MILCH SHAKE: an efficient method for constraint dynamics applied to alkanes.

We describe a method to impose constraints in a molecular dynamics simulation. A technique developed to solve the special case of a linear topology (MILC SHAKE) is hybridized with the SHAKE algorithm. The methodology, which we term MILC-hybridized SHAKE (or MILCH SHAKE), applies to more complex topologies. Here we consider the important case of all atom models of alkanes. Exploiting the mass difference between carbon and hydrogen we show that for higher alkanes MILCH SHAKE can be an order of magnitude faster than SHAKE.

Sedimentation of pairs of hydrodynamically interacting semiflexible filaments.

We describe the effect of hydrodynamic interactions in the sedimentation of a pair of inextensible semiflexible filaments under a uniform constant force at low Reynolds numbers. We have analyzed the different regimes and the morphology of such polymers in simple geometries, which allow us to highlight the peculiarities of the interplay between elastic and hydrodynamic stresses. Cooperative and symmetry breaking effects associated to the geometry of the fibers gives rise to characteristic motion which give them distinct properties from rigid and elastic filaments.

Possible mechanism for aligning microscopic flexible filaments predicted using "caterpillar" hydrodynamics.

We use the "caterpillar" model for accurately calculating the inhomogeneous hydrodynamic friction along a microscopic slender cylindrical filaments using Oseen level hydrodynamics. The methodology is applied to study the motion of a flexible filament in a circularly polarized field. Our results predict that in dilute solution alignment occurs along the axis of the field. For electric fields, the strengths and frequencies required are deduced. These are experimentally accessible. We therefore propose that this is a practical method for aligning filaments such as microtubules and functionalized carbon nanotubes.

Accurate simulation dynamics of microscopic filaments using "caterpillar" Oseen hydrodynamics.

Microscopic semiflexible filaments suspended in a viscous fluid are widely encountered in biophysical problems. The classic example is the flagella used by microorganisms to generate propulsion. Simulating the dynamics of these filaments numerically is complicated because of the coupling between the motion of the filament and that of the surrounding fluid. An attractive idea is to simplify this coupling by modeling the fluid motion by using Stokeslets distributed at equal intervals along the model filament. We show that, with an appropriate choice of the hydrodynamic radii, one can recover accurate hydrodynamic behavior of a filament with a finite cross section without requiring an explicit surface. This is true, however, only if the hydrodynamic radii take specific values and that they differ in the parallel and perpendicular directions leading to a caterpillarlike hydrodynamic shape. Having demonstrated this, we use the model to compare with analytic theory of filament deformation and rotation in the small deformation limit. Generalization of the methodology, including application to simulations using the Rotne-Prager tensor, is discussed.

Mesoscopic simulations of accelerated polymer drift in microfluidic capillaries.

We use a mesoscopic simulation technique to study the transport of polymers in dilute solution flowing through a cylindrical tube. The simulations use an explicit solvent model to include all the relevant hydrodynamic couplings and a coarse grained ideal chain model for the polymers (appropriate for systems near the theta temperature). For the interactions between the solvent and the tube wall we use a novel method that ensures continuity of the stress at the interface. We show that the results for the polymer drift velocity are independent of the degree of coarse graining. Further, for the case where the size of the chains is small but not negligible compared to the tube radius, our results are in excellent agreement with experiment. However, they also show that in this regime, the "accelerated" drift, relative to the average solvent flow velocity, is described by the steric effect of the tube wall excluding the polymer center of mass from sampling the full cross section of the tube. Hydrodynamic interactions have a negligible influence in this regime. Consequently, the agreement between experiment and theories that approximates the former but includes the latter is fortunate. When the undisturbed polymer radius approaches or exceeds the tube radius, the hydrodynamic interactions do have a significant effect. They reduce the drift velocity, in qualitative agreement with theoretical predictions. The accelerated drift still approaches the maximum value, one would expect based on a Poiseuille flow but more slowly than if one neglects hydrodynamics. Finally, we propose an empirical fit that accurately describes data in the intermediate regime.

Diffusion of chain molecules and mixtures in carbon nanotubes: the effect of host lattice flexibility and theory of diffusion in the Knudsen regime.

A novel algorithm for modeling the influence of the host lattice flexibility in molecular dynamics simulations is extended to chain-like molecules and mixtures. This technique, based on a Lowe-Andersen thermostat, maintains the advantages of both simplicity and efficiency. The same diffusivities and other properties of the flexible framework system are reproduced. Advantageously, the computationally demanding flexible host lattice simulations can be avoided. Using this methodology we study the influence of flexibility on diffusion of n-alkanes inside single-walled carbon nanotubes. Furthermore, results are shown for diffusion of two mixtures (methane-helium and ethane-butane). Using these results we investigate the accuracy of theories describing diffusion in the Knudsen regime. For the dynamics in carbon nanotubes the Knudsen diffusivities are much too low. The Smoluchowski model gives better results. Interestingly, the extended Smoluchowski model can reproduce our simulation results obtained with a rigid host lattice. We modify this model to also treat collisions with a flexible interface correctly. As the tangential momentum accommodation coefficient is needed for the theoretical models, we introduce a simple concept to calculate it.

Advantages of a Lowe-Andersen thermostat in molecular dynamics simulations.

The Lowe-Andersen thermostat is a momentum conserving and Galilean invariant analog of the Andersen thermostat. Like the Andersen thermostat it has the advantage of being local. We show that by using a minimal thermostat interaction radius in a molecular dynamics simulation, it perturbs the system dynamics to a far lesser extent than the Andersen method. This alleviates a well known drawback of the Andersen thermostat by allowing high thermostatting rates without the penalty of significantly suppressed diffusion in the system.

A novel algorithm to model the influence of host lattice flexibility in molecular dynamics simulations: loading dependence of self-diffusion in carbon nanotubes.

We describe a novel algorithm that includes the effect of host lattice flexibility into molecular dynamics simulations that use rigid lattices. It uses a Lowe-Andersen thermostat for interface-fluid collisions to take the most important aspects of flexibility into account. The same diffusivities and other properties of the flexible framework system are reproduced at a small fraction of the computational cost of an explicit simulation. We study the influence of flexibility on the self-diffusion of simple gases inside single walled carbon nanotubes. Results are shown for different guest molecules (methane, helium, and sulfur hexafluoride), temperatures, and types of carbon nanotubes. We show, surprisingly, that at low loadings flexibility is always relevant. Notably, it has a crucial influence on the diffusive dynamics of the guest molecules.

The size of a polymer in a symmetric solvent.

Using a simple thermodynamic model, we derive an expression for the excluded volume parameter v of a polymer chain in a symmetric solvent (solvated by its own monomers). For a chain with a given segment length and number of monomers, this parameter determines whether the chain is collapsed or expanded. For the latter it determines the degree of expansion. Using a simple off-lattice version of Flory's model [P. J. Flory, Principles of Polymer Chemistry (Cornell University Press, Ithaca, 1953)] and relaxing the assumption of incompressibility, we obtain the result v=(1-kappa)rho(0), where kappa is the dimensionless compressibility and rho(0) the number density of solvent. In the incompressible limit (in the sense that kappa-->0) the chain is expanded and the inverse of the solvent number density determines the degree of expansion of the chain. Using the van der Waals equation of state to estimate kappa (allowing for nonzero compressibility in a system that can undergo a gas-liquid phase transition), the model predicts that upon raising the temperature at constant pressure there is both a lower (coil to globule) and upper (globule to coil) Flory temperature. This is in quantitative agreement with experiment and computer simulations.

Hydrodynamic induced deformation and orientation of a microscopic elastic filament.

We describe simulations of an elastic filament immersed in a fluid and subjected to a body force. The coupling between the fluid flow and the friction that the filament experiences induces bending and alignment perpendicular to the force. With increasing force there are four shape regimes, ranging from slight distortion to an unsteady tumbling motion. We also find marginally stable structures. The instability of these shapes and the alignment are explained by induced bending and nonlocal hydrodynamic interactions. These effects are experimentally relevant for stiff microfilaments.

Combined length scales in dissipative particle dynamics.

When a particle model simulates fluid behavior, the calculation of all particle interactions causes long computation times. Especially in mesoscale simulations, the bulk areas can be computationally demanding. To reduce the time spent on such regions, we propose a model that combines different length scales in one system. This is a particle analog to mesh refinement in, for instance, finite-element methods. To this end, we define particles of a coarse-grained scale within the framework of dissipative particle dynamics. These particles have a lower number density, but the same mass density, pressure, temperature, and viscosity as the original description. Furthermore, the coarse-grained particles can directly interact with the "normal" particles. The two length scales are combined in one system, coupled by an overlap region. At the edges of this region, particles transform into the other scale, through local refining or coarse graining. The resulting combined system adequately reproduces the properties and flow behavior of a normal system. When half the system is coarse grained, the computation time reduces by a factor of two. Thus, computational efficiency can be greatly increased for a variety of mesoscale applications.

Poiseuille flow to measure the viscosity of particle model fluids.

The most important property of a fluid is its viscosity, it determines the flow properties. If one simulates a fluid using a particle model, calculating the viscosity accurately is difficult because it is a collective property. In this article we describe a new method that has a better signal to noise ratio than existing methods. It is based on using periodic boundary conditions to simulate counter-flowing Poiseuille flows without the use of explicit boundaries. The viscosity is then related to the mean flow velocity of the two flows. We apply the method to two quite different systems. First, a simple generic fluid model, dissipative particle dynamics, for which accurate values of the viscosity are needed to characterize the model fluid. Second, the more realistic Lennard-Jones fluid. In both cases the values we calculated are consistent with previous work but, for a given simulation time, they are more accurate than those obtained with other methods.

Understanding the loading dependence of self-diffusion in carbon nanotubes.

The influence of flexible walls on the self-diffusion of CH4 in an isolated single walled carbon nanotube, as an example, is studied by molecular dynamics simulations. By simulating the carbon nanotube as a flexible framework we demonstrate that the flexibility has a crucial influence on self-diffusion at low loadings. We show how this influence can be incorporated in a simulation of a rigid nanotube by using a Lowe-Andersen thermostat which works on interface-fluid collisions. The reproduction of the results of a flexible carbon nanotube by a rigid nanotube simulation is excellent.

A simulation study of the dynamics of a driven filament in an Aristotelian fluid.

We describe a method, based on techniques used in molecular dynamics, for simulating the inertialess dynamics of an elastic filament immersed in a fluid. The model is used to study the "one-armed swimmer". That is, a flexible appendage externally perturbed at one extremity. For small-amplitude motion our simulations confirm theoretical predictions that, for a filament of given length and stiffness, there is a driving frequency that is optimal for both speed and efficiency. However, we find that to calculate absolute values of the swimming speed we need to slightly modify existing theoretical approaches. For the more relevant case of large-amplitude motion we find that while the basic picture remains the same, the dependence of the swimming speed on both frequency and amplitude is substantially modified. For large-amplitudes we show that the one-armed swimmer is comparatively neither inefficient nor slow. This begs the question, why are there little or no one-armed swimmers in nature?