Distinctive features arising in maximally random jammed packings of superballs. Jiao, Y., Stillinger, F., H., & Torquato, S. PHYSICAL REVIEW E, AMER PHYSICAL SOC, 4, 2010. abstract bibtex Dense random packings of hard particles are useful models of granular
media and are closely related to the structure of nonequilibrium
low-temperature amorphous phases of matter. Most work has been done for
random jammed packings of spheres and it is only recently that
corresponding packings of nonspherical particles (e.g., ellipsoids) have
received attention. Here we report a study of the maximally random
jammed (MRJ) packings of binary superdisks and monodispersed superballs
whose shapes are defined by vertical bar x(1)vertical bar(2p) + ... +
vertical bar x(d)vertical bar(2p) <= 1 with d = 2 and 3, respectively,
where p is the deformation parameter with values in the interval (0,
infinity). As p increases from zero, one can get a family of both
concave (0 < p < 0.5) and convex (p >= 0.5) particles with square
symmetry (d = 2), or octahedral and cubic symmetry (d = 3). In
particular, for p = 1 the particle is a perfect sphere (circular disk)
and for p -> infinity the particle is a perfect cube (square). We find
that the MRJ densities of such packings increase dramatically and
nonanalytically as one moves away from the circular-disk and sphere
point (p = 1). Moreover, the disordered packings are hypostatic, i.e.,
the average number of contacting neighbors is less than twice the total
number of degrees of freedom per particle, and yet the packings are
mechanically stable. As a result, the local arrangements of particles
are necessarily nontrivially correlated to achieve jamming. We term such
correlated structures ``nongeneric.'' The degree of
``nongenericity'' of the packings is quantitatively characterized by
determining the fraction of local coordination structures in which the
central particles have fewer contacting neighbors than average. We also
show that such seemingly ``special'' packing configurations are
counterintuitively not rare. As the anisotropy of the particles
increases, the fraction of rattlers decreases while the minimal
orientational order as measured by the tetratic and cubatic order
parameters increases. These characteristics result from the unique
manner in which superballs break their rotational symmetry, which also
makes the superdisk and superball packings distinctly different from
other known nonspherical hard-particle packings.
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title = {Distinctive features arising in maximally random jammed packings of superballs},
type = {article},
year = {2010},
identifiers = {[object Object]},
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last_modified = {2017-03-14T12:30:08.401Z},
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abstract = {Dense random packings of hard particles are useful models of granular
media and are closely related to the structure of nonequilibrium
low-temperature amorphous phases of matter. Most work has been done for
random jammed packings of spheres and it is only recently that
corresponding packings of nonspherical particles (e.g., ellipsoids) have
received attention. Here we report a study of the maximally random
jammed (MRJ) packings of binary superdisks and monodispersed superballs
whose shapes are defined by vertical bar x(1)vertical bar(2p) + ... +
vertical bar x(d)vertical bar(2p) <= 1 with d = 2 and 3, respectively,
where p is the deformation parameter with values in the interval (0,
infinity). As p increases from zero, one can get a family of both
concave (0 < p < 0.5) and convex (p >= 0.5) particles with square
symmetry (d = 2), or octahedral and cubic symmetry (d = 3). In
particular, for p = 1 the particle is a perfect sphere (circular disk)
and for p -> infinity the particle is a perfect cube (square). We find
that the MRJ densities of such packings increase dramatically and
nonanalytically as one moves away from the circular-disk and sphere
point (p = 1). Moreover, the disordered packings are hypostatic, i.e.,
the average number of contacting neighbors is less than twice the total
number of degrees of freedom per particle, and yet the packings are
mechanically stable. As a result, the local arrangements of particles
are necessarily nontrivially correlated to achieve jamming. We term such
correlated structures ``nongeneric.'' The degree of
``nongenericity'' of the packings is quantitatively characterized by
determining the fraction of local coordination structures in which the
central particles have fewer contacting neighbors than average. We also
show that such seemingly ``special'' packing configurations are
counterintuitively not rare. As the anisotropy of the particles
increases, the fraction of rattlers decreases while the minimal
orientational order as measured by the tetratic and cubatic order
parameters increases. These characteristics result from the unique
manner in which superballs break their rotational symmetry, which also
makes the superdisk and superball packings distinctly different from
other known nonspherical hard-particle packings.},
bibtype = {article},
author = {Jiao, Y and Stillinger, F H and Torquato, S},
journal = {PHYSICAL REVIEW E},
number = {4, 1}
}
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Most work has been done for\nrandom jammed packings of spheres and it is only recently that\ncorresponding packings of nonspherical particles (e.g., ellipsoids) have\nreceived attention. Here we report a study of the maximally random\njammed (MRJ) packings of binary superdisks and monodispersed superballs\nwhose shapes are defined by vertical bar x(1)vertical bar(2p) + ... +\nvertical bar x(d)vertical bar(2p) <= 1 with d = 2 and 3, respectively,\nwhere p is the deformation parameter with values in the interval (0,\ninfinity). As p increases from zero, one can get a family of both\nconcave (0 < p < 0.5) and convex (p >= 0.5) particles with square\nsymmetry (d = 2), or octahedral and cubic symmetry (d = 3). In\nparticular, for p = 1 the particle is a perfect sphere (circular disk)\nand for p -> infinity the particle is a perfect cube (square). We find\nthat the MRJ densities of such packings increase dramatically and\nnonanalytically as one moves away from the circular-disk and sphere\npoint (p = 1). Moreover, the disordered packings are hypostatic, i.e.,\nthe average number of contacting neighbors is less than twice the total\nnumber of degrees of freedom per particle, and yet the packings are\nmechanically stable. As a result, the local arrangements of particles\nare necessarily nontrivially correlated to achieve jamming. We term such\ncorrelated structures ``nongeneric.'' The degree of\n``nongenericity'' of the packings is quantitatively characterized by\ndetermining the fraction of local coordination structures in which the\ncentral particles have fewer contacting neighbors than average. We also\nshow that such seemingly ``special'' packing configurations are\ncounterintuitively not rare. As the anisotropy of the particles\nincreases, the fraction of rattlers decreases while the minimal\norientational order as measured by the tetratic and cubatic order\nparameters increases. These characteristics result from the unique\nmanner in which superballs break their rotational symmetry, which also\nmakes the superdisk and superball packings distinctly different from\nother known nonspherical hard-particle packings.","bibtype":"article","author":"Jiao, Y and Stillinger, F H and Torquato, S","journal":"PHYSICAL REVIEW E","number":"4, 1","bibtex":"@article{\n title = {Distinctive features arising in maximally random jammed packings of superballs},\n type = {article},\n year = {2010},\n identifiers = {[object Object]},\n volume = {81},\n month = {4},\n publisher = {AMER PHYSICAL SOC},\n city = {ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA},\n id = {031ef245-0382-3c64-b53c-672d2040b016},\n created = {2015-12-14T19:51:23.000Z},\n file_attached = {false},\n profile_id = {3187ec9d-0fcc-3ba2-91e0-3075df9b18c3},\n group_id = {d75e47fd-ff52-3a4b-bf1e-6ebc7e454352},\n last_modified = {2017-03-14T12:30:08.401Z},\n read = {false},\n starred = {false},\n authored = {false},\n confirmed = {true},\n hidden = {false},\n citation_key = {ISI:000277265700052},\n source_type = {article},\n user_context = {Article},\n private_publication = {false},\n abstract = {Dense random packings of hard particles are useful models of granular\nmedia and are closely related to the structure of nonequilibrium\nlow-temperature amorphous phases of matter. Most work has been done for\nrandom jammed packings of spheres and it is only recently that\ncorresponding packings of nonspherical particles (e.g., ellipsoids) have\nreceived attention. Here we report a study of the maximally random\njammed (MRJ) packings of binary superdisks and monodispersed superballs\nwhose shapes are defined by vertical bar x(1)vertical bar(2p) + ... +\nvertical bar x(d)vertical bar(2p) <= 1 with d = 2 and 3, respectively,\nwhere p is the deformation parameter with values in the interval (0,\ninfinity). As p increases from zero, one can get a family of both\nconcave (0 < p < 0.5) and convex (p >= 0.5) particles with square\nsymmetry (d = 2), or octahedral and cubic symmetry (d = 3). In\nparticular, for p = 1 the particle is a perfect sphere (circular disk)\nand for p -> infinity the particle is a perfect cube (square). 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