2,498 research outputs found
Multi-filament structures in relativistic self-focusing
A simple model is derived to prove the multi-filament structure of
relativistic self-focusing with ultra-intense lasers. Exact analytical
solutions describing the transverse structure of waveguide channels with
electron cavitation, for which both the relativistic and ponderomotive
nonlinearities are taken into account, are presented.Comment: 21 pages, 12 figures, submitted to Physical Review
Conservation of energy and momenta in nonholonomic systems with affine constraints
We characterize the conditions for the conservation of the energy and of the
components of the momentum maps of lifted actions, and of their `gauge-like'
generalizations, in time-independent nonholonomic mechanical systems with
affine constraints. These conditions involve geometrical and mechanical
properties of the system, and are codified in the so-called
reaction-annihilator distribution
Del Pezzo surfaces with 1/3(1,1) points
We classify del Pezzo surfaces with 1/3(1,1) points in 29 qG-deformation
families grouped into six unprojection cascades (this overlaps with work of
Fujita and Yasutake), we tabulate their biregular invariants, we give good
model constructions for surfaces in all families as degeneracy loci in rep
quotient varieties and we prove that precisely 26 families admit
qG-degenerations to toric surfaces. This work is part of a program to study
mirror symmetry for orbifold del Pezzo surfaces.Comment: 42 pages. v2: model construction added of last remaining surface,
minor corrections, minor changes to presentation, references adde
(0,2) Deformations of Linear Sigma Models
We study (0,2) deformations of a (2,2) supersymmetric gauged linear sigma
model for a Calabi-Yau hypersurface in a Fano toric variety. In the non-linear
sigma model these correspond to some of the holomorphic deformations of the
tangent bundle on the hypersurface. Combinatorial formulas are given for the
number of these deformations, and we show that these numbers are exchanged by
mirror symmetry in a subclass of the models.Comment: 35 pages; uses xy-fig; typos fixed, acknowledgments adde
On Non-Abelian Symplectic Cutting
We discuss symplectic cutting for Hamiltonian actions of non-Abelian compact
groups. By using a degeneration based on the Vinberg monoid we give, in good
cases, a global quotient description of a surgery construction introduced by
Woodward and Meinrenken, and show it can be interpreted in algebro-geometric
terms. A key ingredient is the `universal cut' of the cotangent bundle of the
group itself, which is identified with a moduli space of framed bundles on
chains of projective lines recently introduced by the authors.Comment: Various edits made, to appear in Transformation Groups. 28 pages, 8
figure
The non-equivariant coherent-constructible correspondence and a conjecture of King
The coherent-constructible (CC) correspondence is a relationship between coherent sheaves on a toric variety X and constructible sheaves on a real torus T. This was discovered by Bondal and established in the equivariant setting by Fang, Liu, Treumann, and Zaslow. In this paper, we explore various aspects of the non-equivariant CC correspondence. Also, we use the non-equivariant CC correspondence to prove the existence of tilting complexes in the derived categories of toric orbifolds satisfying certain combinatorial conditions. This has applications to a conjecture of King
C^2/Z_n Fractional branes and Monodromy
We construct geometric representatives for the C^2/Z_n fractional branes in
terms of branes wrapping certain exceptional cycles of the resolution. In the
process we use large radius and conifold-type monodromies, and also check some
of the orbifold quantum symmetries. We find the explicit Seiberg-duality which
connects our fractional branes to the ones given by the McKay correspondence.
We also comment on the Harvey-Moore BPS algebras.Comment: 34 pages, v1 identical to v2, v3: typos fixed, discussion of
Harvey-Moore BPS algebras update
Neutral and Charged Polymers at Interfaces
Chain-like macromolecules (polymers) show characteristic adsorption
properties due to their flexibility and internal degrees of freedom, when
attracted to surfaces and interfaces. In this review we discuss concepts and
features that are relevant to the adsorption of neutral and charged polymers at
equilibrium, including the type of polymer/surface interaction, the solvent
quality, the characteristics of the surface, and the polymer structure. We pay
special attention to the case of charged polymers (polyelectrolytes) that have
a special importance due to their water solubility. We present a summary of
recent progress in this rapidly evolving field. Because many experimental
studies are performed with rather stiff biopolymers, we discuss in detail the
case of semi-flexible polymers in addition to flexible ones. We first review
the behavior of neutral and charged chains in solution. Then, the adsorption of
a single polymer chain is considered. Next, the adsorption and depletion
processes in the many-chain case are reviewed. Profiles, changes in the surface
tension and polymer surface excess are presented. Mean-field and corrections
due to fluctuations and lateral correlations are discussed. The force of
interaction between two adsorbed layers, which is important in understanding
colloidal stability, is characterized. The behavior of grafted polymers is also
reviewed, both for neutral and charged polymer brushes.Comment: a review: 130 pages, 30 ps figures; final form, added reference
Guiding structures with multiply connected cross-sections: evolution of propagation in external fields at complex Robin parameters
Properties of the two-dimensional ring and three-dimensional infinitely long
straight hollow waveguide with unit width and inner radius in the
superposition of the longitudinal uniform magnetic field and
Aharonov-Bohm flux are analyzed within the framework of the scalar Helmholtz
equation under the assumption that the Robin boundary conditions at the inner
and outer confining walls contain extrapolation lengths and
, respectively, with nonzero imaginary parts. It is shown that,
compared to the disk geometry, the annulus opens up additional possibilities of
varying magnetization and currents by tuning imaginary components of the Robin
parameters on each confining circumference; in particular, the possibility of
restoring a lossless longitudinal flux by zeroing imaginary part of the
total transverse energy is discussed. The energy turns real under
special correlation between the imaginary parts of and
with the opposite signs what physically corresponds to the
equal transverse fluxes through the inner and outer interfaces of the annulus.
In the asymptotic case of the very large radius, simple expressions are derived
and applied to the analysis of the dependence of the real energy on
and . New features also emerge in the magnetic
field influence; for example, if, for the quantum disk, the imaginary energy
is quenched by the strong intensities , then for the annulus this
takes place only when the inner Robin distance is real;
otherwise, it almost quadratically depends on with the corresponding
enhancement of the reactive scattering. Closely related problem of the hole in
the otherwise uniform medium is also addressed for real and complex
extrapolation lengths with the emphasis on the comparative analysis with its
dot counterpart.Comment: 37 pages, 9 figure
f(R) theories
Over the past decade, f(R) theories have been extensively studied as one of
the simplest modifications to General Relativity. In this article we review
various applications of f(R) theories to cosmology and gravity - such as
inflation, dark energy, local gravity constraints, cosmological perturbations,
and spherically symmetric solutions in weak and strong gravitational
backgrounds. We present a number of ways to distinguish those theories from
General Relativity observationally and experimentally. We also discuss the
extension to other modified gravity theories such as Brans-Dicke theory and
Gauss-Bonnet gravity, and address models that can satisfy both cosmological and
local gravity constraints.Comment: 156 pages, 14 figures, Invited review article in Living Reviews in
Relativity, Published version, Comments are welcom
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