606 research outputs found
Sharp quadrature error bounds for the nearest-neighbor discretization of the regularized stokeslet boundary integral equation
The method of regularized stokeslets is a powerful numerical method to solve
the Stokes flow equations for problems in biological fluid mechanics. A recent
variation of this method incorporates a nearest-neighbor discretization to
improve accuracy and efficiency while maintaining the ease-of-implementation of
the original meshless method. This method contains three sources of numerical
error, the regularization error associated from using the regularized form of
the boundary integral equations (with parameter ), and two sources
of discretization error associated with the force and quadrature
discretizations (with lengthscales and ). A key issue to address is
the quadrature error: initial work has not fully explained observed numerical
convergence phenomena. In the present manuscript we construct sharp quadrature
error bounds for the nearest-neighbor discretisation, noting that the error for
a single evaluation of the kernel depends on the smallest distance ()
between these discretization sets. The quadrature error bounds are described
for two cases: with disjoint sets () being close to linear in
and insensitive to , and contained sets () being
quadratic in with inverse dependence on . The practical
implications of these error bounds are discussed with reference to the
condition number of the matrix system for the nearest-neighbor method, with the
analysis revealing that the condition number is insensitive to
for disjoint sets, and grows linearly with for contained sets.
Error bounds for the general case () are revealed to be
proportional to the sum of the errors for each case.Comment: 12 pages, 6 figure
Numerical Calculation of Convection with Reduced Speed of Sound Technique
Context. The anelastic approximation is often adopted in numerical
calculation with low Mach number, such as stellar internal convection. This
approximation requires frequent global communication, because of an elliptic
partial differential equation. Frequent global communication is negative factor
for the parallel computing with a large number of CPUs.
Aims. The main purpose of this paper is to test the validity of a method that
artificially reduces the speed of sound for the compressible fluid equations in
the context of stellar internal convection. The reduction of speed of sound
allows for larger time steps in spite of low Mach number, while the numerical
scheme remains fully explicit and the mathematical system is hyperbolic and
thus does not require frequent global communication.
Methods. Two and three dimensional compressible hydrodynamic equations are
solved numerically. Some statistical quantities of solutions computed with
different effective Mach numbers (due to reduction of speed of sound) are
compared to test the validity of our approach.
Results. Numerical simulations with artificially reduced speed of sound are a
valid approach as long as the effective Mach number (based on the reduced speed
of sound) remains less than 0.7.Comment: 16 pages, 10 figures, accepted to A&
Can Superflares Occur on Our Sun?
Recent observations of solar type stars with the Kepler satellite by Maehara
et al. have revealed the existence of superflares (with energy of 10^33 - 10^35
erg) on Sun-like stars, which are similar to our Sun in their surface
temperature (5600 K - 6000 K) and slow rotation (rotational period > 10 days).
From the statistical analysis of these superflares, it was found that
superflares with energy 10^34 erg occur once in 800 years and superflares with
10^35 erg occur once in 5000 years on Sun-like stars. In this paper, we examine
whether superflares with energy of 10^33 - 10^35 erg could occur on the present
Sun through the use of simple order-of-magnitude estimates based on current
ideas relating to the mechanisms of the solar dynamo.Comment: Accepted by Publ. Astron. Soc. Japan on Dec. 6, 2012 (to be published
on PASJ vol. 65, No. 3, (2013) June 25
The Sun's Preferred Longitudes and the Coupling of Magnetic Dynamo Modes
Observations show that solar activity is distributed non-axisymmetrically,
concentrating at "preferred longitudes". This indicates the important role of
non-axisymmetric magnetic fields in the origin of solar activity. We
investigate the generation of the non-axisymmetric fields and their coupling
with axisymmetric solar magnetic field. Our kinematic generation (dynamo) model
operating in a sphere includes solar differential rotation, which approximates
the differential rotation obtained by inversion of helioseismic data, modelled
distributions of the turbulent resistivity, non-axisymmetric mean helicity, and
meridional circulation in the convection zone. We find that (1) the
non-axisymmetric modes are localised near the base of the convection zone,
where the formation of active regions starts, and at latitudes around
; (2) the coupling of non-axisymmetric and axisymmetric modes
causes the non-axisymmetric mode to follow the solar cycle; the phase relations
between the modes are found. (3) The rate of rotation of the first
non-axisymmetric mode is close to that determined in the interplanetary space.Comment: 22 pages, 18 figures. Accepted for publication in the Astrophysical
Journa
Model for the spatio-temporal intermittency of the energy dissipation in turbulent flows
Modeling the intermittent behavior of turbulent energy dissipation processes
both in space and time is often a relevant problem when dealing with phenomena
occurring in high Reynolds number flows, especially in astrophysical and space
fluids. In this paper, a dynamical model is proposed to describe the
spatio-temporal intermittency of energy dissipation rate in a turbulent system.
This is done by using a shell model to simulate the turbulent cascade and
introducing some heuristic rules, partly inspired by the well known -model,
to construct a spatial structure of the energy dissipation rate. In order to
validate the model and to study its spatially intermittency properties, a
series of numerical simulations have been performed. These show that the level
of spatial intermittency of the system can be simply tuned by varying a single
parameter of the model and that scaling laws in agreement with those obtained
from experiments on fully turbulent hydrodynamic flows can be recovered. It is
finally suggested that the model could represent a useful tool to simulate the
spatio-temporal intermittency of turbulent energy dissipation in those high
Reynolds number astrophysical fluids where impulsive energy release processes
can be associated to the dynamics of the turbulent cascade.Comment: 22 pages, 9 figure
Standard Solar models in the Light of New Helioseismic Constraints II. Mixing Below the Convective Zone
In previous work, we have shown that recent updated standard solar models
cannot reproduce the radial profile of the sound speed at the base of the
convective zone (CZ) and fail to predict the Li7 depletion. In parallel,
helioseismology has shown that the transition from differential rotation in the
CZ to almost uniform rotation in the radiative solar interior occurs in a
shallow layer called the tachocline. This layer is presumably the seat of large
scale circulation and of turbulent motions. Here, we introduce a macroscopic
transport term in the structure equations, which is based on a hydrodynamical
description of the tachocline proposed by Spiegel and Zahn, and we calculate
the mixing induced within this layer. We discuss the influence of different
parameters that represent the tachocline thickness, the Brunt-Vaissala
frequency at the base of the CZ, and the time dependence of this mixing process
along the Sun's evolution. We show that the introduction of such a process
inhibits the microscopic diffusion by about 25%. Starting from models including
a pre-main sequence evolution, we obtain: a) a good agreement with the observed
photospheric chemical abundance of light elements such as He3, He4, Li7 and
Be9, b) a smooth composition gradient at the base of the CZ, and c) a
significant improvement of the sound speed square difference between the
seismic sun and the models in this transition region, when we allow the
phostospheric heavy element abundance to adjust, within the observational
incertitude, due to the action of this mixing process. The impact on neutrino
predictions is also discussed.Comment: 15 pages, 7 figures, to be published in ApJ (used emulateapj style
for latex2e). New email for A. S. Brun: [email protected]
Solar Magnetic Field Reversals and the Role of Dynamo Families
The variable magnetic field of the solar photosphere exhibits periodic
reversals as a result of dynamo activity occurring within the solar interior.
We decompose the surface field as observed by both the Wilcox Solar Observatory
and the Michelson Doppler Imager into its harmonic constituents, and present
the time evolution of the mode coefficients for the past three sunspot cycles.
The interplay between the various modes is then interpreted from the
perspective of general dynamo theory, where the coupling between the primary
and secondary families of modes is found to correlate with large-scale polarity
reversals for many examples of cyclic dynamos. Mean-field dynamos based on the
solar parameter regime are then used to explore how such couplings may result
in the various long-term trends in the surface magnetic field observed to occur
in the solar case.Comment: Accepted to ApJ; comments/corrections to this article are welcome via
e-mail, even after publicatio
Higher mortality of patients on haemodialysis with pancreatic diabetes compared to type 2-diabetes
In rare cases (1-8%) diabetic patients with end-stage renal disease (ESRD) suffer from diabetic nephropathy (dNP) due to pancreatic diabetes mellitus (PDM). Aim of this study was to investigate differences in the outcome of patients with PDM and those with type 2 diabetes
Modeling of differential rotation in rapidly rotating solar-type stars
We investigate differential rotation in rapidly rotating solar-type stars by
means of an axisymmetric mean field model that was previously applied to the
sun. This allows us to calculate the latitudinal entropy gradient with a rea-
sonable physical basis. Our conclusions are as follows: (1) Differential
rotation approaches the Taylor-Proudman state when stellar rotation is faster
than so- lar rotation. (2) Entropy gradient generated by the attached
subadiabatic layer beneath the convection zone becomes relatively small with a
large stellar angu- lar velocity. (3) Turbulent viscosity and turbulent angular
momentum transport determine the spatial difference of angular velocity . (4) The results of our mean field model can explain observations of
stellar differential rotation.Comment: 36 pages, 10 figures, accepted to Ap
New dynamo pattern revealed by solar helical magnetic fields
Previously unobservable mirror asymmetry of the solar magnetic field -- a key
ingredient of the dynamo mechanism which is believed to drive the 11-year
activity cycle -- has now been measured. This was achieved through systematic
monitoring of solar active regions carried out for more than 20 years at
observatories in Mees, Huairou, and Mitaka. In this paper we report on detailed
analysis of vector magnetic field data, obtained at Huairou Solar Observing
Station in China. Electric current helicity (the product of current and
magnetic field component in the same direction) was estimated from the data and
a latitude-time plot of solar helicity during the last two solar cycles has
been produced. We find that like sunspots helicity patterns propagate
equatorwards but unlike sunspot polarity helicity in each solar hemisphere does
not change sign from cycle to cycle - confirming the theory. There are,
however, two significant time-latitudinal domains in each cycle when the sign
does briefly invert. Our findings shed new light on stellar and planetary
dynamos and has yet to be included in the theory.Comment: 4 pages, 2 figures 0 tables. MNRAS Letters, accepte
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