2,827 research outputs found
A Sobolev Poincar\'e type inequality for integral varifolds
In this work a local inequality is provided which bounds the distance of an
integral varifold from a multivalued plane (height) by its tilt and mean
curvature. The bounds obtained for the exponents of the Lebesgue spaces
involved are shown to be sharp.Comment: v1: 27 pages, no figures; v2: replaced citations of the author's
dissertation by proofs, material of sections 1 and 3 reorganised, slightly
more general results in section 2, some remarks, some discussion and some
references added, 40 pages, no figure
Basis-independent methods for the two-Higgs-doublet model II. The significance of tan(beta)
In the most general two-Higgs-doublet model (2HDM), there is no distinction
between the two complex hypercharge-one SU(2) doublet scalar fields, Phi_a
(a=1,2). Thus, any two orthonormal linear combinations of these two fields can
serve as a basis for the Lagrangian. All physical observables of the model must
therefore be basis-independent. For example, tan(beta)=/ is
basis-dependent and thus cannot be a physical parameter of the model. In this
paper, we provide a basis-independent treatment of the Higgs sector with
particular attention to the neutral Higgs boson mass-eigenstates, which
generically are not eigenstates of CP. We then demonstrate that all physical
Higgs couplings are indeed independent of tan(beta). In specialized versions of
the 2HDM, tan(beta) can be promoted to a physical parameter of the
Higgs-fermion interactions. In the most general 2HDM, the Higgs-fermion
couplings can be expressed in terms of a number of physical "tan(beta)--like"
parameters that are manifestly basis-independent. The minimal supersymmetric
extension of the Standard Model provides a simple framework for exhibiting such
effects.Comment: 56 pages, 5 tables, with Eq. (65) corrected (erratum to appear in
Physical Review D
Optical microrheology using rotating laser-trapped particles
We demonstrate an optical system that can apply and accurately measure the
torque exerted by the trapping beam on a rotating birefringent probe particle.
This allows the viscosity and surface effects within liquid media to be
measured quantitatively on a micron-size scale using a trapped rotating
spherical probe particle. We use the system to measure the viscosity inside a
prototype cellular structure.Comment: 5 pages, 4 figures. v2: bibliographic details, minor text correction
Do low surface brightness galaxies have dense disks?
The disk masses of four low surface brightness galaxies (LSB) were estimated
using marginal gravitational stability criterion and the stellar velocity
dispersion data which were taken from Pizzella et al., 2008 [1]. The
constructed mass models appear to be close to the models of maximal disk. The
results show that the disks of LSB galaxies may be significantly more massive
than it is usually accepted from their brightnesses. In this case their surface
densities and masses appear to be rather typical for normal spirals. Otherwise,
unlike the disks of many spiral galaxies, the LSB disks are dynamically
overheated.Comment: 14 pages, 10 figures, submitted to Astronomy Report
On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction
In the mean-field limit the dynamics of a quantum Bose gas is described by a
Hartree equation. We present a simple method for proving the convergence of the
microscopic quantum dynamics to the Hartree dynamics when the number of
particles becomes large and the strength of the two-body potential tends to 0
like the inverse of the particle number. Our method is applicable for a class
of singular interaction potentials including the Coulomb potential. We prove
and state our main result for the Heisenberg-picture dynamics of "observables",
thus avoiding the use of coherent states. Our formulation shows that the
mean-field limit is a "semi-classical" limit.Comment: Corrected typos and included an elementary proof of the Kato
smoothing estimate (Lemma 6.1
An estimate for the Morse index of a Stokes wave
Stokes waves are steady periodic water waves on the free surface of an
infinitely deep irrotational two dimensional flow under gravity without surface
tension. They can be described in terms of solutions of the Euler-Lagrange
equation of a certain functional. This allows one to define the Morse index of
a Stokes wave. It is well known that if the Morse indices of the elements of a
set of non-singular Stokes waves are bounded, then none of them is close to a
singular one. The paper presents a quantitative variant of this result.Comment: This version contains an additional reference and some minor change
Long-time discrete particle effects versus kinetic theory in the self-consistent single-wave model
The influence of the finite number N of particles coupled to a monochromatic
wave in a collisionless plasma is investigated. For growth as well as damping
of the wave, discrete particle numerical simulations show an N-dependent long
time behavior resulting from the dynamics of individual particles. This
behavior differs from the one due to the numerical errors incurred by Vlasov
approaches. Trapping oscillations are crucial to long time dynamics, as the
wave oscillations are controlled by the particle distribution inhomogeneities
and the pulsating separatrix crossings drive the relaxation towards thermal
equilibrium.Comment: 11 pages incl. 13 figs. Phys. Rev. E, in pres
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