Uniqueness of reconstruction of multiphase morphologies from two-point correlation functions

The restoration of the spatial structure of heterogeneous media, such as composites, porous materials, microemulsions, ceramics, or polymer blends from two-point correlation functions, is a problem of relevance to several areas of science. In this contribution we revisit the question of the uniqueness of the restoration problem. We present numerical evidence that periodic, piecewise uniform structures with smooth boundaries are completely specified by their two-point correlation functions, up to a translation and, in some cases, inversion. We discuss the physical relevance of the results.     

Tensor products of contexts and complete lattices

Although the categoryCLC of complete lattices and complete homomorphisms does not possess arbitrary coproducts, we show that the tensor product introduced by Wille has the universal property of coproducts for so-called distributing families of morphisms (and only for these). As every family of morphisms into a completely distributive lattice is distributing, this includes the known fact that in the category of completely distributive lattices, arbitrary coproducts exist and coincide with the tensor products. Since the definition of tensor products is based on the notion of contexts and their concept lattices, many results on tensor products extend from complete lattices to contexts. Thus we introduce two kinds of tensor products for arbitrary families of contexts, a partial and a complete one, and establish universal properties of these tensor products.Presented by B. Jonsson.     

Evolution of Orbits and Quantum Correlation Functions by Quadratic Hamiltonians

Quantum systems with quadratic Hamiltonians are considered. Some results about the time evolution of homogeneous polynomials and of quantum correlation functions are given. The image of arbitrary orbit of Weyl–Heisenberg group under this time evolution is shown to be again an orbit of this group. For quantum free particle it is shown that its time evolution intersects arbitrary such orbit at most once. A result about existence of more orbits having the same dispersion of some quantum position is presented.PACS: 02.20.Qs, 02.30.Sa     

Rigidity percolation in particle-laden foams

We study the viscoelastic behavior of aqueous foam mixed with solid noncolloidal particles. We show that adding a tiny amount of grains can enhance the elastic and loss shear moduli by more than 1 order of magnitude. The scaling of these moduli with solid volume fraction is in qualitative agreement with that predicted by an effective-medium rigidity percolation model. We present a simple model, based on capillary attraction, to explain the particle-size dependence of the threshold.     

Algorithmic boundedness-from-below conditions for generic scalar potentials

Checking that a scalar potential is bounded from below (BFB) is an ubiquitous and notoriously difficult task in many models with extended scalar sectors. Exact analytic BFB conditions are known only in simple cases. In this work, we present a novel approach to algorithmically establish the BFB conditions for any polynomial scalar potential. The method relies on elements of multivariate algebra, in particular, on resultants and on the spectral theory of tensors, which is being developed by the mathematical community. We give first a pedagogical introduction to this approach, illustrate it with elementary examples, and then present the working Mathematica implementation publicly available at GitHub. Due to the rapidly increasing complexity of the problem, we have not yet produced ready-to-use analytical BFB conditions for new multi-scalar cases. But we are confident that the present implementation can be dramatically improved and may eventually lead to such results.     

Characterization of rapidly solidified powder of high-speed steel

Ionization and excitation cross sections as well as electron-energy spectra and stopping powers of the alkali metal atoms Li, Na, K, and Rb colliding with antiprotons were calculated using a time-dependent channel-coupling approach. An impact-energy range from 0.25 to 4000 keV was considered. The target atoms are treated as effective one-electron systems using a model potential. The results are compared with calculated cross sections for antiproton-hydrogen atom collisions.     

Direct Minimization of the least-squares spectral element functional – Part I: Direct solver

This paper describes an equivalent but improved least-squares formulation for the numerical approximation of the solution of partial differential equations. Instead of using variational analysis to impose the conditions for minimizing the residual, the residuals are minimized directly, thus leading to a method we will denote by Direct Minimization (DM). DM circumvents setting up the normal equations which consists of matrix–matrix multiplications. Matrix–matrix multiplications are expensive, may lead to loss of accuracy and destroy the sparsity pattern present in the original system. The condition number of the DM formulation is the square root of the condition number which would be obtained if variational analysis was employed. An element-by-element procedure will be presented which allows for parallelization of DM. A computational comparison between DM and the conventional least-squares formulation based on variational analysis will be presented.     

Mid-infrared supercontinuum generation to 4.5 microm in ZBLAN fluoride fibers by nanosecond diode pumping

A mid-infrared supercontinuum (SC) is generated in ZBLAN (ZrF4-BaF2-LaF3-AlF3-NaF...) fluoride fibers from amplified nanosecond laser diode pulses with a continuous spectrum from approximately 0.8 microm to beyond 4.5 microm. The SC has an average power of approximately 23 mW, a pump-to-SC power conversion efficiency exceeding 50%, and a spectral power density of approximately -20 dBm/nm over a large fraction of the spectrum. The SC generation is initiated by the breakup of nanosecond laser diode pulses into femtosecond pulses through modulation instability, and the spectrum is then broadened primarily through fiber nonlinearities in approximately 2-7 m lengths of ZBLAN fiber. The SC long-wavelength edge is consistent with the intrinsic ZBLAN material absorption.     

Optimal branching asymmetry of hydrodynamic pulsatile trees

Most of the studies on optimal transport are done for steady state regime conditions. Yet, there exists numerous examples in living systems where supply tree networks have to deliver products in a limited time due to the pulsatile character of the flow, as it is the case for mammalian respiration. We report here that introducing a systematic branching asymmetry allows the tree to reduce the average delivery time of the products. It simultaneously increases its robustness against the inevitable variability of sizes related to morphogenesis. We then apply this approach to the human tracheobronchial tree. We show that in this case all extremities are supplied with fresh air, provided that the asymmetry is smaller than a critical threshold which happens to match the asymmetry measured in the human lung. This could indicate that the structure is tuned at the maximum asymmetry level that allows the lung to feed all terminal units with fresh air.     

Molecular origin of model membrane bending rigidity

The behavior of the bending modulus kappa of bilayers in lamellar phases was studied by Small Angle X-ray Scattering technique for various nonionic C(i)E(j) surfactants. The bilayers are either unswollen and dispersed in water or swollen by water and dispersed in dodecane. For unswollen bilayers, the values of kappa decrease with both an increase in the area per surfactant molecule and in the polar head length. They increase when the aliphatic chain length increases at constant area per surfactant molecule. Whereas for water-swollen membranes, the values of kappa decrease as the content of water increases converging to the value of the single monolayer bending modulus. Such a behavior results from the decoupling of the fluctuations of the two surfactant membrane monolayers. Our results emphasize the determinant contribution of the surfactant conformation to kappa.