Lipschitz regularity for integro-differential equations with coercive hamiltonians and application to large time behavior

In this paper, we provide suitable adaptations of the "weak version of Bernstein method" introduced by the first author in 1991, in order to obtain Lipschitz regularity results and Lipschitz estimates for nonlinear integro-differential elliptic and parabolic equations set in the whole space. Our interest is to obtain such Lipschitz results to possibly degenerate equations, or to equations which are indeed "uniformly el-liptic" (maybe in the nonlocal sense) but which do not satisfy the usual "growth condition" on the gradient term allowing to use (for example) the Ishii-Lions' method. We treat the case of a model equation with a superlinear coercivity on the gradient term which has a leading role in the equation. This regularity result together with comparison principle provided for the problem allow to obtain the ergodic large time behavior of the evolution problem in the periodic setting

Viscous Boundary Value Problems for Symmetric Systems with Variable Multiplicities

Extending investigations of M\'etivier&Zumbrun in the hyperbolic case, we treat stability of viscous shock and boundary layers for viscous perturbations of multidimensional hyperbolic systems with characteristics of variable multiplicity, specifically the construction of symmetrizers in the low-frequency regime where variable multiplicity plays a role. At the same time, we extend the boundary-layer theory to ``real'' or partially parabolic viscosities, Neumann or mixed-type parabolic boundary conditions, and systems with nonconservative form, in addition proving a more fundamental version of the Zumbrun--Serre--Rousset theorem, valid for variable multiplicities, characterizing the limiting hyperbolic system and boundary conditions as a nonsingular limit of a reduced viscous system. The new effects of viscosity are seen to be surprisingly subtle; in particular, viscous coupling of crossing hyperbolic modes may induce a destabilizing effect. We illustrate the theory with applications to magnetohydrodynamics

Regularity Results and Large Time Behavior for Integro-Differential Equations with Coercive Hamiltonians

In this paper we obtain regularity results for elliptic integro-differential equations driven by the stronger effect of coercive gradient terms. This feature allows us to construct suitable strict supersolutions from which we conclude H\"older estimates for bounded subsolutions. In many interesting situations, this gives way to a priori estimates for subsolutions. We apply this regularity results to obtain the ergodic asymptotic behavior of the associated evolution problem in the case of superlinear equations. One of the surprising features in our proof is that it avoids the key ingredient which are usually necessary to use the Strong Maximum Principle: linearization based on the Lipschitz regularity of the solution of the ergodic problem. The proof entirely relies on the H\"older regularity

Cavitation inception in fast startup

The start-up of rocket engine turbopumps is generally performed only in a few seconds. It implies that these pumps reach their nominal operating conditions after only a few rotations. During these first rotations of the blades, the flow evolution in the pump is governed by transient phenomena, based mainly on the flow rate and rotation speed evolution. These phenomena progressively become negligible when the steady behaviour is reached. The pump transient behaviour induces significant pressure fluctuations which may result in partial flow vaporization, i.e. cavitation. An existing experimental test rig has been updated in the LML laboratory (Lille, France) for the start-ups of a centrifugal pump. The study focuses on cavitation induced during the pump start-up. Instantaneous measurement of torque, mass flow rate, inlet and outlet unsteady pressures, and pump rotation velocity enable to characterize the pump behaviour during rapid starting periods

RNAi efficiency, systemic properties, and novel delivery methods for pest insect control : what we know so far

In recent years, the research on the potential of using RNA interference (RNAi) to suppress crop pests has made an outstanding growth. However, given the variability of RNAi efficiency that is observed in many insects, the development of novel approaches toward insect pest management using RNAi requires first to unravel factors behind the efficiency of dsRNA-mediated gene silencing. In this review, we explore essential implications and possibilities to increase RNAi efficiency by delivery of dsRNA through non-transformative methods. We discuss factors influencing the RNAi mechanism in insects and systemic properties of dsRNA. Finally, novel strategies to deliver dsRNA are discussed, including delivery by symbionts, plant viruses, trunk injections, root soaking, and transplastomic plants

Enabling self, intimacy and a sense of home in dementia

Design and digital technologies to support a sense of self and human relationships for people living with dementia are both urgently needed. We present an enquiry into design for dementia facilitated by a public art commission for an adult mental health unit in a hospital in the UK. The interactive art piece was informed by the notion of personhood in dementia that foregrounds the person's social being and interpersonal relationships as sites where self is maintained and constructed. How clients, clients' family members and staff used the piece is reported and insights related to the notions of home, intimacy, possessions and self are presented. The art piece served as window on both dementia and the institution leading to a number of insights and implications for design