290 research outputs found
Stochastic Dynamics of Bionanosystems: Multiscale Analysis and Specialized Ensembles
An approach for simulating bionanosystems, such as viruses and ribosomes, is
presented. This calibration-free approach is based on an all-atom description
for bionanosystems, a universal interatomic force field, and a multiscale
perspective. The supramillion-atom nature of these bionanosystems prohibits the
use of a direct molecular dynamics approach for phenomena like viral structural
transitions or self-assembly that develop over milliseconds or longer. A key
element of these multiscale systems is the cross-talk between, and consequent
strong coupling of, processes over many scales in space and time. We elucidate
the role of interscale cross-talk and overcome bionanosystem simulation
difficulties with automated construction of order parameters (OPs) describing
supra-nanometer scale structural features, construction of OP dependent
ensembles describing the statistical properties of atomistic variables that
ultimately contribute to the entropies driving the dynamics of the OPs, and the
derivation of a rigorous equation for the stochastic dynamics of the OPs. Since
the atomic scale features of the system are treated statistically, several
ensembles are constructed that reflect various experimental conditions. The
theory provides a basis for a practical, quantitative bionanosystem modeling
approach that preserves the cross-talk between the atomic and nanoscale
features. A method for integrating information from nanotechnical experimental
data in the derivation of equations of stochastic OP dynamics is also
introduced.Comment: 24 page
Self-Assembly of Nanocomponents into Composite Structures: Derivation and Simulation of Langevin Equations
The kinetics of the self-assembly of nanocomponents into a virus,
nanocapsule, or other composite structure is analyzed via a multiscale
approach. The objective is to achieve predictability and to preserve key
atomic-scale features that underlie the formation and stability of the
composite structures. We start with an all-atom description, the Liouville
equation, and the order parameters characterizing nanoscale features of the
system. An equation of Smoluchowski type for the stochastic dynamics of the
order parameters is derived from the Liouville equation via a multiscale
perturbation technique. The self-assembly of composite structures from
nanocomponents with internal atomic structure is analyzed and growth rates are
derived. Applications include the assembly of a viral capsid from capsomers, a
ribosome from its major subunits, and composite materials from fibers and
nanoparticles. Our approach overcomes errors in other coarse-graining methods
which neglect the influence of the nanoscale configuration on the atomistic
fluctuations. We account for the effect of order parameters on the statistics
of the atomistic fluctuations which contribute to the entropic and average
forces driving order parameter evolution. This approach enables an efficient
algorithm for computer simulation of self-assembly, whereas other methods
severely limit the timestep due to the separation of diffusional and complexing
characteristic times. Given that our approach does not require recalibration
with each new application, it provides a way to estimate assembly rates and
thereby facilitate the discovery of self-assembly pathways and kinetic dead-end
structures.Comment: 34 pages, 11 figure
Multiscaling for Classical Nanosystems: Derivation of Smoluchowski and Fokker-Planck Equations
Using multiscale analysis and methods of statistical physics, we show that a
solution to the N-atom Liouville Equation can be decomposed via an expansion in
terms of a smallness parameter epsilon, wherein the long scale time behavior
depends upon a reduced probability density that is a function of slow-evolving
order parameters. This reduced probability density is shown to satisfy the
Smoluchowski equation up to order epsilon squared for a given range of initial
conditions. Furthermore, under the additional assumption that the nanoparticle
momentum evolves on a slow time scale, we show that this reduced probability
density satisfies a Fokker-Planck equation up to the same order in epsilon.
This approach applies to a broad range of problems in the nanosciences.Comment: 23 page
Mesoscopic model of nucleation and Ostwald ripening/stepping: Application to the silica polymorph system
Precipitation is modeled using a particle size distribution ~PSD! approach for the single or multiple
polymorph system. A chemical kinetic-type model for the construction of the molecular clusters of
each polymorph is formulated that accounts for adsorption at a heterogeneous site, nucleation,
growth, and Ostwald ripening. When multiple polymorphs are accounted for, Ostwald stepping is
also predicted. The challenge of simulating the 23 order of magnitude in cluster size ~monomer,
dimer, . . . , 1023-mer! is met by a new formalism that accounts for the macroscopic behavior of
large clusters as well as the structure of small ones. The theory is set forth for the surface kinetic
controlled growth systems and it involves corrections to the Lifshitz–Slyozov, Wagner ~LSW!
equation and preserves the monomer addition kinetics for small clusters. A time independent, scaled
PSD behavior is achieved both analytically and numerically, and the average radius grows with
Rave}t1/2 law for smooth particles. Applications are presented for the silica system that involves five
polymorphs. Effects of the adsorption energetics and the smooth or fractal nature of clusters on the
nucleation, ripening, and stepping behavior are analyzed. The Ostwald stepping scenario is found to
be highly sensitive to adsorption energetics. Long time scaling behavior of the PSD reveals time
exponents greater than those for the classical theory when particles are fractal. Exact scaling
solutions for the PSD are compared with numerical results to assess the accuracy and convergence
of our numerical technique. © 2000 American Institute of Physics. @S0021-9606~00!70123-1
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Mechanical failure of cavities in poroelastic media
The stress-induced failure of cavities in poroelastic media is investigated using an analytical solution of the elastic matrix inclusion problem of Eshelby and a rock failure criterion. The elastic properties of the porous matrix surrounding the cavity are modeled using a self-consistent version of the theory of Berryman while the cavity collapse criterion is based on a failure condition calibrated as a function of matrix mineralogy, grain size and porosity. The influence of the latter textural variables as well as pore fluid pressure and cavity shape and orientation relative to the far-field stress are evaluated. The region of failure on the cavity surface is identified. These results are applied to the prediction of vug stability in a sedimentary basin in the context of vuggy reservoir exploration and production
Visual attention modulates the into ration of goal-relevant evidence and not value
When choosing between options, such as food items presented in plain view, people tend to choose the option they spend longer looking at. The prevailing interpretation is that visual attention increases value. However, in previous studies, ‘value’ was coupled to a behavioural goal, since subjects had to choose the item they preferred. This makes it impossible to discern if visual attention has an effect on value, or, instead, if attention modulates the information most relevant for the goal of the decision-maker. Here, we present the results of two independent studies—a perceptual and a value-based task—that allow us to decouple value from goal-relevant information using specific task-framing. Combining psychophysics with computational modelling, we show that, contrary to the current interpretation, attention does not boost value, but instead it modulates goal-relevant information. This work provides a novel and more general mechanism by which attention interacts with choice
Multiscale Theory of Finite Size Bose Systems: Implications for Collective and Single-Particle Excitations
Boson droplets (i.e., dense assemblies of bosons at low temperature) are
shown to mask a significant amount of single-particle behavior and to manifest
collective, droplet-wide excitations. To investigate the balance between
single-particle and collective behavior, solutions to the wave equation for a
finite size Bose system are constructed in the limit where the ratio
\varepsilon of the average nearest-neighbor boson distance to the size of the
droplet or the wavelength of density disturbances is small. In this limit, the
lowest order wave function varies smoothly across the system, i.e., is devoid
of structure on the scale of the average nearest-neighbor distance. The
amplitude of short range structure in the wave function is shown to vanish as a
power of \varepsilon when the interatomic forces are relatively weak. However,
there is residual short range structure that increases with the strength of
interatomic forces. While the multiscale approach is applied to boson droplets,
the methodology is applicable to any finite size bose system and is shown to be
more direct than field theoretic methods. Conclusions for Helium-4 nanodroplets
are drawn.Comment: 28 pages, 5 figure
Multiscaling for Systems with a Broad Continuum of Characteristic Lengths and Times: Structural Transitions in Nanocomposites
The multiscale approach to N-body systems is generalized to address the broad
continuum of long time and length scales associated with collective behaviors.
A technique is developed based on the concept of an uncountable set of time
variables and of order parameters (OPs) specifying major features of the
system. We adopt this perspective as a natural extension of the commonly used
discrete set of timescales and OPs which is practical when only a few,
widely-separated scales exist. The existence of a gap in the spectrum of
timescales for such a system (under quasiequilibrium conditions) is used to
introduce a continuous scaling and perform a multiscale analysis of the
Liouville equation. A functional-differential Smoluchowski equation is derived
for the stochastic dynamics of the continuum of Fourier component order
parameters. A continuum of spatially non-local Langevin equations for the OPs
is also derived. The theory is demonstrated via the analysis of structural
transitions in a composite material, as occurs for viral capsids and molecular
circuits.Comment: 28 pages, 1 figur
Instabilities in the dissolution of a porous matrix
A reactive fluid dissolving the surrounding rock matrix can trigger an
instability in the dissolution front, leading to spontaneous formation of
pronounced channels or wormholes. Theoretical investigations of this
instability have typically focused on a steadily propagating dissolution front
that separates regions of high and low porosity. In this paper we show that
this is not the only possible dissolutional instability in porous rocks; there
is another instability that operates instantaneously on any initial porosity
field, including an entirely uniform one. The relative importance of the two
mechanisms depends on the ratio of the porosity increase to the initial
porosity. We show that the "inlet" instability is likely to be important in
limestone formations where the initial porosity is small and there is the
possibility of a large increase in permeability. In quartz-rich sandstones,
where the proportion of easily soluble material (e.g. carbonate cements) is
small, the instability in the steady-state equations is dominant.Comment: to be published in Geophysical Research Letter
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Overview of the structural geology and tectonics of the Central Basin Platform, Delaware Basin, and Midland Basin, West Texas and New Mexico
The structural geology and tectonics of the Permian Basin were investigated using an integrated approach incorporating satellite imagery, aeromagnetics, gravity, seismic, regional subsurface mapping and published literature. The two primary emphases were on: (1) delineating the temporal and spatial evolution of the regional stress state; and (2) calculating the amount of regional shortening or contraction. Secondary objectives included delineation of basement and shallower fault zones, identification of structural style, characterization of fractured zones, analysis of surficial linear features on satellite imagery and their correlation to deeper structures. Gandu Unit, also known as Andector Field at the Ellenburger level and Goldsmith Field at Permian and younger reservoir horizons, is the primary area of interest and lies in the northern part of Ector county. The field trends northwest across the county line into Andrews County. The field(s) are located along an Ellenburger thrust anticline trap on the eastern margin of the Central Basin Platform
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