Computing generalized Nash equilibria by polynomial programming

We present a new way to solve generalized Nash equilibrium problems. We assume the feasible set to be compact. Furthermore all functions are assumed to be polynomials. However we do not impose convexity on either the utility functions or the action sets. The key idea is to use Putinar’s Positivstellensatz, a representation result for positive polynomials, to replace each agent’s problem by a convex optimization problem. The Nash equilibria are then feasible solutions to a system of polynomial equations and inequalities. Our application is a model of the New Zealand electricity spot market with transmission losses based on a real dataset.     

On the Potential of Tomographic Methods when Applied to Compacted Crushed Rock Salt

Compacted crushed rock salt is considered as potential backfill material in repositories for nuclear waste. To evaluate the sealing properties of this material knowledge concerning the nature of the pore space is of eminent interest. Here, the pore microstructures of crushed rock salt samples with different compaction states were investigated by X-ray (XCT) computed tomography and Focused Ion Beam nanotomography (FIB-nt). Based on these methods the pore microstructures were reconstructed and quantitatively analyzed with respect to porosity, connectivity and percolation properties. Regarding pores with radii \(> 4\,\upmu \hbox {m}\) , porosity differs substantially in the two analyzed samples ( \(\phi = 0.01\) and 0.10). The pore microstructures are considered isotropic in connectivity and percolation threshold. Using two finite-scaling schemes we found percolation thresholds with critical porosities \(\phi _{c} > 0.05\) . Based on statistical considerations, the millimeter size samples that can be analyzed by XCT are large enough to provide a meaningful picture of the pore geometry related to macroporosity. The samples contain also a small fraction (i.e. \(< 0.01\) ) of pores with radii \(< 1\,\upmu \hbox {m}\) , which were resolved by FIB-nt. Often these pores can be found along grain boundaries. These pores are granular shaped and are not connected to each other. Typical samples size that can be analyzed by FIB-nt is on the order of tens of microns, which turned out to be too small to provide representative geometric information unless an effort is made that involves several FIB-nt realizations per sample.     

Femtosecond-laser-induced bond breaking and structural modifications in silicon, TiO_2, and defective graphene: an ab initio molecular dynamics study

By exciting or heating electrons, ultrashort laser pulses have a direct influence on bond strengths in two- and three-dimensional solids. Here, we present results of ab initio molecular dynamics simulations performed using our in-house Code for Highly-excIted Valence Electron Systems (CHIVES) for three systems, which each shows a distinctly different structural response to a femtosecond laser pulse. In solid silicon, we show that ultrafast laser-induced bond breaking leads to nonthermal melting, a process which occurs in three stages, involving subsequently superdiffusive, fractionally diffusive, and normally diffusive atomic motions. For TiO $_2$ , we find that the A $_{1g}$ phonon is coherently excited. At room temperature, we demonstrate that these oscillations are strongly coupled to other phonon modes. In graphene with a single Stone–Wales defect, we study the in-plane and out-of-plane laser-induced atomic motions and find bond breaking, which destroys the structure, when the electrons are heated to at least 31,000 K.     

Functional Fatigue in polycrystalline Shape Memory Alloys

Shape memory alloys show the well known effect of pseudo-elasticity associated with the formation of two stress plateaus in the stress/strain diagram for tension tests. Due to cyclic loading, the stress plateaus decrease with every load cycle, particularly the upper one. This important effect of functional fatigue results from plastic deformations that are produced during solid-solid phase transformations between the austenitic and martensitic state. Outgoing from a polycrystalline approach for shape memory alloys we develop a micromechanical material model that is based on the Principle of the Minimum of the Dissipation Potential and predicts the evolution of plastic strains. Therefore, only a small number of material parameters is necessary and additionally, only a few assumptions are sufficient to model the effect of functional fatigue. We present yield functions as well as evolution equations for the volume fractions of austenite and martensite, and the plastic strains. Furthermore, we show an exemplary calculation for Nickel Titanium and compare it with experimental measurements to demonstrate the ability of our model. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Foundational Discretization Barriers in STFT Phase Retrieval

Journal of Fourier Analysis and Applications - This topical collection “Harmonic Analysis on Combinatorial Graphs” contains 20 papers devoted to a very broad range of themes written by...     

Implementation problems of manifolds-based model reduction and their generic solution

During the last decades, tabulated chemistry approaches, like manifold-based concepts to implement model reduction, have become a widespread, promising and accurate method to take chemical reactions into account in computing reacting flows. However, there is a number of crucial issues concerning the generation and implementation of the tabulated chemistry approaches. These concern the way manifolds of the arbitrary dimension are generated, parametrised (i.e. tabulated) preserving fast/slow decomposition and implemented rigorously by the formulation of a reduced model in a coordinate independent manner.

This study discusses these problems in detail and suggests generic solutions based on the Reaction–Diffusion Manifolds (REDIM) method. A REDIM tabulated chemistry concept obtained by using the hierarchical nature of the invariant slow system manifolds is presented. Numerical aspects of the implementation are in the focus of the paper. It is shown how the concept is implemented to overcome most problems without a-priori knowledge of the considered system behaviour. As a basic example for discussion and illustration synthesis, gas/air combustion in premixed, freely propagating flames is used.     

Rotational Spectra and Molecular Structures of Ethylanilines

The molecular structures of three ethylanilines, ortho-, meta- and para-ethylaniline, have been obtained by means of Fourier-transform microwave spectroscopy. Rotational spectra of all three molecules display the nuclear quadrupole hyperfine structures arising from the \begin{document}$ ^{14} $\end{document}N nucleus. Comparison of the determined structures allows a direct study of the influence of the position of the ethyl substituent on the structure of the amino group communicated through the phenyl ring.