2,690 research outputs found
A comparative analysis of the value of information in a continuous time market model with partial information: the cases of log-utility and CRRA
We study the question what value an agent in a generalized Black-Scholes model with partial information attributes to the complementary information. To do this, we study the utility maximization problems from terminal wealth for the two cases partial information and full information. We assume that the drift term of the risky asset is a dynamic process of general linear type and that the two levels of observation correspond to whether this drift term is observable or not. Applying methods from stochastic filtering theory we derive an analytical tractable formula for the value of information in the case of logarithmic utility. For the case of constant relative risk aversion (CRRA) we derive a semianalytical formula, which uses as an input the numerical solution of a system of ODEs. For both cases we present a comparative analysis
General relativistic hydrodynamics in curvilinear coordinates
In this paper we report on what we believe is the first successful
implementation of relativistic hydrodynamics, coupled to dynamical spacetimes,
in spherical polar coordinates without symmetry assumptions. We employ a
high-resolution shock-capturing scheme, which requires that the equations be
cast in flux-conservative form. One example of such a form is the :Valencia"
formulation, which has been adopted in numerous applications, in particular in
Cartesian coordinates. Here we generalize this formulation to allow for a
reference-metric approach, which provides a natural framework for calculations
in curvilinear coordinates. In spherical polar coordinates, for example, it
allows for an analytical treatment of the singular r and sin(\theta) terms that
appear in the equations. We experiment with different versions of our
generalized Valencia formulation in numerical implementations of relativistic
hydrodynamics for both fixed and dynamical spacetimes. We consider a number of
different tests -- non-rotating and rotating relativistic stars, as well as
gravitational collapse to a black hole -- to demonstrate that our formulation
provides a promising approach to performing fully relativistic astrophysics
simulations in spherical polar coordinates.Comment: 14 pages, 8 figures, version to be published in PR
Numerical Relativity in Spherical Polar Coordinates: Off-center Simulations
We have recently presented a new approach for numerical relativity
simulations in spherical polar coordinates, both for vacuum and for
relativistic hydrodynamics. Our approach is based on a reference-metric
formulation of the BSSN equations, a factoring of all tensor components, as
well as a partially implicit Runge-Kutta method, and does not rely on a
regularization of the equations, nor does it make any assumptions about the
symmetry across the origin. In order to demonstrate this feature we present
here several off-centered simulations, including simulations of single black
holes and neutron stars whose center is placed away from the origin of the
coordinate system, as well as the asymmetric head-on collision of two black
holes. We also revisit our implementation of relativistic hydrodynamics and
demonstrate that a reference-metric formulation of hydrodynamics together with
a factoring of all tensor components avoids problems related to the coordinate
singularities at the origin and on the axes. As a particularly demanding test
we present results for a shock wave propagating through the origin of the
spherical polar coordinate system.Comment: 13 pages, 11 figures; matches version published in PR
The core helium flash revisited III. From Pop I to Pop III stars
Degenerate ignition of helium in low-mass stars at the end of the red giant
branch phase leads to dynamic convection in their helium cores. One-dimensional
(1D) stellar modeling of this intrinsically multi-dimensional dynamic event is
likely to be inadequate. Previous hydrodynamic simulations imply that the
single convection zone in the helium core of metal-rich Pop I stars grows
during the flash on a dynamic timescale. This may lead to hydrogen injection
into the core, and a double convection zone structure as known from
one-dimensional core helium flash simulations of low-mass Pop III stars. We
perform hydrodynamic simulations of the core helium flash in two and three
dimensions to better constrain the nature of these events. To this end we study
the hydrodynamics of convection within the helium cores of a 1.25 \Msun
metal-rich Pop I star (Z=0.02), and a 0.85 \Msun metal-free Pop III star (Z=0)
near the peak of the flash. These models possess single and double convection
zones, respectively. We use 1D stellar models of the core helium flash computed
with state-of-the-art stellar evolution codes as initial models for our
multidimensional hydrodynamic study, and simulate the evolution of these models
with the Riemann solver based hydrodynamics code Herakles which integrates the
Euler equations coupled with source terms corresponding to gravity and nuclear
burning. The hydrodynamic simulation of the Pop I model involving a single
convection zone covers 27 hours of stellar evolution, while the first
hydrodynamic simulations of a double convection zone, in the Pop III model,
span 1.8 hours of stellar life. We find differences between the predictions of
mixing length theory and our hydrodynamic simulations. The simulation of the
single convection zone in the Pop I model shows a strong growth of the size of
the convection zone due to turbulent entrainment. Hence we predict that for the
Pop I model a hydrogen injection phase (i.e. hydrogen injection into the helium
core) will commence after about 23 days, which should eventually lead to a
double convection zone structure known from 1D stellar modeling of low-mass Pop
III stars. Our two and three-dimensional hydrodynamic simulations of the double
(Pop III) convection zone model show that the velocity field in the convection
zones is different from that predicted by stellar evolutionary calculations.
The simulations suggest that the double convection zone decays quickly, the
flow eventually being dominated by internal gravity waves.Comment: 16 pages, 18 figures, submitted to Aa
The Older Population and the Aged Patient
Modern medical practice requires that the physician and other members of the health team have full appreciation of the impact of disease and disability upon identifiable groups of patients and recognize how nonmedical factors affect treatment and prognosis. It is important for the physician to have some idea of the patient\u27s socioeconomic status and the actual and potential number of patients with not only a common diagnosis, but also similarities in their living conditions. With such knowledge, the physician can be much more realistic and efficient in his therapeutic efforts. Persons 65 years of age and over are commonly referred to as the older population. Brotman (1968) recently identified the special characteristics of those 75 years of age and over, referring to these people as the aged. This subdividing of the older population is of considerable value, as the important health and socioeconomic facts common to a specific group can be lost in the mass of the older population
S-4B orbital workshop attitude control system study
Saturn S-4B orbital workshop attitude control system analysi
From bcc to fcc: interplay between oscillating long-range and repulsive short-range forces
This paper supplements and partly extends an earlier publication, Phys. Rev.
Lett. 95, 265501 (2005). In -dimensional continuous space we describe the
infinite volume ground state configurations (GSCs) of pair interactions \vfi
and \vfi+\psi, where \vfi is the inverse Fourier transform of a nonnegative
function vanishing outside the sphere of radius , and is any
nonnegative finite-range interaction of range , where
. In three dimensions the decay of \vfi can be as slow
as , and an interaction of asymptotic form
is among the examples. At a dimension-dependent
density the ground state of \vfi is a unique Bravais lattice, and
for higher densities it is continuously degenerate: any union of Bravais
lattices whose reciprocal lattice vectors are not shorter than is a GSC.
Adding decreases the ground state degeneracy which, nonetheless, remains
continuous in the open interval , where is the
close-packing density of hard balls of diameter . The ground state is
unique at both ends of the interval. In three dimensions this unique GSC is the
bcc lattice at and the fcc lattice at .Comment: Published versio
Fully covariant and conformal formulation of the Z4 system in a reference-metric approach: comparison with the BSSN formulation in spherical symmetry
We adopt a reference-metric approach to generalize a covariant and conformal
version of the Z4 system of the Einstein equations. We refer to the resulting
system as ``fully covariant and conformal", or fCCZ4 for short, since it is
well suited for curvilinear as well as Cartesian coordinates. We implement this
fCCZ4 formalism in spherical polar coordinates under the assumption of
spherical symmetry using a partially-implicit Runge-Kutta (PIRK) method and
show that our code can evolve both vacuum and non-vacuum spacetimes without
encountering instabilities. Our method does not require regularization of the
equations to handle coordinate singularities, nor does it depend on
constraint-preserving outer boundary conditions, nor does it need any
modifications of the equations for evolutions of black holes. We perform
several tests and compare the performance of the fCCZ4 system, for different
choices of certain free parameters, with that of BSSN. Confirming earlier
results we find that, for an optimal choice of these parameters, and for
neutron-star spacetimes, the violations of the Hamiltonian constraint can be
between 1 and 3 orders of magnitude smaller in the fCCZ4 system than in the
BSSN formulation. For black-hole spacetimes, on the other hand, any advantages
of fCCZ4 over BSSN are less evident.Comment: 13 pages, 10 figure
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