233 research outputs found
Variational Integrators and Generating Functions for Stochastic Hamiltonian Systems
In this work, the stochastic version of the variational principle is established, important for stochastic symplectic integration, and for structure-preserving algorithms of stochastic dynamical systems. Based on it, the stochastic variational integrators in formulation of stochastic Lagrangian functions are proposed, and some applications to symplectic integrations are given. Three types of generating functions in the cases of one and two noises are discussed for constructing new schemes
Effect of Random Parameter Switching on Commensurate Fractional Order Chaotic Systems
This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.The paper explores the effect of random parameter switching in a fractional order (FO) unified chaotic system which captures the dynamics of three popular sub-classes of chaotic systems i.e. Lorenz, Lu and Chen's family of attractors. The disappearance of chaos in such systems which rapidly switch from one family to the other has been investigated here for the commensurate FO scenario. Our simulation study show that a noise-like random variation in the key parameter of the unified chaotic system along with a gradual decrease in the commensurate FO is capable of suppressing the chaotic fluctuations much earlier than that with the fixed parameter one. The chaotic time series produced by such random parameter switching in nonlinear dynamical systems have been characterized using the largest Lyapunov exponent (LLE) and Shannon entropy. The effect of choosing different simulation techniques for random parameter FO switched chaotic systems have also been explored through two frequency domain and three time domain methods. Such a noise-like random switching mechanism could be useful for stabilization and control of chaotic oscillation in many real-world applications
Analysis, simulation and design of nonlinear RF circuits
The PhD project consists of two parts. The first part concerns the development of Computer Aided Design (CAD) algorithms for high-frequency circuits. Novel Padébased
algorithms for numerical integration of ODEs as arise in high-frequency circuits are proposed. Both single- and multi-step methods are introduced. A large part of this
section of the research is concerned with the application of Filon-type integration techniques to circuits subject to modulated signals. Such methods are tested with analog
and digital modulated signals and are seen to be very effective. The results confirm that these methods are more accurate than the traditional trapezoidal rule and Runge-Kutta methods.
The second part of the research is concerned with the analysis, simulation and design of RF circuits with emphasis on injection-locked frequency dividers (ILFD)
and digital delta-sigma modulators (DDSM). Both of these circuits are employed in fractional-N frequency synthesizers. Several simulation methods are proposed to capture the locking range of an ILFD, such as the Warped Multi-time Partial Differential Equation (WaMPDE) and the Multiple-Phase-Condition Envelope Following (MPCENV)
methods. The MPCENV method is the more efficient and accurate simulation technique and it is recommended to obviate the need for expensive experiments. The
Multi-stAge noise Shaping (MASH) digital delta-sigma modulator (DDSM) is simulated in MATLAB and analysed mathematically. A novel structure employing multimoduli,
termed the MM-MASH, is proposed. The goal in this design work is to reduce the noise level in the useful frequency band of the modulator. The success of the novel
structure in achieving this aim is confirmed with simulations
Inference in Nonlinear Systems with Unscented Kalman Filters
An increasing number of scientific disciplines, most notably the life sciences and
health care, have become more quantitative, describing complex systems with coupled nonlinear
di↵erential equations. While powerful algorithms for numerical simulations from these systems
have been developed, statistical inference of the system parameters is still a challenging problem.
A promising approach is based on the unscented Kalman filter (UKF), which has seen
a variety of recent applications, from soft tissue mechanics to chemical kinetics. The present
study investigates the dependence of the accuracy of parameter estimation on the initialisation.
Based on three toy systems that capture typical features of real-world complex systems: limit
cycles, chaotic attractors and intrinsic stochasticity, we carry out repeated simulations on a large
range of independent data instantiations. Our study allows a quantification of the accuracy of
inference, measured in terms of two alternative distance measures in function and parameter
space, in dependence on the initial deviation from the ground truth
Metropolis Integration Schemes for Self-Adjoint Diffusions
We present explicit methods for simulating diffusions whose generator is
self-adjoint with respect to a known (but possibly not normalizable) density.
These methods exploit this property and combine an optimized Runge-Kutta
algorithm with a Metropolis-Hastings Monte-Carlo scheme. The resulting
numerical integration scheme is shown to be weakly accurate at finite noise and
to gain higher order accuracy in the small noise limit. It also permits to
avoid computing explicitly certain terms in the equation, such as the
divergence of the mobility tensor, which can be tedious to calculate. Finally,
the scheme is shown to be ergodic with respect to the exact equilibrium
probability distribution of the diffusion when it exists. These results are
illustrated on several examples including a Brownian dynamics simulation of DNA
in a solvent. In this example, the proposed scheme is able to accurately
compute dynamics at time step sizes that are an order of magnitude (or more)
larger than those permitted with commonly used explicit predictor-corrector
schemes.Comment: 54 pages, 8 figures, To appear in MM
Stochastic quasi-Newton molecular simulations
Article / Letter to editorLeiden Institute of Chemistr
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