Gamma‐convergence of gradient flows with applications to Ginzburg‐Landau

We present a method to prove convergence of gradient flows of families of energies that Γ‐converge to a limiting energy. It provides lower‐bound criteria to obtain the convergence that correspond to a sort of C¹‐order Γ‐convergence of functionals. We then apply this method to establish the limiting dynamical law of a finite number of vortices for the heat flow of the Ginzburg‐Landau energy in dimension 2, retrieving in a different way the existing results for the case without magnetic field and obtaining new results for the case with magnetic field. © 2004 Wiley Periodicals, Inc.     

Status of electroweak phase transition and baryogenesis

I review recent progress on the electroweak phase transition and baryogenesis, focusing on the minimal supersymmetric Standard Model as the source of new physics.     

Lorentz space estimates for the Ginzburg-Landau energy

In this paper we prove novel lower bounds for the Ginzburg-Landau energy with or without magnetic field. These bounds rely on an improvement of the “vortex-balls construction” estimates by extracting a new positive term in the energy lower bounds. This extra term can be conveniently estimated through a Lorentz space norm, on which it thus provides an upper bound. The Lorentz space L2,∞ we use is critical with respect to the expected vortex profiles and can serve to estimate the total number of vortices and get improved convergence results.     

Integral resource capacity planning for inpatient care services based on bed census predictions by hour

The design and operations of inpatient care facilities are typically largely historically shaped. A better match with the changing environment is often possible, and even inevitable due to the pressure on hospital budgets. Effectively organizing inpatient care requires simultaneous consideration of several interrelated planning issues. Also, coordination with upstream departments like the operating theatre and the emergency department is much-needed. We present a generic analytical approach to predict bed census on nursing wards by hour, as a function of the Master Surgical Schedule and arrival patterns of emergency patients. Along these predictions, insight is gained on the impact of strategic (ie, case mix, care unit size, care unit partitioning), tactical (ie, allocation of operating room time, misplacement rules), and operational decisions (ie, time of admission/discharge). The method is used in the Academic Medical Center Amsterdam as a decision-support tool in a complete redesign of the inpatient care operations.     

Ultrasonic monitoring of yoghurt formation by using AT-cut quartz: lighting of casein micelles interactions process during the acidification

The behavior of weak gels during their formation singularly attracts attention of dairy products factories. In our study we investigate acidified pre-heated milk gels formation that are fairly often used to product yoghurts. The gel formation requires a tight control of the first step of micelles modification process and the kinetics reaction parameters. The most current rheological parameters used to achieve the monitoring are the storage G' and the loss G' shear moduli and the gelation time. The study of these parameters is commonly performed at very low frequencies (1 Hz). Our technique uses a 6 MHz AT-cut quartz crystal immersed in an acidified milk solution kept at a constant temperature. This method is singularly effective to ensure a complete and a reliable follow-up of the viscoelastic parameters of casein gels. A suitable new model enables a complete follow-up of the micelles evolution from the viscoelastic properties. The experimental results of the G' and G' moduli versus temperature and versus glucono-delta-lactone (GDL) added to milk are analyzed. In order to understand the micelles modifications, an analysis of the viscoelastic evolution try to explain the validity of the various models of micelles modification. In addition a new accurate kinetics characteristic time is proposed. This time corresponds to the moment for which the elastic effect of material becomes significant. From the kinetics study of casein gels at various temperatures, the Arrhenius relationship and a modified Flory-Stockmayer relationship give us access to the activation energy. By using the proposed technique and the suitable models developed, the structure thus quality of dairy products may be better controlled.     

Characterization of New Titanium Oxide Polymer Hybrid Membranes for Biofilm Formation

Abstract

Presently, there is great need to create new matrices for diverse applications particularly in the fields of biotechnology and food industry. Here, we report on the synthesis of new matrices based on a mixture of polymer cellulose acetate butyrate/copolymer polyacrylonitrile acrylamide/TiO₂. The characterization of the new matrices was performed using IR spectroscopy, QCM technology, and SEM. The tests revealed that when we use our polymers as carriers, there is a limit for the concentration of titanium of 5%. Further increasing of Ti concentration leads to precipitation processes. The QCM analyses show that a low concentration of Ti(OBu)₄ does not influence the viscosity of the matrices obtained, but their elasticity changes significantly. The membranes obtained were successfully applied for biofilm formation of Yeast strain Saccharomyces cerevisiae.     

Ginzburg-Landau minimizers near the first critical field have bounded vorticity

We prove that for fields close enough to the first critical field, minimizers of the Ginzburg-Landau functional have a number of vortices bounded independently from the Ginzburg-Landau parameter. This generalizes a result proved in [SS1] and shows that locally minimizing solutions of the Ginzburg-Landau equation found in [S1, S3] are actually global minimizers. It also gives a partial answer to a question raised by F. Bethuel and T. Rivière in [BR]. Received: 10 July 2002 / Accepted: 23 January 2002 / Published online: 5 September 2002     

Lowest Landau level approach in superconductivity for the Abrikosov lattice close to $$H_{{c}_{2}}$$

We study the Ginzburg–Landau energy for a superconductor submitted to a magnetic field just below the “second critical field” . When the Ginzburg–Landau parameter ε is small, we show that the mean energy per unit volume can be approximated by a reduced energy on a torus. Moreover, we expand this reduced energy in terms of : when this quantity gets small, the problem amounts to a minimization problem on a finite-dimensional space, equivalent to the “lowest Landau level” in other approaches. The functions in this finite-dimensional space can themselves be expressed via the Jacobi Theta function of a lattice. This connects the Ginzburg–Landau energy to the “Abrikosov problem” of locating vortices optimally on a lattice.