1,077 research outputs found
Coorbital Satellites of Saturn: Congenital Formation
Saturn is the only known planet to have coorbital satellite systems. In the
present work we studied the process of mass accretion as a possible mechanism
for coorbital satellites formation. The system considered is composed of
Saturn, a proto-satellite and a cloud of planetesimals distributed in the
coorbital region around a triangular Lagrangian point. The adopted relative
mass for the proto-satellite was 10^-6 of Saturn's mass and for each
planetesimal of the cloud three cases of relative mass were considered, 10^-14,
10^-13 and 10^-12 masses of Saturn. In the simulations each cloud of
planetesimal was composed of 10^3, 5 x 10^3 or 10^4 planetesimals. The results
of the simulations show the formation of coorbital satellites with relative
masses of the same order of those found in the saturnian system (10^-13 -
10^-9). Most of them present horseshoe type orbits, but a significant part is
in tadpole orbit around L_4 or L_5. Therefore, the results indicate that this
is a plausible mechanism for the formation of coorbital satellites.Comment: 10 pages, 9 figures, 4 table
Terrestrial Planet Formation in a protoplanetary disk with a local mass depletion: A successful scenario for the formation of Mars
Models of terrestrial planet formation for our solar system have been
successful in producing planets with masses and orbits similar to those of
Venus and Earth. However, these models have generally failed to produce
Mars-sized objects around 1.5 AU. The body that is usually formed around Mars'
semimajor axis is, in general, much more massive than Mars. Only when Jupiter
and Saturn are assumed to have initially very eccentric orbits (e 0.1),
which seems fairly unlikely for the solar system, or alternately, if the
protoplanetary disk is truncated at 1.0 AU, simulations have been able to
produce Mars-like bodies in the correct location. In this paper, we examine an
alternative scenario for the formation of Mars in which a local depletion in
the density of the protosolar nebula results in a non-uniform formation of
planetary embryos and ultimately the formation of Mars-sized planets around 1.5
AU. We have carried out extensive numerical simulations of the formation of
terrestrial planets in such a disk for different scales of the local density
depletion, and for different orbital configurations of the giant planets. Our
simulations point to the possibility of the formation of Mars-sized bodies
around 1.5 AU, specifically when the scale of the disk local mass-depletion is
moderately high (50-75%) and Jupiter and Saturn are initially in their current
orbits. In these systems, Mars-analogs are formed from the protoplanetary
materials that originate in the regions of disk interior or exterior to the
local mass-depletion. Results also indicate that Earth-sized planets can form
around 1 AU with a substantial amount of water accreted via primitive
water-rich planetesimals and planetary embryos. We present the results of our
study and discuss their implications for the formation of terrestrial planets
in our solar system.Comment: Accepted for publication in The Astrophysical Journa
Integrable discretizations of derivative nonlinear Schroedinger equations
We propose integrable discretizations of derivative nonlinear Schroedinger
(DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation
and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS
systems admit the reduction of complex conjugation between two dependent
variables and possess bi-Hamiltonian structure. Through transformations of
variables and reductions, we obtain novel integrable discretizations of the
nonlinear Schroedinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS,
matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa-Satsuma and
Burgers equations. We also discuss integrable discretizations of the
sine-Gordon equation, the massive Thirring model and their generalizations.Comment: 24 pages, LaTeX2e (IOP style), final versio
Classification of integrable Volterra type lattices on the sphere. Isotropic case
The symmetry approach is used for classification of integrable isotropic
vector Volterra lattices on the sphere. The list of integrable lattices
consists mainly of new equations. Their symplectic structure and associated PDE
of vector NLS-type are discussed.Comment: 16 page
Noncommutative Burgers Equation
We present a noncommutative version of the Burgers equation which possesses
the Lax representation and discuss the integrability in detail. We find a
noncommutative version of the Cole-Hopf transformation and succeed in the
linearization of it. The linearized equation is the (noncommutative) diffusion
equation and exactly solved. We also discuss the properties of some exact
solutions. The result shows that the noncommutative Burgers equation is
completely integrable even though it contains infinite number of time
derivatives. Furthermore, we derive the noncommutative Burgers equation from
the noncommutative (anti-)self-dual Yang-Mills equation by reduction, which is
an evidence for the noncommutative Ward conjecture. Finally, we present a
noncommutative version of the Burgers hierarchy by both the Lax-pair generating
technique and the Sato's approach.Comment: 24 pages, LaTeX, 1 figure; v2: discussions on Ward conjecture, Sato
theory and the integrability added, references added, version to appear in J.
Phys.
Calculating response functions in time domain with non-orthonormal basis sets
We extend the recently proposed order-N algorithms (cond-mat/9703224) for
calculating linear- and nonlinear-response functions in time domain to the
systems described by nonorthonormal basis sets.Comment: 4 pages, no figure
Multiresolution analysis of electronic structure: semicardinal and wavelet bases
This article reviews recent developments in multiresolution analysis which
make it a powerful tool for the systematic treatment of the multiple
length-scales inherent in the electronic structure of matter. Although the
article focuses on electronic structure, the advances described are useful for
non-linear problems in the physical sciences in general. The new language and
notations introduced are well- suited for both formal manipulations and the
development of computer software using higher-level languages such as C++. The
discussion is self-contained, and all needed algorithms are specified
explicitly in terms of simple operators and illustrated with straightforward
diagrams which show the flow of data. Among the reviewed developments is the
construction of_exact_ multiresolution representations from extremely limited
samples of physical fields in real space. This new and profound result is the
critical advance in finally allowing systematic, all electron calculations to
compete in efficiency with state-of-the-art electronic structure calculations
which depend for their celerity upon freezing the core electronic degrees of
freedom. This review presents the theory of wavelets from a physical
perspective, provides a unified and self-contained treatment of non-linear
couplings and physical operators and introduces a modern framework for
effective single-particle theories of quantum mechanics.Comment: A "how-to from-scratch" book presently in press at Reviews of Modern
Physics: 88 pages, 31 figures, 5 tables, 88 references. Significantly
IMPROVED version, including (a) new diagrams illustrating algorithms; (b)
careful proof-reading of equations and text; (c) expanded bibliography; (d)
cosmetic changes including lists of figures and tables and a more reasonable
font. Latest changes (Dec. 11, 1998): a more descriptive abstract, and minor
lexicographical change
O(N) methods in electronic structure calculations
Linear scaling methods, or O(N) methods, have computational and memory
requirements which scale linearly with the number of atoms in the system, N, in
contrast to standard approaches which scale with the cube of the number of
atoms. These methods, which rely on the short-ranged nature of electronic
structure, will allow accurate, ab initio simulations of systems of
unprecedented size. The theory behind the locality of electronic structure is
described and related to physical properties of systems to be modelled, along
with a survey of recent developments in real-space methods which are important
for efficient use of high performance computers. The linear scaling methods
proposed to date can be divided into seven different areas, and the
applicability, efficiency and advantages of the methods proposed in these areas
is then discussed. The applications of linear scaling methods, as well as the
implementations available as computer programs, are considered. Finally, the
prospects for and the challenges facing linear scaling methods are discussed.Comment: 85 pages, 15 figures, 488 references. Resubmitted to Rep. Prog. Phys
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