645 research outputs found
Global minimizers for axisymmetric multiphase membranes
No full textWe consider a Canham-Helfrich-type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes.
It consists of minimizing the sum of the Canham-Helfrich energy, in which the bending rigidities and spontaneous curvatures are now phase-dependent, and a line tension penalization for the phase interfaces. By restricting attention to axisymmetric surfaces and phase distributions, we extend our previous results for a single phase (R. Choksi and M. Veneroni, Global minimizers for the doubly-constrained Helfrich energy: the axisymmetric case. Calc. Var. Partial Differential Equations, 2012. DOI: 10.1007/s00526-012-0553-9) and prove existence of a global minimizer
Veneroni en Espagne:
No full textNombreux sont les chercheurs qui ont mis en relief la grande influence du Maître italien (Paris, 1678) de Giovanni Veneroni (pseudonyme de Jean Vigneron, 1642-1708) sur la production grammaticale postérieure. Aux XVIIIe et XIXe siècles, cet ouvrage a été très souvent traduit, remanié et adapté dans divers pays européens, aussi bien pour l’enseignement de l’italien que pour l’enseignement d’autres langues. Or, malgré l’attention prêtée aux ouvrages dérivés du Maître italien, les chercheurs ne mentionnent aucune édition ou adaptation de cet ouvrage en Espagne dans la première moitié du XVIIIe siècle. On trouve, certes, des commentaires relatifs à l’influence de Veneroni sur des auteurs de grammaires italiennes pour hispanophones publiées dans la seconde moitié du XVIIIe siècle ou au XIXe ; mais on a ignoré jusqu’à présent qu’une partie du Maître italien a été traduite et publiée en Espagne par Antoine Courville à une date aussi précoce que 1728, et ce non pas pour l’enseignement de l’italien, comme on aurait pu s’y attendre, mais pour l’enseignement du français. Ce travail est donc consacré à révéler et prouver cette présence de Veneroni en Espagne, à expliquer les circonstances qui en rendent compte et à analyser l’ouvrage de Courville: l’Explicación de la gramática francesa (Madrid, 1728).Many researchers have highlighted the great influence of Le Maître italien (Paris, 1678) of Giovanni Veneroni (pseudonym of Jean Vigneron, 1642-1708) on other manuals for the teaching of modern languages. In the eighteenth and nineteenth centuries this book was often translated, revised and adapted in various European countries for the teaching of Italian as well as for the teaching of other languages. However, despite the attention given to works derived from Le Maître italien, researchers do not mention any edition or adaptation of this book in Spain in the first half of the eighteenth century. We find comments on the influence of Veneroni on authors of Italian grammars for Spanish speakers published in the second half of the eighteenth century or the first half of the nineteenth; but it thus far been overlooked that a part of Le Maître italien was translated and published in Spain by Antoine Courville as early as 1728, and this not for the teaching of Italian, as one might have expected, but for the teaching of French. This chapter thus aims to reveal and prove the presence of Veneroni in Spain, to expose the factors which explain it and to analyse Courville’s grammar (the Explicación de la gramática francesa (Madrid, 1728)
Calculations of mass distributions using the Balian-Veneroni variational approach.
No full textExisting mean-field models, namely the Hartree-Fock (HF) and time-dependent Hartree-Fock (TDHF) approaches, can be used to determine the expectation values for one-body observables, such as fragment mass, in nuclear reactions and decays but are known to underestimate the fluctuations in these values. This is due to their assumption that each nucleon moves independently in a mean-field generated by the interactions between the nucleons neglecting important two-body correlations. Balian and Veneroni considered the variational determination of expectation values and fluctuations and obtained an improved formula for these fluctuations which can be implemented using existing TDHF codes. This approach has previously been implemented in a small number of test cases but symmetries and simplified interactions were used due to computational limitations. In this work we first review the Balian-Veneroni approach. We then present calculations of the mass distributions for the decay of giant resonances in32S, 40ca and 132Sn and in deep-inelastic and fusion-evaporation reactions for 160+160 and 40Ca+40Ca using a three-dimensional TDHF code with the full Skyrme interaction comparing with the previous calculations and/or experimental data as appropriate. We find that the Balian-Veneroni approach consistently produces fluctuations that exceed the TDHF values but that the numerical problems inherent in running prolonged TDHF calculations, particularly due to emitted nucleons being reflected back from the boundaries of our spatial box, cause significant numerical difficulties for longer nuclear' processes. We are consistently able to obtain converged results for giant resonance calculations but encounter difficulties for the deep-inelastic scattering reactions and are unable to obtain reliable results for the fusion- evaporation reactions. Our results differ from those obtained previously. We discuss the sources of these discrepancies
Reaction-Diffusion systems for the microscopic cellular model of the cardiac electric field
No full textThe paper deals with a mathematical model for the electric activity
of the heart at microscopic level. The membrane model used to describe the
ionic currents is a generalization of the phase-I Luo-Rudy, a model widely used
in 2-D and 3-D simulations of the action potential propagation. From the
mathematical viewpoint the model is made up of a parabolic reaction diffusion
system coupled with an ODE system. We derive existence and some regularity
results
Passing to the limit in a Wasserstein gradient flow : from diffusion to reaction
No full textWe study a singular-limit problem arising in the modelling of chemical reactions. At finite \epsilon > 0, the system is described by a Fokker-Planck convection-diffusion equation with a double-well convection potential. This potential is scaled by , and in the limit , the solution concentrates onto the two wells, resulting into a limiting system that is a pair of ordinary differential equations for the density at the two wells.
This convergence has been proved in Peletier, Savaré, and Veneroni, SIAM Journal on Mathematical Analysis, 42(4):1805-1825, 2010, using the linear structure of the equation. In this paper we re-prove the result by using solely the Wasserstein gradient-flow structure of the system. In particular we make no use of the linearity, nor of the fact that it is a second-order system.
The first key step in this approach is a reformulation of the equation as the minimization of an action functional that captures the property of being a curve of maximal slope in an integrated form. The second important step is a rescaling of space. Using only the Wasserstein gradient-flow structure, we prove that the sequence of rescaled solutions is pre-compact in an appropriate topology. We then prove a Gamma-convergence result for the functional in this topology, and we identify the limiting functional and the differential equation that it represents.
A consequence of these results is that solutions of the -problem converge to a solution of the limiting problem
Stripe patterns and a projection-valued formulation of the eikonal equation
No full textWe describe recent work on striped patterns in a system of block copolymers. A by-product of the characterization of such patterns is a new formulation of the eikonal equation. In this formulation, the unknown is a field of projection matrices of the form P = e e, where e is a unit vector field. We describe how this formulation is better adapted to the description of striped patterns than the classical eikonal equation, and illustrate this with examples
Use of conductance to detect bacteriocin activity
No full textThe inhibitory activity of a bacteriocin produced by Lactobacillus delbrueckii subsp. lactis G4 (Bac+) in milk was investigated by using conductivity measurements. The bacteriocin showed an inhibitory action toward some strains belonging to L. delbrueckii subsp. bulgaricus species. A delay in detection time (δDT) of two milk cultures sensitive to bacteriocin, grown in the presence of preformed bacteriocin, was observed. An inactivation as well as a modified growth rate of the sensitive cultures due to bacteriocin activity might explain the δDT, as indicated by longer generation time (tg). Cells showed the highest sensitivity to bacteriocin during the log phase of growth that corresponded to the beginning of the acceleration of the conductance curve (DT)
Dying after cure : a case of suicide in an adolescent treated for cancer
No full textAlthough suicide among childhood cancer survivors is rare, there is still a significantly higher risk in this population than in healthy adolescents. A 17-year-old girl cured of Burkitt lymphoma committed suicide after completing her treatment. She had never previously shown signs of psychological suffering and was in good general health. This case made the operators wonder how this tragic possibility might be prevented. It is essential for the ongoing monitoring of the psychological and social suffering of young people during follow-up programs to be assured by a multidisciplinary team involved in the patient's global care
Periodic homogenization of the Prandtl-Reuss model with hardening
No full textWe study the n-dimensional wave equation with an elasto-plastic nonlinear stress-strain relation. We investigate the case of heterogeneous materials, i.e. x-dependent parameters that are periodic at the scale η > 0. We study the limit η → 0 and derive the plasticity equations for the homogenized material. We prove the well-posedness for the original and the effective system with a finite-element approximation. The approximate solutions are also used in the homogenization proof which is based on oscillating test function and an adapted version of the div-curl Lemma
On the Structure of Optimal Transportation Plans between Discrete Measures
No full textIt is well known that the optimal transportation plan between two probability measures mu and nu is induced by a transportation map whenever mu is an absolutely continuous measure supported over a compact set in the Euclidean space and the cost function is a strictly convex function of the Euclidean distance. However, when mu and nu are both discrete, this result is generally false. In this paper, we prove that, given any pair of discrete probability measures and a cost function, there exists an optimal transportation plan that can be expressed as the sum of two deterministic plans, i.e., plans induced by transportation maps. As an application, we estimate the infinity-Wasserstein distance between two discrete probability measures mu and nu with the p-Wasserstein distance, times a constant depending on mu, on nu, and on the fixed cost function
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