122,288 research outputs found
Special Lagrangians, stable bundles and mean curvature flow
We make a conjecture about mean curvature flow of Lagrangian submanifolds of
Calabi-Yau manifolds, expanding on \cite{Th}. We give new results about the
stability condition, and propose a Jordan-H\"older-type decomposition of
(special) Lagrangians. The main results are the uniqueness of special
Lagrangians in hamiltonian deformation classes of Lagrangians, under mild
conditions, and a proof of the conjecture in some cases with symmetry: mean
curvature flow converging to Shapere-Vafa's examples of SLags.Comment: 36 pages, 4 figures. Minor referee's correction
Understanding the effects of geometry and rotation on pulsar intensity profiles
We have developed a method to compute the possible distribution of radio
emission regions in a typical pulsar magnetosphere, taking into account the
viewing geometry and rotational effects of the neutron star. Our method can
estimate the emission altitude and the radius of curvature of particle
trajectory as a function of rotation phase for a given inclination angle,
impact angle, spin-period, Lorentz factor, field line constant and the
observation frequency. Further, using curvature radiation as the basic emission
mechanism, we simulate the radio intensity profiles that would be observed from
a given distribution of emission regions, for different values of radio
frequency and Lorentz factor. We show clearly that rotation effects can
introduce significant asymmetries into the observed radio profiles. We
investigate the dependency of profile features on various pulsar parameters. We
find that the radiation from a given ring of field lines can be seen over a
large range of pulse longitudes, originating at different altitudes, with
varying spectral intensity. Preferred heights of emission along discrete sets
of field lines are required to reproduce realistic pulsar profiles, and we
illustrate this for a known pulsar. Finally, we show how our model provides
feasible explanations for the origin of core emission, and also for one-sided
cones which have been observed in some pulsars.Comment: 21 pages, 11 figures, accepted for publication in MNRA
Superconductivity and Quantum Phase Transitions in Weak Itinerant Ferromagnets
It is argued that the phase transition in low-T_c clean itinerant
ferromagnets is generically of first order, due to correlation effects that
lead to a nonanalytic term in the free energy. A tricritical point separates
the line of first order transitions from Heisenberg critical behavior at higher
temperatures. Sufficiently strong quenched disorder suppresses the first order
transition via the appearance of a critical endpoint. A semi-quantitative
discussion is given in terms of recent experiments on MnSi and UGe_2. It is
then shown that the critical temperature for spin-triplet, p-wave
superconductivity mediated by spin fluctuations is generically much higher in a
Heisenberg ferromagnetic phase than in a paramagnetic one, due to the coupling
of magnons to the longitudinal magnetic susceptibility. This qualitatively
explains the phase diagram recently observed in UGe_2 and ZrZn_2.Comment: 10 pp., LaTeX, 5 ps figs., requires World Scientific style files
(included), Invited contribution to MB1
Quantum critical behavior of clean itinerant ferromagnets
We consider the quantum ferromagnetic transition at zero temperature in clean
itinerant electron systems. We find that the Landau-Ginzburg-Wilson order
parameter field theory breaks down since the electron-electron interaction
leads to singular coupling constants in the Landau-Ginzburg-Wilson functional.
These couplings generate an effective long-range interaction between the spin
or order parameter fluctuations of the form 1/r^{2d-1}, with d the spatial
dimension. This leads to unusual scaling behavior at the quantum critical point
in 1 < d\leq 3, which we determine exactly. We also discuss the
quantum-to-classical crossover at small but finite temperatures, which is
characterized by the appearance of multiple temperature scales. A comparison
with recent results on disordered itinerant ferromagnets is given.Comment: 13 pp., REVTeX, psfig, 3 eps figs, final version as publishe
Second-Order Convergence of a Projection Scheme for the Incompressible Navier–Stokes Equations with Boundaries
A rigorous convergence result is given for a projection scheme for the Navies–Stokes equations in the presence of boundaries. The numerical scheme is based on a finite-difference approximation, and the pressure is chosen so that the computed velocity satisfies a discrete divergence-free condition. This choice for the pressure and the particular way that the discrete divergence is calculated near the boundary permit the error in the pressure to be controlled and the second-order convergence in the velocity and the pressure to the exact solution to be shown. Some simplifications in the calculation of the pressure in the case without boundaries are also discussed
Influence of Generic Scale Invariance on Classical and Quantum Phase Transitions
This review discusses a paradigm that has become of increasing importance in
the theory of quantum phase transitions; namely, the coupling of the
order-parameter fluctuations to other soft modes, and the resulting
impossibility of constructing a simple Landau-Ginzburg-Wilson theory in terms
of the order parameter only. The soft modes in question are manifestations of
generic scale invariance, i.e., the appearance of long-range order in whole
regions in the phase diagram. The concept of generic scale invariance, and its
influence on critical behavior, is explained using various examples, both
classical and quantum mechanical. The peculiarities of quantum phase
transitions are discussed, with emphasis on the fact that they are more
susceptible to the effects of generic scale invariance than their classical
counterparts. Explicit examples include: the quantum ferromagnetic transition
in metals, with or without quenched disorder; the metal-superconductor
transition at zero temperature; and the quantum antiferromagnetic transition.
Analogies with classical phase transitions in liquid crystals and classical
fluids are pointed out, and a unifying conceptual framework is developed for
all transitions that are influenced by generic scale invariance.Comment: 55pp, 25 eps figs; final version, to appear in Rev Mod Phy
Axisymmetric stationary solutions with arbitrary multipole moments
In this paper, the problem of finding an axisymmetric stationary spacetime
from a specified set of multipole moments, is studied. The condition on the
multipole moments, for existence of a solution, is formulated as a convergence
condition on a power series formed from the multipole moments. The methods in
this paper can also be used to give approximate solutions to any order as well
as estimates on each term of the resulting power series.Comment: 12 page
- …