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Supramolecular chemistry deals with the chemistry and collective behavior of molecular building blocks that are organized on large length scales (relative to molecular sizes) with long-range order.
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77951096734
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) 2 ≤1, where xi (i=1,2,3 ) are the Cartesian coordinates and ai (i=1,2,3 ) are the semiaxes. In Refs., spheriods (i.e., ellipsoids with two equal semiaxes) were studied. The aspect ratio of a spheroid is defined as the ratio of the distinct semiaxis over one of the two equal semiaxes.
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) 2 ≤ 1, where x i (i = 1, 2, 3) are the Cartesian coordinates and a i (i = 1, 2, 3) are the semiaxes. In Refs., spheriods (i.e., ellipsoids with two equal semiaxes) were studied. The aspect ratio of a spheroid is defined as the ratio of the distinct semiaxis over one of the two equal semiaxes.
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77951141507
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In a previous study of jammed random ellipsoid packings reported in, nontrivially correlated local structures were called "degenerate." In light of the fact that the term "degenerate" has a variety of different meanings, we use instead here the term "nongeneric" to avoid any possible confusion.
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In a previous study of jammed random ellipsoid packings reported in, nontrivially correlated local structures were called "degenerate." In light of the fact that the term "degenerate" has a variety of different meanings, we use instead here the term "nongeneric" to avoid any possible confusion.
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41
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-4 of the particle diameter.
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- 4 of the particle diameter.
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45
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77951139018
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The numerically computed right and left slope of Φ (p) for binary superdisks at p=1 are a+ ≈0.135 and a- ≈-0.083, respectively.
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The numerically computed right and left slope of Φ (p) for binary superdisks at p = 1 are a + ≈ 0.135 and a - ≈ - 0.083, respectively.
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46
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77951124116
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The numerically computed right and left slope of Φ (p) for monodispersed superballs at p=1 are a+ ≈0.229 and a- ≈-0.113, respectively.
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The numerically computed right and left slope of Φ (p) for monodispersed superballs at p = 1 are a + ≈ 0.229 and a - ≈ - 0.113, respectively.
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48
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77951109006
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The fact that the superdisk and superball packings can significantly explore their configurational space associated with the rotational degrees of freedom, i.e., they can rotate significantly, near the jamming point is manifested as long-period oscillations of the pressure of the system, which is also observed for ellipsoid systems.
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The fact that the superdisk and superball packings can significantly explore their configurational space associated with the rotational degrees of freedom, i.e., they can rotate significantly, near the jamming point is manifested as long-period oscillations of the pressure of the system, which is also observed for ellipsoid systems.
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49
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77951129500
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In this sense, it is similar to the ellipse packings in two dimensions, i.e., the isostatic packing requires six contacts per particles, which can only be realized with translational crystallization.
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In this sense, it is similar to the ellipse packings in two dimensions, i.e., the isostatic packing requires six contacts per particles, which can only be realized with translational crystallization.
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50
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77951116401
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Expansion rates γ within the range 0.1-0.5 were employed to suppress the formation of order in the superdisk and superball packings; larger γ would cause numerical instability of the DTS algorithm. Note that for ellipsoids, γ∼0.05 is sufficient to produce random packings with vanishing orientational order.
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Expansion rates γ within the range 0.1-0.5 were employed to suppress the formation of order in the superdisk and superball packings; larger γ would cause numerical instability of the DTS algorithm. Note that for ellipsoids, γ ∼ 0.05 is sufficient to produce random packings with vanishing orientational order.
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51
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23844548357
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53
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77951112899
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) 2p ≤1, where xi (i=1,2,...,d ) are the Cartesian coordinates and ai (i=1,2,...,d ) are the semiaxes along the coordinate axes, p is the deformation parameter. At p=1, one obtains a d -dimensional ellipsoid.
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) 2 p ≤ 1, where x i (i = 1, 2,..., d) are the Cartesian coordinates and a i (i = 1, 2,..., d) are the semiaxes along the coordinate axes, p is the deformation parameter. At p = 1, one obtains a d -dimensional ellipsoid.
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