Interaction of Hopf and period doubling bifurcations of a vibro-impact system

International audienceAn inertial shaker as a vibratory system with impact is considered. By means of differential equations, periodicity and matching conditions, the theoretical solution of periodic n-1 impacting motion can be obtained and the Poincaré map is established. Dynamics of the system are studied with special attention to interaction of Hopf and period doubling bifurcations corresponding to a codimension-2 one when a pair of complex conjugate eigenvalues crosses the unit circle and the other eigenvalue crosses -1 simultaneously for the Jacobi matrix. The four-dimensional map can be reduced to a three-dimensional normal form by the center manifold theorem and the theory of normal forms. The two-parameter unfoldings of local dynamical behavior are put forward and the singularity is investigated. It is proved that there exist curve doubling bifurcation (a torus doubling bifurcation), Hopf bifurcation of 2–2 fixed points as well as period doubling bifurcation and Hopf bifurcation of 1–1 fixed points near the critical point. Numerical results indicate that the vibro-impact system presents complicated and interesting curve doubling bifurcation and Hopf bifurcation as the two controlling parameters vary

Anaerobic co-digestion of oil refinery wastewater and chicken manure to produce biogas, and kinetic parameters determination in batch reactors

ArticleIn order to improve the anaerobic fermentation of oil refinery wastewater (ORWW) via an appropriate nutrients pool for microbial and buffer capacity growth, a study was carried out on related anaerobic co-digestion (AcoD) with a rich organic carbon source, namely chicken manure (CM). The kinetic parameters were investigated (including cumulative biogas production, bio-methane content, retention time, and soluble chemical oxygen demand stabilisation rate) of batch AcoD experiments related to six ORWW:CM-ratio treatments (5:0, 4:1, 3:2, 2:3, 1:4, and 0:5) under mesophilic conditions. The highest soluble chemical oxygen demand removal rate was obtained for the 4:1-ratio treatment. However, the highest biogas production and bio-methane contents were achieved for the 1:4-ratio treatment. When taking into consideration the highest oil refinery wastewater portion in the AcoD mixtures and the statistical test results (LSD0.05) for the kinetic parameters, it can be seen that the 4:1-ratio treatment provided the maximum biogas production levels

Graph Treewidth and Geometric Thickness Parameters

Consider a drawing of a graph $G$ in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of $G$, is the classical graph parameter "thickness". By restricting the edges to be straight, we obtain the "geometric thickness". By further restricting the vertices to be in convex position, we obtain the "book thickness". This paper studies the relationship between these parameters and treewidth. Our first main result states that for graphs of treewidth $k$, the maximum thickness and the maximum geometric thickness both equal $\lceil{k/2}\rceil$. This says that the lower bound for thickness can be matched by an upper bound, even in the more restrictive geometric setting. Our second main result states that for graphs of treewidth $k$, the maximum book thickness equals $k$ if $k \leq 2$ and equals $k+1$ if $k \geq 3$. This refutes a conjecture of Ganley and Heath [Discrete Appl. Math. 109(3):215-221, 2001]. Analogous results are proved for outerthickness, arboricity, and star-arboricity.Comment: A preliminary version of this paper appeared in the "Proceedings of the 13th International Symposium on Graph Drawing" (GD '05), Lecture Notes in Computer Science 3843:129-140, Springer, 2006. The full version was published in Discrete & Computational Geometry 37(4):641-670, 2007. That version contained a false conjecture, which is corrected on page 26 of this versio

Supporting Interoperability of Virtual Factories

The manufacturing industry is entering a new era. This emerging era starts with the integration of new ICT technologies and collaboration applications into traditional manufacturing practices and processes, such as manufacturing 2.0. Manufacturing 2.0 has been conceptualised as a system that goes beyond the factory floor, and paradigms of “manufacturing as an ecosystem” have emerged. The virtual factory is one of the important concepts and foundations central to the realization of future manufacturing. In this paper, we take a look into the current research on virtual factories and propose a new approach to improve interoperability through the integration of different proprietary, legacy and existing solutions

A Coupled Equations Model for Epitaxial Growth on Textured Surfaces

We have developed a continuum model that explains the complex surface shapes observed in epitaxial regrowth on micron scale gratings. This model describes the dependence of the surface morphology on film thickness and growth temperature in terms of a few simple atomic scale processes including adatom diffusion, step-edge attachment and detachment, and a net downhill migration of surface adatoms. The continuum model reduces to the linear part of the Kardar-Parisi-Zhang equation with a flux dependent smoothing coefficient in the long wavelength limit.Comment: 11 pages, 4 figures. Submitted to the Journal of Crystal Growt

Classification of protein interaction sentences via gaussian processes

The increase in the availability of protein interaction studies in textual format coupled with the demand for easier access to the key results has lead to a need for text mining solutions. In the text processing pipeline, classification is a key step for extraction of small sections of relevant text. Consequently, for the task of locating protein-protein interaction sentences, we examine the use of a classifier which has rarely been applied to text, the Gaussian processes (GPs). GPs are a non-parametric probabilistic analogue to the more popular support vector machines (SVMs). We find that GPs outperform the SVM and na\"ive Bayes classifiers on binary sentence data, whilst showing equivalent performance on abstract and multiclass sentence corpora. In addition, the lack of the margin parameter, which requires costly tuning, along with the principled multiclass extensions enabled by the probabilistic framework make GPs an appealing alternative worth of further adoption

Energy landscape of relaxed amorphous silicon

We analyze the structure of the energy landscape of a well-relaxed 1000-atom model of amorphous silicon using the activation-relaxation technique (ART nouveau). Generating more than 40,000 events starting from a single minimum, we find that activated mechanisms are local in nature, that they are distributed uniformly throughout the model and that the activation energy is limited by the cost of breaking one bond, independently of the complexity of the mechanism. The overall shape of the activation-energy-barrier distribution is also insensitive to the exact details of the configuration, indicating that well-relaxed configurations see essentially the same environment. These results underscore the localized nature of relaxation in this material.Comment: 8 pages, 12 figure

Phase transition from a dx2−y2d_{x^2-y^2} to dx2−y2+dxyd_{x^2-y^2}+d_{xy} superconductor

We study the phase transition from a $d_{x^2-y^2}$ to $d_{x^2-y^2}+d_{xy}$ superconductor using the tight-binding model of two-dimensional cuprates. As the temperature is lowered past the critical temperature $T_c$, first a $d_{x^2-y^2}$ superconducting phase is created. With further reduction of temperature, the $d_{x^2-y^2}+d_{xy}$ phase is created at temperature $T=T_{c1}$. We study the temperature dependencies of the order parameter, specific heat and spin susceptibility in these mixed-angular-momentum states on square lattice and on a lattice with orthorhombic distortion. The above-mentioned phase transitions are identified by two jumps in specific heat at $T_c$ and $T_{c1}$.Comment: Latex file, 5 pages, 6 postscript figures, Accepted in Physical Review

Exact two-particle eigenstates in partially reduced QED

We consider a reformulation of QED in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. It is shown that exact few-fermion eigenstates of the resulting Hamiltonian can be obtained in the canonical equal-time formalism for the case where there are no free photons. These eigenstates lead to two- and three-body Dirac-like equations with electromagnetic interactions. Perturbative and some numerical solutions of the two-body equations are presented for positronium and muonium-like systems, for various strengths of the coupling.Comment: 33 pages, LaTex 2.09, 4 figures in EPS forma

Long Range Magnetic Order and the Darwin Lagrangian

We simulate a finite system of $N$ confined electrons with inclusion of the Darwin magnetic interaction in two- and three-dimensions. The lowest energy states are located using the steepest descent quenching adapted for velocity dependent potentials. Below a critical density the ground state is a static Wigner lattice. For supercritical density the ground state has a non-zero kinetic energy. The critical density decreases with $N$ for exponential confinement but not for harmonic confinement. The lowest energy state also depends on the confinement and dimension: an antiferromagnetic cluster forms for harmonic confinement in two dimensions.Comment: 5 figure