Convergence of solutions of kinetic variational inequalities in the rate-independent quasi-static limit

This paper discusses the convergence of kinetic variational inequalities to rate-independent quasi-static variational inequalities. Mathematical formulations as well as existence and uniqueness results for kinetic and rate-independent quasi-static problems are provided. Sharp a priori estimates for the kinetic problem are derived that imply that the kinetic solutions converge to the rate-independent ones, when the size of initial perturbations and the rate of application of the forces tend to 0. An application to three-dimensional elastic-plastic systems with hardening is given.     

Global Existence for Rate-Independent Gradient Plasticity at Finite Strain

We provide a global existence result for the time-continuous elastoplasticity problem using the energetic formulation. For this, we show that the geometric nonlinearities arising from the multiplicative decomposition of the strain can be controlled via polyconvexity and a priori stress bounds in terms of the energy density. While temporal oscillations are controlled via energy dissipation, the spatial compactness is obtained via regularizing terms involving gradients of the internal variables. Dedicated to Sir John Ball on the occasion of his 60th birthday.     

Time-average measurement of velocity, density, temperature, and turbulence velocity fluctuations using Rayleigh and Mie scattering

Measurement of time-averaged velocity, density, temperature, and turbulence velocity fluctuations in sparsely seeded gas flows using a non-intrusive, point-wise technique based on Rayleigh and Mie scattering is discussed. A Fabry-Perot interferometer (FPI) is used to spectrally resolve laser light scattered by molecules and particulates in gas flows. The spectral content of the scattered light provides information about velocity, density, and temperature of the gas. A CCD camera is used to record images of the fringes formed by scattered light passing through the interferometer. Models of the spectral components are used in a least squares fitting routine to estimate the parameters from fringe images. Flow measurements are presented for subsonic and supersonic jet flows. The application range for this technique is mostly for high velocity situations (>25 m/s). Velocity, density, temperature, and turbulence velocity fluctuations were determined with accuracies within 5 m/s, 4%, 2%, and 5 m/s, respectively.     

On the Relation between Gradient Flows and the Large-Deviation Principle,with Applications to Markov Chains and Diffusion

Motivated by the occurrence in rate functions of time-dependent large-deviation principles, we study a class of non-negative functions ? that induce a flow, given by \(\mathcal{L} (\rho _{t},\dot \rho _{t})=0\) . We derive necessary and sufficient conditions for the unique existence of a generalized gradient structure for the induced flow, as well as explicit formulas for the corresponding driving entropy and dissipation functional. In particular, we show how these conditions can be given a probabilistic interpretation when ? is associated to the large deviations of a microscopic particle system. Finally, we illustrate the theory for independent Brownian particles with drift, which leads to the entropy-Wasserstein gradient structure, and for independent Markovian particles on a finite state space, which leads to a previously unknown gradient structure.     

On the chiral anomaly in non-Riemannian spacetimes

Thetranslation Chern-Simons type three-formcoframe∧torsion on a Riemann-Cartan spacetime is related (by differentiation) to the Nieh-Yan fourform. Following Chandia and Zanelli, two spaces with nontrivial translational Chern-Simons forms are discussed. We then demonstrate, first within the classical Einstein-Cartan-Dirac theory and second in the quantum heat kernel approach to the Dirac operator, how the Nieh-Yan form surfaces in both contexts, in contrast to what has been assumed previously.     

Mathematical analysis of sideband instabilities with application to rayleigh-bénard convection

Summary We introduce a new method for the analysis of sideband instabilities which are important for periodic patterns appearing in systems close to the instability threshold. The method relies on a two-fold application of the Liapunov-Schmidt reduction procedure, a first application to the nonlinear bifurcation problem and a second application to the linear spectral problem. We obtain rigorous results on the spectrum of the associated linearization in spaces allowing for general sideband perturbations by treating the sideband vector and the spectral parameter as small bifurcation parameters. We apply the theory to the small roll solutions in the Rayleigh-Bénard convection and derive domains in Rayleigh, Prandtl, and wave number space where the rolls are unstable. We recover the Eckhaus, zigzag, and skew-varicose instabilities obtained earlier by formal methods. This paper is dedicated to the memory of Juan C. Simo This paper was solicited by the editors to be part of a volume dedicated to the memory of Juan C. Simo.     

Clustering of sulfamic acid: ESI MS and theoretical study

Sulfamic acid has wide application in industry and has been suggested to act as an effective nucleation agent for the formation of aerosols and cloud particles. From the point of view of the role that sulfamic acid may play in aerosol formation, the study of its homoaggregation is important. Gas phase clustering study was performed for sulfamic acid H₃N·SO₃, (ASA), from water and methanol–water solutions, by help of a TOF‐Q spectrometer equipped with electrospray ionization source, in the negative‐ion mode. The structure and stability of the (H₃N·SO₃)_n and [(H₃N·SO₃)_n‐H]^? (n = 1–6) were studied using DFT/B3LYP/aug‐cc‐pVDZ method. The ESI MS study evidenced that both singly and doubly charged clusters are formed when the acids are electrosprayed from water solutions; they may be described as [(H₃N·SO₃)_n‐zH]^z? where z = 1 or 2. The largest identified clusters are built of 20 monomers. The theoretical studies showed that formation of higher order (ASA)_n aggregates in the gas phase is energetically profitable. In contrast with the gas phase, aqueous solution does not favor the formation of (ASA)_n aggregates. The study led to the conclusion that the ASA clusters are formed in the gas phase under the experimental conditions of the mass spectrometer. A hypothetical mechanism concerning the formation of the doubly negatively charged anionic aggregates is discussed. The obtained data suggest that small (NH₃·SO₃)_n aggregates may also contribute to formation of aerosols in heavily polluted atmospheres with relatively large NH₃ concentration. Copyright © 2015 John Wiley & Sons, Ltd.     

Infinite-Dimensional Hyperbolic Sets and Spatio-Temporal Chaos in Reaction Diffusion Systems in $${\mathbb{R}^{n}}$$

The paper is devoted to a rigorous construction of a parabolic system of partial differential equations which displays space–time chaotic behavior in its global attractor. The construction starts from a periodic array of identical copies of a temporally chaotic reaction-diffusion system (RDS) on a bounded domain with Dirichlet boundary conditions. We start with the case without coupling where space–time chaos, defined via embedding of multi- dimensional Bernoulli schemes, is easily obtained. We introduce small coupling by replacing the Dirichlet boundary conditions by strong absorption between the active islands. Using hyperbolicity and delicate PDE estimates we prove persistence of the embedded Bernoulli scheme. Furthermore we smoothen the nonlinearity and obtain a RDS which has polynomial interaction terms with space and time-periodic coefficients and which has a hyperbolic invariant set on which the dynamics displays spatio-temporal chaos. Finally we show that such a system can be embedded in a bigger system which is autonomous and homogeneous and still contains space–time chaos. Obviously, hyperbolicity is lost in this step. Research partially supported by the INTAS project Attractors for Equations of Mathematical Physics, by CRDF and by the Alexander von Humboldt–Stiftung.