3,703 research outputs found
Disturbing effect of free hydrogen on fuel combustion in internal combustion engines
Experiments with fuel mixtures of varying composition, have recently been conducted by the Motor Vehicle and Airplane Engine Testing Laboratories of the Royal Technical High School in Berlin and at Fort Hahneberg, as well as at numerous private engine works. The behavior of hydrogen during combustion in engines and its harmful effect under certain conditions, on the combustion in the engine cylinder are of general interest. Some of the results of these experiments are given here, in order to elucidate the main facts and explain much that is already a matter of experience with chauffeurs and pilots
Laws of large numbers and Langevin approximations for stochastic neural field equations
In this study we consider limit theorems for microscopic stochastic models of
neural fields. We show that the Wilson-Cowan equation can be obtained as the
limit in probability on compacts for a sequence of microscopic models when the
number of neuron populations distributed in space and the number of neurons per
population tend to infinity. Though the latter divergence is not necessary.
This result also allows to obtain limits for qualitatively different stochastic
convergence concepts, e.g., convergence in the mean. Further, we present a
central limit theorem for the martingale part of the microscopic models which,
suitably rescaled, converges to a centered Gaussian process with independent
increments. These two results provide the basis for presenting the neural field
Langevin equation, a stochastic differential equation taking values in a
Hilbert space, which is the infinite-dimensional analogue of the Chemical
Langevin Equation in the present setting. On a technical level we apply
recently developed law of large numbers and central limit theorems for
piecewise deterministic processes taking values in Hilbert spaces to a master
equation formulation of stochastic neuronal network models. These theorems are
valid for processes taking values in Hilbert spaces and by this are able to
incorporate spatial structures of the underlying model.Comment: 38 page
Large Deviations for Nonlocal Stochastic Neural Fields
We study the effect of additive noise on integro-differential neural field
equations. In particular, we analyze an Amari-type model driven by a -Wiener
process and focus on noise-induced transitions and escape. We argue that
proving a sharp Kramers' law for neural fields poses substanial difficulties
but that one may transfer techniques from stochastic partial differential
equations to establish a large deviation principle (LDP). Then we demonstrate
that an efficient finite-dimensional approximation of the stochastic neural
field equation can be achieved using a Galerkin method and that the resulting
finite-dimensional rate function for the LDP can have a multi-scale structure
in certain cases. These results form the starting point for an efficient
practical computation of the LDP. Our approach also provides the technical
basis for further rigorous study of noise-induced transitions in neural fields
based on Galerkin approximations.Comment: 29 page
Two-Dimensional Lattice Gravity as a Spin System
Quantum gravity is studied in the path integral formulation applying the
Regge calculus. Restricting the quadratic link lengths of the originally
triangular lattice the path integral can be transformed to the partition
function of a spin system with higher couplings on a Kagome lattice. Various
measures acting as external field are considered. Extensions to matter fields
and higher dimensions are discussed.Comment: 3 pages, uuencoded postscript file; Proceedings of the 2nd IMACS
Conference on Computational Physics, St. Louis, Oct. 199
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