819 research outputs found
Emergence of Conduction Channels in Lithium Silicate
The existence of conduction channels in lithium silicate (Li_2O)(SiO_2) is
investigated. Regions of the system where many different ions pass by form
channels and are thus spatially correlated. For a closer analysis the
properties of the individual ionic sites are elucidated. The mobility of ions
in single sites is found to depend strongly on the number of bridging oxygens
in the coordination shell. The channels are not reflected in the network
structure as obtained from the distribution of the bridging oxygens. Spatial
correlations similar to those found in the silicate also emerge from studying
the dynamics of particles in a simple random lattice model. This supports the
suggestion that the observed spatial correlations can be viewed in analogy to
the emergence of percolation paths.Comment: 5 pages, 8 figures, submitted to Phys. Rev.
The cationic energy landscape in alkali silicate glasses: properties and relevance
Individual cationic site--energies are explicitly determined from molecular
dynamics simulations of alkali silicate glasses, and the properties and
relevance of this local energetics to ion transport are studied. The absence of
relaxations on the timescale of ion transport proves the validity of a static
description of the energy landscape, as it is generally used in hopping models.
The Coulomb interaction among the cations turns out essential to obtain an
average energy landscape in agreement with typical simplified hopping models.
Strong correlations exist both between neighboring sites and between different
energetic contributions at one site, and they shape essential characteristics
of the energy landscape. A model energy landscape with a single vacancy is used
to demonstrate why average site--energies, including the full Coulomb
interaction, are still insufficient to describe the site population of ions, or
their dynamics. This model explains how the relationship between energetics and
ion dynamics is weakened, and thus establishes conclusively that a hopping
picture with static energies fails to capture all the relevant information. It
is therefore suggested that alternative simplified models of ion conduction are
needed.Comment: 19 pages, 1 table, 7 figures; submitted to JC
Bypassing slip velocity: rotational and translational velocities of autophoretic colloids in terms of surface flux
A standard approach to propulsion velocities of autophoretic colloids with
thin interaction layers uses a reciprocity relation applied to the slip
velocity. But the surface flux (chemical, electrical, thermal, etc.), which is
the source of the field driving the slip is often more accessible. We show how,
under conditions of low Reynolds number and a field obeying the Laplace
equation in the outer region, the slip velocity can be bypassed in velocity
calculations. In a sense, the actual slip velocity and a normal field
proportional to the flux density are equivalent for this type of calculation.
Using known results for surface traction induced by rotating or translating an
inert particle in a quiescent fluid, we derive simple and explicit integral
formulas for translational and rotational velocities of arbitrary spheroidal
and slender-body autophoretic colloids.Comment: 11 page
Triangular Ising antiferromagnet through a fermionic lens, part 2: information-theoretic aspects of zero-temperature states on cylinders
A classical lattice spin model wrapped on a cylinder is profitably viewed as
a chain of rings of spins. From that perspective, mutual information between
ring configurations plays much the same role as spin-spin correlation functions
in simpler settings. We study zero-temperature states of triangular lattice
Ising antiferromagnet (TIAFM) systems from this point of view using a fermionic
representation presented in a companion paper (Part 1). On infinite cylinders,
ring-to-ring mutual information falls off asymptotically at a rate which
decreases smoothly with cylinder circumference, but the end-to-end mutual
information for finite cylinders depends strongly on the residue class modulo 3
of the circumference as well as on whether spin periodicity or antiperiodicity
is imposed in the circumferential direction. In some cases, the falloff is only
as the inverse square of the cylinder length. These features, puzzling within
the original spin formulation, are easily understood and calculated within the
fermionic formulation
Gaussian Memory in Kinematic Matrix Theory for Self-Propellers
We extend the kinematic matrix ("kinematrix") formalism [Phys. Rev. E 89,
062304 (2014)], which via simple matrix algebra accesses ensemble properties of
self-propellers influenced by uncorrelated noise, to treat Gaussian correlated
noises. This extension brings into reach many real-world biological and
biomimetic self-propellers for which inertia is significant. Applying the
formalism, we analyze in detail ensemble behaviors of a 2D self-propeller with
velocity fluctuations and orientation evolution driven by an Ornstein-Uhlenbeck
process. On the basis of exact results, a variety of dynamical regimes
determined by the inertial, speed-fluctuation, orientational diffusion, and
emergent disorientation time scales are delineated and discussed.Comment: 8 pages, 4 figure
Triangular Ising antiferromagnet through a fermionic lens, part 1: free energy, zero-temperature phases and spin-spin correlation
We develop a fermionic formulation of the triangular lattice Ising
antiferromagnet (TIAFM) which is both calculationally convenient and
intuitively appealing to imaginations steeped in conventional condensed matter
physics. It is used to elucidate a variety of aspects of zero-temperature
models. Cylindrical systems possess multiple "phases" distinguished by the
number of circumferential satisfied bonds and by entropy density. On the plane,
phases are labelled by densities of satisfied bonds of two different
orientations. A local particle (semi)conservation law in the fermionic picture
lies behind both these features as well as the classic power-law falloff of the
spin-spin correlation function, which is also derived from the fermionic
perspective
Fractional Quantum Hall Effect in Graphene
Unlike regular electron spin, the pseudospin degeneracy of Fermi points in
graphene does not couple directly to magnetic field. Therefore, graphene
provides a natural vehicle to observe the integral and fractional quantum Hall
physics in an elusive limit analogous to zero Zeeman splitting in GaAs systems.
This limit can exhibit new integral plateaus arising from interactions, large
pseudoskyrmions, fractional sequences, even/odd numerator effects,
composite-fermion pseudoskyrmions, and a pseudospin-singlet composite-fermion
Fermi sea. The Dirac nature of the B=0 spectrum, which induces qualitative
changes in the overall spectrum, has no bearing on the fractional quantum Hall
effect in the Landau level of graphene. The second Landau level of
graphene is predicted to show more robust fractional quantum Hall effect than
the second Landau level of GaAs.Comment: 4 pages, 1 figur
Annealing a Magnetic Cactus into Phyllotaxis
The appearance of mathematical regularities in the disposition of leaves on a
stem, scales on a pine-cone and spines on a cactus has puzzled scholars for
millennia; similar so-called phyllotactic patterns are seen in self-organized
growth, polypeptides, convection, magnetic flux lattices and ion beams. Levitov
showed that a cylindrical lattice of repulsive particles can reproduce
phyllotaxis under the (unproved) assumption that minimum of energy would be
achieved by 2-D Bravais lattices. Here we provide experimental and numerical
evidence that the Phyllotactic lattice is actually a ground state. When
mechanically annealed, our experimental "magnetic cactus" precisely reproduces
botanical phyllotaxis, along with domain boundaries (called transitions in
Botany) between different phyllotactic patterns. We employ a structural genetic
algorithm to explore the more general axially unconstrained case, which reveals
multijugate (multiple spirals) as well as monojugate (single spiral)
phyllotaxis.Comment: 9 Pages 11 Figure
Comparing artificial frustrated magnets: tuning symmetry in nanomagnet arrays
We study the impact of geometry on magnetostatically frustrated single-domain
nanomagnet arrays. We examine square and hexagonal lattice arrays, as well as a
brickwork geometry that combines the anisotropy of the square lattice and the
topology of the hexagonal lattice. We find that the more highly frustrated
hexagonal lattice allows for the most thorough minimization of the
magnetostatic energy, and that the pair-wise correlations between moments
differ qualitatively between hexagonal and brickwork lattices, although they
share the same lattice topology. The results indicate that the symmetry of
local interaction is more important than overall lattice topology in the
accommodation of frustrated interactions.Comment: 18 pages and 4 figure
Characterization of switching field distributions in Ising-like magnetic arrays
The switching field distribution within arrays of single-domain ferromagnetic
islands incorpo- rates both island-island interactions and quenched disorder in
island geometry. Separating these two contributions is important for
disentangling the effects of disorder and interactions in the magnetization
dynamics of island arrays. Using sub-micron, spatially resolved Kerr imaging in
an external magnetic field for islands with perpendicular magnetic anisotropy,
we map out the evolution of island arrays during hysteresis loops. Resolving
and tracking individual islands across four different lattice types and a range
of inter-island spacings, we extract the individual switching fields of every
island and thereby determine the relative contributions of interactions and
quenched disorder in the arrays. The width of the switching field distribution
is well explained by a simple model comprising the sum of an array-independent
contribution (interpreted as disorder-induced), and a term proportional to the
maximum field the fully polarized array could exert on a single island. We
conclude that disorder in these arrays is primarily a single-island property
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