16,177 research outputs found
Strain-controlled criticality governs the nonlinear mechanics of fibre networks
Disordered fibrous networks are ubiquitous in nature as major structural
components of living cells and tissues. The mechanical stability of networks
generally depends on the degree of connectivity: only when the average number
of connections between nodes exceeds the isostatic threshold are networks
stable (Maxwell, J. C., Philosophical Magazine 27, 294 (1864)). Upon increasing
the connectivity through this point, such networks undergo a mechanical phase
transition from a floppy to a rigid phase. However, even sub-isostatic networks
become rigid when subjected to sufficiently large deformations. To study this
strain-controlled transition, we perform a combination of computational
modeling of fibre networks and experiments on networks of type I collagen
fibers, which are crucial for the integrity of biological tissues. We show
theoretically that the development of rigidity is characterized by a
strain-controlled continuous phase transition with signatures of criticality.
Our experiments demonstrate mechanical properties consistent with our model,
including the predicted critical exponents. We show that the nonlinear
mechanics of collagen networks can be quantitatively captured by the
predictions of scaling theory for the strain-controlled critical behavior over
a wide range of network concentrations and strains up to failure of the
material
Stress-stabilized sub-isostatic fiber networks in a rope-like limit
The mechanics of disordered fibrous networks such as those that make up the
extracellular matrix are strongly dependent on the local connectivity or
coordination number. For biopolymer networks this coordination number is
typically between three and four. Such networks are sub-isostatic and linearly
unstable to deformation with only central force interactions, but exhibit a
mechanical phase transition between floppy and rigid states under strain.
Introducing weak bending interactions stabilizes these networks and suppresses
the critical signatures of this transition. We show that applying external
stress can also stabilize sub-isostatic networks with only tensile central
force interactions, i.e., a rope-like potential. Moreover, we find that the
linear shear modulus shows a power law scaling with the external normal stress,
with a non-mean-field exponent. For networks with finite bending rigidity, we
find that the critical stain shifts to lower values under prestress
Two-dimensional epitaxial superconductor-semiconductor heterostructures: A platform for topological superconducting networks
Progress in the emergent field of topological superconductivity relies on
synthesis of new material combinations, combining superconductivity, low
density, and spin-orbit coupling (SOC). For example, theory [1-4] indicates
that the interface between a one-dimensional (1D) semiconductor (Sm) with
strong SOC and a superconductor (S) hosts Majorana modes with nontrivial
topological properties [5-8]. Recently, epitaxial growth of Al on InAs
nanowires was shown to yield a high quality S-Sm system with uniformly
transparent interfaces [9] and a hard induced gap, indicted by strongly
suppressed sub gap tunneling conductance [10]. Here we report the realization
of a two-dimensional (2D) InAs/InGaAs heterostructure with epitaxial Al,
yielding a planar S-Sm system with structural and transport characteristics as
good as the epitaxial wires. The realization of 2D epitaxial S-Sm systems
represent a significant advance over wires, allowing extended networks via
top-down processing. Among numerous potential applications, this new material
system can serve as a platform for complex networks of topological
superconductors with gate-controlled Majorana zero modes [1-4]. We demonstrate
gateable Josephson junctions and a highly transparent 2D S-Sm interface based
on the product of excess current and normal state resistance
Sample path large deviations for queues with many inputs
This paper presents a large deviations principle for the average of real-valued processes indexed by the positive integers, one which is particularly suited to queueing systems with many traffic flows. Examples are given of how it may be applied to standard queues with finite and infinite buffers, to priority queues and to finding most likely paths to overflow
A Microscopic Model for Packet Transport in the Internet
A microscopic description of packet transport in the Internet by using a
simple cellular automaton model is presented. A generalised exclusion process
is introduced which allows to study travel times of the particles ('data
packets') along a fixed path in the network. Computer simulations reveal the
appearance of a free flow and a jammed phase separated by a (critical)
transition regime. The power spectra are compared to empirical data for the RTT
(Round Trip Time) obtained from measurements in the Internet. We find that the
model is able to reproduce the characteristic statistical behaviour in
agreement with the empirical data for both phases (free flow and congested).
The phases are therefore jamming properties and not related to the structure of
the network. Moreover the model shows, as observed in reality, critical
behaviour (1/f-noise) for paths with critical load.Comment: 9 pages, 7 figure
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