24,087 research outputs found
Finite volume schemes for diffusion equations: introduction to and review of modern methods
We present Finite Volume methods for diffusion equations on generic meshes,
that received important coverage in the last decade or so. After introducing
the main ideas and construction principles of the methods, we review some
literature results, focusing on two important properties of schemes (discrete
versions of well-known properties of the continuous equation): coercivity and
minimum-maximum principles. Coercivity ensures the stability of the method as
well as its convergence under assumptions compatible with real-world
applications, whereas minimum-maximum principles are crucial in case of strong
anisotropy to obtain physically meaningful approximate solutions
Formation of clumps and patches in self-aggregation of finite size particles
New model equations are derived for dynamics of self-aggregation of
finite-size particles. Differences from standard Debye-Huckel and Keller-Segel
models are: a) the mobility of particles depends on the locally-averaged
particle density and b) linear diffusion acts on that locally-averaged particle
density. The cases both with and without diffusion are considered here.
Surprisingly, these simple modifications of standard models allow progress in
the analytical description of evolution as well as the complete analysis of
stationary states. When remains positive, the evolution of collapsed
states in our model reduces exactly to finite-dimensional dynamics of
interacting particle clumps. Simulations show these collapsed (clumped) states
emerging from smooth initial conditions, even in one spatial dimension. If
vanishes for some averaged density, the evolution leads to spontaneous
formation of \emph{jammed patches} (weak solution with density having compact
support). Simulations confirm that a combination of these patches forms the
final state for the system.Comment: 38 pages, 8 figures; submitted to Physica
Dynamics and stability of vortex-antivortex fronts in type II superconductors
The dynamics of vortices in type II superconductors exhibit a variety of
patterns whose origin is poorly understood. This is partly due to the
nonlinearity of the vortex mobility which gives rise to singular behavior in
the vortex densities. Such singular behavior complicates the application of
standard linear stability analysis. In this paper, as a first step towards
dealing with these dynamical phenomena, we analyze the dynamical stability of a
front between vortices and antivortices. In particular we focus on the question
of whether an instability of the vortex front can occur in the absence of a
coupling to the temperature. Borrowing ideas developed for singular bacterial
growth fronts, we perform an explicit linear stability analysis which shows
that, for sufficiently large front velocities and in the absence of coupling to
the temperature, such vortex fronts are stable even in the presence of in-plane
anisotropy. This result differs from previous conclusions drawn on the basis of
approximate calculations for stationary fronts. As our method extends to more
complicated models, which could include coupling to the temperature or to other
fields, it provides the basis for a more systematic stability analysis of
nonlinear vortex front dynamics.Comment: 13 pages, 8 figure
Atmospheric Heat Redistribution on Hot Jupiters
Infrared lightcurves of transiting hot Jupiters present a trend in which the
atmospheres of the hottest planets are less efficient at redistributing the
stellar energy absorbed on their daysides---and thus have a larger day-night
temperature contrast---than colder planets. No predictive atmospheric model has
been published that identifies which dynamical mechanisms determine the
atmospheric heat redistribution efficiency on tidally locked exoplanets. Here
we present a two-layer shallow water model of the atmospheric dynamics on
synchronously rotating planets that explains the observed trend. Our model
shows that planets with weak friction and weak irradiation exhibit a banded
zonal flow with minimal day-night temperature differences, while models with
strong irradiation and/or strong friction exhibit a day-night flow pattern with
order-unity fractional day-night temperature differences. To interpret the
model, we develop a scaling theory that shows that the timescale for gravity
waves to propagate horizontally over planetary scales, t_wave, plays a dominant
role in controlling the transition from small to large temperature contrasts.
This implies that heat redistribution is governed by a wave-like process,
similar to the one responsible for the weak temperature gradients in the
Earth's tropics. When atmospheric drag can be neglected, the transition from
small to large day-night temperature contrasts occurs when t_wave ~
sqrt(t_rad/Omega), where t_rad is the radiative relaxation time and Omega is
the planetary rotation frequency. Alternatively, this transition criterion can
be expressed as t_rad ~ t_vert, where t_vert is the timescale for a fluid
parcel to move vertically over the difference in day-night thickness. These
results subsume the commonly used timescale comparison for estimating heat
redistribution efficiency between t_rad and the global horizontal advection
timescale, t_adv.Comment: Accepted to ApJ with minor edits compared to version 1; 17 pages, 11
figure
Generation of internal gravity waves by penetrative convection
The rich harvest of seismic observations over the past decade provides
evidence of angular momentum redistribution in stellar interiors that is not
reproduced by current evolution codes. In this context, transport by internal
gravity waves can play a role and could explain discrepancies between theory
and observations. The efficiency of the transport of angular momentum by waves
depends on their driving mechanism. While excitation by turbulence throughout
the convective zone has already been investigated, we know that penetrative
convection into the stably stratified radiative zone can also generate internal
gravity waves. Therefore, we aim at developing a semianalytical model to
estimate the generation of IGW by penetrative plumes below an upper convective
envelope. We derive the wave amplitude considering the pressure exerted by an
ensemble of plumes on the interface between the radiative and convective zones
as source term in the equation of momentum. We consider the effect of a thermal
transition from a convective gradient to a radiative one on the transmission of
the wave into the radiative zone. The plume-induced wave energy flux at the top
of the radiative zone is computed for a solar model and is compared to the
turbulence-induced one. We show that, for the solar case, penetrative
convection generates waves more efficiently than turbulence and that
plume-induced waves can modify the internal rotation rate on shorter time
scales. We also show that a smooth thermal transition significatively enhances
the wave transmission compared to the case of a steep transition. We conclude
that driving by penetrative convection must be taken into account as much as
turbulence-induced waves for the transport of internal angular momentum.Comment: Accepted for publication in A&A, 21 page
Self-similar solution of fast magnetic reconnection: Semi-analytic study of inflow region
An evolutionary process of the fast magnetic reconnection in ``free space''
which is free from any influence of outer circumstance has been studied
semi-analytically, and a self-similarly expanding solution has been obtained.
The semi-analytic solution is consistent with the results of our numerical
simulations performed in our previous paper (see Nitta et al. 2001). This
semi-analytic study confirms the existence of self-similar growth. On the other
hand, the numerical study by time dependent computer simulation clarifies the
stability of the self-similar growth with respect to any MHD mode. These
results confirm the stable self-similar evolution of the fast magnetic
reconnection system.Comment: 15 pages, 7 figure
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