Magnetospheric particle acceleration and X-ray emission of pulsars

The available data on isolated X-ray pulsars, their wind nebulae, and the supernova remnants which are connected to some of these sources are analyzed. It is shown that electric fields of neutron stars tear off charged particles from the surface of neutron star and trigger the acceleration of particles. The charged particles are accelerated mainly in the field of magneto-dipole radiation wave. Power and energy spectra of the charged particles depend on the strength of the magneto-dipole radiation. Therefore, the X-ray radiation is strongly dependent on the rate of rotational energy loss and weakly dependent on the electric field intensity. Coulomb interaction between the charged particles is the main factor for the energy loss and the X-ray spectra of the charged particles.Comment: minor correction on table format, 20 pages (4 figures, 1 table), submitted to International Journal of Modern Physics

Mutation, selection, and ancestry in branching models: a variational approach

We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated genealogical tree is viewed both in the forward and the backward direction of time. The stationary type distribution of the reversed process, the so-called ancestral distribution, turns out as a key for the study of mutation-selection balance. This balance can be expressed in the form of a variational principle that quantifies the respective roles of reproduction and mutation for any possible type distribution. It shows that the mean growth rate of the population results from a competition for a maximal long-term growth rate, as given by the difference between the current mean reproduction rate, and an asymptotic decay rate related to the mutation process; this tradeoff is won by the ancestral distribution. Our main application is the quasispecies model of sequence evolution with mutation coupled to reproduction but independent across sites, and a fitness function that is invariant under permutation of sites. Here, the variational principle is worked out in detail and yields a simple, explicit result.Comment: 45 pages,8 figure

THE WAIT-AND-SEE OPTION IN ASCENDING PRICE AUCTIONS

Cake-cutting protocols aim at dividing a ``cake'' (i.e., a divisible resource) and assigning the resulting portions to several players in a way that each of the players feels to have received a ``fair'' amount of the cake. An important notion of fairness is envy-freeness: No player wishes to switch the portion of the cake received with another player's portion. Despite intense efforts in the past, it is still an open question whether there is a \emph{finite bounded} envy-free cake-cutting protocol for an arbitrary number of players, and even for four players. We introduce the notion of degree of guaranteed envy-freeness (DGEF) as a measure of how good a cake-cutting protocol can approximate the ideal of envy-freeness while keeping the protocol finite bounded (trading being disregarded). We propose a new finite bounded proportional protocol for any number n \geq 3 of players, and show that this protocol has a DGEF of 1 + \lceil (n^2)/2 \rceil. This is the currently best DGEF among known finite bounded cake-cutting protocols for an arbitrary number of players. We will make the case that improving the DGEF even further is a tough challenge, and determine, for comparison, the DGEF of selected known finite bounded cake-cutting protocols.Comment: 37 pages, 4 figure

Molybdenum sound velocity and shear modulus softening under shock compression

We measured the longitudinal sound velocity in Mo shock compressed up to 4.4 Mbars on the Hugoniot. Its sound speed increases linearly with pressure up to 2.6 Mbars; the slope then decreases up to the melting pressure of ∼3.8 Mbars. This suggests a decrease of shear modulus before the melt. A linear extrapolation of our data to 1 bar agrees with the ambient sound speed. The results suggest that Mo remains in the bcc phase on the Hugoniot up to the melting pressure. There is no statistically significant evidence for a previously reported bcc→hcp phase transition on the Hugoniot

Topological chaos: what may this mean ?

We confront existing definitions of chaos with the state of the art in topological dynamics. The article does not propose any new definition of chaos but, starting from several topological properties that can be reasonably called chaotic, tries to sketch a theoretical view of chaos. Among the main ideas in this article are the distinction between overall chaos and partial chaos, and the fact that some dynamical properties may be considered more chaotic than others

Reply to “Comment on ‘Molybdenum sound velocity and shear modulus softening under shock compression’ ”

We respond to the Comment by Errandonea et al. [Phys. Rev. B 92, 026101 (2015)] on their reinterpretation of our published data [Nguyen et al., Phys. Rev. B 89, 174109 (2014)]. In the original paper, we argued that there is no solid-solid phase transition along the Hugoniot at 2.1 Mbars. There is, however, a softening of the shear modulus starting at 2.6 Mbars. Errandonea et al. [Phys. Rev. B 92, 026101 (2015)] reinterpreted our data and concluded that there is a structural change near 2.3 Mbars on the Hugoniot. We will explore the differences and agreements in the two interpretations of our data