11,638 research outputs found
Synchronization of Coupled Boolean Phase Oscillators
We design, characterize, and couple Boolean phase oscillators that include
state-dependent feedback delay. The state-dependent delay allows us to realize
an adjustable coupling strength, even though only Boolean signals are
exchanged. Specifically, increasing the coupling strength via the range of
state-dependent delay leads to larger locking ranges in uni- and bi-directional
coupling of oscillators in both experiment and numerical simulation with a
piecewise switching model. In the unidirectional coupling scheme, we unveil
asymmetric triangular-shaped locking regions (Arnold tongues) that appear at
multiples of the natural frequency of the oscillators. This extends
observations of a single locking region reported in previous studies. In the
bidirectional coupling scheme, we map out a symmetric locking region in the
parameter space of frequency detuning and coupling strength. Because of large
scalability of our setup, our observations constitute a first step towards
realizing large-scale networks of coupled oscillators to address fundamental
questions on the dynamical properties of networks in a new experimental
setting.Comment: 8 pages, 8 figure
Computational modelling and experimental characterisation of heterogeneous materials
Heterogeneous materials can exhibit behaviour under load that cannot be described by classical continuum elasticity. Beams in bending can show a relative stiffening as the beam depth tends to zero, a size effect. Size effects are recognised in higher order continuum elastic theories such as micropolar elasticity. The drawback of higher order theories is the requirement of addition constitutive relations and associated properties that are often difficult to establish experimentally. Furthermore the finite element method, of great benefit in classical elasticity, has shown limitations when applied to micropolar elasticity. The determination of additional constitutive properties and the computational modelling of micropolar elasticity will be discussed in the context of a model heterogeneous material loaded in simple 3 point bending. The model material was created by drilling holes in aluminium bar in a regular pattern, with the hole axis normal to the plane of bending. The bending tests show that a size effect is present. These results are compared against modelling the detailed beam geometries in the finite element package ANSYS, which again shows the size effect. These two bending test are used to extract the additional micropolar elastic material properties. A comparison is then made against analytical solutions,numerical solutions using a micropolar beam finite element and a micropolar plane stress control volume method.It will be shown that the need for extensive experimental testing to determine the additional constitutive properties may not be necessary with the appropriate use of numerical methods
High-gain nonlinear observer for simple genetic regulation process
High-gain nonlinear observers occur in the nonlinear automatic control theory
and are in standard usage in chemical engineering processes. We apply such a
type of analysis in the context of a very simple one-gene regulation circuit.
In general, an observer combines an analytical differential-equation-based
model with partial measurement of the system in order to estimate the
non-measured state variables. We use one of the simplest observers, that of
Gauthier et al., which is a copy of the original system plus a correction term
which is easy to calculate. For the illustration of this procedure, we employ a
biological model, recently adapted from Goodwin's old book by De Jong, in which
one plays with the dynamics of the concentrations of the messenger RNA coding
for a given protein, the protein itself, and a single metabolite. Using the
observer instead of the metabolite, it is possible to rebuild the non-measured
concentrations of the mRNA and the proteinComment: 9 pages, one figur
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