On the particle paths and the stagnation points in small-amplitude deep-water waves

In order to obtain quite precise information about the shape of the particle paths below small-amplitude gravity waves travelling on irrotational deep water, analytic solutions of the nonlinear differential equation system describing the particle motion are provided. All these solutions are not closed curves. Some particle trajectories are peakon-like, others can be expressed with the aid of the Jacobi elliptic functions or with the aid of the hyperelliptic functions. Remarks on the stagnation points of the small-amplitude irrotational deep-water waves are also made.Comment: to appear in J. Math. Fluid Mech. arXiv admin note: text overlap with arXiv:1106.382

Substitution induced pinning in MgB_2 superconductor doped with SiC nano-particles

By doping MgB_2 superconductor with SiC nano-particles, we have successfully introduced pinning sites directly into the crystal lattice of MgB_2 grains (intra-grain pinning). It became possible due to the combination of counter-balanced Si and C co-substitution for B, leading to a large number of intra-granular dislocations and the dispersed nano-size impurities induced by the substitution. The magnetic field dependence of the critical current density was significantly improved in a wide temperature range, whereas the transition temperature in the sample MgB_2(SiC)_x having x = 0.34, the highest doping level prepared, dropped only by 2.6 K.Comment: 4 pages, 6 figure

PMN transendothelial migration decreases nuclear NFκB in IL-1β–activated endothelial cells: role of PECAM-1

During the systemic inflammatory response, circulating cytokines interact with the vascular endothelium, resulting in activation and nuclear accumulation of the nuclear transcription factor, nuclear factor kappa B (NFκB). In turn, NFκB transactivates relevant proinflammatory genes, resulting in an amplification of the inflammatory response. Because this scenario is potentially detrimental to the host, mechanisms exist to limit this amplification. Using an in vitro system that mimics the vascular–interstitial interface during inflammation (cell culture inserts), we provide evidence for the existence of a novel negative feedback mechanism on NFκB activity. We show that the interleukin 1β–induced accumulation of nuclear NFκB in human umbilical vein endothelial cell monolayers is dramatically reduced when polymorphonuclear leukocytes (PMN) are allowed to migrate across these monolayers. This effect does not appear to be due to PMN-derived elastase or nitric oxide. Fixed PMN (adhere but do not migrate) did not affect nuclear NFκB. Furthermore, cross-linking of platelet-endothelial cell adhesion molecule-1 (PECAM-1), but not intercellular adhesion molecule-1, reduces human umbilical vein endothelial cell nuclear NFκB induced by interleukin 1β. Finally, interaction of PMN with PECAM-1–deficient endothelial cells does not reduce nuclear NFκB. These observations indicate that engagement of PECAM-1 by emigrating PMN is a pivotal event in this negative feedback on NFκB activity

Superconductivity, critical current density, and flux pinning in MgB_{2-x}(SiC)_{x/2} superconductor after SiC nanoparticle doping

We investigated the effect of SiC nano-particle doping on the crystal lattice structure, critical temperature T_c, critical current density J_c, and flux pinning in MgB_2 superconductor. A series of MgB_{2-x}(SiC)_{x/2} samples with x = 0 to 1.0 were fabricated using in-situ reaction process. The contraction of the lattice and depression of T_c with increasing SiC doping level remained rather small due to the counter-balanced effect of Si and C co-doping. The high level Si and C co-doping allowed the creation of intra-grain defects and highly dispersed nano-inclusions within the grains which can act as effective pinning centers for vortices, improving J_c behavior as a function of the applied magnetic field. The enhanced pinning is mainly attributable to the substitution-induced defects and a local structure fluctuations within grains. A pinning mechanism is proposed to account for different contributions of different defects in MgB_{2-x}(SiC)_{x/2} superconductors.Comment: 7 pages, 8 figure

Learning 3D Human Pose from Structure and Motion

3D human pose estimation from a single image is a challenging problem, especially for in-the-wild settings due to the lack of 3D annotated data. We propose two anatomically inspired loss functions and use them with a weakly-supervised learning framework to jointly learn from large-scale in-the-wild 2D and indoor/synthetic 3D data. We also present a simple temporal network that exploits temporal and structural cues present in predicted pose sequences to temporally harmonize the pose estimations. We carefully analyze the proposed contributions through loss surface visualizations and sensitivity analysis to facilitate deeper understanding of their working mechanism. Our complete pipeline improves the state-of-the-art by 11.8% and 12% on Human3.6M and MPI-INF-3DHP, respectively, and runs at 30 FPS on a commodity graphics card.Comment: ECCV 2018. Project page: https://www.cse.iitb.ac.in/~rdabral/3DPose

Generalized KdV Equation for Fluid Dynamics and Quantum Algebras

We generalize the non-linear one-dimensional equation of a fluid layer for any depth and length as an infinite order differential equation for the steady waves. This equation can be written as a q-differential one, with its general solution written as a power series expansion with coefficients satisfying a nonlinear recurrence relation. In the limit of long and shallow water (shallow channels) we reobtain the well known Korteweg-de-Vries equation together with its single-soliton solution.Comment: 17 pages, Latex, PACS: 47.20.Ky, 43.25.Rq, 47.35.+i, 03.40.Kf, 43.25.Fe, 02.20.Tw, MSC: 16W30, 17B37, 81R50, 35Q51, 34B15, 34L30, 76E3

Manufacture of micro-electro-mechanical-system using sacrificial layer made of silicon, useful for micro-electro-mechanical-system device architecture, e.g. radio-frequency capacitive switch and current switch

NOVELTY - A micro-electro-mechanical-system (MEMS) is manufactured by the use of a sacrificial layer that is made of silicon. USE - The invention is used in surface micromachining for the manufacture of a MEMS containing a suspended metal layer or MEMS device architecture. MEMS device is a suspended gate metal oxide semiconductor field effect transistor (SG-MOSFET). It is used as radio-frequency capacitive switch, current switch, radio-frequency tuneable capacitor, magnetic field sensor, accelerometer, and pressure sensor. (all claimed

Non-invasive methods applied for complex signals

This paper presents the application of a novel algorithm on virtually generated data from patients during anesthesia. Realistic artefacts are simulated in order to validate the usefulness of the proposed methods in separating the signal components: biological trend and artefacts. The results show that the proposed new algorithm can be successfully employed on biological signals to dynamically extract information and distil useful parameters for clinical evaluation

Equations of the Camassa-Holm Hierarchy

The squared eigenfunctions of the spectral problem associated with the Camassa-Holm (CH) equation represent a complete basis of functions, which helps to describe the inverse scattering transform for the CH hierarchy as a generalized Fourier transform (GFT). All the fundamental properties of the CH equation, such as the integrals of motion, the description of the equations of the whole hierarchy, and their Hamiltonian structures, can be naturally expressed using the completeness relation and the recursion operator, whose eigenfunctions are the squared solutions. Using the GFT, we explicitly describe some members of the CH hierarchy, including integrable deformations for the CH equation. We also show that solutions of some $(1+2)$ - dimensional members of the CH hierarchy can be constructed using results for the inverse scattering transform for the CH equation. We give an example of the peakon solution of one such equation.Comment: 10 page

Lines on projective varieties and applications

The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined by quadratic equations the base locus of the projective second fundamental form at a general point coincides, as a scheme, with the variety of lines. The second part concerns the problem of extending embedded projective manifolds, using the geometry of the variety of lines. Some applications to the case of homogeneous manifolds are included.Comment: 15 pages. One example removed; one remark and some references added; typos correcte