Ionel Ciuperca

The Effect of Periodic Textures on the Static Characteristics of Thrust Bearings

Given a bearing of some specified macroscopic shape, what is the effect of texturing its surfaces uniformly? Experimental and numerical investigations on this question have recently been pursued, which we complement here with a mathematical analysis based on a seemingly novel combination of homogenization techniques and perturbation analysis. The flow is assumed governed by the Reynolds equation, with cavitation effects disregarded, and the texture length is assumed much smaller than the bearings length. The results, which hold true for small-amplitude periodic textures and in the limit of vanishing period, can be summarized as follows: (a) The texture that maximizes the load for a given minimum clearance is no texture at all (i.e., the untextured shape); and (b) the texture that minimizes the friction coefficient is again the untextured shape.

Approximate Transmission Conditions through a rough thin layer. The case of the periodic roughness

We study the behavior of the steady-state voltage potentials in a material composed by a bidimensional medium surrounded by a rough thin layer and embedded in an ambient medium. The roughness of the layer is supposed to be

Asymptotic behaviour of solutions of lubrication problem in a thin domain with a rough boundary and Tresca fluid-solid interface law

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THE STEADY STATE CONFIGURATIONAL DISTRIBUTION DIFFUSION EQUATION OF THE STANDARD FENE DUMBBELL POLYMER MODEL: EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR ARBITRARY VELOCITY GRADIENTS

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Existence, uniqueness, and homogenization of the second order slip Reynolds equation

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The FENE Dumbbell Polymer Model: Existence and Uniqueness of Solutions for the Momentum Balance Equation

beeing the small thickness of the layer. We build approximate transmission conditions in order to replace the rough thin layer by these conditions on the boundary of the interior material. This paper extends previous works of the third author, in which the layer had constant or weakly oscillating thickness.

Existence and uniqueness results for the Doi–Edwards polymer melt model: the case of the (full) nonlinear configurational probability density equation

We study the asymptotic behavior of the solution of a Stokes flow in a thin domain, with a thickness of order e, and a rough surface. The roughness is defined by a quasi-periodic function with period e. We suppose that the flow is subject to a Tresca fluid-solid interface condition. We prove a new result on the lower-semicontinuity for the two-scale convergence, which allows us to obtain rigorously the limit problem and to establish the uniqueness of its solution.

On the Existence of Solutions of Equilibria in Lubricated Journal Bearings

The configurational distribution function, solution of an evolution (diffusion) equation of the Fokker-Planck-Smoluchowski type, is (at least part of) the corner stone of polymer dynamics: it is the key to calculating the stress tensor components. This can be reckoned from \cite{bird2}, where a wealth of calculation details is presented regarding various polymer chain models and their ability to accurately predict viscoelastic flows. One of the simplest polymer chain idealization is the Bird and Warners model of finitely extensible nonlinear elastic (FENE) chains. In this work we offer a proof that the steady state configurational distribution equation has unique solutions irrespective of the (outer) flow velocity gradients (i.e. for both slow and fast flows).

Fragmentation and monomer lengthening of rod-like polymers, a relevant model for prion proliferation

The decreasing of the distance between the head and the magnetic disk surface leads to a model of the behaviour of the air by using a modified Reynolds equation. The existence and the uniqueness of this stationary equation is, under some conditions on the data, proved using both fixed point and monotonicity techniques. Double-scale analysis allows us to obtain the associated homogenized equation.

LACK OF CONTACT IN A LUBRICATED SYSTEM

We consider the FENE dumbbell polymer model which is the coupling of the incompressible Navier-Stokes equations with the corresponding Fokker–Planck–Smoluchowski diffusion equation. We show global well-posedness in the case of a 2D bounded domain. We assume in the general case that the initial velocity is sufficiently small and the initial probability density is sufficiently close to the equilibrium solution; moreover an additional condition on the coefficients is imposed. In the corotational case, we only assume that the initial probability density is sufficiently close to the equilibrium solution.