587 research outputs found
Collars and partitions of hyperbolic cone-surfaces
For compact Riemann surfaces, the collar theorem and Bers' partition theorem
are major tools for working with simple closed geodesics. The main goal of this
paper is to prove similar theorems for hyperbolic cone-surfaces. Hyperbolic
two-dimensional orbifolds are a particular case of such surfaces. We consider
all cone angles to be strictly less than to be able to consider
partitions.Comment: 11 pages, 9 figures; v2: minor changes, to appear in Geometriae
Dedicat
Hyperelliptic Theta-Functions and Spectral Methods: KdV and KP solutions
This is the second in a series of papers on the numerical treatment of
hyperelliptic theta-functions with spectral methods. A code for the numerical
evaluation of solutions to the Ernst equation on hyperelliptic surfaces of
genus 2 is extended to arbitrary genus and general position of the branch
points. The use of spectral approximations allows for an efficient calculation
of all characteristic quantities of the Riemann surface with high precision
even in almost degenerate situations as in the solitonic limit where the branch
points coincide pairwise. As an example we consider hyperelliptic solutions to
the Kadomtsev-Petviashvili and the Korteweg-de Vries equation. Tests of the
numerics using identities for periods on the Riemann surface and the
differential equations are performed. It is shown that an accuracy of the order
of machine precision can be achieved.Comment: 16 pages, 8 figure
Susceptibility and Percolation in 2D Random Field Ising Magnets
The ground state structure of the two-dimensional random field Ising magnet
is studied using exact numerical calculations. First we show that the
ferromagnetism, which exists for small system sizes, vanishes with a large
excitation at a random field strength dependent length scale. This {\it
break-up length scale} scales exponentially with the squared random
field, . By adding an external field we then study the
susceptibility in the ground state. If , domains melt continuously and
the magnetization has a smooth behavior, independent of system size, and the
susceptibility decays as . We define a random field strength dependent
critical external field value , for the up and down spins to
form a percolation type of spanning cluster. The percolation transition is in
the standard short-range correlated percolation universality class. The mass of
the spanning cluster increases with decreasing and the critical
external field approaches zero for vanishing random field strength, implying
the critical field scaling (for Gaussian disorder) , where and .
Below the systems should percolate even when H=0. This implies that
even for H=0 above the domains can be fractal at low random fields, such
that the largest domain spans the system at low random field strength values
and its mass has the fractal dimension of standard percolation .
The structure of the spanning clusters is studied by defining {\it red
clusters}, in analogy to the ``red sites'' of ordinary site-percolation. The
size of red clusters defines an extra length scale, independent of .Comment: 17 pages, 28 figures, accepted for publication in Phys. Rev.
Nonlinear Dynamics of Aeolian Sand Ripples
We study the initial instability of flat sand surface and further nonlinear
dynamics of wind ripples. The proposed continuous model of ripple formation
allowed us to simulate the development of a typical asymmetric ripple shape and
the evolution of sand ripple pattern. We suggest that this evolution occurs via
ripple merger preceded by several soliton-like interaction of ripples.Comment: 6 pages, 3 figures, corrected 2 typo
Coexistence of Single and Double-Quantum Vortex Lines
We discuss the configurations in which singly and doubly quantized vortex
lines may coexist in a rotating superfluid. General principles of energy
minimization lead to the conclusion that in equilibrium the two vortex species
segregate within a cylindrical vortex cluster in two coaxial domains where the
singly quantized lines are in the outer annular region. This is confirmed with
simulation calculations on discrete vortex lines. Experimentally the
coexistence can be studied in rotating superfluid He-A. With cw NMR
techniques we find the radial distribution of the two vortex species to depend
on how the cluster is prepared: (i) By cooling through in rotation,
coexistence in the minimum energy configuration is confirmed. (ii) A glassy
agglomerate is formed if one starts with an equilibrium cluster of
single-quantum vortex lines and adds to it sequentially double-quantum lines,
by increasing the rotation velocity in the superfluid state. This proves that
the energy barriers, which separate different cluster configurations, are too
high for metastabilities to anneal.Comment: 12 pages, 11 figures; Changed content, 15 pages, 14 figure
Three-dimensional molecular dynamics simulations of void coalescence during dynamic fracture of ductile metals
Void coalescence and interaction in dynamic fracture of ductile metals have
been investigated using three-dimensional strain-controlled multi-million atom
molecular dynamics simulations of copper. The correlated growth of two voids
during the coalescence process leading to fracture is investigated, both in
terms of its onset and the ensuing dynamical interactions. Void interactions
are quantified through the rate of reduction of the distance between the voids,
through the correlated directional growth of the voids, and through correlated
shape evolution of the voids. The critical inter-void ligament distance marking
the onset of coalescence is shown to be approximately one void radius based on
the quantification measurements used, independent of the initial separation
distance between the voids and the strain-rate of the expansion of the system.
The interaction of the voids is not reflected in the volumetric asymptotic
growth rate of the voids, as demonstrated here. Finally, the practice of using
a single void and periodic boundary conditions to study coalescence is examined
critically and shown to produce results markedly different than the coalescence
of a pair of isolated voids.Comment: Accepted for publication in Physical Review
The devices, experimental scaffolds, and biomaterials ontology (DEB): a tool for mapping, annotation, and analysis of biomaterials' data
The size and complexity of the biomaterials literature makes systematic data analysis an excruciating manual task. A practical solution is creating databases and information resources. Implant design and biomaterials research can greatly benefit from an open database for systematic data retrieval. Ontologies are pivotal to knowledge base creation, serving to represent and organize domain knowledge. To name but two examples, GO, the gene ontology, and CheBI, Chemical Entities of Biological Interest ontology and their associated databases are central resources to their respective research communities. The creation of the devices, experimental scaffolds, and biomaterials ontology (DEB), an open resource for organizing information about biomaterials, their design, manufacture, and biological testing, is described. It is developed using text analysis for identifying ontology terms from a biomaterials gold standard corpus, systematically curated to represent the domain's lexicon. Topics covered are validated by members of the biomaterials research community. The ontology may be used for searching terms, performing annotations for machine learning applications, standardized meta-data indexing, and other cross-disciplinary data exploitation. The input of the biomaterials community to this effort to create data-driven open-access research tools is encouraged and welcomed.Preprin
Random manifolds in non-linear resistor networks: Applications to varistors and superconductors
We show that current localization in polycrystalline varistors occurs on
paths which are, usually, in the universality class of the directed polymer in
a random medium. We also show that in ceramic superconductors, voltage
localizes on a surface which maps to an Ising domain wall. The emergence of
these manifolds is explained and their structure is illustrated using direct
solution of non-linear resistor networks
Demonstration of astrocytes in cultured amniotic fluid cells of three cases with neural-tube defect
We have investigated the origin of rapidly adhering (RA) cells in three cases of neural tube defects (two anencephali, one encephalocele). We were able to demonstrate the presence of glial fibrillary acidic (GFA) protein in variable percentages (4–80%) of RA cells cultured for 4–6 days by use of indirect immunofluorescence with GFA antiserum. Cells cultured from amniotic fluids of normal pregnancies and fetal fibroblasts were completely GFA protein negative. GFA protein is well established as a highly specific marker for astrocytes. Demonstration of astrocytes may prove to be a criterion of high diagnostic value for neural tube defects. The percentage of astrocytes decreased with increasing culture time, while the percentage of fibronectin positive cells increased both in amniotic fluid cell cultures from neural tube defects and normal pregnancies
Statistical Physics of Fracture Surfaces Morphology
Experiments on fracture surface morphologies offer increasing amounts of data
that can be analyzed using methods of statistical physics. One finds scaling
exponents associated with correlation and structure functions, indicating a
rich phenomenology of anomalous scaling. We argue that traditional models of
fracture fail to reproduce this rich phenomenology and new ideas and concepts
are called for. We present some recent models that introduce the effects of
deviations from homogeneous linear elasticity theory on the morphology of
fracture surfaces, succeeding to reproduce the multiscaling phenomenology at
least in 1+1 dimensions. For surfaces in 2+1 dimensions we introduce novel
methods of analysis based on projecting the data on the irreducible
representations of the SO(2) symmetry group. It appears that this approach
organizes effectively the rich scaling properties. We end up with the
proposition of new experiments in which the rotational symmetry is not broken,
such that the scaling properties should be particularly simple.Comment: A review paper submitted to J. Stat. Phy
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