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

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

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

Orbital and asymptotic stability for standing waves of a NLS equation with concentrated nonlinearity in dimension three

We begin to study in this paper orbital and asymptotic stability of standing waves for a model of Schr\"odinger equation with concentrated nonlinearity in dimension three. The nonlinearity is obtained considering a {point} (or contact) interaction with strength $\alpha$, which consists of a singular perturbation of the laplacian described by a selfadjoint operator $H_{\alpha}$, where the strength $\alpha$ depends on the wavefunction: $i\dot u= H_\alpha u$, $\alpha=\alpha(u)$. If $q$ is the so-called charge of the domain element $u$, i.e. the coefficient of its singular part, we let the strength $\alpha$ depend on $u$ according to the law $\alpha=-\nu|q|^\sigma$, with $\nu > 0$. This characterizes the model as a focusing NLS with concentrated nonlinearity of power type. For such a model we prove the existence of standing waves of the form $u (t)=e^{i\omega t}\Phi_{\omega}$, which are orbitally stable in the range $\sigma \in (0,1)$, and orbitally unstable for $\sigma \geq 1.$ Moreover, we show that for $\sigma \in (0,\frac{1}{\sqrt 2})$ every standing wave is asymptotically stable in the following sense. Choosing initial data close to the stationary state in the energy norm, and belonging to a natural weighted $L^p$ space which allows dispersive estimates, the following resolution holds: $u(t) = e^{i\omega_{\infty} t} \Phi_{\omega_{\infty}} +U_t*\psi_{\infty} +r_{\infty}, \quad \textrm{as} \;\; t \rightarrow +\infty$, where $U$ is the free Schr\"odinger propagator, $\omega_{\infty} > 0$ and $\psi_{\infty}$, $r_{\infty} \in L^2(\R^3)$ with $\| r_{\infty} \|_{L^2} = O(t^{-5/4}) \quad \textrm{as} \;\; t \rightarrow +\infty$. Notice that in the present model the admitted nonlinearity for which asymptotic stability of solitons is proved is subcritical.Comment: Comments and clarifications added; several misprints correcte

A comparative study of electrochemical, spectroscopic and structural properties of phenyl, thienyl and furyl substituted ethylenes

a detailed electrochemical and photophysical comparative study of three parallel series of phenyl, thienyl and furyl substituted ethylenes has been carried out, implemented by the computational calculation of selected terms. Relationships have been highlighted between molecular structure (number and type of aromatic rings) and important functional properties (in particular, electronic features and oligomerization ability). Interestingly, some of the studied heteroaryl-ethylenes show emission in the solid state displaying an aggregation-induced emission behavior

Predicting the natural state of fractured carbonate reservoirs: An Andector Field, West Texas test of a 3-D RTM simulator

The power of the reaction, transport, mechanical (RTM) modeling approach is that it directly uses the laws of geochemistry and geophysics to extrapolate fracture and other characteristics from the borehole or surface to the reservoir interior. The objectives of this facet of the project were to refine and test the viability of the basin/reservoir forward modeling approach to address fractured reservoir in E and P problems. The study attempts to resolve the following issues: role of fracturing and timing on present day location and characteristics; clarifying the roles and interplay of flexure dynamics, changing rock rheological properties, fluid pressuring and tectonic/thermal histories on present day reservoir location and characteristics; and test the integrated RTM modeling/geological data approach on a carbonate reservoir. Sedimentary, thermal and tectonic data from Andector Field, West Texas, were used as input to the RTM basin/reservoir simulator to predict its preproduction state. The results were compared with data from producing reservoirs to test the RTM modeling approach. The effects of production on the state of the field are discussed in a companion report. The authors draw the following conclusions: RTM modeling is an important new tool in fractured reservoir E and P analysis; the strong coupling of RTM processes and the geometric and tensorial complexity of fluid flow and stresses require the type of fully coupled, 3-D RTM model for fracture analysis as pioneered in this project; flexure analysis cannot predict key aspects of fractured reservoir location and characteristics; fracture history over the lifetime of a basin is required to understand the timing of petroleum expulsion and migration and the retention properties of putative reservoirs

Controlling domain patterns far from equilibrium

A high degree of control over the structure and dynamics of domain patterns in nonequilibrium systems can be achieved by applying nonuniform external fields near parity breaking front bifurcations. An external field with a linear spatial profile stabilizes a propagating front at a fixed position or induces oscillations with frequency that scales like the square root of the field gradient. Nonmonotonic profiles produce a variety of patterns with controllable wavelengths, domain sizes, and frequencies and phases of oscillations.Comment: Published version, 4 pages, RevTeX. More at http://t7.lanl.gov/People/Aric

Domain Walls in Non-Equilibrium Systems and the Emergence of Persistent Patterns

Domain walls in equilibrium phase transitions propagate in a preferred direction so as to minimize the free energy of the system. As a result, initial spatio-temporal patterns ultimately decay toward uniform states. The absence of a variational principle far from equilibrium allows the coexistence of domain walls propagating in any direction. As a consequence, *persistent* patterns may emerge. We study this mechanism of pattern formation using a non-variational extension of Landau's model for second order phase transitions. PACS numbers: 05.70.Fh, 42.65.Pc, 47.20.Ky, 82.20MjComment: 12 pages LaTeX, 5 postscript figures To appear in Phys. Rev.