Fitting coarse-grained distribution functions through an iterative force-matching method

Abstract. In this paper we investigate the statistical properties of magnetic field fluctuations measured by the four Cluster spacecraft in the cusp and close to the interface with the magnetospheric lobes, magnetopause and magnetosheath. At lower altitudes along the outbound orbit of 26 February 2001, the magnetic field fluctuations recorded by all four spacecraft are random and their Probability Distribution Functions (PDFs) are Gaussian at all scales. The flatness parameter, F – related to the kurtosis of the time series, is equal to 3. At higher altitudes, in the cusp and its vicinity, closer to the interface with the magnetopause and magnetosheath, the PDFs from all Cluster satellites are non-Gaussian and show a clear intermittent behavior at scales smaller than τG≈ 61 s (or 170 km). The flatness parameter increases to values greater than 3 for scales smaller than τG. A Haar wavelet transform enables the identification of the "events" that produce sudden variations of the magnetic field and of the scales that have most of the power. The LIM parameter (i.e. normalized wavelet power) indicates that events for scales below 65 s are non-uniformly distributed throughout the cusp passage. PDFs, flatness and wavelet analysis show that at coarse-grained scales larger than τG the intermittency is absent in the cusp. Fluctuations of the magnetic energy observed during the same orbit in the magnetosheath show PDFs that tend toward a Gaussian at scales smaller than τG found in the cusp. The flatness analysis confirms the decreasing of τG from cusp to magnetosheath. Our analysis reveals the turbulent cusp as a transition region from a non-intermittent turbulent state inside the magnetosphere to an intermittent turbulent state in the magnetosheath that has statistical properties resembling the solar wind turbulence. The observed turbulent fluctuations in the cusp suggests a phenomenon of nonlinear interactions of plasma coherent structures as in contemporary models of space plasma turbulence.

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Multiscale modeling of polymers closely coupled to Broad Q neutron scattering from NIMROD

MRS Proceedings ◽

10.1557/opl.2012.1765 ◽

2013 ◽

Vol 1524 ◽

Cited By ~ 2

Author(s):

Thomas Gkourmpis ◽

Daniel Lopez ◽

Geoffrey R. Mitchell

Keyword(s):

Structure Factor ◽

Chain Structure ◽

Distribution Functions ◽

Chain Conformation ◽

Coarse Grained ◽

Lamellar Thickness ◽

Single Chain ◽

Crystal Unit Cell ◽

Key Length ◽

Using Data

ABSTRACTWe use data over an extended Q range from 0.01 to 100Å-1 from the recently commissioned NIMROD instrument at the ISIS pulsed neutron source to develop a multi-scale inverse modeling procedure which will provide insight in to the phase transformations of polymer systems. The first level of our procedure is atomistic and we use internal coordinates (bond length, bond angles and torsion angles) to define the polymer chain in full atomistic detail. Values were assigned to each internal coordinate within the chain using a stochastic Monte Carlo method in which the probabilities were drawn from distributions representing the possible range of values. Using this approach, random chain configurations could be rapidly built and the intrachain structure factor calculated utilizing a small set of parameters and compared with the experimental function. Parameters representing the probability distribution functions were systematically varied using a grid search to find the values which gave the best fit to the structure factor for Q > 3Å-1 in order to determine the details of the chain conformation in the molten phase. This process was repeated for data over the same extended Q range obtained at lower temperatures where the polymer was expected to crystallize. Polymers crystallize via chainfolded thin lamellae crystals. Such crystals give rise to an intense peak at Q ∼ 0.03Å-1. This scattering can be calculated using a lamellar stack model, coarse-grained from the single chain structure. We describe this approach using data obtained on the crystallization from the melt phase of perdeuterated polymers. The objective here is to follow the three key length scales; the chain folded lamellar thickness of ∼ 10nm, the crystal unit cell ∼ 1nm and the detail of the chain conformation is ∼ 0.1nm.

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