731 research outputs found
The Discrete Frenet Frame, Inflection Point Solitons And Curve Visualization with Applications to Folded Proteins
We develop a transfer matrix formalism to visualize the framing of discrete
piecewise linear curves in three dimensional space. Our approach is based on
the concept of an intrinsically discrete curve, which enables us to more
effectively describe curves that in the limit where the length of line segments
vanishes approach fractal structures in lieu of continuous curves. We verify
that in the case of differentiable curves the continuum limit of our discrete
equation does reproduce the generalized Frenet equation. As an application we
consider folded proteins, their Hausdorff dimension is known to be fractal. We
explain how to employ the orientation of carbons of amino acids along
a protein backbone to introduce a preferred framing along the backbone. By
analyzing the experimentally resolved fold geometries in the Protein Data Bank
we observe that this framing relates intimately to the discrete
Frenet framing. We also explain how inflection points can be located in the
loops, and clarify their distinctive r\^ole in determining the loop structure
of foldel proteins.Comment: 14 pages 12 figure
On the curvature of vortex moduli spaces
We use algebraic topology to investigate local curvature properties of the
moduli spaces of gauged vortices on a closed Riemann surface. After computing
the homotopy type of the universal cover of the moduli spaces (which are
symmetric powers of the surface), we prove that, for genus g>1, the holomorphic
bisectional curvature of the vortex metrics cannot always be nonnegative in the
multivortex case, and this property extends to all Kaehler metrics on certain
symmetric powers. Our result rules out an established and natural conjecture on
the geometry of the moduli spaces.Comment: 25 pages; final version, to appear in Math.
On asymptotic stability of the Skyrmion
We study the asymptotic behavior of spherically symmetric solutions in the
Skyrme model. We show that the relaxation to the degree-one soliton (called the
Skyrmion) has a universal form of a superposition of two effects: exponentially
damped oscillations (the quasinormal ringing) and a power law decay (the tail).
The quasinormal ringing, which dominates the dynamics for intermediate times,
is a linear resonance effect. In contrast, the polynomial tail, which becomes
uncovered at late times, is shown to be a \emph{nonlinear} phenomenon.Comment: 4 pages, 4 figures, minor changes to match the PRD versio
Dynamical algebra and Dirac quantum modes in Taub-NUT background
The SO(4,1) gauge-invariant theory of the Dirac fermions in the external
field of the Kaluza-Klein monopole is investigated. It is shown that the
discrete quantum modes are governed by reducible representations of the o(4)
dynamical algebra generated by the components of the angular momentum operator
and those of the Runge-Lenz operator of the Dirac theory in Taub-NUT
background. The consequence is that there exist central and axial discrete
modes whose spinors have no separated variables.Comment: 17 pages, latex, no figures. Version to appear in Class.Quantum Gra
Algorithms and literate programs for weighted low-rank approximation with missing data
Linear models identification from data with missing values is posed as a weighted low-rank approximation problem with weights related to the missing values equal to zero. Alternating projections and variable projections methods for solving the resulting problem are outlined and implemented in a literate programming style, using Matlab/Octave's scripting language. The methods are evaluated on synthetic data and real data from the MovieLens data sets
Forced Topological Nontrivial Field Configurations
The motion of a one-dimensional kink and its energy losses are considered as
a model of interaction of nontrivial topological field configurations with
external fields. The approach is based on the calculation of the zero modes
excitation probability in the external field. We study in the same way the
interaction of the t'Hooft-Polyakov monopole with weak external fields. The
basic idea is to treat the excitation of a monopole zero mode as the monopole
displacement. The excitation is found perturbatively. As an example we consider
the interaction of the t'Hooft-Polyakov monopole with an external uniform
magnetic field.Comment: 18 pages, 3 Postscript figures, RevTe
New Integrable Sectors in Skyrme and 4-dimensional CP^n Model
The application of a weak integrability concept to the Skyrme and
models in 4 dimensions is investigated. A new integrable subsystem of the
Skyrme model, allowing also for non-holomorphic solutions, is derived. This
procedure can be applied to the massive Skyrme model, as well. Moreover, an
example of a family of chiral Lagrangians providing exact, finite energy
Skyrme-like solitons with arbitrary value of the topological charge, is given.
In the case of models a tower of integrable subsystems is obtained. In
particular, in (2+1) dimensions a one-to-one correspondence between the
standard integrable submodel and the BPS sector is proved. Additionally, it is
shown that weak integrable submodels allow also for non-BPS solutions.
Geometric as well as algebraic interpretations of the integrability conditions
are also given.Comment: 23 page
Topological solitons in highly anisotropic two dimensional ferromagnets
e study the solitons, stabilized by spin precession in a classical
two--dimensional lattice model of Heisenberg ferromagnets with non-small
easy--axis anisotropy. The properties of such solitons are treated both
analytically using the continuous model including higher then second powers of
magnetization gradients, and numerically for a discrete set of the spins on a
square lattice. The dependence of the soliton energy on the number of spin
deviations (bound magnons) is calculated. We have shown that the
topological solitons are stable if the number exceeds some critical value
. For and the intermediate values of anisotropy
constant ( is an exchange constant), the soliton
properties are similar to those for continuous model; for example, soliton
energy is increasing and the precession frequency is decreasing
monotonously with growth. For high enough anisotropy we found some fundamentally new soliton features absent for continuous
models incorporating even the higher powers of magnetization gradients. For
high anisotropy, the dependence of soliton energy E(N) on the number of bound
magnons become non-monotonic, with the minima at some "magic" numbers of bound
magnons. Soliton frequency have quite irregular behavior with
step-like jumps and negative values of for some regions of . Near
these regions, stable static soliton states, stabilized by the lattice effects,
exist.Comment: 17 page
Orbit-based deformation procedure for two-field models
We present a method for generating new deformed solutions starting from
systems of two real scalar fields for which defect solutions and orbits are
known. The procedure generalizes the approach introduced in a previous work
[Phys. Rev. D 66, 101701(R) (2002)], in which it is shown how to construct new
models altogether with its defect solutions, in terms of the original model and
solutions. As an illustration, we work out an explicit example in detail.Comment: 15 pages, 14 figures; version to appear in PR
2+1 Dimensional Georgi-Glashow Instantons in Weyl Gauge
Semiclassical instanton solutions in the 3D SU(2) Georgi-Glashow model are
transformed into the Weyl gauge. This illustrates the tunneling interpretation
of these instantons and provides a smooth regularization of the singular
unitary gauge. The 3D Georgi-Glashow model has both instanton and sphaleron
solutions, in contrast to 3D Yang-Mills theory which has neither, and 4D
Yang-Mills theory which has instantons but no sphaleron, and 4D electroweak
theory which has a sphaleron but no instantons. We also discuss the spectral
flow picture of fundamental fermions in a Georgi-Glashow instanton background.Comment: 22 pages, 8 figures, revtex4; v2 - references and comments adde
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