1,596 research outputs found
Early Thermal Evolution of Planetesimals and its Impact on Processing and Dating of Meteoritic Material
Radioisotopic ages for meteorites and their components provide constraints on
the evolution of small bodies: timescales of accretion, thermal and aqueous
metamorphism, differentiation, cooling and impact metamorphism. Realising that
the decay heat of short-lived nuclides (e.g. 26Al, 60Fe), was the main heat
source driving differentiation and metamorphism, thermal modeling of small
bodies is of utmost importance to set individual meteorite age data into the
general context of the thermal evolution of their parent bodies, and to derive
general conclusions about the nature of planetary building blocks in the early
solar system. As a general result, modelling easily explains that iron
meteorites are older than chondrites, as early formed planetesimals experienced
a higher concentration of short-lived nuclides and more severe heating.
However, core formation processes may also extend to 10 Ma after formation of
Calcium-Aluminum-rich inclusions (CAIs). A general effect of the porous nature
of the starting material is that relatively small bodies (< few km) will also
differentiate if they form within 2 Ma after CAIs. A particular interesting
feature to be explored is the possibility that some chondrites may derive from
the outer undifferentiated layers of asteroids that are differentiated in their
interiors. This could explain the presence of remnant magnetization in some
chondrites due to a planetary magnetic field.Comment: 24 pages, 9 figures, Accepted for publication as a chapter in
Protostars and Planets VI, University of Arizona Press (2014), eds. H.
Beuther, R. Klessen, C. Dullemond, Th. Hennin
Clausius inequality and optimality of quasi static transformations for nonequilibrium stationary states
Nonequilibrium stationary states of thermodynamic systems dissipate a
positive amount of energy per unit of time. If we consider transformations of
such states that are realized by letting the driving depend on time, the amount
of energy dissipated in an unbounded time window becomes then infinite.
Following the general proposal by Oono and Paniconi and using results of the
macroscopic fluctuation theory, we give a natural definition of a renormalized
work performed along any given transformation. We then show that the
renormalized work satisfies a Clausius inequality and prove that equality is
achieved for very slow transformations, that is in the quasi static limit. We
finally connect the renormalized work to the quasi potential of the macroscopic
fluctuation theory, that gives the probability of fluctuations in the
stationary nonequilibrium ensemble
Time Evolution of Spin Waves
A rigorous derivation of macroscopic spin-wave equations is demonstrated. We
introduce a macroscopic mean-field limit and derive the so-called
Landau-Lifshitz equations for spin waves. We first discuss the ferromagnetic
Heisenberg model at T=0 and finally extend our analysis to general spin
hamiltonians for the same class of ferromagnetic ground states.Comment: 4 pages, to appear in PR
Spatial structures and dynamics of kinetically constrained models for glasses
Kob and Andersen's simple lattice models for the dynamics of structural
glasses are analyzed. Although the particles have only hard core interactions,
the imposed constraint that they cannot move if surrounded by too many others
causes slow dynamics. On Bethe lattices a dynamical transition to a partially
frozen phase occurs. In finite dimensions there exist rare mobile elements that
destroy the transition. At low vacancy density, , the spacing, ,
between mobile elements diverges exponentially or faster in . Within the
mobile elements, the dynamics is intrinsically cooperative and the
characteristic time scale diverges faster than any power of (although
slower than ). The tagged-particle diffusion coefficient vanishes roughly
as .Comment: 4 pages. Accepted for pub. in Phys. Rev. Let
Replica Bethe ansatz derivation of the Tracy-Widom distribution of the free energy fluctuations in one-dimensional directed polymers
The distribution function of the free energy fluctuations in one-dimensional
directed polymers with -correlated random potential is studied by
mapping the replicated problem to the -particle quantum boson system with
attractive interactions. We find the full set of eigenfunctions and eigenvalues
of this many-body system and perform the summation over the entire spectrum of
excited states. It is shown that in the thermodynamic limit the problem is
reduced to the Fredholm determinant with the Airy kernel yielding the universal
Tracy-Widom distribution, which is known to describe the statistical properties
of the Gaussian unitary ensemble as well as many other statistical systems.Comment: 23 page
RankPL: A Qualitative Probabilistic Programming Language
In this paper we introduce RankPL, a modeling language that can be thought of
as a qualitative variant of a probabilistic programming language with a
semantics based on Spohn's ranking theory. Broadly speaking, RankPL can be used
to represent and reason about processes that exhibit uncertainty expressible by
distinguishing "normal" from" surprising" events. RankPL allows (iterated)
revision of rankings over alternative program states and supports various types
of reasoning, including abduction and causal inference. We present the
language, its denotational semantics, and a number of practical examples. We
also discuss an implementation of RankPL that is available for download
Prediction of anomalous diffusion and algebraic relaxations for long-range interacting systems, using classical statistical mechanics
We explain the ubiquity and extremely slow evolution of non gaussian
out-of-equilibrium distributions for the Hamiltonian Mean-Field model, by means
of traditional kinetic theory. Deriving the Fokker-Planck equation for a test
particle, one also unambiguously explains and predicts striking slow algebraic
relaxation of the momenta autocorrelation, previously found in numerical
simulations. Finally, angular anomalous diffusion are predicted for a large
class of initial distributions. Non Extensive Statistical Mechanics is shown to
be unnecessary for the interpretation of these phenomena
Quantum transport through single-molecule junctions with orbital degeneracies
We consider electronic transport through a single-molecule junction where the
molecule has a degenerate spectrum. Unlike previous transport models, and
theories a rate-equations description is no longer possible, and the quantum
coherences between degenerate states have to be taken into account. We present
the derivation and application of a master equation that describes the system
in the weak-coupling limit and give an in-depth discussion of the parameter
regimes and the new phenomena due to coherent on-site dynamics
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