Abstract We present the practicality of structuring ceramic tiles for enhancing sound absorption on rigid walls. By introducing embedded cavities, tiled walls are engineered to function as heterogeneous acoustic absorbers over a broad frequency range. The design exploits the intrinsic geometry of tiled assemblies: 1 mm wide empty joints serve as resonator necks, while the gap between the ceramic tiles and the wall functions as the resonator chamber. Through spatial grading of the resonators, we achieve broadband sound absorption in the low-frequency range of 100–1500 Hz, effectively targeting common household noises such as footsteps, impacts and neighbouring activities. Remarkably, even with a thin profile (only 1 cm thick), the structure achieves an average absorption coefficient exceeding 0.7, with near-unity absorption in the 480–700 Hz range. Numerical modelling, analytical formulation and experimental validation consistently demonstrate the effectiveness of the proposed design. The results indicate a practical strategy for integrating acoustic functionality into tiled wall systems for noise mitigation.
Abstract Species persistence in ecosystems results from the interplay between ecological interactions and behavioural strategies. Classical niche theory explains how resource overlap determines the strength of interactions, while evolutionary game theory (EGT) describes how cooperation and defection strategies arise from payoff-dependent decisions. Most eco-evolutionary models assume that strategies remain fixed over generations, overlooking the potential for behavioural adjustments on ecological time scales. Here, we develop a mathematical framework that integrates Lotka–Volterra niche competition (LVNC) dynamics with an adaptive strategy model, allowing species to update their strategies based on the payoff-sensitive Fermi rule. We examine community outcomes on four symmetric games: prisoner's dilemma (PD), snowdrift, stag hunt (SH) and trivial (TR) (also known as harmony), implemented on networks with varying topologies and connectivity. We find that adaptive strategy updates significantly reduce the likelihood of species extinction in comparison to static strategies, enabling coexistence in payoff regions that would otherwise lead to collapse. The structure of the network plays an important role in determining persistence, particularly in snowdrift and PD games. Furthermore, regular ecological networks may experience abrupt extinction with changes in connectivity, whereas scale-free networks support persistence through cooperative hubs. Overall, our results demonstrate that behavioural adaptation is pivotal in promoting species persistence, more so than network architecture alone.
Abstract This work focuses on the derivation and investigation of constitutive relations depending on the stress, the rate of the stress and the temperature, describing the response of viscoelastic solids. Using a thermodynamical approach, we derive conditions to be satisfied in order for the material response to be stable. Under the assumption that the strain function depends on the stress, the stress-rate and the temperature as separate variables, we further investigate these conditions both for large and small strains for various scenarios including isotropic bodies. For each of these cases, there certainly exists an analogy between the current approach and the classical approach where the stress is given in terms of the strain and its rates. We also study the corresponding boundary value problems of the extension/compression of a cylinder, the biaxial extension of a thin plate, and the triaxial compression of a slab, for both of the cases of large deformations and small strains. We look at the case of transversely isotropic viscoelastic solids, when the body is assumed to be inextensible, as well as the case of a viscoelastic body whose mechanical properties depend on the spherical stress (the pressure). Finally, we discuss the potential applications of these constitutive theories.
Abstract The apparent softening of harsh collimated light sources into diffuse patterns with fading gradients that is foundational in fields such as diffuse optics and astrophysics was first studied and exploited by Renaissance artists, most famously Leondardo da Vinci. It is now understood that harsh, ballistic light is well described by radiation transport whereas diffusion theory becomes more appropriate as features in the radiation field soften. Because diffusion theory is far more tractable analytically and numerically, examples of reckoning with or exploitation of the transition between the two regimes may be found in many disciplines concerned with radiation systems; complete descriptions, however, are rarely attempted. Thorough asymptotic analyses of radiation transport dynamics are given and applied to long open problems in two radiation transport topics: diffuse optical tomography measurements and radiation transport code verification. The asymptotic analyses give mathematical expressions that do not require transport solutions yet are able to capture important phenomena of the more detailed, angularly-dependent physics.
Abstract Acoustical tweezers are now widely used to manipulate micro-particles. Typically, such devices use lenses or a phased array to create a pressure field in the vicinity of the particle that acts to confine the particle. This paper uses an efficient finite element scattering model in conjunction with a global optimizer to find the phases of an ensemble of planar incident waves that maximize the minimum trapping stiffness. It is shown that for small spherical particles, a vortex of unity topological charge is optimal and for larger, Mie-sized spheres, higher topological charges are required. A symmetric trap that carries no net angular momentum also emerges from the optimization. The use of a numerical scattering model enables the optimal trap for non-spherical objects to be explored. For cylindrical objects, it is shown that vortex traps perform poorly, and in some cases fails to trap altogether. Conversely, optimal traps with uniform stiffnesses exist for all the cylinders considered. In a similar scenario, a uniform-stiffness trap is found for an object shaped as a frog and imported from a three-dimensional-printing file. Hence, this paper provides a route to improved trapping and the trapping of a wider range of objects than was previously possible.
Abstract We investigate the isothermal, steady, creeping flow of generalized Newtonian fluids (GNFs) in symmetric tubes with slowly varying cross-sections, allowing for wall slip. Within the lubrication framework, a closed integro-algebraic equation governing the shear-rate distribution is derived. The formulation accommodates arbitrary shear-dependent viscosity functions and wall geometries. Exact analytical solutions are obtained for Newtonian and power-law fluids, while more complex viscosity laws are treated numerically through the development of an efficient algorithm. The formulation provides direct prediction of the shear-rate distribution, from which the remaining flow quantities follow. It is shown that slip modifies the streamline structure, while strongly nonlinear viscosity models lead to a more fundamental change in the flow kinematics, with streamlines no longer aligned with lines of constant transverse coordinates. The influence of configuration (axisymmetric or planar), geometry (linear or hyperbolic), rheology and slip on the pressure drop required to sustain a prescribed flow rate is quantified.
Abstract Socio-ecological systems (SESs) couple human activities and ecological processes through networks of economic, social and environmental interactions. These systems are often treated as if their connectivity were given, yet the resources required to preserve network structure under uncertainty are rarely quantified. We develop a stochastic optimal control framework for connectivity-constrained SES on a multiplex network whose edge weights are Mahalanobis distances between node-level feature vectors. The law of these distances evolves under a controlled Fokker–Planck partial differential equation, and we formulate a Hamiltonian via an infinite-dimensional minimum principle. A Feynman–Kac representation links the adjoint (co-state) field to discounted shadow prices for marginal reductions in edge distances. Numerically, we instantiate the framework on a stylized U.S. corn-ethanol corridor modeled as a tri-layer socio-ecological multiplex and compute an open-loop stabilization policy. The optimal control is front-loaded: early interventions compress economic, social and environmental distances and keep the supra-Laplacian within a resilience band, after which the policy relaxes to a low-intensity maintenance regime. To improve numerical performance, we augment the base control with a recurrent neural-network residual that learns network-level corrections. The results show how these controllers can stabilize multiplex SES against shocks and reveal how policies respond to volatility parameters.
Downward-looking radar systems are widely used to infer the structure and basal conditions of glaciers and ice sheets. Oblique propagation, in contrast, is rarely considered even though polarimetric traveltime tomography is sensitive to the full crystal orientation fabric, which exerts important viscous control on ice masses. This study presents a polarimetric common midpoint (CMP) framework for ice sheets that accounts for the dielectric anisotropy arising from preferred crystal orientations and preferred bubble shapes in firn, including refractive bending due to density variations. Traveltimes are modelled along oblique ray paths using a Maxwell-Garnett effective medium formulation coupled to a single-stage Herron-Langway density model with a power-law bubble eccentricity profile, validated against Antarctic firn cores from Dome Fuji. An optimization problem is proposed for simultaneously inferring the crystal fabric profile and bubble close-off (BCO) depth of any firn-ice column, which is shown to be robust to noise in observed traveltimes and may require limited acquisition obliquities of up to 30 degrees. The inverse problem is applied to the Ekstr & ouml;m ice shelf, Antarctica, revealing a girdle-type fabric that strengthens with depth despite restricted CMP offset. Finally, shortcomings and potential improvements are discussed, including suggestions for designing CMP surveys that aim to infer crystal fabrics.
An isolated spherical void exhibits a strong monopolar resonance in media with Poisson's ratio close to 1/2. For all angles of incidence, there is a single resonance peak which occurs for shear wavenumbers ks such that ksa approximate to 2, where a is the void radius. When a secondary void is introduced to the neighbourhood of the evacuated cavity, there are interaction effects that modify the resonance response. Here, we seek to understand the influence of multiple scattering interactions on the resonance characteristics by considering the scattering cross sections associated with a pair of resonators that are excited by a compressional field. The three-dimensional problem is modelled using a T-matrix approach in which the elastic fields are represented in a vector spherical harmonic basis. It is shown that two nearby voids are capable of producing two distinct resonances; this feature widens the range of frequencies at which resonance phenomena is observed. We derive an analytical approximation for the resonance frequency that is shown to be accurate for sufficiently soft media. We additionally consider the scattering response from a void in the presence of a soft-coated rigid particle; this configuration is shown to be capable of inducing simultaneous monopole and dipole resonances.
We analyse ion transport in a prototypical electrochemical cell consisting of a binary asymmetric electrolyte confined between planar electrodes that sustain Faradaic cation reactions described by Butler-Volmer kinetics. Ion transport is governed by the Poisson-Nernst-Planck (PNP) equations, which are analysed in the thin-Debye-layer limit using matched asymptotic expansions. This procedure replaces explicit resolution of the interfacial double layers with effective boundary conditions, yielding a closed set of nonlinear equations for the bulk ion concentrations and electrostatic potential under a time-dependent current, from which the cell voltage is obtained. Comparisons with full numerical PNP simulations show excellent agreement across a wide range of regimes. For suddenly applied DC currents, the model captures both diffusion- and kinetics-limited responses, including large overpotentials and the influence of ionic diffusivity mismatch on concentration polarization. Under sinusoidal forcing, it reproduces linear behaviour at small amplitudes and nonlinear dynamics at larger amplitudes, including waveform distortion and higher harmonics. Deviations are limited to short times associated with rapid double-layer charging, demonstrating that the macroscale model provides a compact, predictive alternative to direct PNP simulations while retaining the essential physics of time-dependent electrochemical processes.
Under investigation is the modified Bogoyavlensky lattice, which serves as a generalization of the modified Volterra lattice. By introducing a discrete 3 & times;3 matrix spectral problem, we propose an integrable hierarchy of the modified Bogoyavlensky lattice with the help of the zero-curvature equation and Lenard recursion relations. Based on the characteristic polynomial of Lax matrix for the hierarchy, we define a trigonal curve Km-1 of arithmetic genus m-1 and present the corresponding Baker-Akhiezer function and meromorphic function on it. By virtue of the asymptotic properties of the Baker-Akhiezer function and meromorphic function, we derive their explicit Riemann theta function representations. Algebro-geometric quasi-periodic solutions of the entire modified Bogoyavlensky hierarchy are obtained in terms of the asymptotic expansion of the meromorphic function and its Riemann theta function representation.
We uncover subtle and previously unexplored phenomena arising from the interplay of nonlinearity and non-reciprocity in topological mechanical metamaterials. We study a non-reciprocal topological Klein-Gordon chain of asymmetrically coupled nonlinear oscillators, which serves as a minimal mass-spring model capturing the features of several active nonreciprocal metamaterials across mechanical, electronic and acoustic platforms. We demonstrate that continuous families of non-reciprocal edge breathers (NEBs), namely boundary-localized, time-periodic waves, emerge from the linear edge mode as its amplitude increases. Remarkably, despite the absence of chiral or sublattice symmetries, we identify insensitive NEBs whose nonlinear frequency remains fixed to that of the linear edge mode with increasing nonlinearity. Our analysis reveals that the mechanism underlying this insensitivity stems from a competition between mode non-orthogonality and nonlinear interactions, yielding an exponential decay of the NEB nonlinear frequency shift with system size. Crucially, these insensitive NEBs also persist in the strongly nonlinear regime. Our work establishes a novel pathway towards realizing robust nonlinear topological waves in mechanical metamaterials without relying on symmetry-protected nonlinearities.
Abstract Interpolatory reduced-order models (ROMs) rapidly approximate high-dimensional systems by constructing and blending low-order systems at selected interpolation points. This avoids repeated projection of full-order operators and yields orders-of-magnitude speed-ups, making these methods well-suited for real-time prediction, optimization and control. Existing surveys examine individual techniques in isolation and employ advanced differential-geometric or system-theoretic formalisms, limiting accessibility to the broader engineering and computational communities. In contrast, this review proposes a novel taxonomy categorizing all interpolation-based ROM families without cataloguing every variant. For each family, the core mathematical ideas are conveyed through pseudocode and originally integrated into a unified six-stage workflow, accompanied by explicit O(⋅) cost analyses. We then highlight key methodological extensions required for complex, real-world applications focusing on computational mechanics. A combined quantitative and qualitative assessment against six canonical benchmarks and traditional projection–based ROMs provides performance insights. The result is a practical roadmap enabling engineers and scientists to select, adapt and deploy interpolation-based ROMs with clarity and assurance.
We derive global stress fields through time using an analytical asthenospheric flow estimation that involves plate motions, subduction geometry and variable plume flux. Among these, the most effective way to drive rapid regional stress changes in the continents is by varying plume flux, especially when more than one plume is present, as is the case for Europe. We apply our paleostress model to the case study of western Europe, a region that experienced rapid, substantial and large-scale lithospheric stress changes in the Late Mesozoic and Cenozoic. We find that the behaviour of pressure-driven asthenosphere flow, resulting from variations in plume flux, dominates the rapidly temporo-spatially varying stress signal. Given the potential causes of stress change in this particular region, we further interpret the tectonic changes in the context of dynamic topography as expressed by the stratigraphic record, shifts in plate motion, paleostress indicators and past interpretations of the tectonic evolution of Europe. Through this approach, we move away from the paradigm of stress changes being driven by plate-boundary or body forces in the lithosphere and emphasize the active role of the mantle and the importance of interpreting models in relation to multiple process-linked observations.
Kresling origami and tensegrity frustums have been studied extensively in two related but separate lines of research, ranging in the fields of mechanics, physics, robotics and materials science. Although these two systems share the same geometry and connectivity of vertices and edges, the analogies between their mechanical properties have not yet been fully highlighted in the literature. Here, a unified description of Kresling origami and tensegrity frustums is presented. Starting with the form-finding analysis, a new geometric compatibility condition for the realization of load-free and stress-free configurations is derived, and it is proved that the Kresling origami can also exist in self-stressed configurations. The self-stress state of rigid Kresling origami with frictionless hinges at folds is obtained analytically, and its relationship with the self-stress of tensegrity frustums is elucidated. Next, two regimes of mechanical response are distinguished in terms of a frustration parameter, which is associated with a prestress-tunable stiffening response when it is positive and with a bistable response when it is negative. Finally, comparative and parametric analyses, including those regarding flat-foldable Kresling origami, are performed to gain insight and a comprehensive understanding of the design possibilities of these structures.
Abstract For elastic–plastic materials that can undergo large deformations, the general theory of Green and Naghdi is supplemented by incorporating a novel three-factor decomposition of the deformation gradient. A certain unique right stretch tensor emerges as an appropriate variable for describing finite elastic behaviour at large plastic strains. Convenient objective forms of response functions for strain energy and stress are presented.
Abstract We examine travelling wave solutions of a reaction–diffusion equation that incorporates a strong Allee effect in the population growth term and a Stefan-like moving boundary condition governing the advance of the population front. These two mechanisms, which have been examined separately in other model frameworks, have not previously been analysed together. We investigate the sharp-fronted travelling wave solutions that arise using both direct numerical simulation and travelling wave analysis, enabling us to obtain the relationship between the wave speed and the parameter associated with the moving boundary condition. Our results show that this model admits sharp-front travelling waves with wave speed c
In several countries, animal welfare regulations ban fish keeping in spherical aquaria. A reason for this is the belief that fish behaviour is adversely affected in spherical aquaria, because the light refraction at the aquarium's wall severely disrupts the image of the aerial world, which may disturb the fish. Using analytical calculations and geometric optical ray-tracing, we determined the paths of light rays originating from various locations in water-filled spherical and cubic aquaria to the surrounding aerial target space, in order to find out which aquarium causes greater angular refraction distortions of the aerial world perceived by fishes. We found that if a fish is not in the aquarium's centre, there are always viewing directions where either the spherical or the cubic aquarium's wall causes greater refraction distortions. However, depending on the fish's position in the aquarium, a cubic aquarium causes greater fish-perceived refraction distortions of the aerial world in 2-9 times larger angular volume than a spherical aquarium. This finding is corroborated by optical demonstrations of the refraction distortion of an aerial quadratic grid seen from water-filled spherical and cubic aquaria. We conclude that there is not an optical basis for the prohibition of fish keeping in spherical aquaria.
