Lemmingpuggaard7022

The increasing exponent is shown to have profound implications for turbulence at atmospheric and astrophysical Reynolds numbers. The present results strongly suggest that intermittent significant shear layer structures are key to understanding and quantifying the dissipation extremes, and, more generally, extreme velocity gradients.Nonlinear dynamic analysis of complex engineering structures modelled using commercial finite element (FE) software is computationally expensive. Indirect reduced-order modelling strategies alleviate this cost by constructing low-dimensional models using a static solution dataset from the FE model. The applicability of such methods is typically limited to structures in which (a) the main source of nonlinearity is the quasi-static coupling between transverse and in-plane modes (i.e. membrane stretching); and (b) the amount of in-plane displacement is limited. We show that the second requirement arises from the fact that, in existing methods, in-plane kinetic energy is assumed to be negligible. For structures such as thin plates and slender beams with fixed/pinned boundary conditions, this is often reasonable, but in structures with free boundary conditions (e.g. cantilever beams), this assumption is violated. Here, we exploit the concept of nonlinear manifolds to show how the in-plane kinetic energy can be accounted for in the reduced dynamics, without requiring any additional information from the FE model. selleckchem This new insight enables indirect reduction methods to be applied to a far wider range of structures while maintaining accuracy to higher deflection amplitudes. The accuracy of the proposed method is validated using an FE model of a cantilever beam.Having knowledge of the contact network over which an infection is spreading opens the possibility of making individualized predictions for the likelihood of different nodes to become infected. When multiple infective strains attempt to spread simultaneously we may further ask which strain, or strains, are most likely to infect a particular node. In this article we investigate the heterogeneity in likely outcomes for different nodes in two models of multi-type epidemic spreading processes. For models allowing co-infection we derive message-passing equations whose solution captures how the likelihood of a given node receiving a particular infection depends on both the position of the node in the network and the interaction between the infection types. For models of competing epidemics in which co-infection is impossible, a more complicated analysis leads to the simpler result that node vulnerability factorizes into a contribution from the network topology and a contribution from the infection parameters.Liquid crystal elastomers exhibit stress softening with residual strain under cyclic loads. Here, we model this phenomenon by generalizing the classical pseudo-elastic formulation of the Mullins effect in rubber. Specifically, we modify the neoclassical strain-energy density of liquid crystal elastomers, depending on the deformation and the nematic director, by incorporating two continuous variables that account for stress softening and the associated set strain. As the material behaviour is governed by different forms of the strain-energy density on loading and unloading, the model is referred to as pseudo-anelastic. We then analyse qualitatively the mechanical responses of the material under cyclic uniaxial tension, which is easier to reproduce in practice, and further specialize the model in order to calibrate its parameters to recent experimental data at different temperatures. The excellent agreement between the numerical and experimental results confirms the suitability of our approach. Since the pseudo-energy function is controlled by the strain-energy density for the primary deformation, it is valid also for materials under multiaxial loads. Our study is relevant to mechanical damping applications and serves as a motivation for further experimental tests.In this study, we couple intracellular signalling and cell-based mechanical properties to develop a novel free boundary mechanobiological model of epithelial tissue dynamics. Mechanobiological coupling is introduced at the cell level in a discrete modelling framework, and new reaction-diffusion equations are derived to describe tissue-level outcomes. The free boundary evolves as a result of the underlying biological mechanisms included in the discrete model. To demonstrate the accuracy of the continuum model, we compare numerical solutions of the discrete and continuum models for two different signalling pathways. First, we study the Rac-Rho pathway where cell- and tissue-level mechanics are directly related to intracellular signalling. Second, we study an activator-inhibitor system which gives rise to spatial and temporal patterning related to Turing patterns. In all cases, the continuum model and free boundary condition accurately reflect the cell-level processes included in the discrete model.An approximation is developed that lends itself to accurate description of the physics of fluid motions and motional induction on short time scales (e.g. decades), appropriate for planetary cores and in the geophysically relevant limit of very rapid rotation. Adopting a representation of the flow to be columnar (horizontal motions are invariant along the rotation axis), our characterization of the equations leads to the approximation we call plesio-geostrophy, which arises from dedicated forms of integration along the rotation axis of the equations of motion and of motional induction. Neglecting magnetic diffusion, our self-consistent equations collapse all three-dimensional quantities into two-dimensional scalars in an exact manner. For the isothermal magnetic case, a series of fifteen partial differential equations is developed that fully characterizes the evolution of the system. In the case of no forcing and absent viscous damping, we solve for the normal modes of the system, called inertial modes. A comparison with a subset of the known three-dimensional modes that are of the least complexity along the rotation axis shows that the approximation accurately captures the eigenfunctions and associated eigenfrequencies.