Formation time distribution of dark matter haloes: theories versus N-body simulations

This paper uses numerical simulations to test the formation time distribution of dark matter haloes predicted by the analytic excursion set approaches. The formation time distribution is closely linked to the conditional mass function and this test is therefore an indirect probe of this distribution. The excursion set models tested are the extended Press-Schechter (EPS) model, the ellipsoidal collapse (EC) model, and the non-spherical collapse boundary (NCB) model. Three sets of simulations (6 realizations) have been used to investigate the halo formation time distribution for halo masses ranging from dwarf-galaxy like haloes ($M=10^{-3} M_*$, where $M_*$ is the characteristic non-linear mass scale) to massive haloes of $M=8.7 M_*$. None of the models can match the simulation results at both high and low redshift. In particular, dark matter haloes formed generally earlier in our simulations than predicted by the EPS model. This discrepancy might help explain why semi-analytic models of galaxy formation, based on EPS merger trees, under-predict the number of high redshift galaxies compared with recent observations.Comment: 7 pages, 5 figures, accepted for publication in MNRA

A sharp stability criterion for the Vlasov-Maxwell system

We consider the linear stability problem for a 3D cylindrically symmetric equilibrium of the relativistic Vlasov-Maxwell system that describes a collisionless plasma. For an equilibrium whose distribution function decreases monotonically with the particle energy, we obtained a linear stability criterion in our previous paper. Here we prove that this criterion is sharp; that is, there would otherwise be an exponentially growing solution to the linearized system. Therefore for the class of symmetric Vlasov-Maxwell equilibria, we establish an energy principle for linear stability. We also treat the considerably simpler periodic 1.5D case. The new formulation introduced here is applicable as well to the nonrelativistic case, to other symmetries, and to general equilibria

A Comprehensive View of the 2006 December 13 CME: From the Sun to Interplanetary Space

The biggest halo coronal mass ejection (CME) since the Halloween storm in 2003, which occurred on 2006 December 13, is studied in terms of its solar source and heliospheric consequences. The CME is accompanied by an X3.4 flare, EUV dimmings and coronal waves. It generated significant space weather effects such as an interplanetary shock, radio bursts, major solar energetic particle (SEP) events, and a magnetic cloud (MC) detected by a fleet of spacecraft including STEREO, ACE, Wind and Ulysses. Reconstruction of the MC with the Grad-Shafranov (GS) method yields an axis orientation oblique to the flare ribbons. Observations of the SEP intensities and anisotropies show that the particles can be trapped, deflected and reaccelerated by the large-scale transient structures. The CME-driven shock is observed at both the Earth and Ulysses when they are separated by 74$^{\circ}$ in latitude and 117$^{\circ}$ in longitude, the largest shock extent ever detected. The ejecta seems missed at Ulysses. The shock arrival time at Ulysses is well predicted by an MHD model which can propagate the 1 AU data outward. The CME/shock is tracked remarkably well from the Sun all the way to Ulysses by coronagraph images, type II frequency drift, in situ measurements and the MHD model. These results reveal a technique which combines MHD propagation of the solar wind and type II emissions to predict the shock arrival time at the Earth, a significant advance for space weather forecasting especially when in situ data are available from the Solar Orbiter and Sentinels.Comment: 26 pages, 10 figures. 2008, ApJ, in pres

Computing the lower and upper bounds of Laplace eigenvalue problem: by combining conforming and nonconforming finite element methods

This article is devoted to computing the lower and upper bounds of the Laplace eigenvalue problem. By using the special nonconforming finite elements, i.e., enriched Crouzeix-Raviart element and extension $Q_1^{\rm rot}$, we get the lower bound of the eigenvalue. Additionally, we also use conforming finite elements to do the postprocessing to get the upper bound of the eigenvalue. The postprocessing method need only to solve the corresponding source problems and a small eigenvalue problem if higher order postprocessing method is implemented. Thus, we can obtain the lower and upper bounds of the eigenvalues simultaneously by solving eigenvalue problem only once. Some numerical results are also presented to validate our theoretical analysis.Comment: 19 pages, 4 figure

Geometric phases for neutral and charged particles in a time-dependent magnetic field

It is well known that any cyclic solution of a spin 1/2 neutral particle moving in an arbitrary magnetic field has a nonadiabatic geometric phase proportional to the solid angle subtended by the trace of the spin. For neutral particles with higher spin, this is true for cyclic solutions with special initial conditions. For more general cyclic solutions, however, this does not hold. As an example, we consider the most general solutions of such particles moving in a rotating magnetic field. If the parameters of the system are appropriately chosen, all solutions are cyclic. The nonadiabatic geometric phase and the solid angle are both calculated explicitly. It turns out that the nonadiabatic geometric phase contains an extra term in addition to the one proportional to the solid angle. The extra term vanishes automatically for spin 1/2. For higher spin, however, it depends on the initial condition. We also consider the valence electron of an alkaline atom. For cyclic solutions with special initial conditions in an arbitrary strong magnetic field, we prove that the nonadiabatic geometric phase is a linear combination of the two solid angles subtended by the traces of the orbit and spin angular momenta. For more general cyclic solutions in a strong rotating magnetic field, the nonadiabatic geometric phase also contains extra terms in addition to the linear combination.Comment: revtex, 18 pages, no figur