scispace - formally typeset
Search or ask a question
Author

Anthony J. C. Ladd

Bio: Anthony J. C. Ladd is an academic researcher from University of Florida. The author has contributed to research in topics: Lattice Boltzmann methods & Reynolds number. The author has an hindex of 55, co-authored 149 publications receiving 16191 citations. Previous affiliations of Anthony J. C. Ladd include Lawrence Livermore National Laboratory & University of California, Davis.


Papers
More filters
Journal ArticleDOI
TL;DR: In this article, a general technique for simulating solid-fluid suspensions is described, which combines Newtonian dynamics of the solid particles with a discretized Boltzmann equation for the fluid phase; the many-body hydrodynamic interactions are fully accounted for, both in the creeping flow regime and at higher Reynolds numbers.
Abstract: A new and very general technique for simulating solid–fluid suspensions is described; its most important feature is that the computational cost scales linearly with the number of particles. The method combines Newtonian dynamics of the solid particles with a discretized Boltzmann equation for the fluid phase; the many-body hydrodynamic interactions are fully accounted for, both in the creeping-flow regime and at higher Reynolds numbers. Brownian motion of the solid particles arises spontaneously from stochastic fluctuations in the fluid stress tensor, rather than from random forces or displacements applied directly to the particles. In this paper, the theoretical foundations of the technique are laid out, illustrated by simple analytical and numerical examples; in a companion paper (Part 2), extensive numerical tests of the method, for stationary flows, time-dependent flows, and finite-Reynolds-number flows, are reported.

2,073 citations

Journal ArticleDOI
TL;DR: In this paper, a general technique for simulating solid-fluid suspensions is described, which combines Newtonian dynamics of the solid particles with a discretized Boltzmann equation for the fluid phase; the many-body hydrodynamic interactions are fully accounted for, both in the creeping flow regime and at higher Reynolds numbers.
Abstract: A new and very general technique for simulating solid-fluid suspensions is described; its most important feature is that the computational cost scales linearly with the number of particles. The method combines Newtonian dynamics of the solid particles with a discretized Boltzmann equation for the fluid phase; the many-body hydrodynamic interactions are fully accounted for, both in the creeping-flow regime and at higher Reynolds numbers. Brownian motion of the solid particles arises spontaneously from stochastic fluctuations in the fluid stress tensor, rather than from random forces or displacements applied directly to the particles. In this paper, the theoretical foundations of the technique are laid out, illustrated by simple analytical and numerical examples; in the companion paper, extensive numerical tests of the method, for stationary flows, time-dependent flows, and finite Reynolds number flows, are reported.

1,335 citations

Journal ArticleDOI
TL;DR: In this paper, extensive numerical tests of the method are described; results are presented for creeping flows, both with and without Brownian motion, and at finite Reynolds numbers, and the short-time dynamics of random dispersions of up to 1024 colloidal particles have been simulated.
Abstract: A new and very general technique for simulating solid–fluid suspensions has been described in a previous paper (Part 1); the most important feature of the new method is that the computational cost scales linearly with the number of particles. In this paper (Part 2), extensive numerical tests of the method are described; results are presented 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.

1,331 citations

Journal ArticleDOI
TL;DR: In this paper, a review of applications of the lattice-Boltzmann method to simulations of particle-fluid suspensions is presented, together with some of the important applications of these methods.
Abstract: This paper reviews applications of the lattice-Boltzmann method to simulations of particle-fluid suspensions. We first summarize the available simulation methods for colloidal suspensions together with some of the important applications of these methods, and then describe results from lattice-gas and lattice-Boltzmann simulations in more detail. The remainder of the paper is an update of previously published work,(69, 70) taking into account recent research by ourselves and other groups. We describe a lattice-Boltzmann model that can take proper account of density fluctuations in the fluid, which may be important in describing the short-time dynamics of colloidal particles. We then derive macro-dynamical equations for a collision operator with separate shear and bulk viscosities, via the usual multi-time-scale expansion. A careful examination of the second-order equations shows that inclusion of an external force, such as a pressure gradient, requires terms that depend on the eigenvalues of the collision operator. Alternatively, the momentum density must be redefined to include a contribution from the external force. Next, we summarize recent innovations and give a few numerical examples to illustrate critical issues. Finally, we derive the equations for a lattice-Boltzmann model that includes transverse and longitudinal fluctuations in momentum. The model leads to a discrete version of the Green–Kubo relations for the shear and bulk viscosity, which agree with the viscosities obtained from the macro-dynamical analysis. We believe that inclusion of longitudinal fluctuations will improve the equipartition of energy in lattice-Boltzmann simulations of colloidal suspensions.

1,117 citations

Journal ArticleDOI
TL;DR: In this article, the authors presented a method to compute the absolute free energy of arbitrary solid phases by Monte Carlo simulation based on the construction of a reversible path from the solid phase under consideration to an Einstein crystal with the same crystallographic structure.
Abstract: We present a new method to compute the absolute free energy of arbitrary solid phases by Monte Carlo simulation. The method is based on the construction of a reversible path from the solid phase under consideration to an Einstein crystal with the same crystallographic structure. As an application of the method we have recomputed the free energy of the fcc hard‐sphere solid at melting. Our results agree well with the single occupancy cell results of Hoover and Ree. The major source of error is the nature of the extrapolation procedure to the thermodynamic limit. We have also computed the free energy difference between hcp and fcc hard‐sphere solids at densities close to melting. We find that this free energy difference is not significantly different from zero: −0.001<ΔF<0.002.

1,025 citations


Cited by
More filters
01 May 1993
TL;DR: Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems.
Abstract: Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

29,323 citations

Journal ArticleDOI
TL;DR: In this paper, a method is described to realize coupling to an external bath with constant temperature or pressure with adjustable time constants for the coupling, which can be easily extendable to other variables and to gradients, and can be applied also to polyatomic molecules involving internal constraints.
Abstract: In molecular dynamics (MD) simulations the need often arises to maintain such parameters as temperature or pressure rather than energy and volume, or to impose gradients for studying transport properties in nonequilibrium MD A method is described to realize coupling to an external bath with constant temperature or pressure with adjustable time constants for the coupling The method is easily extendable to other variables and to gradients, and can be applied also to polyatomic molecules involving internal constraints The influence of coupling time constants on dynamical variables is evaluated A leap‐frog algorithm is presented for the general case involving constraints with coupling to both a constant temperature and a constant pressure bath

25,256 citations

Journal ArticleDOI
TL;DR: In this paper, a new Lagrangian formulation is introduced to make molecular dynamics (MD) calculations on systems under the most general externally applied, conditions of stress, which is well suited to the study of structural transformations in solids under external stress and at finite temperature.
Abstract: A new Lagrangian formulation is introduced. It can be used to make molecular dynamics (MD) calculations on systems under the most general, externally applied, conditions of stress. In this formulation the MD cell shape and size can change according to dynamical equations given by this Lagrangian. This new MD technique is well suited to the study of structural transformations in solids under external stress and at finite temperature. As an example of the use of this technique we show how a single crystal of Ni behaves under uniform uniaxial compressive and tensile loads. This work confirms some of the results of static (i.e., zero temperature) calculations reported in the literature. We also show that some results regarding the stress‐strain relation obtained by static calculations are invalid at finite temperature. We find that, under compressive loading, our model of Ni shows a bifurcation in its stress‐strain relation; this bifurcation provides a link in configuration space between cubic and hexagonal close packing. It is suggested that such a transformation could perhaps be observed experimentally under extreme conditions of shock.

13,937 citations

Journal ArticleDOI
TL;DR: In this article, the authors compared the canonical distribution in both momentum and coordinate space with three recently proposed constant temperature molecular dynamics methods by: (i) Nose (Mol. Phys., to be published); (ii) Hoover et al. [Phys. Rev. Lett. 77, 63 (1983); and (iii) Haile and Gupta [J. Chem. Phys. 79, 3067 (1983).
Abstract: Three recently proposed constant temperature molecular dynamics methods by: (i) Nose (Mol. Phys., to be published); (ii) Hoover et al. [Phys. Rev. Lett. 48, 1818 (1982)], and Evans and Morriss [Chem. Phys. 77, 63 (1983)]; and (iii) Haile and Gupta [J. Chem. Phys. 79, 3067 (1983)] are examined analytically via calculating the equilibrium distribution functions and comparing them with that of the canonical ensemble. Except for effects due to momentum and angular momentum conservation, method (1) yields the rigorous canonical distribution in both momentum and coordinate space. Method (2) can be made rigorous in coordinate space, and can be derived from method (1) by imposing a specific constraint. Method (3) is not rigorous and gives a deviation of order N−1/2 from the canonical distribution (N the number of particles). The results for the constant temperature–constant pressure ensemble are similar to the canonical ensemble case.

13,921 citations

Journal ArticleDOI
TL;DR: In this paper, a molecular dynamics simulation method which can generate configurations belonging to the canonical (T, V, N) ensemble or the constant temperature constant pressure ensemble was proposed, which is tested for an atomic fluid (Ar) and works well.
Abstract: A molecular dynamics simulation method which can generate configurations belonging to the canonical (T, V, N) ensemble or the constant temperature constant pressure (T, P, N) ensemble, is proposed. The physical system of interest consists of N particles (f degrees of freedom), to which an external, macroscopic variable and its conjugate momentum are added. This device allows the total energy of the physical system to fluctuate. The equilibrium distribution of the energy coincides with the canonical distribution both in momentum and in coordinate space. The method is tested for an atomic fluid (Ar) and works well.

8,110 citations