657 research outputs found
Diffraction behaviour of three-component fibonacci Ta/Al multilayer films
A class of quasiperiodic structure three-component Fibonacci (3CF) Ta/Al multilayer films is fabricated by dual-target magnetron sputtering. The microstructure of this film is investigated by transmission electron microscopy and electron and X-ray diffraction. Cross-section transmission electron microscopy demonstrates a well formed layer structure of 3CF Ta/Al superlattices. The electron-diffraction satellite spots, which can be indexed by three integers, correspond to the X-ray diffraction peaks in both position and intensity. The scattering vectors observed in electron and X-ray diffraction are in good agreement with the analytical treatment from the projection method
Bayesian Probabilistic Numerical Methods in Time-Dependent State Estimation for Industrial Hydrocyclone Equipment
The use of high-power industrial equipment, such as large-scale mixing equipment or a hydrocyclone for separation of particles in liquid suspension, demands careful monitoring to ensure correct operation. The fundamental task of state-estimation for the liquid suspension can be posed as a time-evolving inverse problem and solved with Bayesian statistical methods. In this article, we extend Bayesian methods to incorporate statistical models for the error that is incurred in the numerical solution of the physical governing equations. This enables full uncertainty quantification within a principled computation-precision trade-off, in contrast to the over-confident inferences that are obtained when all sources of numerical error are ignored. The method is cast within a sequential Monte Carlo framework and an optimized implementation is provided in Python
Rules for Computing Symmetry, Density and Stoichiometry in a Quasi-Unit-Cell Model of Quasicrystals
The quasi-unit cell picture describes the atomic structure of quasicrystals
in terms of a single, repeating cluster which overlaps neighbors according to
specific overlap rules. In this paper, we discuss the precise relationship
between a general atomic decoration in the quasi-unit cell picture atomic
decorations in the Penrose tiling and in related tiling pictures. Using these
relations, we obtain a simple, practical method for determining the density,
stoichiometry and symmetry of a quasicrystal based on the atomic decoration of
the quasi-unit cell taking proper account of the sharing of atoms between
clusters.Comment: 14 pages, 8 figure
Fourier Transform Scanning Tunneling Spectroscopy: the possibility to obtain constant energy maps and the band dispersion using a local measurement
We present here an overview of the Fourier Transform Scanning Tunneling
spectroscopy technique (FT-STS). This technique allows one to probe the
electronic properties of a two-dimensional system by analyzing the standing
waves formed in the vicinity of defects. We review both the experimental and
theoretical aspects of this approach, basing our analysis on some of our
previous results, as well as on other results described in the literature. We
explain how the topology of the constant energy maps can be deduced from the FT
of dI/dV map images which exhibit standing waves patterns. We show that not
only the position of the features observed in the FT maps, but also their shape
can be explained using different theoretical models of different levels of
approximation. Thus, starting with the classical and well known expression of
the Lindhard susceptibility which describes the screening of electron in a free
electron gas, we show that from the momentum dependence of the susceptibility
we can deduce the topology of the constant energy maps in a joint density of
states approximation (JDOS). We describe how some of the specific features
predicted by the JDOS are (or are not) observed experimentally in the FT maps.
The role of the phase factors which are neglected in the rough JDOS
approximation is described using the stationary phase conditions. We present
also the technique of the T-matrix approximation, which takes into account
accurately these phase factors. This technique has been successfully applied to
normal metals, as well as to systems with more complicated constant energy
contours. We present results recently obtained on graphene systems which
demonstrate the power of this technique, and the usefulness of local
measurements for determining the band structure, the map of the Fermi energy
and the constant-energy maps.Comment: 33 pages, 15 figures; invited review article, to appear in Journal of
Physics D: Applied Physic
Hamiltonian Theory of the Composite Fermion Wigner Crystal
Experimental results indicating the existence of the high magnetic field
Wigner Crystal have been available for a number of years. While variational
wavefunctions have demonstrated the instability of the Laughlin liquid to a
Wigner Crystal at sufficiently small filling, calculations of the excitation
gaps have been hampered by the strong correlations. Recently a new Hamiltonian
formulation of the fractional quantum Hall problem has been developed. In this
work we extend the Hamiltonian approach to include states of nonuniform
density, and use it to compute the excitation gaps of the Wigner Crystal
states. We find that the Wigner Crystal states near are
quantitatively well described as crystals of Composite Fermions with four
vortices attached. Predictions for gaps and the shear modulus of the crystal
are presented, and found to be in reasonable agreement with experiments.Comment: 41 page, 6 figures, 3 table
Phason elasticity of a three-dimensional quasicrystal: transfer-matrix method
We introduce a new transfer matrix method for calculating the thermodynamic
properties of random-tiling models of quasicrystals in any number of
dimensions, and describe how it may be used to calculate the phason elastic
properties of these models, which are related to experimental measurables such
as phason Debye-Waller factors, and diffuse scattering wings near Bragg peaks.
We apply our method to the canonical-cell model of the icosahedral phase,
making use of results from a previously-presented calculation in which the
possible structures for this model under specific periodic boundary conditions
were cataloged using a computational technique. We give results for the
configurational entropy density and the two fundamental elastic constants for a
range of system sizes. The method is general enough allow a similar calculation
to be performed for any other random tiling model.Comment: 38 pages, 3 PostScript figures, self-expanding uuencoded compressed
tar file, LaTeX using RevTeX macros and epsfig.st
Interstitials, Vacancies, and Supersolid Order in Vortex Crystals
Interstitials and vacancies in the Abrikosov phase of clean Type II
superconductors are line imperfections, which cannot extend across macroscopic
equilibrated samples at low temperatures. We argue that the entropy associated
with line wandering nevertheless can cause these defects to proliferate at a
sharp transition which will exist if this occurs below the temperature at which
the crystal actually melts. Vortices are both entangled and crystalline in the
resulting ``supersolid'' phase, which in a dual ``boson'' analog system is
closely related to a two-dimensional quantum crystal of He with
interstitials or vacancies in its ground state. The supersolid {\it must} occur
for , where is the decoupling field above which
vortices begin to behave two-dimensionally. Numerical calculations show that
interstitials, rather than vacancies, are the preferred defect for , and allow us to estimate whether proliferation also
occurs for B\,\lot\,B_\times.The implications of the supersolid phase for
transport measurements, dislocation configurations and neutron diffraction are
discussed.Comment: 53 pages and 15 figures, available upon request, written in plain TE
Statistical Mechanics of Vacancy and Interstitial Strings in Hexagonal Columnar Crystals
Columnar crystals contain defects in the form of vacancy/interstitial loops
or strings of vacancies and interstitials bounded by column ``heads'' and
``tails''. These defect strings are oriented by the columnar lattice and can
change size and shape by movement of the ends and forming kinks along the
length. Hence an analysis in terms of directed living polymers is appropriate
to study their size and shape distribution, volume fraction, etc. If the
entropy of transverse fluctuations overcomes the string line tension in the
crystalline phase, a string proliferation transition occurs, leading to a
supersolid phase. We estimate the wandering entropy and examine the behaviour
in the transition regime. We also calculate numerically the line tension of
various species of vacancies and interstitials in a triangular lattice for
power-law potentials as well as for a modified Bessel function interaction
between columns as occurs in the case of flux lines in type-II superconductors
or long polyelectrolytes in an ionic solution. We find that the centered
interstitial is the lowest energy defect for a very wide range of interactions;
the symmetric vacancy is preferred only for extremely short interaction ranges.Comment: 22 pages (revtex), 15 figures (encapsulated postscript
Novel Ground-State Crystals with Controlled Vacancy Concentrations: From Kagom\'{e} to Honeycomb to Stripes
We introduce a one-parameter family, , of pair potential
functions with a single relative energy minimum that stabilize a range of
vacancy-riddled crystals as ground states. The "quintic potential" is a
short-ranged, nonnegative pair potential with a single local minimum of height
at unit distance and vanishes cubically at a distance of \rt. We have
developed this potential to produce ground states with the symmetry of the
triangular lattice while favoring the presence of vacancies. After an
exhaustive search using various optimization and simulation methods, we believe
that we have determined the ground states for all pressures, densities, and . For specific areas below 3\rt/2, the ground states of the
"quintic potential" include high-density and low-density triangular lattices,
kagom\'{e} and honeycomb crystals, and stripes. We find that these ground
states are mechanically stable but are difficult to self-assemble in computer
simulations without defects. For specific areas above 3\rt/2, these systems
have a ground-state phase diagram that corresponds to hard disks with radius
\rt. For the special case of H=0, a broad range of ground states is
available. Analysis of this case suggests that among many ground states, a
high-density triangular lattice, low-density triangular lattice, and striped
phases have the highest entropy for certain densities. The simplicity of this
potential makes it an attractive candidate for experimental realization with
application to the development of novel colloidal crystals or photonic
materials.Comment: 25 pages, 11 figure
- …