Radius Perturbations Research Articles

Long‐Wavelength Topography and Multiscale Velocity Heterogeneity at the Core‐Mantle Boundary

AbstractThe structure of the lowermost mantle and the core‐mantle boundary (CMB) has profound implications for Earth's evolution and current‐day dynamics. Whilst tomographic studies of VS show good agreement in the lowermost mantle, consensus as to VP and especially CMB radius has not yet been reached. We perform a hierarchical Bayesian inversion for VP in the lowermost 300 km of the mantle and the radius of the CMB using differential travel time data. Concurrent with finding VP perturbations of 0.56% RMS amplitude that spatially agree with previous studies in areas of low posterior variance, we find 4.5 km RMS amplitude CMB radius perturbations with a broadly north‐south hemispherical character, with spherical harmonic power evenly distributed between degrees 1–3. These results suggest that CMB radial processes are set by a longer scale process than the VP perturbations.

Parameter-dependent robust anti-saturation control of supercavitating vehicle with time-delay characteristics

Aiming at the time-delay characteristics and nonlinear planing force of supercavitating vehicles in the process of motion, a parameter-dependent robust controller with anti-saturation compensator is proposed. First, the system model with nonlinear planing force is transformed into a parameter dependent linear-parameter-varying model containing time-delay part and non-time-delay part. Then consider the external disturbance input to design a robust controller and use convex polyhedron theory and the parameter dependence characteristics of controller to ensure the stability of the system with cavitation radius perturbation. Finally, the anti-saturation compensation method is used to overcome the input constraints caused by the physical limitations of the control mechanism. The simulation results show that the controller has good control effect and robust performance for supercavitating vehicles with time-delay characteristics.

Robust predictive control of a supercavitating vehicle based on time-delay characteristics and parameter uncertainty

Supercavitating vehicle can realize high-speed underwater sailing. However, the nonlinear force and time-delay characteristics caused by the tail flapping the cavity wall become the main challenge of the vehicle controller design. Aiming at time-delay characteristics, the nonlinear of planing force, cavity radius perturbation and parameter uncertainty, the paper establishes a time-delay linear-parameter-varying (LPV) model and designs a robust predictive controller with anti-interference performance. In the process of predictive controller design, the variable quadratic function is used to achieve the robustness of the vehicle and reduce the conservatism of the controller design. Meanwhile, the memory state feedback is used to solve the problems of cavitation radius perturbation, control constraints, vehicle parameter uncertainty and external disturbance. The simulation results show that the controller has strong robustness against the disturbance of external parameters, and can guarantee the stability of the system.

3-D Printed Directional Couplers in Circular Waveguide

The design of an additively manufactured circular waveguide 3-dB hybrid directional coupler is proposed and demonstrated. Asymmetric corner radius perturbations at the in-plane orthogonal junction of the four waveguides along with curvilinear inductive posts designed to interact with the TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> mode of the circular waveguide are used to facilitate directivity and isolation. Capacitive waveguide perturbations at each of the four ports provide impedance matching. The proposed design is engineered to operate within V-band from 57 to 64 GHz and provide both 10-dB isolation and return loss and a 90° phase difference between the direct and coupled ports. A commercially available stereolithography (SLA) printer is used to fabricate the hybrid coupler as well as the rectangular-to-circular tapered mode transducers and the thru, reflect, line (TRL) calibration components required for experiments. The printed couplers are metallized using an electroless silver plating process by a closed-loop bidirectional multiport pump-driven fluidic system. Results from the experiment and the simulation are provided.

A Fast Correction Method of Model Deformation Effects in Wind Tunnel Tests

The influence of model deformation needs to be corrected before the aerodynamic force data measured in the wind tunnel is applied to aircraft design. In order to obtain the aerodynamic forces on rigid model shape, this paper presents a fast correction method by establishing a mathematical modelling method connecting aerodynamic forces and wing section torsion. The aerodynamic force coefficients on rigid model shape can then be calculated quickly just by setting section torsion to zero. A 25-point simulation dataset of the High Reynolds Number Aero-Structural Dynamics (HIRENASD) model generated by Computational Fluid Dynamics (CFD) and Static Computational Aeroelasticity (CAE) approach is used to investigate the influence of section locations, basis function type, support radius, and deformation perturbation on the prediction accuracy. Finally, the present correction method is applied to predict the aerodynamic forces on the rigid shape of a NASA common research model. The results of parametric analysis and application show that the present correction method with the Wendland’s C6 function and a support radius of 1.0 can provide a reasonable prediction of aerodynamic forces on the rigid model shape.

Feasibility of imaging epileptic seizure onset with EIT and depth electrodes

Imaging ictal and interictal activity with Electrical Impedance Tomography (EIT) using intracranial electrode mats has been demonstrated in animal models of epilepsy. In human epilepsy subjects undergoing presurgical evaluation, depth electrodes are often preferred. The purpose of this work was to evaluate the feasibility of using EIT to localise epileptogenic areas with intracranial electrodes in humans. The accuracy of localisation of the ictal onset zone was evaluated in computer simulations using 9M element FEM models derived from three subjects. 5 mm radius perturbations imitating a single seizure onset event were placed in several locations forming two groups: under depth electrode coverage and in the contralateral hemisphere. Simulations were made for impedance changes of 1% expected for neuronal depolarisation over milliseconds and 10% for cell swelling over seconds. Reconstructions were compared with EEG source modelling for a radially orientated dipole with respect to the closest EEG recording contact. The best accuracy of EIT was obtained using all depth and 32 scalp electrodes, greater than the equivalent accuracy with EEG inverse source modelling. The localisation error was 5.2 ± 1.8, 4.3 ± 0 and 46.2 ± 25.8 mm for perturbations within the volume enclosed by depth electrodes and 29.6 ± 38.7, 26.1 ± 36.2, 54.0 ± 26.2 mm for those without (EIT 1%, 10% change, EEG source modelling, n = 15 in 3 subjects, p < 0.01). As EIT was insensitive to source dipole orientation, all 15 perturbations within the volume enclosed by depth electrodes were localised, whereas the standard clinical method of visual inspection of EEG voltages, only localised 8 out of 15 cases. This suggests that adding EIT to SEEG measurements could be beneficial in localising the onset of seizures.

Multifrequency Microwave Backscatter From a Highly Saline Snow Cover on Smooth First-Year Sea Ice: First-Order Theoretical Modeling

A theoretical understanding of a multifrequency microwave approach to understand complex microwave interactions from a highly saline snow cover on a relatively smooth first-year sea ice is presented. We examine the sensitivity of Ku-, X-, and C-band ${\sigma }_{{\text {VV}}}^{0}$ and ${\sigma }_{{\text {HH}}}^{0}$ to variability in snow geophysical properties such as salinity, density, temperature, and snow grain radius, sampled from a highly saline snow cover on first-year sea ice. A first-order multilayer snow and ice backscatter model is used to calculate ${\sigma }_{{\text {VV}}}^{0}$ and ${\sigma }_{{\text {HH}}}^{0}$ by taking into account the surface and volume scattering contributions within each snow layer of the snow pack. Penetration depth models are used to calculate the potential penetration of all three frequencies, at initial and perturbed snow property conditions. Sensitivity analyses suggest that variability in salinity and snow grain radius have the greatest effect, followed by density and temperature. This phenomenon is observed for all three frequencies, influencing microwave penetration and backscatter. Dielectric loss associated with highly saline snow covers and substantial changes in scattering contributions from snow grain radius perturbations were found to be the dominant factors affecting microwave penetration and backscatter. Results from this paper demonstrate the potential of using a multifrequency theoretical approach to correlate with active microwave observations to determine the geophysical and electrical state of snow/sea ice system. The paper also represents an evolution in a theoretical understanding on how an active microwave approach using multiple frequencies can be further utilized toward the development of snow thickness and/or snow water equivalent algorithm on smooth FYI.

Theoretical study of mode evolution in active long tapered multimode fiber.

A concise and effective model based on coupled mode theory to describe mode evolution in long tapered active fiber is presented in this manuscript. The mode coupling due to variation of core radius and slight perturbation have been analyzed and local gain with transverse spatial hole burning (TSHB) effect, loss and curvature have been taken into consideration in our model. On the base of this model, the mode evolution behaviors under different factors have been numerically investigated. Our model and results can provide instructive suggestions when designing long tapered fiber based laser and amplifiers.

Dynamic stability of detached solidification

A dynamic stability analysis model is developed for meniscus-defined crystal growth processes. The Young–Laplace equation is used to analyze the response of a growing crystal to perturbations to its radius and a thermal transport model is used to analyze the effect of perturbations on the evolution of the crystal-melt interface. A linearized differential equation is used to analyze radius perturbations but a linear integro-differential equation is required for the height perturbations. The stability model is applied to detached solidification under zero-gravity and terrestrial conditions. A numerical analysis is supplemented with an approximate analytical analysis, valid in the limit of small Bond numbers. For terrestrial conditions, a singularity is found to exist in the capillary stability coefficients where, at a critical value of the pressure differential across the meniscus, there is a transition from stability to instability. For the zero-gravity condition, exact formulas for the capillary stability coefficients are derived.

Computation of the Real Controllability Radius and Minimum-Norm Perturbations of Higher-Order, Descriptor, and Time-Delay LTI Systems

A linear time-invariant (LTI) system's controllability radius measures the norm of the smallest parametric perturbation such that the perturbed system is uncontrollable, and is of practical importance. In this note, we study the real controllability radii of i) higher-order systems; ii) descriptor systems; and iii) time-delay systems, where the perturbations are restricted to the set of real values, and the spectral norm is considered. Formulas for these radii are presented using a framework involving generalized real perturbation values, which has certain computational advantages over other formulations found in the literature. In particular, the formulas are readily more computable, especially for higher-dimensional systems, and a minimum-norm perturbation can also easily be obtained. Numerical examples are presented.

Phase field study of interfacial diffusion-driven spheroidization in a composite comprised of two mutually insoluble phases

The phase field approach is a powerful computational technique to simulate morphological and microstructural evolution at the mesoscale. Spheroidization is a frequently observed morphological change of mesoscale heterogeneous structures during annealing. In this study, we used the diffuse interface phase field method to investigate the interfacial diffusion-driven spheroidization of cylindrical rod structures in a composite comprised of two mutually insoluble phases in a two-dimensional case. Perturbation of rod radius along a cylinder's axis has long been known to cause the necessary chemical potential gradient that drives spheroidization of the rod by Lord Rayleigh's instability theory. This theory indicates that a radius perturbation wavelength larger than the initial rod circumference would lead to cylindrical spheroidization. We investigated the effect of perturbation wavelength, interfacial energy, volume diffusion, phase composition, and interfacial percentage on the kinetics of spheroidization. The results match well with both the Rayleigh's instability criterion and experimental observations.

Mode identification based on time-series spectrophotometry for the bright rapid sdB pulsator EC 01541−1409

We present an analysis of time-resolved spectrophotometry gathered with FORS/VLT for the rapidly pulsating hot B subdwarf EC 01541−1409 with the aim of identifying the degree indexof the larger amplitude modes. This mode identification can be extremely useful in detailed searches for viable asteroseismic models in parameter space, and can be crucial for testing the validity of a solution a posteriori. To achieve it, we exploit the � -dependence of the monochromatic amplitude, phase, and velocity-to-amplitude ratio of a mode as a function of wavelength. We use the � -sensitive phase lag between the flux perturbation and the radial velocity as an additional diagnostic tool. On this basis, we are able to unambiguously identify the dominant 140.5 s pulsation of our target as a radial mode, and the second-highest amplitude periodicity at 145.8 s as an � = 2 mode. We further exploit the exceptionally high-sensitivity data that we gathered for the dominant mode to infer modal properties that are usually quite difficult to estimate in sdB pulsators, namely the physical values of the dimensionless radius, temperature, and surface gravity perturbations.

Study of a W-band TE62 mode generator by the waveguide mode transformation

In this paper, based on the theory of mode-matching and the coupled wave theory, A W-band TE62 mode generator by using waveguide mode transformation is presented. Because of the eigen-mode selection of coaxial waveguide, a TE1 mode in standard rectangular waveguide is coupled into a coaxial waveguide to excite a TE61 mode by an aperture. A transition follows on it to change the coaxial waveguide into a circular one. Finally, TE61–TE62 mode converter is achieved by using a periodic radius perturbation in circular waveguide. Calculation and analysis of the relationship between the mode conversion efficiency and structure parameters of waveguide also are finished. The validity of this study is confirmed by using electromagnetic simulation software. The conversion efficiency of TE62 mode reaches 94.5% at the center frequency 95 GHz, and the mode purity reaches 98.16% The bandwidth of the efficiency above 85% reaches 1 GHz, which can meet the demand of the high–frequency cold test of gyrotrons.

SMALL ESSENTIAL SPECTRAL RADIUS PERTURBATIONS OF OPERATORS WITH TOPOLOGICAL UNIFORM DESCENT

AbstractIn this paper we consider small essential spectral radius perturbations of operators with topological uniform descent—small essential spectral radius perturbations which cover compact, quasinilpotent and Riesz perturbations.

“Numerical Simulation of the Process of Autoregulation of the Arterial Blood Flow”

For describing the autoregulation of the blood flow in an artery under constant transmural pressure a mathematical model that takes into account the multilayer structure of the arterial wall, the diffusion and kinetic processes in the wall, and the nonlinear viscoelastic properties of the wall material is proposed. The limiting case of a thin-walled artery is studied analytically. The arterial-wall viscosity range on which the equilibrium state of the system is stable is estimated. Accurate stationary distributions of the nitric oxide, calcium and myosin concentrations in the arterial wall are found. Numerical simulation of the autoregulation process demonstrated the possibility of arterial adaptation to radius perturbations, the existence of slow oscillations, and system transition to a new equilibrium state with change in blood flow level. The results are in good agreement with the experimental data.

On the temporal stability of steady-state quasi-1D bubbly cavitating nozzle flow solutions

Quasi-1D unsteady bubbly cavitating nozzle flows are considered by employing a homogeneous bubbly liquid flow model, where the non-linear dynamics of cavitating bubbles is described by a modified Rayleigh–Plesset equation. The various damping mechanisms are considered by a single damping coefficient lumping them together in the form of viscous dissipation and by assuming a polytropic law for the expansion and compression of the gas. The complete system of equations, by appropriate uncoupling, are then reduced to two evolution equations, one for the flow speed and the other for the bubble radius when all damping mechanisms are considered by a single damping coefficient. The evolution equations for the bubble radius and flow speed are then perturbed with respect to flow unsteadiness resulting in a coupled system of linear partial differential equations (PDEs) for the radius and flow speed perturbations. This system of coupled linear PDEs is then cast into an eigenvalue problem and the exact solution of the eigenvalue problem is found by normal mode analysis in the inlet region of the nozzle. Results show that the steady-state cavitating nozzle flow solutions are stable only for perturbations with very small wave numbers. The stable regions of the stability diagram for the inlet region of the nozzle are seen to be broadened by the effect of turbulent wall shear stress.

Variational Estimates of Internal Interface Perturbations and a New Variational Functional for Inhomogeneous Transport Problems

Variational perturbation theory is applied to internal interface perturbations in neutral-particle inhomogeneous transport problems. The leakage from a radioactive system is the quantity of interest. The Schwinger and Roussopolos variational functionals are used with volume- and surface-integral formulations of the integrals of perturbed quantities. In numerical one-dimensional spherical tests of source radius perturbations, the Roussopolos functional in the surface-integral formulation worked better when the source was large, and the Schwinger functional in the volume-integral formulation worked better when the source was small. A new variational functional is presented that formally allows a combination of the Schwinger and Roussopolos functionals; the contribution of each to the total estimate is adjusted with a parameter introduced in one of the trial functions. When the parameter is correctly chosen, the new functional is generally more accurate than either the Schwinger or Roussopolos functional alone. An analytic monodirectional slab transport problem is also considered.

The Potential of Multicolor Photometry for Pulsating Subdwarf B Stars

We investigate the potential of multicolor photometry for partial mode identification in both long- and short-period variable subdwarf B stars. The technique presented is based on the fact that the frequency dependence of an oscillation's amplitude and phase bears the signature of the mode's degree index l, among other things. Unknown contributing factors can be eliminated through the evaluation of the amplitude ratios and phase differences arising from the brightness variation in different wavebands, theoretically enabling the inference of the degree index from observations in two or more bandpasses. Employing a designated model atmosphere code, we calculate the brightness variation expected across the visible disk during a pulsation cycle in terms of temperature, radius, and surface gravity perturbations to the emergent flux for representative EC 14026 and PG 1716 star models. Nonadiabatic effects are considered in detail and found to be significant from nonadiabatic pulsation calculations applied to our state-of-the-art models of subdwarf B stars. Our results indicate that the brightness variations observed in subdwarf B stars are caused primarily by changes in temperature and radius, with surface gravity perturbations playing a small role. For PG 1716 stars, temperature effects dominate in the limit of long periods with the result that the oscillatory amplitudes and phases lose their period dependence and nonadiabatic effects become unimportant. Outside this regime, however, their values are strongly influenced by both factors. We find that the phase shifts between brightness variations in different wavebands are generally small but may lie above the experimental detection threshold in certain cases. The prospect of mode discrimination seems much more promising on the basis of the corresponding amplitude ratios. While in EC 14026 stars the amplitude ratios predicted are very similar for modes with l = 0, 1, or 2, they are well separated from those of modes with l = 3, l = 5, and l = 4 or 6, each of which form a distinct group. For the case of the PG 1716 stars it should be possible to discriminate between modes with l = 1, 2, 4, or 6 and those of degree indices l = 3 and l = 5. Identifying modes within a given group is challenging for both types of pulsator and requires multicolor photometry of extremely high quality. Nevertheless, we demonstrate that it is feasible using the example of the largest amplitude peak detected for the fast pulsator KPD 2109+4401 by Jeffery et al.

Synthetic photometry for non-radial pulsations in subdwarf B stars

We describe a method for computing theoretical photometric amplitude ratios for a number of modes of nonradially pulsating subdwarf B stars in both SDSS and UBVR systems. In order to avoid costly solutions of the non-adiabatic non- radial pulsation equations, we have adopted the adiabatic approximation. We argue that this is a valid approach, at least for the V361 Hya stars, because observations show that the temperature perturbations dominate the radius perturbations in the flux variation. We find that for V361 Hya stars, low-degree (� = 0, 1, 2) modes may be difficult to distinguish using optical photometry. However, the high degree modes (� = 3, 4) are relatively well separated and may be distinguished more easily. We have also computed the amplitude ratios for a number of modes in PG 1716+426 stars. For these stars, the amplitude ratios for low degree modes (� = 0, 1) are well resolved. For oscillations with periods ∼40 min, higher-degree modes (� = 2−4) may also be identified easily from their amplitude ratios. However for longer period oscillations, the � = 3a nd the� = 2, 4 modes approach the � = 0a nd� = 1 modes respectively.

Photometric modelling of slowly pulsating B stars

The photometric characteristics of slowly pulsating B stars are investigated using a numerical approach. Stability calculations are performed for a set of stellar models representative of the mid-B type, using a non-radial non-adiabatic pulsation code. The results from these calculations are used to synthesize photometry, in several common systems, for unstable modes of harmonic degrees l = 1...4. Focusing on the Geneva system for illustrative purposes, a variety of techniques are employed to analyse and visualize the synthetic data, including the use of multicolour-amplitudes and amplitude-phase diagnostic diagrams. One outstanding aspect of the analysis is the discovery, for the l = 2...4 modes, of 'inter-term cancellation' (ITC) - the process of destructive interference between the flux variations originating from surface temperature perturbations and those arising from radius perturbations. The ITC can be severe enough that a mode may be excited to a significant amplitude, and yet exhibit levels of photometric variability that fall below typical observational detection thresholds. Furthermore, it can affect not only the light variations in a given photometric passband, but also the variations of the bolometric flux. However, the cancellation is dependent on wavelength, and will not occur to the same degree in more than one passband. Therefore, simultaneous observation in a multitude of passbands represents the best approach to ensuring that no modes are overlooked during searches for variability in B-type stars. A consequence of ITC is that ratios between the variability amplitude, in differing passbands, become very sensitive towards mode-to-mode changes in the pulsation. This increased sensitivity will tend to complicate any attempts at identifying the harmonic degrees of the modes responsible for observed variability. However, the cancellation also introduces significant phase differences between the light variations in each passband, especially for the l = 3 and l = 4 modes. On the grounds that correspondingly large phase differences are not seen in observational data, it is argued that the variability seen in slowly pulsating B stars can tentatively be attributed to l = 1 and l = 2 modes.