30 research outputs found
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
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
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
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
An in-host model of HIV incorporating latent infection and viral mutation
We construct a seven-component model of the in-host dynamics of the Human
Immunodeficiency Virus Type-1 (i.e, HIV) that accounts for latent infection and
the propensity of viral mutation. A dynamical analysis is conducted and a
theorem is presented which characterizes the long time behavior of the model.
Finally, we study the effects of an antiretroviral drug and treatment
implications.Comment: 10 pages, 7 figures, Proceedings of AIMS Conference on Differential
Equations and Dynamical Systems (2015
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
On the spatially homogeneous and isotropic Einstein-Vlasov-Fokker-Planck system with cosmological scalar field
The Einstein-Vlasov-Fokker-Planck system describes the kinetic diffusion dynamics of self-gravitating particles within the Einstein theory of general relativity. We study the Cauchy problem for spatially homogeneous and isotropic solutions and prove the existence of both global-in-time solutions and solutions that blow-up in finite time depending on the size of certain functions of the initial data. We also derive information on the large-time behavior of global solutions and toward the singularity for solutions which blow-up in finite time. Our results entail the existence of a phase of decelerated expansion followed by a phase of accelerated expansion, in accordance with the physical expectations in cosmology