Radial Distribution Functions from the Born-Green Integral Equation

Broyles, A. A.

doi:10.1063/1.1731166

Cited by 131 publications

(33 citation statements)

References 2 publications

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“…This approximation has been used in the calculation of the pair distribution function for both an equilibrium system [16] and a non-equilibrium system under shear [17]. With this approximation, the evolution equation for the pair distribution function is derived as…”

Section: Modelmentioning

confidence: 99%

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An order parameter equation for the dynamic yield stress in dense colloidal suspensions

Otsuki

Sasa

2006

J. Stat. Mech.

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Abstract. We study the dynamic yield stress in dense colloidal suspensions by analyzing the time evolution of the pair distribution function for colloidal particles interacting through a Lennard-Jones potential. We find that the equilibrium pair distribution function is unstable with respect to a certain anisotropic perturbation in the regime of low temperature and high density. By applying a bifurcation analysis to a system near the critical state at which the stability changes, we derive an amplitude equation for the critical mode. This equation is analogous to order parameter equations used to describe phase transitions. It is found that this amplitude equation describes the appearance of the dynamic yield stress, and it gives a value of 2/3 for the shear thinning exponent. This value is related to δ in the Ising model.

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Section: Modelmentioning

confidence: 99%

“…This equation is called the Born-Green equation [15], which has been solved numerically [16]. Then, writing…”

Section: Modelmentioning

confidence: 99%

An order parameter equation for the dynamic yield stress in dense colloidal suspensions

Otsuki

Sasa

2006

J. Stat. Mech.

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“…At a particular iteration step i, the result from the previous iteration, ϕ i−1 (r), and the analytic result (24) are used as input to compute the r.h.s of Eq. (20). The resulting potential ϕ(r) is then used to produce the input for the next iteration step by mixing it with ϕ i−1 (r) according to…”

Section: Green's Function Methodologymentioning

confidence: 99%

Nonlinear Poisson-Boltzmann theory of a Wigner-Seitz model for swollen clays

2000

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Swollen stacks of finite-size disc-like Laponite clay platelets are investigated within a Wigner-Seitz cell model. Each cell is a cylinder containing a coaxial platelet at its centre, together with an overall charge-neutral distribution of microscopic co and counterions, within a primitive model description. The non-linear Poisson-Boltzmann (PB) equation for the electrostatic potential profile is solved numerically within a highly efficient Green's function formulation. Previous predictions of linearised Poisson-Boltzmann (LPB) theory are confirmed at a qualitative level, but large quantitative differences between PB and LPB theories are found at physically relevant values of the charge carried by the platelets. A hybrid theory treating edge effect at the linearised level yields good potential profiles. The force between two coaxial platelets, calculated within PB theory, is an order of magnitude smaller than predicted by LPB theory

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“…This yields a new estimate h 1 (r) which is input to the closure relation to yield an improved estimate c 1 (r). This procedure usually only converges at low densities, and in order to obtain convergence at higher densities, it is necessary to mix old and new estimates to obtain a converged solution [1,24,25]. When using the Fourier space version Eq.…”

Section: Standard Algorithmsmentioning

confidence: 99%

Solution of the Ornstein–Zernike Equation in the Critical Region

Brader

2006

Int J Thermophys

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A new numerical scheme for the solution of liquid state integral equations using the Baxter factorization of the Ornstein-Zernike equation is proposed. For short range potentials the method yields reliable results over the whole fluid region, including the vicinity of the critical point, and opens up new possibilities for numerical study of the critical behavior of integral equation approximations. To demonstrate the effectiveness of the method, numerical results are compared with the analytical solution of the mean spherical approximation for a hard-core plus Yukawa tail interaction potential. Accurate results for the critical exponents δ, γ, and η for this model are obtained.

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Radial Distribution Functions from the Born-Green Integral Equation

Cited by 131 publications

References 2 publications

An order parameter equation for the dynamic yield stress in dense colloidal suspensions

An order parameter equation for the dynamic yield stress in dense colloidal suspensions

Nonlinear Poisson-Boltzmann theory of a Wigner-Seitz model for swollen clays

Solution of the Ornstein–Zernike Equation in the Critical Region

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