Curvature Properties Research Articles

SARS-CoV fusion peptides induce membrane surface ordering and curvature

Viral membrane fusion is an orchestrated process triggered by membrane-anchored viral fusion glycoproteins. The S2 subunit of the spike glycoprotein from severe acute respiratory syndrome (SARS) coronavirus (CoV) contains internal domains called fusion peptides (FP) that play essential roles in virus entry. Although membrane fusion has been broadly studied, there are still major gaps in the molecular details of lipid rearrangements in the bilayer during fusion peptide-membrane interactions. Here we employed differential scanning calorimetry (DSC) and electron spin resonance (ESR) to gather information on the membrane fusion mechanism promoted by two putative SARS FPs. DSC data showed the peptides strongly perturb the structural integrity of anionic vesicles and support the hypothesis that the peptides generate opposing curvature stresses on phosphatidylethanolamine membranes. ESR showed that both FPs increase lipid packing and head group ordering as well as reduce the intramembrane water content for anionic membranes. Therefore, bending moment in the bilayer could be generated, promoting negative curvature. The significance of the ordering effect, membrane dehydration, changes in the curvature properties and the possible role of negatively charged phospholipids in helping to overcome the high kinetic barrier involved in the different stages of the SARS-CoV-mediated membrane fusion are discussed.

Surface pencils in Euclidean 4-space 𝔼4

In this paper, we study the problem of constructing a family of surfaces (surface pencils) from a given curve in [Formula: see text]-dimensional Euclidean space [Formula: see text]. We have shown that the generalized rotation surfaces in [Formula: see text] are the special type of surface pencils. Further, the curvature properties of these surfaces are investigated. Finally, we give some examples of flat surface pencils in [Formula: see text].

On Lorentzian Ricci solitons on nilpotent Lie groups

The aim of this article is to exhibit the variety of different Ricci soliton structures that a nilpotent Lie group can support when one allows for the metric tensor to be Lorentzian. In stark contrast to the Riemannian case, we show that a nilpotent Lie group can support a number of non-isometric Lorentzian Ricci soliton structures with decidedly different qualitative behaviors and that Lorentzian Ricci solitons need not be algebraic Ricci solitons. The analysis is carried out by classifying all left invariant Lorentzian metrics on the connected, simply-connected five-dimensional Lie group having a Lie algebra with basis vectors E1,E2,E3,E4 and E5 and non-trivial bracket relations E1,E5=E3 and E2,E5=E4, investigating the various curvature properties of the resulting families of metrics, and classifying all Lorentzian Ricci soliton structures.

Implications on the cosmic coincidence by a dynamical extrinsic curvature

In this work, we apply the smooth deformation concept in order to obtain a modification of Friedmann’s equations. It is shown that the cosmic coincidence can be at least alleviated using the dynamical properties of the extrinsic curvature. We investigate the transition from nucleosynthesis to the coincidence era obtaining a very small variation of the ratio that compares the matter energy density to extrinsic energy density, compatible with the known behavior of the deceleration parameter. We also show that the calculated ‘equivalence’ redshift matches the transition redshift from a deceleration to accelerated phase and the coincidence ceases to be. The dynamics on r is also studied based on Hubble parameter observations as the latest Baryons Acoustic Oscillations/Cosmic Microwave Background Radiation (BAO/CMBR) + SNIa.

Curvature properties of metric nilpotent Lie algebras which are independent of metric

This paper consists of two parts. First, motivated by classic results, we determine the subsets of a given nilpotent Lie algebra \(\mathfrak {g}\) (respectively, of the Grassmannian of two-planes of \(\mathfrak {g}\)) whose sign of Ricci (respectively, sectional) curvature remains unchanged for an arbitrary choice of a positive definite inner product on \(\mathfrak {g}\). In the second part we study the subsets of \(\mathfrak {g}\) which are, for some inner product, the eigenvectors of the Ricci operator with the maximal and with the minimal eigenvalue, respectively. We show that the closure of these subsets is the whole algebra \(\mathfrak {g}\), apart from two exceptional cases: when \(\mathfrak {g}\) is two-step nilpotent and when \(\mathfrak {g}\) contains a codimension one abelian ideal.

On curvature properties of Som–Raychaudhuri spacetime

Som–Raychaudhuri (Proc R Soc Lond A 304:81–86, 1968) spacetime is a stationary cylindrical symmetric solution of Einstein field equation corresponding to a charged dust distribution in rigid rotation. The main object of the present paper is to investigate the curvature restricted geometric structures admitting by the Som–Raychaudhuri spacetime and it is shown that such a spacetime is a 2-quasi-Einstein, generalized Roter type, Ein(3) manifold satisfying \(R\cdot R = Q(S,R)\), \(C\cdot C = \frac{2a^2}{3} Q(g,C)\), and its Ricci tensor is cyclic parallel and Riemann compatible. Finally, we make a comparison between Godel spacetime and Som–Raychaudhuri spacetime.

Properties of the Riemannian Curvature of (α, β)-Metrics

In this paper, we discuss some important properties of the Riemannian curvature of (α, β)-metrics. When the dimension of the manifold is greater than 2, we classify Randers metrics of weakly isotropic flag curvature (that is, Randers metrics of scalar flag curvature with isotropic S-curvature). Further, we characterize (α, β)-metrics of scalar flag curvature with isotropic S-curvature. We also characterize Einstein (α, β)-metrics and determine completely the local structure of Ricci-flat Douglas (α, β)-metrics when the dimension dim M ≥ 3.

The effect of surface nano-corrugation on the squeeze-out of molecular thin hydrocarbon films between curved surfaces with long range elasticity

The properties of linear alkane lubricants confined between two approaching solids are investigated by a model that accounts for the roughness, curvature and elastic properties of the solid surfaces. We consider linear alkanes of different chain lengths from to , confined between corrugated solid walls. The pressure necessary to squeeze out the lubricant increases rapidly with the alkane chain length, but is always much lower than in the case of smooth surfaces. The longest alkanes form domains of ordered chains and the squeeze-out appears to nucleate in the more disordered regions between these domains. The short alkanes stay fluid-like during the entire squeeze out process which result in a very small squeeze-out pressure which is almost constant during the squeeze-out of the last monolayer of the fluid. In all cases we observe lubricant trapped in the valley of the surface roughness, which cannot be removed independent of the magnitude of the squeezing pressures.

The Phospholipase D2 Knock Out Mouse Has Ectopic Purkinje Cells and Suffers from Early Adult-Onset Anosmia.

Phospholipase D2 (PLD2) is an enzyme that produces phosphatidic acid (PA), a lipid messenger molecule involved in a number of cellular events including, through its membrane curvature properties, endocytosis. The PLD2 knock out (PLD2KO) mouse has been previously reported to be protected from insult in a model of Alzheimer's disease. We have further analysed a PLD2KO mouse using mass spectrophotometry of its lipids and found significant differences in PA species throughout its brain. We have examined the expression pattern of PLD2 which allowed us to define which region of the brain to analyse for defect, notably PLD2 was not detected in glial-rich regions. The expression pattern lead us to specifically examine the mitral cells of olfactory bulbs, the Cornus Amonis (CA) regions of the hippocampus and the Purkinje cells of the cerebellum. We find that the change to longer PA species correlates with subtle architectural defect in the cerebellum, exemplified by ectopic Purkinje cells and an adult-onset deficit of olfaction. These observations draw parallels to defects in the reelin heterozygote as well as the effect of high fat diet on olfaction.

Single Tree Stem Profile Detection Using Terrestrial Laser Scanner Data, Flatness Saliency Features and Curvature Properties

A method for automatic stem detection and stem profile estimation based on terrestrial laser scanning (TLS) was validated. The root-mean-square error was approximately 1 cm for stem diameter estimations. The method contains a new way of extracting the flatness saliency feature using the centroid of a subset of a point cloud within a voxel cell that approximates the point by point calculations. The loss of accuracy is outweighed by a much higher computational speed, making it possible to cover large datasets. The algorithm introduces a new way to connect surface patches belonging to a stem and investigates if they belong to curved surfaces. Thereby, cylindrical objects, like stems, are found in the pre-filtering stage. The algorithm uses a new cylinder fitting method that estimates the axis direction by transforming the TLS points into a radial-angular coordinate system and evaluates the deviations by a moving window convex hull algorithm. Once the axis direction is found, the cylinder center is chosen as the position with the smallest radial deviations. The cylinder fitting method works on a point cloud in both the single-scan setup, as well as a multiple scan setup of a TLS system.

Modeling of FRP-strengthened curved masonry specimens and proposal of a simple design formula

The present paper aims at developing a simple but effective numerical model for the study of the bond behavior of Fiber Reinforced Strengthening systems (FRP) externally applied on curved masonry substrates. The main peculiarities of the proposed model are its simplicity and the possibility to straightforwardly introduce at the interface level coupled cohesive laws for accounting a mixed mode debonding mechanism. Indeed, the model relies on a discretization based on in-series and in-parallel springs for modeling the substrate, the reinforcement and the reinforcement/substrate interface layer. In particular, while both the substrate and the reinforcement springs are assumed linear-elastic, nonlinear constitutive laws are accounted for the interface springs where, in addition, a coupled behavior between normal and shear springs is assumed considering the Mohr-Coulomb failure domain. The proposed numerical model is used in the paper as a tool for the assessment of formulas specifically devoted to the evaluation of the bond resistance of curved masonry samples strengthened with FRPs. In particular, both formulas derived from the closed form solution of equilibrium equations and a formula derived by approximating the closed form solution through an exponential law are here presented. With the main purpose to validate the proposed model, numerical analyses are preliminary presented in the paper with reference to experimental bond tests on masonry samples with concave and convex substrate configurations strengthened by glass FRP strips. Then, further numerical analyses developed by considering different values of the geometry curvature and mechanical properties of the interface, are subsequently developed with the main goal to check the reliability of the proposed formulas.

An estimate of spherical impactor energy transfer for mechanical frequency up-conversion energy harvester

Vibration energy harvesters, which use the impact mechanical frequency up-conversion technique, utilize an impactor, which gains kinetic energy from low frequency ambient environmental vibrations, to excite high frequency systems that efficiently convert mechanical energy to electrical energy. To take full advantage of the impact mechanical frequency up-conversion technique, it is prudent to understand the energy transfer from the low frequency excitations, to the impactor, and finally to the high frequency systems. In this work, the energy transfer from a spherical impactor to a multi degree of freedom spring / mass system, due to Hertzian impact, is investigated to gain insight on how best to design impact mechanical frequency up-conversion energy harvesters. Through this academic work, it is shown that the properties of the contact (or impact) area, i.e., radius of curvature and material properties, only play a minor role in energy transfer and that the equivalent mass of the target system (i.e., the spring / mass system) dictates the total amount of energy transferred during the impact. The novel approach of utilizing the well-known Hertzian impact methodology to gain an understanding of impact mechanical frequency up-conversion energy harvesters has made it clear that the impactor and the high frequency energy generating systems must be designed together as one system to ensure maximum energy transfer, leading to efficient ambient vibration energy harvesters.

Continuous-Curvature Path Planning With Obstacle Avoidance Using Four Parameter Logistic Curves

Continuous-curvature path planning with obstacle avoidance is considered. Two path shapes, namely, S and half-S shapes derived from four parameter logistic curves are proposed as solution paths. Closed-form analytic conditions are derived for avoiding rectangular and circular obstacles. Using the zero end curvature property of the proposed paths, a complete path planner is presented joining the individual paths. An analytic bound on the maximum curvature of the paths is derived. A comparison is carried out with existing smooth path planning methodologies based on number of design parameters, complexity in obstacle avoidance, and nature of computations involved. The work highlights the use of logistic curves as a novel, analytically feasible, and applicable path planning methodology.

Planning Collision-Free Trajectories for Reversing Multiply-Articulated Vehicles

A global path-planning strategy is proposed which defines the geometric path of the rear trailer axle of a multiply-articulated vehicle traveling in reverse. This is intended for use in conjunction with a path-tracking reversing controller. A general multiple-trailer vehicle model is derived and used to model a “B-double” heavy vehicle combination, which has two trailers. The curvature properties of a path for the rear trailer axle are investigated, and an empirical relationship is defined between the curvature and the length over which the curvature changes. This is used to generate a library of feasible path segments, and the vehicle model is used to calculate swept paths. A Dijkstra grid search algorithm is then used to connect the path segments together to generate a collision-free composite path. An example path generation is presented for the B-double.

Improved Hessian Curvature for Fingerprint Analysis

Curvature analysis is important to the fingerprint image which is constructed by a group of regular ridgelines. Five kinds of curvatures constructed by the eigenvalues are tested, including the Gaussian curvature, Mean curvature, Laplacian curvature, Hessian curvature and our improved Hessian curvature. Researching on these five kinds of curvature, we find the relative advantages of our improved Hessian curvature for fingerprint curves. A measure for fingerprint reference point determination based on the eigenvalues of the covariance matrix of the ridges. Fingerprint reference points are determined by combining the global and local proposed curvature properties of ridges by using multi-resolution levels. The performance of the proposed one is verified through simulations and its analysis.

Finsler metrics with special Riemannian curvature properties

The Weyl curvature is one of the fundamental quantities in Finsler geometry because it is a projective invariant. By determining the Weyl curvature of a class of Finsler metrics, we find a lot of Finsler metrics of quadratic Weyl curvature which are non-trivial in the sense that they are not of quadratic Riemann curvature.

Some Curvature Properties in LP-Sasakian Manifolds with Respect to Generalized Tanaka Webster Okumura Connection

The object of the present paper is to study LP-Sasakian manifolds with respect to generalized Tanaka Webster Okumura connection. We have studied locally ?-symmetric as well as locally projectively ?-symmetric LP-Sasakian manifolds with respect to a generalized Tanaka Webster Okumura connection. Locally ?-recurrent LP-Sasakian manifolds have also been studied with respect to generalized Tanaka Webster Okumura connection.GANIT J. Bangladesh Math. Soc.Vol. 34 (2014) 47-55

Analysis of cornea curvature using radial basis functions – Part II: Fitting to data-set

In part I we discussed the solution of corneal curvature using a 2D meshless method based on radial basis functions (RBFs). In Part II we use these methods to fit a full nonlinear thin membrane model to a measured data-set in order to generate a topological mathematical description of the cornea. In addition, we show how these results can lead to estimations for corneal radius of curvature and certain physical properties of the cornea; namely, tension and elasticity coefficient. Again all calculations and graphics generation were performed using the R language programming environment.The model describes corneal topology extremely well, and the estimated properties fall well within the expected range of values. The method is straight forward to implement and offers scope for further analysis using more detailed 3D models that include corneal thickness.

On the Weil–Petersson Curvature of the Moduli Space of Riemann Surfaces of Large Genus

Let $S_g$ be a closed surface of genus $g$ and $\mathbb{M}_g$ be the moduli space of $S_g$ endowed with the Weil-Petersson metric. In this paper we investigate the Weil-Petersson curvatures of $\mathbb{M}_g$ for large genus $g$. First, we study the asymptotic behavior of the extremal Weil-Petersson holomorphic sectional curvatures at certain thick surfaces in $\mathbb{M}_g$ as $g \to \infty$. Then we prove two curvature properties on the whole space $\mathbb{M}_g$ as $g\to \infty$ in a probabilistic way.

Spherical gravitational curvature boundary-value problem

Values of scalar, vector and second-order tensor parameters of the Earth’s gravitational field have been collected by various sensors in geodesy and geophysics. Such observables have been widely exploited in different parametrization methods for the gravitational field modelling. Moreover, theoretical aspects of these quantities have extensively been studied and well understood. On the other hand, new sensors for observing gravitational curvatures, i.e., components of the third-order gravitational tensor, are currently under development. As the gravitational curvatures represent new types of observables, their exploitation for modelling of the Earth’s gravitational field is a subject of this study. Firstly, the gravitational curvature tensor is decomposed into six parts which are expanded in terms of third-order tensor spherical harmonics. Secondly, gravitational curvature boundary-value problems defined for four combinations of the gravitational curvatures are formulated and solved in spectral and spatial domains. Thirdly, properties of the corresponding sub-integral kernels are investigated. The presented mathematical formulations reveal some important properties of the gravitational curvatures and extend the so-called Meissl scheme, i.e., an important theoretical framework that relates various parameters of the Earth’s gravitational field.