On the Reduction of Singularly-Perturbed Linear Differential Systems

In this article, we recover singularly-perturbed linear differential systems from their turning points and reduce the rank of the singularity in the parameter to its minimal integer value. Our treatment is Moser-based; that is to say it is based on the reduction criterion introduced for linear singular differential systems by Moser. Such algorithms have proved their utility in the symbolic resolution of the systems of linear functional equations, giving rise to the package ISOLDE, as well as in the perturbed algebraic eigenvalue problem. Our algorithm, implemented in the computer algebra system Maple, paves the way for efficient symbolic resolution of singularly-perturbed linear differential systems as well as further applications of Moser-based reduction over bivariate (differential) fields.Comment: Keywords: Moser-based Reduction, Perturbed linear Differential systems, turning points, Computer algebr

Formal Solutions of a Class of Pfaffian Systems in Two Variables

In this paper, we present an algorithm which computes a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in two variables, based on (Barkatou, 1997). A first step was set in (Barkatou-LeRoux, 2006) where the problem of rank reduction was tackled via the approach of (Levelt, 1991). We give instead a Moser-based approach. And, as a complementary step, we associate to our problem a system of ordinary linear singular differential equations from which the formal invariants can be efficiently derived via the package ISOLDE, implemented in the computer algebra system Maple.Comment: Keywords: Linear systems of partial differential equations, Pfaffian systems, Formal solutions, Moser-based reduction, Hukuhara- Turritin normal for

Wall friction and its effects on the density distribution in the compaction of pharmaceutical excipients

International audienceThe effect of powder-die wall friction during the compaction of pharmaceutical excipients has been investigated for three modes of lubrication: lubricated die, non-lubricated die and with the lubricant mixed with the powder. Coulomb friction is assumed and the wall friction coefficient was evaluated from the transmission ratio (applied pressure/transmitted pressure), the transfer ratio (radial pressure/axial pressure) and the aspect ratio (height/diameter of tablet). The friction coefficient of three pharmaceutical excipients was measured with respect to the relative density of the tablet by means of an instrumented press. It was found that the behaviour of the friction depends on the powder and the lubrication mode. Mixing the powder with a lubricant reduces the friction with respect to that of the lubricated die, but the evolution of the friction coefficient with the densification is different. The effect of the wall friction on the axial density distribution in the tablet was investigated by experiment and by modelling. The model was based on Janssen-Walker analysis coupled with the Heckel equation. For comparison, only the single action compaction in a non-lubricated die was considered. It was found that the measured and predicted axial density decrease from the top to the bottom of the tablet. Moreover, the predicted and measured density had the same tendency, but different values. However, the analysis should not be applied to the compaction of the powder mixed with lubricant because no physical parameter for this mode of lubrication is taken into account in the model

Instabilities of a sand layer subjected to an upward water flow by a 2D coupled discrete element - Lattice Boltzmann hydromechanical model

This work deals with the numerical simulation of the instabilities occurring in a sand layer subjected to an upward water flow. A coupled Discrete Elements - Lattice Boltzmann hydromechanical model is used for this end. After a brief presentation of the numerical model, simulations of an upward fluid flow through granular deposits are performed for two cases namely under controlled hydraulic gradients and under controlled volumetric flow rates. In the first case i.e. under controlled hydraulic gradient, the simulations show that the quicksand condition is actually reached for a hydraulic gradient very close to the critical hydraulic gradient calculated from the global analysis of classical soil mechanics. The simulations point out moreover that the quicksand phenomenon could be produced locally under slightly lower gradients. In the second case i.e. under controlled volumetric flow rates, the simulations show that there are three levels of flow ; low flow rates that allow infiltration without any destabilization, medium flow rates that cause expansion of the deposit to increase its permeability and high flow rates which may cause the formation continuous tunnel between the upstream and the downstream sides as well as sand boils. It is shown also that under the controlled flow rate condition the hydraulic gradient remains in all cases less than the average critical hydraulic gradient

Holter monitoring for syncope: diagnostic yield in different patient groups and impact on device implantation

Background: Holter monitoring is routinely used in patients referred for the evaluation of syncope, but its diagnostic value in different patient groups is unclear, as is its impact on device implantation (pacemaker or cardioverter-defibrillator). Aim: To determine the diagnostic yield of Holter monitoring in the routine evaluation of syncope, and its impact on subsequent device implantation. Design: Retrospective record review. Methods: We reviewed all Holter studies in patients referred with syncope between 2000 and 2005. Strict criteria were applied to determine whether a study was diagnostic. The diagnostic value of Holter monitoring (overall and in five subgroups: age, gender, structural heart disease, ejection fraction, medication) and its impact on the implantation of devices, were determined. Results: Of 4877 Holter studies, 826 were performed in patients with syncope (age 72 ± 15 years): 71 (8.6%) were considered to explain the syncope. Structural heart disease, ejection fraction and age were significant predictors of a diagnostic study (all p < 0.01), whereas gender and cardiac medication were not. A device was implanted in 33 patients (4.4%) whose initial Holter did not explain their syncope, after mean 7 months, whereas 45 patients (5.4%) received a pacemaker based on the Holter results (p = 0.32). Discussion: The overall diagnostic yield of Holter monitoring in the evaluation of syncope was 8.6%, with dramatic differences between subgroups. Our data suggest that the impact of Holter monitoring on device implantation is generally overestimate

The effects of ambient temperature on the compaction of pharmaceutical powders

International audienceThis article presents an experimental study of the effects of raised ambient temperature in dies and punches on the compaction of pharmaceutical powders. The experiments use an instrumented hydraulic press having a temperature-controlled enclosure allowing the ambient temperature of die and punch to be varied from 20 to 57 degrees C. A pharmaceutical powder was compacted at temperatures in this range and mechanical parameters, such as stress transfer ratio, stress transmission ratio, and die-wall friction, were analysed to examine the effects of heat transfer between tools and powder. In particular, it is shown that increasing the environmental temperature of die and punch increases the transfer ratio and the die-wall friction. The radial pressure is also slightly increased at the first stages of the compaction. However, the stress transmission is reduced by increasing the temperature. This may indicate an increase of shear stress. It is also observed that the particles undergoing compaction are `softened' by increase of the temperature. This softening is certainly due to rise in temperature of the powder generated by the compaction and by the heat flux transfer between the die and the tablet. It is suggested that these effects could be important in industrial tablet production installations without air conditioning and thus subject to variations in ambient temperature

Higher order Schrodinger and Hartree-Fock equations

The domain of validity of the higher-order Schrodinger equations is analyzed for harmonic-oscillator and Coulomb potentials as typical examples. Then the Cauchy theory for higher-order Hartree-Fock equations with bounded and Coulomb potentials is developed. Finally, the existence of associated ground states for the odd-order equations is proved. This renders these quantum equations relevant for physics.Comment: 19 pages, to appear in J. Math. Phy

Regularity of solutions to higher-order integrals of the calculus of variations

We obtain new regularity conditions for problems of calculus of variations with higher-order derivatives. As a corollary, we get non-occurrence of the Lavrentiev phenomenon. Our main regularity result asserts that autonomous integral functionals with a Lagrangian having coercive partial derivatives with respect to the higher-order derivatives admit only minimizers with essentially bounded derivatives