Torsional Geometry Research Articles

Large volume torsion (LVT) apparatuses for rock deformation at high pressure and temperature.

Laboratory studies of rock rheology rely on purpose-built devices that can apply planetarily relevant pressures, temperatures, and non-hydrostatic stresses. Generating these pressures and stresses requires the application of large forces over small specimen areas. However, because rocks are generally polymineralic and deformation microstructures form across many length scales, it is advantageous to study relatively large (millimetric) specimens. In addition, many microstructures continue to evolve with progressive strain, so it is vital that some apparatus are able to generate enough shear strain to study these deformation phenomena. This contribution describes two new rock deformation apparatus-the Large Volume Torsion apparatus-at Washington University in St. Louis, which are capable of deforming geological specimens at high pressure and temperature (P = 3GPa; T = 1800K). Deformation is imposed in a torsional geometry, which enables the generation of extremely large shear strains (γ > 100) relevant to Earth's plate boundaries and convecting mantle. A large specimen (diameter up to 4.2mm) permits detailed postmortem microstructural analysis. Apparatus design, calibration, experimental procedures, and some examples of applications are reviewed.

Recent progress in the study of lattice-preferred orientation of olivine

Recent progress on the study of olivine LPO after (Karato et al., 2008) is reviewed with the emphasis on three issues: (i) LPO formed by the rotation of olivine crystals with anisotropic shape (euhedral crystals) in diffusion creep (Miyazaki et al., 2013), (ii) B-type LPO in the olivine + basaltic melt (Holtzman et al., 2003), and (iii) pressure change in the influence of LPO (Ohuchi and Irifune, 2013). Regarding the role of euhedral crystals, we show that euhedral olivine crystals occur in a mixture of forsterite and diopside (used by (Miyazaki et al., 2013)) but not in a mixture of olivine and enstatite. Consequently, the results by reported by (Miyazaki et al., 2013) are not applicable to the Earth’s upper mantle where olivine co-exists mostly with enstatite. Also we show that the LPO reported by (Miyazaki et al., 2013) is not consistent with the shape of olivine, and the observed LPO is likely due to dislocation glide (A-type fabric) under the conditions near the diffusion-dislocation creep regime boundary.Regarding the LPO of olivine with the presence of melt, (Qi et al., 2018)’s experimental study with the torsion geometry did not reproduce the B-type fabric reported by (Holtzman et al., 2003) indicating that the B-type fabric reported by (Holtzman et al., 2003) was indeed an artifact of the direct shear experiments. The weak LPO found by (Qi et al., 2018) (compared to that by (Zimmerman et al., 1999)) can be explained by the smaller grain size in their experiments. I conclude that a majority of the experimental results on olivine LPO at relatively low pressures (<2 GPa) can be understood based on the basics of deformation mechanism map and LPO caused by various slip systems in olivine. Regarding a claim by (Ohuchi and Irifune, 2013) that the A-type LPO (a-slip) dominates at high water content and c-slip dominates at low water content at pressures higher than ∼7 GPa, a compilation of experimental studies by (Masuti et al., 2019) and the observed LPO of the ultra-deep xenolith do not support their claim. However, experimental studies under these high-pressure conditions are limited and there remain large uncertainties regarding the LPO at high pressures (P>3 GPa).

Torsion at Different Scales: From Materials to the Universe

The concept of torsion in geometry, although known for a long time, has not gained considerable attention from the physics community until relatively recently, due to its diverse and potentially important applications to a plethora of contexts of physical interest. These range from novel materials, such as graphene and graphene-like materials, to advanced theoretical ideas, such as string theory and supersymmetry/supergravity, and applications thereof in terms of understanding the dark sector of our Universe. This work reviews such applications of torsion at different physical scales.

Systematic Comparison of Experimental Crystallographic Geometries and Gas-Phase Computed Conformers for Torsion Preferences.

We performed exhaustive torsion sampling on more than 3 million compounds using the GFN2-xTB method and performed a comparison of experimental crystallographic and gas-phase conformers. Many conformer sampling methods derive torsional angle distributions from experimental crystallographic data, limiting the torsion preferences to molecules that must be stable, synthetically accessible, and able to be crystallized. In this work, we evaluate the differences in torsional preferences of experimental crystallographic geometries and gas-phase computed conformers from a broad selection of compounds to determine whether torsional angle distributions obtained from semiempirical methods are suitable priors for conformer sampling. We find that differences in torsion preferences can be mostly attributed to a lack of available experimental crystallographic data with small deviations derived from gas-phase geometry differences. GFN2 demonstrates the ability to provide accurate and reliable torsional preferences that can provide a basis for new methods free from the limitations of experimental data collection. We provide Gaussian-based fits and sampling distributions suitable for torsion sampling and propose an alternative to the widely used "experimental torsion and knowledge distance geometry" (ETKDG) method using quantum torsion-derived distance geometry (QTDG) methods.

Unexplored Isomerization Pathways of Azobis(benzo-15-crown-5): Computational Studies on a Butterfly Crown Ether.

Computational studies on trans → cis and cis → trans isomerizations of photoresponsive azobis(benzo-15-crown-5) have been reported in this work. The photoexcited ππ* state (S2) of the trans isomer relaxes through the planar S2 minimum and the planar S2/S1 conical intersection (both situated around 9 kcal/mol below the vertically excited S2 state) arising along the N═N stretching coordinate. The nπ* state (S1) of this isomer has both planar and rotated (clockwise and anticlockwise) minima, which may lead to a torsional conical intersection (S0/S1) geometry having a <CNNC dihedral angle value close to 90°. This rotational isomerization path is found to have an energy barrier. It has been noticed that an N-N-out-of-plane motion coupled with the torsion can bring down the barrier and may facilitate the isomerization process. On the other hand, the vertically excited S1 state of the cis-isomer undergoes a barrierless path to reach a torsional conical intersection (S0/S1) geometry (<CNNC = 88°), responsible for the trans-isomer formation. The cis-S2/S1 CI (conical intersection) torsional geometry (<CNNC = 45°) is situated around 16 kcal/mol above the vertically excited ππ* state of the cis-isomer and not reachable on S2 photoexcitation. The two optimized torsional S2 minima of this system are close to the S1 surface and seem to be involved in the S2-S1 internal conversion. A less efficient concerted inversion photoisomerization path through a linear geometry has also been identified. The thermal cis → trans isomerization has been found to undergo an inversion motion, which forms a less stable trans isomer. Possible differences between the isomerization channels of this azobis(benzo-15-crown-5) and the unsubstituted azobenzene system have also been highlighted in the work.

Emergent geometry, torsion and anomalies in non-relativistic topological matter

I review and discuss aspects of the interplay of emergent geometry and anomalies in topological semimetals and insulators, focusing on effects of torsion. This correspondence identifies torsional topological responses in terms of anomalies and anomaly related hydrodynamic phenomena involving gauge fields and geometry. I discuss how torsional emergent geometry arises from elastic deformations in crystalline materials and how this background couples to thee low-energy continuum models inherited from lattice models, utilizing the semiclassical expansion. Via the coupling of momentum space topology and emergent vielbein geometry, non-relativistic topological matter can realise new geometrical responses of mixed gauge-gravitational character. The topological low-energy torsional responses depend momentum space geometry, lattice momenta and the regularization and UV completion, provided by the non-relativistic physics and symmetries of topological materials.

Torsion Geometry 5-Fold Symmetry, Anholonomic Phases, Klein Bottle Logophysics, Chaos, Resonance: Applications Towards a Novel Paradigm for the Neurosciences and Consciousness

Torsion Geometry 5-Fold Symmetry, Anholonomic Phases, Klein Bottle Logophysics, Chaos, Resonance: Applications Towards a Novel Paradigm for the Neurosciences and Consciousness

The Good, the Bad, and the Twisted Revisited: An Analysis of Ligand Geometry in Highly Resolved Protein-Ligand X-ray Structures.

An analysis of the rotatable bond geometry of drug-like ligand models is reported for high-resolution (<1.1 Å) crystallographic protein-ligand complexes. In cases where the ligand fit to the electron density is very good, unusual torsional geometry is rare and, most often, though not exclusively, associated with strong polar, metal, or covalent ligand-protein interactions. It is rarely associated with a torsional strain of greater than 2 kcal mol-1 by calculation. An unusual torsional geometry is more prevalent where the fit to electron density is not perfect. Multiple low-strain conformer bindings were observed in 21% of the set and, it is suggested, may also lie behind many of the 35% of single-occupancy cases, where a poor fit to the e-density was found. It is concluded that multiple conformer ligand binding is an under-recognized phenomenon in structure-based drug design and that there is a need for more robust crystallographic refinement methods to better handle such cases.

The quaternionic Calabi Conjecture on abelian Hypercomplex Nilmanifolds Viewed as Tori Fibrations

Abstract We study the quaternionic Calabi–Yau problem in HyperKähler manifolds with torsion geometry, introduced by Alesker and Verbitsky in [ 5], on eight-dimensional two-step nilmanifolds $M$ with an Abelian hypercomplex structure. We show that on these manifolds the quaternionic Monge–Ampère equation can always be solved for any data that are invariant under the action of a three-torus.

Dynamic mechanical analysis with torsional rectangular geometry: A critical assessment of constrained warping models

Dynamic mechanical oscillatory shear measurements with torsional rectangular geometry are widely carried out in order to determine the mechanical properties of soft solid materials in a quick and practical way. This technique has the advantage of avoiding slip effects, thus being particularly attractive for testing stiff elastomers such as vulcanized rubber compounds. However, one of its drawbacks is the clamping system required to keep the specimen edges in place. Since it imposes a constraint to warping deformations (i.e., out-of-plane cross-section distortions about the torsional axis), a certain increase of dynamic moduli with respect to their values in simple shear is observed and considered as an experimental artifact (i.e., de Saint-Venant's assumption of primary torsion of the specimen is no longer valid). The increase of dynamic moduli in torsion depends on the specimen's cross-section geometry and relative dimensions. We test here the capability of different torsion models to describe the constrained warping effect for an industrial rubber with rectangular specimen cross section using a wide range of different geometric parameters (length-to-width p ratio and width-to-thickness u ratio). We compare two theoretical models (Vlasov's model and Timoshenko's approach) and a phenomenological model (based on finite element simulations by Diani and Gilormini) with our experimental data set. We propose a slight modification of Vlasov's model to obtain realistic predictions of torsion over a wider parameter range. It is shown to be particularly useful in soft rubber testing, and the limitations in the choice of specimen geometry to obtain sufficient torque signal are overcome.

Torsional Newton Cartan gravity from non-relativistic strings

We study propagation of closed bosonic strings in torsional Newton-Cartan geometry based on a recently proposed Polyakov type action derived by dimensional reduction of the ordinary bosonic string along a null direction. We generalize the Polyakov action proposal to include matter, i.e. the 2-form and the 1-form that originates from the Kalb- Ramond field and the dilaton. We determine the conditions for Weyl invariance which we express as the beta-function equations on the worldsheet, in analogy with the usual case of strings propagating on a pseudo-Riemannian manifold. The critical dimension of the TNC space-time turns out to be 25. We find that Newton’s law of gravitation follows from the requirement of quantum Weyl invariance in the absence of torsion. Presence of the 1-form requires torsion to be non vanishing. Torsion has interesting consequences, in particular it yields a mass term and an advection term in the generalized Newton’s law. U(1) mass invariance of the theory is an important ingredient in deriving the beta functions.

Non-relativistic supersymmetry on curved three-manifolds

We construct explicit examples of non-relativistic supersymmetric field theories on curved Newton-Cartan three-manifolds. These results are obtained by performing a null reduction of four-dimensional supersymmetric field theories on Lorentzian manifolds and the Killing spinor equations that their supersymmetry parameters obey. This gives rise to a set of algebraic and differential Killing spinor equations that are obeyed by the supersymmetry parameters of the resulting three-dimensional non-relativistic field theories. We derive necessary and sufficient conditions that determine whether a Newton-Cartan background admits non-trivial solutions of these Killing spinor equations. Two classes of examples of Newton-Cartan backgrounds that obey these conditions are discussed. The first class is characterised by an integrable foliation, corresponding to so-called twistless torsional geometries, and includes manifolds whose spatial slices are isomorphic to the Poincaŕe disc. The second class of examples has a non-integrable foliation structure and corresponds to contact manifolds.

Newton-Cartan D0 branes from D1 branes and integrability

We explore analytic integrability criteria for D1 branes probing 4D relativistic background with a null isometry direction. We use both the Kovacic’s algorithm of classical (non)integrability as well as the standard formulation of Lax connections to show the analytic integrability of the associated dynamical configuration. We further use the notion of double null reduction and obtain the world-volume action corresponding to a torsional Newton-Cartan (TNC) D0 brane probing a 3D torsional Newton-Cartan geometry. Moreover, following Kovacic’s method, we show the classical integrability of the TNC D0 brane configuration thus obtained. Finally, considering a trivial field redefinition for the D1 brane world-volume fields, we show the equivalence between two configurations in the presence of vanishing NS fluxes.

Topological magnetotorsional effect in Weyl semimetals

In this work we introduce a thermal magnetotorsional effect (TME) as a novel topological response in magnetic Weyl semimetals. We predict that magnetization gradients perpendicular to the Weyl node separation give rise to temperature gradients depending only on the local positions of the Weyl nodes. The TME is a consequence of magnetization-induced effective torsional spacetime geometry and the finite temperature Nieh-Yan anomaly. Similarly to anomalous Hall effect and chiral anomaly, the TME has a universal material-independent form. We predict that the TME can be observed in magnetic Weyl semimetal EuCd$_2$As$_2$.

Traversable wormhole magnetic monopoles from Dymnikova metric

We study a traversable wormhole originated by a transformation over the 4D Dymnikova metric, which describes analytic black holes (BH). By using a transformation of coordinates which is adapted from the one used in the Einstein-Rosen bridge, we study a specific family of geodesics in which a test particle with non-zero electric charge induces an effective magnetic monopole, that is perceived by observers outside the wormhole. Because the Riemannian geometry cannot explain the presence of magnetic monopoles, we propose a torsional geometry in order to explore the possibility that magnetic monopoles can be geometrically induced. We obtain an expression that relates torsion and magnetic fields jointly with a Dirac-like expression for magnetic and electric charges, such that torsion makes it possible to define a fundamental length that provides a magnetic field and a spacetime discretization.

A worldsheet supersymmetric Newton-Cartan string

We construct a (locally) supersymmetric worldsheet action for a string in a non-relativistic Newton-Cartan background. We do this using a doubled string action, which describes the target space geometry in an O(D, D) covariant manner using a doubled metric and doubled vielbeins. By adopting different parametrisations of these doubled background fields, we can describe both relativistic and non-relativistic geometries. We focus on the torsional Newton-Cartan geometry which can be obtained by null duality/reduction (such null duality is particularly simple for us to implement). The doubled action we use gives the Hamiltonian form of the supersymmetric Newton-Cartan string action automatically, from which we then obtain the equivalent Lagrangian. We extract geometric quantities of interest from the worldsheet couplings and write down the supersymmetry transformations. Our general results should apply to other non-relativistic backgrounds. We comment on the usefulness of the doubled approach as a tool for studying non-relativistic string theory.

Limitations of Global Hybrids in Predicting the Geometries and Torsional Energy Barriers of Dimeric Systems and the Role of Hartree Fock and DFT Exchange.

Prediction of accurate geometries is a prerequisite for accurate prediction of molecular properties. Impact of Hartree Fock (HF) exchange (a0 ) on geometry in the framework of DFT is investigated by monitoring dihedral angles, bond length alternations, and torsional energy barriers of 10 dimeric systems against CCSD (ADZ/ATZ) benchmarks. A strong correlation is observed between the fraction of HF exchange, equilibrium dihedral angles, and the potential energy barriers in global hybrids. Full HF exchange is critical to accurately predict the nonplanarity. Lower fractions of (a0 )/larger DFT exchange (1-a0 ) results in overestimation of torsional energy barriers at 900 and underestimation at 00 . Large contributions of (1-a0 ) in global hybrid functionals tend to overestimate torsional energy barriers (900 ) and are biased toward planar geometries. However, inclusion of larger fractions of (a0 )/lower (1-a0 ) also overestimate the torsional energy barriers in syn-conformations due to the localization errors associated with HF exchange in global hybrids. Hence, irrespective of the fraction of HF/DFT exchange incorporated, global hybrids fail to accurately predict torsional energy barriers at 00 and 900 simultaneously. Long-range corrected (LC) functionals, which employ full HF exchange at longer regions, outperform global hybrid functionals in predicting geometries and torsional energy barriers of the dimeric molecules. The distance dependence of (a0 ) thus provides a balanced fraction of HF exchange as the dihedral torsion varies. Impact of range separation parameter on geometries is marginal in altering the planarity/nonplanarity. However, range separation parameter within 0.20-0.40 bohr-1 predicts more reliable torsional energies and geometries. © 2019 Wiley Periodicals, Inc.

The Generalised Complex Geometry of (p,\xa0q) Hermitian Geometries

We define (p, q) Hermitian geometry as the target space geometry of the two dimensional (p, q) supersymmetric sigma model. This includes generalised Kähler geometry for (2, 2), generalised hyperkähler geometry for (4, 2), strong Kähler with torsion geometry for (2, 1) and strong hyperkähler with torsion geometry for (4, 1). We provide a generalised complex geometry formulation of hermitian geometry, generalising Gualtieri’s formulation of the (2, 2) case. Our formulation involves a chiral version of generalised complex structure and we provide explicit formulae for the map to generalised geometry.

Gene-specific features enhance interpretation of mutational impact on acid α-glucosidase enzyme activity.

We present a computational model for predicting mutational impact on enzymatic activity of human acid α-glucosidase (GAA), an enzyme associated with Pompe disease. Using a model that combines features specific to GAA with other general evolutionary and physiochemical features, we made blind predictions of enzymatic activity relative to wildtype human GAA for >300 GAA mutants, as part of the Critical Assessment of Genome Interpretation 5 GAA challenge. We found that gene-specific features can improve the performance of existing impact prediction tools that mostly rely on general features for pathogenicity prediction. Majority of the poorly predicted mutants that lower wildtype GAA enzyme activity occurred on the surface of the GAA protein. We also found that gene-specific features were uncorrelated with existing methods and provided orthogonal information for interpreting the origin of pathogenicity, particular in variants that are poorly predicted by existing general methods. Specific variants in GAA, when investigated in the context of its protein structure, suggested gene-specific information like the disruption of local backbone torsional geometry and disruption of particular sidechain-sidechain hydrogen bonds as some potential sources for pathogenicity.

Side chain torsion dictates planarity and ionizability of green fluorescent protein’s chromophore leading to spectral perturbations

Spectral characteristics of fluorescent proteins (FPs) are well studied, and through protein engineering, several FP variants constituting entire visible spectrum have been created. One of the most common mechanisms attributed to spectral shifts in FP is excited state proton transfer (ESPT), hydroxyl moiety protonation and deprotonation, along with chromophore cis–trans isomerism. The most widely studied FPs are those derived from avGFP (Aequorea victoria GFP) and Dsred (Discosoma coral). Apart from the above mechanism, certain interacting residues are said to play a vital role in altering the proton transfer pathway leading to numerous spectral variants. Similarly, the hydrogen-bonded networks solely cannot dictate the energy landscape of FPs. Non-bonded interactions also can create secondary harmonic shifts by dipole–dipole inductions. Side chain contacts tend to alter the topological and torsional geometry, thereby disturbing the chromophore’s planarity. Side chain torsional variations have almost been unaccounted for their distortions in FPs. We hypothesize the torsional landscape and altered residual interactions as prominent factors for the spectral shifts. Through our 200 ns molecular dynamics investigation, we prospect that van der Waals packing in Dsred is more compact than that of avGFP, thus creating a low solvent occupiable environment and reduced solvent interactions having higher red spectral shift. The torsional changes of wild avGFP, S65T avGFP and Dsred have been studied to comprehend the inter-residual contact distance and the geometrical descriptors.Communicated by Ramaswamy H. Sarma