Time-varying Interface Research Articles

Harnessing the Natural Resonances of Time-Varying Dispersive Interfaces.

Space-time modulation of electromagnetic parameters offers novel exciting possibilities for advanced field manipulations. In this study, we explore wave scattering from a time-varying interface characterized by a Lorentz-type dispersion with a steplike temporal variation in its parameters. Our findings reveal a new process: an unconventional frequency generation at the natural resonances of the system. Remarkably, this phenomenon enables the coupling of propagating waves to evanescent ones, allowing the direct far-field excitation of surface-wave modes without the mediation of spatial gratings or prisms. These results suggest a novel strategy for designing compact and ultrafast photonic devices, eliminating the necessity for subwavelength spatial structuring or prolonged temporal modulations.

Second harmonic generation at a time-varying interface

Time-varying metamaterials rely on large and fast changes of the linear permittivity. Beyond the linear terms, however, the effect of a non-perturbative modulation of the medium on harmonic generation remains largely unexplored. In this work, we study second harmonic generation at an optically pumped time-varying interface between air and a 310 nm Indium Tin Oxide film. We observe a modulation contrast at the second harmonic wavelength up to 93% for a pump intensity of 100 GW/cm2, leading to large frequency broadening and shift. We experimentally demonstrate that a significant contribution to the enhancement comes from the temporal modulation of the second order nonlinear susceptibility. Moreover, we show the frequency-modulated spectra resulting from single and double-slit time diffraction could be exploited for enhanced optical computing and sensing, enabling broadband time-varying effects on the harmonic signal and extending the application of Epsilon-Near-Zero materials to the visible range.

High-order unfitted characteristic finite element methods for moving interface problem of Oseen equations

Moving interface problems have broad applications in multi-phase flows and fluid–structure interactions. The design of high-order numerical methods for such problems becomes challenging, in particular, when the interface is severely deformed. We propose kth-order unfitted characteristic finite element methods (k=2,3,4) for solving two-dimensional Oseen equations with a time-varying interface. In each time step, the interface is not specified with an explicit function, but constructed numerically with a (k+1)th-order interface-tracking algorithm. We obtain optimal convergence orders of both the discrete velocity and the discrete pressure under the H1-norm. Our convergence analysis includes errors of the approximate interface and the time integration and spatial discretization of the governing equations. Numerical experiments are performed on a rotating object and a severely deformed interface and show optimal convergence orders of the method.

Two-dimensional stability analysis of finite-amplitude interfacial gravity waves in a two-layer fluid

We explore basic mechanisms for the instability of finite-amplitude interfacial gravity waves through a two-dimensional linear stability analysis of the periodic and irrotational plane motion of the interface between two unbounded homogeneous fluids of different density in the absence of background currents. The flow domains are conformally mapped into two half-planes, where the time-varying interface is always mapped onto the real axis. This unsteady conformal mapping technique with a suitable representation of the interface reduces the linear stability problem to a generalized eigenvalue problem, and allows us to accurately compute the growth rates of unstable disturbances superimposed on steady waves for a wide range of parameters. Numerical results show that the wave-induced Kelvin–Helmholtz (KH) instability due to the tangential velocity jump across the interface produced by the steady waves is the major instability mechanism. Any disturbances whose dominant wavenumbers are greater than a critical value grow exponentially. This critical wavenumber that depends on the steady wave steepness and the density ratio can be approximated by a local KH stability analysis, where the spatial variation of the wave-induced currents is neglected. It is shown, however, that the growth rates need to be found numerically with care and the successive collisions of eigenvalues result in the wave-induced KH instability. In addition, the present study extends the previous results for the small-wavenumber instability, such as modulational instability, of relatively small-amplitude steady waves to finite-amplitude ones.

Reconstruction of the heat transfer coefficient at the interface of a bi-material

ABSTRACTThe knowledge of heat transfer behaviour of composite thermal systems requires the characterization of the heat transfer coefficient at the contact interfaces between the constituent materials. The present work is devoted to investigating an inverse problem with generalized interface condition containing an unknown space- and time-varying interface coefficient from non-invasive temperature measurements on an accessible boundary. The uniqueness of the solution holds, but the problem does not depend continuously on the input measured temperature data. A new preconditioned conjugate gradient method (CGM) is utilized to address the ill-posedness of the inverse problem. In comparison with the standard CGM with no preconditioning, this method has the merit that the gradient of the objective functional does not vanish at the final time, which restores accuracy and stability when the input data is contaminated with noise and when the initial guess is not close to the true solution. Several numerical examples corresponding to linear thermal contact and nonlinear Stefan-Boltzmann radiation condition are tested for determining thermal contact conductance and Stefan-Boltzmann coefficient, respectively. The numerical results in both one- and two-dimensions illustrate that the reconstructions are robust and stable.

A space-time discontinuous Galerkin spectral element method for the Stefan problem

A novel space-time discontinuous Galerkin (DG) spectral element method is presented to solve the one dimensional Stefan problem in an Eulerian coordinate system. This method employs the level set procedure to describe the time-evolving interface. To deal with the prior unknown interface, a backward transformation and a forward transformation are introduced in the space-time mesh. By combining an Eulerian description, i.e., a fixed frame of reference, with a Lagrangian description, i.e., a moving frame of reference, the issue of dealing with implicitly defined arbitrary shaped space-time elements is avoided. The backward transformation maps the unknown time-varying interface in the fixed frame of reference to a known stationary interface in the moving frame of reference. In the moving frame of reference, the transformed governing equations, written in the space-time framework, are discretized by a DG spectral element method in each space-time slab. The forward transformation is used to update the level set function and then to project the solution in each phase back from the moving frame of reference to the fixed Eulerian grid. Two options for calculating the interface velocity are presented, and both options exhibit spectral accuracy. Benchmark tests indicate that the method converges with spectral accuracy in both space and time for the temperature distribution and the interface velocity. A Picard iteration algorithm is introduced in order to solve the nonlinear algebraic system of equations and it is found that just a few iterations lead to convergence.

On blade/casing rub problems in turbomachinery: An efficient delayed differential equation approach

This paper presents an alternative pathway in studying the ubiquitous blade/casing rub problem in turbomachinery. Bladed disks interfere with the stationary shroud (casing) for a variety of reasons, such as axial offsets, thermal expansions. Both components being compliant, time-varying interface characteristics, nonlinearities and uncertainties in the rub forces make this dynamics very complex to model and analyze. The main idea in this paper originates from the conjecture that this dynamics is inherently akin to internal machining operation which also deals with compliant cutters (blades) but relatively more rigid workpiece (casing). This analogy directs our attention to the fact that the blade/casing impingement dynamics manifests a ‘regenerative mechanism’ which is impregnated with time delays. The ensuing time-delayed system (TDS) can be stable, which is ideal. If it is unstable, however, the interference amplitudes between the blade and the casing grow, and the nonlinear effects become dominant. If the components survived the exercise, this evolution would reach a limit-cycle behavior. Existing literature indicates that this limit cycle mode is the common state of operation in most modern-day turbomachinery. Consequently, the state-of-the-art research effort is focused on minimizing its amplitude to alleviate the destructive levels of fatigue effect. In this article we consider a different perspective in looking at these problems, by proposing the conditions to achieve stable rub interference. For this, a recent mathematical tool of the authors’ group called the Cluster Treatment of Characteristic Roots (CTCR) is deployed. CTCR declares the complete stability outlook of such time-delayed systems in the space of the operational and design parameters. We show how this new capability can assist the design process of the blade-casing interface. Simulations, relevant stability observations and comparisons with a peer technique are provided for some case studies to demonstrate the capabilities of the approach.

Parametric vibration of two shrink-fitted thin rings with time-varying interface pressure; nonlinear analysis and experimental study

In a shrink-fitted joint, the interface pressure plays an important role as it is the main source of the joint and it keeps the joining components together. However, time-variation of the interface pressure causes parametric instability in the system. In this paper, the effect of time-variant interface pressure on the dynamics of two shrink-fitted rings has been studied. Deriving a dynamic equation of motion of the joint of two shrink-fitted rings and substituting time-variant interface pressure in the equation, the problem extends to nonlinear vibration. The obtained equation of motion, which contains parametrically excited terms, is a general form of Mathieu’s equation. A perturbation method, to determine the instability regions of motion, is applied to obtain the transition curves. To validate the obtained stability regions, an experiment has been performed. Both the analytical and experimental results demonstrate that by increasing the value of the interface pressure, the natural frequencies of the joint increase.

Electrical resistance imaging of a time-varying interface in stratified flows using an unscented Kalman filter

In this paper, we estimate a time-varying interfacial boundary in stratified flows of two immiscible liquids using electrical resistance tomography. The interfacial boundary is approximated with front points spaced discretely along the interface. The design variables to be estimated are the locations of the front points, which are varying with the moving interface. The inverse problem is treated as a stochastic nonlinear state estimation problem with the nonstationary phase boundary (state) being estimated with the aid of an unscented Kalman filter. Numerical experiments are performed to evaluate the performance of an unscented Kalman filter. Specifically, a detailed analysis has been done on the effect of the number of front points and contrast ratio on the reconstruction performance. The reconstruction results show that an unscented Kalman filter is better suited for estimation in comparison to the conventional extended Kalman filter.

Possible role of surface electrochemical electron-transfer and semiconductor charge transport processes in ion channel function

Conductivity measurements and theoretical electronic structure calculations have been made in proteins, the calculations giving allowed energies for electrons that would enable them to participate in charge transport processes, probably by hopping and with close similarity to amorphous semiconductors. These theoretical computations have confirmed that the experimental results are probably due to electronic conduction. The foregoing considerations allow us to describe the protein-electrolyte interface as a semiconductor-electrolyte interface. Electron-transfer (ET) at such interfaces has been studied and experimentally established to occur from semiconductor electronic energy states to redox energy states in solution, or to redox surface states. ET has also been measured between organic and biochemical conducting compounds (particularly proteins and conducting membranes) and electrodes or redox solutions. Therefore, it is assumed in this paper that ET occurs at the ion channel protein interfaces with the cytoplasm and extracellular electrolytes, and that electron transport processes occur through the channel α-helices. A possible ET mechanism is proposed involving surface state oxygen-derived free radicals like Superoxide. The mathematical expressions for the biophysical phenomena discussed give two time-varying interface potentials and charge distributions that could provide the energy for the conformational changes that open and close the channel; these potentials could also change the ion permeation energy barriers by electrostatic influence. An expression is thus obtained for channel conductance as a function of membrane and interface potentials. Using this expression for sodium and potassium complemented by the usual passive components, gives a mathematical model that produces action potentials, intrinsic repetitive firing, and bursting, all of which can be modulated by changes in the biophysical parameters. Implications for ionic channel voltage gating are discussed and compared with existing experimental results and models. The possible relationships with redox and oxygen sensitivities, superoxide oxidative stress and neurotoxicity, drug and neurotransmitter effects, and ionic channel modulation are also discussed.

Flexible-body dynamics modeling of a vehicle moving on the rails of a structure

The problem of dynamics modeling of a flexible structure that moves on the surface of another flexible structure is nominally beyond the scope of available commercial codes, and is addressed in the published literature only in a limited sense. The dynamics of the system comprising the space station and the moving mobile transporter, mated to the orbiter or to the payload-carrying robotic arm, offers related challenges. A novel analytical approach is presented that can be used to study the dynamics behavior of such time-variant structural systems as the mobile transporter during space station operation and/or assembly. The approach developed herein is based on the formation of a linear transformation that expressses displacement compatibility at the time-variant interface domain of two flexible bodies. The methodology is readily applicable to large structural systems. The required inputs that characterize the structural system constitute readily available finite-element data. A model reduction scheme is developed wherein component modes of the parent linear-time-invariant problem are employed. Numerical results are provided.