411 research outputs found
Zone Determinant Expansions for Nuclear Lattice Simulations
We introduce a new approximation to nucleon matrix determinants that is
physically motivated by chiral effective theory. The method involves breaking
the lattice into spatial zones and expanding the determinant in powers of the
boundary hopping parameter.Comment: 20 pages, 6 figures, revtex4 (version to appear in PRC
Self-organized stable pacemakers near the onset of birhythmicity
General amplitude equations for reaction-diffusion systems near to the soft
onset of birhythmicity described by a supercritical pitchfork-Hopf bifurcation
are derived. Using these equations and applying singular perturbation theory,
we show that stable autonomous pacemakers represent a generic kind of
spatiotemporal patterns in such systems. This is verified by numerical
simulations, which also show the existence of breathing and swinging pacemaker
solutions. The drift of self-organized pacemakers in media with spatial
parameter gradients is analytically and numerically investigated.Comment: 4 pages, 4 figure
Monte Carlo simulations of fluid vesicles with in plane orientational ordering
We present a method for simulating fluid vesicles with in-plane orientational
ordering. The method involves computation of local curvature tensor and
parallel transport of the orientational field on a randomly triangulated
surface. It is shown that the model reproduces the known equilibrium
conformation of fluid membranes and work well for a large range of bending
rigidities. Introduction of nematic ordering leads to stiffening of the
membrane. Nematic ordering can also result in anisotropic rigidity on the
surface leading to formation of membrane tubes.Comment: 11 Pages, 12 Figures, To appear in Phys. Rev.
Spectral plots and the representation and interpretation of biological data
It is basic question in biology and other fields to identify the char-
acteristic properties that on one hand are shared by structures from a
particular realm, like gene regulation, protein-protein interaction or neu- ral
networks or foodwebs, and that on the other hand distinguish them from other
structures. We introduce and apply a general method, based on the spectrum of
the normalized graph Laplacian, that yields repre- sentations, the spectral
plots, that allow us to find and visualize such properties systematically. We
present such visualizations for a wide range of biological networks and compare
them with those for networks derived from theoretical schemes. The differences
that we find are quite striking and suggest that the search for universal
properties of biological networks should be complemented by an understanding of
more specific features of biological organization principles at different
scales.Comment: 15 pages, 7 figure
C24 Sphingolipids Govern the Transbilayer Asymmetry of Cholesterol and Lateral Organization of Model and Live-Cell Plasma Membranes
Mammalian sphingolipids, primarily with C24 or C16 acyl chains, reside in the outer leaflet of the plasma membrane. Curiously, little is known how C24 sphingolipids impact cholesterol and membrane microdomains. Here, we present evidence that C24 sphingomyelin, when placed in the outer leaflet, suppresses microdomains in giant unilamellar vesicles and also suppresses submicron domains in the plasma membrane of HeLa cells. Free energy calculations suggested that cholesterol has a preference for the inner leaflet if C24 sphingomyelin is in the outer leaflet. We indeed observe that cholesterol enriches in the inner leaflet (80%) if C24 sphingomyelin is in the outer leaflet. Similarly, cholesterol primarily resides in the cytoplasmic leaflet (80%) in the plasma membrane of human erythrocytes where C24 sphingolipids are naturally abundant in the outer leaflet. We conclude that C24 sphingomyelin uniquely interacts with cholesterol and regulates the lateral organization in asymmetric membranes, potentially by generating cholesterol asymmetry
On the Convergence of Ritz Pairs and Refined Ritz Vectors for Quadratic Eigenvalue Problems
For a given subspace, the Rayleigh-Ritz method projects the large quadratic
eigenvalue problem (QEP) onto it and produces a small sized dense QEP. Similar
to the Rayleigh-Ritz method for the linear eigenvalue problem, the
Rayleigh-Ritz method defines the Ritz values and the Ritz vectors of the QEP
with respect to the projection subspace. We analyze the convergence of the
method when the angle between the subspace and the desired eigenvector
converges to zero. We prove that there is a Ritz value that converges to the
desired eigenvalue unconditionally but the Ritz vector converges conditionally
and may fail to converge. To remedy the drawback of possible non-convergence of
the Ritz vector, we propose a refined Ritz vector that is mathematically
different from the Ritz vector and is proved to converge unconditionally. We
construct examples to illustrate our theory.Comment: 20 page
Three-dimensional pattern formation, multiple homogeneous soft modes, and nonlinear dielectric electroconvection
Patterns forming spontaneously in extended, three-dimensional, dissipative
systems are likely to excite several homogeneous soft modes (
hydrodynamic modes) of the underlying physical system, much more than quasi
one- and two-dimensional patterns are. The reason is the lack of damping
boundaries. This paper compares two analytic techniques to derive the patten
dynamics from hydrodynamics, which are usually equivalent but lead to different
results when applied to multiple homogeneous soft modes. Dielectric
electroconvection in nematic liquid crystals is introduced as a model for
three-dimensional pattern formation. The 3D pattern dynamics including soft
modes are derived. For slabs of large but finite thickness the description is
reduced further to a two-dimensional one. It is argued that the range of
validity of 2D descriptions is limited to a very small region above threshold.
The transition from 2D to 3D pattern dynamics is discussed. Experimentally
testable predictions for the stable range of ideal patterns and the electric
Nusselt numbers are made. For most results analytic approximations in terms of
material parameters are given.Comment: 29 pages, 2 figure
Exact Solutions for Domain Walls in Coupled Complex Ginzburg - Landau Equations
The complex Ginzburg Landau equation (CGLE) is a ubiquitous model for the
evolution of slowly varying wave packets in nonlinear dissipative media. A
front (shock) is a transient layer between a plane-wave state and a zero
background. We report exact solutions for domain walls, i.e., pairs of fronts
with opposite polarities, in a system of two coupled CGLEs, which describe
transient layers between semi-infinite domains occupied by each component in
the absence of the other one. For this purpose, a modified Hirota bilinear
operator, first proposed by Bekki and Nozaki, is employed. A novel
factorization procedure is applied to reduce the intermediate calculations
considerably. The ensuing system of equations for the amplitudes and
frequencies is solved by means of computer-assisted algebra. Exact solutions
for mutually-locked front pairs of opposite polarities, with one or several
free parameters, are thus generated. The signs of the cubic gain/loss, linear
amplification/attenuation, and velocity of the coupled-front complex can be
adjusted in a variety of configurations. Numerical simulations are performed to
study the stability properties of such fronts.Comment: Journal of the Physical Society of Japan, in pres
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