Pseudo Modes Research Articles

Spin relaxation dynamics with a continuous spin environment: The dissipaton equation of motion approach.

We investigate the quantum dynamics of a spin coupling to a bath of independent spins via the dissipaton equation of motion (DEOM) approach. The bath, characterized by a continuous spectral density function, is composed of spins that are independent level systems described by the su(2) Lie algebra, representing an environment with a large magnitude of anharmonicity. Based on the previous work by Suarez and Silbey [J. Chem. Phys. 95, 9115 (1991)] and by Makri [J. Chem. Phys. 111, 6164 (1999)] that the spin bath can be mapped to a Gaussian environment under its linear response limit, we use the time-domain Prony fitting decomposition scheme to the bare-bath time correlation function (TCF) given by the bosonic fluctuation-dissipation theorem to generate the exponential decay basis (or pseudo modes) for DEOM construction. The accuracy and efficiency of this strategy have been explored by a variety of numerical results. We envision that this work provides new insights into extending the hierarchical equations of motion and DEOM approach to certain types of anharmonic environments with arbitrary TCF or spectral density.

Improving the performance of a multi-material topology optimization model involving stress and dynamic constraints

In this study, an approach for multi-material topology optimization (MMTO) that addresses several distinct matters is proposed. The proposed formulation, which is based on the alternating active-phase algorithm (AAPA) and the Jacobi approach, can firstly deal with dynamic topology optimization. As a second execution, the method is used to resolve the strength-enhancing, globally applicable von Mises stress limitations. In addition, stress constraints are applied concurrently to the dynamic issues. As a result, the stability and strength of the structures are both improved at the same time. Thirdly, the eigenvalues shift approach and the modified interpolation scheme are proposed to prevent the mode switching and pseudo modes in the MMTO problem, respectively. Multi-material architectures with and without stress limitations reveal different optimum results for each frequency constraint. The design variables are required the method of moving asymptotes (MMA) for updating new design variables after main loop. Extensive numerical examples are given, and the authors highlight outstanding questions that are the focus of current studies.

Experimental Synthesis and Demonstration of the Twisted Laguerre–Gaussian Schell-Mode Beam

The twisted Laguerre–Gaussian Schell-model (TLGSM) beam is a novel type of partially coherent beam embedded with both the second-order twist phase and the classical vortex phase. The intriguing properties induced by the interaction of the two types of phases have been demonstrated theoretically quite recently. In this work, we introduce a flexible way to experimentally synthesize a TLGSM beam with controllable twist strength. The protocol relies on the discrete pseudo-mode representation for the cross-spectral density of a TLGSM beam, in which the beam is viewed as an incoherent superposition of a finite number of spatially coherent modes. We show that all these pseudo modes endowed with random phases are mutually uncorrelated and can be encoded into a single frame of a dynamic computer-generated hologram. By sequentially displaying dynamic holograms on a single spatial-light modulator, the controllable TLGSM beam can be synthesized experimentally. The joint effect of the two phases on the propagation and self-reconstruction characteristics of the synthesized beam has also been studied in the experiment.

Generating non-uniformly correlated twisted sources.

The inverse method of proving the twistability of cross-spectral density (CSD) inevitably falls into spontaneous difficulties. Based on a nonnegative self-consistent design guideline for generating genuine CSDs introduced by Gori and Santarsiero, we demonstrate a feasible way for twisting partially coherent sources by sticking a Schell-model function to CSDs, which also determines the upper bound of the twisting strength. Analysis shows that the degree of coherence of a new class of twisted pseudo-Gaussian Schell-model beam is neither shift invariant nor shift-circular symmetric. In the presence of a vortex phase, the two different types of chiral phases affect each other and together control the propagation behavior. We further carry out an experiment to generate this non-uniformly correlated twisted beam using weighted superposition of mutually uncorrelated pseudo modes. The result is beneficial for devising nontrivial twisted beams and offers new opportunities.

Topology optimization of steel frame structures with constraints on overall and individual member instabilities

A computationally efficient structural topology optimization framework is proposed for design of steel frame structures with user-defined factors of safety against overall structure (global) and individual member instabilities. The objective function is minimization of either compliance or the maximum of von Mises stresses within the frame structure. Within optimization, overall structure buckling modes are found via an eigenvalue analysis, a subset of “pseudo modes” are identified using a newly proposed methodology and are discarded to obtain a set of real eigenvalues. Moreover, individual member buckling loads are estimated with Euler buckling analysis and are aggregated into a single constraint. The minimum of each instability constraint is then estimated with separate differentiable negative p-norm functions. Sensitivities of these newly developed constraints are explicitly derived for application of gradient-based optimizers. The topology of four frame structures featuring moment-resisting connections and member cross-sectional properties mapped from the American Institute of Steel Construction design manual are optimized with the proposed algorithm to verify its effectiveness in optimizing structural performance while maintaining factors of safety against overall and individual member instabilities. The interaction effects of preventing instabilities at different safety levels and the choice of objective function on the final designs and their performances are investigated.

EMD self-adaptive selecting relevant modes algorithm for FBG spectrum signal

Abstract Noise may reduce the demodulation accuracy of fiber Bragg grating (FBG) sensing signal so as to affect the quality of sensing detection. Thus, the recovery of a signal from observed noisy data is necessary. In this paper, a precise self-adaptive algorithm of selecting relevant modes is proposed to remove the noise of signal. Empirical mode decomposition (EMD) is first used to decompose a signal into a set of modes. The pseudo modes cancellation is introduced to identify and eliminate false modes, and then the Mutual Information (MI) of partial modes is calculated. MI is used to estimate the critical point of high and low frequency components. Simulation results show that the proposed algorithm estimates the critical point more accurately than the traditional algorithms for FBG spectral signal. While, compared to the similar algorithms, the signal noise ratio of the signal can be improved more than 10 dB after processing by the proposed algorithm, and correlation coefficient can be increased by 0.5, so it demonstrates better de-noising effect.

MODELING SOLAR OSCILLATION POWER SPECTRA. II. PARAMETRIC MODEL OF SPECTRAL LINES OBSERVED IN DOPPLER-VELOCITY MEASUREMENTS

We describe a global parametric model for the observed power spectra of solar oscillations of intermediate and low degree. A physically motivated parameterization is used as a substitute for a direct description of mode excitation and damping as these mechanisms remain poorly understood. The model is targeted at the accurate fitting of power spectra coming from Doppler velocity measurements and uses an adaptive response function that accounts for both the vertical and horizontal components of the velocity field on the solar surface and for possible instrumental and observational distortions. The model is continuous in frequency, can easily be adapted to intensity measurements and extends naturally to the analysis of high-frequency pseudo modes (interference peaks at frequencies above the atmospheric acoustic cutoff).

Topology Optimization of Passive Constrained Layer Damping with Partial Coverage on Plate

The potential of using topology optimization as a tool to optimize the passive constrained layer damping (PCLD) layouts with partial coverage on flat plates is investigated. The objective function is defined as a combination of several modal loss factors solved by finite element-modal strain energy (FE-MSE) method. An interface finite element is introduced to modeling the viscoelastic core of PCLD patch to save the computational space and time in the optimization procedure. Solid isotropic material with penalization (SIMP) method is used as the material interpolation scheme and the parameters are well selected to avoid local pseudo modes. Then, the method of moving asymptote (MMA) is employed as an optimizer to search the optimal topologies of PCLD patch on plates. Applications of two flat plates with different shapes have been applied to demonstrate the validation of the proposed approach. The results show that the objective function is in a steady convergence process and the damping effect of the plates can be enhanced by the optimized PCLD layouts.

Topology Optimization of Passive Constrained Layer Damping with Partial Coverage on Plate

The potential of using topology optimization as a tool to optimize the passive constrained layer damping (PCLD) layouts with partial coverage on flat plates is investigated. The objective function is defined as a combination of several modal loss factors solved by finite element-modal strain energy (FE-MSE) method. An interface finite element is introduced to modeling the viscoelastic core of PCLD patch to save the computational space and time in the optimization procedure. Solid isotropic material with penalization (SIMP) method is used as the material interpolation scheme and the parameters are well selected to avoid local pseudo modes. Then, the method of moving asymptote (MMA) is employed as an optimizer to search the optimal topologies of PCLD patch on plates. Applications of two flat plates with different shapes have been applied to demonstrate the validation of the proposed approach. The results show that the objective function is in a steady convergence process and the damping effect of the plates can be enhanced by the optimized PCLD layouts.

Solarpmodes in 10 years of the IRIS network

IRIS data (the low degree f < 3 helioseismology network) have been analysed for the study of p-mode parameters variability over the falling phase of the solar activity cycle 22 and the rising phase of the solar activity cycle 23. The IRIS duty cycle has been improved by the so-called repetitive music method, a method of partial gap filling. We present in this paper an analysis of the dependence of p-mode frequencies and linewidths with frequency and with solar magnetic activity. We confirm also the periodicity of about 70 μHz of the high-frequency pseudo modes, with a much reduced visibility during the phase of higher activity.

Fidelity of the periodical self-reconstruction of wavefield

The periodical self-reconstruction of the wave function is examined for monochromatic wavefields fulfilling the Helmholtz equation. The effect is possible for an arbitrary signal wavefield with the predetermined wave function due to the pseudosampling of its spatial spectrum in cylindrical coordinates. The simplest description of the effect, based on the decomposition of the wave function into the base of ideal non-diffracting modes carrying infinite energy, is replaced by the model dealing with the pseudo non-diffracting modes. It can be closely related to the experimental realization. The fidelity of the self-reconstruction is examined applying the criterion based on the correlation concept.

Effects of layer thickness for SAW, PSAW, and HVPSAW devices.

Considerable efforts in recent SAW device design and development have been aimed at obtaining high frequency, low loss, and high performance. A large number of applications relate to cellular and mobile telephony, pagers, local area networks, cordless phones, global positioning systems (GPS), and security systems. Pseudo-SAW (PSAW) and high velocity PSAW (HVPSAW) have received great attention because of their high phase velocities and, therefore, the high frequencies of operation that these modes provide. In addition to high phase velocities, the pseudomodes must also present low propagation losses and considerably high electromechanical coupling coefficients to be considered for surface acoustic wave (SAW) devices. This paper verifies that the metallic layer thickness is a relevant SAW device parameter, which must be considered to achieve lower losses for high frequency, low loss SAW devices. Popular PSAW and HVPSAW material orientations, such as 64 degrees YX LiNbO3 (0 degree -26 degrees 0 degree), 36 degrees YX LiTaO3 (0 degree -54 degrees 0 degree), LiNbO3 (90 degrees 90 degrees 36 degrees), LiTaO3 (90 degrees 90 degrees 31 degrees), and Li2B4O7 (0 degree 47.3 degrees 90 degrees), are considered as examples. In addition to the reduced loss analysis and the dispersion analysis for the pseudo modes, the present work discusses the transitions with respect to the layer thickness from the PSAWs and HVPSAWs to the generalized SAWs (GSAWs) and Rayleigh (sagittal particle motion) modes. In addition to contributing to the knowledge of the pseudomodes behavior with layer thickness, this mode transition analysis enlightens the situation in which the losses in the pseudo modes go to zero because of the merging of the pseudo modes into the SAWs (GSAWs and Rayleigh). The fact that the SAWs are a continuation as a function of thickness for the pseudo modes may be conveniently used in the fabrication of low loss devices. In addition, the effects of heavy layer metals, such as gold, in reducing the layer thickness at which the pseudo modes merge to the SAWs are discussed. Numerical results are compared with experimental data available in the literature, and the present analysis elucidates experimentally observed higher order pseudo modes and values of layer thickness for which lower losses are achieved.

Pseudo and High Velocity Pseudo SAWs

This article discusses the characteristics of pseudo surface waves (PSAWs) and high velocity pseudo surface waves (HVPSAWs). The fundamental properties of these waves, the matrix method formulation, the different solution types due to crystal symmetry, early experiments on HVPSAWs, and practical applications of pseudo surface acoustic waves serve as an introduction. The solutions to the pseudo modes are discussed by analyzing the boundary condition function for several orientations. The relation between the radiating partial modes and the sagittal plane bulk slowness reveals new characteristics of the different symmetry types of HVPSAW, and helps classify and understand the pseudo modes. The acoustoelectric Poynting vector is used along different crystal symmetry orientations to reveal and discuss the pseudo SAW characteristics: penetration depth, declination of the power vector, and an estimation of power flow angle. Experimental data and numerical solutions of HVPSAW and PSAW along selected planes and orientations are discussed. This article concludes with a brief analysis of layered structures on different symmetry type substrates and a discussion of the layered pseudo surface wave properties.

PSEUDO AND HIGH VELOCITY PSEUDO SAWs

This article discusses the characteristics of pseudo surface waves (PSAWs) and high velocity pseudo surface waves (HVPSAWs). The fundamental properties of these waves, the matrix method formulation, the different solution types due to crystal symmetry, early experiments on HVPSAWs, and practical applications of pseudo surface acoustic waves serve as an introduction. The solutions to the pseudo modes are discussed by analyzing the boundary condition function for several orientations. The relation between the radiating partial modes and the sagittal plane bulk slowness reveals new characteristics of the different symmetry types of HVPSAW, and helps classify and understand the pseudo modes. The acoustoelectric Poynting vector is used along different crystal symmetry orientations to reveal and discuss the pseudo SAW characteristics: penetration depth, declination of the power vector, and an estimation of power flow angle. Experimental data and numerical solutions of HVPSAW and PSAW along selected planes and orientations are discussed. This article concludes with a brief analysis of layered structures on different symmetry type substrates and a discussion of the layered pseudo surface wave properties.

Analysis of the propagation of strongly attenuated leaky acoustic modes as method of the detection of the low scale interface defects in the layered structures

Abstract Propagation of pseudo surface modes, PSMs, propagating on SrF2 epitaxial layers deposited on GaAs(111) was studied by means of Brillouin spectroscopy. A lowering of 3 ÷ 77% of the velocity values of the PSMs was detected in case of leaky modes of a relatively strong leakage. The observed deviations of the velocity of the PSMs are connected with the presence of a roughness region of fluoride/GaAs(111) interface extending on several nm.

Overview no. 67 The deformation twinning of superlattice structures derived from disordered B.C.C. or F.C.C. solid solutions

The theory of deformation twinning is developed and applied to superlattice structures. With the exception of some hypothetical structures at rather improbable stoichiometric compositions, the normal b.c.c. or f.c.c. twinning shears always lead to “pseudo modes” when applied without “shuffles” to a cubic superlattice. In non-cubic superlattices, however, some variants of the usual disordered mode correspond to true twins whereas others give pseudo twins. True twins in non-cubic superlattices may have type I, type II or “combined” orientation relations, even though all twinning elements are rational, so that all twins are “compound” in the conventional definition. True twins in cubic superlattices may form (geometrically) by non-shuffle modes of higher shear or by modes requiring some “non-interchange” shuffling; there is recent experimental evidence for the operation of such a shuffle mode in a B2 superlattice structure. The paper includes a full discussion of the various true and pseudo twinning modes in all the cubic and non-cubic superlattices which appear in the Richards and Cahn ground state diagrams. Recent experimental work has shown that twinning is often an important deformation mode in superlattices; these experimental results are discussed and shown to be in general agreement with the theory.

On the detection of pseudo surface modes in Ag(111) with He-surface scattering

Abstract We evaluate the surface phonon dispersion relations of Ag(111) within a force constants parametrization of the bulk dynamics. By changing the surface force constants we are able to explain all the salient features appearing in the experimental time of flight spectra. The parallel momentum Q has been considered along the direction [1 1 0] of the surface Brillouin zone. We show that the peaks of the time of flight spectra are related to the Rayleigh wave, to the pseudo Rayleigh wave and to a new resonance of longitudinal character. A comparison is made with the [11 2 ] direction.

Effect of lateral leakage on neutron waves in polycrystalline media

Abstract The reduced three-dimensional transport equation for neutron wave propagation is solved in the velocity-dependent case with a separable scattering kernel by the eigenfunction-expansion method. The full-and half-range orthogonalities for the eigenfunctions are derived. The former is applied to solve the transport equation in an infinite system. In the case of a discontinuous total cross section, the contribution from the two-dimensional continuum in the spectral plane is reduced to an integral along the branch cut by applying the analytical continuation of the dispersion function. The effects of transverse buckling on the discrete and pseudo modes are examined by numerical calculations of the solution for beryllium and graphite.

Transport Theory of Neutron Wave Propagation by Eigenfunction Expansion Method

An eigenfunction expansion method is developed for the neutron wave propagation theory with a cut off cross section. The full and half range orthogonality relations for the eigenfunctions are derived, which are respectively applied to obtain an infinite space solution and the space eigenvalue formula. The formula is tried on some actual evaluations, and found to reduce considerably the laborious procedure required hitherto. The existence of marked interference phenomena between the discrete and the pseudo modes is demonstrated by numerical calculations performed on the solutions for graphite and beryllium.

Body waves as normal and leaking modes, 3. Pseudo modes and partial derivatives on the (+ −) sheet

In a multiple elastic wave guide, the phase velocity curves of the Π and Σ modes on the (+ −) sheet combine to form two families of almost continuous curves. The curves of the first family, called Π pseudo modes, are formed by the plateaus of the dispersion curves; they have a high group velocity, a low attenuation, and a low excitation; they depend solely on the P velocities. The curves of the second family, called Σ pseudo modes, are formed by the slopes of the dispersion curves and have the opposite characteristics. The Π pseudo modes make up the oscillatory part of the seismogram between P and S. The study is based on a simplified CIT 11 GB model, which consists of 6 layers, is 653 km thick, and contains a 54‐km low‐velocity P channel. The frequency range studied is from 0 to 0.146 Hz. The influence of the P channel is very restricted. At wavelengths smaller than ⅓ of its thickness, the layer below the channel (α = 8.19 km/sec) supports what is essentially a head wave.