Anisotropic Cross Sections Research Articles

Numerical simulation of fluid-vegetation coupled dynamic using a promoted semi-resolved coupling model

Flexible vegetation is an important component of riverine and coastal ecosystems. The numerical simulation is difficult due to the complex motions of flexible vegetation and fluid. In this work, a semi-resolved numerical model coupling the computational fluid dynamics (CFD) and flexible rod dynamics (FRD) using a promoted two-way domain expansion method was proposed with the accuracy of the resolved model and the efficiency of the unresolved model. The governing equations of the flexible rod dynamics are solved by the finite element method (FEM). The effect of vegetation is added as source terms to the Reynolds-averaged Navier-Stokes equations, which are discretized and solved by the finite volume method (FVM). The anisotropic Gaussian kernel function is adopted to calculate the interactive forces between the fluid and the flexible rod with an anisotropic cross-section. The model was first validated by simulating the flow passing through a single flexible rod with a rectangular cross-section. Meanwhile, the main factors were calibrated. The engineering application of the model was further validated by simulating the flow passing through a finite patch of flexible vegetation. These results indicate that the proposed model could well simulate the open channel flows with the flexible vegetation.

Are Coronal Loops Projection Effects?

We report results of an in-depth numerical investigation of three-dimensional projection effects that could influence the observed loop-like structures in an optically thin solar corona. Several archetypal emitting geometries are tested, including collections of luminous structures with circular cross sections of fixed and random size, and light-emitting structures with highly anisotropic cross sections, as well as two-dimensional stochastic current density structures generated by fully developed magnetohydrodynamic turbulence. A comprehensive set of statistical signatures is used to compare the line-of-sight (LOS) integrated emission signals predicted by the constructed numerical models with the loop profiles observed by the extreme ultraviolet telescope on board the flight 2.1 of the High-Resolution Coronal Imager (Hi-C). The results suggest that typical cross-sectional emission envelopes of the Hi-C loops are unlikely to have high eccentricity, and that the observed loops cannot be attributed to randomly oriented quasi-two-dimensional emitting structures, some of which would produce anomalously strong optical signatures due to an accidental LOS alignment, as expected in the ''coronal veil“ scenario proposed recently by Malanushenko et al. The possibility of apparent loop-like projections of very small (close to the resolution limit) or very large (comparable with the size of an active region) light-emitting sheets remains open, but the intermediate range of scales commonly associated with observed loop systems is most likely filled with true quasi-one-dimensional (roughly axisymmetric) structures embedded into the three-dimensional coronal volume.

Development of three-dimensional co-rotational beam model for nonlinear dynamic analysis of highly flexible slender composite blades

The main purpose of this work is to introduce a novel method analyzing the dynamic response of a highly flexible slender composite beam having anisotropic property and variable cross-section. A three-dimensional co-rotational model is developed. The beam deformation in dynamic conditions is obtained by applying HHT-α method as dynamic analysis tool. Validation studies with various boundary conditions, multiple external loads and pre-curved structures are performed. Furthermore, dynamic analysis with a large, flexible, and slender composite blade is performed with and without structural couplings. It is shown the developed beam model accurately predicts nonlinear three-dimensional response and anisotropic structural coupling effects.

Sulfated Cellulose Nanofibrils from Chlorosulfonic Acid Treatment and Their Wet Spinning into High-Strength Fibers.

This paper presents the proof of concept for a facile sulfation-disintegration approach toward generating sulfated cellulose nanofibrils (SCNF) via direct sulfation of rice straw cellulose with chlorosulfonic acid (HSO3Cl) followed by blending. The direct sulfation of cellulose with chlorosulfonic acid (HSO3Cl) was optimized at acid ratios of 1-1.5 HSO3Cl per anhydroglucose unit (AGU) and short reaction times (30-60 min) at ambient temperature to produce SCNF with tunable charges of 1.0-2.2 mmol/g, all in impressively high yields of 94-97%. SCNF were characterized via AFM, TEM, FTIR, and XRD. SCNF lengths (L: 0.75-1.24 μm) and widths (W: 3.9-5.9 nm) decreased with harsher sulfation, while heights (H: 1.23-1.32 nm) remained relatively static. The SCNF had uniquely anisotropic cross sections (W/H: 3.0-4.7) and high aspect ratios (L/H: 568-984) while also exhibiting amphiphilicity, thixotropy, and shear thinning behaviors that closely followed a power law model. Aqueous SCNF dispersions could be wet spun into organic and mixed organic/ionic coagulants, producing continuous fibers possessing an impressively high tensile strength and Young's modulus of up to 675 ± 120 MPa and 26 ± 5 GPa, respectively.

Generation of elastic geodesic gridshells with anisotropic cross sections

Geodesic gridshells are shell structures made of continuous elements following geodesic lines. Their properties ease the use of beams with anisotropic cross-sections by avoiding bending about their strong axis. However, such bending may arise when flattening arbitrary geodesic grids, which forbids their initial assembly on the ground. This study provides a process to design elastic geodesic gridshells, that is, gridshells that minimise bending moments in both formed and near-flat configurations. The generation process first brings a target geodesic network onto a plane by maintaining arc lengths. The flat mesh is then relaxed to minimise its main curvatures and hence bending moments in its members. The result is an elastic geodesic gridshell that can be assembled flat on the ground and then lifted up into its target surface. The method is applied to the design of six geodesic gridshells made of reclaimed skis.

Helically Grooved Gold Nanoarrows: Controlled Fabrication, Superhelix, and Transcribed Chiroptical Switching

Plasmonic chiroptical materials, coupled by chirality and surface plasmons, have been attracting great interest due to their potential applications, such as photonics, chiral recognition, asymmetri...

Design and characterization of axisymmetric auxetic metamaterials

Traditional three dimensional (3D) block auxetics exhibit anisotropic cross-section changes even they exist in isotropic forms due to finite size and boundary effect. Herein, a systematic design strategy of axisymmetric auxetic metamaterials is proposed with rotationally symmetric transverse deformation mode. The axisymmetric auxetics are obtained by the revolution of two-dimensional curved auxetic configurations along the axis of rotation and composed with shell elements. Finite element simulations and mechanical experiments reveal that the axisymmetric deformation mechanism cause transversely isotropic negative Poisson's ratio and enhance the specific Young's modulus compared to corresponding 2D and 3D cellular structures. The influence of geometric parameters on elastic constants is investigated numerically. Three kinds of 3D printing technologies are adopted to fabricate the axisymmetric auxetics which shows the relative Young's modulus and equivalent Poisson's ratio are independent of constitute materials. This study systematically characterizes the mechanical responses of axisymmetric auxetic metamaterials and expounds the potential multifunctional applications, such as reusable energy absorption.

Water-stressed or not, the mechanical acclimation is a priority requirement for trees

Periodic bending of young poplars increase the wood production whatever their hydric status; especially in the most highly stressed zones; improving the mechanical behaviour of the stem. The ability of trees to acclimate the building of their structures to windy conditions under various hydric conditions is essential in the context of the predicted climate changes. In this study, we investigated the biomechanical responses of young poplar trees to periodic controlled bending stimulations that mimic the mechanical effect of trees growing under windy conditions. This treatment was conducted for 5 months in well-watered conditions or under hydric stress. Results demonstrate the high impact of thigmomorphogenesis on growth processes, even under the water shortage. While axial growth was reduced by mechanical stimulations and hydric stress, radial growth was strongly increased by the periodic stem bending. The secondary growth was preferentially increased in the direction of highest longitudinal strains leading to the ovalisation of the cross-section. This ovalisation yielded 16%, regardless the hydric condition and generated a huge increase of the bending rigidity of the trees (+ 212%). Further, we observed a differential growth between the side growing under tension and the side growing under compression. A Finite Element model was built to investigate the mechanical benefits of the anisotropic cross-section shapes. This FE model enlightened the modulation of the spatial stress distribution that lead to a reduction of the stress in the weakest zones of the trunk; suggesting an improvement of the mechanical safety margin of wood. Thigmomorphogenesis acclimation appears as a complex and costly, but necessary process for the long-term mechanical support of the trees, even under hydric stress conditions.

Improved Accuracy in the 2-D/1-D Method with Anisotropic Transverse Leakage and Cross-Section Homogenization

The Two-Dimensional (2-D)/One-Dimensional (1-D) method allows pin-resolved computational transport solutions for large, full-core light water reactor simulations at relatively low computational cost compared to a true three-dimensional (3-D) transport method. The 2-D/1-D method constructs an approximation to the 3-D transport equation with (1) a 2-D transport equation in the radial variables and , discretized on a fine radial spatial grid, and (2) a 1-D transport (or approximate PN) equation in the axial variable , discretized on a radially coarse spatial grid. The 2-D and 1-D equations are coupled through transverse leakage (TL) terms. In this paper, a new 2-D/1-D P3 method with anisotropic transverse leakages and anisotropic homogenized 1-D cross sections (XSs) is proposed to improve the accuracy of conventional 2-D/1-D with pin homogenization. It is shown that only the polar component of the anisotropic homogenized XS has a significant effect on the solution; the azimuthal component is negligible. However, the polar and azimuthal components of the leakage terms are both important. The new method is implemented in the 2-D/1-D code Michigan PArallel Characteristics Transport (MPACT). The method in this paper is shown to achieve nearly 3-D transport accuracy with sufficient refinement in space and angle. The improvement of this new method compared to the previous 2-D/1-D method in MPACT is most notable in problems with strong axial leakage and sharp axial discontinuities, such as control rod tips or part-length rods. The method is computationally more expensive than the existing 2-D/1-D method with isotropic TL and XSs, but this additional cost may be justified when the axial flux shape does not vary smoothly due to axial heterogeneity and needs to be resolved well.

Neutronic calculation of an axially heterogeneous ASTRID fuel assembly with APOLLO3®: Analysis of biases and foreseen improvements

Design of modern sodium fast reactors such as the French SFR project ASTRID are axially heterogeneous in order to maximize neutron leakage and therefore improve their natural behavior during transients. This feature is however challenging for neutronic calculations that usually rely on a first step based upon the generation of averaged cross sections over planar geometries. It is in particular the case of the APOLLO3® reference calculation route that is currently considered for SFR applications. This paper investigates the corresponding biases in the case of a 3D fissile assembly calculation and highlights the consequences of the fundamental mode assumption. It is shown that even though an acceptable global accuracy can be achieved, the flux distribution presents a slight axial drift. The homogenization and energy collapsing of anisotropic cross sections over radial geometries is pointed responsible for it. Several proposals are made to correct this inconsistency, leading to new calculation schemes and enhanced performances.

Geometrically Exact Finite Element Formulations for Slender Beams: Kirchhoff–Love Theory Versus Simo–Reissner Theory

The present work focuses on geometrically exact finite elements for highly slender beams. It aims at the proposal of novel formulations of Kirchhoff-Love type, a detailed review of existing formulations of Kirchhoff-Love and Simo-Reissner type as well as a careful evaluation and comparison of the proposed and existing formulations. Two different rotation interpolation schemes with strong or weak Kirchhoff constraint enforcement, respectively, as well as two different choices of nodal triad parametrizations in terms of rotation or tangent vectors are proposed. The combination of these schemes leads to four novel finite element variants, all of them based on a C1-continuous Hermite interpolation of the beam centerline. Essential requirements such as representability of general 3D, large-deformation, dynamic problems involving slender beams with arbitrary initial curvatures and anisotropic cross-section shapes or preservation of objectivity and path-independence will be investigated analytically and verified numerically for the different formulations. It will be shown that the geometrically exact Kirchhoff-Love beam elements proposed in this work are the first ones of this type that fulfill all the considered requirements. On the contrary, Simo-Reissner type formulations fulfilling these requirements can be found in the literature very well. However, it will be argued that the shear-free Kirchhoff-Love formulations can provide considerable numerical advantages when applied to highly slender beams. Concretely, several representative numerical test cases confirm that the proposed Kirchhoff-Love formulations exhibit a lower discretization error level as well as a considerably improved nonlinear solver performance in the range of high beam slenderness ratios as compared to two representative Simo-Reissner element formulations from the literature.

Tuning Nonlinear Mechanical Mode Coupling in GaAs Nanowires Using Cross-Section Morphology Control.

We investigate the nonlinear mechanical properties of GaAs nanowires with anisotropic cross-section. Fundamental and second order flexural modes are studied using laser interferometry with good agreement found between experiment and theory describing the nonlinear response under mechanical excitation. In particular, we demonstrate that the sign of the nonlinear coupling between orthogonal modes is dependent on the cross-section aspect ratio. The findings are of interest for applications such as amplitude to frequency conversion and vectorial force sensing.

A finite-difference formulation of elastic rod for the design of actively bent structures

A discrete formulation of elastic rod has been tailored for the particular design task of geometric modelling, form finding and analysis of actively bent structural systems. The rod element is fully described by using vector based quantities, hence making it easy to implement and be suitable for explicit resolution methods such as the Dynamic Relaxation (DR). From this point of view, the model under consideration aims to provide a natural enhancement, of existing DR schemes of elastic rods, primarily formulated for analysis/design of stressed spline structures with isotropic cross-section, whilst, the proposed formulation allows for the general case of initially straight rods with anisotropic cross-section and torsional stiffness effects, to be taken into consideration. In order to avoid numerical conditioning problems, the method adopts a reduced Degrees of Freedom approach, however, the design limitations usually involved with such an approach, are ‘removed’ by adopting the Bishop theory of framed curves, hence making it possible to reduce to only three (translations) the Degrees of Freedom to be explicitly computed by numerical integration of the corresponding acceleration terms.

Self-Assembly and Formation of Chromonic Liquid Crystals from the Dyes Quinaldine Red Acetate and Pyronin Y

The aqueous self-assembly behavior of the dyes Quinaldine red acetate and Pyronin Y in a wide range of concentrations is reported here for the first time. (1)H NMR spectroscopy, polarized-light optical microscopy, and small and wide X-ray scattering were used to get insight into molecular interactions, phase boundaries and aggregate structure. Quinaldine red acetate and Pyronin Y self-organize into unimolecular stacks driven by attractive aromatic interactions. At high concentrations, spatial correlation among the molecular stacks gives rise to nematic liquid crystals in both systems. Quinaldine red acetate additionally produces a rare chromonic O phase built of columnar aggregates with anisotropic cross-section ordered in a rectangular lattice. The O phase changes into a columnar lamellar structure as a result of a temperature-induced phase transition. Results open the possibility of finding chromonic liquid crystals in other commercially available dyes with a similar molecular structure. This would eventually expand the availability of these unique soft materials and thus introduce new applications for marketed dyes.

Fabrication of Electrospun Polymer Fibers with Nonspherical Cross-Sections Using a Nanopressing Technique.

The fabrication of electrospun polymer fibers is demonstrated with anisotropic cross-sections by applying a simple pressing method. Electrospun polystyrene or poly(methyl methacrylate) fibers are pressed by flat or patterned substrates while the samples are annealed at elevated temperatures. The shapes and morphologies of the pressed polymer fibers are controlled by the experimental conditions such as the pressing force, the pressing temperature, the pressing time, and the surface pattern of the substrate. At the same pressing force, the shape changes of the polymer fibers can be controlled by the pressing time. For shorter pressing times, the deformation process is dominated by the effect of pressing and fibers with barrel-shaped cross-sections can be generated. For longer pressing times, the effect of wetting becomes more important and fibers with dumbbell-shaped cross-sections can be obtained. Hierarchical polymer fibers with nanorods are fabricated by pressing the fibers with porous anodic aluminum oxide templates.

Two-dimensional spatial manipulation of microparticles in continuous flows in acoustofluidic systems.

We report a modeling and experimental study of techniques to acoustically focus particles flowing through a microfluidic channel. Our theoretical model differs from prior works in that we solve an approximate 2-D wave transmission model that accounts for wave propagation in both the solid and fluid phases. Our simulations indicate that particles can be effectively focused at driving frequencies as high as 10% off of the resonant condition. This conclusion is supported by experiments on the acoustic focusing of particles in nearly square microchannels, which are studied for different flow rates, driving frequencies and placements of the lead zirconate titanate transducer, either underneath the microchannel or underneath a parallel trough. The relative acoustic potential energy and the resultant velocity fields for particles with positive acoustic contrast coefficients are estimated in the 2-D limit. Confocal microscopy was used to observe the spatial distribution of the flowing microparticles in three dimensions. Through these studies, we show that a single driving frequency from a single piezoelectric actuator can induce the 2-D concentration of particles in a microchannel with a nearly square cross section, and we correlate these behaviors with theoretical predictions. We also show that it is possible to control the extent of focusing of the microparticles, and that it is possible to decouple the focusing of microparticles in the vertical direction from the lateral direction in rectangular channels with anisotropic cross sections. This study provides guidelines to design and operate microchip-based acoustofluidic devices for precise control over the spatial arrangement of microparticles for applications such as flow cytometry and cellular sorting.

Morphology Selection through Geometric Frustration in Twisted Filament Bundles and Fibers

Rope-like assemblies of twisted protein filaments constitute a common materials archetype appearing in a range of biological contexts from extracellular filament bundles to amyloid fibrils. Owing to the numerous distinctions in molecular structure and interactions underlying these diverse assemblies, a common framework to predict and classify the basic mechanisms of structure formation in twisted filament assemblies is still lacking. In this study, we exploit a recent and surprising connection between the assembly of self-twisting filaments and assembly on spherically-curved 2D surfaces to develop a universal theory of morphology selection in twisted fibers and bundles. This theory shows that the size and cross-sectional shape of self-assembled fibers is determined by competition between the elastic costs of inter-filament frustration, bending deformation of constituent filaments and surface energy of fibers. We find that for sufficiently large twist, isotropic (cylindrical) bundles are generically unstable to developing anisotropic cross-sections (helical tapes). Critically, the anisotropy of fiber cross-sections is found to give a direct measure of the anisotropy of inter-filament vs. intra-filament elasticity. We corroborate the universal predictions of our theory with numerical simulations of self-twisting fibers and compare the morphology diagram structural observations of anisotropy of micron-scale amyloid fibers assembled from hydrolyzed protein fragments.

Electric conductivity from the solution of the relativistic Boltzmann equation

We present numerical results of electric conductivity ${\ensuremath{\sigma}}_{\text{el}}$ of a fluid obtained solving the relativistic transport Boltzmann equation in a box with periodic boundary conditions. We compute ${\ensuremath{\sigma}}_{\text{el}}$ using two methods: the definition itself, i.e., applying an external electric field, and the evaluation of the Green-Kubo relation based on the time evolution of the current-current correlator. We find a very good agreement between the two methods. We also compare numerical results with analytic formulas in relaxation time approximation (RTA) where the relaxation time for ${\ensuremath{\sigma}}_{\text{el}}$ is determined by the transport cross section ${\ensuremath{\sigma}}_{\text{tr}}$, i.e., the differential cross section weighted with the collisional momentum transfer. We investigate the electric conductivity dependence on the microscopic details of the two-body scatterings: isotropic and anisotropic cross section as well as massless and massive particles. We find that the RTA underestimates considerably ${\ensuremath{\sigma}}_{\text{el}}$; for example, at screening masses ${m}_{D}\ensuremath{\sim}T$, such underestimation can be as large as a factor of 2. Furthermore, we study a more realistic case for a quark-gluon system (QGP) considering both a quasiparticle model tuned to lattice QCD (lQCD) thermodynamics, as well as the case of a perturbative QCD (pQCD) gas with running coupling. Also, for these cases more directly related to the description of the QGP system, we find that the RTA significantly underestimates the ${\ensuremath{\sigma}}_{\text{el}}$ by about 60%--80%.

Stiffness Constants of Homogeneous, Anisotropic, Prismatic Beams

This paper presents a complete set of analytical expressions for the stiffness constants of a generalized Euler–Bernoulli beam theory for homogeneous, anisotropic, prismatic beams with arbitrary cross-sectional shapes. These expressions are extracted from exact solutions of the linear equations of three-dimensional elasticity for the cases of loading by axial forces, torques, and bending moments about two orthogonal directions. Closed-form expressions are derived for the extensional stiffness and the extension-related coupling terms. Expressions for the remaining stiffness constants are derived in terms of the torsional stiffness: the expression of which is in terms of a function that needs to be obtained. The resulting expressions reveal both similarities and differences from its isotropic and orthotropic counterparts. For elliptical, anisotropic cross sections and rectangular, orthotropic cross sections, all stiffness constants are known in closed form. These closed-form expressions constitute a standard with which the ability of two-dimensional beam cross-sectional analyses to model material anisotropy may be assessed. The calculated stiffness constants, from one such cross-sectional analysis, are successfully validated in this manner.

Transport coefficients of Quark-Gluon Plasma in a Kinetic Theory approach

One of the main results of heavy ions collision at relativistic energy experiments is the very small shear viscosity to entropy density ratio of the Quark-Gluon Plasma, close to the conjectured lower bound η/s = 1/4π for systems in the infinite coupling limit. Transport coefficients like shear viscosity are responsible of non-equilibrium properties of a system: Green- Kubo relations give us an exact expression to compute these coefficients. We computed shear viscosity numerically using Green-Kubo relation in the framework of Kinetic Theory solving the relativistic transport Boltzmann equation in a finite box with periodic boundary conditions. We investigated different cases of particles, for one component system (gluon matter), interacting via isotropic or anisotropic cross-section in the range of temperature of interest for HIC. Green-Kubo results are in agreement with Chapman-Enskog approximation while Relaxation Time approximation can underestimates the viscosity of a factor 2. Another transport coefficient of interest is the electric conductivity σel which determines the response of QGP to the electromagnetic fields present in the early stage of the collision. We study the σel dependence on microscopic details of interaction and we find also in this case that Relaxation Time Approximation is a good approximation only for isotropic cross-section.