Simple deformation measures for discrete elastic rods and ribbons

The discrete elastic rod method (Bergou et al. 2008 ACM Trans. Graph . 27 , 63:1–63:12. ( doi:10.1145/1360612.1360662 )) is a numerical method for simulating slender elastic bodies. It works by representing the centreline as a polygonal chain, attaching two perpendicular directors to each segment and defining discrete stretching, bending and twisting deformation measures and a discrete strain energy. Here, we investigate an alternative formulation of this model based on a simpler definition of the discrete deformation measures. Both formulations are equally consistent with the continuous rod model. Simple formulae for the first and second gradients of the discrete deformation measures are derived, making it easy to calculate the Hessian of the discrete strain energy. A few numerical illustrations are given. The approach is also extended to inextensible ribbons described by the Wunderlich model, and both the developability constraint and the dependence of the energy on the strain gradients are handled naturally.

Dynamo seeds from Gravitational Torsional Anomalies and De Sitter Magnetized Metrics

Recently gravitational and Nieh-Yan chiral anomalies have been obtained in Riemann-Cartan spacetime Class and Quantum Gravity 38 (2021)], where electrodynamics is encoddded in the metric. In this paper we follow the path of obtaining a class of deformed de Sitter metrics in teleparallelism. The existence of the unmagnetized DSMM without axial anomalies is proved. Here we obtain unified theories a la Einstein and Eddington and Schroedinger, called modified de Sitter metric (MDSM) with the novel following features: (i) First we show that a pure de Sitter unmagnetized metric in T4 does not induce gravitational anomalies. Therefore this is a motivation to study modifications of De Sitter metric. What is done in the following items. (ii) Nieh-Yan torsion anomaly in (DSMM) in teleparallel T4 geometry is shown to vanish in all cases. Gravitational non-tivial anomalies are obtained from these metrics. But torsional anomaly much used in condensed matter physics, does not vanish. From these magnetized metrics, we show that with dynamo equation with torsion gradients sources is valid from class 3 of the metrics but is torsionless sourced in second class. (iii) We show that in the gravitational anomaly of new deformed de Sitter metric one may cancell the gravitational anomaly by a proper choice of the metric function. The axial anomaly is obtained for some metric deformation as well. Use original de Sitter nonconformal metric . A simple deformation leads to the existence of the NY form in the case of magnetized de Sitter metric. This would be class IV of DSMM.

High-throughput prediction of the carrier relaxation time via data-driven descriptor

It has been demonstrated that many promising thermoelectric materials, such as tetradymite compounds are also three-dimensional topological insulators. In both cases, a fundamental question is the evaluation of carrier relaxation time, which is usually a rough task due to the complicated scattering mechanisms. Previous works using the simple deformation potential theory or considering complete electron-phonon coupling are, however, restricted to small systems. By adopting a data-driven method named SISSO (Sure Independence Screening and Sparsifying Operator) with the training data obtained via deformation potential theory, we propose an efficient and physically interpretable descriptor to evaluate the relaxation time, using tetradymites as prototypical examples. Without any input from first-principles calculations, the descriptor contains only several elemental properties of the constituent atoms, and could be utilized to quickly and reliably predict the carrier relaxation time of a substantial number of tetradymites with arbitrary stoichiometry.

The Crystal Chemistry of Inorganic Hydroborates

The crystal structures of inorganic hydroborates (salts and coordination compounds with anions containing hydrogen bonded to boron) except for the simplest anion, borohydride BH4−, are analyzed regarding their structural prototypes found in the inorganic databases such as Pearson’s Crystal Data [Villars and Cenzual (2015), Pearson’s Crystal Data. Crystal Structure Database for Inorganic Compounds, Release 2019/2020, ASM International, Materials Park, Ohio, USA]. Only the compounds with hydroborate as the only type of anion are reviewed, although including compounds gathering more than one different hydroborate (mixed anion). Carbaborane anions and partly halogenated hydroborates are included. Hydroborates containing anions other than hydroborate or neutral molecules such as NH3 are not discussed. The coordination polyhedra around the cations, including complex cations, and the hydroborate anions are determined and constitute the basis of the structural systematics underlying hydroborates chemistry in various variants of anionic packing. The latter is determined from anion–anion coordination with the help of topology analysis using the program TOPOS [Blatov (2006), IUCr CompComm. Newsl. 7, 4–38]. The Pauling rules for ionic crystals apply only to smaller cations with the observed coordination number within 2–4. For bigger cations, the predictive power of the first Pauling rule is very poor. All non-molecular hydroborate crystal structures can be derived by simple deformation of the close-packed anionic lattices, i.e., cubic close packing (ccp) and hexagonal close packing (hcp), or body-centered cubic (bcc), by filling tetrahedral or octahedral sites. This review on the crystal chemistry of hydroborates is a contribution that should serve as a roadmap for materials engineers to design new materials, synthetic chemists in their search for promising compounds to be prepared, and materials scientists in understanding the properties of novel materials.

Fabrication and Testing of Kirigami-Inspired Multi-Stable Composites

This paper aims at highlighting the fabrication procedures and proof-of-concept tests of a Kirigami inspired multi-stable composite laminate. Bistable composites consisting of asymmetric fiber layout have shown great potentials for shape morphing and energy harvesting applications. However, a patch of such a bistable composite is limited to very simple deformation when being snapped between its two stable equilibria (or states). To address this issue, this study investigates the idea of utilizing Kirigami, the ancient art of paper cutting, into the design and fabrication of bistable composite laminates. Via combining multiple patches of laminates and cutting according to prescribed Kirigami pattern, one can create a structure with multiple stable states and sophisticated deformation paths between them. This can significantly expand the application potentials of the multi-stable composites. This paper details the fabrication procedures for an elementary unit cell in the envisioned Kirigami composite and the results of proof-of-concept experiments, which measure the force required to switch the Kirigami composite between its different stable states. Preliminary results confirm that the Kirigami unit cell possesses multiple stable states depending on the underlying fiber layout. Each patch in the Kirigami composite could be snapped independently between stable states without triggering any undesired snapping in other patches. Moreover, a transient propagation of curvature change is observed when a patch in the Kirigami composite is snapped between its stable states. Such a phenomenon has not been reported in the bistable composite studies before. Results of this paper indicate that Kirigami is a powerful approach for designing and fabricating multi-stable composites with a strong appeal for morphing and adaptive systems. This paper highlights the feasibility and novelty of combining Kirigami art and bistable adaptive composites.