1,605 research outputs found
Block partitions: an extended view
Given a sequence , a block of is a
subsequence . The size of a block is the sum
of its elements. It is proved in [1] that for each positive integer , there
is a partition of into blocks with for every . In this paper, we consider a generalization of the problem
in higher dimensions
Faceting and branching in 2D crystal growth
The official published version of the Article can be accessed from the link below - Copyright @ 2011 APSUsing atomic scale time-dependent density functional calculations we confirm that both diffusion-controlled and diffusionless crystallization modes exist in simple 2D systems. We provide theoretical evidence that a faceted to nonfaceted transition is coupled to these crystallization modes, and faceting is governed by the local supersaturation at the fluid-crystalline interface. We also show that competing modes of crystallization have a major influence on mesopattern formation. Irregularly branched and porous structures are emerging at the crossover of the crystallization modes. The proposed branching mechanism differs essentially from dendritic fingering driven by diffusive instability.This work has been supported by the EU FP7
Collaborative Project ENSEMBLE under Grant
Agreement NMP4-SL-2008-213669 and by the
Hungarian Academy of Sciences under Contract
No. OTKA-K-62588
On the decay of Burgers turbulence
This work is devoted to the decay ofrandom solutions of the unforced Burgers
equation in one dimension in the limit of vanishing viscosity. The initial
velocity is homogeneous and Gaussian with a spectrum proportional to at
small wavenumbers and falling off quickly at large wavenumbers. In physical
space, at sufficiently large distances, there is an ``outer region'', where the
velocity correlation function preserves exactly its initial form (a power law)
when is not an even integer. When the spectrum, at long times, has
three scaling regions : first, a region at very small \ms1 with a
time-independent constant, stemming from this outer region, in which the
initial conditions are essentially frozen; second, a region at
intermediate wavenumbers, related to a self-similarly evolving ``inner region''
in physical space and, finally, the usual region, associated to the
shocks. The switching from the to the region occurs around a wave
number , while the switching from to
occurs around (ignoring logarithmic
corrections in both instances). The key element in the derivation of the
results is an extension of the Kida (1979) log-corrected law for the
energy decay when to the case of arbitrary integer or non-integer .
A systematic derivation is given in which both the leading term and estimates
of higher order corrections can be obtained. High-resolution numerical
simulations are presented which support our findings.Comment: In LaTeX with 11 PostScript figures. 56 pages. One figure contributed
by Alain Noullez (Observatoire de Nice, France
Searching for electromagnetic counterpart of LIGO gravitational waves in the Fermi GBM data with ADWO
The Fermi collaboration identified a possible electromagnetic counterpart of
the gravitational wave event of September 14, 2015. Our goal is to provide an
unsupervised data analysis algorithm to identify similar events in Fermi's
Gamma-ray Burst Monitor CTTE data stream. We are looking for signals that are
typically weak. Therefore, they can only be found by a careful analysis of
count rates of all detectors and energy channels simultaneously. Our
Automatized Detector Weight Optimization (ADWO) method consists of a search for
the signal, and a test of its significance. We developed ADWO, a virtual
detector analysis tool for multi-channel multi-detector signals, and performed
successful searches for short transients in the data-streams. We have
identified GRB150522B, as well as possible electromagnetic candidates of the
transients GW150914 and LVT151012. ADWO is an independently developed,
unsupervised data analysis tool that only relies on the raw data of the Fermi
satellite. It can therefore provide a strong, independent test to any
electromagnetic signal accompanying future gravitational wave observations.Comment: 4 pages and 4 figures, A&A Letters accepte
Multidimensional analysis of Fermi GBM gamma-ray bursts
The Fermi GBM catalog provides a large database with many measured variables
that can be used to explore and verify gamma-ray burst classification results.
We have used Principal Component Analysis and statistical clustering techniques
to look for clustering in a sample of 801 gamma-ray bursts described by sixteen
classification variables. The analysis recovers what appears to be the Short
class and two long-duration classes that differ from one another via peak flux,
with negligible variations in fluence, duration and spectral hardness. Neither
class has properties entirely consistent with the Intermediate GRB class.
Spectral hardness has been a critical Intermediate class property. Rather than
providing spectral hardness, Fermi GBM provides a range of fitting variables
for four different spectral models; it is not intuitive how these variables can
be used to support or disprove previous GRB classification results.Comment: accepte
Density matrix numerical renormalization group for non-Abelian symmetries
We generalize the spectral sum rule preserving density matrix numerical
renormalization group (DM-NRG) method in such a way that it can make use of an
arbitrary number of not necessarily Abelian, local symmetries present in the
quantum impurity system. We illustrate the benefits of using non-Abelian
symmetries by the example of calculations for the T-matrix of the two-channel
Kondo model in the presence of magnetic field, for which conventional NRG
methods produce large errors and/or take a long run-time.Comment: 12 pages, 6 figures, PRB forma
Phase field theory of interfaces and crystal nucleation in a eutectic system of fcc structure: I. Transitions in the one-phase liquid region
The published version of this Article can be accessed from the link below - Copyright @ 2007 American Institute of PhysicsThe phase field theory (PFT) has been applied to predict equilibrium interfacial properties and nucleation barrier in the binary eutectic system Ag-Cu using double well and interpolation functions deduced from a Ginzburg-Landau expansion that considers fcc (face centered cubic) crystal symmetries. The temperature and composition dependent free energies of the liquid and solid phases are taken from CALculation of PHAse Diagrams-type calculations. The model parameters of PFT are fixed so as to recover an interface thickness of approximately 1 nm from molecular dynamics simulations and the interfacial free energies from the experimental dihedral angles available for the pure components. A nontrivial temperature and composition dependence for the equilibrium interfacial free energy is observed. Mapping the possible nucleation pathways, we find that the Ag and Cu rich critical fluctuations compete against each other in the neighborhood of the eutectic composition. The Tolman length is positive and shows a maximum as a function of undercooling. The PFT predictions for the critical undercooling are found to be consistent with experimental results. These results support the view that heterogeneous nucleation took place in the undercooling experiments available at present. We also present calculations using the classical droplet model classical nucleation theory (CNT) and a phenomenological diffuse interface theory (DIT). While the predictions of the CNT with a purely entropic interfacial free energy underestimate the critical undercooling, the DIT results appear to be in a reasonable agreement with the PFT predictions.This work has been supported by the Hungarian Academy of Sciences under Contract No. OTKA-K-62588 and by the ESA PECS Contract Nos. 98005, 98021, and 98043
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