Geometric Torsion Research Articles

RETRACTED ARTICLE: Emergent D-Instanton as a Source of Dark Energy

We revisit a non-perturbative formulation leading to a vacuum created gravitational pair of (33)-brane by a Poincare dual higher form U (1) gauge theory on a D4 -brane. In particular, the analysis has revealed a dynamical geometric torsion H 3 for an on-shell Neveu-Schwarz (NS) form on a fat 4-brane. We argue that a D-instanton can be a viable candidate to incorporate the quintessence correction hidden to an emergent (3 + 1)-dimensional brane universe. It is shown that a dynamical non-perturbative correction may be realized with an axionic scalar QFT on an emergent anti 3-brane within a gravitational pair. The theoretical tool provokes thought to believe for an extra instantaneous dimension transverse to our classical brane-universe in an emergent scenario. Interestingly a D-instanton correction, sourced by an axion on an anti 3-brane, may serve as a potential candidate to explain the accelerated rate of expansion of our 3-brane universe and may provide a clue to the origin of dark energy.

The geometric torsion conjecture for abelian varieties with real multiplication

The geometric torsion conjecture asserts that the torsion part of the Mordell–Weil group of a family of abelian varieties over a complex quasi-projective curve is uniformly bounded in terms of the genus of the curve. We prove the conjecture for abelian varieties with real multiplication, uniformly in the field of multiplication. Fixing the field, we, furthermore, show that the torsion is bounded in terms of the gonality of the base curve, which is the closer analog of the arithmetic conjecture. The proof is a hybrid technique employing both the hyperbolic and algebraic geometry of the toroidal compactifications of the Hilbert modular varieties $\overline{X}(1)$ parameterizing such abelian varieties. We show that only finitely many torsion covers $\overline{X}_1 (\mathfrak{n})$ contain $d$-gonal curves outside of the boundary for any fixed $d$; the same is true for entire curves $\mathbb{C} \to \overline{X}_1 (\mathfrak{n})$. We also deduce some results about the birational geometry of Hilbert modular varieties.

Atmospheric Boundary Layer Simulation Using Wall Function Approach in OpenFoam CFD Software

The significant development in computer resources in the past years has increased the awareness of computational fluid dynamics as an alternative tool to the costly wind tunnel testing. The paper presented the application of CFD technique for a case study in simulating an existing site together with a proposed building and the local landscape. Finally, the limitations of the code analytical methods to the CFD method for wind around building analysis were discussed. From the result obtained, it was observed that the British standard (BS6399-2:1997) procedures are based on general assumptions and are not always conservative and do not provide accurate wind load results due to complex geometrical shapes, aerodynamic interaction, torsion, and load combinations as discussed in section VII.

Atmospheric Boundary Layer Simulation Using Wall Function Approach in OpenFoam CFD Software

The significant development in computer resources in the past years has increased the awareness of computational fluid dynamics as an alternative tool to the costly wind tunnel testing. The paper presented the application of CFD technique for a case study in simulating an existing site together with a proposed building and the local landscape. Finally, the limitations of the code analytical methods to the CFD method for wind around building analysis were discussed. From the result obtained, it was observed that the British standard (BS6399-2:1997) procedures are based on general assumptions and are not always conservative and do not provide accurate wind load results due to complex geometrical shapes, aerodynamic interaction, torsion, and load combinations as discussed in section VII.

Rationalisation of the geometry for production of the 80-m glazed Sphere for the Expo 2017 in Astana

The emblematic entrance pavilion for the Expo 2017 in Astana is the so-called ‘Sphere’, which with its 80-m diameter is worldwide the largest closed sphere completely covered with glass. The continuous external surface of the Sphere was designed to be built with spherically curved glass panels of parallelogramic shape. The panels are fixed at their perimeter to a structural grid of bent round tubes of steel. This secondary grid is fixed in turn to a coarser primary structural grid at evenly spaced supports. The purpose of this article is to give insight into the constructive geometry design of the Sphere. One of the main targets of ‘geometric design for production’ is to specify the geometry of a construction in such a way that fabrication and installation procedures can be simplified and carried out with a minimum of effort, cost and time. The main measure for the Sphere was to simplify the basic grid by replacing all original three-dimensional free-form curves with series of interconnected circular arcs. Thus, a typical curved tubular segment could be bent on the plane with a constant radius. A further approach to get a simple and sound construction eliminating geometric torsion and minimising eccentricities among construction subsystems, for example, glazing, sealing, fixings and substructure, was the extensive usage of conical systems inherent in the geometry of the sphere for orienting and positioning the various subsystems components. These two geometric simplification measures were determinant for the practical and economic implementation of the construction, fabrication and installation of the Sphere.

Geometric Torsion in Adolescent Idiopathic Scoliosis: A New Method to Differentiate Between Lenke 1 Subtypes.

Consecutive case series. To study geometric torsion in thoracic adolescent idiopathic scoliosis (AIS) to propose it as a numerical three-dimensional (3D) parameter that quantifies the scoliosis deformity. AIS is a 3D deformity of the spine. The most widely accepted and used classification systems, however, still rely on two-dimensional aspects of x-rays. Yet, a 3D classification of AIS remains elusive because there is no widely accepted 3D parameter in the clinical practice. Analysis of 141 patients with Lenke type-1 deformity recruited in our institution. The Lenke classification was identified by two observers and 3D reconstructions were obtained using biplanar radiographs. Geometric torsion measuring the twisting effect of the spine was computed using a novel technique by approximating local arc lengths at the neutral vertebra in the thoracolumbar segment. An inter- and intragroup statistical analysis was performed to evaluate the torsion index, and how it relates to other 3D indices. A statistically significant increase in torsion was observed between Lenke 1A (1.15 mm) and Lenke 1C (2.10 mm) subgroups. No differences were found between the Lenke 1B (1.75 mm) subgroup with either of the other two subgroups. An automatic classification based on torsion indices identified two groups: one with high torsion values (3.02 mm) and one with low torsion values (0.82 mm). Statistically significant differences were found between the main thoracic planes of maximum curvature (PMC) orientation of the high-torsion group (73.72°) and the low-torsion group (79.85°). Statistically significant differences were also found for the thoracolumbar/lumbar PMC orientation between the high-torsion group (56.41°) and the low-torsion group (49.25°). These results suggest that a numerical method of describing scoliosis in 3D is within reach. They also suggest the existence of two subgroups of 3D deformations based on torsion values (high and low) with links to PMC orientation. 4.

Physically based real-time interactive assembly simulation of cable harness

In this paper, we designed and developed an interactive assembly simulation system of cable harness. First, we establish a real-time physical model of cable harness based on an extension of the mass–spring model. We use various kinds of springs to describe the different properties of the cable harness: linear springs for stretching, bending springs for bending, and torsion springs for geometrical torsion and material twisting. The constraints of connectors and clips on cable harness are both considered. We also associate the elastic coefficients of various springs with the material parameters of the cable. Moreover, we use spherical bounding volume hierarchy and triangular facets for collision detection of cable harness during the assembly simulation. By applying contact forces to both ends of the cable links that collide with the surrounding environment, we obtain the real-time contact response of cable harness. Finally, we apply the proposed model to a cable assembly task. The results show that the proposed model successfully expressed the deformation of the cable harness and the interactive manipulation is computationally efficient.

Using sequence signatures and kink-turn motifs in knowledge-based statistical potentials for RNA structure prediction

Kink turns are widely occurring motifs in RNA, located in internal loops and associated with many biological functions including translation, regulation and splicing. The associated sequence pattern, a 3-nt bulge and G-A, A-G base-pairs, generates an angle of ∼50° along the helical axis due to A-minor interactions. The conserved sequence and distinct secondary structures of kink-turns (k-turn) suggest computational folding rules to predict k-turn-like topologies from sequence. Here, we annotate observed k-turn motifs within a non-redundant RNA dataset based on sequence signatures and geometrical features, analyze bending and torsion angles, and determine distinct knowledge-based potentials with and without k-turn motifs. We apply these scoring potentials to our RAGTOP (RNA-As-Graph-Topologies) graph sampling protocol to construct and sample coarse-grained graph representations of RNAs from a given secondary structure. We present graph-sampling results for 35 RNAs, including 12 k-turn and 23 non k-turn internal loops, and compare the results to solved structures and to RAGTOP results without special k-turn potentials. Significant improvements are observed with the updated scoring potentials compared to the k-turn-free potentials. Because k-turns represent a classic example of sequence/structure motif, our study suggests that other such motifs with sequence signatures and unique geometrical features can similarly be utilized for RNA structure prediction and design.

Geometric Torsion in Adolescent Idiopathic Scoliosis: A Surgical Outcomes Study of Lenke Type 1 Patients.

Consecutive case series analysis. To evaluate the surgical outcomes of patients with thoracic adolescent idiopathic scoliosis (AIS) in relation to different degrees of geometric torsion. AIS is a three-dimensional (3D) deformity of the spine. A 3D classification of AIS, however, remains elusive because there is no widely accepted 3D parameter in the clinical practice. Recently, a new method of estimating geometric torsion has been proposed and detected two potential new 3D subgroups based on geometric torsion values. This is an analysis of 93 patients with Lenke type-1 deformity from our institution. 3D reconstructions were obtained using biplanar radiographs both pre- and postoperatively. Geometric torsion was computed using a novel technique by approximating local arc lengths at the neutral vertebra in the thoracolumbar segment. An inter- and intragroup statistical analysis was performed to compare clinical indices of patients with different torsion values. A qualitative assessment was also performed on each patient by two senior staff surgeons. Statistically significant differences were observed in clinical indices between high (2.85 mm) and low torsion (0.83 mm) Lenke type 1 subgroups. Preoperatively, the high torsion group showed higher Cobb angle values in the thoracic segment (71.18° vs. 63.74°), as well as higher angulation in the thoracolumbar plane of maximum deformity (67.79° vs. 53.30°). Postoperatively, a statistically significant difference was found in the orientation of the plane of maximum deformity in the thoracolumbar segment between the high and low torsion groups (47.95° vs. 30.03°). Results from the qualitative evaluation of surgical results showed different results between the two staff surgeons. These results suggest a link between preoperative torsion values and surgical outcomes within Lenke type 1 deformities. These results will need to be validated by an independent group, as it is a single-center study. 4.

Uniform bounds for the number of rational points on curves of small Mordell–Weil rank

Let X be a curve of genus g≥2 over a number field F of degree d=[F:Q]. The conjectural existence of a uniform bound N(g,d) on the number #X(F) of F-rational points of X is an outstanding open problem in arithmetic geometry, known by the work of Caporaso, Harris, and Mazur to follow from the Bombieri–Lang conjecture. A related conjecture posits the existence of a uniform bound Ntors,†(g,d) on the number of geometric torsion points of the Jacobian J of X which lie on the image of X under an Abel–Jacobi map. For fixed X, the finiteness of this quantity is the Manin–Mumford conjecture, which was proved by Raynaud. We give an explicit uniform bound on #X(F) when X has Mordell–Weil rank r≤g−3. This generalizes recent work of Stoll on uniform bounds for hyperelliptic curves of small rank to arbitrary curves. Using the same techniques, we give an explicit, unconditional uniform bound on the number of F-rational torsion points of J lying on the image of X under an Abel–Jacobi map. We also give an explicit uniform bound on the number of geometric torsion points of J lying on X when the reduction type of X is highly degenerate. Our methods combine Chabauty–Coleman’s p-adic integration, non-Archimedean potential theory on Berkovich curves, and the theory of linear systems and divisors on metric graphs.

ENGLISH

We obtain axionic charged primordial black holes on a vacuum created gravitational pair of (3¯ by the Kalb-Ramond field on a D4-brane in presence of a background open string metric. The new geometries on an emergent pair of (3¯ universe is shown to be influenced by the non-perturbative quantum effects underlying a geometric torsion in a second order formalism. The presence of small extra dimensions transverse to the pair in the formalism ensures dynamical � ¯

Kinetic pathway for interfacial electron transfer from a semiconductor to a molecule.

Molecular approaches to solar-energy conversion require a kinetic optimization of light-induced electron-transfer reactions. At molecular-semiconductor interfaces, this optimization has previously been accomplished through control of the distance between the semiconductor donor and the molecular acceptor and/or the free energy that accompanies electron transfer. Here we show that a kinetic pathway for electron transfer from a semiconductor to a molecular acceptor also exists and provides an alternative method for the control of interfacial kinetics. The pathway was identified by the rational design of molecules in which the distance and the driving force were held near parity and only the geometric torsion about a xylyl- or phenylthiophene bridge was varied. Electronic coupling through the phenyl bridge was a factor of ten greater than that through the xylyl bridge. Comparative studies revealed a significant bridge dependence for electron transfer that could not be rationalized by a change in distance or driving force. Instead, the data indicate an interfacial electron-transfer pathway that utilizes the aromatic bridge orbitals.

State of the art of current 3-D scoliosis classifications: a systematic review from a clinical perspective.

Scoliosis is a complex three dimensional (3D) deformity: the current lack of a 3D classification could hide something fundamental for scoliosis prognosis and treatment. A clear picture of the actually existing 3D classifications lacks. The aim of this systematic review was to identify all the 3D classification systems proposed until now in the literature with the aim to identify similarities and differences mainly in a clinical perspective.After a MEDLINE Data Base review, done in November 2013 using the search terms “Scoliosis/classification” [Mesh] and “scoliosis/classification and Imaging, three dimensional” [Mesh], 8 papers were included with a total of 1164 scoliosis patients, 23 hyperkyphosis and 25 controls, aged between 8 and 20 years, with curves from 10° to 81° Cobb, and various curve patterns. Six studies looked at the whole 3D spine and found classificatory parameters according to planes, angles and rotations, including: Plane of Maximal Curvature (PMC), Best Fit Plane, Cobb angles in bodily plane and PMC, Axial rotation of the apical vertebra and of the PMC, and geometric 3D torsion. Two studies used the regional (spinal) Top View of the spine and found classificatory parameters according to its geometrical properties (area, direction and barycenter) including: Ratio of the frontal and the sagittal size, Phase, Directions (total, thoracic and lumbar), and Shift. It was possible to find similarities among 10 out of the 16 the sub-groups identified by different authors with different methods in different populations.In summation, the state of the art of 3D classification systems include 8 studies which showed some comparability, even though of low level. The most useful one in clinical everyday practice, is far from being defined. More than 20 years passed since the definition of the third dimension of the scoliosis deformity, now the time has come for clinicians and bioengineers to start some real clinical application, and develop means to make this approach an everyday tool.

The energy of naturally curved elastic rods with an application to the stretching and contraction of a free helical spring as a model for DNA.

We give a contemporary and direct derivation of a classical, but insufficiently familiar, result in the theory of linear elasticity-a representation for the energy of a stressed elastic rod with central axis that intrinsically takes the shape of a general space curve. We show that the geometric torsion of the space curve, while playing a crucial role in the bending energy, is physically unrelated to the elastic twist. We prove that the twist energy vanishes in the lowest-energy states of a rod subject to constraints that do not restrict the twist. The stretching and contraction energies of a free helical spring are computed. There are local high-energy minima. We show the possibility of using the spring to model the chirality of DNA. We then compare our results with an available atomic level energy simulation that was performed on DNA unconstrained in the same sense as the free spring. We find some possible reflections of springlike behavior in the mechanics of DNA, but, unsurprisingly, the base pairs lend a material substance to the core of DNA that a spring does not capture.

Quintessence and effective AdS brane geometries

A geometric torsion dynamics leading to an effective curvature in a second-order formalism on a D4-brane is revisited with a renewed interest. We obtain two effective AdS 4 brane geometries on a vacuum created pair of [Formula: see text]-brane. One of them is shown to describe an AdS Schwarzschild spinning black hole and the other is shown to describe a spinning black hole bound state. It is argued that a D-instanton in a vacuum created anti-D3-brane within a pair may describe a quintessence. It may seem to incorporate a varying vacuum energy density in a brane universe. We consider the effective curvature scalar on S1 × S1 to analyze torsionless geometries on a vacuum created pair of [Formula: see text]-brane. The emergent AdS 3 brane is shown to describe a Schwarzschild and a Reissner–Nordstrom (RN) geometries in the presence of extra dimension(s).

Fundamental groups of clique complexes of random graphs

We study fundamental groups of clique complexes associated to random graphs. We establish thresholds for their cohomological and geometric dimension and torsion. We also show that in certain regime any aspherical subcomplex of a random clique complex satisfies the Whitehead conjecture, i.e. all irs subcomplexes are also aspherical.

Schroth treatment results in AIS at high risk for surgery - 2 case studies

Scoliosis is a 3D deformity of the spine combined with pathological structural changes. Scoliosis tend to progress through growth. BSPTS method based on Schroth principles is a specific physiotherapeutic treatment method for scoliosis. It considers the 3d changes of the spine, the geometrical and axial torsion of the hole spine, thorax and pelvic. Using specific exercise to achieve better muscle balance and corrected posture in order to prevent progression, improve esthetic and function.

Effect of geometrical torsion on the rectification properties of diblock conjugated molecular diodes

We model several Au/conjugated molecule/Au junctions in the presence of molecular geometrical torsions. A rectification ratio of around 10 in the twisty diphenyldipyrimidinyl system is obtained, which is in good agreement with experiment. Deeper insight into the rectification mechanism of the conjugated molecular diodes is presented on the basis of simulations in a set of simpler but similar junctions. The rectification effect (the ratio) is significantly improved with increasing the molecular twist, while the conductance is reduced accordingly. Our results suggest that the rectification can be enhanced by the geometrical-torsion-induced reduction in the conjugation length of organic molecules.

Interactive operation of physically-based slender flexible parts in an augmented reality environment

In order to deal with the problems of laying and assembly planning of slender flexible parts in electromechanical products, a novel approach to operate the physically-based slender flexible parts in an augmented reality environment is presented in this paper. A discrete dynamic method is used to efficiently build the physical model of slender flexible parts, which is very well suited for interactive operation in the augmented reality environment. In this model, bending penalty force can be calculated by the bending energy function to improve dynamic bending behavior, and a penalty method is used to simplify the calculation of geometric torsion. With a reasonable construction of augmented reality environment, a real-time interactive algorithm based on the operating panel is proposed to enable users to interact with the virtual slender flexible parts in the mixed reality-based scene. A case study in the augmented reality environment shows that the proposed approach is efficient and feasible.

THE EFFECT OF THE PRESSURE DISTRIBUTION CHARACTERISTICS OF PLATA SURFACE ON THE FLUTTER DERIVATIVES AND VIBRATION FORM

The aerodynamic derivatives were expressed by the fluctuation pressure on the plate surface through rational simplification. The influence of fluctuation pressure distribution characteristics on the aerodynamic derivatives was studied by using of numerical simulation method based on the fluid-solid loosely coupled calculation strategy and existing fluid software user defined function (UDF). The influence of aerodynamic derivatives on the model vibration and aerodynamic coupling phenomenon were explained at micro level. The study shows that aerodynamic coupling flutter derivative which produced different action on the flutter depended on the model surface fluctuating pressure distribution. So the main factor of model flutter was determined by the fluctuating pressure distribution. The main component of fluctuation pressure was drifted to the model windward side in the flutter critical state, which caused the center of torsional vibration move forward and not coincide with the geometric torsion level.