Largest Real Part Research Articles

Analysis and Design of Configurable Rectifier With Compensated Near-Zero Impedance Angle for Megahertz Wireless Power Transfer

Adapting to wide load range variations is always one of the main goals pursued by megahertz (MHz) wireless power transfer (WPT) systems. For this, the nonlinear phenomenon of the rectifier has become a problem that must be solved. Compared with the method of optimizing the efficiency around the maximum power point in the traditional design, this paper proposes a global load optimization method. Meanwhile, a novel configurable compensated near-zero impedance angle rectifier (NIAR) is proposed to take full advantage of the global optimization method. The NIAR not only realizes the compression of a wide range of impedance angles, but also solves the classic problems of Class E rectifiers such as large stress, voltage asymmetry, and low real part of input impedance. The configurable design allows the system to adjust the rectifier unit according to the output index, thereby fully improving the coil efficiency, and providing a solution for the application of high-voltage and high-power MHz WPT systems in the future. To verify the effectiveness of the proposed NIAR and design method, a 60 W prototype was built, and a traditional full-wave rectifier was used for comparison. The results show that the proposed NIAR system exhibits better characteristics in terms of system efficiency, voltage stress, and symmetry.

Ultra-broadband absorber based on photonic topological transition with large-[formula omitted] metals

We propose and experimentally demonstrate an ultra-broadband metamaterial absorber based on photonic topological transition by using metals with large real part of permittivity (ε′). The simulation results show that the absorptivity is larger than 0.9 in the wavelength range from 400 nm to 2832 nm. The simulation results also show that the absorption effect is insensitive to the incident angle and polarization. According to the effective medium theory, the ultra-broad bandwidth is originated from the photonic topological transition. In addition, the analyses reveal that the absorption bandwidths can be extended by manipulating the wavelengths of photonic topological transition (PTT) points with large-ε′ metals. Furthermore, an ultra-broadband metamaterial absorber with multilayer films is fabricated by using standard film deposition techniques. The measured results show that the absorptivity is larger than 0.9 under normal incidence over the measured wavelength range of 400–2500 nm. This metamaterial absorber is expected to be potential candidate for various applications, such as thermal photovoltaic energy conversion, detectors, and solar cells.

A POD Reduced Order Method Applied to an Instability Problem of Rayleigh–Bénard Convection

The application of a proper orthogonal decomposition (POD) reduced order method to a two-dimensional instability problem of Rayleigh–Bénard convection is described in this work. The partial differential equations that model the problem along with the corresponding eigenvalue problems of the linear stability analysis of stationary solutions are numerically solved for different values of the bifurcation parameter, i.e. the Rayleigh number [Formula: see text]. The POD reduced order method considers spaces derived from different stationary solutions depending on [Formula: see text] as snapshots. The eigenvalue with the largest real part and its corresponding eigenfunction are calculated for the POD solutions. The resulting matrices of the eigenvalue problems are low-dimensional. There is a drastic reduction in the computational cost.

Tensor-Krylov method for computing eigenvalues of parameter-dependent matrices

In this paper we extend the Residual Arnoldi method for calculating an extreme eigenvalue (e.g. largest real part, dominant, etc.) to the case where the matrices depend on parameters. The difference between this Arnoldi method and the classical Arnoldi algorithm is that in the former the residual is added to the subspace. We develop a Tensor-Krylov method that can be interpreted as an application of the Residual Arnoldi algorithm to a set of matrices obtained by evaluating a parameter-dependent matrix in parameter values on a grid. The subspace contains an approximate Krylov space for all these points. Instead of adding the residuals for all parameter values to the subspace we create a low-rank approximation of the matrix consisting of these residuals and add only the column space to the subspace. In order to keep the computations efficient, it is needed to limit the dimension of the subspace and to restart once the subspace has reached the prescribed maximal dimension. The novelty of this approach is twofold. Firstly, we observed that a large error in the low-rank approximations is allowed without slowing down the convergence, which implies that we can do more iterations before restarting. Secondly, we pay particular attention to the way the subspace is restarted, since classical restarting techniques give a too large subspace in our case. We motivate why it is good enough to just keep the approximation of the searched eigenvector. At the end of the paper we extend this algorithm to shift-and-invert Residual Arnoldi method to calculate the eigenvalue close to a shift σ for a specific parameter dependency. We provide theoretical results and report numerical experiments. The Matlab code is publicly available.

The Impact of Small Time Delays on the Onset of Oscillations and Synchrony in Brain Networks.

The human brain constitutes one of the most advanced networks produced by nature, consisting of billions of neurons communicating with each other. However, this communication is not in real-time, with different communication or time-delays occurring between neurons in different brain areas. Here, we investigate the impacts of these delays by modeling large interacting neural circuits as neural-field systems which model the bulk activity of populations of neurons. By using a Master Stability Function analysis combined with numerical simulations, we find that delays (1) may actually stabilize brain dynamics by temporarily preventing the onset to oscillatory and pathologically synchronized dynamics and (2) may enhance or diminish synchronization depending on the underlying eigenvalue spectrum of the connectivity matrix. Real eigenvalues with large magnitudes result in increased synchronizability while complex eigenvalues with large magnitudes and positive real parts yield a decrease in synchronizability in the delay vs. instantaneously coupled case. This result applies to networks with fixed, constant delays, and was robust to networks with heterogeneous delays. In the case of real brain networks, where the eigenvalues are predominantly real, owing to the nearly symmetric nature of these weight matrices, biologically plausible, small delays, are likely to increase synchronization, rather than decreasing it.

Exploring the route from leaky Berreman modes to bound states in continuum

We study coupling of leaky Berreman modes in polar dielectric films (SiO2) through a thin metallic layer (gold) and show the familiar signatures of normal mode splitting. Due to very large negative real part of the dielectric function of gold, the splitting shows up only for extremely thin coupling layers. In contrast, coupling of Berreman modes through a dielectric spacer layer reveals novel possibilities of having bound states in continuum, albeit in the limit of vanishing losses. It is shown that the corresponding dispersion branches of the symmetric and antisymmetric modes can cross. BIC is shown to occur on one of these branches which is characterized by lower loss. In fact the BIC corresponds to the point where the radiative losses are minimized. For thicker layers (both spacer and the polar dielectric) BIC is shown to occur on the higher order dispersion branches. The origin of BIC is traced to the Fabry–Perot type mechanism due of the excitation of the leaky guided modes in the central layer.

On relaxed filtered Krylov subspace method for non-symmetric eigenvalue problems

In this paper, by introducing a class of relaxed filtered Krylov subspaces, we propose the relaxed filtered Krylov subspace method for computing the eigenvalues with the largest real parts and the corresponding eigenvectors of non-symmetric matrices. As by-products, the generalizations of the filtered Krylov subspace method and the Chebyshev–Davidson method for solving non-symmetric eigenvalue problems are also presented. We give the convergence analysis of the complex Chebyshev polynomial, which plays a significant role in the polynomial acceleration technique. In addition, numerical experiments are carried out to show the robustness of the relaxed filtered Krylov subspace method and its great superiority over some state-of-the-art iteration methods.

Spectral Analysis of Optimal Disturbances of Stratified Turbulent Couette Flow

For a stratified turbulent Couette flow, the eigenmodes and optimal disturbances of corresponding simplified equations linearized around a steady state are considered. It is shown that the spectrum of these equations is symmetric with respect to the real axis and lies strictly in the left half-plane, i.e., all eigenmodes are stable, and the main part of an optimal disturbance is a linear combination of a large number of modes corresponding to eigenvalues with largest real parts. The number of the most significant modes in this linear combination grows with increasing Reynolds number.

Highly sensitive bimetallic plasmonic sensing probe for aqueous samples

In spite of having very large real part of permittivity, Rhodium (Rh) is rarely used as a plasmonic metal in surface plasmon resonance (SPR) based sensing applications. Here, we theoretically present a simple SPR based prism-coupled refractive index sensor in Kretschmann geometry utilizing a bimetallic layer of Rhodium (Rh) and Silver (Ag) as plasmonic metal layer on the base of the SF10 glass prism. In addition Silicon is used as an upper most layer, which not only protects the oxidation-prone Ag film but also enhances the field and thereby the sensor’s performance. Each of the layers is optimized for maximum sensitivity in the visible region at 632 nm wavelength of excitation. The sensor exhibits an extremely high sensitivity of 229 degree/refractive index unit (RIU) for analyte refractive indices (RIs) varying from 1.33 to 1.37 RIU.

A light-scattering study of highly refractive, irregularly shaped MoS2 particles

We present measurements of light scattering intensity from aerosolized, micron sized, irregularly shaped, molybdenum disulfide (MoS2) particles in order to study the effects of a refractive index, m = n + iκ, with large real and imaginary parts. Light scattering was measured over a range of angles from 0.32° to 157°. Calibration was achieved by scattering with micron sized, spherical silica particles. Light scattering for both particle types was compared to theoretical Mie scattering calculations using size distributions determined by an aerodynamic particle sizer. Effects of the intensity weighted size distribution are discussed. We find that scattering by these irregularly shaped, highly refractive particles is well described by Mie scattering. We also find that when the quantity κkR, where kR = 2πR/λ is the size parameter, is greater than one, there is no enhancement in the backscattering. Finally, we show that Guinier analysis of light scattering by highly refractive particles yields intensity weighted mean sizes of reasonable accuracy for any shape.

PHASE SPACE ERROR CONTROL WITH VARIABLE TIME-STEPPING ALGORITHMS APPLIED TO THE FORWARD EULER METHOD FOR AUTONOMOUS DYNAMICAL SYSTEMS

We consider a phase space stability error control for numerical simulation of dynamical systems. Standard adaptive algorithm used to solve the linear systems perform well during the finite time of integration with fixed initial condition and performs poorly in three areas. To overcome the difficulties faced the Phase Space Error control criterion was introduced. A new error control was introduced by R. Vigneswaran and Tony Humbries which is generalization of the error control first proposed by some other researchers. For linear systems with a stable hyperbolic fixed point, this error control gives a numerical solution which is forced to converge to the fixed point. In earlier, it was analyzed only for forward Euler method applied to the linear system whose coefficient matrix has real negative eigenvalues. In this paper we analyze forward Euler method applied to the linear system whose coefficient matrix has complex eigenvalues with negative large real parts. Some theoretical results are obtained and numerical results are given.

Reduced Basis Method Applied to Eigenvalue Problems from Convection

The reduced basis method is a suitable technique for finding numerical solutions to partial differential equations that must be obtained for many values of parameters. This method is suitable when researching bifurcations and instabilities of stationary solutions for partial differential equations. It is necessary to solve numerically the partial differential equations along with the corresponding eigenvalue problems of the linear stability analysis of stationary solutions for a large number of bifurcation parameter values. In this paper, the reduced basis method has been used to solve eigenvalue problems derived from the linear stability analysis of stationary solutions in a two-dimensional Rayleigh–Bénard convection problem. The bifurcation parameter is the Rayleigh number, which measures buoyancy. The reduced basis considered belongs to the eigenfunction spaces derived from the eigenvalue problems for different types of solutions in the bifurcation diagram depending on the Rayleigh number. The eigenvalue with the largest real part and its corresponding eigenfunction are easily calculated and the bifurcation points are correctly captured. The resulting matrices are small, which enables a drastic reduction in the computational cost of solving the eigenvalue problems.

Calculating Time Eigenvalues of the Neutron Transport Equation with Dynamic Mode Decomposition

A novel method to compute time eigenvalues of neutron transport problems is presented based on solutions to the time-dependent transport equation. Using these solutions, we use the dynamic mode decomposition to form an approximate transport operator. This approximate operator has eigenvalues that are mathematically related to the time eigenvalues of the neutron transport equation. This approach works for systems of any level of criticality and does not require the user to have estimates for the eigenvalues. Numerical results are presented for homogeneous and heterogeneous media. The numerical results indicate that the method finds the eigenvalues that contribute the most to the change in the solution over a given time range, and the eigenvalue with the largest real part is not necessarily important to the system evolution at short and intermediate times.

Subspace Identification of Linear Systems with Partial Eigenvalue Constraints

For subspace identification methods with eigenvalue constraints, the constraints are enforced by means of an optimization problem subject to LMI constraints. First principals or step response tests could be used as a source of auxiliary information in order to build LMI regions. In these cases, all the eigenvalues of the identified state space model are subject to the same constraints. However, it often happens that the non-dominant eigenvalues have larger real part or larger natural frequencies. In this paper, we propose a two-step method in order to constrain the dominant dynamics of SISO models into LMI regions. In virtue of this result, in addition, the model eigenvalues could be constrained into disjoint LMI regions. Numerical examples illustrate the e effectiveness of our proposed method.

Population persistence in Cayley trees

This paper is concerned with the persistence of a single species population in a habitat represented by a finite rooted tree with a lethal boundary and whose interior is a Cayley tree. This Cayley tree is a habitat outside which the organisms cannot live. The population is assumed to be governed by an irreducible cooperative system of differential equations that admits zero as an equilibrium solution. The system is determined by five parameters that describes the structure of the tree representing the habitat and the demographic aspects of the population such as migration and reproduction. It is shown that the population is persistent if, and only if, the zero solution is unstable. The stability of the zero solution is determined by the eigenvalue of the Jacobian of the system at zero with largest real part. After obtaining analytically such eigenvalue in terms of the parameters of the system, two criteria for evaluation of persistence are derived. One of them is the minimum patch size, which, here, is defined as the minimum number of levels that makes the tree a habitat capable of sustaining the population.

Near-Field Surface Waves in Few-Layer MoS2

Recently emerged layered transition metal dichalcogenides have attracted great interest due to their intriguing fundamental physical properties and potential applications in optoelectronics. Using scattering-type scanning near-field optical microscope (s-SNOM) and theoretical modeling, we study propagating surface waves in the visible spectral range that are excited at sharp edges of layered transition metal dichalcogenides (TMDC) such as molybdenum disulfide and tungsten diselenide. These surface waves form fringes in s-SNOM measurements. By measuring how the fringes change when the sample is rotated with respect to the incident beam, we obtain evidence that exfoliated MoS2 on a silicon substrate supports two types of Zenneck surface waves that are predicted to exist in materials with large real and imaginary parts of the permittivity. We have compared MoS2 interference fringes with those formed on layered insulator such as hexagonal boron nitride where only leaky modes are possible due to its small permittivity. Interpretation of experimental data is supported by theoretical models. Our results could pave the way to the investigation of surface waves on TMDCs and other van der Waals materials and their novel photonics applications.

On the convergence and the steady state in a delayed Solow model

The Solow-Swan model is analyzed with constant population growth rate and fix delay in the production process and in the depreciation. The linear stability of the trivial equilibrium and the steady state is investigated via stability charts after the identification of the effect of the delay on the level of the steady state. After that, the rate of convergence is approximated close to the steady state with the help of the estimation of the characteristic exponent with the largest real part. The identity of the convergence of the capital and the output in per capita is proven in the presence of delay too.

An All‐Dielectric Metasurface Building Block for the Kerker Effect between Excitons and Nanocavities: Germanium Nanogroove

AbstractCoupling between light and matter has many infusive physical effects and potential applications. Large Rabi splitting energy is achieved in many plasmonic nanostructures; however, these noble metallic materials generally suffer from a high level of Joule heating losses at optical frequencies. As an alternative strategy, all‐dielectric materials for manipulating light at the subwavelength scale have attracted enormous interest. However, the understanding of the interactions between all‐dielectric nanostructures and molecular excitons remains limited to date. Here, the use of a germanium nanogroove as a new all‐dielectric metasurface building block is demonstrated for the Kerker effect between molecular excitons and nanocavities. A distinct dip in the backward scattering spectra is observed, indicating relatively strong light–matter interaction due to the cavity magnetic resonance mode in the grooves. Germanium with a large real part and nonnegligible imaginary part of the refractive index in the visible region provides magnetic field enhancement similar to that of other all‐dielectric nanostructures; this phenomenon is theoretically explained by simulating the magnetic field distribution in the grooves. These findings may help researchers to better understand the interactions between all‐dielectric nanostructures and molecular excitons and indicate that germanium nanogrooves can potentially be used as metasurface building blocks in nanophotonic devices.

Optimization of Damping for Squeal Avoidance in Disc Brakes

AbstractThis paper deals with the optimization of the linear stability behavior of circulatory systems with respect to particularly advantageous damping properties. The technique is demonstrated by applying it to an industrial finite element model of a disc brake in order to reduce the propensity of squeal noise. After decomposing the damping matrix into several component matrices, which may have some special structure or physical relevance, the ratio of these are varied to either stabilize or make more stable the equilibrium state subject to sensible constraints. For the purpose of this study, a system is defined to be more stable if its eigenvalue with largest real part is as negative as possible. For a certain velocity range, it is shown to be beneficial to reduce the material damping in the pads and in the caliper, which might be counterintuitive from an engineer's perspective. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Calculation of Critical Oscillation Modes for Large Delayed Cyber-Physical Power System Using Pseudo-Spectral Discretization of Solution Operator

In eigenanalysis of large delayed cyber-physical power system (DCPPS), power engineers are interested in critical electromechanical oscillation modes with damping ratios less than a specified threshold. To efficiently compute these modes, a method based on pseudo-spectral discretization of the solution operator of DCPPS (SOD-PS) is presented in this paper. First, the unique spectral mapping properties of solution operator are analyzed. The largest eigenvalues in moduli of the operator correspond to the ones of DCPPS with the largest real parts. Second, a rotation-and-multiplication preconditioning technique is presented to enhance the dispersion among eigenvalues of the solution operator's discretized matrix. Third, critical electromechanical oscillation modes of DCPPS with the least damping ratios are captured with priority and an accelerated convergence rate by the implicitly restarted Arnoldi algorithm. Subsequently, the small signal stability of DCPPS can be readily and reliably determined. In SOD-PS, the unique property of Kronecker product and the inherent sparsity in augmented system matrices are fully exploited to guarantee efficiency and scalability. The accuracy and efficiency of the presented method are intensively studied and thoroughly validated on the 16-generator 68-bus test system and a real-life large transmission grid.