Effective equations for two-phase flow in porous media: the effect of trapping on the microscale

In this article, we consider a two-phase flow model in a heterogeneous porous column. The medium consists of many homogeneous layers that are perpendicular to the flow direction and have a periodic structure resulting in a one-dimensional flow. Trapping may occur at the interface between a coarse and a fine layer. Assuming that capillary effects caused by the surface tension are in balance with the viscous effects, we apply the homogenization approach to derive an effective (upscaled) model. Numerical experiments show a good agreement between the effective solution and the averaged solution taking into account the detailed microstructure.     

Optimization of the deflagration to detonation transition: reduction of length and time of transition

The aim of this experimental investigation is the study of Deflagration to Detonation Transition (DDT) in tubes in order to (i) reduce both run-up distance and time of transition (L _DDT and t _DDT) in connection with Pulsed Detonation Engine applications and to (ii) attempt to scale L _DDT with λ_CJ (the detonation cellular structure width). In DDT, the production of turbulence during the long flame run-up can lead to L _DDT values of several meters. To shorten L _DDT, an experimental set-up is designed to quickly induce highly turbulent initial flow. It consists of a double chamber terminated with a perforated plate of high Blockage Ratio (BR) positioned at the beginning of a 26 mm inner diameter tube containing a “Shchelkin spiral” of BR ≈ 0.5. The study involves stoichiometric reactive mixtures of H₂, CH₄, C₃H₈, and C₂H₄ with oxygen and diluted with N₂ in order to obtain the same cell width λ_CJ≈10 mm at standard conditions. The results show that a shock-flame system propagating with nearly the isobaric speed of sound of combustion products, called the choking regime, is rapidly obtained. This experimental set-up allows a L _DDT below 40 cm for the mixtures used and a ratio L _DDT/λ_CJ ranging from 23 to 37. The transition distance seems to depend on the reduced activation energy (E _a/RT _c) and on the normalized heat of reaction (Q/a ₀ ²). The higher these quantities are, the shorter the ratio L _DDT/λ_CJ is. PACS 47.40.Rs · 47.60.+i · 47.70.Pq · 47.80.CbThis paper was based on the work that was presented at the 19th International Colloquium on the Dynamics of Explosions and Reactive Systems, Hakone, Japan, July 27–August 1, 2003.     

A II1 Factor Approach to the Kadison–Singer Problem

We show that the Kadison–Singer problem, asking whether the pure states of the diagonal subalgebra \({\ell^\infty\mathbb{N}\subset \mathcal{B}(\ell^2\mathbb{N})}\) have unique state extensions to \({\mathcal{B}(\ell^2\mathbb{N})}\) , is equivalent to a similar statement in II₁ factor framework, concerning the ultrapower inclusion \({D^\omega \subset R^\omega}\) , where D is the Cartan subalgebra of the hyperfinite II₁ factor R (i.e., a maximal abelian *-subalgebra of R whose normalizer generates R, e.g. \({D=L^\infty([0, 1]^{\mathbb{Z}}) \subset L^\infty([0,1]^{\mathbb{Z}} \rtimes \mathbb{Z} = R)}\) , and ω is a free ultrafilter. Instead, we prove here that if A is any singular maximal abelian *-subalgebra of R (i.e., whose normalizer consists of the unitary group of A, e.g. \({A=L(\mathbb{Z})\subset L^\infty([0,1]^\mathbb{Z})\rtimes \mathbb{Z}=R}\) ), then the inclusion \({A^\omega \subset R^\omega}\) does satisfy the Kadison–Singer property.     

Piezoelectric non-linearity in PbSc0.5Ta0.5O3 thin films

Epitaxial (001)-oriented PbSc_0.5Ta_0.5O₃ (PST) thin films were deposited by pulsed laser deposition. Local piezoelectric investigations performed by piezoelectric force microscopy show a dual slope for the piezoelectric coefficient. A piezoelectric coefficient of 3 pm/V was observed at voltages up to 0.8 V. However, at voltages above 0.8 V, there is a steep increase in piezoelectric coefficient mounting to 23.2 pm/V. This nonlinear piezoelectric response was observed to be irreversible in nature. In order to better understand this nonlinear behavior, voltage dependent dielectric constant measurements were performed. These confirmed that the piezoelectric non-linearity is indeed a manifestation of a dielectric non-linearity. In contrast to classical ferroelectric systems, the observed dielectric non-linearity in this relaxor material cannot be explained by the Rayleigh model. Thus the dielectric non-linearity in the PST films is tentatively explained as a manifestation of a percolation of the polar nano regions.     

Levi Harmonic Maps of Contact Riemannian Manifolds

We study Levi harmonic maps, i.e., C ^∞ solutions f:M→M′ to \(\tau_{\mathcal{H}} (f) \equiv \operatorname{trace}_{g} ( \varPi_{\mathcal{H}}\beta_{f} ) = 0\) , where (M,η,g) is an (almost) contact (semi) Riemannian manifold, M′ is a (semi) Riemannian manifold, β _f is the second fundamental form of f, and \(\varPi_{\mathcal{H}} \beta_{f}\) is the restriction of β _f to the Levi distribution \({\mathcal{H}} = \operatorname{Ker}(\eta)\) . Many examples are exhibited, e.g., the Hopf vector field on the unit sphere S ²ⁿ⁺¹, immersions of Brieskorn spheres, and the geodesic flow of the tangent sphere bundle over a Riemannian manifold of constant curvature 1 are Levi harmonic maps. A CR map f of contact (semi) Riemannian manifolds (with spacelike Reeb fields) is pseudoharmonic if and only if f is Levi harmonic. We give a variational interpretation of Levi harmonicity. Any Levi harmonic morphism is shown to be a Levi harmonic map.     

Fluctuation forces in a three-layer medium with rough boundaries. IV. Calculations in the second order of perturbation theory (Casimir range)

The perturbation theory developed in the previous paper of the series is used to calculate the correction to the Casimir force due to the surface roughness.Scientific Council on the Problem Complex Kibernetika, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 92, No. 1, pp. 113–118, July, 1992.     

A new constraint qualification for the formula of the subdifferential of composed convex functions in infinite dimensional spaces

In this paper we work in separated locally convex spaces where we give equivalent statements for the formulae of the conjugate function of the sum of a convex lower‐semicontinuous function and the precomposition of another convex lower‐semicontinuous function which is also K ‐increasing with a K ‐convex K ‐epi‐closed function, where K is a nonempty closed convex cone. These statements prove to be the weakest constraint qualifications given so far under which the formulae for the subdifferential of the mentioned sum of functions are valid. Then we deliver constraint qualifications inspired from them that guarantee some conjugate duality assertions. Two interesting special cases taken from the literature conclude the paper. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simple models of firms emergence

We present a dynamical model of the emergence of firms as opposed to a flat labour market where entrepreneurs would recruit workers for each business opportunity. The model uses a preferential choice of partners based on previous collaborations experience. A sharp transition in the parameter space separates an ordered regime, where preferential links establish, from a disordered regime corresponding to a fast turnover of employees.