gevrey-class bounded domain. Using Lagrangian coordinates we obtain the Gevrey-class persistence of the solution, up to the boundary, with an explicit estimate on the rate of decay of the Gevrey-class regularity radius

On the Identification of the Synchronous Machine Parameters Using Standstill DC Decay Test.

This paper presents a refined approach to obtain the parameters of synchronous machine equivalent circuits from standstill DC decay tests. A dedicated program for the time- constants and reactances identification was developed and applied for both d- and q- axis, as well as for a random position of the rotor, with good results

Nonlinear Instability for the Critically Dissipative Quasi-Geostrophic Equation

We prove that linear instability implies non-linear instability in the energy norm for the critically dissipative quasi-geostrophic equation.Comment: 16 pages, corrected typos, a global bound that was obtained for the unforced equation by Kiselev-Nazarov-Volberg obtained for the forced equation and utilized in the paper

Contract Farming, Ecological Change and the Transformations of Reciprocal Gendered Social Relations in Eastern India

Debates on gender and the commodification of land highlight the loss of land rights, intensification of demands on women’s labour, and decline in their decision-making control. Supported by ‘extra-economic forces’ of religious nationalism (Hindutva), such neoliberal interventions are producing new gender ideologies involving a subtle shift from relations of reciprocity to those of subordination. Using data from fine grained fieldwork in Koraput district, Odisha, we analyse the tensions and transformations created jointly by corporate interventions (contract farming of eucalyptus by the paper industry) and religious nationalism in the local landscape. We examine how these phenomena are reshaping relations of asymmetric mutuality between nature and society, and between men and women