Existence for evolutionary problems with linear growth by stability methods

We establish that solutions to the Cauchy–Dirichlet problem

${?}_{t}u?\mathrm{div}(D_{\xi }f(x,Du))=0$

for functionals $f:\mathrm{\Omega }\times {\mathbb{R}}^{N\times n}\to [0,\infty )$ of linear growth can be obtained as limits of solutions to flows with p-growth in the limit $p\downarrow 1$. The result can be interpreted on the one hand as a stability result. On the other hand it provides an existence result for general flows with linear growth.     

Effets d'une modulation en phase de température à la frontière sur l'instabilité convective d'une couche liquide viscoélastiqueEffects of a temperature modulation in phase at the frontier on the convective instability of a viscoelastic layer

In this Note we study the effects of the temperature modulation, applied at the horizontal boundaries, on the onset of convection of a horizontal liquid Maxwellian layer. It is assumed that the temperature imposed features a steady component and a time dependent component. To analyse the effect of the temperature modulation, the study is restricted to a linear stability analysis. Thus the Floquet theory and a technique of converting a boundary value problem to an initial value problem are used to solve the system of equations corresponding to the onset of convection. Results obtained may be used to characterize the influence of modulation effects and that of the viscoelastic nature of liquid on the critical Rayleigh number. To cite this article: B. Oukada et al., C. R. Mecanique 334 (2006).     

Tiling solutions for optimal biological sensing

Biological systems, from cells to organisms, must respond to the ever-changing environment in order to survive and function. This is not a simple task given the often random nature of the signals they receive, as well as the intrinsically stochastic, many-body and often self-organized nature of the processes that control their sensing and response and limited resources. Despite a wide range of scales and functions that can be observed in the living world, some common principles that govern the behavior of biological systems emerge. Here I review two examples of very different biological problems: information transmission in gene regulatory networks and diversity of adaptive immune receptor repertoires that protect us from pathogens. I discuss the trade-offs that physical laws impose on these systems and show that the optimal designs of both immune repertoires and gene regulatory networks display similar discrete tiling structures. These solutions rely on locally non-overlapping placements of the responding elements (genes and receptors) that, overall, cover space nearly uniformly.     

On the concept and existence of solutions for fractional impulsive systems with Hadamard derivatives

In this paper, a class of nonlinear fractional order differential impulsive systems with Hadamard derivative is discussed. First, a reasonable concept on the solutions of fractional impulsive Cauchy problems with Hadamard derivative and the corresponding fractional integral equations are established. Second, two fundamental existence results are presented by using standard fixed point methods. Finally, two examples are given to illustrate our theoretical results.     

Resonant equations with the Neumann p-Laplacian plus an indefinite potential

We consider a nonlinear Neumann problem driven by the p  -Laplacian plus an indefinite potential and a Carathéodory reaction which at ±∞ is resonant with respect to any nonprincipal variational eigenvalue of the differential operator. Using critical point theory and Morse theory (critical groups), we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign. In the process we prove some results of independent interest concerning the unique continuation property of eigenfunctions and the critical groups at infinity of a C¹$C^1$-functionals.     

Transient gas flow simulation using an Adaptive Method of LinesSimulation d'écoulements dans un gazoduc par la méthode adaptative de lignes

Designing natural gas pipelines to safely and efficiently handle unsteady flows, requires knowledge of pressure drop, flowrate and temperature distribution throughout the system. The accurate prediction of these parameters is essential in order to achieve optimum cumulative deliverability, and safe and reliable operation. An Adaptive Method of Lines algorithm is formulated for the solution of Euler system of equations, which fully simulates slow and fast transients. Two test cases present the improvement of the numerical solution from grid adaptation. Good results are obtained both for slow and fast transients simulations proving that the suggested numerical procedure is appropriate for such predictions. To cite this article: E. Tentis et al., C. R. Mecanique 331 (2003).     

α-三Ⅰ约束问题的形式解

提出了α-三Ⅰ约束问题,并在逻辑系统L~*和Luk中给出了这些问题的形式解,建立了这两个逻辑系统中三Ⅰ约束算法的形式推理机制,为α-三Ⅰ约束算法建立了严格的理论基础。     

Ternary mutual diffusion in aqueous (ethambutol dihydrochloride + hydrochloric acid) solutions

Ternary mutual diffusion coefficients measured by the Taylor dispersion method are reported for aqueous solutions of {ethambutol dihydrochloride (1) + HCl (2)} at 25 °C and various carrier solution compositions. Mutual diffusion coefficients estimated from limiting ionic conductivities using Nernst equations are used to discuss the composition dependence of the measured diffusion coefficients. ¹H NMR studies, combined with DFT calculations, confirm a fully extended conformation for the diprotonated form of the drug present under these conditions, and are consistent with an electrostatic mechanism for the strongly coupled diffusion of diprotonated ethambutol and HCl.     

Self-similar vortex reconnection

As shown by Crow in 1970, the evolution of two almost parallel vortex filaments with opposite circulation exhibits a long-wave instability. Ultimately, the symmetric mode increases its amplitude reconnecting both filaments and ending into the formation of an almost periodic structure of vortex rings. This is a universal process, which appears in a wide range of scales: from the vortex trails behind an airplane to a microscopic scale of superfluids and Bose–Einstein condensates. In this paper, I will focus on the vortex reconnection for the latter case by employing Gross–Pitaevskii theory. Essentially, I focus on the well-known laws of interaction and motion of vortex filaments. By means of numerical simulations, as well as theoretically, I show that a self-similar finite-time dynamics manifests near the reconnection time. A self-similar profile is selected showing excellent agreement with numerical simulations.     

A variational approach for a generalized emden-fowler equation

Existence of positive solutions of singular boundary value problems related to Emden-Fowler equation is proved. A general minimization theorem in Sobolev spaces is applied.