Ribbon Model Research Articles

Optimization of a tensile strength prediction model for compacted ribbons using NIR-HIS analysis

The tensile strength (TS) of compacted ribbon is a critical quality attribute in the roller compaction process that impacts the quality of the finished product. This study investigated the use of Near Infrared Hyperspectral Imaging Spectroscopy (NIR-HIS) technology for predicting TS of compacted ribbons, considering the effects of surface curvature, different spectral preprocessing methods, and variable selection methods on a predictive model based on Partial Least Squares regression (PLSr). The spectral preprocessing methods evaluated were Mean Centering (MC) and Standard Normal Variate (SNV). The variable selection methods were Filter by Regression Coefficient (REG), Variable Importance in Projection (VIP), Competitive Adaptive Reweighted Sampling (CARS), and Genetic Algorithm (GA). The results indicated that curved surfaces had no significant impact on the predictive performance of the model (p-value of 0.39 for RMSEP). The PLSr-CARS method, combined with MC spectral preprocessing, was successful in selecting and reducing the number of wavelengths from 182 to 5, as indicated by high values of R2pred and RPD, and a low RMSEP value (0.97, 5.75, and 7.60%, respectively). An MLR model using the 5 wavelengths was also developed, showing similar performance to the PLSr model. Both the MLR and PLSr models demonstrated high predictive accuracy and reliability. These models can perform well even when developed using only a few wavelengths, leading to significant reductions in processing time and measurement costs, making them valuable tools for quality control in the pharmaceutical industry.

MERCI: Mixed curvature-based elements for computing equilibria of thin elastic ribbons

Thin elastic ribbons represent a class of intermediary objects lying in-between thin elastic plates and thin elastic rods. Although the two latter families of thin structures have received much interest from the Computer Graphics community over the last decades, ribbons have seldom been considered and modelled numerically so far, in spite of a growing number of applications in Computer Design. In this paper, starting from the reduced developable ribbon models [Sadowsky 1929; Wunderlich 1962] recently popularised in Soft Matter Physics, we propose a both accurate and efficient algorithm for computing the statics of thin elastic ribbons. Inspired by the super-clothoid model for thin elastic rods, our method relies on compact ribbon elements whose normal curvature varies linearly with respect to arc length s , while their geodesic torsion is quadratic in s . In contrast however, for the sake of efficiency, our algorithm avoids building a fully reduced kinematic chain and instead treats each element independently, gluing them only at the final solving stage through well-chosen bilateral constraints. Thanks to this mixed variational strategy, which yields a banded Hessian, our algorithm recovers the linear complexity of low-order models while preserving the quadratic convergence of curvature-based models. As a result, our approach is scalable to a large number of elements, and suitable for various boundary conditions and unilateral contact constraints, making it possible to handle challenging scenarios such as confined buckling experiments or Möbius bands with contact. Remarkably, our mixed algorithm proves an order of magnitude faster compared to Discrete Elastic Ribbon models of the literature while achieving, in a few seconds only, high accuracy levels that remain out of reach for such low-order models. Additionally, our numerical model can incorporate various ribbon energies, including the RibExt model for quasi-developable ribbons recently introduced in Physics [Audoly and Neukirch 2021], which allows to transition smoothly between a rectangular Kirchhoff rod and a (developable) Sadowsky ribbon. Our numerical scheme is carefully validated against demanding experiments of the Physics literature, which demonstrates its accuracy, efficiency, robustness, and versatility. Our Merci code is publicly available at https://gitlab.inria.fr/elan-public-code/merci for the sake of reproducibility and future benchmarking.

Single-molecule orientation-localization microscopy resolves the nanoscale organization of self-assembled peptides.

Self-assembling peptides have remarkable applications in biomaterials and therapeutics. Amphipathic peptides with alternating polar and nonpolar residues tend to self-assemble into cross-β-rich fibrils, which are usually signatures of various protein-misfolding pathologies. Key to understanding the mechanisms of self-assembly is the ability to visualize and quantify the complex, heterogeneous organization of these peptides with single-aggregate sensitivity. Here, we utilize single-molecule orientation-localization microscopy (SMOLM), a variant of super-resolution microscopy, to measure amphipathic KFE8 (Ac-FKFEFKFE-NH2) assemblies. Using the transient binding of Nile red (NR) as a blinking mechanism, we find that the orientation distribution of NR on KFE8 is significantly different from that bound to amyloid-beta fibrils, where NR is simply oriented parallel to the coverslip and along the long axis of each fiber. A detailed analysis of NR orientations on KFE8 shows that they bind in a manner consistent with a helical ribbon model of the underlying peptide assembly. Further, the 3D orientations of NR enable us to quantify the pitch-to-diameter ratio of the underlying helix. Finally, we show that SMOLM can resolve a variety of nanoscale structures formed by model self-assembling peptides. Due to limited spatial resolution, standard localization-based super-resolution microscopy cannot resolve these details. These experiments are the first demonstration of utilizing fluorophore orientation “spectra”, i.e., the 3D orientations of dye molecules, to resolve the complex nanoscale organization of self-assembled peptides in solution.

Analysis of cone-like singularities in twisted elastic ribbons

Twisting a thin elastic ribbon is known to produce a localised deformation pattern resembling a cone whose tip is located on the edge of the ribbon. Using the theory of inextensional ribbons, we present a matched asymptotic analysis of these singularities for ribbons whose width-to-length ratio w/ℓ≪1 is small. An inner layer solution is derived from the finite-w Wunderlich model and captures the fast, local variations of the bending and twisting strains in the neighbourhood of the cone-like region; it is universal up to a load intensity factor. The outer solution is given by the zero-w Sadowsky model. Based on this analysis, we propose a new standalone ribbon model that combines the Sadowsky equations with jump conditions providing a coarse-grained description of cone-like singularities, and give a self-contained variational derivation of this model. Applications to the Möbius band and to an end-loaded open ribbon are presented. Overall, the new model delivers highly accurate approximations to the solutions of the Wunderlich model in the limit w≪ℓ while avoiding the numerical difficulties associated with cone-like singularities.

An isogeometric one-dimensional Kirchhoff–Love type model for developable elastic ribbons

This paper proposes a kinematical reduction for Kirchhoff–Love shells in the special case of developable base surfaces. The resulting model considers a curve and a director field along it, reducing the shell to one-dimensional items and thereby decreasing the number of degrees of freedom involved. The presented overview of the geometry of developable surfaces covers dissolution of two types of singularities: a relatively parallel frame allows for points or segments of zero curvature along the curve and an explicit condition accounts for local self-intersections of the ruled surface description. We generalise earlier results after which the geometric constraints proposed are equivalent to isometric shell deformation. We also give a more general update of the elastic bending energy of the ribbon, which yields equilibrium states as minimisers. Subsequently, we discuss the numerical details of the approach and illustrate the feasibility at hand of several examples, among them the famous Möbius ribbon.

Imputation of the major histocompatibility complex region identifies major independent variants associated with bullous pemphigoid and dermatomyositis in Han Chinese.

As autoimmune skin diseases, both bullous pemphigoid (BP) and dermatomyositis (DM) show significant associations with the major histocompatibility complex (MHC) region. In fact, the coexistence of BP and DM has been previously reported. Therefore, we hypothesized that there may be a potential genetic correlation between BP and DM. Based on data for 312 BP patients, 128 DM patients, and 6793 healthy control subjects, in the MHC region, we imputed single-nucleotide polymorphisms (SNP), insertions and deletions (INDEL), and copy number variations (CNV) using the 1KGP phase 3 dataset and amino acids (AA) and SNP using a Han-MHC reference database. An association study revealed the most significant SNP associated with BP, namely, rs580921 (p=1.06E-08, odds ratio [OR]=1.61, 95% confidence interval [CI]=1.37-1.90), which is located in the C6orf10 gene, and the most significant classic human leukocyte antigen (HLA) allele associated with DM, namely, HLA-DPB1*1701 (p=6.56E-10, OR=3.61, 95% CI=2.40-5.42). Further stepwise regression analyses with rs580921 identified a threonine at position 163 of the HLA-B gene as a new independent disease-associated AA, and HLA-DPB1*1701 indicated that no loci were significant. Three-dimensional ribbon models revealed that the HLA-B AA position 163 (p=3.93E-07, OR=1.64, 95% CI=1.35-1.98) located in the α2 domain of the HLA-B molecule was involved in the process of specific antigen presentation. The calculations showed that there was no significant genetic correlation between BP and DM. Our study identified three significant loci in the MHC region, proving that the HLA region was significantly correlated with BP and DM separately. Our research highlights the key role of the MHC region in disease susceptibility.

A Ribbon Model for Nematic Polymer Networks

We present a theory of deformation of ribbons made of nematic polymer networks (NPNs). These materials exhibit properties of rubber and nematic liquid crystals, and can be activated by external stimuli of heat and light. A two-dimensional energy for a sheet of such a material has already been derived from the celebrated neo-classical energy of nematic elastomers in three space dimensions. Here, we use a dimension reduction method to obtain the appropriate energy for a ribbon from the aforementioned sheet energy. We also present an illustrative example of a rectangular NPN ribbon that undergoes in-plane serpentine deformations upon activation under an appropriate set of boundary conditions.

Finite element modeling of α-helices and tropocollagen molecules referring to spike of SARS-CoV-2

The newly developed finite element (FE) modeling at the atomic scale was used to predict the static and dynamic response of the α-helix (AH) and tropocollagen (TC) protein fragments, the main building blocks of the spike of the SARS-CoV-2. The geometry and morphology of the spike’s stalk and its connection to the viral envelope were determined from the combination of most recent molecular dynamics (MD) simulation and images of cryoelectron microscopy. The stiffness parameters of the covalent bonds in the main chain of the helix were taken from the literature. The AH and TC were modeled using both beam elements (wire model) and shell elements (ribbon model) in FE analysis to predict their mechanical properties under tension. The asymptotic stiffening features of AH and TC under tensile loading were revealed and compared with a new analytical solution. The mechanical stiffnesses under other loading conditions, including compression, torsion, and bending, were also predicted numerically and correlated with the results of the existing MD simulations and tests. The mode shapes and natural frequencies of the spike were predicted using the built FE model. The frequencies were shown to be within the safe range of 1–20 MHz routinely used for medical imaging and diagnosis by means of ultrasound. These results provide a solid theoretical basis for using ultrasound to study damaging coronavirus through transient and resonant vibration at large deformations.

Boron Silicon B2Si3qand B3Si2pClusters: The Smallest Aromatic Ribbons

The small binary boron silicon clusters B2Si3q with q going from -2 to +2 and B3Si2p with p varying from -3 to +1 were reinvestigated using quantum chemical methods. The thermodynamic stability of these smallest ribbon structures is governed by both Hückel and ribbon models for aromaticity. The more negative the cluster charge, the more ribbon character is shown. In contrast, the more positive the charge state, the more pronounced the Hückel character becomes. The ribbon aromaticity character can also be classified into ribbon aromatic, semiaromatic, antiaromatic, and triplet aromatic when the electron configuration of a ribbon structure is described as [...π2(n+1)σ2n], [...π2n+1σ2n], [...π2nσ2n], and [...π2n+1σ2n-1], respectively. Geometry optimizations of the B2Si3 lowest-energy structure by some density functional theory (DFT) functionals result in a nonplanar shape because it possesses an antiaromatic ribbon character. However, its π aromaticity assigned by the Hückel rule is stronger in such a way that several other DFT and coupled-cluster theory CCSD(T) calculations show that B2Si3 is indeed stable in a planar form (Cs). A new global equilibrium structure for the anion B2Si32-, which is a ribbon semiaromatic species, was identified. Some benchmark tests were also carried out to evaluate the performance of popular methods for the treatment of binary B-Si clusters. At odds with some previous studies, we found that with reference to the high accuracy CCSD(T)/CBS method, the hybrid TPSSh functional is reliable for a structure search, whereas the hybrid B3LYP functional is more suitable for simulations of some experimental spectroscopic results.

A discrete differential geometry-based numerical framework for extensible ribbons

As a typical mechanical structure, ribbons are characterized with three distinctly different dimensions, i.e., length ≫ width ≫ thickness, which leads to their exclusive behaviors different from the one-dimensional (1D) case of slender rods and the two-dimensional (2D) case of thin plates. In this paper, we report a discrete differential geometry (DDG)-based numerical method to simulate the geometrically nonlinear deformations of extensible ribbons. With a cross section-dependent regularized parameter introduced, the proposed 1D framework allows both in-plane stretching and out-of-plane bending in the ribbon mid-surface, aimed at bridging the gap between the linear Kirchhoff rod theory and the developable Sadowsky ribbon model. Instead of solving the ordinary differential equations (ODEs) directly with the associated boundary conditions, the mechanical object is discretized into a mass–spring system, and its equilibrium configuration is obtained through a dynamic relaxation method. The numerical framework is applied to seven typical occasions based on either experimental or published datasets in order to verify its performance. Quantitative agreements demonstrate the effectiveness and accuracy of the proposed discrete approach for extensible ribbons, which, as a computationally efficient numerical simulator, could provide a pivotal understanding of a batch of slender structures, and further inspire the simulation-guided design of man-made systems.

Whence the Interstellar Magnetic Field Shaping the Heliosphere?

Abstract Measurements of starlight polarized by aligned interstellar dust grains are used to probe the relation between the orientation of the ambient interstellar magnetic field (ISMF) and the ISMF traced by the ribbons of energetic neutral atoms discovered by the Interstellar Boundary Explorer spacecraft. We utilize polarization data, many acquired specifically for this study, to trace the configuration of the ISMF within 40 pc. A statistical analysis yields a best-fit ISMF orientation, B magpol, aligned with Galactic coordinates ℓ = 42°, b = 49°. Further analysis shows the ISMF is more orderly for “downfield” stars located over 90° from B magpol. The data subset of downfield stars yields an orientation for the nearby ISMF at ecliptic coordinates λ, β ≈ 219° ± 15°, 43° ± 9° (Galactic coordinates l, b ≈ 40°, 56°, ±17°). This best-fit ISMF orientation from polarization data is close to the field direction obtained from ribbon models. This agreement suggests that the ISMF shaping the heliosphere belongs to an extended ordered magnetic field. Extended filamentary structures are found throughout the sky. A previously discovered filament traversing the heliosphere nose region, “Filament A,” extends over 300° of the sky, and crosses the upwind direction of interstellar dust flowing into the heliosphere. Filament A overlaps the locations of the Voyager kilohertz emissions, three quasar intraday variables, cosmic microwave background (CMB) components, and the inflow direction of interstellar grains sampled by Ulysses and Galileo. These features are likely located in the upstream outer heliosheath where ISMF drapes over the heliosphere, suggesting Filament A coincides with a dusty magnetized plasma. A filament 55° long is aligned with a possible shock interface between local interstellar clouds. A dark spot in the CMB is seen within 5° of the filament and within 10° of the downfield ISMF direction. Two large magnetic arcs are centered on the directions of the heliotail. The overlap between CMB components and the aligned dust grains forming Filament A indicates the configuration of dust entrained in the ISMF interacting with the heliosphere provides a measurable foreground to the CMB.

A convenient formulation of Sadowsky's model for elastic ribbons

Elastic ribbons are elastic structures whose length-to-width and width-to-thickness aspect ratios are both large. Sadowsky proposed a one-dimensional model for ribbons featuring a nonlinear constitutive relation for bending and twisting: it brings in both rich behaviours and numerical difficulties. By discarding non-physical solutions to this constitutive relation, we show that it can be inverted; this simplifies the system of differential equations governing the equilibrium of ribbons. Based on the inverted form, we propose a natural regularization of the constitutive law that eases the treatment of singularities often encountered in ribbons. We illustrate the approach with the classical problem of the equilibrium of a Möbius ribbon, and compare our findings with the predictions of the Wunderlich model. Overall, our approach provides a simple method for simulating the statics and the dynamics of elastic ribbons.

Effect of spin polarization and supercell size on specific energy and electronic structure of MoS2 edge calculated by DFT method in the plane-wave basis

The effect of supercell size in the ribbon model of molybdenum disulfide edge on the cell electronic structure and specific energy was investigated, with and without spin polarization. The differences found were discussed in terms of electron count. Diagnostic criteria for the model applicability and the effect of opposite edge were discussed.

A one-dimensional model for elastic ribbons: A little stretching makes a big difference

Starting from the theory of elastic plates, we derive a non-linear one-dimensional model for elastic ribbons with thickness t, width a and length ℓ, assuming t≪a≪ℓ. It takes the form of a rod model with a specific non-linear constitutive law accounting for both the stretching and the bending of the ribbon mid-surface. The model is asymptotically correct and can handle finite rotations. Two popular theories can be recovered as limiting cases, namely Kirchhoff’s rod model for small bending and twisting strains, |κi|≪t∕a2, and Sadowsky’s inextensible ribbon model for |κi|≫t∕a2; we point out that Sadowsky’s inextensible model may be a poor approximation even for ribbons having a very thin cross-section (say, with t∕a as small as 0.02). By way of illustration, the one-dimensional model is applied (i) to the lateral-torsional instability of a ribbon, showing good agreement with both experiments and finite-element shell simulations, and (ii) to the stability of a twisted ribbon subjected to a tensile force. The non-convexity of the one-dimensional model is discussed; it is addressed by a convexification argument.

Mechanics of tubular helical assemblies: ensemble response to axial compression and extension

Nature and technology often adopt structures that can be described as tubular helical assemblies. However, the role and mechanisms of these structures remain elusive. In this paper, we study the mechanical response under compression and extension of a tubular assembly composed of 8 helical Kirchhoff rods, arranged in pairs with opposite chirality and connected by pin joints, both analytically and numerically. We first focus on compression and find that, whereas a single helical rod would buckle, the rods of the assembly deform coherently as stable helical shapes wound around a common axis. Moreover, we investigate the response of the assembly under different boundary conditions, highlighting the emergence of a central region where rods remain circular helices. Secondly, we study the effects of different hypotheses on the elastic properties of rods, i.e., stress-free rods when straight versus when circular helices, Kirchhoff’s rod model versus Sadowsky’s ribbon model. Summing up, our findings highlight the key role of mutual interactions in generating a stable ensemble response that preserves the helical shape of the individual rods, as well as some interesting features, and they shed some light on the reasons why helical shapes in tubular assemblies are so common and persistent in nature and technology.Graphic We study the mechanical response under compression/extension of an assembly composed of 8 helical rods, pin-jointed and arranged in pairs with opposite chirality. In compression we find that, whereas a single rod buckles (a), the rods of the assembly deform as stable helical shapes (b). We investigate the effect of different boundary conditions and elastic properties on the mechanical response, and find that the deformed geometries exhibit a common central region where rods remain circular helices. Our findings highlight the key role of mutual interactions in the ensemble response and shed some light on the reasons why tubular helical assemblies are so common and persistent.

Car wheel models using the distributions laws of forces on a contact patch with the road surface

It is natural to consider the rolling dynamics of an automobile wheel when it interacts with the road surface. At the same time the most difficult and important task is to determine the force components applied to the wheel, such as the friction driving force, the drag force, the rolling and spinning resistance moments that occur in the contact spot from the side of the roadbed. The paper investigates the aspects of dry friction, rolling and sliding of an automobile wheel presented as a deformable body. In this case, it is of great importance to take into account the treads, which is reflected in the tire models. An important aspect is the study of the laws of distribution of normal stresses in the contact area. To solve practical issues of road transport, approaches based on the Magic Formula of Pacejka and calculation methods based on brush, ribbon and string models, in particular, the Brush model of Svendenius, are highlighted. The conditions of its applicability are obtained and justified.

Skeletal animation for visualizing dynamic shapes of macromolecules

AbstractWe apply a skeletal animation technique developed for general computer graphics animation to display the dynamic shape of protein molecules. Polygon-based models for macromolecules such as atomic representations, surface models, and protein ribbon models are deformed by the motion of skeletal bones that provide coarse-grained descriptions of detailed computer graphics models. Using the animation software Blender, we developed methods to generate the skeletal bones for molecules. Our example of the superposition of normal modes demonstrates the thermal fluctuating motion obtained from normal mode analysis. The method is also applied to display the motions of protein molecules using trajectory coordinates of a molecular dynamics simulation. We found that a standard motion capture file was practical and useful for describing the motion of the molecule using available computer graphics tools.

Valley pumping via edge states and the nonlocal valley Hall effect in two-dimensional semiconductors

Recent experiments have studied the temperature and gate voltage dependence of nonlocal transport in bilayer graphene, identifying features thought to be associated with the two-dimensional semiconductor's bulk intrinsic valley Hall effect. Here, we use both simple microscopic tight-binding ribbon models and phenomenological bulk transport equations to emphasize the impact of sample edges on the nonlocal voltage signals. We show that the nonlocal valley Hall response is sensitive to electronic structure details at the sample edges, and that it is enhanced when the local longitudinal conductivity is larger near the sample edges than in the bulk. We discuss recent experiments in light of these findings and also discuss the close analogy between electron pumping between valleys near two-dimensional sample edges in the valley Hall effect, and bulk pumping between valleys due to the chiral anomaly in three-dimensional topological semimetals.

An investigation of models for elastic ribbons: Simulations & experiments

Understanding the feature-rich buckling-dominated behavior of thin elastic ribbons is ripe with opportunities for fundamental studies exploring the nexus between geometry and mechanics, and for conceiving of engineering applications that exploit geometric nonlinearity as a functioning principle. Predictive mechanical models play an instrumental role to this end. As a direct consequence of their physical appearance, ribbons are usually modeled either as one-dimensional rods having wide cross sections, or as narrow two-dimensional plates/shells. These models employ drastically different kinematic assumptions, which in turn play a decisive role in their predictive capabilities. Here, we critically examine three modeling approaches for elastic ribbons using detailed measurements of their complex three-dimensional deformations realized in quasistatic experiments with annulus-shaped ribbons. We find that simple and practically realizable ribbon deformations contradict assumptions underlying strain-displacement relationships in nonlinear rod and von Kármán plate models. These observations do not point at shortcomings of the theories themselves, but highlight fallacies in their application to modeling ribbon-like structures that are capable of undergoing large displacements and rotations. We identify and validate, seemingly for the first time, the 1-director Cosserat plate theory as a model for elastic ribbons over a useful range of loading conditions. In the process, we demonstrate annular ribbons to be prototypical systems for studying the mechanics of elastic ribbons. Annular ribbons exhibit a tunable degree of geometric nonlinearity in response to simple displacement and rotation boundary conditions— a feature that we exploit here for highlighting the consequences of kinematic assumptions underlying different ribbon models. We additionally provide experimental evidence for the existence of multiple stable equilibria, bifurcation phenomena correlated with the number of zero crossings in the mean curvature, and localization of energy, thus making annular ribbons interesting mechanical systems to study in their own right.

A high-performance haptic rendering system for virtual reality molecular modeling

To provide a virtual reality 3D user interface with comprehensive molecular modeling, we have developed a novel haptic rendering system with a fingertip haptic rendering device and a hand-tracking Leap Motion controller. The system handles virtual molecular objects with real hands motion captured by the Leap Motion controller in a virtual reality environment. The fingertip haptic rendering device attached on each finger and a wrist gives haptic display, when virtual hands manipulating virtual molecular objects. Based on preliminary software development studies using existing 3D graphics toolkit such as CHAI3D and Unity, the fingertip haptic rendering device works with a reasonable performance for a polygon surface model and a ribbon model, but not for an atomic model due to the low rendering performance. On the other hand, the device provides us a grasping feeling of a large molecule represented by an atomic model, when used with the particle simulation system running on graphics library, DirectX 12. The haptic rendering performances, among the three software systems are discussed.