108 research outputs found
The initial stages of cave formation: Beyond the one-dimensional paradigm
The solutional origin of limestone caves was recognized over a century ago,
but the short penetration length of an undersaturated solution made it seem
impossible for long conduits to develop. This is contradicted by field
observations, where extended conduits, sometimes several kilometers long, are
found in karst environments. However, a sharp drop in the dissolution rate of
CaCO_3 near saturation provides a mechanism for much deeper penetration of
reactant. The notion of a "kinetic trigger" - a sudden change in rate constant
over a narrow concentration range - has become a widely accepted paradigm in
speleogenesis modeling. However, it is based on one-dimensional models for the
fluid and solute transport inside the fracture, assuming that the dissolution
front is planar in the direction perpendicular to the flow. Here we show that
this assumption is incorrect; a planar dissolution front in an entirely uniform
fracture is unstable to infinitesimal perturbations and inevitably breaks up
into highly localized regions of dissolution. This provides an alternative
mechanism for cave formation, even in the absence of a kinetic trigger. Our
results suggest that there is an inherent wavelength to the erosion pattern in
dissolving fractures, which depends on the reaction rate and flow rate, but is
independent of the initial roughness. In contrast to one-dimensional models,
two-dimensional simulations indicate that there is only a weak dependence of
the breakthrough time on kinetic order; localization of the flow tends to keep
the undersaturation in the dissolution front above the threshold for non-linear
kinetics.Comment: to be published in Earth and Planetary Science Letter
Numerical Simulations of Particulate Suspensions via a Discretized Boltzmann Equation Part II. Numerical Results
A new and very general technique for simulating solid-fluid suspensions has
been described in a previous paper (Part I); the most important feature of the
new method is that the computational cost scales with the number of particles.
In this paper (Part II), extensive numerical tests of the method are described;
for creeping flows, both with and without Brownian motion, and at finite
Reynolds numbers. Hydrodynamic interactions, transport coefficients, and the
short-time dynamics of random dispersions of up to 1024 colloidal particles
have been simulated.Comment: Text and figures in uuencode-tar-compressed postcript Email
[email protected]
Reactive-infiltration instabilities in rocks. Fracture dissolution
A reactive fluid dissolving the surface of a uniform fracture will trigger an
instability in the dissolution front, leading to spontaneous formation of
pronounced well-spaced channels in the surrounding rock matrix. Although the
underlying mechanism is similar to the wormhole instability in porous rocks
there are significant differences in the physics, due to the absence of a
steadily propagating reaction front. In previous work we have described the
geophysical implications of this instability in regard to the formation of long
conduits in soluble rocks. Here we describe a more general linear stability
analysis, including axial diffusion, transport limited dissolution, non-linear
kinetics, and a finite length system.Comment: to be published in J. Fluid. Mec
Statistical Mechanics of the Fluctuating Lattice Boltzmann Equation
We propose a new formulation of the fluctuating lattice Boltzmann equation
that is consistent with both equilibrium statististical mechanics and
fluctuating hydrodynamics. The formalism is based on a generalized lattice-gas
model, with each velocity direction occupied by many particles. We show that
the most probable state of this model corresponds to the usual equilibrium
distribution of the lattice Boltzmann equation. Thermal fluctuations about this
equilibrium are controlled by the mean number of particles at a lattice site.
Stochastic collision rules are described by a Monte Carlo process satisfying
detailed balance. This allows for a straightforward derivation of discrete
Langevin equations for the fluctuating modes. It is shown that all
non-conserved modes should be thermalized, as first pointed out by Adhikari et
al.; any other choice violates the condition of detailed balance. A
Chapman-Enskog analysis is used to derive the equations of fluctuating
hydrodynamics on large length and time scales; the level of fluctuations is
shown to be thermodynamically consistent with the equation of state of an
isothermal, ideal gas. We believe this formalism will be useful in developing
new algorithms for thermal and multiphase flows.Comment: Submitted to Physical Review E-11 pages Corrected Author(s) field on
submittal for
Lattice Thermal Conductivity: A Comparison of Molecular Dynamics and Anharmonic Lattice Dynamics,” Phys.
The thermal conductivity of a monatomic face-centered-cubic lattice has been calculated over a range of temperatures from one-twentieth to one-half the melting temperature. An inverse-twelfth power "soft-sphere" potential was used to represent the interatomic forces. We have examined, quantitatively, the approximations involved in deriving the Peierls phonon-transport expression for the thermal conductivity and have determined the temperature range over which it is useful. This has involved extensive comparisons with the formally exact Green-Kubo method, using molecular dynamics to generate the phase-space trajectories. At low temperatures, the relaxation processes in a crystal can be described in terms of phonon lifetimes. We have calculated the lifetimes of all the phonon states of 108-, 256-, and 864-particle classical crystals, with periodic boundaries, by molecu lar dynamics and by anharmonic perturbation theory. These lifetimes were then used to estimate the thermal conductivity.~
A symplectic integration method for elastic filaments
A new method is proposed for integrating the equations of motion of an
elastic filament. In the standard finite-difference and finite-element
formulations the continuum equations of motion are discretized in space and
time, but it is then difficult to ensure that the Hamiltonian structure of the
exact equations is preserved. Here we discretize the Hamiltonian itself,
expressed as a line integral over the contour of the filament. This discrete
representation of the continuum filament can then be integrated by one of the
explicit symplectic integrators frequently used in molecular dynamics. The
model systematically approximates the continuum partial differential equations,
but has the same level of computational complexity as molecular dynamics and is
constraint free. Numerical tests show that the algorithm is much more stable
than a finite-difference formulation and can be used for high aspect ratio
filaments, such as actin
Fluctuating Motor Forces Bend Growing Microtubules
Despite their rigidity, microtubules in living cells bend significantly during polymerization resulting in greater curvature than can be explained by thermal forces alone. However, the source of the non-thermal forces that bend growing microtubules remains obscure. We analyzed the motion of microtubule tips in NIH-3T3 fibroblasts expressing EGFP-EB1, a fluorescent +TIP protein that specifically binds to the growing ends of microtubules. We found that dynein inhibition significantly reduced the deviation of the growing tip from its initial trajectory. Inhibiting myosin modestly reduced tip fluctuations, while simultaneous myosin and dynein inhibition caused no further decrease in fluctuations compared to dynein inhibition alone. Our results can be interpreted with a model in which dynein linkages play a key role in generating and transmitting fluctuating forces that bend growing microtubules.National Institutes of Health (U.S.) (NIH GM102486)National Science Foundation (U.S.) (NSF CMMI 0954302, NSF CMMI 0927945, and NSF CTS-0505929
A comparison of the static and dynamic properties of a semi-flexible polymer using lattice-Boltzmann and Brownian dynamics simulations
The aim of this paper is to compare results from lattice-Boltzmann and
Brownian dynamics simulations of linear chain molecules. We have systematically
varied the parameters that may affect the accuracy of the lattice-Boltzmann
simulations, including grid resolution, temperature, polymer mass, and fluid
viscosity. The effects of the periodic boundary conditions are minimized by an
analytic correction for the different long-range interactions in periodic and
unbounded systems. Lattice-Boltzmann results for the diffusion coefficient and
Rouse mode relaxation times were found to be insensitive to temperature, which
suggests that effects of hydrodynamic retardation are small. By increasing the
resolution of the lattice-Boltzmann grid with respect to the polymer size,
convergent results for the diffusion coefficient and relaxation times were
obtained; these results agree with Brownian dynamics to within 1--2%.Comment: Corrected LB reduced time step () in Fig. 1 and Table
- …