5,191 research outputs found
Understanding the nucleation mechanisms of Carbon Nanotubes in catalytic Chemical Vapor Deposition
The nucleation of carbon caps on small nickel clusters is studied using a
tight binding model coupled to grand canonical Monte Carlo simulations. It
takes place in a well defined carbon chemical potential range, when a critical
concentration of surface carbon atoms is reached. The solubility of carbon in
the outermost Ni layers, that depends on the initial, crystalline or
disordered, state of the catalyst and on the thermodynamic conditions, is
therefore a key quantity to control the nucleation
Estimating statistical distributions using an integral identity
We present an identity for an unbiased estimate of a general statistical
distribution. The identity computes the distribution density from dividing a
histogram sum over a local window by a correction factor from a mean-force
integral, and the mean force can be evaluated as a configuration average. We
show that the optimal window size is roughly the inverse of the local
mean-force fluctuation. The new identity offers a more robust and precise
estimate than a previous one by Adib and Jarzynski [J. Chem. Phys. 122, 014114,
(2005)]. It also allows a straightforward generalization to an arbitrary
ensemble and a joint distribution of multiple variables. Particularly we derive
a mean-force enhanced version of the weighted histogram analysis method (WHAM).
The method can be used to improve distributions computed from molecular
simulations. We illustrate the use in computing a potential energy
distribution, a volume distribution in a constant-pressure ensemble, a radial
distribution function and a joint distribution of amino acid backbone dihedral
angles.Comment: 45 pages, 7 figures, simplified derivation, a more general mean-force
formula, add discussions to the window size, add extensions to WHAM, and 2d
distribution
Langlands duality for finite-dimensional representations of quantum affine algebras
We describe a correspondence (or duality) between the q-characters of
finite-dimensional representations of a quantum affine algebra and its
Langlands dual in the spirit of q-alg/9708006 and 0809.4453. We prove this
duality for the Kirillov-Reshetikhin modules and their irreducible tensor
products. In the course of the proof we introduce and construct "interpolating
(q,t)-characters" depending on two parameters which interpolate between the
q-characters of a quantum affine algebra and its Langlands dual.Comment: 40 pages; several results and comments added. Accepted for
publication in Letters in Mathematical Physic
Enhancement of kinetic energy fluctuations due to expansion
Global equilibrium fragmentation inside a freeze out constraining volume is a
working hypothesis widely used in nuclear fragmentation statistical models. In
the framework of classical Lennard Jones molecular dynamics, we study how the
relaxation of the fixed volume constraint affects the posterior evolution of
microscopic correlations, and how a non-confined fragmentation scenario is
established. A study of the dynamical evolution of the relative kinetic energy
fluctuations was also performed. We found that asymptotic measurements of such
observable can be related to the number of decaying channels available to the
system at fragmentation time.Comment: 6 pages, 4 figure
Structure and thermodynamics of platelet dispersions
Various properties of fluids consisting of platelike particles differ from
the corresponding ones of fluids consisting of spherical particles because
interactions between platelets depend on their mutual orientations. One of the
main issues in this topic is to understand how structural properties of such
fluids depend on factors such as the shape of the platelets, the size
polydispersity, the orientational order, and the platelet number density. A
statistical mechanics approach to the problem is natural and in the last few
years there has been a lot of work on the study of properties of platelet
fluids. In this contribution some recent theoretical developments in the field
are discussed and experimental investigations are described.Comment: 23 pages, 18 figure
WavePacket: A Matlab package for numerical quantum dynamics. III: Quantum-classical simulations and surface hopping trajectories
WavePacket is an open-source program package for numerical simulations in
quantum dynamics. Building on the previous Part I [Comp. Phys. Comm. 213,
223-234 (2017)] and Part II [Comp. Phys. Comm. 228, 229-244 (2018)] which dealt
with quantum dynamics of closed and open systems, respectively, the present
Part III adds fully classical and mixed quantum-classical propagations to
WavePacket. In those simulations classical phase-space densities are sampled by
trajectories which follow (diabatic or adiabatic) potential energy surfaces. In
the vicinity of (genuine or avoided) intersections of those surfaces
trajectories may switch between surfaces. To model these transitions, two
classes of stochastic algorithms have been implemented: (1) J. C. Tully's
fewest switches surface hopping and (2) Landau-Zener based single switch
surface hopping. The latter one offers the advantage of being based on
adiabatic energy gaps only, thus not requiring non-adiabatic coupling
information any more.
The present work describes the MATLAB version of WavePacket 6.0.2 which is
essentially an object-oriented rewrite of previous versions, allowing to
perform fully classical, quantum-classical and quantum-mechanical simulations
on an equal footing, i.e., for the same physical system described by the same
WavePacket input. The software package is hosted and further developed at the
Sourceforge platform, where also extensive Wiki-documentation as well as
numerous worked-out demonstration examples with animated graphics are
available
Geometrical Frustration: A Study of 4d Hard Spheres
The smallest maximum kissing-number Voronoi polyhedron of 3d spheres is the
icosahedron and the tetrahedron is the smallest volume that can show up in
Delaunay tessalation. No periodic lattice is consistent with either and hence
these dense packings are geometrically frustrated. Because icosahedra can be
assembled from almost perfect tetrahedra, the terms "icosahedral" and
"polytetrahedral" packing are often used interchangeably, which leaves the true
origin of geometric frustration unclear. Here we report a computational study
of freezing of 4d hard spheres, where the densest Voronoi cluster is compatible
with the symmetry of the densest crystal, while polytetrahedral order is not.
We observe that, under otherwise comparable conditions, crystal nucleation in
4d is less facile than in 3d. This suggest that it is the geometrical
frustration of polytetrahedral structures that inhibits crystallization.Comment: 4 pages, 3 figures; revised interpretatio
A general theory of DNA-mediated and other valence-limited interactions
We present a general theory for predicting the interaction potentials between
DNA-coated colloids, and more broadly, any particles that interact via
valence-limited ligand-receptor binding. Our theory correctly incorporates the
configurational and combinatorial entropic factors that play a key role in
valence-limited interactions. By rigorously enforcing self-consistency, it
achieves near-quantitative accuracy with respect to detailed Monte Carlo
calculations. With suitable approximations and in particular geometries, our
theory reduces to previous successful treatments, which are now united in a
common and extensible framework. We expect our tools to be useful to other
researchers investigating ligand-mediated interactions. A complete and
well-documented Python implementation is freely available at
http://github.com/patvarilly/DNACC .Comment: 18 pages, 10 figure
Phase behavior of the Lattice Restricted Primitive Model with nearest-neighbor exclusion
The global phase behavior of the lattice restricted primitive model with
nearest neighbor exclusion has been studied by grand canonical Monte Carlo
simulations. The phase diagram is dominated by a fluid (or charge-disordered
solid) to charge-ordered solid transition that terminates at the maximum
density, and reduced temperature . At
that point, there is a first-order phase transition between two phases of the
same density, one charge-ordered and the other charge-disordered. The
liquid-vapor transition for the model is metastable, lying entirely within the
fluid-solid phase envelope.Comment: 6 pages, color. submitted to J. Chem. Phy
Off-lattice Monte Carlo Simulation of Supramolecular Polymer Architectures
We introduce an efficient, scalable Monte Carlo algorithm to simulate
cross-linked architectures of freely-jointed and discrete worm-like chains.
Bond movement is based on the discrete tractrix construction, which effects
conformational changes that exactly preserve fixed-length constraints of all
bonds. The algorithm reproduces known end-to-end distance distributions for
simple, analytically tractable systems of cross-linked stiff and freely jointed
polymers flawlessly, and is used to determine the effective persistence length
of short bundles of semi-flexible worm-like chains, cross-linked to each other.
It reveals a possible regulatory mechanism in bundled networks: the effective
persistence of bundles is controlled by the linker density.Comment: 4 pages, 4 figure
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