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101.
102.
Paritosh Mokhasi 《Physica D: Nonlinear Phenomena》2008,237(24):3197-3213
In this paper, the problem of approximating velocity fields at future and past times based on information available at the current time is addressed. A novel method called “episodic POD” is described and developed that enables us to achieve our objective. Application of episodic POD to an ensemble of flow data results in a set of spatio-temporal eigenfunctions and a set of coefficients associated with the eigenfunctions. From these eigenfunctions, we develop two models called the “forward model” and “inverse model” that enable us to approximate the velocity fields at future and past times, based on information provided at the current time. A second set of models, the forward and inverse sequential models are also developed that enable the dynamic update of approximated velocity fields when new information is made available, making these models more adept at on-line estimation. The various properties associated with these models are described in detail, and four different examples are used to validate the models and show the different properties associated with episodic POD. It is shown through numerical validation, that the episodic POD model has a form that is dynamically consistent with the original system. It is also shown that episodic POD outperforms linear Kalman filters in the presence of noise. 相似文献
103.
Jiankun Shao Rishav Choudhary David F. Davidson Ronald K. Hanson Samuel Barak Subith Vasu 《Proceedings of the Combustion Institute》2019,37(4):4555-4562
The need for more efficient power cycles has attracted interest in super-critical CO2 (sCO2) cycles. However, the effects of high CO2 dilution on auto-ignition at extremely high pressures has not been studied in depth. As part of the effort to understand oxy-fuel combustion with massive CO2 dilution, we have measured shock tube ignition delay times (IDT) for methane/O2/CO2 mixtures and hydrogen/O2/CO2 mixtures using sidewall pressure and OH* emission near 306?nm. Ignition delay time was measured in two different facilities behind reflected shock waves over a range of temperatures, 1045–1578?K, in different pressures and mixture regimes, i.e., CH4/O2/CO2 mixtures at 27–286 atm and H2/O2/CO2 mixtures at 37–311 atm. The measured data were compared with the predictions of two recent kinetics models. Fair agreement was found between model and experiment over most of the operating conditions studied. For those conditions where kinetic models fail, the current ignition delay time measurements provide useful target data for development and validation of the mechanisms. 相似文献
104.
The Note is concerned with a feasibility study of time reversal in a non-homogeneous elastic medium, from data recorded in an acoustic medium. Our aim here is to determine the presence and some physical properties of elastic “inclusions” (unknown, not observable solid objects, characterized by their elastic properties) from partial observations of acoustic waves scattered by these inclusions. A finite element numerical method, based on a variational acousto-elastodynamics formulation, is derived and used to solve the forward, and then, the time-reversed problem. A criterion, derived from the reverse time migration framework, is introduced, to help construct images of the inclusions to be determined. Numerical illustrations on configurations that mimic the breast cancer configuration are proposed, and show that one can differentiate between two inclusions, even with different properties. 相似文献
105.
The Aharonov-Bohm effect (ABE) for steady magnetic fields is a well known phenomenon. However, if the current in the infinite solenoid that creates the magnetic field is time-dependent, that is in the presence of both magnetic and electric fields, there is no agreement whether the effect would be present. In this note, we try to investigate time varying ABE by a direct calculation in a set-up with a weak time dependent magnetic field. We find that the electric field arising out of the time-varying magnetic field in the path of the electrons does not enter the action integral but only changes the path of the electron from the source to the slits and then on to the detector. We find a frequency dependent AB phase shift. At low frequencies the result smoothly approaches the one for a constant field as the frequency tends towards zero. On the other hand, for high frequencies such that the AB-phase induced in the path of the wave packet oscillates rapidly, the net effect will be very small which is borne out by our results. 相似文献
106.
This article studies a class of nonlocal stochastic differential equations driven by G-Brownian motion (G-NSDEs for short). We show the existence and uniqueness results of solutions by means of fixed point theorem. In addition, exponential estimation of (1) has been discussed. Furthermore, we present global solution to Equation (1) with the help of G-Lyapunov functional and ψ-type function. 相似文献
107.
In this paper, we consider an elastic beam equation with delay, source term, and boundary conditions together with some suitable initial data. Using the Faedo-Galerkin approximation and some estimates, we get the local existence of solution. Moreover, we obtain the finite time blow-up of solution by constructing suitable Lyapunov functionals. 相似文献
108.
《Stochastic Processes and their Applications》2020,130(6):3687-3710
In this article, we prove Herglotz’s theorem for Hilbert-valued time series. This requires the notion of an operator-valued measure, which we shall make precise for our setting. Herglotz’s theorem for functional time series allows to generalize existing results that are central to frequency domain analysis on the function space. In particular, we use this result to prove the existence of a functional Cramér representation of a large class of processes, including those with jumps in the spectral distribution and long-memory processes. We furthermore obtain an optimal finite dimensional reduction of the time series under weaker assumptions than available in the literature. The results of this paper therefore enable Fourier analysis for processes of which the spectral density operator does not necessarily exist. 相似文献
109.
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