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This allowed us not to rely on other uncertain epidemiological model parameters and, in particular, to bypass uncertainties about the role of the carriers in the transmission.We present a solid theoretical foundation for interpreting the origin of Allee effects by providing the missing link in understanding how local individual-based mechanisms translate to global population dynamics. Allee effects were originally proposed to describe population dynamics that cannot be explained by exponential and logistic growth models. However, standard methods often calibrate Allee effect models to match observed global population dynamics without providing any mechanistic insight. By introducing a stochastic individual-based model, with proliferation, death and motility rates that depend on local density, we present a modelling framework that translates particular global Allee effects to specific individual-based mechanisms. Using data from ecology and cell biology, we unpack individual-level mechanisms implicit in an Allee effect model and provide simulation tools for others to repeat this analysis.Long-wave propagation on a uniformly sloping beach is formulated as a transient-response problem, with initially stationary water subjected to an incident wave. Both the water surface elevation and the horizontal flow velocity on the slope can be represented as convolutions of the rate of displacement of the water surface at the toe of the slope with a singular kernel function of time and space. The kernel, which is typically expressed in the form of an infinite series, accommodates the dynamic processes of long waves, such as shoaling, reflection, and multiple reflections over the slope and yields exact solutions of the linear shallow water equations for any smooth incident wave. The kernel convolution can be implemented numerically by using double exponential formulas to avoid the kernel singularity. The kernel formulation can be extended readily to nonlinear dynamics via the hodograph transform, which in turn enables the instantaneous prediction of nonlinear wave properties and of the occurrence of wave breaking in the near-shore area. This general description of long-wave dynamics provides new insights into the long-studied problem.Road corrugation refers to the formation of periodic, transverse ripples on unpaved road surfaces. It forms spontaneously on an initially flat surface under heavy traffic and can be considered to be a type of unstable growth phenomenon, possibly caused by the local volume contraction of the underlying soil due to a moving vehicle's weight. In the present work, we demonstrate a possible mechanism for road corrugation using experimental data of soil consolidation and numerical simulations. The results indicate that the vertical oscillation of moving vehicles, which is excited by the initial irregularities of the surface, plays a key role in the development of corrugation.Liquid crystals with molecules constrained to the tangent bundle of a curved surface show interesting phenomena resulting from the tight coupling of the elastic and bulk-free energies of the liquid crystal with geometric properties of the surface. We derive a thermodynamically consistent Landau-de Gennes-Helfrich model which considers the simultaneous relaxation of the Q-tensor field and the surface. The resulting system of tensor-valued surface partial differential equation and geometric evolution laws is numerically solved to tackle the rich dynamics of this system and to compute the resulting equilibrium shape. The results strongly depend on the intrinsic and extrinsic curvature contributions and lead to unexpected asymmetric shapes.Within a framework of the state space method, an axisymmetric solution for functionally graded one-dimensional hexagonal piezoelectric quasi-crystal circular plate is presented in this paper. find more Applying the finite Hankel transform onto the state space vector, an ordinary differential equation with constant coefficients is obtained for the circular plate provided that the free boundary terms are zero and an exponential function distribution of material properties is assumed. The ordinary differential equation is then used to obtain the stress, displacement and electric components in the physical domain of the elastic simply supported circular plate through the use of the propagator matrix method and the inverse Hankel transform. The numerical studies are carried out to show the validity of the present solution and reveal the influence of material inhomogeneity on the axisymmetric bending of the circular plate with different layers and loadings, which provides guidance for the design and manufacture of functionally graded one-dimensional hexagonal piezoelectric quasi-crystal circular plate.Fibre-reinforced, fluid-filled structures are commonly found in nature and emulated in devices. Researchers in the field of soft robotics have used such structures to build lightweight, impact-resistant and safe robots. The polymers and biological materials in many soft actuators have these advantageous characteristics because of viscoelastic energy dissipation. Yet, the gross effects of these underlying viscoelastic properties have not been studied. We explore nonlinear viscoelasticity in soft, pressurized fibre-reinforced tubes, which are a popular type of soft actuation and a common biological architecture. Relative properties of the reinforcement and matrix materials lead to a rich parameter space connecting actuator inputs, loading response and energy dissipation. We solve a mechanical problem in which both the fibre and the matrix are nonlinearly viscoelastic, and the tube deforms into component materials' nonlinear response regimes. We show that stress relaxation of an actuator can cause the relationship between the working fluid input and the output force to reverse over time compared to the equivalent, non-dissipative case. We further show that differences in design parameter and viscoelastic material properties can affect energy dissipation throughout the use cycle. This approach bridges the gap between viscoelastic behaviour of fibre-reinforced materials and time-dependent soft robot actuation.