72 research outputs found
Effects of kinked linear defects on planar flux line arrays
In the hard core limit, interacting vortices in planar type II
superconductors can be modeled as non-interacting one dimensional fermions
propagating in imaginary time. We use this analogy to derive analytical
expressions for the probability density and imaginary current of vortex lines
interacting with an isolated bent line defect and to understand the pinning
properties of such systems. When there is an abrupt change of the direction of
the pinning defect, we find a sinusoidal modulation of the vortex density in
directions both parallel and perpendicular to the defect.Comment: 13 figure
Threading the spindle: a geometric study of chiral liquid crystal polymer microparticles
Polymeric particles are strong candidates for designing artificial materials
capable of emulating the complex twisting-based functionality observed in
biological systems. In this letter, we provide the first detailed investigation
of the swelling behavior of bipolar polymer liquid crystalline microparticles.
Deswelling from the spherical bipolar configuration causes the microparticle to
contract anisotropically and twist in the process, resulting in a twisted
spindle shaped structure. We propose a model to describe the observed spiral
patterns and twisting behavior
Quantum versus Classical Dynamics in a driven barrier: the role of kinematic effects
We study the dynamics of the classical and quantum mechanical scattering of a
wave packet from an oscillating barrier. Our main focus is on the dependence of
the transmission coefficient on the initial energy of the wave packet for a
wide range of oscillation frequencies. The behavior of the quantum transmission
coefficient is affected by tunneling phenomena, resonances and kinematic
effects emanating from the time dependence of the potential. We show that when
kinematic effects dominate (mainly in intermediate frequencies), classical
mechanics provides very good approximation of quantum results. Moreover, in the
frequency region of optimal agreement between classical and quantum
transmission coefficient, the transmission threshold, i.e. the energy above
which the transmission coefficient becomes larger than a specific small
threshold value, is found to exhibit a minimum. We also consider the form of
the transmitted wave packet and we find that for low values of the frequency
the incoming classical and quantum wave packet can be split into a train of
well separated coherent pulses, a phenomenon which can admit purely classical
kinematic interpretation
Vortex pinning by meandering line defects in planar superconductors
To better understand vortex pinning in thin superconducting slabs, we study
the interaction of a single fluctuating vortex filament with a curved line
defect in (1+1) dimensions. This problem is also relevant to the interaction of
scratches with wandering step edges in vicinal surfaces. The equilibrium
probability density for a fluctuating line attracted to a particular fixed
defect trajectory is derived analytically by mapping the problem to a straight
line defect in the presence of a space and time-varying external tilt field.
The consequences of both rapid and slow changes in the frozen defect
trajectory, as well as finite size effects are discussed. A sudden change in
the defect direction leads to a delocalization transition, accompanied by a
divergence in the trapping length, near a critical angle.Comment: 9 pages, 9 figure
Fluctuations and redundancy in optimal transport networks
The structure of networks that provide optimal transport properties has been
investigated in a variety of contexts. While many different formulations of
this problem have been considered, it is recurrently found that optimal
networks are trees. It is shown here that this result is contingent on the
assumption of a stationary flow through the network. When time variations or
fluctuations are allowed for, a different class of optimal structures is found,
which share the hierarchical organization of trees yet contain loops. The
transitions between different network topologies as the parameters of the
problem vary are examined. These results may have strong implications for the
structure and formation of natural networks, as is illustrated by the example
of leaf venation networks.Comment: 4 pages, 4 figure
Quantifying loopy network architectures
Biology presents many examples of planar distribution and structural networks
having dense sets of closed loops. An archetype of this form of network
organization is the vasculature of dicotyledonous leaves, which showcases a
hierarchically-nested architecture containing closed loops at many different
levels. Although a number of methods have been proposed to measure aspects of
the structure of such networks, a robust metric to quantify their hierarchical
organization is still lacking. We present an algorithmic framework, the
hierarchical loop decomposition, that allows mapping loopy networks to binary
trees, preserving in the connectivity of the trees the architecture of the
original graph. We apply this framework to investigate computer generated
graphs, such as artificial models and optimal distribution networks, as well as
natural graphs extracted from digitized images of dicotyledonous leaves and
vasculature of rat cerebral neocortex. We calculate various metrics based on
the Asymmetry, the cumulative size distribution and the Strahler bifurcation
ratios of the corresponding trees and discuss the relationship of these
quantities to the architectural organization of the original graphs. This
algorithmic framework decouples the geometric information (exact location of
edges and nodes) from the metric topology (connectivity and edge weight) and it
ultimately allows us to perform a quantitative statistical comparison between
predictions of theoretical models and naturally occurring loopy graphs.Comment: 17 pages, 8 figures. During preparation of this manuscript the
authors became aware of the work of Mileyko at al., concurrently submitted
for publicatio
Collapse and folding of pressurized rings in two dimensions
Hydrostatically pressurized circular rings confined to two dimensions (or
cylinders constrained to have only z-independent deformations) undergo Euler
type buckling when the outside pressure exceeds a critical value. We perform a
stability analysis of rings with arc-length dependent bending moduli and
determine how weakened bending modulus segments affect the buckling critical
pressure. Rings with a 4-fold symmetric modulation are particularly susceptible
to collapse. In addition we study the initial post-buckling stages of the
pressurized rings to determine possible ring folding patterns
Limited Urban Growth: London's Street Network Dynamics since the 18th Century
We investigate the growth dynamics of Greater London defined by the
administrative boundary of the Greater London Authority, based on the evolution
of its street network during the last two centuries. This is done by employing
a unique dataset, consisting of the planar graph representation of nine time
slices of Greater London's road network spanning 224 years, from 1786 to 2010.
Within this time-frame, we address the concept of the metropolitan area or city
in physical terms, in that urban evolution reveals observable transitions in
the distribution of relevant geometrical properties. Given that London has a
hard boundary enforced by its long-standing green belt, we show that its street
network dynamics can be described as a fractal space-filling phenomena up to a
capacitated limit, whence its growth can be predicted with a striking level of
accuracy. This observation is confirmed by the analytical calculation of key
topological properties of the planar graph, such as the topological growth of
the network and its average connectivity. This study thus represents an example
of a strong violation of Gibrat's law. In particular, we are able to show
analytically how London evolves from a more loop-like structure, typical of
planned cities, toward a more tree-like structure, typical of self-organized
cities. These observations are relevant to the discourse on sustainable urban
planning with respect to the control of urban sprawl in many large cities,
which have developed under the conditions of spatial constraints imposed by
green belts and hard urban boundaries.Comment: PlosOne, in publicatio
A framework for the discovery of retinal biomarkers in Optical Coherence Tomography Angiography (OCTA)
Leaf venation, as a resistor, to optimize a switchable IR absorber
Leaf vascular patterns are the mechanisms and mechanical support for the transportation of fluidics for photosynthesis and leaf development properties. Vascular hierarchical networks in leaves have far-reaching functions in optimal transport efficiency of functional fluidics. Embedding leaf morphogenesis as a resistor network is significant in the optimization of a translucent thermally functional material. This will enable regulation through pressure equalization by diminishing flow pressure variation. This paper investigates nature’s vasculature networks that exhibit hierarchical branching scaling applied to microfluidics. To enable optimum potential for pressure drop regulation by algorithm design. This code analysis of circuit conduit optimization for transport fluidic flow resistance is validated against CFD simulation, within a closed loop network. The paper will propose this self-optimization, characterization by resistance seeking targeting to determine a microfluidic network as a resistor. To advance a thermally function material as a switchable IR absorber
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