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Theory and simulation of anisotropic pair correlations in ferrofluids in magnetic fields
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10.1063/1.4717718
/content/aip/journal/jcp/136/19/10.1063/1.4717718
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/19/10.1063/1.4717718

Figures

Image of FIG. 1.
FIG. 1.

Laboratory frame (x, y, z) and shifted frame (x , y , z ) for the calculation of I 3 and I 4 described in Sec. III C. is the separation vector between particles i and j.

Image of FIG. 2.
FIG. 2.

Pair distribution functions calculated in MC simulations of DHS fluids with φ = 0.2: (a) λ = 1 and α = 0; (b) λ = 1 and α = 5; (c) λ = 2 and α = 0; (d) λ = 2 and α = 5. The horizontal axis is x = x sin θ and the vertical axis is x = x cos θ, where θ is the angle of with respect to the field.

Image of FIG. 3.
FIG. 3.

Pair distribution functions g(x, θ) parallel to the field (θ = 0, shifted along the ordinate by one unit, for clarity) and perpendicular to the field (θ = π/2) in DHS fluids with φ = 0.1, λ = 1, and (a) α = 0, (b) α = 1, (c) α = 2, and (d) α = 5. The points are from simulations, and the lines are from theory.

Image of FIG. 4.
FIG. 4.

Pair distribution functions g(x, θ) parallel to the field (θ = 0, shifted along the ordinate by one unit, for clarity) and perpendicular to the field (θ = π/2) in DHS fluids with φ = 0.1, λ = 2, and (a) α = 0, (b) α = 1, (c) α = 2, and (d) α = 5. The points are from simulations, and the lines are from theory.

Image of FIG. 5.
FIG. 5.

Pair distribution functions g(x, θ) parallel to the field (θ = 0, shifted along the ordinate by one unit, for clarity) and perpendicular to the field (θ = π/2) in DHS fluids with φ = 0.2, λ = 1, and (a) α = 0, (b) α = 1, (c) α = 2, and (d) α = 5. The points are from simulations, and the lines are from theory.

Image of FIG. 6.
FIG. 6.

Pair distribution functions g(x, θ) parallel to the field (θ = 0, shifted along the ordinate by one unit, for clarity) and perpendicular to the field (θ = π/2) in DHS fluids with φ = 0.2, λ = 2, and (a) α = 0, (b) α = 1, (c) α = 2, and (d) α = 5. The points are from simulations, and the lines are from theory.

Image of FIG. 7.
FIG. 7.

Structure factors parallel to the field [S(k ), shifted up one unit for clarity] and perpendicular to the field [S(k )] in DHS fluids with φ = 0.1 and λ = 1, and (a) α = 0, (b) α = 1, (c) α = 2, and (d) α = 5. The points are from simulations, and the lines are from theory with the unphysical regions highlighted with dashed lines.

Image of FIG. 8.
FIG. 8.

Structure factors parallel to the field [S(k ), top row] and perpendicular to the field [S(k ), bottom row] in DHS fluids with φ = 0.01–0.2, λ = 1, and α = 0 (left column) and α = 5 (right column). The points are from simulations, and the lines are from theory: (black circles and lines) φ = 0.01; (red squares and lines) φ = 0.02; (green diamonds and lines) φ = 0.05; (blue up triangles and lines) φ = 0.1; (magenta left triangles and lines) φ = 0.2.

Image of FIG. 9.
FIG. 9.

Structure factors parallel to the field [S(k ), top row] and perpendicular to the field [S(k ), bottom row] in DHS fluids with φ = 0.01–0.2, λ = 2, and α = 0 (left column) and α = 5 (right column). The points are from simulations, and the lines are from theory: (black circles and lines) φ = 0.01; (red squares and lines) φ = 0.02; (green diamonds and lines) φ = 0.05; (blue up triangles and lines) φ = 0.1; (magenta left triangles and lines) φ = 0.2.

Image of FIG. 10.
FIG. 10.

Structure factor perpendicular to the field [S(k )] in DHS fluids with φ = 0.01–0.1, λ = 2, and α = 5. The points are from simulations, and the lines are fits to the function : (black circles and line) φ = 0.01; (red squares and line) φ = 0.02; (green diamonds and line) φ = 0.05; (blue up triangles and line) φ = 0.1.

Tables

Generic image for table
Table I.

Expansion coefficients β kl (x) for the case of zero field (from Refs. 19 and 35), and functions γ kl (x) for the case of non-zero field. Each of the functions is equal to zero for x < 1.

Generic image for table
Table II.

Expansion coefficients h i (x) and h ij (x) for the calculation of β12(x, θ) in non-zero field. Each of the functions is equal to zero for x < 1.

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/content/aip/journal/jcp/136/19/10.1063/1.4717718
2012-05-16
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Theory and simulation of anisotropic pair correlations in ferrofluids in magnetic fields
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/19/10.1063/1.4717718
10.1063/1.4717718
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