21,127 research outputs found
Classical Disordered Ground States: Super-Ideal Gases, and Stealth and Equi-Luminous Materials
Using a collective coordinate numerical optimization procedure, we construct
ground-state configurations of interacting particle systems in various space
dimensions so that the scattering of radiation exactly matches a prescribed
pattern for a set of wave vectors. We show that the constructed ground states
are, counterintuitively, disordered (i.e., possess no long-range order) in the
infinite-volume limit. We focus on three classes of configurations with unique
radiation scattering characteristics: (i)``stealth'' materials, which are
transparent to incident radiation at certain wavelengths; (ii)``super-ideal''
gases, which scatter radiation identically to that of an ensemble of ideal gas
configurations for a selected set of wave vectors; and (iii)``equi-luminous''
materials, which scatter radiation equally intensely for a selected set of wave
vectors. We find that ground-state configurations have an increased tendency to
contain clusters of particles as one increases the prescribed luminosity.
Limitations and consequences of this procedure are detailed.Comment: 44 pages, 16 figures, revtek
Clustering and coalescence from multiplicative noise: the Kraichnan ensemble
We study the dynamics of the two-point statistics of the Kraichnan ensemble
which describes the transport of a passive pollutant by a stochastic turbulent
flow characterized by scale invariant structure functions. The fundamental
equation of this problem consists in the Fokker-Planck equation for the
two-point correlation function of the density of particles performing spatially
correlated Brownian motions with scale invariant correlations. This problem is
equivalent to the stochastic motion of an effective particle driven by a
generic multiplicative noise. In this paper we propose an alternative and more
intuitive approach to the problem than the original one leading to the same
conclusions. The general features of this new approach make possible to fit it
to other more complex contexts.Comment: IOP-LaTeX, 17 pages J. Phys. A: Theor. Mat. 2008 in pres
Ground states of stealthy hyperuniform potentials: I. Entropically favored configurations
Systems of particles interacting with "stealthy" pair potentials have been
shown to possess infinitely degenerate disordered hyperuniform classical ground
states with novel physical properties. Previous attempts to sample the
infinitely degenerate ground states used energy minimization techniques,
introducing algorithmic dependence that is artificial in nature. Recently, an
ensemble theory of stealthy hyperuniform ground states was formulated to
predict the structure and thermodynamics that was shown to be in excellent
agreement with corresponding computer simulation results in the canonical
ensemble (in the zero-temperature limit). In this paper, we provide details and
justifications of the simulation procedure, which involves performing molecular
dynamics simulations at sufficiently low temperatures and minimizing the energy
of the snapshots for both the high-density disordered regime, where the theory
applies, as well as lower densities. We also use numerical simulations to
extend our study to the lower-density regime. We report results for the pair
correlation functions, structure factors, and Voronoi cell statistics. In the
high-density regime, we verify the theoretical ansatz that stealthy disordered
ground states behave like "pseudo" disordered equilibrium hard-sphere systems
in Fourier space. These results show that as the density decreases from the
high-density limit, the disordered ground states in the canonical ensemble are
characterized by an increasing degree of short-range order and eventually the
system undergoes a phase transition to crystalline ground states. We also
provide numerical evidence suggesting that different forms of stealthy pair
potentials produce the same ground-state ensemble in the zero-temperature
limit. Our techniques may be applied to sample this limit of the canonical
ensemble of other potentials with highly degenerate ground states
Bayesian learning of joint distributions of objects
There is increasing interest in broad application areas in defining flexible
joint models for data having a variety of measurement scales, while also
allowing data of complex types, such as functions, images and documents. We
consider a general framework for nonparametric Bayes joint modeling through
mixture models that incorporate dependence across data types through a joint
mixing measure. The mixing measure is assigned a novel infinite tensor
factorization (ITF) prior that allows flexible dependence in cluster allocation
across data types. The ITF prior is formulated as a tensor product of
stick-breaking processes. Focusing on a convenient special case corresponding
to a Parafac factorization, we provide basic theory justifying the flexibility
of the proposed prior and resulting asymptotic properties. Focusing on ITF
mixtures of product kernels, we develop a new Gibbs sampling algorithm for
routine implementation relying on slice sampling. The methods are compared with
alternative joint mixture models based on Dirichlet processes and related
approaches through simulations and real data applications.Comment: Appearing in Proceedings of the 16th International Conference on
Artificial Intelligence and Statistics (AISTATS) 2013, Scottsdale, AZ, US
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