109 research outputs found
Laplace transform analysis of a multiplicative asset transfer model
We analyze a simple asset transfer model in which the transfer amount is a
fixed fraction of the giver's wealth. The model is analyzed in a new way by
Laplace transforming the master equation, solving it analytically and
numerically for the steady-state distribution, and exploring the solutions for
various values of . The Laplace transform analysis is superior to
agent-based simulations as it does not depend on the number of agents, enabling
us to study entropy and inequality in regimes that are costly to address with
simulations. We demonstrate that Boltzmann entropy is not a suitable (e.g.
non-monotonic) measure of disorder in a multiplicative asset transfer system
and suggest an asymmetric stochastic process that is equivalent to the asset
transfer model
Cyclotron line signatures of thermal and magnetic mountains from accreting neutron stars
Cyclotron resonance scattering features (CRSFs) in the X-ray spectrum of an
accreting neutron star are modified differently by accretion mounds sustained
by magnetic and thermocompositional gradients. It is shown that one can
discriminate, in principle, between mounds of different physical origins by
studying how the line energy, width, and depth of a CRSF depend on the
orientation of the neutron star, accreted mass, surface temperature
distribution, and equation of state. CRSF signatures including gravitational
light bending are computed for both phase-resolved and phase-averaged spectra
on the basis of self-consistent Grad-Shafranov mound equilibria satisfying a
global flux-freezing constraint. The prospects of multimessenger X-ray and
gravitational-wave observations with future instruments are canvassed briefly.Comment: 17 pages, 12 figures, accepted for publication in MNRA
Neutron star deformation due to poloidal-toroidal magnetic fields of arbitrary multipole order: a new analytic approach
A recipe is presented to construct an analytic, self-consistent model of a
non-barotropic neutron star with a poloidal-toroidal field of arbitrary
multipole order, whose toroidal component is confined in a torus around the
neutral curve inside the star, as in numerical simulations of twisted tori. The
recipe takes advantage of magnetic-field-aligned coordinates to ensure
continuity of the mass density at the surface of the torus. The density
perturbation and ellipticity of such a star are calculated in general and for
the special case of a mixed dipole-quadrupole field as a worked example. The
calculation generalises previous work restricted to dipolar, poloidal-toroidal
and multipolar, poloidal-only configurations. The results are applied, as an
example, to magnetars whose observations (e.g., spectral features and pulse
modulation) indicate that the internal magnetic fields may be at least one
order of magnitude stronger than the external fields, as inferred from their
spin downs, and are not purely dipolar.Comment: 14 pages, 6 figures, 1 table. Accepted for publication in the Monthly
Notices of the Royal Astronomical Societ
- β¦