308 research outputs found
Self Organization and Self Avoiding Limit Cycles
A simple periodically driven system displaying rich behavior is introduced
and studied. The system self-organizes into a mosaic of static ordered regions
with three possible patterns, which are threaded by one-dimensional paths on
which a small number of mobile particles travel. These trajectories are
self-avoiding and non-intersecting, and their relationship to self-avoiding
random walks is explored. Near the distribution of path lengths
becomes power-law like up to some cutoff length, suggesting a possible critical
state
An Extended Kalman Filter with a Computed Mean Square Error Bound
The paper proposes a new recursive filter for non-linear systems that
inherently computes a valid bound on the mean square estimation error. The
proposed filter, bound based extended Kalman, (BEKF) is in the form of an
extended Kalman filter. The main difference of the proposed filter from the
conventional extended Kalman filter is in the use of a computed mean square
error bound matrix, to calculate the filter gain, and to serve as bound on the
actual mean square error. The paper shows that when the system is linear the
proposed filtering algorithm reduces to the conventional Kalman filter. The
theory presented in the paper is applicable to a wide class of systems, but if
the system is polynomial, then the recently developed theory of positive
polynomials considerably simplifies the filter's implementation.Comment: 7 pages, 1 figur
Tug-of-war in motility assay experiments
The dynamics of two groups of molecular motors pulling in opposite directions
on a rigid filament is studied theoretically. To this end we first consider the
behavior of one set of motors pulling in a single direction against an external
force using a new mean-field approach. Based on these results we analyze a
similar setup with two sets of motors pulling in opposite directions in a
tug-of-war in the presence of an external force. In both cases we find that the
interplay of fluid friction and protein friction leads to a complex phase
diagram where the force-velocity relations can exhibit regions of bistability
and spontaneous symmetry breaking. Finally, motivated by recent work, we turn
to the case of motility assay experiments where motors bound to a surface push
on a bundle of filaments. We find that, depending on the absence or the
presence of a bistability in the force-velocity curve at zero force, the bundle
exhibits anomalous or biased diffusion on long-time and large-length scales
Periodic training of creeping solids
We consider disordered solids in which the microscopic elements can deform
plastically in response to stresses on them. We show that by driving the system
periodically, this plasticity can be exploited to train in desired elastic
properties, both in the global moduli and in local "allosteric" interactions.
Periodic driving can couple an applied "source" strain to a target strain over
a path in the energy landscape. This coupling allows control of the system's
response even at large strains well into the nonlinear regime, where it can be
difficult to achieve control simply by design
- …