Sobolev spaces on non-Lipschitz subsets of Rn with application to boundary integral equations on fractal screens

We study properties of the classical fractional Sobolev spaces on non-Lipschitz subsets of Rn. We investigate the extent to which the properties of these spaces, and the relations between them, that hold in the well-studied case of a Lipschitz open set, generalise to non-Lipschitz cases. Our motivation is to develop the functional analytic framework in which to formulate and analyse integral equations on non-Lipschitz sets. In particular we consider an application to boundary integral equations for wave scattering by planar screens that are non-Lipschitz, including cases where the screen is fractal or has fractal boundary

Lipid-Induced Peroxidation in the Intestine Is Involved in Glucose Homeostasis Imbalance in Mice

BACKGROUND: Daily variations in lipid concentrations in both gut lumen and blood are detected by specific sensors located in the gastrointestinal tract and in specialized central areas. Deregulation of the lipid sensors could be partly involved in the dysfunction of glucose homeostasis. The study aimed at comparing the effect of Medialipid (ML) overload on insulin secretion and sensitivity when administered either through the intestine or the carotid artery in mice. METHODOLOGY/PRINCIPAL FINDINGS: An indwelling intragastric or intracarotid catheter was installed in mice and ML or an isocaloric solution was infused over 24 hours. Glucose and insulin tolerance and vagus nerve activity were assessed. Some mice were treated daily for one week with the anti-lipid peroxidation agent aminoguanidine prior to the infusions and tests. The intestinal but not the intracarotid infusion of ML led to glucose and insulin intolerance when compared with controls. The intestinal ML overload induced lipid accumulation and increased lipid peroxidation as assessed by increased malondialdehyde production within both jejunum and duodenum. These effects were associated with the concomitant deregulation of vagus nerve. Administration of aminoguanidine protected against the effects of lipid overload and normalized glucose homeostasis and vagus nerve activity. CONCLUSIONS/SIGNIFICANCE: Lipid overload within the intestine led to deregulation of gastrointestinal lipid sensing that in turn impaired glucose homeostasis through changes in autonomic nervous system activity

Lawson criterion for ignition exceeded in an inertial fusion experiment

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37 MJ of fusion for 1.92 MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion

Self-gravity in curved mesh elements

The local character of self-gravity along with the number of spatial dimensions are critical issues when computing the potential and forces inside massive systems like stars and disks. This appears from the discretisation scale where each cell of the numerical grid is a self-interacting body in itself. There is apparently no closed-form expression yet giving the potential of a three-dimensional homogeneous cylindrical or spherical cell, in contrast with the Cartesian case. By using Green's theorem, we show that the potential integral for such polar-type 3D sectors -- initially, a volume integral with singular kernel -- can be converted into a regular line-integral running over the lateral contour, thereby generalising a formula already known under axial symmetry. It therefore is a step towards the obtention of another potential/density pair. The new kernel is a finite function of the cell's shape (with the simplest form in cylindrical geometry), and mixes incomplete elliptic integrals, inverse trigonometric and hyperbolic functions. The contour integral is easy to compute; it is valid in the whole physical space, exterior and interior to the sector itself and works in fact for a wide variety of shapes of astrophysical interest (e.g. sectors of tori or flared discs). This result is suited to easily providing reference solutions, and to reconstructing potential and forces in inhomogeneous systems by superposition. The contour integrals for the 3 components of the acceleration vector are explicitely given