Search Results (686)

MEMS resonators vibrate about equilibria deflected by whatever combination of temperature, pressure, and bias voltage is present—not about the flat, unloaded plate—raising a basic design question: does the resulting natural frequency depend on the specific loads that produced the deflection, or mainly on the deflection itself? We address this for annular and circular plates through a self-contained derivation of the governing multi-load equations and the linearized vibration eigenvalue problem about an arbitrary thermal, mechanical, and electrostatic equilibrium, validated against two classical benchmarks and applied to a parametric study spanning radius ratio, Poisson’s ratio, and five load combinations at matched deflection. The spread in squared frequency, ${\omega }_1^2$, across combinations shrinks monotonically from $29\%$ at $w/h=0.4$ to $6\%$ at $w/h=2.4$, a dynamic counterpart to a known static result in which the large-deflection boundary layer at a clamped edge depends only on the local membrane stress, not on which loads produced it. Going beyond the linear eigenfrequency, a single-mode Duffing-type reduction, compared against four independent classical benchmarks, reproduces the same asymmetry direction and hardening-to-softening crossover reported in the literature. For the one annular geometry and axisymmetric motion studied here, the results suggest that once deflection exceeds about twice the plate thickness, resonator frequency can be tabulated against deflection amplitude alone, rather than the full space of operating conditions. Full article

Non-destructive in situ tests, such as the plate bearing (plate load) test, are widely used to estimate the equivalent deformation modulus (e.g., $E_{v2}$) of existing road embankments. However, the depth of influence sampled by such a test is governed by the loading plate diameter, so a single test yields only an average, diameter-dependent modulus rather than the actual variation in stiffness with depth. This study investigates whether systematically varying the plate diameter and inverting the resulting settlement–diameter (dispersion) curves can recover the full depth-dependent stiffness profile, $E\left(z\right)$. Synthetic settlement–diameter curves were generated using a Boussinesq-based forward model for four families of reference stiffness profiles, representing normal (stiffness increasing with depth) and reverse (stiffness decreasing with depth) linear and exponential trends, combined with six Poisson’s ratios and five profile slopes/exponents (30 cases per profile family, 120 cases in total). Two inversion strategies were applied to back-calculate $E\left(z\right)$ from each dispersion curve: a classical Occam-type, smoothness-constrained (Tikhonov-regularized) nonlinear inversion, and a direct, closed-form simplified inversion method (SIM) based on differencing the apparent-modulus-versus-diameter curve. The results were benchmarked against the known reference profiles. Once calibrated so that its governing parameters depend only on Poisson’s ratio and the shape of the measured dispersion curve, SIM could be applied blindly—without knowledge of the reference profile or a starting model, requiring only an assumed Poisson’s ratio and the established calibration—and recovered $E\left(z\right)$ with markedly lower error than Occam’s inversion (WAD = 2.2–4.7% and RMSPE = 2.6–5.8%, versus 7.4–19.1% and 9.4–28.3%, respectively, across the four profile families). For the Poisson’s ratio most typical of earth materials, $\nu =0.3$, the calibration further collapses to a single parameter set common to all four families investigated ($I=0.66$; $c=1.3$ for stiffness increasing with depth, $c=2.5$ for stiffness decreasing with depth), which attains WAD ≤ 4.2% across all four families with no calibration equation at all. Notably, Occam’s inversion reproduced the settlement–diameter curve itself with good accuracy in most cases, yet this close data fit did not guarantee an accurate stiffness profile—a direct manifestation of the intrinsic non-uniqueness of the settlement-based inverse problem. These findings are bounded by their evidence base: noise-free data from the same forward operator used in the inversion, smooth profiles, a calibration evaluated on the cases that produced it, and an Occam comparison specific to L-curve-selected regularization. Within these limits, SIM is a promising alternative to regularized inversion; measurement noise, layered profiles and field validation are the next steps. Full article

Background/Objectives: Musculoskeletal disorders (MSDs) represent a significant occupational health concern among medical laboratory workers (MLWs) worldwide. However, in cross-sectional epidemiological assessments, these are more accurately characterized as self-reported musculoskeletal symptoms (MSSs). Despite growing awareness of physical ergonomic risk factors, the multifactorial etiology of these symptoms, such as psychosocial factors, remains incompletely understood in research laboratory settings. Consequently, this study aimed to determine the prevalence of MSSs among MLWs in a Malaysian research institute, assess physical ergonomic risk in their daily tasks, and evaluate the empirical association between MSSs and psychosocial work engagement. Methods: A cross-sectional study was conducted among MLWs at a Malaysian medical research institute. The 12-month prevalence of self-reported MSSs was assessed using the Nordic Musculoskeletal Questionnaire. Physical ergonomic risk was evaluated utilizing the Rapid Entire Body Assessment (REBA). Psychosocial work engagement was measured using the 17-item Utrecht Work Engagement Scale. Results: A total of 115 MLWs participated, with 73 (63.5%) reporting MSSs. The neck had the highest complaints (n = 43, 37.4%), followed by the lower back (n = 35, 30.4%) and shoulders (n = 33, 28.7%). Multivariable modified Poisson Generalized Estimating Equations revealed that physical ergonomic risk (REBA) was significantly associated with symptoms in the shoulder, upper back, and lower back. Female sex was independently correlated with the overall prevalence of MSSs (aPR = 1.39; 95% CI = 1.14–1.68), with marked associations observed for the neck and knees. Psychosocially, high “absorption” in work was significantly associated with upper back symptom prevalence (aPR = 1.57; 95% CI = 1.15–2.14). Conclusions: Ergonomic strain demonstrates a strong association with axial and shoulder symptoms among MLWs, while demographic characteristics and cumulative tenure correlate with specific extremity symptoms. Paradoxically, high psychological absorption emerges as a distinct correlate of upper back symptoms, likely due to prolonged postural neglect during deep concentration. Occupational health programs may benefit from combining targeted ergonomic accommodations with strategies designed to mitigate the potential physical vulnerabilities of highly absorbed personnel. Full article

The negative differential resistance (NDR) effect provides nonlinear control over ionic current and has important potential in ion sensing and information storage. A multiphys-ics numerical model is established using COMSOL Multiphysics 6.3, coupling the Poisson−Nernst−Planck and Navier−Stokes equations to investigate the effects of solution concentration gradient, pore length, pore diameter, and surface charge density on NDR effect. The results indicate that the NDR effect occurs only in the negative voltage range, where concentration gradient diffusion competes with electric field driven migration. The characteristic voltage window stabilizes between −0.2 V and −0.5 V, and the total current reaches a local extremum near −0.2 V. Electromigration dominates in this range and sup-presses Cl⁻ ion diffusion, while K⁺ transport is less affected, resulting in decreased total ionic current. Under baseline conditions, the total current decreases by 26.19%, from −0.42 nA to −0.31 nA. Increasing the concentration gradient, shortening the pore length, enlarging the pore diameter, and reducing the surface charge density enhance local vortices or maintain Cl⁻ diffusion pathways, thereby strengthening NDR characteristics. This study reveals the regulation mechanisms of NDR effect by solution conditions, macropore structures, and surface properties, providing theoretical guidance for tunable ionic current devices. Full article

Physics-informed neural networks (PINNs) approximate partial differential equations (PDEs) by enforcing governing equations and boundary conditions during training, but their accuracy depends on how collocation points are distributed and updated. We propose spatiotemporal compositional active sampling (STCAS), a reference-assisted offline configuration procedure that uses an analytic or high-accuracy numerical solution to rank complete three-stage sampling plans. It screens eight fixed rules, forms a task-specific shortlist, and evaluates bounded fixed, switched, and locally blended plans with independent selection sets and a composition guard. A safety-anchor decision retains the standard PINN unless the selected candidate is at least 5% better. Across five evaluations on 18 analytically specified two-dimensional Poisson tasks, this protocol improves 16 task means and ties two, reducing aggregate relative-$L_2$ error by 12.8% (hierarchical-bootstrap 95% interval $[6.78\%,19.32\%]$; one-sided paired Wilcoxon $p=2.19\times {10}^{-4}$). Against the confirmed fixed plan, aggregate error decreases by 8.2%. In comparison experiments designed for two transfer tasks and matched for main PINN training budgets, STCAS achieves the lowest aggregate mean reported error among the compared methods for both a steady convection–diffusion equation and a nonlinear time-dependent Burgers equation; its offline search cost is additional. Full article

Searching by numerical simulation for structures with optimal damping properties among viscoelastic hollow cylindrical bodies with a filler is usually associated with a large amount of computation. Formulating the mechanical problem as one of natural vibrations and natural wave propagation makes it possible to evaluate the dissipative properties of such a structure independently of external force and kinematic actions, and thereby to reduce the computational cost substantially. The solution of the natural vibration problem for a piecewise homogeneous viscoelastic hollow cylindrical body with a filler yields complex natural frequencies, the real part of which represents the vibration frequency and the imaginary part the damping factor (attenuation rate). The mechanical behavior of the viscoelastic material is described by the linear Boltzmann–Volterra hereditary theory with a three-parameter Koltunov–Rzhanitsyn relaxation kernel, within which the material characteristics are represented by complex dynamic moduli—the shear modulus and the bulk modulus—that, as a rule, depend on frequency. In the natural vibration problem these moduli become functions of the real part of the sought complex natural frequency alone, which makes the standard eigenvalue procedures of commercial finite-element codes inapplicable. The paper presents an algorithm that removes this difficulty. The dispersion relation of the piecewise homogeneous cylinder is obtained analytically in the form of a complex determinant of order 12 for a two-layer and 18 for a three-layer configuration, the elements of which are Bessel and Neumann functions of complex argument; the global stiffness and mass matrices needed for the general configuration can be assembled automatically in a general-purpose finite-element code such as ABAQUS; the resulting complex characteristic equation is solved by Muller’s method—every iteration of which evaluates the determinant by Gaussian elimination with partial pivoting, so that no expansion of the determinant is required. The efficiency of the algorithm is demonstrated for a two-layer viscoelastic hollow cylindrical body with a filler, the outer load-carrying layer being made of Kh12 steel and the inner layer (the filler) of 30 L steel. The real and imaginary parts of the complex natural frequencies, of the phase velocities and of the attenuation are obtained as functions of the dimensionless wave number, of Poisson’s ratio, of the ratio of the layer radii and of the ratio of the instantaneous elastic moduli of the layers. Full article

Boundary value problems in the theory of elasticity are traditionally formulated in terms of displacements, while stresses and strains are calculated from the displacements. Usually, the calculation of stresses and strains is accompanied by approximation errors. In this paper, alternative formulations of elasticity problems in stresses and strains are developed. It is shown that, to formulate boundary value problems (BVP) in stresses, it suffices to consider the three off-diagonal Beltrami–Michell equations together with the three equilibrium equations. Similarly, the off-diagonal strain compatibility equations are considered in conjunction with the three equilibrium equations expressed in terms of strains. In addition, the Beltrami–Michell equations and the strain compatibility equations are reduced to the Poisson equations for the stress and strain tensors, respectively. For the numerical solution of the formulated BVP in stresses and strains, the finite difference method and the finite element method within the FreeFEM++ framework were applied. A comparison of numerical results for the problems of stretching a rectangular plate under a parabolic load and of a dam subjected to hydrostatic pressure and self-weight with known solutions demonstrates good agreement, thereby confirming the validity of the proposed boundary value problems regarding stresses and strains. Full article

In this short perspective, we analyze the different linear response functions relevant to surface diffusion as studied by helium atom scattering, organizing them around a single object: the intermediate scattering function (ISF), which is also a characteristic function (CF) in the sense of probability theory. This organizing role of the CF is, to our knowledge, not made explicit elsewhere in the surface-diffusion literature. The exponential time dependence of the ISF observed in the diffusive regime (times much greater than the inverse of the friction coefficient) is a special case of the classical continuous-time random walk (CTRW) theory. Special emphasis is placed on this regime where quantum features of the diffusion process are washed out. We show how the entire hierarchy of response functions—the after-effect function, the generalized susceptibility, the relaxation function, and the Green function—can be written directly in terms of the time moments of the ISF at $t=0$. Moreover, the standard Pauli master equation and the Chudley–Elliott (CE) jump model follow as particular lattice realizations of a general compound-Poisson process. The extension to finite surface coverage is discussed within the interacting single adsorbate (ISA) model. Full article

Online detection of micro-leakage in complex high-pressure gas pipeline networks is difficult to achieve using conventional methods. A high-pressure pipeline micro-leakage detection method based on background-oriented schlieren measurement and feature matching was proposed in this study to address this issue. Through the BOS measurement, the density distribution of the leakage fields was reconstructed through cross-correlation calculation and Poisson equation solving, which was further compared with numerical simulation results under specific operating conditions. The morphological characteristics of the jet field at different leakage pressures were revealed by comparing the density fields from different experimental conditions. Subsequently, the displacement field data were compressed into one-dimensional feature representations for structure-oriented matching of leakage-field characteristics, with temporal smoothing and a dual-threshold hysteresis strategy incorporated to improve matching robustness. The results show that the error in the peak density remains below 10%, which indicates good consistency between the background-oriented schlieren measurements and the numerical simulations. Meanwhile, the one-dimensional feature curve accelerates computation while retaining the dominant characteristics of the leakage field. The proposed framework achieves an area under the ROC curve of 0.992 and an average precision of 0.998. At the selected threshold of 0.650, the overall evaluation metric reaches 0.972, reflecting a favorable balance between sensitivity and reliability. Furthermore, the temporal stabilization strategy improves alarm continuity and suppresses chattering during detection. Full article

We study the positive, radial ground-state profile of the stationary Schrödinger–Newton system in the fixed-energy normalization $\mu =1$ with $V(\infty )=0$. Using regularity and radial symmetry of solutions, we derive convergent even Taylor expansions for the wave function and Newtonian potential near the origin, with explicit recurrence relations expressing all the coefficients in terms of the initial data $(a_0,b_0)=(y\left(0\right),V\left(0\right))$ with $a_0>0$ and $b_0>1$. Global existence and uniqueness of the positive radial ground state are taken from the known Schrödinger–Newton/Choquard theory, while the present work focuses on the local coefficient structure and the far-field expansion. In the far field, the Poisson equation yields the Coulomb tail $V\left(r\right)=\widehat{M}/r+O\left(e^{-2r}{r}^{\widehat{M}-2}\right)$ with no algebraic corrections at any order, where $\widehat{M}={\int }_0^{\infty }{r}^2{y}^{2}dr$ is the determined reduced mass. The decaying wave profile admits the Coulomb-corrected asymptotic expansion $y\left(r\right)=C{e}^{-r}{r}^{\widehat{M}/2-1}{\sum }_{m\ge 0}{c}_m{r}^{-m}$, obtained by reducing the radial equation to a Whittaker equation with an exponentially small perturbation controlled by asymptotic integration. The inverse-power series is divergent and interpreted in the Poincaré sense. The mass, energy and virial identities serve as compatibility conditions for the globally selected profile. Full article

The Lambert W is a Bernstein function and hence the cumulant function of a positive infinitely divisible law, the Lambert law $L(\Lambda )$. The Lambert law is self-decomposable with a unit rate compound Poisson background driving Lévy process (BDLP) with a certain jump law $L\left(J\right)$. Thus, it satisfies the random perpetuity relation $\Lambda \stackrel{L}{=}U(\Lambda +J)$, where U has the standard uniform law, as well as the relation $\Lambda \stackrel{L}{=}U\mathcal{S}J$, where $\mathcal{S}$ is the stationary-excess operator. If the law of J is unspecified, then these two in-law relations together characterise the law of $\Lambda$. Generalisations are pursued in which the Poisson jump rate a is arbitrary. If $a\ne 1$, the above two conditions determine a family of positive infinitely divisible laws for which the Laplace–Stieltjes transforms satisfy an algebraic trinomial equation investigated by Lambert and Euler. These laws occur as limiting distributions of shot noise processes and continuous-time branching processes. A sequence of n-times self-decomposable positive laws derived from a given subordinator is called a BDLP ladder. The BDLP ladder that includes the Lambert law has cumulant functions which are polynomial forms of the Lambert function. Under moment conditions, general BDLP ladder laws are asymptotically normal or stable. Full article

Koshlyakov’s 1954 paper is an opus magnum containing almost all (a.a.) buds of modular relations, equivalent assertions to the functional equation of Dedekind zeta-functions of the rational and quadratic fields. We shall restore this in the framework of Koshlyakov–Oberhettinger–Soni consisting of zeta-functions corresponding to the gamma factor $\Gamma \left(\frac{s}{2}\right)$ (Riemann), Γ(s) (Hecke) and $\Gamma {\left(\frac{s}{2}\right)}^2$ (Voronoĭ-Bochner) and locate more recent developments in their proper position in the framework. In partic-ular, we elucidate the situation where Ramanujan’s kernels, the sinus cardinalis function, Poisson and Plana summation formulas, etc., take place, thus giving a clue for them to be modular relations. Full article

Urban flood resilience depends not only on the scale of infrastructure investment, but also on whether such investment can be translated into observable flood-mitigation outcomes. Focusing on the transformation from infrastructure response to flood outcomes, this study uses panel data for 21 prefecture-level cities in Guangdong Province from 2016 to 2022. Annual maximum monthly precipitation is used to represent rainfall pressure, stormwater pipe density to represent infrastructure scale, and the number of reported flood events to represent the outcome variable. A two-way fixed-effects Poisson pseudo-maximum likelihood (PPML) model is employed. The results show that, in the full sample, rainfall pressure is positively, but not significantly, associated with reported flood occurrence, while stormwater pipe density does not exhibit a stable negative moderating effect. The main conclusion remains broadly unchanged when alternative outcome and precipitation indicators are used, when pipe density is lagged by one period, and when a conservative sample is adopted. Extended analysis provides only limited weak negative evidence for Pearl River Delta cities, and this evidence is not robust across alternative specifications. The findings indicate that pipe length per unit of built-up area primarily reflects the scale of infrastructure provision and cannot be directly equated with the operational performance of the drainage system. By separating response inputs from outcome performance, this study reveals the conditional nature of the transformation from infrastructure scale to operational performance in urban flood resilience research and provides empirical support for a shift from infrastructure expansion toward performance-oriented and integrated governance in high-density coastal cities. Full article

We study a fractional Schrödinger–Poisson system involving the spectral fractional Laplacian on a bounded domain $\mathrm{\Omega }\subset {\mathbb{R}}^N$$(N>2s)$ subject to homogeneous Dirichlet boundary conditions. The model consists of a fractional Schrödinger equation coupled with a fractional Poisson equation through a self-consistent potential. Using the spectral Green operator associated with ${(-\Delta )}^t$, the coupled system is reduced to a single nonlocal integro-differential equation. The associated Green kernel admits a spectral representation in terms of the Dirichlet eigenpairs of the Laplacian. Under suitable assumptions on the Green kernel and Lipschitz conditions on the nonlinearities, we establish the existence of weak solutions together with local uniqueness within the contraction framework via the Banach fixed point theorem for sufficiently small coupling parameters. We further investigate the regularity of the self-consistent potential, continuous dependence on the model parameters, and a conditional convergence to the classical Schrödinger–Poisson system as $s,t\to 1^{-}$. A numerical illustration based on truncated spectral expansions is presented to demonstrate the practical implementation of the proposed framework. Unlike the predominantly variational methods available in the literature, the proposed framework combines a spectral Green-operator reduction with an operator-theoretic fixed-point analysis, providing a constructive formulation that is directly amenable to numerical implementation. Full article