41,652 research outputs found
Nonlinear analysis of pressure oscillations in ramjet engines
Pressure oscillations in ramjet engines have been studied using an approximate method which treats the flow fields in the inlet and the combustor separately. The acoustic fields in the combustor are expressed as syntheses of coupled nonlinear oscillators corresponding to the acoustic modes of the chamber. The influences of the inlet flow appear in the admittance function at the inlet /combustor interface, providing the necessary boundary condition for calculation of the combustor flow. A general framework dealing with nonlinear multi-degree-of-freedom system has also been constructed to study the time evolution of each mode. Both linear and nonlinear stabilities are treated. The results obtained serve as a basis for investigating the existence and stabilities of limit cycles for acoustic modes. As a specific example, the analysis is applied to a problem of nonlinear transverse oscillations in ramjet engines
Particle filtering in high-dimensional chaotic systems
We present an efficient particle filtering algorithm for multiscale systems,
that is adapted for simple atmospheric dynamics models which are inherently
chaotic. Particle filters represent the posterior conditional distribution of
the state variables by a collection of particles, which evolves and adapts
recursively as new information becomes available. The difference between the
estimated state and the true state of the system constitutes the error in
specifying or forecasting the state, which is amplified in chaotic systems that
have a number of positive Lyapunov exponents. The purpose of the present paper
is to show that the homogenization method developed in Imkeller et al. (2011),
which is applicable to high dimensional multi-scale filtering problems, along
with important sampling and control methods can be used as a basic and flexible
tool for the construction of the proposal density inherent in particle
filtering. Finally, we apply the general homogenized particle filtering
algorithm developed here to the Lorenz'96 atmospheric model that mimics
mid-latitude atmospheric dynamics with microscopic convective processes.Comment: 28 pages, 12 figure
Non-averaged regularized formulations as an alternative to semi-analytical orbit propagation methods
This paper is concerned with the comparison of semi-analytical and
non-averaged propagation methods for Earth satellite orbits. We analyse the
total integration error for semi-analytical methods and propose a novel
decomposition into dynamical, model truncation, short-periodic, and numerical
error components. The first three are attributable to distinct approximations
required by the method of averaging, which fundamentally limit the attainable
accuracy. In contrast, numerical error, the only component present in
non-averaged methods, can be significantly mitigated by employing adaptive
numerical algorithms and regularized formulations of the equations of motion.
We present a collection of non-averaged methods based on the integration of
existing regularized formulations of the equations of motion through an
adaptive solver. We implemented the collection in the orbit propagation code
THALASSA, which we make publicly available, and we compared the non-averaged
methods to the semi-analytical method implemented in the orbit propagation tool
STELA through numerical tests involving long-term propagations (on the order of
decades) of LEO, GTO, and high-altitude HEO orbits. For the test cases
considered, regularized non-averaged methods were found to be up to two times
slower than semi-analytical for the LEO orbit, to have comparable speed for the
GTO, and to be ten times as fast for the HEO (for the same accuracy). We show
for the first time that efficient implementations of non-averaged regularized
formulations of the equations of motion, and especially of non-singular element
methods, are attractive candidates for the long-term study of high-altitude and
highly elliptical Earth satellite orbits.Comment: 33 pages, 10 figures, 7 tables. Part of the CMDA Topical Collection
on "50 years of Celestial Mechanics and Dynamical Astronomy". Comments and
feedback are encourage
A universal model for spike-frequency adaptation
Spike-frequency adaptation is a prominent feature of neural dynamics. Among other mechanisms, various ionic currents modulating spike generation cause this type of neural adaptation. Prominent examples are voltage-gated potassium currents (M-type currents), the interplay of calcium currents and intracellular calcium dynamics with calcium-gated potassium channels (AHP-type currents), and the slow recovery from inactivation of the fast sodium current. While recent modeling studies have focused on the effects of specific adaptation currents, we derive a universal model for the firing-frequency dynamics of an adapting neuron that is independent of the specific adaptation process and spike generator. The model is completely defined by the neuron's onset f-I curve, the steady-state f-I curve, and the time constant of adaptation. For a specific neuron, these parameters can be easily determined from electrophysiological measurements without any pharmacological manipulations. At the same time, the simplicity of the model allows one to analyze mathematically how adaptation influences signal processing on the single-neuron level. In particular, we elucidate the specific nature of high-pass filter properties caused by spike-frequency adaptation. The model is limited to firing frequencies higher than the reciprocal adaptation time constant and to moderate fluctuations of the adaptation and the input current. As an extension of the model, we introduce a framework for combining an arbitrary spike generator with a generalized adaptation current
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