Sparse Plane Wave Approximation of Acoustic Modes to Address Basis Mismatch

Low-frequency sound field reconstruction in an enclosed space has many applications where the plane wave approximation of acoustic modes plays a crucial role. However, the basis mismatch of the plane wave directions degrades the approximation accuracy. In this study, a two-stage method combining ℓ1-norm relaxation and parametric sparse Bayesian learning is proposed to address this problem. This method involves selecting sparse dominant plane wave directions from pre-discretized directions and constructing a parameterized dictionary of low dimensionality. This dictionary is used to re-estimate the plane wave complex amplitudes and directions based on the sparse Bayesian framework using the variational Bayesian expectation and maximization method. Numerical simulations show that the proposed method can efficiently optimize the plane wave directions to reduce the basis mismatch and improve acoustic mode approximation accuracy. The proposed method involves slightly increased computational cost but obtains a higher reconstruction accuracy at extrapolated field points and is more robust under low signal-to-noise ratios compared with conventional methods.

On band gaps of nonlocal acoustic lattice metamaterials: a robust strain gradient model

We have proposed an “exact” strain gradient (SG) continuum model to properly predict the dispersive characteristics of diatomic lattice metamaterials with local and nonlocal interactions. The key enhancement is proposing a wavelength-dependent Taylor expansion to obtain a satisfactory accuracy when the wavelength gets close to the lattice spacing. Such a wavelength-dependent Taylor expansion is applied to the displacement field of the diatomic lattice, resulting in a novel SG model. For various kinds of diatomic lattices, the dispersion diagrams given by the proposed SG model always agree well with those given by the discrete model throughout the first Brillouin zone, manifesting the robustness of the present model. Based on this SG model, we have conducted the following discussions. (I) Both mass and stiffness ratios affect the band gap structures of diatomic lattice metamaterials, which is very helpful for the design of metamaterials. (II) The increase in the SG order can enhance the model performance if the modified Taylor expansion is adopted. Without doing so, the higher-order continuum model can suffer from a stronger instability issue and does not necessarily have a better accuracy. The proposed SG continuum model with the eighth-order truncation is found to be enough to capture the dispersion behaviors all over the first Brillouin zone. (III) The effects of the nonlocal interactions are analyzed. The nonlocal interactions reduce the workable range of the well-known long-wave approximation, causing more local extrema in the dispersive diagrams. The present model can serve as a satisfactory continuum theory when the wavelength gets close to the lattice spacing, i.e., when the long-wave approximation is no longer valid. For the convenience of band gap designs, we have also provided the design space from which one can easily obtain the proper mass and stiffness ratios corresponding to a requested band gap width.

Time Evolution of the Position Operators in a Bilayer Graphene

In this work, the researchers mainly focus on the trembling motion which is known as Zitterbewegung in a bilayer grapheme. This is effectively achieved by means of the long-wave approximation. That is, the Heisenberg representation is ultimately employed in order to derive the analytical expression concerning the expectation value related to the position operator along the longitudinal and transversal orientation, which describes the motion concerning the electronic wave packet inside the bilayer graphene. Parameters’ numbers are considered to explicate the packet of Gaussian wave, including the polarization of initial pseudo-spin as well as the wave number of the initial carrier number along with the localized wave packet’s width along the longitudinal as well as transversal orientation. Consequently, the researchers show that the obvious oscillation in position operator can be effectively controlled not only by what is known as the initial parameters concerning the wave packet. Rather, it can mainly be controlled by selecting the localized quantum state’s components. Furthermore, the interference’s analysis between the conduction as well as valence bands concerning quantum states is really emphasized as the ability of what can be described as the transient’s emergence, or in a sense, aperiodic temporal oscillations concerning the average value of position operator in the bilayer graphene.

Magnetic structure study of the sawtooth chain antiferromagnet $$\hbox {Fe}_2\hbox {Se}_2\hbox {O}_7$$

A magnetic structure of the sawtooth-chain antiferromagnet $$\hbox {Fe}_2\hbox {Se}_2\hbox {O}_7$$ Fe 2 Se 2 O 7 was investigated by magnetization measurements, single crystalline and powder neutron diffraction experiments, and a further analysis on the Mössbauer spectra. These experiments revealed a nearly collinear antiferromagnetic structure with magnetic moments aligned along the b-axis, indicating dominant antiferromagnetic exchanges between Fe(1)–Fe(2) and Fe(2)–Fe(3) sites. The magnon dispersion relation derived from the linear spin wave approximation suggests the possible flat band nature of magnons.

Wave-induced Lagrangian drift in a porous seabed

The mean drift in a porous seabed caused by long surface waves in the overlying fluid is investigated theoretically. We use a Lagrangian formulation for the fluid and the porous bed. For the wave field we assume inviscid flow, and in the seabed, we apply Darcy’s law. Throughout the analysis, we assume that the long-wave approximation is valid. Since the pressure gradient is nonlinear in the Lagrangian formulation, the balance of forces in the porous bed now contains nonlinear terms that yield the mean horizontal Stokes drift. In addition, if the waves are spatially damped due to interaction with the underlying bed, there must be a nonlinear balance in the fluid layer between the mean surface gradient and the gradient of the radiation stress. This causes, through continuity of pressure, an additional force in the porous layer. The corresponding drift is larger than the Stokes drift if the depth of the porous bed is more than twice that of the fluid layer. The interaction between the fluid layer and the seabed can also cause the waves to become temporally attenuated. Again, through nonlinearity, this leads to a horizontal Stokes drift in the porous layer, but now damped in time. In the long-wave approximation only the horizontal component of the permeability in the porous medium appears, so our analysis is valid for a medium that has different permeabilities in the horizontal and vertical directions. It is suggested that the drift results may have an application to the transport of microplastics in the porous oceanic seabed.

A Multivariate Polynomial Regression to Reconstruct Ground Contact and Flight Times Based on a Sine Wave Model for Vertical Ground Reaction Force and Measured Effective Timings

Effective contact (tce) and flight (tfe) times, instead of ground contact (tc) and flight (tf) times, are usually collected outside the laboratory using inertial sensors. Unfortunately, tce and tfe cannot be related to tc and tf because the exact shape of vertical ground reaction force is unknown. However, using a sine wave approximation for vertical force, tce and tc as well as tfe and tf could be related. Indeed, under this approximation, a transcendental equation was obtained and solved numerically over a tce x tfe grid. Then, a multivariate polynomial regression was applied to the numerical outcome. In order to reach a root-mean-square error of 0.5 ms, the final model was given by an eighth-order polynomial. As a direct application, this model was applied to experimentally measured tce values. Then, reconstructed tc (using the model) was compared to corresponding experimental ground truth. A systematic bias of 35 ms was depicted, demonstrating that ground truth tc values were larger than reconstructed ones. Nonetheless, error in the reconstruction of tc from tce was coming from the sine wave approximation, while the polynomial regression did not introduce further error. The presented model could be added to algorithms within sports watches to provide robust estimations of tc and tf in real time, which would allow coaches and practitioners to better evaluate running performance and to prevent running-related injuries.

Optical Amplification and Fast-Slow Light in a Three-Mode Cavity Optomechanical System without Rotating Wave Approximation

We investigate the optical amplification of the output field and fast-slow light effect in a three-mode cavity optomechanical system without rotating wave approximation and discuss two ways of realizing the optical amplification effect. Resorting to the Coulomb coupling between the nanomechanical resonators, the asymmetric double optomechanically induced amplification effect can be achieved by utilizing the counterrotating term. Moreover, we find a remarkable optical amplification effect and observe the prominent fast-slow light effect at the singular point since the introduction of mechanical gain. Meanwhile, the transmission rate of the output field is increased by four orders of magnitude and the group delay time can reach in the order of 105μs. Our work is of great significance for the potential applications of optomechanically induced amplification in quantum information processing and quantum precision measurement.