Symplectic capacity and short periodic billiard trajectory

We prove that a bounded domain $\Omega$ in $\R^n$ with smooth boundary has a periodic billiard trajectory with at most $n+1$ bounce times and of length less than $C_n r(\Omega)$, where $C_n$ is a positive constant which depends only on $n$, and $r(\Omega)$ is the supremum of radius of balls in $\Omega$. This result improves the result by C.Viterbo, which asserts that $\Omega$ has a periodic billiard trajectory of length less than C'_n \vol(\Omega)^{1/n}. To prove this result, we study symplectic capacity of Liouville domains, which is defined via symplectic homology.Comment: 32 pages, final version with minor modifications. Published online in Mathematische Zeitschrif

A fast weakly intrusive multiscale method in explicit dynamics

This paper presents new developments on a weakly intrusive approach for the simplified implementation of space and time multiscale methods within an explicit dynamics software. The 'substitution' method proposed in previous works allows to take advantage of a global coarse model, typically used in an industrial context, running separate, refined in space and in time, local analyses only where needed. The proposed technique is iterative, but the explicit character of the method allows to perform the global computation only once per global time step, while a repeated solution is required for the small local problems only. Nevertheless, a desirable goal is to reach convergence with a reduced number of iterations. To this purpose, we propose here a new iterative algorithm based on an improved interface inertia operator. The new operator exploits a combined property of velocity Hermite time interpolation on the interface and of the central difference integration scheme, allowing the consistent upscaling of interface inertia contributions from the lower scale. This property is exploited to construct an improved mass matrix operator for the interface coupling, allowing to significantly enhance the convergence rate. The efficiency and robustness of the procedure are demonstrated through several examples of growing complexity. Copyright {\copyright} 2014 John Wiley \& Sons, Ltd

A weakly-intrusive multi-scale substitution method in explicit dynamics

For virtual testing of composite structures, the use of fine modeling seems preferable to simulate complex mechanisms like delamination. However, the associated computational costs are prohibitively high for large structures. Multi-scale coupling techniques aim at reducing such computational costs, limiting the fine model only where necessary. The dynamic adaptivity of the models represents a crucial feature to follow evolutive phenomena. Domain decomposition methods would have to be combined with re-meshing strategies, that are considered intrusive implementations within commercial software. Global-local approaches are considered less intrusive, because they allow one to use a global coarse model on the overall structure and a fine local patch eventually adapted to cover the interest zone. In our work, we developed a global-local coupling method for explicit dynamics, presented in [1] and [2] and implemented in Abaqus/Explicit via the co-simulation technique for the simulation of delamination under high velocity impact

A two-mechanism and multiscale compatible approach for solid state electrolytes of (Li-ion) batteries

All solid state batteries are claimed to be the next-generation battery system, in view of their safety accompanied by high energy densities. A new advanced, multiscale compatible, and fully three dimensional model for solid electrolytes is presented in this note. The response of the electrolyte is profoundly studied theoretically and numerically, analyzing the equilibrium and steady state behaviors, the limiting factors, as well as the most relevant constitutive parameters according to the sensitivity analysis of the model

XRD Analysis in Front of a Corrosion Crack Tip

During exploitation of the heat exchangers some damages can appear in the contact region between the gaskets and the stainless steel walls. The studies upon the material were performed using SEM microscopy, X-ray diffractometry and the finite element method. The obtained data allow the explanation of the complex damage mechanism of the heat exchanger wall. Following our research, the manufacturing technology of the heat exchangers was changed and this way the rebuts were eliminated. The performed research is based upon physical methods and the damage mechanism of the heat exchanger plates is explained by means of the physical phenomena that appear and develop during working conditions

Nanosize Titanium Dioxide Stimulates Reactive Oxygen Species in Brain Microglia and Damages Neurons in Vitro

BackgroundTitanium dioxide is a widely used nanomaterial whose photo-reactivity suggests that it could damage biological targets (e.g., brain) through oxidative stress (OS).ObjectivesBrain cultures of immortalized mouse microglia (BV2), rat dopaminergic (DA) neurons (N27), and primary cultures of embryonic rat striatum, were exposed to Degussa P25, a commercially available TiO2 nanomaterial. Physical properties of P25 were measured under conditions that paralleled biological measures.FindingsP25 rapidly aggregated in physiological buffer (800–1,900 nm; 25°C) and exposure media (~ 330 nm; 37°C), and maintained a negative zeta potential in both buffer (–12.2 ± 1.6 mV) and media (–9.1 ± 1.2 mV). BV2 microglia exposed to P25 (2.5–120 ppm) responded with an immediate and prolonged release of reactive oxygen species (ROS). Hoechst nuclear stain was reduced after 24-hr (≥100 ppm) and 48-hr (≥2.5 ppm) exposure. Microarray analysis on P25-exposed BV2 microglia indicated up-regulation of inflammatory, apoptotic, and cell cycling pathways and down-regulation of energy metabolism. P25 (2.5–120 ppm) stimulated increases of intracellular ATP and caspase 3/7 activity in isolated N27 neurons (24–48 hr) but did not produce cytotoxicity after 72-hr exposure. Primary cultures of rat striatum exposed to P25 (5 ppm) showed a reduction of immunohistochemically stained neurons and microscopic evidence of neuronal apoptosis after 6-hr exposure. These findings indicate that P25 stimulates ROS in BV2 microglia and is nontoxic to isolated N27 neurons. However, P25 rapidly damages neurons at low concentrations in complex brain cultures, plausibly though microglial generated ROS

Synthesis and characterization of some carbon based nanostructures

The aim of present paper is to present the latest results on investigations of the carbon thin film deposited by Thermionic Vacuum Arc (TVA) method and laser pyrolysis. X-ray photoelectron spectroscopy (XPS) and X-ray generated Auger electron spectroscopy (XAES) were used to determine composition and sp2 to sp3 ratios in the outer layers of the film surfaces. The analyses were conducted in a Thermoelectron ESCALAB 250 electron spectrometer equipped with a hemispherical sector energy analyser. Monochromated Al K X-radiation was employed for the XPS examination, at source excitation energy of 15 KeV and emission current of 20 mA. Analyzer pass energy of 20 eV with step size of 0.1 eV and dwell time of 100 ms was used throughout

Challenges in QCD matter physics - The Compressed Baryonic Matter experiment at FAIR

Substantial experimental and theoretical efforts worldwide are devoted to explore the phase diagram of strongly interacting matter. At LHC and top RHIC energies, QCD matter is studied at very high temperatures and nearly vanishing net-baryon densities. There is evidence that a Quark-Gluon-Plasma (QGP) was created at experiments at RHIC and LHC. The transition from the QGP back to the hadron gas is found to be a smooth cross over. For larger net-baryon densities and lower temperatures, it is expected that the QCD phase diagram exhibits a rich structure, such as a first-order phase transition between hadronic and partonic matter which terminates in a critical point, or exotic phases like quarkyonic matter. The discovery of these landmarks would be a breakthrough in our understanding of the strong interaction and is therefore in the focus of various high-energy heavy-ion research programs. The Compressed Baryonic Matter (CBM) experiment at FAIR will play a unique role in the exploration of the QCD phase diagram in the region of high net-baryon densities, because it is designed to run at unprecedented interaction rates. High-rate operation is the key prerequisite for high-precision measurements of multi-differential observables and of rare diagnostic probes which are sensitive to the dense phase of the nuclear fireball. The goal of the CBM experiment at SIS100 (sqrt(s_NN) = 2.7 - 4.9 GeV) is to discover fundamental properties of QCD matter: the phase structure at large baryon-chemical potentials (mu_B > 500 MeV), effects of chiral symmetry, and the equation-of-state at high density as it is expected to occur in the core of neutron stars. In this article, we review the motivation for and the physics programme of CBM, including activities before the start of data taking in 2022, in the context of the worldwide efforts to explore high-density QCD matter.Comment: 15 pages, 11 figures. Published in European Physical Journal