7,191 research outputs found
Reply to "Comment on `Jamming at zero temperature and zero applied stress: The epitome of disorder' "
We answer the questions raised by Donev, Torquato, Stillinger, and Connelly
in their "Comment on "Jamming at zero temperature and zero applied stress: The
epitome of disorder.' " We emphasize that we follow a fundamentally different
approach than they have done to reinterpret random close packing in terms of
the "maximally random jammed" framework. We define the "maximally random jammed
packing fraction" to be where the largest number of initial states, chosen
completely randomly, have relaxed final states at the jamming threshold in the
thermodynamic limit. Thus, we focus on an ensemble of states at the jamming
threshold, while DTSC are interested in determining the amount of order and
degree of jamming for a particular configuration. We also argue that
soft-particle systems are as "clean" as those using hard spheres for studying
jammed packings and point out the benefits of using soft potentials
Stabilization of nonlinear velocity profiles in athermal systems undergoing planar shear flow
We perform molecular dynamics simulations of model granular systems
undergoing boundary-driven planar shear flow in two spatial dimensions with the
goal of developing a more complete understanding of how dense particulate
systems respond to applied shear. In particular, we are interested in
determining when these systems will possess linear velocity profiles and when
they will develop highly localized velocity profiles in response to shear. In
previous work on similar systems we showed that nonlinear velocity profiles
form when the speed of the shearing boundary exceeds the speed of shear waves
in the material. However, we find that nonlinear velocity profiles in these
systems are unstable at very long times. The degree of nonlinearity slowly
decreases in time; the velocity profiles become linear when the granular
temperature and density profiles are uniform across the system at long times.
We measure the time required for the velocity profiles to become linear
and find that increases as a power-law with the speed of the shearing
boundary and increases rapidly as the packing fraction approaches random close
packing. We also performed simulations in which differences in the granular
temperature across the system were maintained by vertically vibrating one of
the boundaries during shear flow. We find that nonlinear velocity profiles form
and are stable at long times if the difference in the granular temperature
across the system exceeds a threshold value that is comparable to the glass
transition temperature in an equilibrium system at the same average density.
Finally, the sheared and vibrated systems form stable shear bands, or highly
localized velocity profiles, when the applied shear stress is lowered below the
yield stress of the static part of the system.Comment: 11 pages, 14 figure
Tuning Jammed Frictionless Disk Packings from Isostatic to Hyperstatic
We perform extensive computational studies of two-dimensional static
bidisperse disk packings using two distinct packing-generation protocols. The
first involves thermally quenching equilibrated liquid configurations to zero
temperature over a range of thermal quench rates and initial packing
fractions followed by compression and decompression in small steps to reach
packing fractions at jamming onset. For the second, we seed the system
with initial configurations that promote micro- and macrophase-separated
packings followed by compression and decompression to . We find that
amorphous, isostatic packings exist over a finite range of packing fractions
from in the large-system limit,
with . In agreement with previous calculations,
we obtain for , where is the rate
above which is insensitive to rate. We further compare the structural
and mechanical properties of isostatic versus hyperstatic packings. The
structural characterizations include the contact number, bond orientational
order, and mixing ratios of the large and small particles. We find that the
isostatic packings are positionally and compositionally disordered, whereas
bond-orientational and compositional order increase with contact number for
hyperstatic packings. In addition, we calculate the static shear modulus and
normal mode frequencies of the static packings to understand the extent to
which the mechanical properties of amorphous, isostatic packings are different
from partially ordered packings. We find that the mechanical properties of the
packings change continuously as the contact number increases from isostatic to
hyperstatic.Comment: 11 pages, 15 figure
Entropy and Temperature of a Static Granular Assembly
Granular matter is comprised of a large number of particles whose collective
behavior determines macroscopic properties such as flow and mechanical
strength. A comprehensive theory of the properties of granular matter,
therefore, requires a statistical framework. In molecular matter, equilibrium
statistical mechanics, which is founded on the principle of conservation of
energy, provides this framework. Grains, however, are small but macroscopic
objects whose interactions are dissipative since energy can be lost through
excitations of the internal degrees of freedom. In this work, we construct a
statistical framework for static, mechanically stable packings of grains, which
parallels that of equilibrium statistical mechanics but with conservation of
energy replaced by the conservation of a function related to the mechanical
stress tensor. Our analysis demonstrates the existence of a state function that
has all the attributes of entropy. In particular, maximizing this state
function leads to a well-defined granular temperature for these systems.
Predictions of the ensemble are verified against simulated packings of
frictionless, deformable disks. Our demonstration that a statistical ensemble
can be constructed through the identification of conserved quantities other
than energy is a new approach that is expected to open up avenues for
statistical descriptions of other non-equilibrium systems.Comment: 5 pages, 4 figure
The [4+2]âCycloaddition of αâNitrosoalkenes with Thiochalcones as a Prototype of Periselective HeteroâDielsâAlder ReactionsâExperimental and Computational Studies
The [4+2]âcycloadditions of αânitrosoalkenes with thiochalcones occur with high selectivity at the thioketone moiety of the dienophile providing styrylâsubstituted 4Hâ1,5,2âoxathiazines in moderate to good yields. Of the eight conceivable heteroâDielsâAlder adducts only this isomer was observed, thus a prototype of a highly periselective and regioselective cycloaddition has been identified. Analysis of crude product mixtures revealed that the αânitrosoalkene also adds competitively to the thioketone moiety of the thiochalcone dimer affording bisâheterocyclic [4+2]âcycloadducts. The experiments are supported by highâlevel DFT calculations that were also extended to related heteroâDielsâAlder reactions of other nitroso compounds and thioketones. These calculations reveal that the title cycloadditions are kinetically controlled processes confirming the role of thioketones as superdienophiles. The computational study was also applied to the experimentally studied thiochalcone dimerization, and showed that the 1,2âdithiin and 2Hâthiopyran isomers are in equilibrium with the monomer. Again, the DFT calculations indicate kinetic control of this process
Geometrical families of mechanically stable granular packings
We enumerate and classify nearly all of the possible mechanically stable (MS)
packings of bidipserse mixtures of frictionless disks in small sheared systems.
We find that MS packings form continuous geometrical families, where each
family is defined by its particular network of particle contacts. We also
monitor the dynamics of MS packings along geometrical families by applying
quasistatic simple shear strain at zero pressure. For small numbers of
particles (N < 16), we find that the dynamics is deterministic and highly
contracting. That is, if the system is initialized in a MS packing at a given
shear strain, it will quickly lock into a periodic orbit at subsequent shear
strain, and therefore sample only a very small fraction of the possible MS
packings in steady state. In studies with N>16, we observe an increase in the
period and random splittings of the trajectories caused by bifurcations in
configuration space. We argue that the ratio of the splitting and contraction
rates in large systems will determine the distribution of MS-packing
geometrical families visited in steady-state. This work is part of our
long-term research program to develop a master-equation formalism to describe
macroscopic slowly driven granular systems in terms of collections of small
subsystems.Comment: 18 pages, 23 figures, 5 table
Reconciling Semiclassical and Bohmian Mechanics: II. Scattering states for discontinuous potentials
In a previous paper [J. Chem. Phys. 121 4501 (2004)] a unique bipolar
decomposition, Psi = Psi1 + Psi2 was presented for stationary bound states Psi
of the one-dimensional Schroedinger equation, such that the components Psi1 and
Psi2 approach their semiclassical WKB analogs in the large action limit.
Moreover, by applying the Madelung-Bohm ansatz to the components rather than to
Psi itself, the resultant bipolar Bohmian mechanical formulation satisfies the
correspondence principle. As a result, the bipolar quantum trajectories are
classical-like and well-behaved, even when Psi has many nodes, or is wildly
oscillatory. In this paper, the previous decomposition scheme is modified in
order to achieve the same desirable properties for stationary scattering
states. Discontinuous potential systems are considered (hard wall, step, square
barrier/well), for which the bipolar quantum potential is found to be zero
everywhere, except at the discontinuities. This approach leads to an exact
numerical method for computing stationary scattering states of any desired
boundary conditions, and reflection and transmission probabilities. The
continuous potential case will be considered in a future publication.Comment: 18 pages, 8 figure
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