2,586 research outputs found
Generalized nonlinear sigma model approach to alternating spin chains and ladders
We generalize the nonlinear sigma model treatment of quantum spin chains to
cases including ferromagnetic bonds. When these bonds are strong enough, the
classical ground state is no longer the standard Neel order and we present an
extension of the known formalism to deal with this situation. We study the
alternating ferromagnetic-antiferromagnetic spin chain introduced by Hida. The
smooth crossover between decoupled dimers and the Haldane phase is
semi-quantitatively reproduced. We study also a spin ladder with diagonal
exchange couplings that interpolates between the gapped phase of the two-leg
spin ladder and the Haldane phase. Here again we show that there is good
agreement between DMRG data and our analytical results.Comment: 10 pages, 5 encapsulated figures, REVTeX 3.
Tasting edge effects
We show that the baking of potato wedges constitutes a crunchy example of
edge effects, which are usually demonstrated in electrostatics. A simple model
of the diffusive transport of water vapor around the potato wedges shows that
the water vapor flux diverges at the sharp edges in analogy with its
electrostatic counterpart. This increased evaporation at the edges leads to the
crispy taste of these parts of the potatoes.Comment: to appear in American Journal of Physic
Estimating model evidence using data assimilation
We review the field of data assimilation (DA) from a Bayesian perspective and show that, in addition to its by now common application to state estimation, DA may be used for model selection. An important special case of the latter is the discrimination between a factual modelâwhich corresponds, to the best of the modeller's knowledge, to the situation in the actual world in which a sequence of events has occurredâand a counterfactual model, in which a particular forcing or process might be absent or just quantitatively different from the actual world. Three different ensembleâDA methods are reviewed for this purpose: the ensemble Kalman filter (EnKF), the ensemble fourâdimensional variational smoother (Enâ4DâVar), and the iterative ensemble Kalman smoother (IEnKS). An original contextual formulation of model evidence (CME) is introduced. It is shown how to apply these three methods to compute CME, using the approximated timeâdependent probability distribution functions (pdfs) each of them provide in the process of state estimation. The theoretical formulae so derived are applied to two simplified nonlinear and chaotic models: (i) the Lorenz threeâvariable convection model (L63), and (ii) the Lorenz 40âvariable midlatitude atmospheric dynamics model (L95). The numerical results of these three DAâbased methods and those of an integration based on importance sampling are compared. It is found that better CME estimates are obtained by using DA, and the IEnKS method appears to be best among the DA methods. Differences among the performance of the three DAâbased methods are discussed as a function of model properties. Finally, the methodology is implemented for parameter estimation and for event attribution
Effective interactions and phase behaviour for a model clay suspension in an electrolyte
Since the early observation of nematic phases of disc-like clay colloids by
Langmuir in 1938, the phase behaviour of such systems has resisted theoretical
understanding. The main reason is that there is no satisfactory generalization
for charged discs of the isotropic DLVO potential describing the effective
interactions between a pair of spherical colloids in an electrolyte. In this
contribution, we show how to construct such a pair potential, incorporating
approximately both the non-linear effects of counter-ion condensation (charge
renormalization) and the anisotropy of the charged platelets. The consequences
on the phase behaviour of Laponite dispersions (thin discs of 30 nm diameter
and 1 nm thickness) are discussed, and investigation into the mesostructure via
Monte Carlo simulations are presented.Comment: LaTeX, 12 pages, 11 figure
Nuclear Matter in Intense Magnetic Field and Weak Processes
We study the effect of magnetic field on the dominant neutrino emission
processes in neutron stars.The processes are first calculated for the case when
the magnetic field does not exceed the critical value to confine electrons to
the lowest Landau state.We then consider the more important case of intense
magnetic field to evaluate the direct URCA and the neutronisation processes. In
order to estimate the effect we derive the composition of cold nuclear matter
at high densities and in beta equilibrium, a situation appropriate for neutron
stars. The hadronic interactions are incorporated through the exchange of
scalar and vector mesons in the frame work of relativistic mean field theory.
In addition the effects of anomalous magnetic moments of nucleons are also
considered.Comment: 29 pages (LaTeX) including 7 figure
Quark deconfinement in neutron star cores: The effects of spin-down
We study the role of spin-down in driving quark deconfinement in the high
density core of isolated neutron stars. Assuming spin-down to be solely due to
magnetic braking, we obtain typical timescales to quark deconfinement for
neutron stars that are born with Keplerian frequencies. Employing different
equations of state (EOS), we determine the minimum and maximum neutron star
masses that will allow for deconfinement via spin-down only. We find that the
time to reach deconfinement is strongly dependent on the magnetic field and
that this time is least for EOS that support the largest minimum mass at zero
spin, unless rotational effects on stellar structure are large. For a fiducial
critical density of for the transition to the quark phase
(g/cm is the saturation density of nuclear
matter), we find that neutron stars lighter than cannot reach a
deconfined phase. Depending on the EOS, neutron stars of more than
can enter a quark phase only if they are spinning faster than
about 3 milliseconds as observed now, whereas larger spin periods imply that
they are either already quark stars or will never become one.Comment: 4 pages, 4 figures, submitted to ApJ
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