127 research outputs found
Phase Transitions of Soft Disks in External Periodic Potentials: A Monte Carlo Study
The nature of freezing and melting transitions for a system of model colloids
interacting by a DLVO potential in a spatially periodic external potential is
studied using extensive Monte Carlo simulations. Detailed finite size scaling
analyses of various thermodynamic quantities like the order parameter, its
cumulants etc. are used to map the phase diagram of the system for various
values of the reduced screening length and the amplitude of the
external potential. We find clear indication of a reentrant liquid phase over a
significant region of the parameter space. Our simulations therefore show that
the system of soft disks behaves in a fashion similar to charge stabilized
colloids which are known to undergo an initial freezing, followed by a
re-melting transition as the amplitude of the imposed, modulating field
produced by crossed laser beams is steadily increased. Detailed analysis of our
data shows several features consistent with a recent dislocation unbinding
theory of laser induced melting
Defect-unbinding transitions and inherent structures in two dimensions
We present a large-scale (36000-particle) computational study of the
"inherent structures" (IS) associated with equilibrium, two-dimensional,
one-component Lennard-Jones systems. Our results provide strong support both
for the inherent-structures theory of classical fluids, and for the KTHNY
theory of two-stage melting in two dimensions. This support comes from the
observation of three qualitatively distinct "phases" of inherent structures: a
crystal, a "hexatic glass", and a "liquid glass". We also directly observe, in
the IS, analogs of the two defect-unbinding transitions (respectively, of
dislocations, and disclinations) believed to mediate the two equilibrium phase
transitions. Each transition shows up in the inherent structures---although the
free disclinations in the "liquid glass" are embedded in a percolating network
of grain boundaries. The bond-orientational correlation functions of the
inherent structures show the same progressive loss of order as do the three
equilibrium phases: long-range to quasi-long-range to short-range.Comment: RevTeX, 8 pages, 15 figure
Prediction of Emerging Technologies Based on Analysis of the U.S. Patent Citation Network
The network of patents connected by citations is an evolving graph, which
provides a representation of the innovation process. A patent citing another
implies that the cited patent reflects a piece of previously existing knowledge
that the citing patent builds upon. A methodology presented here (i) identifies
actual clusters of patents: i.e. technological branches, and (ii) gives
predictions about the temporal changes of the structure of the clusters. A
predictor, called the {citation vector}, is defined for characterizing
technological development to show how a patent cited by other patents belongs
to various industrial fields. The clustering technique adopted is able to
detect the new emerging recombinations, and predicts emerging new technology
clusters. The predictive ability of our new method is illustrated on the
example of USPTO subcategory 11, Agriculture, Food, Textiles. A cluster of
patents is determined based on citation data up to 1991, which shows
significant overlap of the class 442 formed at the beginning of 1997. These new
tools of predictive analytics could support policy decision making processes in
science and technology, and help formulate recommendations for action
Intermittency in Dynamics of Two-Dimensional Vortex-like Defects
We examine high-order dynamical correlations of defects (vortices,
disclinations etc) in thin films starting from the Langevin equation for the
defect motion. We demonstrate that dynamical correlation functions of
vorticity and disclinicity behave as where is the
characteristic scale and is the fugacity. As a consequence, below the
Berezinskii-Kosterlitz-Thouless transition temperature are
characterized by anomalous scaling exponents. The behavior strongly differs
from the normal law occurring for simultaneous correlation
functions, the non-simultaneous correlation functions appear to be much larger.
The phenomenon resembles intermittency in turbulence.Comment: 30 pages, 11 figure
Crystallization of a classical two-dimensional electron system: Positional and orientational orders
Crystallization of a classical two-dimensional one-component plasma
(electrons interacting with the Coulomb repulsion in a uniform neutralizing
positive background) is investigated with a molecular dynamics simulation. The
positional and the orientational correlation functions are calculated for the
first time. We have found an indication that the solid phase has a
quasi-long-range (power-law) positional order along with a long-range
orientational order. This indicates that, although the long-range Coulomb
interaction is outside the scope of Mermin's theorem, the absence of ordinary
crystalline order at finite temperatures applies to the electron system as
well. The `hexatic' phase, which is predicted between the liquid and the solid
phases by the Kosterlitz-Thouless-Halperin-Nelson-Young theory, is also
discussed.Comment: 3 pages, 4 figures; Corrected typos; Double columne
Van der Waals loops and the melting transition in two dimensions
Evidence for the existence of van der Waals loops in pressure p versus volume
v plots has for some time supported the belief that melting in two dimensions
is a first order phase transition. We report rather accurate equilibrium p(v)
curves for systems of hard disks obtained from long Monte Carlo simulations.
These curves, obtained in the constant volume ensemble, using periodic boundary
conditions, exhibit well defined van der Waals loops. We illustrate their
existence for finite systems that are known to undergo a continuous transition
in the thermodynamic limit. To this end, we obtain magnetization m versus
applied field curves from Monte Carlo simulations of the 2D Ising model, in the
constant m ensemble, at the critical point. Whether van der Waals loops for
disk systems behave in the thermodynamic limit as they do for the 2D Ising
model at the critical point cannot be ruled out. Thus, the often made claim
that melting in 2D is a first order phase transition, based on the evidence
that van der Waals loops exist, is not sound.Comment: 10 pages, 6 Postscript figures (submitted to Phys.Rev.E). For related
work, see http://pipe.unizar.es/~jf
Phase Transitions Driven by Vortices in 2D Superfluids and Superconductors: From Kosterlitz-Thouless to 1st Order
The Landau-Ginzburg-Wilson hamiltonian is studied for different values of the
parameter which multiplies the quartic term (it turns out that this
is equivalent to consider different values of the coherence length in
units of the lattice spacing ). It is observed that amplitude fluctuations
can change dramatically the nature of the phase transition: for small values of
(), instead of the smooth Kosterlitz-Thouless transition
there is a {\em first order} transition with a discontinuous jump in the vortex
density and a larger non-universal drop in the helicity modulus. In
particular, for sufficiently small (), the density of
bound pairs of vortex-antivortex below is so low that, drops to zero
almost for all temperature .Comment: 8 pages, 5 .eps figure
A Natural Experiment on Innovation Without Patents
Innovation occurs within a complex web of law. Of the myriad legal doctrines that affect innovation, the most directly relevant is intellectual property, particularly patent law. The United States Constitution, in Article I, Section 8, states a strong public policy goal for the granting of patents (and copyrights) to inventors: “To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries.” Despite the Founding Fathers’ apparent faith in the societal benefits afforded by patent protection, a crescendo of recent critics have accused the patent system of complicating, slowing, or even thwarting innovation. Patents certainly present significant hurdles for open and user innovation. Moreover, von Hippel (2005) and Strandburg (2008) have demonstrated that user innovators, especially individuals, tend to be poorly served, and often harmed, by the patent system
Topological Defects, Orientational Order, and Depinning of the Electron Solid in a Random Potential
We report on the results of molecular dynamics simulation (MD) studies of the
classical two-dimensional electron crystal in the presence disorder. Our study
is motivated by recent experiments on this system in modulation doped
semiconductor systems in very strong magnetic fields, where the magnetic length
is much smaller than the average interelectron spacing , as well as by
recent studies of electrons on the surface of helium. We investigate the low
temperature state of this system using a simulated annealing method. We find
that the low temperature state of the system always has isolated dislocations,
even at the weakest disorder levels investigated. We also find evidence for a
transition from a hexatic glass to an isotropic glass as the disorder is
increased. The former is characterized by quasi-long range orientational order,
and the absence of disclination defects in the low temperature state, and the
latter by short range orientational order and the presence of these defects.
The threshold electric field is also studied as a function of the disorder
strength, and is shown to have a characteristic signature of the transition.
Finally, the qualitative behavior of the electron flow in the depinned state is
shown to change continuously from an elastic flow to a channel-like, plastic
flow as the disorder strength is increased.Comment: 31 pages, RevTex 3.0, 15 figures upon request, accepted for
publication in Phys. Rev. B., HAF94MD
Monte Carlo simulation of a two-dimensional continuum Coulomb gas
We study the classical two-dimensional Coulomb gas model for thermal vortex
fluctuations in thin superconducting/superfluid films by Monte Carlo simulation
of a grand canonical vortex ensemble defined on a continuum. The
Kosterlitz-Thouless transition is well understood at low vortex density, but at
high vortex density the nature of the phase diagram and of the vortex phase
transition is less clear. From our Monte Carlo data we construct phase diagrams
for the 2D Coulomb gas without any restrictions on the vortex density. For
negative vortex chemical potential (positive vortex core energy) we always find
a Kosterlitz-Thouless transition. Only if the Coulomb interaction is
supplemented with a short-distance repulsion, a first order transition line is
found, above some positive value of the vortex chemical potential.Comment: 10 pages RevTeX, 7 postscript figures included using eps
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