1,313 research outputs found
Relating quanta conservation and compartmental epidemiological models of airborne disease outbreaks in buildings
We investigate the underlying assumptions and limits of applicability of several documented models for outbreaks of airborne disease inside buildings by showing how they may each be regarded as special cases of a system of equations which combines quanta conservation and compartmental epidemiological modelling. We investigate the behaviour of this system analytically, gaining insight to its behaviour at large time. We then investigate the characteristic timescales of an indoor outbreak, showing how the dilution rate of the space, and the quanta generation rate, incubation rate and removal rate associated with the illness may be used to predict the evolution of an outbreak over time, and may also be used to predict the relative performances of other indoor airborne outbreak models. The model is compared to a more commonly used model, in which it is assumed the environmental concentration of infectious aerosols adheres to a quasi-steady-state, so that the the dimensionless quanta concentration is equal to the the infectious fraction. The model presented here is shown to approach this limit exponentially to within an interval defined by the incubation and removal rates. This may be used to predict the maximum extent to which a case will deviate from the quasi steady state condition
Rate- and State-Dependent Friction Law and Statistical Properties of Earthquakes
In order to clarify how the statistical properties of earthquakes depend on
the constitutive law characterizing the stick-slip dynamics, we make an
extensive numerical simulation of the one-dimensional spring-block model with
the rate- and state-dependent friction law. Both the magnitude distribution and
the recurrence-time distribution are studied with varying the constitutive
parameters characterizing the model. While a continuous spectrum of seismic
events from smaller to larger magnitudes is obtained, earthquakes described by
this model turn out to possess pronounced ``characteristic'' features.Comment: Minor revisions are made in the text and in the figures. Accepted for
publication in Europhys. Letter
Network of recurrent events for the Olami-Feder-Christensen model
We numerically study the dynamics of a discrete spring-block model introduced
by Olami, Feder and Christensen (OFC) to mimic earthquakes and investigate to
which extent this simple model is able to reproduce the observed spatiotemporal
clustering of seismicty. Following a recently proposed method to characterize
such clustering by networks of recurrent events [Geophys. Res. Lett. {\bf 33},
L1304, 2006], we find that for synthetic catalogs generated by the OFC model
these networks have many non-trivial statistical properties. This includes
characteristic degree distributions -- very similar to what has been observed
for real seismicity. There are, however, also significant differences between
the OFC model and earthquake catalogs indicating that this simple model is
insufficient to account for certain aspects of the spatiotemporal clustering of
seismicity.Comment: 11 pages, 16 figure
Functional Electrical Stimulation mediated by Iterative Learning Control and 3D robotics reduces motor impairment in chronic stroke
Background: Novel stroke rehabilitation techniques that employ electrical stimulation (ES) and robotic technologies are effective in reducing upper limb impairments. ES is most effective when it is applied to support the patients’ voluntary effort; however, current systems fail to fully exploit this connection. This study builds on previous work using advanced ES controllers, and aims to investigate the feasibility of Stimulation Assistance through Iterative Learning (SAIL), a novel upper limb stroke rehabilitation system which utilises robotic support, ES, and voluntary effort. Methods: Five hemiparetic, chronic stroke participants with impaired upper limb function attended 18, 1 hour intervention sessions. Participants completed virtual reality tracking tasks whereby they moved their impaired arm to follow a slowly moving sphere along a specified trajectory. To do this, the participants’ arm was supported by a robot. ES, mediated by advanced iterative learning control (ILC) algorithms, was applied to the triceps and anterior deltoid muscles. Each movement was repeated 6 times and ILC adjusted the amount of stimulation applied on each trial to improve accuracy and maximise voluntary effort. Participants completed clinical assessments (Fugl-Meyer, Action Research Arm Test) at baseline and post-intervention, as well as unassisted tracking tasks at the beginning and end of each intervention session. Data were analysed using t-tests and linear regression. Results: From baseline to post-intervention, Fugl-Meyer scores improved, assisted and unassisted tracking performance improved, and the amount of ES required to assist tracking reduced. Conclusions: The concept of minimising support from ES using ILC algorithms was demonstrated. The positive results are promising with respect to reducing upper limb impairments following stroke, however, a larger study is required to confirm this
Stick-Slip Motion and Phase Transition in a Block-Spring System
We study numerically stick slip motions in a model of blocks and springs
being pulled slowly. The sliding friction is assumed to change dynamically with
a state variable. The transition from steady sliding to stick-slip is
subcritical in a single block and spring system. However, we find that the
transition is continuous in a long chain of blocks and springs. The size
distribution of stick-slip motions exhibits a power law at the critical point.Comment: 8 figure
Simulation study of spatio-temporal correlations of earthquakes as a stick-slip frictional instability
Spatio-temporal correlations of earthquakes are studied numerically on the
basis of the one-dimensional spring-block (Burridge-Knopoff) model. As large
events approach, the frequency of smaller events gradually increases, while,
just before the mainshock, it is dramatically suppressed in a close vicinity of
the epicenter of the upcoming mainshock, a phenomenon closely resembling the
``Mogi doughnut'
Dynamics of Elastic Excitable Media
The Burridge-Knopoff model of earthquake faults with viscous friction is
equivalent to a van der Pol-FitzHugh-Nagumo model for excitable media with
elastic coupling. The lubricated creep-slip friction law we use in the
Burridge-Knopoff model describes the frictional sliding dynamics of a range of
real materials. Low-dimensional structures including synchronized oscillations
and propagating fronts are dominant, in agreement with the results of
laboratory friction experiments. Here we explore the dynamics of fronts in
elastic excitable media.Comment: Int. J. Bifurcation and Chaos, to appear (1999
Near mean-field behavior in the generalized Burridge-Knopoff earthquake model with variable range stress transfer
Simple models of earthquake faults are important for understanding the
mechanisms for their observed behavior in nature, such as Gutenberg-Richter
scaling. Because of the importance of long-range interactions in an elastic
medium, we generalize the Burridge-Knopoff slider-block model to include
variable range stress transfer. We find that the Burridge-Knopoff model with
long-range stress transfer exhibits qualitatively different behavior than the
corresponding long-range cellular automata models and the usual
Burridge-Knopoff model with nearest-neighbor stress transfer, depending on how
quickly the friction force weakens with increasing velocity. Extensive
simulations of quasiperiodic characteristic events, mode-switching phenomena,
ergodicity, and waiting-time distributions are also discussed. Our results are
consistent with the existence of a mean-field critical point and have important
implications for our understanding of earthquakes and other driven dissipative
systems.Comment: 24 pages 12 figures, revised version for Phys. Rev.
Scaling and Correlation Functions in a Model of a Two-dimensional Earthquake Fault
We study numerically a two-dimensional version of the Burrige-Knopoff model.
We calculate spatial and temporal correlation functions and compare their
behavior with the results found for the one-dimensional model. The
Gutenberg-Richter law is only obtained for special choices of parameters in the
relaxation function. We find that the distribution of the fractal dimension of
the slip zone exhibits two well-defined peaks coeersponding to intermediate
size and large events.Comment: 14 pages, 23 Postscript figure
Self-Similarity of Friction Laws
The change of the friction law from a mesoscopic level to a macroscopic level
is studied in the spring-block models introduced by Burridge-Knopoff. We find
that the Coulomb law is always scale invariant. Other proposed scaling laws are
only invariant under certain conditions.}Comment: Plain TEX. Figures not include
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