31,624 research outputs found
Diffusion runs low on persistence fast
Interpreting an image as a function on a compact sub- set of the Euclidean plane, we get its scale-space by diffu- sion, spreading the image over the entire plane. This gener- ates a 1-parameter family of functions alternatively defined as convolutions with a progressively wider Gaussian ker- nel. We prove that the corresponding 1-parameter family of persistence diagrams have norms that go rapidly to zero as time goes to infinity. This result rationalizes experimental observations about scale-space. We hope this will lead to targeted improvements of related computer vision methods
Limits of feedback control in bacterial chemotaxis
Inputs to signaling pathways can have complex statistics that depend on the
environment and on the behavioral response to previous stimuli. Such behavioral
feedback is particularly important in navigation. Successful navigation relies
on proper coupling between sensors, which gather information during motion, and
actuators, which control behavior. Because reorientation conditions future
inputs, behavioral feedback can place sensors and actuators in an operational
regime different from the resting state. How then can organisms maintain proper
information transfer through the pathway while navigating diverse environments?
In bacterial chemotaxis, robust performance is often attributed to the zero
integral feedback control of the sensor, which guarantees that activity returns
to resting state when the input remains constant. While this property provides
sensitivity over a wide range of signal intensities, it remains unclear how
other parameters affect chemotactic performance, especially when considering
that the swimming behavior of the cell determines the input signal. Using
analytical models and simulations that incorporate recent experimental
evidences about behavioral feedback and flagellar motor adaptation we identify
an operational regime of the pathway that maximizes drift velocity for various
environments and sensor adaptation rates. This optimal regime is outside the
dynamic range of the motor response, but maximizes the contrast between run
duration up and down gradients. In steep gradients, the feedback from
chemotactic drift can push the system through a bifurcation. This creates a
non-chemotactic state that traps cells unless the motor is allowed to adapt.
Although motor adaptation helps, we find that as the strength of the feedback
increases individual phenotypes cannot maintain the optimal operational regime
in all environments, suggesting that diversity could be beneficial.Comment: Corrected one typo. First two authors contributed equally. Notably,
there were various typos in the values of the parameters in the model of
motor adaptation. The results remain unchange
A model for the dynamics of extensible semiflexible polymers
We present a model for semiflexible polymers in Hamiltonian formulation which
interpolates between a Rouse chain and worm-like chain. Both models are
realized as limits for the parameters. The model parameters can also be chosen
to match the experimental force-extension curve for double-stranded DNA. Near
the ground state of the Hamiltonian, the eigenvalues for the longitudinal
(stretching) and the transversal (bending) modes of a chain with N springs,
indexed by p, scale as lambda_lp ~ (p/N)^2 and lambda_tp ~ p^2(p-1)^2/N^4
respectively for small p. We also show that the associated decay times tau_p ~
(N/p)^4 will not be observed if they exceed the orientational time scale tau_r
~ N^3 for an equally-long rigid rod, as the driven decay is then washed out by
diffusive motion.Comment: 28 pages, 2 figure
Synchronization in dynamical networks of locally coupled self-propelled oscillators
Systems of mobile physical entities exchanging information with their
neighborhood can be found in many different situations. The understanding of
their emergent cooperative behaviour has become an important issue across
disciplines, requiring a general conceptual framework in order to harvest the
potential of these systems. We study the synchronization of coupled oscillators
in time-evolving networks defined by the positions of self-propelled agents
interacting in real space. In order to understand the impact of mobility in the
synchronization process on general grounds, we introduce a simple model of
self-propelled hard disks performing persistent random walks in 2 space and
carrying an internal Kuramoto phase oscillator. For non-interacting particles,
self-propulsion accelerates synchronization. The competition between agent
mobility and excluded volume interactions gives rise to a richer scenario,
leading to an optimal self-propulsion speed. We identify two extreme dynamic
regimes where synchronization can be understood from theoretical
considerations. A systematic analysis of our model quantifies the departure
from the latter ideal situations and characterizes the different mechanisms
leading the evolution of the system. We show that the synchronization of
locally coupled mobile oscillators generically proceeds through coarsening
verifying dynamic scaling and sharing strong similarities with the phase
ordering dynamics of the 2 XY model following a quench. Our results shed
light into the generic mechanisms leading the synchronization of mobile agents,
providing a efficient way to understand more complex or specific situations
involving time-dependent networks where synchronization, mobility and excluded
volume are at play
Persistence in nonequilibrium surface growth
Persistence probabilities of the interface height in (1+1)- and
(2+1)-dimensional atomistic, solid-on-solid, stochastic models of surface
growth are studied using kinetic Monte Carlo simulations, with emphasis on
models that belong to the molecular beam epitaxy (MBE) universality class. Both
the initial transient and the long-time steady-state regimes are investigated.
We show that for growth models in the MBE universality class, the nonlinearity
of the underlying dynamical equation is clearly reflected in the difference
between the measured values of the positive and negative persistence exponents
in both transient and steady-state regimes. For the MBE universality class, the
positive and negative persistence exponents in the steady-state are found to be
and ,
respectively, in (1+1) dimensions, and and
, respectively, in (2+1) dimensions. The noise
reduction technique is applied on some of the (1+1)-dimensional models in order
to obtain accurate values of the persistence exponents. We show analytically
that a relation between the steady-state persistence exponent and the dynamic
growth exponent, found earlier to be valid for linear models, should be
satisfied by the smaller of the two steady-state persistence exponents in the
nonlinear models. Our numerical results for the persistence exponents are
consistent with this prediction. We also find that the steady-state persistence
exponents can be obtained from simulations over times that are much shorter
than that required for the interface to reach the steady state. The dependence
of the persistence probability on the system size and the sampling time is
shown to be described by a simple scaling form.Comment: 28 pages, 16 figure
The role of step edge diffusion in epitaxial crystal growth
The role of step edge diffusion (SED) in epitaxial growth is investigated. To
this end we revisit and extend a recently introduced simple cubic
solid-on-solid model, which exhibits the formation and coarsening of pyramid or
mound like structures. By comparing the limiting cases of absent, very fast
(significant), and slow SED we demonstrate how the details of this process
control both the shape of the emerging structures as well as the scaling
behavior. We find a sharp transition from significant SED to intermediate
values of SED, and a continuous one for vanishing SED. We argue that one should
be able to control these features of the surface in experiments by variation of
the flux and substrate temperature.Comment: revised and enlarged version 12 pages, 5 figures, to appear in
Surface Scienc
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