Controlling chaotic oscillators by altering their energy

We developed the control technique for nonlinear oscillators when simple feedback alters the oscillation energy. The control does not require any computation nor knowledge of the system equations. Depending on the control perturbation parameters, two scenarios take place: (i) changing (linearly or nonlinearly) the oscillator damping, and (ii) suppressing (enhancing) the driving force. In the case of large deviations between phases of the chaotic oscillator and the driving force, only first scenario holds. Generalization of the technique to the case of oscillator networks is considered.     

Direct numerical simulation of the flow around a wall-mounted square cylinder under various inflow conditions

The flow around a wall-mounted square cylinder of side d is investigated by means of direct numerical simulation (DNS). The effect of inflow conditions is assessed by considering two different cases with matching momentum-thickness Reynolds numbers Re_θ ? 1000 at the obstacle: the first case is a fullyturbulent zero pressure gradient boundary layer, and the second one is a laminar boundary layer with prescribed Blasius inflow profile further upstream. An auxiliary simulation carried out with the pseudo-spectral Fourier–Chebyshev code SIMSON is used to obtain the turbulent time-dependent inflow conditions which are then fed into the main simulation where the actual flow around the cylinder is computed. This main simulation is performed, for both laminar and turbulent-inflows, with the spectral-element method code Nek5000. In both cases the wake is completely turbulent, and we find the same Strouhal number St ? 0.1, although the two wakes exhibit structural differences for x > 3d downstream of the cylinder. Transition to turbulence is observed in the laminar-inflow case, induced by the recirculation bubble produced upstream of the obstacle, and in the turbulent-inflow simulation the streamwise fluctuations modulate the horseshoe vortex. The wake obtained in our laminar-inflow case is in closer agreement with reference particle image velocimetry measurements of the same geometry, revealing that the experimental boundary layer was not fully turbulent in that dataset, and highlighting the usefulness of DNS to assess the quality of experimental inflow conditions.     

Aspect ratio effects in turbulent duct flows studied through direct numerical simulation

Three-dimensional effects in turbulent duct flows, i.e., sidewall boundary layers and secondary motions, are studied by means of direct numerical simulation (DNS). The spectral element code Nek5000 is used to compute turbulent duct flows with aspect ratios 1–7 (at Re_{b, c} = 2800, Re_{τ, c} ? 180) and aspect ratio 1 (at Re_{b, c} = 5600, Re_{τ, c} ? 330), in streamwise-periodic boxes of length 25h. The total number of grid points ranges from 28 to 145 million, and the pressure gradient is adjusted iteratively in order to keep the same bulk Reynolds number in the centreplane with changing aspect ratio. Turbulence is initiated via a trip forcing active during the initial stages of the simulation, and the statistical convergence of the data is discussed both in terms of transient approach and averaging period. Spanwise variations in wall shear, mean-flow profiles, and turbulence statistics are analysed as a function of aspect ratio, and also compared with the spanwise-periodic channel (as idealisation of an infinite aspect ratio duct). The computations show good agreement with experimental measurements carried out in parallel at the Illinois Institute of Technology (IIT) in Chicago, and highlight the relevance of sidewall boundary layers and secondary vortices in the physics of the duct flow. The rich array of secondary vortices extending throughout the upper and lower walls of the duct, and their dependence on Reynolds number and aspect ratio, had not been reported in the literature before.     

Quantum–chemical study of photo–excited states in tetragonal SrTiO3 lattice

The nature of photo-excited states in SrTiO₃ has been a topic of intense debate during the last few decades. Using a quantum-chemical method developed for crystals, we present a theoretical interpretation of the structural and electronic properties of triplet excitons in the tetragonal SrTiO₃ crystal. Our study demonstrates that the defect structure may correspond to the Mott–Wannier-type exciton having a considerable distance, 2.14Å, between the hole and the electron parts of the defect. The geometry optimization leads to an extensive defective region containing up to five atoms. However, the obtained magnitudes of atomic movements do not exceed 0.15Å. It is also observed that the self-trapped exciton polarizes the lattice around it. Using the so-called (ΔSCF method, the luminescence energy due to the exciton is found to be equal to 1.13 eV. As it corresponds to the infrared part of the spectrum, the experimentally detected green luminescence due to photo-excited states should be attributed to the singlet excitons.     

A discrete time method to the first variation of fractional order variational functionals

The fact that the first variation of a variational functional must vanish along an extremizer is the base of most effective solution schemes to solve problems of the calculus of variations. We generalize the method to variational problems involving fractional order derivatives. First order splines are used as variations, for which fractional derivatives are known. The Grünwald-Letnikov definition of fractional derivative is used, because of its intrinsic discrete nature that leads to straightforward approximations.     

Isotope hydrology and baseflow geochemistry in natural and human-altered watersheds in the Inland Pacific Northwest,USA

This study presents a stable isotope hydrology and geochemical analysis in the inland Pacific Northwest (PNW) of the USA. Isotope ratios were used to estimate mean transit times (MTTs) in natural and human-altered watersheds using the FLOWPC program. Isotope ratios in precipitation resulted in a regional meteoric water line of δ²H?=?7.42·δ¹⁸O?+?0.88 (n?=?316; r²?=?0.97). Isotope compositions exhibited a strong temperature-dependent seasonality. Despite this seasonal variation, the stream δ¹⁸O variation was small. A significant regression (τ?=?0.11D^?1.09; r²?=?0.83) between baseflow MTTs and the damping ratio was found. Baseflow MTTs ranged from 0.4 to 0.6 years (human-altered), 0.7 to 1.7 years (mining-altered), and 0.7 to 3.2 years (forested). Greater MTTs were represented by more homogenous aqueous chemistry whereas smaller MTTs resulted in more dynamic compositions. The isotope and geochemical data presented provide a baseline for future hydrological modelling in the inland PNW.     

On the exact separation of mixed integer knapsack cuts

During the last decades, much research has been conducted on deriving classes of valid inequalities for mixed integer knapsack sets, which we call knapsack cuts. Bixby et?al. (The sharpest cut: the impact of Manfred Padberg and his work. MPS/SIAM Series on Optimization, pp. 309?C326, 2004) empirically observe that, within the context of branch-and-cut algorithms to solve mixed integer programming problems, the most important inequalities are knapsack cuts derived by the mixed integer rounding (MIR) procedure. In this work we analyze this empirical observation by developing an algorithm to separate over the convex hull of a mixed integer knapsack set. The main feature of this algorithm is a specialized subroutine for optimizing over a mixed integer knapsack set which exploits dominance relationships. The exact separation of knapsack cuts allows us to establish natural benchmarks by which to evaluate specific classes of them. Using these benchmarks on MIPLIB 3.0 and MIPLIB 2003 instances we analyze the performance of MIR inequalities. Our computations, which are performed in exact arithmetic, are surprising: In the vast majority of the instances in which knapsack cuts yield bound improvements, MIR cuts alone achieve over 87% of the observed gain.     

Galerkin and Runge–Kutta methods: unified formulation,a posteriori error estimates and nodal superconvergence

We unify the formulation and analysis of Galerkin and Runge–Kutta methods for the time discretization of parabolic equations. This, together with the concept of reconstruction of the approximate solutions, allows us to establish a posteriori superconvergence estimates for the error at the nodes for all methods.     

Poly[[tetra‐μ3‐acetato‐hexa‐μ2‐acetato‐diaqua‐μ2‐oxalato‐tetrapraseodymium(III)] dihydrate]

The title complex, {[Pr₄(C₂H₃O₂)₁₀(C₂O₄)(H₂O)₂]·2H₂O}_n, was synthesized under hydrothermal conditions from praseodymium acetate and the ionic liquid 1‐butyl‐3‐methylimidazolium chloride via an in situ oxalate‐ligand synthesis. The compound is a two‐dimensional polymer and in the structure presents tightly bound planes parallel to (100), which are in turn linked into a three‐dimensional network by hydrogen bonds involving both coordinated and solvent water molecules. The oxalate anion lies across an inversion centre and acts as a bridge between pairs of Pr atoms within a tetranuclear segment of the polymer.