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In this study, the moist buffering halo region of shallow maritime cumulus clouds is systematically investigated using large eddy simulations with various grid resolutions and numerical choices. Autocorrelation analyses of cloud liquid water and relative humidity suggest a converged size of 200–300 m for moist patches outside clouds when the model resolution is below 50 m, but may overestimate this size due to noncloudy moist regions. Based on a composite analysis, the structure of the moist halo immediately outside individual clouds is examined. It is found that, regardless of model resolution, the distribution of relative humidity in the halo region does not depend on cloud size, but on the real distance away from the cloud boundary, indicating some size‐independent length scales are responsible for the halo formation. The relative humidity decays with distance more quickly with finer horizontal resolution, which is possibly related to the model resolution dependence of the cloud spectrum. The halo size near the cloud base is larger than that within the cloud layer and this feature is robust across all simulations. Further analyses of backward and forward Lagrangian trajectories originating from the moist halo region reveal the possible role for subcloud coherent structures in cloud‐base halo formation. Possible mechanisms explaining cloud halo sizes and associated length scales are discussed. [ABSTRACT FROM AUTHOR]

The turbulent flow characteristics over bed-mounted three different cubical shape bluff bodies are examined experimentally in the water channel facility. The steady and fluctuating flow fields are investigated to analyze the effect of corner radius and shapes of the bluff body on turbulent flow structure, particularly in the wake region. It is found that the sharp corner region significantly impacts the flow separation and alters the characteristics of the shear-layer flow. In particular, the relatively suitable change in geometry resulted in a remarkable variation of the mean flow in the wake is observed. The anisotropic nature of flow is analyzed using the turbulence triangle for the different cubical structures. The variation of the turbulent length scales is presented in the near- and far-wake regions of the submerged obstacles. [ABSTRACT FROM AUTHOR]

In this work we investigate the connection between two fundamental features of solutions of partial differential equations (PDEs), namely the crest factor and the length scale associated to each solution. We illustrate how the crest factor of solutions of some linear and non-linear PDEs, including the incompressible two-dimensional Navier-Stokes equations, has the capability for detecting turbulent and non-turbulent behaviour.

Mucoadhesion is a special case of bioadhesion in which a material adheres to soft mucosal tissues. This review elucidates our current understanding of mucoadhesion across length, time, and energy scales by focusing on relevant structural features of mucus. We highlight the importance of both covalent and non-covalent interactions that can be tailored to maximize mucoadhesive interactions, particularly concerning proteinaceous mucoadhesives, which have been explored only to a limited extent so far in the literature. In particular, we highlight the importance of thiol groups, hydrophobic moieties, and charged species inherent to proteins as key levers to fine tune mucoadhesive performance. Some aspects of protein surface modification by grafting specific functional groups or coupling with polysaccharides to influence mucoadhesive performance are examined. Insights from this review offer a physicochemical roadmap to inform the development of biocompatible, protein-based mucoadhesive systems that can fulfil dual roles for both adhesion and delivery of actives, enabling the fabrication of advanced biomedical, nutritional and allied soft material technologies. [Display omitted] • Mucoadhesive interactions occurs across length and strength scales. • The structure of mucins and mucus gel properties may dictate mucoadhesion. • Proteins' isoelectric point and surface hydrophobicity influence mucoadhesive force. • Thiol groups are inherent to some proteins and are related to enhanced mucoadhesion. • Combining proteins and polysaccharides lead to mucoadhesives with new features. [ABSTRACT FROM AUTHOR]

The capacity to devise order metrics to characterize and classify microstructures of multiphase heterogeneous media across length scales is an outstanding but highly challenging task, given the richness of the possible geometries and topologies of the phases that can arise. This investigation initiates a program to formulate order metrics to characterize the degree of order/disorder of the microstructures of two-phase media in d -dimensional Euclidean space R d across length scales. In particular, we propose the use of the local volume-fraction variance σ V 2 (R) associated with a spherical window of radius R as an order metric. We determine σ V 2 (R) as a function of R for 22 different models across the first three space dimensions, including both hyperuniform and nonhyperuniform systems with varying degrees of short- and long-range order. We find that the local volume-fraction variance as well as asymptotic coefficients and integral measures derived from it provide reasonably robust and sensitive order metrics to categorize disordered and ordered two-phase media across all length scales. Such order metrics could be employed to accelerate the discovery of novel heterogeneous materials by tailoring their degree of order/disorder. [ABSTRACT FROM AUTHOR]

Long waves caused by storm surges or river floods can significantly impact marine and fluvial structures such as bridge piers. Apart from the forces that they generate on the structure, they also contribute to the formation of turbulent eddies downstream of the obstacle. This is relevant, as in this way they can affect both an erodible bottom and the ecosystem. The present study describes a medium-scale experiment, in which the propagation of two different long waves released on a steady current is investigated in the presence of a bottom-mounted rigid emergent cylinder. Velocity measurements were acquired by a Particle Image Velocimetry (PIV) system, providing instantaneous flow velocity vectors on selected 2D planes. For each experimental condition, the time-varying velocity field near the cylinder was examined in selected vertical and horizontal planes. First, we tested which analytical theory or approximated method can best represent the experimental waves. After this, we estimated the horizontal maps of velocity and vorticity downstream of the obstacle and finally processed the velocity signals by means of a wavelet-based technique, to derive the length scales of turbulent eddies. In such a way, we specifically derived how the spreading of coherent turbulent structures downstream of the cylinder depends on the features of the flume, cylinder, and wave. [ABSTRACT FROM AUTHOR]

An experimental study of periodic surface waves acting against the turbulent currents under the influence of smooth and rough side wall is presented. Flow structure for current alone, and combined wave against current flows over smooth and rough side walls were measured with Acoustic Doppler Velocimeter to resolve the changes in the mean flow and turbulence characteristics resulting from the interaction of the flow and the wall roughness. Turbulent velocity fluctuations were analysed to characterise the turbulence and coherent structures and integral length and time scales were evaluated from the autocorrelation function estimates. Further the Kolmogorov length scales were determined using energy dissipation rate. Results show that the dissipation rate is greater for wave against current flow compared to the current alone flow for rough side walls. The streamwise integral length scale at the measured locations reduced with the increase in wave frequency acting against the current flow. Close to the wall surface, the effect of roughness attenuated the integral length scale and increased the turbulent dissipation rate. Continuous wavelet transform (CWT) was used as a tool to detect and establish the average time and length scales of largest horizontal coherent structures that existed in the wave against current combined flow. [ABSTRACT FROM AUTHOR]

An attempt has been made to develop hierarchically crackabridged, strain-hardened cementitious composite by judiciously incorporating hybrid fibers of three distinctly different length scales (nano-, micro-, and continuous fibers). Unlike textilereinforced cement composites, here, the nano- to macrofibers are used to improve the cementitious matrix properties through appropriate crack bridging, and at the macroscale, only onedimensional (1-D) long fibers/yarns are used. A distinct and categorical improvement in the property(ies) is found to take place at each scale of bridging. The structural composite systems made using the developed composite exhibited very promising properties, such as high strength (flexural) of approximately 20 MPa (2.90 ksi), an ultimate strain of 8000 με, and rotational capacity of approximately 10 degrees. A detailed numerical model is developed to carry out nonlinear finite element analysis where the interface properties, strain state, and so on are the parameters. Finally, a constitutive model is proposed for the developed composite through inverse analysis. The proposed constitutive model will help engineers design structural components/retrofit schemes by employing the developed composite without complex analysis (using smeared properties). [ABSTRACT FROM AUTHOR]

This study examines the turbulent stress anisotropy tensor based on the Lumley triangle technique and eigenvalues in wave-current combined flows. The invariant functions are also presented at a different vertical location from the bed to comprehend the level of anisotropy in the combined flow. The spectral variation of the ratio of momentum flux to the turbulent kinetic energy is examined and discussed in comparison to the canonical value. The combined wave-current data display spectral variation considerably smaller than the canonical value (≈ 0.3) through the spectral frequencies domain. To characterize the behaviors of eddies in the wave-current turbulent flow, the Taylor and Kolmogorov length and time scales were analyzed and discussed. Furthermore, to enumerate the degree of organization of complex eddy motions in the combined flow, the normalized Shannon entropy is also evaluated using a discrete probability distribution. [ABSTRACT FROM AUTHOR]

Wakes and higher-order turbulence around circular cylinders of different diameters are investigated using particle image velocimetry measurements. The cylinder Reynolds number (Red) is defined by the depth-averaged velocity, cylinder diameter, and kinematic viscosity. The influence of Red on third-order moment of velocity fluctuations, turbulent kinetic energy (TKE) flux, TKE budget, and turbulent length scales are presented. The intermittency factor (IF) and quadrant analysis around the cylinders are discussed for Red values ranging from 12,600 to 21,000. The energy budget mostly near free surface upstream and near-bed downstream is changed due to Red. Stream-wise and transverse TKE fluxes decreased significantly with Red, but not the vertical flux. Stream-wise skewness changed sign from positive to negative at a certain critical distance downstream, while vertical skewness showed reversed effect with Red. Negative stream-wise skewness and positive vertical skewness indicate the occurrence of ejection events. On the downstream, the production and dissipation rates increased with Red, whereas an opposite trend was observed for dissipation only on the upstream. Increase of Red led to an increase in the Kolmogorov length-scale much higher on the upstream than the downstream, whereas it showed depleting effect on Taylor's length-scale on the upstream and an increasing effect on the downstream. Ejection and sweep events were more prominent in the downstream near the cylinder than upstream with higher values of shear stress on the downstream. The sum of the shear stress contributions of all quadrant events increased consistently with an increase in Red near the cylinder. [ABSTRACT FROM AUTHOR]

We consider the Janjic (NCEP Office Note 437:61, 2001) boundary-layer model, which is one of the most widely used in numerical weather prediction models. This boundary-layer model is based on a number of length scales that are, in turn, obtained from a master length multiplied by constants. We analyze the simulation results obtained using different sets of constants with respect to measurements using sonic anemometers, and interpret these results in terms of the turbulence processes in the atmosphere and of the role played by the different length scales. The simulations are run on a virtual machine on the Chameleon cloud for low-wind-speed, unstable, and stable conditions. [ABSTRACT FROM AUTHOR]

To develop cementitious composites with improved properties, engineering has to be judiciously done at different scales. In this study, a multi-scale engineered cementitious composite (MS-ECC) with high tensile strength and strain-hardening properties is developed by incorporating nano-, micro-, and macro- (in the form of continuous fibers) fibers into it. At first, a cementitious composite is developed by individually incorporating nano- and microfibers to understand the influence of each type of fiber and to arrive at the optimum dosage level. Digital image correlation information is employed to investigate the crack properties and fracture process in the developed composite with individual scale fibers. Next, a hybrid cementitious composite, developed by incorporating nanoand microfibers, is found to demonstrate an improvement in the strength and strain hardening properties. Further improvement in higher scale is carried out by incorporating continuous fibers into it to develop MS-ECC which exhibited tensile strength of 23 MPa (3.63 ksi) and strain capacity more than 8000 micron. [ABSTRACT FROM AUTHOR]

Motivated by recent, unexpected, experimental observations of "intersonic" rupture growth in which both shear and dilatational Mach fronts were observed at the tips of dynamic frictional ruptures propagating at rupture speeds below the dilatational wave speed of the surrounding solid, and we formulate the general dynamic flexoelectric problem and we investigate its plane strain/plane polarization specialization. The coupling of the mechanical problem is analogous to a problem of Toupin-Mindlin gradient elasticity, where two micromechanical characteristic lengths and two microinertial lengths emerge as a combination of the mechanical, dielectric, and flexoelectric constants. The solution of the rupture growth problem allows us to provide an explanation of the experimental results. This becomes possible since flexoelectricity predicts a new aspect that was not observed in the classical analysis: subsonic super shear and supersonic crack tip (or rupture) motions are not related exclusively with the problem being elliptic or hyperbolic, respectively. This is due to the influence of the microinertial lengths, which, in addition to the ratios of the rupture to the wave speeds, also affect the slopes of the Mach cones. Moreover, we are able to explain the experimental paradox of the observation of double Mach cone pairs at the tips of supershear, but subsonic, frictional, ruptures in poly-methyl-methacrtylate (PMMA) by demonstrating that both dilatational and shear Mach cones could appear in flexoelectric solids at rupture speeds below the material dilatation wave speed, something that is impossible from the classical elasticity analysis and is due to the dispersive nature of the present problem. Our analysis is of relevance to the dynamic deformation and fracture of both synthetic and naturally occurring flexoelectric materials and systems, with implications to both engineering and earthquake source mechanics. [ABSTRACT FROM AUTHOR]

The present study focuses on the mechanical chirality in plate-type topologically interlocked material systems. Topologically interlocked material (TIM) systems are a class of dense architectured materials for which the mechanical response emerges from the elastic behavior of the building blocks and the contact-frictions interactions between the blocks. The resulting mechanical behavior is strongly non-linear due to the stability-instability characteristics of the internal load transfer pattern. Two tessellations are considered (square and hexagonal) and patches from each are used as templates. While individual building blocks are achiral, chirality emerges from the assembly pattern. The measure of microstructure circulation is introduced to identify the geometric chirality of TIM systems. TIM systems identified as geometrically chiral are demonstrated to possess mechanical chiral response with a force-torque coupling under transverse mechanical loading of the TIM plate. The chiral length is found to be constant during the elastic response, yet size-dependent. During nonlinear deformation, the chiral length scale increases significantly and again exhibits a strong size dependence. The principle of dissection is introduced to transform non-chiral TIM systems into chiral ones. In the linear deformation regime, the framework of chiral elasticity is shown to be applicable. In the non-linear deformation regime, chirality is found to strongly affect the mechanical behavior more significantly than in the linear regime. Experiments on selected TIM systems validate key findings of the main computational study with the finite element method. • Topologically interlocked structures in achiral and chiral configurations. • Architecture characterization as microstructure circulation. • Force-deflection and moment-deflection response measured and computed. • A chiral length scale emerges. • Chiral length scale is dependent on the magnitude of deformation. [ABSTRACT FROM AUTHOR]

Over the last three decades, a number of researchers have used the gradient-enhanced plasticity theory to model the microstructural material behavior, which is not able to be captured by the conventional plasticity theory, within the continuum based framework. This paper aims to review the strain gradient continuum plasticity in the context of the theoretical, experimental and numerical investigations. A review of the theoretical developments by the several research groups and their applications to the finite element method is presented in this paper. In addition, a review of the various experimental methodologies to study the size effects is presented. Lastly, some open issues in the gradient-enhanced plasticity such as the physical nature of the strain gradients and the physical interpretation of the material length scales are discussed. • Review of strain gradient continuum plasticity. • A review of the theoretical developments by several research groups is presented. • Also applications to finite element method is presented. • A review of various experiments that study the size effects is presented. • Some open issues in the gradient-enhanced plasticity are discussed. [ABSTRACT FROM AUTHOR]

The mode I crack tip asymptotic response of a solid characterised by strain gradient plasticity is investigated. It is found that elastic strains dominate plastic strains near the crack tip, and thus the Cauchy stress and the strain state are given asymptotically by the elastic K -field. This crack tip elastic zone is embedded within an annular elasto-plastic zone. This feature is predicted by both a crack tip asymptotic analysis and a finite element computation. When small scale yielding applies, three distinct regimes exist: an outer elastic K field, an intermediate elasto-plastic field, and an inner elastic K field. The inner elastic core significantly influences the crack opening profile. Crack tip plasticity is suppressed when the material length scale ℓ of the gradient theory is on the order of the plastic zone size estimation, as dictated by the remote stress intensity factor. A generalized J -integral for strain gradient plasticity is stated and used to characterise the asymptotic response ahead of a short crack. Finite element analysis of a cracked three point bend specimen reveals that the crack tip elastic zone persists in the presence of bulk plasticity and an outer J -field. • We investigate, numerically and analytically, the crack tip asymptotic behaviour of strain gradient plasticity solids. • Results reveal the existence of an elastic stress state near the crack tip, reminiscent of a dislocation-free zone. • The nature of the crack tip stress elevation is analytically assessed and full field asymptotic solutions obtained. • Strain gradient plasticity delays the onset of crack tip plasticity. • The elastic K-field persists in the case of short cracks and a regime of J-dominance. [ABSTRACT FROM AUTHOR]

Particle Image Velocimetry, PIV, is employed to characterise the near-homogeneous, isotropic, turbulence generated inside a large spherical vessel by four rotating fans. Spatial and temporal distributions of mean and root mean square, rms, velocity fluctuations are investigated, as well as integral length scales, , Taylor microscales, , and Kolmogorov length scales, , in the fan speed range, 1000–6000 rpm. Mean velocities are about 10% of the turbulence velocity, and turbulence is close to homogeneous and isotropic in the central volume. This volume decreases with increasing fan speed, and its radius and other characteristics are expressed in terms of the fan speed. At each speed, the mean gas velocity scarcely varies with time. Relationships are presented for the variations of and with fan speed, temperature and pressure. A new relationship between the autocorrelation function and integral length scale is obtained, for when Taylor's hypothesis is invalid. [ABSTRACT FROM AUTHOR]

Ocean data assimilation systems can take into account time and space scale variations by representing background error covariance functions with more complex shapes than the classical Gaussian function. In particular, the construction of the correlation functions can be improved to give more flexibility. We describe a correlation operator that features high correlations within a short scale and weak correlations within a larger scale. This multiple length scale correlation operator is defined as a linear combination of Whittle–Matérn functions with different length scales. The main characteristics of the resulting correlation function are described. In particular, a focus is given on features that might be of interest to determine the parameters of the model: the Daley length scale, the normalised spectrum inflexion point and the kurtosis coefficient.The multiple length scale operator has been implemented in NEMOVAR, a variational ocean data assimilation system. A dual length scale formulation was tested in a one-year reanalysis and compared with a single length scale formulation. The results emphasise the importance of estimating with great care the factors used within the combination. They also demonstrate the potential of the dual length scale formulation, in particular through a decrease of the innovation statistics for salinity profiles. The dual length scale formulation is now operational at the Met Office.

Using the scale invariance of the Navier-Stokes equations to define appropriate space-and-time-averaged inverse length scales associated with weak solutions of the 3D Navier-Stokes equations, on a periodic domain V=[0,L]3 an infinite 'chessboard' of estimates for these inverse length scales is displayed in terms of labels (n,m) corresponding to n derivatives of the velocity field in L2m(V). The (1,1) position corresponds to the inverse Kolmogorov length Re3/4. These estimates ultimately converge to a finite limit, Re3, as n,m→∞, although this limit is too large to lie within the physical validity of the equations for realistically large Reynolds numbers. Moreover, all the known time-averaged estimates for weak solutions can be rolled into one single estimate, labelled by (n,m). In contrast, those required for strong solutions to exist can be written in another single estimate, also labelled by (n,m), the only difference being a factor of 2 in the exponent. This appears to be a generalization of the Prodi-Serrin conditions for n≥1. [ABSTRACT FROM AUTHOR]

Reactive solutes flow, transport, and transform in natural subsurface that is ubiquitously heterogeneous. How much are the heterogeneity effects on solute reactive transport? At what spatial scale heterogeneity effects diminish? Answers to these questions are important to understand controls of and to predict solute reactive transport in natural environments. Although these questions have been explored for non-reactive tracers and solutes that go through relatively simple single-component sorption, heterogeneity effects remain poorly understood for solutes that go through surface complexation. These reactions typically include multi-component and are subject to influences of local geochemical conditions. This work aims to address these questions and to understand how and how much effective capacity ( C sc,m ), early ( k c1 ) and late ( k c2 ) rates of Cr(VI) surface complexation are influenced by heterogeneity characteristics and length scales. A two-dimensional model with Cr(VI) surface complexation were calibrated using column data. Numerical experiments were carried out in heterogeneous media characterized by different permeability variance σ 2 lnκ (0.2, 4.5), correlation length λ L (0–6.0 cm), and domain length (0.1–1.0 m). Results show that long λ L and high σ 2 lnκ facilitate the formation of preferential flow and elongate the diffusion length, leading to high connectivity that minimizes C sc,m and k c1 . In highly connected media (>2.0), C sc,m and k c1 can be >2 orders of magnitude lower than those in corresponding homogeneous media. Connectivity however is not a good indicator for k c2 that is predominantly controlled by diffusion. The heterogeneity effects are scale dependent. As the domain length increases, C sc,m and k c1 values approach those of homogeneous media due to longer mixing lengths and continued pH increase during Cr(VI) surface complexion. The “critical length” at which heterogeneity effects disappear occurs at about 20λ L and differs only slightly at different σ 2 lnκ values. The heterogeneity effects however linger at much longer lengths for k c2 , the values of which are >2 orders of magnitude lower in heterogeneous media even at 20λ because of the longer characteristic times of diffusive transport. These results underscore the strong regulation of solute reactive transport by mineral spatial patterns, suggesting the importance of subsurface characteristics and spatial scales at which they are important in estimating natural attenuation, residence times, and natural system capacity to sorb chemicals. [ABSTRACT FROM AUTHOR]

Modulation of turbulent flow in an oscillating grid system due to controlled release of a bubble train was experimentally investigated using particle image velocimetry (PIV) technique wherein flow field modulation was reported in single bubble resolved manner. The bubble diameter was varied in the range ∼2.70 to 3.52 mm (∼26 to 34 times the single-phase Kolmogorov scale, and ∼1.05 to 1.35 times the single-phase integral length scale). The two-dimensional (2D) instantaneous velocity fields were obtained for both single–phase and bubble train cases at grid Reynolds numbers ( Re g ) ranging from 1080 to 10,800. The modulation of single-phase turbulence due to bubble was analysed based on the turbulence intensity, isotropy ratio ( IR ), length scales, specific energy dissipation rates and energy spectra. The single-phase turbulence fluctuating velocity increased ∼5–76% in the inertial subrange region in the presence of bubbles. Presence of bubbles also led to enhancement in the flow field isotropy ratio due to upward acting buoyancy force. It was noted that at high Re g (6480–10800), the IR value of the flow was found to be more dependent on the grid Reynolds number compared with bubble diameter. The integral length scale of the single-phase flow decreased following a power law dependency over the Re g . It was found that the specific energy dissipation rate of single–phase flow increased with an increase in bubble diameter. The energy spectra exhibited a slope less steep than −5/3 which indicates the additional turbulence production by the bubbles in the inertial subrange region. Energy transfer augmentation from large scale to small scale due to bubble was explianed by the dissipative spectrum which showed reduction of the energy in the small scale and an enhancement of the energy in both large scale and inertial subrange. [ABSTRACT FROM AUTHOR]

Abstract: Suppressing crystallization of a metallic melt results in a disordered solid, also known as a metallic glass. One may conclude that a metallic glass is free of defined structural length scales beyond some atomic‐scale value that characterizes short‐ and medium‐range order. While it is well known from atomistic modeling that a metallic glass is structurally heterogeneous, heterogeneities at such a small length scale can hardly be resolved in experiments. This review highlights experimental insights into elastic fluctuations and structural heterogeneities that emerge at scales between a few nanometers and tens to hundreds of micrometers. It distinguishes between structural and property fluctuations in as‐cast metallic glasses, and heterogeneities introduced by elastic and inhomogeneous plastic deformation. As‐cast glasses reveal elastic fluctuations across 3 orders of magnitude, suggesting a hierarchy of length scales that can be tuned by thermomechanical processing. Similarly, nanoscale strain localization into shear bands drives the formation of structural and elastic heterogeneities at both the nano‐ and the microscale. It is proposed that both types of fluctuations will allow one to quantitatively define structure–property relationships via measurable length scales—an approach that has largely contributed to the engineering success of crystalline metals. [ABSTRACT FROM AUTHOR]

The laminated circular cylindrical shells are complicated to analyze and more complicated when anisotropic materials are used with different thickness and different material properties. Also computing the critical stresses under various boundary and loading conditions is exceptionally sensitive and therefore reasonable simplification of the governing equation is in demand for practical design purpose. This article first formulated a shell theory for hybrid anisotropic materials by use of asymptotic integration method, the results are same as classical Donnell-Vlasov theory of single layer isotropic material, then a simplified governing equation was developed by means of adopting a different length scale. The new simplified version can be very useful when multiple materials and thicknesses are designed for practical purpose. Comparison of two different shell bending theories is discussed. Also presented are proper choices of the governing equations for different loading conditions. The theories are extremely useful for the analysis and design of advanced space vehicles and pressure vessels featured cylindrical shells with laminated walls of various materials and thicknesses. [ABSTRACT FROM AUTHOR]

The behavior and characteristics of classical membrane theory of isotropic materials are different from that of anisotropic materials, care must be taken to prevent secondary bending moments due to the unbalanced arrangement of laminates of anisotropic materials. At times, bending theory may have to be adopted and the current design codes, such as ASME, API and ACI must be reviewed for the case of anisotropic materials. The stresses and strains can be significantly different between the pure membrane and bending theories. This paper derives a membrane type shell theory of hybrid anisotropic materials, governing differential equations together with the procedures to locate the mechanical neutral axis. The theory is derived by first considering generalized stress strain relationship of a three dimensional anisotropic body which is subjected to 21 compliance matrix and then non-dimensionalizing each variable with asymptotic expansion. After applying to the equilibrium and stress-displacement equations, we are allowed to proceed asymptotic integration to reach the first approximation theory. Also possible secondary moments due to the unbalanced built up of lamination are quantifiably expressed. The theory is different from the so called pure membrane or the semi-membrane analysis. [ABSTRACT FROM AUTHOR]

Hillslope length is a fundamental attribute of landscapes, intrinsically linked to drainage density, landslide hazard, biogeochemical cycling and hillslope sediment transport. Existing methods to estimate catchment average hillslope lengths include inversion of drainage density or identification of a break in slope-area scaling, where the hillslope domain transitions into the fluvial domain. Here we implement a technique which models flow from point sources on hilltops across pixels in a digital elevation model (DEM), based on flow directions calculated using pixel aspect, until reaching the channel network, defined using recently developed channel extraction algorithms. Through comparisons between these measurement techniques, we show that estimating hillslope length from plots of topographic slope versus drainage area, or by inverting measures of drainage density, systematically underestimates hillslope length. In addition, hillslope lengths estimated by slope-area scaling breaks show large variations between catchments of similar morphology and area. We then use hillslope length-relief structure of landscapes to explore nature of sediment flux operating on a landscape. Distinct topographic forms are predicted for end-member sediment flux laws which constrain sediment transport on hillslopes as being linearly or nonlinearly dependent on hillslope gradient. Because our method extracts hillslope profiles originating from every ridgetop pixel in a DEM, we show that the resulting population of hillslope length-relief measurements can be used to differentiate between linear and nonlinear sediment transport laws in soil mantled landscapes. We find that across a broad range of sites across the continental United States, topography is consistent with a sediment flux law in which transport is nonlinearly proportional to topographic gradient. © 2016 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd. [ABSTRACT FROM AUTHOR]

Ocean data assimilation systems can take into account time and space scale variations by representing background error covariance functions with more complex shapes than the classical Gaussian function. In particular, the construction of the correlation functions can be improved to give more flexibility. We describe a correlation operator that features high correlations within a short scale and weak correlations within a larger scale. This multiple length scale correlation operator is defined as a linear combination of Whittle--Matérn functions with different length scales. The main characteristics of the resulting correlation function are described. In particular, a focus is given on features that might be of interest to determine the parameters of the model: the Daley length scale, the normalised spectrum inflexion point and the kurtosis coefficient. The multiple length scale operator has been implemented in NEMOVAR, a variational ocean data assimilation system. A dual length scale formulation was tested in a one-year reanalysis and compared with a single length scale formulation. The results emphasise the importance of estimating with great care the factors used within the combination. They also demonstrate the potential of the dual length scale formulation, in particular through a decrease of the innovation statistics for salinity profiles. The dual length scale formulation is now operational at the Met Office. [ABSTRACT FROM AUTHOR]

A micropolar cohesive damage model for delamination of composites is proposed. The main idea is to embed micropolarity, which brings an additional layer of kinematics through the micro-rotation degrees of freedom within a continuum model to account for the micro-structural effects during delamination. The resulting cohesive model, describing the modified traction separation law, includes micro-rotational jumps in addition to displacement jumps across the interface. The incorporation of micro-rotation requires the model to be supplemented with physically relevant material length scale parameters, whose effects during delamination of modes I and II are brought forth using numerical simulations appropriately supported by experimental evidences. [ABSTRACT FROM AUTHOR]

A state-based micropolar peridynamic theory for linear elastic solids is proposed. The main motivation is to introduce additional micro-rotational degrees of freedom to each material point and thus naturally bring in the physically relevant material length scale parameters into peridynamics. Non-ordinary type modeling via constitutive correspondence is adopted here to define the micropolar peridynamic material. Along with a general three dimensional model, homogenized one dimensional Timoshenko type beam models for both the proposed micropolar and the standard non-polar peridynamic variants are derived. The efficacy of the proposed models in analyzing continua with length scale effects is established via numerical simulations of a few beam and plane-stress problems. [ABSTRACT FROM AUTHOR]

Loads associated with downbursts represent a significant vulnerability on various structures. Designing the structures to withstand such loads requires the knowledge about the turbulent characteristics of downbursts, which are the focus of the current study. To this effect, large eddy simulations (LES) of downbursts impinging over four different exposures namely open, countryside, suburban and urban, are performed. Ground surface roughness is simulated using fractal surfaces generated by random Fourier modes (RFM) and scaled to match a targeted aerodynamic roughness z 0 . Simulated wind velocities are averaged spatially and temporally to extract the mean and turbulent components. Properties of both the mean and the turbulent components are discussed. Turbulence length scales, which govern the wide band correlations of the turbulence, are determined in the circumferential, the vertical and the longitudinal directions. It is found that the length scales in the circumferential direction are larger than those in the vertical direction by at least an order of magnitude, indicating that downburst turbulence is more correlated in the circumferential direction. This has a particular importance for long horizontal structures such as transmission lines and long span bridges. Narrow band correlations and the turbulent spectra, which have a particular importance for flexible structures, are also discussed. Applicability of using the resulting turbulent characteristics to estimate the peak forces on structures, e.g. transmission lines, is deduced by employing the gust factor approach. [ABSTRACT FROM AUTHOR]

The morphology of hydrophobic CF 4 plasma fluorinated polybutadiene surfaces has been characterised using atomic force microscopy (AFM). Judicious choice of the plasma power and exposure duration leads to formation of three different surface morphologies (Micro, Nano, and Micro + Nano). Scaling theory analysis shows that for all three surface topographies, there is an initial increase in roughness with length scale followed by a levelling-off to a saturation level. At length scales around 500 nm, it is found that the roughness is very similar for all three types of surfaces, and the saturation roughness value for the Micro + Nano morphology is found to be intermediate between those for the Micro and Nano surfaces. Fast Fourier Transform (FFT) analysis has shown that the Micro + Nano topography comprises a hierarchical superposition of Micro and Nano morphologies. Furthermore, the Micro + Nano surfaces display the highest local roughness (roughness exponent α = 0.42 for length scales shorter than ∼500 nm), which helps to explain their superhydrophobic behaviour (large water contact angle (>170°) and low hysteresis (<1°)). [ABSTRACT FROM AUTHOR]

A Reynolds-averaged Navier-Stokes model is used to investigate the evolution of the sectional drag coefficient and turbulent length scales with the layouts of aligned arrays of cubes. Results show that the sectional drag coefficient is determined by the non-dimensional streamwise distance (sheltering parameter), and the non-dimensional spanwise distance (channelling parameter) between obstacles. This is different than previous approaches that consider only plan area density $$(\lambda _\mathrm{p})$$ . On the other hand, turbulent length scales behave similarly to the staggered case (e. g. they are function of $$\lambda _\mathrm{p}$$ only). Analytical formulae are proposed for the length scales and for the sectional drag coefficient as a function of sheltering and channelling parameters, and implemented in a column model. This approach demonstrates good skill in the prediction of vertical profiles of the spatially-averaged horizontal wind speed. [ABSTRACT FROM AUTHOR]

• For practical use size effect law can replace the energy-equilibrium criterion in Grady's energy-horizon theory of fragmentation. As to the upper non-equilibrium flaw-kinetics failure and fragmentation curve at high strain rate, the energy criterion can be adopted. • Using Maxwell model of deformation and fracture of rock we obtained relationship between dynamic strength, strain rate and fragment size. Which provide the interval of the power-law distribution of the cumulative mass distribution. • Used the experimental data to confirm the validity of the proposed model. Grady's energy-horizon theory of dynamic fragmentation (EHTDF) is reviewed. The energy-horizon essence is explored, and a new approach for determining the related dynamic fragmentation length scales is proposed. It is shown that energy-horizon is the effective size of the equivalent sample covered by dynamic disturbance, and the lower energy-equilibrium failure criterion in Grady's EHTDF may be replaced by static size effect law, with the upper bounding failure criterion curve used instead of the energy-based criterion. The length scales in Grady's EHTDF can be determined by combining the energy-based criterion and static size effect law with the relation between dynamic strength, strain rate, and fragment size obtained from the Maxwell model of rock deformation and fracture. Comparison of the theoretically predicted and the experimentally measured values of length scales in dynamic fragmentation of rock shows the validity of the proposed approach. [ABSTRACT FROM AUTHOR]