10,512 research outputs found
First order hyperbolic formalism for Numerical Relativity
The causal structure of Einstein's evolution equations is considered. We show
that in general they can be written as a first order system of balance laws for
any choice of slicing or shift. We also show how certain terms in the evolution
equations, that can lead to numerical inaccuracies, can be eliminated by using
the Hamiltonian constraint. Furthermore, we show that the entire system is
hyperbolic when the time coordinate is chosen in an invariant algebraic way,
and for any fixed choice of the shift. This is achieved by using the momentum
constraints in such as way that no additional space or time derivatives of the
equations need to be computed. The slicings that allow hyperbolicity in this
formulation belong to a large class, including harmonic, maximal, and many
others that have been commonly used in numerical relativity. We provide details
of some of the advanced numerical methods that this formulation of the
equations allows, and we also discuss certain advantages that a hyperbolic
formulation provides when treating boundary conditions.Comment: To appear in Phys. Rev.
Fabrication of Pt/Ru Nanoparticle Pair Arrays with Controlled Separation and their Electrocatalytic Properties
Aiming at the investigation of spillover and transport effects in electrocatalytic reactions on bimetallic catalyst electrodes, we have prepared novel, nanostructured electrodes consisting of arrays of homogeneously distributed pairs of Pt and Ru nanodisks of uniform size and with controlled separation on planar glassy carbon substrates. The nanodisk arrays (disk diameter approximate to 60 nm) were fabricated by hole-mask colloidal lithography; the separation between pairs of Pt and Ru disks was varied from -25 nm (overlapping) via +25 nm to +50 nm. Morphology and (surface) composition of the Pt/Ru nanodisk arrays Were characterized by scanning electron microscopy, energy dispersive X-ray analysis, and X-ray Photoelectron spectroscopy, the electrochemical/electrocatalytic properties were explored by cyclic voltammetry, COad monolayer oxidation ("COad stripping"), and potentiodynamic hydrogen oxidation. Detailed analysis of the 2 COad oxidation peaks revealed that on all bimetallic pairs these cannot be reproduced by superposition of the peaks obtained on electrodes with Pt/Pt or Ru/Ru pairs, pointing to effective Pt-Ru interactions even between rather distant pairs (50 nm). Possible reasons for this observation and its relevance for the understanding of previous reports of highly active catalysts with separate Pt and Ru nanoparticles are discussed. The results clearly demonstrate that this preparation method is perfectly suited for fabrication of planar model electrodes with well-defined arrays of bimetallic nanodisk pairs, which opens up new possibilities for model studies of electrochemical/electrocatalytic reactions
Evolution of the Schr\"odinger--Newton system for a self--gravitating scalar field
Using numerical techniques, we study the collapse of a scalar field
configuration in the Newtonian limit of the spherically symmetric
Einstein--Klein--Gordon (EKG) system, which results in the so called
Schr\"odinger--Newton (SN) set of equations. We present the numerical code
developed to evolve the SN system and topics related, like equilibrium
configurations and boundary conditions. Also, we analyze the evolution of
different initial configurations and the physical quantities associated to
them. In particular, we readdress the issue of the gravitational cooling
mechanism for Newtonian systems and find that all systems settle down onto a
0--node equilibrium configuration.Comment: RevTex file, 19 pages, 26 eps figures. Minor changes, matches version
to appear in PR
Intersections of quadrics, moment-angle manifolds, and Hamiltonian-minimal Lagrangian embeddings
We study the topology of Hamiltonian-minimal Lagrangian submanifolds N in C^m
constructed from intersections of real quadrics in a work of the first author.
This construction is linked via an embedding criterion to the well-known
Delzant construction of Hamiltonian toric manifolds. We establish the following
topological properties of N: every N embeds as a submanifold in the
corresponding moment-angle manifold Z, and every N is the total space of two
different fibrations, one over the torus T^{m-n} with fibre a real moment-angle
manifold R, and another over a quotient of R by a finite group with fibre a
torus. These properties are used to produce new examples of Hamiltonian-minimal
Lagrangian submanifolds with quite complicated topology.Comment: 14 pages, published version (minor changes
Influence of Josephson current second harmonic on stability of magnetic flux in long junctions
We study the long Josephson junction (LJJ) model which takes into account the
second harmonic of the Fourier expansion of Josephson current. The dependence
of the static magnetic flux distributions on parameters of the model are
investigated numerically. Stability of the static solutions is checked by the
sign of the smallest eigenvalue of the associated Sturm-Liouville problem. New
solutions which do not exist in the traditional model, have been found.
Investigation of the influence of second harmonic on the stability of magnetic
flux distributions for main solutions is performed.Comment: 4 pages, 6 figures, to be published in Proc. of Dubna-Nano2010, July
5-10, 2010, Russi
A detailed study of quasinormal frequencies of the Kerr black hole
We compute the quasinormal frequencies of the Kerr black hole using a
continued fraction method. The continued fraction method first proposed by
Leaver is still the only known method stable and accurate for the numerical
determination of the Kerr quasinormal frequencies. We numerically obtain not
only the slowly but also the rapidly damped quasinormal frequencies and analyze
the peculiar behavior of these frequencies at the Kerr limit. We also calculate
the algebraically special frequency first identified by Chandrasekhar and
confirm that it coincide with the quasinormal frequency only at the
Schwarzschild limit.Comment: REVTEX, 15 pages, 7 eps figure
Calculation of AGARD Wing 445.6 Flutter Using Navier-Stokes Aerodynamics
An unsteady, 3D, implicit upwind Euler/Navier-Stokes algorithm is here used to compute the flutter characteristics of Wing 445.6, the AGARD standard aeroelastic configuration for dynamic response, with a view to the discrepancy between Euler characteristics and experimental data. Attention is given to effects of fluid viscosity, structural damping, and number of structural model nodes. The flutter characteristics of the wing are determined using these unsteady generalized aerodynamic forces in a traditional V-g analysis. The V-g analysis indicates that fluid viscosity has a significant effect on the supersonic flutter boundary for this wing
Persistence length of a polyelectrolyte in salty water: a Monte-Carlo study
We address the long standing problem of the dependence of the electrostatic
persistence length of a flexible polyelectrolyte (PE) on the screening
length of the solution within the linear Debye-Huckel theory. The
standard Odijk, Skolnick and Fixman (OSF) theory suggests ,
while some variational theories and computer simulations suggest . In this paper, we use Monte-Carlo simulations to study the conformation
of a simple polyelectrolyte. Using four times longer PEs than in previous
simulations and refined methods for the treatment of the simulation data, we
show that the results are consistent with the OSF dependence . The linear charge density of the PE which enters in the coefficient of
this dependence is properly renormalized to take into account local
fluctuations.Comment: 7 pages, 6 figures. Various corrections in text and reference
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