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In this work, topological resonance behaviors of surface acoustic wave (SAW) under surface liquid-layer loadings are investigated. The results show that through the coupling of waveguide and resonant cavity, a resonant peak with high Q-factor can emerge, and the frequency of which is significantly sensitive to the liquid parameters. Based on that, a topological-resonance SAW liquid-phase sensor is proposed. The results show that the formation of the topological phase transition is closely related to the liquid-layer loading. Furthermore, by changing the thickness of the liquid-layer loading, the operating-frequency range of the device can be significantly expanded, which is vital for biomedical detecting applications. Based on which, the sensing performances of topological-resonance SAW liquid-phase sensor are simulated, which are used to sensing the concentration of albumin and hemoglobin concentration in blood, and high sensitivities and Q-factors can be obtained for this device. The results presented in this paper can provide an important basis for the realization of highly sensitive and stable SAW biomedical sensors in the future.

The design of cell-free massive MIMO (CF-mMIMO) systems requires accurate, measurement-based channel models. This paper provides the first results from the by far most extensive outdoor measurement campaign for CF-mMIMO channels in an urban environment. We measured impulse responses between over 20,000 potential access point (AP) locations and 80 user equipments (UEs) at 3.5 GHz with 350 MHz bandwidth (BW). Measurements use a "virtual array" approach at the AP and a hybrid switched/virtual approach at the UE. This paper describes the sounder design, measurement environment, data processing, and sample results, particularly the evolution of the power-delay profiles (PDPs) as a function of the AP locations, and its relation to the propagation environment., Comment: Submitted to: VTC 2024-Fall

Counter-rotating mechanical metamaterials have previously been found to have anomalous characteristics or functions such as auxetics effects, shape changers, and soliton transports, which are all under monostable conditions. The properties of counter-rotating mechanical metamaterials under bistable conditions have not yet been explored. Here, we found that for a bistable counter-rotating metamaterial chain, the effective stiffnesses of the two steady states are different in the chain with even-numbered nodes. For the chain with odd-numbered nodes, the effective stiffnesses corresponding to the two steady states are exactly the same. This special property is not characterized by the characteristic attenuation lengths of the underlying mechanism, but depends on the different symmetries of the underlying mechanism of the chains with odd and even nodes. In addition, the relationship between the abnormal non-monotonic size effect and equilibrium angle are clarified. More interestingly, for one-dimensional chains with even-numbered nodes, the size effect of effective stiffness bifurcates at a specific equilibrium angle, and the according mechanisms are revealed.

This paper describes a trapezoidal quadrature method for the discretization of weakly singular, singular and hypersingular boundary integral operators with complex symmetric quadratic forms. Such integral operators naturally arise when complex coordinate methods or complexified contour methods are used for the solution of time-harmonic acoustic and electromagnetic interface problems in three dimensions. The quadrature is an extension of a locally corrected punctured trapezoidal rule in parameter space wherein the correction weights are determined by fitting moments of error in the punctured trapezoidal rule, which is known analytically in terms of the Epstein zeta function. In this work, we analyze the analytic continuation of the Epstein zeta function and the generalized Wigner limits to complex quadratic forms; this analysis is essential to apply the fitting procedure for computing the correction weights. We illustrate the high-order convergence of this approach through several numerical examples., Comment: 21 pages, 3 figures

In this work, elastic fractal higher-order topological states are investigated. Bott index is adopted to characterize the topological property of elastic fractal structures. The topological corner and edge states of elastic waves in fractal structures are realized theoretically and experimentally. Different from traditional two-dimension (2D) high-order topological insulators based on periodic structures, the high-order topological states based on elastic fractal structures in this work support not only abundant topological inner corner states and edge states, but also topological outer corner states. The richness of corner states is much higher than that of topological insulators based on periodic structures. The strong robustness of the topological corner states in the fractal structure are verified by introducing disorders and defects. The topological phenomenon of elastic fractal structures revealed in this work enriches the topological physics of elastic systems and breaks the limitation of that relies on periodic elastic structures. The results have important application prospects in energy harvesting, information transmissions, elastic energy acquisitions and high-sensitivity detections.

A boundary integral equation method for the 3-D Helmholtz equation in multilayered media with many quasi-periodic layers is presented. Compared with conventional quasi-periodic Green's function method, the new method is robust at all scattering parameters. A periodizing scheme is used to decompose the solution into near- and far-field contributions. The near-field contribution uses the free-space Green's function in an integral equation on the interface in the unit cell and its immediate eight neighbors; the far-field contribution uses proxy point sources that enclose the unit cell. A specialized high-order quadrature is developed to discretize the underlying surface integral operators to keep the number of unknowns per layer small. We achieve overall linear computational complexity in the number of layers by reducing the linear system into block tridiagonal form and then solving the system directly via block LU decomposition. The new solver is capable of handling a 100-interface structure with 961.3k unknowns to $10^{-5}$ accuracy in less than 2 hours on a desktop workstation., Comment: 17 pages, 6 figures, 1 table

This paper describes a trapezoidal quadrature method for the discretization of singular and hypersingular boundary integral operators (BIOs) that arise in solving boundary value problems for elliptic partial differential equations. The quadrature is based on a uniform grid in parameter space coupled with the standard punctured Trapezoidal rule. A key observation is that the error incurred by the singularity in the kernel can be expressed exactly using generalized Euler-Maclaurin formulae that involve the Riemann zeta function in 2D and the Epstein zeta functions in 3D. These expansions are exploited to correct the errors via local stencils at the singular point using a novel systematic moment-fitting approach. This new method provides a unified treatment of all common BIOs (Laplace, Helmholtz, Stokes, etc.). We present numerical examples that show convergence of up to 32nd-order in 2D and 9th-order in 3D with respect to the mesh size., Comment: 26 pages, 7 figures, 1 table

A high-order accurate quadrature rule for the discretization of boundary integral equations (BIEs) on closed smooth contours in the plane is introduced. This quadrature can be viewed as a hybrid of the spectral quadrature of Kress (1991) and the locally corrected trapezoidal quadrature of Kapur and Rokhlin (1997). The new technique combines the strengths of both methods, and attains high-order convergence, numerical stability, ease of implementation, and compatibility with the "fast" algorithms (such as the Fast Multipole Method or Fast Direct Solvers). Important connections between the punctured trapezoidal rule and the Riemann zeta function are introduced, which enable a complete convergence analysis and lead to remarkably simple procedures for constructing the quadrature corrections. The paper reports a detailed comparison between the new method and the methods of Kress, of Kapur and Rokhlin, and of Alpert (1999)., Comment: 18 pages, 4 figures, 1 table. For accompanying Matlab code, see https://github.com/bobbielf2/ZetaTrap2D

The manuscript describes a quadrature rule that is designed for the high order discretization of boundary integral equations (BIEs) using the Nystr\"{o}m method. The technique is designed for surfaces that can naturally be parameterized using a uniform grid on a rectangle, such as deformed tori, or channels with periodic boundary conditions. When a BIE on such a geometry is discretized using the Nystr\"{o}m method based on the Trapezoidal quadrature rule, the resulting scheme tends to converge only slowly, due to the singularity in the kernel function. The key finding of the manuscript is that the convergence order can be greatly improved by modifying only a very small number of elements in the coefficient matrix. Specifically, it is demonstrated that by correcting only the diagonal entries in the coefficient matrix, $O(h^{3})$ convergence can be attained for the single and double layer potentials associated with both the Laplace and the Helmholtz kernels. A nine-point correction stencil leads to an $O(h^5)$ scheme. The method proposed can be viewed as a generalization of the quadrature rule of Duan and Rokhlin, which was designed for the 2D Lippmann-Schwinger equation in the plane. The techniques proposed are supported by a rigorous error analysis that relies on Wigner-type limits involving the Epstein zeta function and its parametric derivatives., Comment: 39 pages, 4 figures, 3 tables. For accompanying Matlab code, see https://github.com/bobbielf2/ZetaTrap3D

We present two approaches to system identification, i.e. the identification of partial differential equations (PDEs) from measurement data. The first is a regression-based Variational System Identification procedure that is advantageous in not requiring repeated forward model solves and has good scalability to large number of differential operators. However it has strict data type requirements needing the ability to directly represent the operators through the available data. The second is a Bayesian inference framework highly valuable for providing uncertainty quantification, and flexible for accommodating sparse and noisy data that may also be indirect quantities of interest. However, it also requires repeated forward solutions of the PDE models which is expensive and hinders scalability. We provide illustrations of results on a model problem for pattern formation dynamics, and discuss merits of the presented methods.

We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The key ingredient is a set of panel quadrature rules capable of evaluating weakly-singular, nearly-singular and hyper-singular integrals to high accuracy. Near-singular integral evaluation, in particular, is done using an extension of the scheme developed in J.~Helsing and R.~Ojala, {\it J. Comput. Phys.} {\bf 227} (2008) 2899--2921. The boundary of the given geometry is ``panelized'' automatically to achieve user-prescribed precision. We show that this adaptive panel refinement procedure works well in practice even in the case of complex geometries with large number of corners. In one example, for instance, a model 2D vascular network with 378 corners required less than 200K discretization points to obtain a 9-digit solution accuracy., Comment: 24 pages, 8 figures, 1 table

The electrohydrodynamics of vesicle suspensions is characterized by studying their pairwise interactions in applied DC electric fields in two dimensions. In the dilute limit, the rheology of the suspension is shown to vary nonlinearly with the electric conductivity ratio of the interior and exterior fluids. The prolate-oblate-prolate transition and other transitionary dynamics observed in experiments and previously confirmed via numerical simulations is further investigated here for smaller reduced areas. When two vesicles are initially un-aligned with the external electric field, three different responses are observed when the key parameters are varied: (i) chain formation--they self-assemble to form a chain that is aligned along the field direction, (ii) circulatory motion--they rotate about each other, (iii) oscillatory motion--they form a chain but oscillate about each other., Comment: 15 pages, 10 figures, second revision on Oct 18, 2018

Dense particulate flow simulations using integral equation methods demand accurate evaluation of Stokes layer potentials on arbitrarily close interfaces. In this paper, we generalize techniques for close evaluation of Laplace double-layer potentials in J. Helsing and R. Ojala, J. Comput. Phys. 227 (2008) 2899-2921. We create a "globally compensated" trapezoid rule quadrature for the Laplace single-layer potential on the interior and exterior of smooth curves. This exploits a complex representation, a product quadrature (in the style of Kress) for the sawtooth function, careful attention to branch cuts, and second-kind barycentric-type formulae for Cauchy integrals and their derivatives. Upon this we build accurate single- and double-layer Stokes potential evaluators by expressing them in terms of Laplace potentials. We test their convergence for vesicle-vesicle interactions, for an extensive set of Laplace and Stokes problems, and when applying the system matrix in a boundary value problem solver in the exterior of multiple close-to-touching ellipses. We achieve typically 12 digits of accuracy using very small numbers of discretization nodes per curve. We provide documented codes for other researchers to use., Comment: 21 pages, 7 figures; submitted to SIAM J. Sci. Comput