12,198 research outputs found
Deformed SPDE models with an application to spatial modeling of significant wave height
A non-stationary Gaussian random field model is developed based on a
combination of the stochastic partial differential equation (SPDE) approach and
the classical deformation method. With the deformation method, a stationary
field is defined on a domain which is deformed so that the field becomes
non-stationary. We show that if the stationary field is a Mat'ern field defined
as a solution to a fractional SPDE, the resulting non-stationary model can be
represented as the solution to another fractional SPDE on the deformed domain.
By defining the model in this way, the computational advantages of the SPDE
approach can be combined with the deformation method's more intuitive
parameterisation of non-stationarity. In particular it allows for independent
control over the non-stationary practical correlation range and the variance,
which has not been possible with previously proposed non-stationary SPDE
models.
The model is tested on spatial data of significant wave height, a
characteristic of ocean surface conditions which is important when estimating
the wear and risks associated with a planned journey of a ship. The model
parameters are estimated to data from the north Atlantic using a maximum
likelihood approach. The fitted model is used to compute wave height exceedance
probabilities and the distribution of accumulated fatigue damage for ships
traveling a popular shipping route. The model results agree well with the data,
indicating that the model could be used for route optimization in naval
logistics.Comment: 22 pages, 12 figure
Stability of Travelling Waves for Reaction-Diffusion Equations with Multiplicative Noise
We consider reaction-diffusion equations that are stochastically forced by a
small multiplicative noise term. We show that spectrally stable travelling wave
solutions to the deterministic system retain their orbital stability if the
amplitude of the noise is sufficiently small.
By applying a stochastic phase-shift together with a time-transform, we
obtain a semilinear sPDE that describes the fluctuations from the primary wave.
We subsequently develop a semigroup approach to handle the nonlinear stability
question in a fashion that is closely related to modern deterministic methods
A Stochastic Compartmental Model for Fast Axonal Transport
In this paper we develop a probabilistic micro-scale compartmental model and
use it to study macro-scale properties of axonal transport, the process by
which intracellular cargo is moved in the axons of neurons. By directly
modeling the smallest scale interactions, we can use recent microscopic
experimental observations to infer all the parameters of the model. Then, using
techniques from probability theory, we compute asymptotic limits of the
stochastic behavior of individual motor-cargo complexes, while also
characterizing both equilibrium and non-equilibrium ensemble behavior. We use
these results in order to investigate three important biological questions: (1)
How homogeneous are axons at stochastic equilibrium? (2) How quickly can axons
return to stochastic equilibrium after large local perturbations? (3) How is
our understanding of delivery time to a depleted target region changed by
taking the whole cell point-of-view
The contribution of statistical physics to evolutionary biology
Evolutionary biology shares many concepts with statistical physics: both deal
with populations, whether of molecules or organisms, and both seek to simplify
evolution in very many dimensions. Often, methodologies have undergone parallel
and independent development, as with stochastic methods in population genetics.
We discuss aspects of population genetics that have embraced methods from
physics: amongst others, non-equilibrium statistical mechanics, travelling
waves, and Monte-Carlo methods have been used to study polygenic evolution,
rates of adaptation, and range expansions. These applications indicate that
evolutionary biology can further benefit from interactions with other areas of
statistical physics, for example, by following the distribution of paths taken
by a population through time.Comment: 18 pages, 3 figures, glossary. Accepted in Trend in Ecology and
Evolution (to appear in print in August 2011
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