Flow-aligned, single-shot fiber diffraction using a femtosecond X-ray free-electron laser

A major goal for X-ray free-electron laser (XFEL) based science is to elucidate structures of biological molecules without the need for crystals. Filament systems may provide some of the first single macromolecular structures elucidated by XFEL radiation, since they contain one-dimensional translational symmetry and thereby occupy the diffraction intensity region between the extremes of crystals and single molecules. Here, we demonstrate flow alignment of as few as 100 filaments (Escherichia coli pili, F-actin, and amyloid fibrils), which when intersected by femtosecond X-ray pulses result in diffraction patterns similar to those obtained from classical fiber diffraction studies. We also determine that F-actin can be flow-aligned to a disorientation of approximately 5 degrees. Using this XFEL-based technique, we determine that gelsolin amyloids are comprised of stacked β-strands running perpendicular to the filament axis, and that a range of order from fibrillar to crystalline is discernable for individual α-synuclein amyloids

Large-scale unit commitment under uncertainty: an updated literature survey

The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject

On comparison principles for parabolic equations with nonlocal boundary conditions

A generalization of the comparison principle for a semilinear and a quasilinear parabolic equations with nonlocal boundary conditions including changing sign kernels is obtained. This generalization uses a positivity result obtained here for a parabolic problem with nonlocal boundary conditions

Some relaxation results for functionalsdepending on constrained strain and chemical composition

We prove some relaxation results in the spirit of Anza Hafsa and Mandallena for integral functionals arising in the study of coherent thermochemical equilibria for multiphase solids. The energy density exhibits all explicit dependence oil the deformation gradient and oil a vector field representing the chemical composition. The deformation gradient satisfies a determinant type constraint and the chemical composition a constraint on the modulus

Heterogeneous against homogeneous spectral response of polar molecules adsorbed on a real surface

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Curved thin films made of second grade materials

We consider a curved thin film made of a second grade material. The behaviour of the film is described by a nonconvex bulk energy depending on the first and second order derivatives of the deformation. When the thickness of the curved film goes to zero, we show, using $Gamma$-convergence arguments that the quasiminizers of three-dimensional energy converge to the minimizers of an energy whose grade two energy density has been $mathcal A$-quasiconvexified, depending on a two dimensional deformation and a Cosserat vector

Dimensional reduction for energies with linear growth involving the bending moment

Abstract A Γ -convergence analysis is used to perform a 3D–2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external loadings inducing a bending moment, may depend on the average in the transverse direction of a Cosserat vector field, as well as on the deformation of the mid-plane. The assumption of linear growth on the energy leads to an asymptotic analysis in the spaces of measures and of functions with bounded variation

Films courbés composés d'un matériaux non simple de second grade

The behavior of a curved thin film made of a nonsimple grade two material isdescribed by a nonconvex bulk energy depending on the first and second order derivatives of the deformation. We show usingΓ-convergence arguments that the quasiminimizers of the three-dimensional energy converge, when the thickness of the curvedfilm vanishes, to the minimizers of an energy which is a function of a two-dimensional deformation and of a Cosserat vector. Partof the energy density is obtained by A-quasiconvexification arguments