Adaptive Brownian dynamics for shape estimation of sodium ion channels

Ion channels are protein macromolecules that form biological nanotubes across the membranes of living cells. Given many possible geometrical shapes of an ion channel, we propose a computational scheme of selecting the model that best replicates experimental observations, using adaptive Brownian dynamics simulations together with discrete optimization algorithms. Brownian dynamics simulations emulate the propagation of individual ions through the sodium channel nanotube at a femto time second time scale and Angstrom unit (10(-10) meter) spatial scale.     

A molecular dynamics approach in simulations of fluid-solid particles flow

In the paper a discrete system of particles carried by fluid is considered in a planar motion. The volumetric density of particles is assumed to be small enough such that they can be treated within the framework of a molecular dynamics model. The fluid is then considered as a carrier of particles. The Landau-Lifshitz concept of turbulence is used to describe the fluctuating part of fluid velocity. This approach is applied to simulate different regimes (laminar and turbulent) and various states of particle motion (moving bed, heterogeneous flow, and homogeneous flow) using only two parameters, which have to be determined experimentally. These two parameters, found for a particular pipe and for a particular velocity from a simple experiment, then can be used for other pipe diameters and different velocities. The computer simulations performed for the flow of particles in pipes at different flow velocities and different pipe diameters agree favorably with experimental observations of the type of flow and critical velocities identifying transitions from one type to another. Received: 8 January 1999     

Growth of Ag nanometre-sized particles in solution: molecular dynamics simulations

This work focuses on the growth of nanometre-sized Ag clusters in solution. Molecular dynamics simulations have been employed to gain the necessary detail on the dynamics of solute species and to study the mechanistic features of the processes governing the association of solute atoms in aggregates. Supersaturated liquid solutions of Ag in tetrachloromethane have been considered. A systematic variation of the concentration of Ag atoms in solution permitted us to show the different mechanistic scenarios responsible for the growth processes of solid Ag clusters. It is shown that such processes are limited by the thermal diffusion of solute in the solution bulk at relatively low supersaturation degrees, whereas the growth is limited by interfacial effects at relatively high supersaturation degrees.     

Theoretical rheology of suspensions of ferromagnetic rod-like particles

We extend the linear response-like derivation of the generalized Navier-Stokes equation to non-Newtonian flows with rate of strain-dependent transport coefficients. We derive a time correlation function expression for the viscosity tensor and point out possible ambiguities in the operational definitions of viscosity coefficients. Our analysis is specific to a suspension of polar, rod-like ferromagnetic particles. A commentary is included about the approximations that lead from the time correlation function and the molecular definition of the viscosity tensor to the standard, Brownian dynamics model used in the theoretical rheology of suspensions. Some theoretical difficulties and logical inconsistencies are pointed out. Preliminary results for the transport coefficients of dilute suspension of magnetic rod-like particles are presented.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Flagellar dynamics of a connected chain of active,polar, Brownian particles

We show that active, self-propelled particles that are connected together to form a single chain that is anchored at one end can produce the graceful beating motions of flagella. Changing the boundary condition from a clamp to a pivot at the anchor leads to steadily rotating tight coils. Strong noise in the system disrupts the regularity of the oscillations. We use a combination of detailed numerical simulations, mean-field scaling analysis and first passage time theory to characterize the phase diagram as a function of the filament length, passive elasticity, propulsion force and noise. Our study suggests minimal experimental tests for the onset of oscillations in an active polar chain.     

Coarse-grained molecular dynamics simulations on size effect of glassy polyethylene particles

The size effect on mechanical properties of glassy polyethylene (PE) nanoscale particles has been investigated by extensive coarse-grained molecular dynamics simulations. The diameter of the PE particles varies in the range of 5-40 nm, we confirm that the particle's behaviour under compressive stress strongly depends on its size-the smaller the particle diameter is, the stiffer the particle behaves. The present mechanical responses of compressed particles are in good agreement with our previous experimental phenomena of micron-sized polymer particles measured by a nanoindentation-based flat punch method. Possible reasons for the size effect are discussed.     

Flow control through polymer-grafted smart nanofluidic channels: molecular dynamics simulations

Presented are results of molecular dynamics simulations that demonstrate flow gating through a polymer-grafted nanopore as a function of effective solvent quality. Analysis of density and flow profiles from the simulations show that the difference in drag force exerted on the flowing solvent due to different polymer brush configurations produces the effective fluid gating. Shear-induced permeability changes through these nanopores has also been investigated. These results establish a critical starting point in nanofluidics from which continuum modeling can be developed to design this emerging class of smart nanoporous materials with tailor-made properties.     

Mass-transport enhancement in regions bounded by rigid walls

The mass transport into a fluid bounded by stationary rigid walls in the limit of large Péclet number, Pe, is examined analytically. Two model systems are considered in detail: a stationary cavity and a model involving two concentric rotating cylinders. A macroscopic gradient is imposed between the top and bottom surfaces. It is demonstrated that mass transport into the fluid is enhanced owing to a recirculation zone which is connected to the solid boundary through a boundary layer of thickness O(Pe ^–1/3) in which cross-stream molecular diffusion is balanced by convection. The associated enhancement is large and scales as Pe ^1/3. Our asymptotic analysis is found to be in good agreement with numerical solutions of the full transport equation.     

Brownian dynamics study of polymer-stabilized nanoparticles

A Brownian dynamics simulation was carried out for a spherical nanoparticle with polymer chains tethered to its surface. These simulations are relevant to understanding the transport properties of polymer-stabilized nanoparticles in environmental and other applications. Hydrodynamic interactions (HI) were taken into account to properly describe the diffusion properties of a stabilized particle. HI are important in this context because of the close proximity of the surface-tethered polymer chains. HI were implemented using a method introduced by Fixman (1986 Macromolecules 19 1204), which uses a Chebyshev polynomial expansion to calculate the square root of the diffusion tensor. Simulation predictions were compared to published experimental data for the hydrodynamic radius of a silica particle stabilized by polystyrene tethered chains, and good agreement was achieved. A relationship that allows polymer-stabilized particles with arbitrary polymer-chain densities to be modelled is developed.     

Dynamics of interacting Brownian particles in concentrated colloidal suspensions

We are concerned with dynamic properties of interacting Brownian particles in concentrated colloidal suspensions. An effective diffusion coefficient measured by the modulated in phase low-coherence dynamic light scattering technique is investigated as a function of the volume fraction. The experimental results are compared with the numerical ones calculated under both the Cohen-de Schepper approximation for hydrodynamic interaction and the Percus-Yevick approximations for structural effect. It is confirmed that the Brownian motion of particles in the range of volume fraction from 0.01 to 0.2 is mainly dominated by the hydrodynamic interaction rather than the structural effect, which can be described well by the Cohen-de Schepper approximation.     

无机刚性粒子增韧聚合物研究进展

简要综述了无机刚性粒子对聚合物的增韧机理,以及其增韧研究进展,并指出存在问题及发展方向。     

Exact solutions of the Boeder differential equation for macromolecular orientations in a flowing liquid

The Boeder differential equation is solved in this work over a wide range of , yielding the probability density functions (PDF), that describe the average orientations of rod-like macromolecules in a flowing liquid. The quantity is the ratio of the hydrodynamic shear rate to the rotational diffusion coefficient. It characterises the coupling of the motion of the macromolecules in the hydrodynamic flow to their thermal diffusion. Previous analytical work is limited to approximate solutions for small values of . Special analytical as well as numerical methods are developed in the present work in order to calculate accurately the PDF for a range of covering several orders of magnitude, 10⁻⁶10⁸. The mathematical nature of the differential equation is revealed as a singular perturbation problem when becomes large. Scaling results are obtained over the differential equation for 10³. Monte Carlo Brownian simulations are also constructed and shown to agree with the numerical solutions of the differential equation in the bulk of the flowing liquid, for an extensive range of . This confirms the solidity of the developed analytical and numerical methods.     

Phase transformation and growth of rod-like α-SiAlON particles during combustion synthesis

Yttrium- and ytterbium-stabilized α-SiAlON powders consisting of rod-like microcrystals were prepared by combustion synthesis. A quenching method was used to investigate the phase formation and microstructure evolution during the combustion synthesis of α-SiAlON. Three reaction stages were proposed for the formation of α-SiAlON as follows: nitridation of metal powders, formation of the co-existing liquid phase, and precipitation of α-SiAlON with the dissolution of nitrides. Different nucleation and growth modes of rod-like α-SiAlON crystals were observed: crystallization from liquid phase, or nucleation and growth based on the surface of as-existed large crystals.     

Investigating the flow of rod-like particles in a horizontal rotating drum using DEM simulation

Understanding the flow and mixing of rod-like particles is fundamental because of the widespread use of rods in the process industry. In this paper, discrete element method is used to investigate the flow and mixing of rod-like particles in a horizontal rotating drum, with rod-like particles being modeled by super-ellipsoids. The influence of the aspect ratio of the rod and the rotation speed of the drum on the flow of rod-like particles is studied. The investigation of spherical particles is also included in this paper to reveal the differences between rod-like and spherical particles. The simulation results show that the flow of rods is more intermittent than that of spheres and that there is more intermittent flow for rod-like particles with larger aspect ratios. Both the aspect ratio of the rod and the rotation speed of the drum considerably influence particle mixing. The mixing rate, as quantified by the slope of the variation in the mixing index with respect to drum revolution, increases as rotation speed and aspect ratio decrease. The study of particle orientation indicates that rod-like particles have a preferred orientation during rotation of the drum: the major axis of the rod inclines to be parallel to the end plate of the drum.     

A general formulation in rigid multibody dynamics

The dynamics of rigid multibodies is traditionally formulated by means of either minimal or redundant co-ordinates methods. An alternative approach is here proposed whereby a highly redundant set of coordinates is adopted. As a result, the equations of motion of the constrained bodies are decoupled. Several meaningful parameters are directly available and the constraint conditions are enforced in a very natural way. The first part of the paper presents the basic meanings and the theoretical developments of the formulation. The second develops a numerical approximation for the methodology proposed in the first part. The non-linear system of differential-algebraic equations governing the motion of the multibody is reduced to its weak form. It is linearized by applying a Newton–Raphson procedure and approximated through the method of finite elements in time. The details of the numerical application of this method are discussed and a solution procedure is presented. Finally, some numerical examples involving tree and closed loop topologies prove the capability of the present formulation in handling multibody dynamics.     

Singular perturbation theory for predicting extravasation of Brownian particles

Motivated by recent studies on tumor treatments using the drug delivery of nanoparticles, we provide a singular perturbation theory and perform Brownian dynamics simulations to quantify the extravasation rate of Brownian particles in a shear flow over a circular pore with a lumped mass transfer resistance. The analytic theory we present is an expansion in the limit of a vanishing Péclet number ( $P$ ), which is the ratio of convective fluxes to diffusive fluxes on the length scale of the pore. We state the concentration of particles near the pore and the extravasation rate (Sherwood number) to $O(P^{1/2})$ . This model improves upon previous studies because the results are valid for all values of the particle mass transfer coefficient across the pore, as modeled by the Damköhler number ( $\kappa $ ), which is the ratio of the reaction rate to the diffusive mass transfer rate at the boundary. Previous studies focused on the adsorption-dominated regime (i.e., $\kappa \rightarrow \infty $ ). Specifically, our work provides a theoretical basis and an interpolation-based approximate method for calculating the Sherwood number (a measure of the extravasation rate) for the case of finite resistance [ $\kappa \sim O(1)$ ] at small Péclet numbers, which are physiologically important in the extravasation of nanoparticles. We compare the predictions of our theory and an approximate method to Brownian dynamics simulations with reflection–reaction boundary conditions as modeled by $\kappa $ . They are found to agree well at small $P$ and for the $\kappa \ll 1$ and $\kappa \gg 1$ asymptotic limits representing the diffusion-dominated and adsorption-dominated regimes, respectively. Although this model neglects the finite size effects of the particles, it provides an important first step toward understanding the physics of extravasation in the tumor vasculature.     

Boundary element analysis of thin plates internally bounded by rigid patches

Procedures are described for modelling a structural system consisting of thin Kirchhoff plates with internal patch areas capable of displacing as rigid flat surfaces. The physical prototype for these patches could be interconnection points for one-dimensional frame type elements of various shapes and layout, rigidly connected at these finite size 'joints' in the plate. The numerical procedure for modelling the thin plate is the Direct Boundary Element Method (DBEM) and a simple overview of this procedure is provided. Potential trouble spots, of which the user should be aware, are described. The paper will be of interest to structural engineers for analysis of frames having both plate and simple frame elements, for example, building frames; and also to researchers seeking the greater detail that this refined procedure can provide. As a practical tool, the methods described are computationally competitive with existing procedures, including the more rugged approaches used by building structural engineers for dynamic and torsional analysis.