Justification of the kinematic assumptions for thin-walled rods with shallow profile

In this Note we present a justification of the kinematic assumptions for thin-walled rods with shallow profile. These assumptions are fundamental to writing the one-dimensional equilibrium equations for such structures. The obtained kinematics are different from the Vlassov case, which is only valid for strongly curved profiles. They are also different from the that classically used in shell theory. The justification given in this Note is based on an asymptotic approach. To cite this article: L. Grillet et al., C. R. Mecanique 333 (2005).     

Treatment of nonlinear terms in the numerical solution of partial differential equations for multiphase flow in porous media

Simultaneous flow of two or three immiscible fluids in porous media is modelled by a system of coupled, nonlinear partial differential equations. These equations are reduced to a system of nonlinear algebraic equations through the use of finite-difference approximations for derivatives. Several types of nonlinearities requiring careful analysis exist in this model. Here, we present a systematic study of all available, and some new, methods for the treatment of nonlinearitics in this model. It is believed that the solution techniques presented here may also prove useful for other strongly nonlinear partial differential equations.     

Subgrid models preserving the symmetry group of the Navier–Stokes equations

In order to preserve the physical properties of the flow (scaling laws, conservation laws, …) during the simulation, a class of subgrid models respecting the symmetry group of the Navier–Stokes equations is built. The class is then refined such that models satisfy the second law of thermodynamics and are suited to take into account the inverse energy cascade. A simple model belonging to the class is tested and a better result than those provided by Smagorinsky and dynamic models is obtained. To cite this article: D. Razafindralandy, A. Hamdouni, C. R. Mecanique 333 (2005).     

Contact between the β1 and β2 Segments of α‐Synuclein that Inhibits Amyloid Formation

Conversion of the intrinsically disordered protein α‐synuclein (α‐syn) into amyloid aggregates is a key process in Parkinson’s disease. The sequence region 35–59 contains β‐strand segments β1 and β2 of α‐syn amyloid fibril models and most disease‐related mutations. β1 and β2 frequently engage in transient interactions in monomeric α‐syn. The consequences of β1–β2 contacts are evaluated by disulfide engineering, biophysical techniques, and cell viability assays. The double‐cysteine mutant α‐synCC, with a disulfide linking β1 and β2, is aggregation‐incompetent and inhibits aggregation and toxicity of wild‐type α‐syn. We show that α‐syn delays the aggregation of amyloid‐β peptide and islet amyloid polypeptide involved in Alzheimer’s disease and type 2 diabetes, an effect enhanced in the α‐synCC mutant. Tertiary interactions in the β1–β2 region of α‐syn interfere with the nucleation of amyloid formation, suggesting promotion of such interactions as a potential therapeutic approach.     

Real-time tracking of hydrogen peroxide secreted by live cells using MnO2 nanoparticles intercalated layered doubled hydroxide nanohybrids

We report a facile and green method for the fabrication of new type of electrocatalysts based on MnO₂ nanoparticles incorporated on MgAl LDH P-type semiconductive channel and explore its practical applications as high-performance electrode materials for electrochemical biosensor. A series of MgAl layered doubled hydroxide (LDH) nanohybrids with fixed Mg/Al (M²⁺/M³⁺ atomic ratio of 3) and varied amount of MnCl₂.4H₂O are fabricated by a facile co-precipitation method. This approach demonstrates the combination of distinct properties including excellent intercalation features of LDH for entrapping nanoparticles and high loading of MnO₂ nanoparticles in the host layers of LDH. Among all samples, Mn5–MgAl with 0.04% loaded manganese has a good crystalline morphology. A well-dispersed MnO₂ nanoparticles encapsulated into the host matrix of hydrotalcite exhibit enhanced electrocatalytic activity towards the reduction of H₂O₂ as well as excellent stability, selectivity and reproducibility due to synergistic effect of good catalytic ability of MnO₂ and conductive MgAl LDH. Glass carbon electrode (GCE) modified with Mn5–MgAl possesses a wide linear range of 0.05–78 mM, lowest detection limit 5 μM (S/N = 3) and detection sensitivity of 0.9352 μAmM⁻¹. This outstanding performance enables it to be used for real-time tracking of H₂O₂ secreted by live HeLa cells. This work may provide new insight in clinical diagnosis, on-site environmental analysis and point of care testing devices.     

Some characterizations of almost limited operators

In this paper we give several characterizations of almost limited operators. Mainly, it is proved that an operator \(T:X\rightarrow E\) from a Banach space X into a \(\sigma \)-Dedekind complete Banach lattice E is almost limited if and only if \(\left\| T^{*}\left( f_{n}\right) \right\| \rightarrow 0\) for every positive weak\(^{*}\) null sequence \(\left( f_{n}\right) \) of \(E^{*}\). Moreover, we present some interesting connections between almost limited, almost Dunford–Pettis and limited operators.     

The behavior of a gas bubble in a shock wave

The phenomenon of thermal relaxation of the gas bubbles in a fluid behind a shock front is analyzed. The approach to solving the problem of heat transfer between a gas bubble and a fluid developed by the author is used to obtain a solution describing the initial stage of bubble collapse behind the shock front.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 187–189, September–October, 1993.     

Exponential Behavior of Solutions to Stochastic Integrodifferential Equations with Distributed Delays

In this work, we study the existence, uniqueness, and exponential asymptotic behavior of mild solutions to stochastic integrodifferential delay evolution equations. We assume that the non-delay part generates a C₀-semigroup.