Dynamics of freely falling perforated disks

The primary goal of this research is to better understand the dynamics of non-spherical particles in turbulence. This includes their preferential alignment with ow structures and their rotations in response to the velocity gradients of the ow or external forces, or both. We perform experimental measurements to study the dynamics of neutrally buoyant fibers and complex-shaped particles, and heavy, ramified particles as they sediment under the influence of gravity and turbulence.\nIn 3D homogeneous, isotropic turbulence, we measure the translational and rotational dynamics of small fibers while simultaneously resolving the fluid velocity field around the particles for the first time in experiments. To fully determine the dynamics of fibers in turbulence, it is required to specify a seven-dimensional joint probability density function of five scalars characterizing the velocity gradient tensor and two scalars describing the relative orientation of the fiber. We look at a lower-dimensional projection to simplify the problem and explore conditional averages. The preferential alignment of fibers with the velocity gradient tensor is observed and is in good agreement with direct numerical simulations.\nThe preferential alignment of elongated particles inspired us to design functionalized particles that show a preferential rotation in 3D homogeneous isotropic turbulence. We use 3D printing to fabricate so-called chiral dipoles, a rod with two helices of opposite handedness at either end. High aspect ratio chiral dipoles preferentially align with the extensional stretching field where the helical ends couple to the ow which results in a preferential rotation of the particle. These particles can be used to measure the rate at which fluid elements are stretched, one of the fundamental processes responsible for the energy cascade in turbulent flows.\nThe preferential alignment of non-spherical particles not only depends on particle shape, but also on the density difference between the particles and the fluid. To study the dynamics of heavy, non-spherical particles, we built a new apparatus that allows us to keep particles suspended and independently control the amount of turbulence they experience. We measure orientation distributions of ramified particles, quantify the dependence on turbulence intensity and look at preferential alignment. Moreover, we study the sedimentation and rotation rates and show that under certain conditions, a simple model is sufficient to capture most of the physics.

A novel approach for natural frequency hallow shift calculation using non contact impulse method

This work presents a closed-loop guidance algorithm for six-degrees of freedom spacecraft rendezvous with a passive target flying in an eccentric orbit. The main assumption is that the chaser vehicle has an attitude control system, based on reaction wheels, providing the necessary torque to change its orientation whereas the number of thrusters is arbitrary. The goal is to design fuel optimal maneuvers while satisfying operational constraints and rejecting disturbances. The proposed method is as follows; first, the coupled translational and angular dynamics are transformed to equivalent algebraic relations using the relative translational states transition matrix and the attitude flatness property. Then, a direct transcription method, based on B-splines parameterization and discretization of time continuous constraints, is developed to obtain a tractable static program. Finally, a Model Predictive Controller, based on linearization around the previously computed solution, is considered to handle disturbances. Numerical results are shown and discussed.

In the 1966 Kampe de Fernet suggested to study the dynamical of turbulence through Gram-Charlier expansion. The Gram-Charlier expansion allows to approximate a probability densities function throught a series expansions involving the normal density and its derivatives. In this work a modified formulation of Gram-Charlier expansion is applied to estimate the probability density function of vertical wind velocity. The theoretical progress consists of a new choice of the parameters of the Gaussian density (standard deviation and the mean values) that appears in the expansion. In fact in the classic Gram-Charlier expansion the random variable is standardized and the Gaussian parameters are equal to zero and one. This assumption is sometimes too restrictive and abetter performance can be obtained changing the parameters values. The probability density function of vertical wind velocity is calculated from an experimental parametrization of moments, using as input data the first three moments. These moments are function of the dimensionless ratio (Z/Zi) and atmospheric stability, represented by the ratio U*/W* (where U* is the friction velocity and W* is the convective velocity scale). The new methodology is used to determine the values of the Gaussian parameters in Gram-Charlier expansion, that better reproduce the probability density function, for different Z/Zi levels (from 0 to 1 with a step of 0.01) in three different atmospheric turbulence conditions (U*/W*=0.2, 0.4 and 0.6). Further the analytical trends of both mean and standard deviation versus Z/Zi are calculated.

We study the coupled translational and internal dynamics of a two-level atom in a spatially periodic optical potential created by a single-mode field in a high-finesse Fabry-Perot cavity. The strongly coupled atom-cavity system with atomic center-of-mass motion included is modeled by semiclassical nonlinear Heisenberg equations of motion with two degrees of freedom. At exact resonance between the internal atomic transition and the cavity eigenfrequency, the internal and translational degrees of freedom are separated from each other resulting in periodically modulated Rabi oscillations and regular translational motion. Near the atom-field resonance, the coupled dynamics is found to be irregular and even chaotic in the sense of extremal sensitivity to initial conditions. It is manifested as a chaotic motion of an atom in an absolutely regular spatially periodic potential in the absence of any random fluctuations. This effect may be explained as a result of the interaction of nonlinear resonances in the atom-field nonlinear pendulum whose low-frequency translational motion is modulated by the high-frequency Rabi oscillations. The irregular motion is studied in detail in numerical experiments using the arsenal of methods of the dynamical systems theory. The results obtained are compared with recent experiments with ultracold single atoms interacting with single photons in the strong-coupling regime. We estimate the ranges of the system's control parameters, the detuning, the recoil frequency, and the mean number of intracavity photons, in which the interaction of nonlinear resonances may lead, under realistic conditions, to local instability of the center-of-mass motion and some manifestations of dynamical chaos, which is the effect of interest in studying the quantum-classical correspondence and quantum chaos in atomic optics.

Probabilistic Neural Network(PNN) based on Alphastable distribution is proposed to improve former algorithm's poor fitting ability caused by independent identically distributed Gaussian assumption in intrusion detection's non-Gaussian data. Fast Fourier Transform Numerical Computation is used in the algorithm to establish its Alphastable distribution probability density function(PDF), and then the Samples Characteristic Function Algorithm is adopted to estimate the parameters, and finally Alpha-stable distribution PDF instead of Gaussian function is used as the activation function of PNN. In the simulation, intrusion detection dataset, KDD CUP 99, is used to validate the algorithm, which shows that compared with previous PNN and BPNN, the new algorithm has a stronger ability of fitting the non-Gaussian data and has improved the detection rate and false negative rate in intrusion detection greatly while the false alarm rate is stable.

<p><span>Measurement uncertainty analysis based on combining the state-of-knowledge distributions requires evaluation of the probability density function (PDF), the cumulative distribution function (CDF), and/or the quantile function (QF) of a random variable reasonably associated with the measurand. This can be derived from the characteristic function (CF), which is defined as a Fourier transform of its probability distribution function. Working with CFs provides an alternative and frequently much simpler route than working directly with PDFs and/or CDFs. In particular, derivation of the CF of a weighted sum of independent random variables is a simple and trivial task. However, the analytical derivation of the PDF and/or CDF by using the inverse Fourier transform is available only in special cases. Thus, in most practical situations, a numerical derivation of the PDF/CDF from the CF is an indispensable tool. In metrological applications, such approach can be used to form the probability distribution for the output quantity of a measurement model of additive, linear or generalized linear form. In this paper we propose new original algorithmic implementations of methods for numerical inversion of the characteristic function which are especially suitable for typical metrological applications. The suggested numerical approaches are based on the Gil-Pelaez inverse formulae and on using the approximation by discrete Fourier transform and the fast Fourier transform (FFT) algorithm for computing PDF/CDF of the univariate continuous random variables. As illustrated here, for typical metrological applications based on linear measurement models the suggested methods are an efficient alternative to the standard Monte Carlo methods.</span></p>

Dogs with rapid ventricular pacing (RVP)-induced congestive heart failure (CHF) have inducible atrial tachycardia, flutter, and fibrillation (AF). We tested the hypothesis that rapid atrial activation in multiple regions and at different rates is responsible for sustained AF in this CHF model. We studied 12 episodes of sustained (>10 minutes) AF induced in 12 dogs with CHF produced by 3-6 weeks of RVP at 230 beats/minute. High-density mapping of AF was performed using 382 unipolar atrial electrograms recorded simultaneously from epicardial electrodes on the right (RA) and left atria (LA) and Bachmann's bundle. AF mechanisms were based on Fast Fourier Transform (FFT) analysis and activation sequence mapping. A driver was defined as a rapid stable activation region with a single dominant frequency peak in FFT analysis. During AF, three FFT and activation patterns were seen: (1) a single LA driver (7.8 +/- 1.1 Hz) near the pulmonary veins (PVs) with irregular activation in the rest of the atria (n = 4); (2) simultaneous, multisite, biatrial drivers at differing frequencies (LA vs RA dominant frequency gradient: 1.3 +/- 0.8 Hz) near the PVs (8.4 +/- 0.3 Hz) and high RA (8.5 +/- 1.5 Hz) (n = 7); and (3) biatrial irregular activation with multiple and/or broadband frequency peaks without a dominant frequency. (LA: 7.1-11.4 Hz; RA: 5.9-7.7 Hz) (n = 1). Atrial drivers had either a focal activation pattern or were due to a macroreentrant circuit around the PVs. In this CHF model, FFT analysis and activation sequence mapping demonstrate that sustained AF is characterized by single and multiple, stable LA and RA drivers with predominant sources in the PVs and high RA causing fibrillatory conduction.

The paper presents the results of a study aimed to compare different signal processing techniques for the condition monitoring of a mechanical system for indexing motion. Artificial feed-forward neural networks (ANN) are used as classifiers. The mechanical system can work in different conditions (variable loads and velocities, lubricant oil with different viscosity) and the ANN identifies the working condition. The monitored variable is the acceleration signal of the rotating table, opportunely pre-processed. The signal processing techniques compared are: Power Spectral Density (PSD), Fast Fourier Transform (FFT), Wavelet, Amplitude Probability Density Function (PDF), Higher Order Spectra (HOS).

Measuring financial risk and portfolio reversion with time changed tempered stable Lévy processes

Eulerian–Lagrangian multiscale numerical analysis of multimodal partial shedding dynamics

Autonomous Satellite Rendezvous and Proximity Operations with Time-Constrained Sub-Optimal Model Predictive Control

We evaluate the extent to which within‐year rainfall variability controls interannual variability of catchment water balance. To this end, we analytically derive the probability density function of the annual Budyko evaporation index, B (i.e., the ratio of annual actual evapotranspiration to annual precipitation), by accounting for the stochastic nature of intra‐annual rainfall fluctuation and neglecting all other sources of variability. We apply our analytical model to 424 catchments located in different climatic regions across the conterminous United States to perform this assessment. In general, we found that the model is capable of explaining mean B but is less accurate in predicting its coefficient of variation. Nonetheless, in a significant number of catchments the model can provide adequate predictions of the probability density function of B. Clear geographic patterns can be distinguished in the residuals between observed and predicted statistics of B. Interannual variability is thus not always associated with random intra‐annual rainfall fluctuations. In some regions, other controls, such as seasonality and vegetation adaptations, are possibly more important. A sensitivity analysis of model parameters helped characterize the dominant controls on the distribution of B in terms of three dimensionless ratios that include climatic and soil characteristics. This study represents the first step in a diagnostic, data‐driven analysis of the climatic controls on the interannual variability of catchment water balance.

This work studies the spectrum of discrete-time Uniform-sampling pulse width modulation (UPWM) signals originating from stochastic input signals. It demonstrates that for ergodic input sequences of independent and identically distributed random variables, the Discrete Fourier Transform (DFT) of the UPWM signals can be directly estimated from the input signal’s statistics. Consequently, it is shown that if the input signal can be modeled as such a random sequence, only statistical information of the sequence is required for the accurate estimation of the DFT of the UPWM signal. This is achieved here by proving that the DFT estimators obtained by observation of the input sequence within a time window are consistent estimators of the DFT coefficients of the underlying random process. Moreover, for signals whose generalized probability density functions can be expressed as functions of a small number of parameters, the DFT coefficients can be estimated or even calculated via closed-form expressions with linear complexity. Examples are given for input signals derived from symmetric and asymmetric distributions. The results are validated by comparison with evaluations of the UPWM signal’s DFT via the Fast Fourier Transform (FFT). The proposed method provides a mathematical framework for the analysis and design of UPWM systems whose inputs have known statistical properties.

Simultaneous investigation of macro- and micro-mixing in a static mixer