Refine
Has Fulltext
- no (32)
Year of publication
Document Type
- Article (32) (remove)
Language
- English (32) (remove)
Is part of the Bibliography
- yes (32)
Keywords
- Genetic programming (3)
- Dynamical systems (2)
- Hydraulic models (2)
- Hydraulic networks (2)
- Maximum entropy method (2)
- Pipe networks (2)
- Probability (2)
- Synchronization control (2)
- Water distribution systems (2)
- Active flow control (1)
We investigate localized periodic solutions (breathers) in a lattice of parametrically driven, nonlinear dissipative oscillators. These breathers are demonstrated to be exponentially localized, with two characteristic localization lengths. The crossover between the two lengths is shown to be related to the transition in the phase of the lattice oscillations.
We prove the existence of nonlinear localized time-periodic solutions in a chain of symplectic mappings with nearest neighbour coupling. This is a class of systems whose behaviour can be seen as representation of a lattice of pendula. The effect of discrete time changes the mathematical as well as the numerical procedures. Applying the discrete version of Floquet theory eases and clarifies the procedure of proving the existence of the localized time-periodic solutions. As an extension of the concept of rotobreathers one can produce solutions which rotate at every site of the lattice. To consider these we use a general definition of localization.
We study spatially localized excitations in a lattice of coupled standard maps. Time-periodic solutions (breathers) exist in a range of coupling that is shown to shrink as the period grows to infinity, thus excluding the possibility of time-quasiperiodic breathers. The evolution of initially localized chaotic and quasiperiodic states in a lattice is studied numerically. Chaos is demonstrated to spread
The Problem of front propagation in flowing media is addressed for laminar velocity fields in two dimensions. Three representative cases are discussed: stationary cellular flow, stationary shear flow, and percolating flow. Production terms of Fisher-Kolmogorov-Petrovskii-Piskunov type and of Arrhenius type are considered under the assumption of no feedback of the concentration on the velocity. Numerical simulations of advection-reaction-diffusion equations have been performed by an algorithm based on discrete-time maps. The results show a generic enhancement of the speed of front propagation by the underlying flow. For small molecular diffusivity, the front speed <i>V<sub><i>f</sub> depends on the typical flow velocity <i>U as<sup> </sup>a power law with an exponent depending on the topological properties of the flow, and on the ratio of reactive and advective time scales. For open-streamline flows we find always<sup> </sup><i>V<sub><i>f</sub>~<i>U, whereas for cellular flows we observe <i>V<sub><i>f</ sub>~<i>U<sup>1/4</sup> for fast advection and <i>V<sub><i>f</sub>~<i>U<sup>3/4</sup> for slow advection.
Vortex ripples in sand are studied experimentally in a one-dimensional setup with periodic boundary conditions. The nonlinear evolution, far from the onset of instability, is analyzed in the framework of a simple model developed for homogeneous patterns. The interaction function describing the mass transport between neighboring ripples is extracted from experimental runs using a recently proposed method for data analysis, and the predictions of the model are compared to the experiment. An analytic explanation of the wavelength selection mechanism in the model is provided, and the width of the stable band of ripples is measured.
This article describes how to use statistical data analysis to obtain models directly from data. The focus is put on finding nonlinearities within a generalized additive model. These models are found by means of backfitting or more general algorithms, like the alternating conditional expectation value one. The method is illustrated by numerically generated data. As an application, the example of vortex ripple dynamics, a highly complex fluid-granular system, is treated
We develop a theory describing the transition to a spatially homogeneous regime in a mixing flow with a chaotic in time reaction. The transverse Lyapunov exponent governing the stability of the homogeneous state can be represented as a combination of Lyapunov exponents for spatial mixing and temporal chaos. This representation, being exact for time- independent flows and equal Peclet numbers of different components, is demonstrated to work accurately for time- dependent flows and different Peclet numbers
We present a nonparametric way to retrieve an additive system of differential equations in embedding space from a single time series. These equations can be treated with dynamical systems theory and allow for long-term predictions. We apply our method to a modified chaotic Chua oscillator in order to demonstrate its potential
A key technology for large eddy simulation (LES) of complex flows is an appropriate wall modeling strategy. In this paper we apply for the first time a fully nonparametric procedure for the estimation of generalized additive models (GAM) by conditional statistics. As a database, we use DNS and wall-resolved LES data of plane channel flow for Reynolds numbers, Re = 2800, 4000 (DNS) and 10,935, 22,776 (LES). The statistical method applied is a quantitative tool for the identification of important model terms, allowing for an identification of some of the near-wall physics. The results are given as nonparametric functions which cannot be attained by other methods. We investigated a generalized model which includes Schumann's and Piomelli et al.'s model. A strong influence of the pressure gradient in the viscous sublayer is found; for larger wall distances the spanwise pressure gradient even dominates the tau(w,zy). component. The first a posteriori LES results are given.
We report measurements on the synchronization properties of organ pipes. First, we investigate influence of an external acoustical signal from a loudspeaker on the sound of an organ pipe. Second, the mutual influence of two pipes with different pitch is analyzed. In analogy to the externally driven, or mutually coupled self-sustained oscillators, one observes a frequency locking, which can be explained by synchronization theory. Further, we measure the dependence of the frequency of the signals emitted by two mutually detuned pipes with varying distance between the pipes. The spectrum shows a broad '' hump '' structure, not found for coupled oscillators. This indicates a complex coupling of the two organ pipes leading to nonlinear beat phenomena.
Wave energy harvesting could be a substantial renewable energy source without impact on the global climate and ecology, yet practical attempts have struggled with the problems of wear and catastrophic failure. An innovative technology for ocean wave energy harvesting was recently proposed, based on the use of soft capacitors. This study presents a realistic theoretical and numerical model for the quantitative characterization of this harvesting method. Parameter regions with optimal behavior are found, and novel material descriptors are determined, which dramatically simplify analysis. The characteristics of currently available materials are evaluated, and found to merit a very conservative estimate of 10 years for raw material cost recovery.
Characterization and calibration of piezoelectric polymers in situ measurements of body vibrations
(2011)
Piezoelectric polymers are known for their flexibility in applications, mainly due to their bending ability, robustness, and variable sensor geometry. It is an optimal material for minimal-invasive investigations in vibrational systems, e.g., for wood, where acoustical impedance matches particularly well. Many applications may be imagined, e. g., monitoring of buildings, vehicles, machinery, alarm systems, such that our investigations may have a large impact on technology. Longitudinal piezoelectricity converts mechanical vibrations normal to the polymer-film plane into an electrical signal, and the respective piezoelectric coefficient needs to be carefully determined in dependence on the relevant material parameters. In order to evaluate efficiency and durability for piezopolymers, we use polyvinylidene fluoride and measure the piezoelectric coefficient with respect to static pressure, amplitude of the dynamically applied force, and long-term stability. A known problem is the slow relaxation of the material towards equilibrium, if the external pressure changes; here, we demonstrate how to counter this problem with careful calibration. Since our focus is on acoustical measurements, we determine accurately the frequency response curve - for acoustics probably the most important characteristic. Eventually, we show that our piezopolymer transducers can be used as a calibrated acoustical sensors for body vibration measurements on a wooden musical instrument, where it is important to perform minimal-invasive measurements. A comparison with the simultaneously recorded airborne sound yields important insight of the mechanism of sound radiation in comparison with the sound propagating in the material. This is especially important for transient signals, where not only the long-living eigenmodes contribute to the sound radiation. Our analyses support that piezopolymer sensors can be employed as a general tool for the determination of the internal dynamics of vibrating systems.
Ordinary differential equations (ODEs) have been studied for centuries as a means to model complex dynamical processes from the real world. Nevertheless, their application to sound synthesis has not yet been fully exploited. In this article we present a systematic approach to sound synthesis based on first-order complex and real ODEs. Using simple time-dependent and nonlinear terms, we illustrate the mapping between ODE coefficients and physically meaningful control parameters such as pitch, pitch bend, decay rate, and attack time. We reveal the connection between nonlinear coupling terms and frequency modulation, and we discuss the implications of this scheme in connection with nonlinear synthesis. The ability to excite a first-order complex ODE with an external input signal is also examined; stochastic or impulsive signals that are physically or synthetically produced can be presented as input to the system, offering additional synthesis possibilities, such as those found in excitation/filter synthesis and filter-based modal synthesis.
Small- and large-scale characterization and mixing properties in a thermally driven thin liquid film
(2015)
We study aqueous, freestanding, thin films stabilized by a surfactant with respect to mixing and dynamical systems properties. With this special setup, a two-dimensional fluid can be realized experimentally. The physics of the system involves a complex interplay of thermal convection and interface and gravitational forces. Methodologically, we characterize the system using two classical dynamical systems properties: Lyapunov exponents and entropies. Our experimental setup produces convection with two stable eddies by applying a temperature gradient in one spot that yields weakly turbulent mixing. From dynamical systems theory, one expects a relation of entropies, Lyapunov exponents, a prediction with little experimental support. We can confirm the corresponding statements experimentally, on different scales using different methods. On the small scale the motion and deformation of fluid filaments of equal size (color imaging velocimetry) are used to compute Lyapunov exponents. On the large scale, entropy is computed by tracking the left-right motion of the center fluid jet at the separatrix between the two convection rolls. We thus combine here dynamical systems methods with a concrete application of mixing in a nanoscale freestanding thin film.