Invariant Variation Problems

The problems in variation here concerned are such as to admit a continuous group (in Lie's sense); the conclusions that emerge from the corresponding differential equations find their most general expression in the theorems formulated in Section 1 and proved in following sections. Concerning these differential equations that arise from problems of variation, far more precise statements can be made than about arbitrary differential equations admitting of a group, which are the subject of Lie's researches. What is to follow, therefore, represents a combination of the methods of the formal calculus of variations with those of Lie's group theory. For special groups and problems in variation, this combination of methods is not new; I may cite Hamel and Herglotz for special finite groups, Lorentz and his pupils (for instance Fokker), Weyl and Klein for special infinite groups. Especially Klein's second Note and the present developments have been mutually influenced by each other, in which regard I may refer to the concluding remarks of Klein's Note.Comment: M. A. Tavel's English translation of Noether's Theorems (1918), reproduced by Frank Y. Wang. Thanks to Lloyd Kannenberg for corrigend

A phase I clinical and pharmacological study evaluating vinflunine in combination with doxorubicin as first line treatment in metastatic breast cancer

Vinfunine (VFL) is a novel bifluorinated tubulin-targeted agent of the vinca alkaloids class active in advanced stage breast cancer. We conducted a phase I study combining VFL with doxorubicin (DXR) to define the recommended dose (RD), safety, pharmacokinetic (PK) interaction and efficacy. Two schedules (day 1 every 3weeks; days 1 and 8 every 3weeks) were investigated as first line chemotherapy in metastatic breast cancer patients. Thirty-two patients received a total of 162 cycles of the VFL-DXR combination (median 6). The RDs were VFL 250mg/m2/DXR 40mg/m2 every 3weeks for schedule 1 and VFL 120mg/m2/DXR 25mg/m2 days 1 and 8 every 3weeks for schedule 2. The main dose-limiting toxicity was neutropenia. The most frequent non-hematological adverse events were nausea, fatigue, constipation, vomiting, anorexia, stomatitis and dyspnea. Objective response rate was reached in 47.1% of the patients. No PK interaction was observed. VFL-DXR combination is feasible with manageable toxicity. The antitumor activity was promising and supports further evaluatio

Transport in rough self-affine fractures

Transport properties of three-dimensional self-affine rough fractures are studied by means of an effective-medium analysis and numerical simulations using the Lattice-Boltzmann method. The numerical results show that the effective-medium approximation predicts the right scaling behavior of the permeability and of the velocity fluctuations, in terms of the aperture of the fracture, the roughness exponent and the characteristic length of the fracture surfaces, in the limit of small separation between surfaces. The permeability of the fractures is also investigated as a function of the normal and lateral relative displacements between surfaces, and is shown that it can be bounded by the permeability of two-dimensional fractures. The development of channel-like structures in the velocity field is also numerically investigated for different relative displacements between surfaces. Finally, the dispersion of tracer particles in the velocity field of the fractures is investigated by analytic and numerical methods. The asymptotic dominant role of the geometric dispersion, due to velocity fluctuations and their spatial correlations, is shown in the limit of very small separation between fracture surfaces.Comment: submitted to PR

Patterns and flow in frictional fluid dynamics

Pattern-forming processes in simple fluids and suspensions have been studied extensively, and the basic displacement structures, similar to viscous fingers and fractals in capillary dominated flows, have been identified. However, the fundamental displacement morphologies in frictional fluids and granular mixtures have not been mapped out. Here we consider Coulomb friction and compressibility in the fluid dynamics, and discover surprising responses including highly intermittent flow and a transition to quasi-continuodynamics. Moreover, by varying the injection rate over several orders of magnitude, we characterize new dynamic modes ranging from stick-slip bubbles at low rate to destabilized viscous fingers at high rate. We classify the fluid dynamics into frictional and viscous regimes, and present a unified description of emerging morphologies in granular mixtures in the form of extended phase diagrams

Coupled electrohydrodynamic transport through fractures

by Uddipta Ghosh, T. Le Borgne and Y. Meheus

A Lubrication-Based Solver for Shear-Thinning Flow in Rough Fractures

The depth-averaged (2D) lubrication theory is often adopted to simulate Newtonian flow in rough fractures. This approach, which is computationally much less expensive than using 3D CFD solvers, allows addressing large ensembles of stochastic fracture realizations. For creeping flow, the degree of approximation introduced is limited as long as the apertures vary relatively smoothly. We propose the first generalization of this approach addressing the flow of fluids whose rheology, described by the Ellis model, is shear-thinning (ST) above a crossover shear stress and Newtonian (of viscosity μ0) below. The resulting nonlinear Reynolds equation for pressures is solved for a vast range of realistic rheological parameter values using a novel and specifically designed finite volume-based numerical model. The spatial discretization takes inspiration from the graph p-Laplacian to yield a symmetric Newton Jacobian, allowing for a highly efficient inexact implementation of the preconditioned conjugate gradient-based Newton-Krylov method. This is combined with a parameter continuation strategy to increase code robustness and ensure global convergence for flow indices as low as 0.1 with an excellent efficiency. This original solver is used to investigate realistic synthetic rough fracture geometries, which exhibits both self-affinity and a correlation length. The results show that the ST rheology mitigates the effects of aperture heterogeneities, increasing fracture transmissivity by several orders of magnitudes as compared to the Newtonian flow of viscosity μ0 if the imposed macroscopic gradient is sufficiently large, and even rendering the rough fracture up to 10 times more permeable than a smooth fracture of identical mean aperture