1,096 research outputs found
Ueber das Leben und die Meinungen des Herrn Magister Sebaldus Nothanker
http://tartu.ester.ee/record=b1335141~S1*es
Remodeling of cardiac passive electrical properties and susceptibility to ventricular and atrial arrhythmias
Coordinated electrical activation of the heart is essential for the maintenance of a regular cardiac rhythm and effective contractions. Action potentials spread from one cell to the next via gap junction channels. Because of the elongated shape of cardiomyocytes, longitudinal resistivity is lower than transverse resistivity causing electrical anisotropy. Moreover, non-uniformity is created by clustering of gap junction channels at cell poles and by non-excitable structures such as collagenous strands, vessels or fibroblasts. Structural changes in cardiac disease often affect passive electrical properties by increasing non-uniformity and altering anisotropy. This disturbs normal electrical impulse propagation and is, consequently, a substrate for arrhythmia. However, to investigate how these structural changes lead to arrhythmias remains a challenge. One important mechanism, which may both cause and prevent arrhythmia, is the mismatch between current sources and sinks. Propagation of the electrical impulse requires a sufficient source of depolarizing current. In the case of a mismatch, the activated tissue (source) is not able to deliver enough depolarizing current to trigger an action potential in the non-activated tissue (sink). This eventually leads to conduction block. It has been suggested that in this situation a balanced geometrical distribution of gap junctions and reduced gap junction conductance may allow successful propagation. In contrast, source-sink mismatch can prevent spontaneous arrhythmogenic activity in a small number of cells from spreading over the ventricle, especially if gap junction conductance is enhanced. Beside gap junctions, cell geometry and non-cellular structures strongly modulate arrhythmogenic mechanisms. The present review elucidates these and other implications of passive electrical properties for cardiac rhythm and arrhythmogenesis
Towards an understanding of the stability properties of the 3+1 evolution equations in general relativity
We study the stability properties of the standard ADM formulation of the 3+1
evolution equations of general relativity through linear perturbations of flat
spacetime. We focus attention on modes with zero speed of propagation and
conjecture that they are responsible for instabilities encountered in numerical
evolutions of the ADM formulation. These zero speed modes are of two kinds:
pure gauge modes and constraint violating modes. We show how the decoupling of
the gauge by a conformal rescaling can eliminate the problem with the gauge
modes. The zero speed constraint violating modes can be dealt with by using the
momentum constraints to give them a finite speed of propagation. This analysis
sheds some light on the question of why some recent reformulations of the 3+1
evolution equations have better stability properties than the standard ADM
formulation.Comment: 15 pages, 9 figures. Added a new section, plus incorporated many
comments made by refere
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.
DNA cleavage site selection by Type III restriction enzymes provides evidence for head-on protein collisions following 1D bidirectional motion
DNA cleavage by the Type III Restriction–Modification enzymes requires communication in 1D between two distant indirectly-repeated recognitions sites, yet results in non-specific dsDNA cleavage close to only one of the two sites. To test a recently proposed ATP-triggered DNA sliding model, we addressed why one site is selected over another during cleavage. We examined the relative cleavage of a pair of identical sites on DNA substrates with different distances to a free or protein blocked end, and on a DNA substrate using different relative concentrations of protein. Under these conditions a bias can be induced in the cleavage of one site over the other. Monte-Carlo simulations based on the sliding model reproduce the experimentally observed behaviour. This suggests that cleavage site selection simply reflects the dynamics of the preceding stochastic enzyme events that are consistent with bidirectional motion in 1D and DNA cleavage following head-on protein collision
Dynamical Gauge Conditions for the Einstein Evolution Equations
The Einstein evolution equations have been written in a number of symmetric
hyperbolic forms when the gauge fields--the densitized lapse and the shift--are
taken to be fixed functions of the coordinates. Extended systems of evolution
equations are constructed here by adding the gauge degrees of freedom to the
set of dynamical fields, thus forming symmetric hyperbolic systems for the
combined evolution of the gravitational and the gauge fields. The associated
characteristic speeds can be made causal (i.e. less than or equal to the speed
of light) by adjusting 14 free parameters in these new systems. And 21
additional free parameters are available, for example to optimize the stability
of numerical evolutions. The gauge evolution equations in these systems are
generalizations of the ``K-driver'' and ``Gamma-driver'' conditions that have
been used with some success in numerical black hole evolutions.Comment: New appendix on constraint evolution adde
Numerical Evolution of Black Holes with a Hyperbolic Formulation of General Relativity
We describe a numerical code that solves Einstein's equations for a
Schwarzschild black hole in spherical symmetry, using a hyperbolic formulation
introduced by Choquet-Bruhat and York. This is the first time this formulation
has been used to evolve a numerical spacetime containing a black hole. We
excise the hole from the computational grid in order to avoid the central
singularity. We describe in detail a causal differencing method that should
allow one to stably evolve a hyperbolic system of equations in three spatial
dimensions with an arbitrary shift vector, to second-order accuracy in both
space and time. We demonstrate the success of this method in the spherically
symmetric case.Comment: 23 pages RevTeX plus 7 PostScript figures. Submitted to Phys. Rev.
Treating instabilities in a hyperbolic formulation of Einstein's equations
We have recently constructed a numerical code that evolves a spherically
symmetric spacetime using a hyperbolic formulation of Einstein's equations. For
the case of a Schwarzschild black hole, this code works well at early times,
but quickly becomes inaccurate on a time scale of 10-100 M, where M is the mass
of the hole. We present an analytic method that facilitates the detection of
instabilities. Using this method, we identify a term in the evolution equations
that leads to a rapidly-growing mode in the solution. After eliminating this
term from the evolution equations by means of algebraic constraints, we can
achieve free evolution for times exceeding 10000M. We discuss the implications
for three-dimensional simulations.Comment: 13 pages, 9 figures. To appear in Phys. Rev.
Energy Norms and the Stability of the Einstein Evolution Equations
The Einstein evolution equations may be written in a variety of equivalent
analytical forms, but numerical solutions of these different formulations
display a wide range of growth rates for constraint violations. For symmetric
hyperbolic formulations of the equations, an exact expression for the growth
rate is derived using an energy norm. This expression agrees with the growth
rate determined by numerical solution of the equations. An approximate method
for estimating the growth rate is also derived. This estimate can be evaluated
algebraically from the initial data, and is shown to exhibit qualitatively the
same dependence as the numerically-determined rate on the parameters that
specify the formulation of the equations. This simple rate estimate therefore
provides a useful tool for finding the most well-behaved forms of the evolution
equations.Comment: Corrected typos; to appear in Physical Review
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