21,782 research outputs found
Hybrid binomial Langevin-multiple mapping conditioning modeling of a reacting mixing layer
A novel, stochastic, hybrid binomial Langevin-multiple mapping conditioning (MMC) model—that utilizes the strengths of each component—has been developed for inhomogeneous flows. The implementation has the advantage of naturally incorporating velocity-scalar interactions through the binomial Langevin model and using this joint probability density function (PDF) to define a reference variable for the MMC part of the model. The approach has the advantage that the difficulties encountered with the binomial Langevin model in modeling scalars with nonelementary bounds are removed. The formulation of the closure leads to locality in scalar space and permits the use of simple approaches (e.g., the modified Curl’s model) for transport in the reference space. The overall closure was evaluated through application to a chemically reacting mixing layer. The results show encouraging comparisons with experimental data for the first two moments of the PDF and plausible results for higher moments at a relatively modest computational cost
Algebraic Structures and Stochastic Differential Equations driven by Levy processes
We construct an efficient integrator for stochastic differential systems
driven by Levy processes. An efficient integrator is a strong approximation
that is more accurate than the corresponding stochastic Taylor approximation,
to all orders and independent of the governing vector fields. This holds
provided the driving processes possess moments of all orders and the vector
fields are sufficiently smooth. Moreover the efficient integrator in question
is optimal within a broad class of perturbations for half-integer global root
mean-square orders of convergence. We obtain these results using the
quasi-shuffle algebra of multiple iterated integrals of independent Levy
processes.Comment: 41 pages, 11 figure
The theory of stochastic cosmological lensing
On the scale of the light beams subtended by small sources, e.g. supernovae,
matter cannot be accurately described as a fluid, which questions the
applicability of standard cosmic lensing to those cases. In this article, we
propose a new formalism to deal with small-scale lensing as a diffusion
process: the Sachs and Jacobi equations governing the propagation of narrow
light beams are treated as Langevin equations. We derive the associated
Fokker-Planck-Kolmogorov equations, and use them to deduce general analytical
results on the mean and dispersion of the angular distance. This formalism is
applied to random Einstein-Straus Swiss-cheese models, allowing us to: (1) show
an explicit example of the involved calculations; (2) check the validity of the
method against both ray-tracing simulations and direct numerical integrations
of the Langevin equation. As a byproduct, we obtain a
post-Kantowski-Dyer-Roeder approximation, accounting for the effect of tidal
distortions on the angular distance, in excellent agreement with numerical
results. Besides, the dispersion of the angular distance is correctly
reproduced in some regimes.Comment: 37+13 pages, 8 figures. A few typos corrected. Matches published
versio
Integration of continuous-time dynamics in a spiking neural network simulator
Contemporary modeling approaches to the dynamics of neural networks consider
two main classes of models: biologically grounded spiking neurons and
functionally inspired rate-based units. The unified simulation framework
presented here supports the combination of the two for multi-scale modeling
approaches, the quantitative validation of mean-field approaches by spiking
network simulations, and an increase in reliability by usage of the same
simulation code and the same network model specifications for both model
classes. While most efficient spiking simulations rely on the communication of
discrete events, rate models require time-continuous interactions between
neurons. Exploiting the conceptual similarity to the inclusion of gap junctions
in spiking network simulations, we arrive at a reference implementation of
instantaneous and delayed interactions between rate-based models in a spiking
network simulator. The separation of rate dynamics from the general connection
and communication infrastructure ensures flexibility of the framework. We
further demonstrate the broad applicability of the framework by considering
various examples from the literature ranging from random networks to neural
field models. The study provides the prerequisite for interactions between
rate-based and spiking models in a joint simulation
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