173,659 research outputs found
Synchronicity From Synchronized Chaos
The synchronization of loosely coupled chaotic oscillators, a phenomenon
investigated intensively for the last two decades, may realize the
philosophical notion of synchronicity. Effectively unpredictable chaotic
systems, coupled through only a few variables, commonly exhibit a predictable
relationship that can be highly intermittent. We argue that the phenomenon
closely resembles the notion of meaningful synchronicity put forward by Jung
and Pauli if one identifies "meaningfulness" with internal synchronization,
since the latter seems necessary for synchronizability with an external system.
Jungian synchronization of mind and matter is realized if mind is analogized to
a computer model, synchronizing with a sporadically observed system as in
meteorological data assimilation. Internal synchronization provides a recipe
for combining different models of the same objective process, a configuration
that may also describe the functioning of conscious brains. In contrast to
Pauli's view, recent developments suggest a materialist picture of
semi-autonomous mind, existing alongside the observed world, with both
exhibiting a synchronistic order. Basic physical synchronicity is manifest in
the non-local quantum connections implied by Bell's theorem. The quantum world
resides on a generalized synchronization "manifold", a view that provides a
bridge between nonlocal realist interpretations and local realist
interpretations that constrain observer choice .Comment: 1) clarification regarding the connection with philosophical
synchronicity in Section 2 and in the concluding section 2) reference to
Maldacena-Susskind "ER=EPR" relation in discussion of role of wormholes in
entanglement and nonlocality 3) length reduction and stylistic changes
throughou
Coarse Graining of Nonbonded Inter-particle Potentials Using Automatic Simplex Optimization to Fit Structural Properties
We implemented a coarse-graining procedure to construct mesoscopic models of
complex molecules. The final aim is to obtain better results on properties
depending on slow modes of the molecules. Therefore the number of particles
considered in molecular dynamics simulations is reduced while conserving as
many properties of the original substance as possible. We address the problem
of finding nonbonded interaction parameters which reproduce structural
properties from experiment or atomistic simulations. The approach consists of
optimizing automatically nonbonded parameters using the simplex algorithm to
fit structural properties like the radial distribution function as target
functions. Moreover, any mix of structural and thermodynamic properties can be
included in the target function. Different spherically symmetric inter-particle
potentials are discussed. Besides demonstrating the method for Lennard--Jones
liquids, it is applied to several more complex molecular liquids such as
diphenyl carbonate, tetrahydrofurane, and monomers of poly(isoprene).Comment: 24 pages, 3 tables, 14 figures submitted to the Journal of Chemical
Physics (JCP
Mapping atomistic to coarse-grained polymer models using automatic simplex optimization to fit structural properties
We develop coarse-grained force fields for poly (vinyl alcohol) and poly
(acrylic acid) oligomers. In both cases, one monomer is mapped onto a
coarse-grained bead. The new force fields are designed to match structural
properties such as radial distribution functions of various kinds derived by
atomistic simulations of these polymers. The mapping is therefore constructed
in a way to take into account as much atomistic information as possible. On the
technical side, our approach consists of a simplex algorithm which is used to
optimize automatically non-bonded parameters as well as bonded parameters.
Besides their similar conformation (only the functional side group differs),
poly (acrylic acid) was chosen to be in aqueous solution in contrast to a poly
(vinyl alcohol) melt. For poly (vinyl alcohol) a non-optimized bond angle
potential turns out to be sufficient in connection with a special, optimized
non-bonded potential. No torsional potential has to be applied here. For poly
(acrylic acid), we show that each peak of the radial distribution function is
usually dominated by some specific model parameter(s). Optimization of the bond
angle parameters is essential. The coarse-grained forcefield reproduces the
radius of gyration of the atomistic model. As a first application, we use the
force field to simulate longer chains and compare the hydrodynamic radius with
experimental data.Comment: 34 pages, 3 tables, 16 figure
A quasi-diagonal approach to the estimation of Lyapunov spectra for spatio-temporal systems from multivariate time series
We describe methods of estimating the entire Lyapunov spectrum of a spatially
extended system from multivariate time-series observations. Provided that the
coupling in the system is short range, the Jacobian has a banded structure and
can be estimated using spatially localised reconstructions in low embedding
dimensions. This circumvents the ``curse of dimensionality'' that prevents the
accurate reconstruction of high-dimensional dynamics from observed time series.
The technique is illustrated using coupled map lattices as prototype models for
spatio-temporal chaos and is found to work even when the coupling is not
strictly local but only exponentially decaying.Comment: 13 pages, LaTeX (RevTeX), 13 Postscript figs, to be submitted to
Phys.Rev.
Mapping atomistic to coarse-grained polymer models using automatic simplex optimization to fit structural properties
We develop coarse-grained force fields for poly (vinyl alcohol) and poly
(acrylic acid) oligomers. In both cases, one monomer is mapped onto a
coarse-grained bead. The new force fields are designed to match structural
properties such as radial distribution functions of various kinds derived by
atomistic simulations of these polymers. The mapping is therefore constructed
in a way to take into account as much atomistic information as possible. On the
technical side, our approach consists of a simplex algorithm which is used to
optimize automatically non-bonded parameters as well as bonded parameters.
Besides their similar conformation (only the functional side group differs),
poly (acrylic acid) was chosen to be in aqueous solution in contrast to a poly
(vinyl alcohol) melt. For poly (vinyl alcohol) a non-optimized bond angle
potential turns out to be sufficient in connection with a special, optimized
non-bonded potential. No torsional potential has to be applied here. For poly
(acrylic acid), we show that each peak of the radial distribution function is
usually dominated by some specific model parameter(s). Optimization of the bond
angle parameters is essential. The coarse-grained forcefield reproduces the
radius of gyration of the atomistic model. As a first application, we use the
force field to simulate longer chains and compare the hydrodynamic radius with
experimental data.Comment: 34 pages, 3 tables, 16 figure
A Bayesian Approach to Manifold Topology Reconstruction
In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated
Coarse-graining the Dynamics of a Driven Interface in the Presence of Mobile Impurities: Effective Description via Diffusion Maps
Developing effective descriptions of the microscopic dynamics of many
physical phenomena can both dramatically enhance their computational
exploration and lead to a more fundamental understanding of the underlying
physics. Previously, an effective description of a driven interface in the
presence of mobile impurities, based on an Ising variant model and a single
empirical coarse variable, was partially successful; yet it underlined the
necessity of selecting additional coarse variables in certain parameter
regimes. In this paper we use a data mining approach to help identify the
coarse variables required. We discuss the implementation of this diffusion map
approach, the selection of a similarity measure between system snapshots
required in the approach, and the correspondence between empirically selected
and automatically detected coarse variables. We conclude by illustrating the
use of the diffusion map variables in assisting the atomistic simulations, and
we discuss the translation of information between fine and coarse descriptions
using lifting and restriction operators.Comment: 28 pages, 10 figure
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