Leaf-wise intersections and Rabinowitz Floer homology

In this article we explain how critical points of a particular perturbation of the Rabinowitz action functional give rise to leaf-wise intersection points in hypersurfaces of restricted contact type. This is used to derive existence and multiplicity results for leaf-wise intersection points in hypersurfaces of restricted contact type in general exact symplectic manifolds. The notion of leaf-wise intersection points was introduced by Moser.Comment: 18 pages, 1 figure; v3: completely rewritten, improved result

EPOBF: Energy Efficient Allocation of Virtual Machines in High Performance Computing Cloud

Cloud computing has become more popular in provision of computing resources under virtual machine (VM) abstraction for high performance computing (HPC) users to run their applications. A HPC cloud is such cloud computing environment. One of challenges of energy efficient resource allocation for VMs in HPC cloud is tradeoff between minimizing total energy consumption of physical machines (PMs) and satisfying Quality of Service (e.g. performance). On one hand, cloud providers want to maximize their profit by reducing the power cost (e.g. using the smallest number of running PMs). On the other hand, cloud customers (users) want highest performance for their applications. In this paper, we focus on the scenario that scheduler does not know global information about user jobs and user applications in the future. Users will request shortterm resources at fixed start times and non interrupted durations. We then propose a new allocation heuristic (named Energy-aware and Performance per watt oriented Bestfit (EPOBF)) that uses metric of performance per watt to choose which most energy-efficient PM for mapping each VM (e.g. maximum of MIPS per Watt). Using information from Feitelson's Parallel Workload Archive to model HPC jobs, we compare the proposed EPOBF to state of the art heuristics on heterogeneous PMs (each PM has multicore CPU). Simulations show that the EPOBF can reduce significant total energy consumption in comparison with state of the art allocation heuristics.Comment: 10 pages, in Procedings of International Conference on Advanced Computing and Applications, Journal of Science and Technology, Vietnamese Academy of Science and Technology, ISSN 0866-708X, Vol. 51, No. 4B, 201

Prediction of an undimerized, insulating, antiferromagnetic ground-state in halogen-bridged linear-chain Ni compounds

A parameter-free, mean-field, multi-orbital Hubbard model with nonspherical Coulomb and exchange interactions, implemented around all-electron local-density approximation (LDA) calculations, correctly predicts the band-gap energy, the absence of dimerization, and the antiferromagnetic ground state of halogen-bridged linear-chain Ni compounds. This approach also reproduces the insulating ground state and dimerization in PtX linear-chain compounds in agreement with experiment and previous calculations. Three "ps" figures are included at the end of the RevTex file and compressed using uufiles.Comment: 11 RevTex pages and three ps figures. Paper accepted by PRB Rapid Com

Coulomb correlation in presence of spin-orbit coupling: application to plutonium

Attempts to go beyond the local density approximation (LDA) of Density Functional Theory (DFT) have been increasingly based on the incorporation of more realistic Coulomb interactions. In their earliest implementations, methods like LDA+$U$, LDA + DMFT (Dynamical Mean Field Theory), and LDA+Gutzwiller used a simple model interaction $U$. In this article we generalize the solution of the full Coulomb matrix involving $F^{(0)}$ to $F^{(6)}$ parameters, which is usually presented in terms of an $\ell m_\ell$ basis, into a $jm_{j}$ basis of the total angular momentum, where we also include spin-orbit coupling; this type of theory is needed for a reliable description of $f$-state elements like plutonium, which we use as an example of our theory. Close attention will be paid to spin-flip terms, which are important in multiplet theory but that have been usually neglected in these kinds of studies. We find that, in a density-density approximation, the $jm_j$ basis results provide a very good approximation to the full Coulomb matrix result, in contrast to the much less accurate results for the more conventional $\ell m_\ell$ basis

On magnetic leaf-wise intersections

In this article we introduce the notion of a magnetic leaf-wise intersection point which is a generalization of the leaf-wise intersection point with magnetic effects. We also prove the existence of magnetic leaf-wise intersection points under certain topological assumptions.Comment: 43 page

Probability of local bifurcation type from a fixed point: A random matrix perspective

Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties as universal approximators (neural networks). The eigenvalue spectra is considered both numerically and analytically using previous work of Edelman et. al. Based upon the numerical evidence, various conjectures are presented. The conclusion is that in many circumstances, most bifurcations from fixed points of large dynamical systems will be due to complex eigenvalues. Nevertheless, surprising situations are presented for which the aforementioned conclusion is not general, e.g. real random matrices with Gaussian elements with a large positive mean and finite variance.Comment: 21 pages, 19 figure

Exploring atomic-scale lateral forces in the attractive regime: a case study on graphite (0001)

Cataloged from PDF version of article.A non-contact atomic force microscopy-based method has been used to map the static lateral forces exerted on an atomically sharp Pt/Ir probe tip by a graphite surface. With measurements carried out at low temperatures and in the attractive regime, where the atomic sharpness of the tip can be maintained over extended time periods, the method allows the quantification and directional analysis of lateral forces with piconewton and picometer resolution as a function of both the in-plane tip position and the vertical tip-sample distance, without limitations due to a finite contact area or to stick-slip-related sudden jumps of tip apex atoms. After reviewing the measurement principle, the data obtained in this case study are utilized to illustrate the unique insight that the method offers. In particular, the local lateral forces that are expected to determine frictional resistance in the attractive regime are found to depend linearly on the normal force for small tip-sample distances