Foliation Structure Research Articles

On the Upper Maastrichtian Oysters of the Genus Rhynchostreon Bayle (Bivalvia, Gryphaeidae) from the Mountainous Crimea

The morphology and shell microstructure of smooth exogyrid oysters from the Upper Maastrichtian of the Mountainous Crimea (SW Russia) are studied. Their shell microstructure consists of a simple regularly foliated, irregular crossed foliated, and transitional irregular simple prismatic/irregular complex crossed foliated structures. The latter has been only identified in oysters of the genus Rhynchostreon Bayle. Along with specific shell morphology, it allows to attribute the studied oysters to the species Rhynchostreon aralensis (Arkhangelsky, 1912). The occurrence of the genus Rhynchostreon in the Upper Maastrichtian of the Mountainous Crimea allows to clarify its stratigraphic distribution.

Adequate mathematical modelling by wide-sense robust control design in a thrust-vectored flight dynamics problem

The conflict between the accuracy and the complexity of the adequate mathematical modelling approximations of physical phenomena is discussed. The need of finding certain types of topological equivalency between nonlinear mathematical models as the keystone to successful study is emphasized. We formulate the control problem when the controlling functions cannot directly act on the phase variables defining a given terminal manifold as a control aim through the right-hand sides of differential equations describing a mathematical model under study. The idea of creating a hierarchical cascade of controlling attractors–mediators is introduced. It is shown how the method of the goal-oriented formation of the local topological structure of one-codimensional foliations as the basis of Poincare’s-strategy-based backstepping method can be successfully used for designing terminal control. One brings up the problem of developing the tools intended for the creation of the topologically equivalent and quantitative–deviation–tolerable simplifications of the complex original mathematical models suitable for the synthesis of the control laws that are supposed to be applied to the latter ones. The two-dimensional example is analytically investigated to explain the procedure of constructing the cascade of controlling one-codimensional attractor mediators. The essentially nonlinear five-dimensional mathematical model of the longitudinal flight dynamics of a thrust-vectored aircraft in a wing-body coordinate system with two controls, namely, the angular deflections of a movable horizontal stabilizer and a turbojet engine nozzle, is investigated. The core of the designed wide-sense robust and stable in the large-tracking control algorithm is a hierarchical cascade of controlling attractor–mediators consisting of the two one-codimensional manifolds. The results of the computer simulation are presented. The topicality in creating the general theory of nonlinear mathematical modelling, as the tools to construct and manipulate the sets of topologically equivalent models being qualitative–quantitative adequate to corresponding physical phenomena, is pointed up in conclusion.

Vertical–horizontal decomposition of Laplacians and cohomologies of manifolds with trivial tangent bundles

In this paper, we obtain a vertical–horizontal decomposition formula of Laplacians on manifolds with a special foliation structure. Two Nomizu-type theorems for cohomologies of nilmanifolds follow as applications.

Laser-Shock-Induced Nanoscale Kink-Bands in WSe2 2D Crystals.

The response of materials to high stress and strain rates in nature has been a long-term scientific interest. The formation of kinks is a common deformation feature under high pressure and strain rates among foliated structures, such as rock-forming minerals. Although deformation of foliated rock layers in geology has been investigated for a century, the deformation behavior of their nanoscale counterparts, such as two-dimensional (2D) layered materials, under high stress and strain rates has not been investigated. 2D transition metal dichalcogenides have very strong in-plane rigidity, whereas the interlayer shear modulus is 3 orders of magnitude lower than their in-plane Young's modulus. Here, we study the structure and property changes in multilayer WSe2 2D layers during a 3D nanoshaping process where laser-shock pressure at the GPa level is applied to imprint the 2D multilayers into a designed nanomold, forming a large local bending strain of 5-6%. The microstructure of the 2D multilayers after laser shock is observed to be a nanoscale kink-band, similar to that of strained geological layered crystals, due to the high-pressure-induced bending and shearing. The deformed kink-band structure is investigated experimentally by high-resolution transmission electron microscopy and atomic force microscopy and validated by molecular dynamics simulations. The changes in the resulting electronic band structure are investigated by first-principles calculations. The laser-shock straining technology to induce kink-band structures can enrich the understanding and facilitate the applications of many 2D materials.

Nonlinear mechanics of accretion

We formulate a geometric nonlinear theory of the mechanics of accretion. In this theory, the material manifold of an accreting body is represented by a time-dependent Riemannian manifold with a time-independent metric that at each point depends on the state of deformation at that point at its time of attachment to the body, and on the way the new material is added to the body. We study the incompatibilities induced by accretion through the analysis of the material metric and its curvature in relation to the foliated structure of the accreted body. Balance laws are discussed and the initial boundary value problem of accretion is formulated. The particular cases where the growth surface is either fixed or traction-free are studied and some analytical results are provided. We numerically solve several accretion problems and calculate the residual stresses in nonlinear elastic bodies induced from accretion.

Petrography, Geology Structure and Landslide Characterization of Sumatra Fault Deformation: Study Case In Km 10-15 Highway, Koto Baru Sub District, West of Sumatra

Research area is around Tanjung Balik, Koto Baru Sub Base, Lima Puluh Kota District, West Sumatra Province. Located along the highway Km 10-15 Riau – West Sumatra and the coordinate around 00˚08'40 '' LU - 0˚11'20 '' N and 100˚45'20 '' BT - 100˚47'00 '' BT. The purpose of research to identify petrography, microstructure, types of landslides and the geological condition. The methods using polarization microscope, stereography, landslide identification survey and geological mapping. The result of study shows the petrography analysis of lithology of study area are classified into three types of rocks are Feldspathic Greywacke, Lithic Arenite, and Slate. Microstructures trending system show the foliation structure that is relatively Southeast-Northwest. Types of landslide which dominates in the research area are debris avalanche and translational landslide. Geological analysis show some of rock units are classified into two units: Sandstone Unit and Slate Unit. Sandstone Unit spread in the northern part of the study area, while Slate Unit spread in the southern part of the study area. The characteristics of these rocks showed Pematang Formation.

On Foliations with Semi-positive Anti-canonical Bundle

In this note, we describe the structure of regular foliations with semi-positive anti-canonical bundle on smooth projective varieties.

Information Geometry of Randomized Quantum State Tomography.

Suppose that a d-dimensional Hilbert space admits a full set of mutually unbiased bases , where . A randomized quantum state tomography is a scheme for estimating an unknown quantum state on through iterative applications of measurements for , where the numbers of applications of these measurements are random variables. We show that the space of the resulting probability distributions enjoys a mutually orthogonal dualistic foliation structure, which provides us with a simple geometrical insight into the maximum likelihood method for the quantum state tomography.

Experimental study of low molecular weight polymer/nanoparticle dispersed gel for water plugging in fractures

A low molecular weight polymer/nanoparticle dispersed (LPND) gel system applied for water plugging in fractured media was studied. Results of rheological and gelation properties measurements show that the LPND gelant has a satisfactory shear resistance performance and its shear viscosity can continuously level off under high shear rate condition. The internal structure of the LPND gelant which shows a state of “buttery” can rapidly recover from the state of nanoparticle random distribution to the foliated structure and finally to the reticular structure, and the increase of temperature contributes to the structural recovery ability. Moreover, the increase of the accelerating agent concentration can significantly enhance the gel strength of the LPND gel which shows a “rubbery” state and evidently shorten both the critical and final gelation times. The propagation, plugging and enhanced oil recovery (EOR) performances of the LPND gel system in fractured media were also investigated. Results show that the LPND gelant has slight gravity settling phenomenon which contributes to the uniform gelant propagation in fracture; it can effectively fill the whole water-flooded fracture space and improve the water plugging performance after the gel formation. In the multi-stage fractures, the LPND gelant manifests a selective filling characteristic; it preferentially fills the fracture with high water content and then diverts the subsequent injected water to the adjacent fracture and matrix with low water content after gel formation, resulting in the significant enhancement of the sweep efficiency and oil recovery.

Zooming in on AdS3/CFT2 near a BPS bound

Any (d + 1)-dimensional CFT with a U(1) flavor symmetry, a BPS bound and an exactly marginal coupling admits a decoupling limit in which one zooms in on the spectrum close to the bound. This limit is an Inönü-Wigner contraction of so(2, d+1)⊕u(1) that leads to a relativistic algebra with a scaling generator but no conformal generators. In 2D CFTs, Lorentz boosts are abelian and by adding a second u(1) we find a contraction of two copies of sl(2, ℝ) ⊕ u(1) to two copies of P2c, the 2-dimensional centrally extended Poincaré algebra. We show that the bulk is described by a novel non-Lorentzian geometry that we refer to as pseudo-Newton-Cartan geometry. Both the Chern-Simons action on sl(2, ℝ) ⊕ u(1) and the entire phase space of asymptotically AdS3 spacetimes are well-behaved in the corresponding limit if we fix the radial component for the u(1) connection. With this choice, the resulting Newton-Cartan foliation structure is now associated not with time, but with the emerging holographic direction. Since the leaves of this foliation do not mix, the emergence of the holographic direction is much simpler than in AdS3 holography. Furthermore, we show that the asymptotic symmetry algebra of the limit theory consists of a left- and a right-moving warped Virasoro algebra.

The existence of attractors of Weyl foliations modelled on pseudo-Riemannian manifolds

A foliation that admits a Weyl structure arising from a pseudo-Riemannian metric of any signature as its transverse structure is called a pseudo-Riemannian Weyl foliation or (for short) a Weyl foliation. We investigate codimension q ≥ 2 Weyl foliations on (not necessarily compact) manifolds. Different interpretations of their holonomy groups are given. We prove a criterion for a Weyl foliation to be pseudo-Riemannian. We find a condition on the holonomy groups which guarantees the existence of a transitive attractor of (M, F ). Moreover, if the Weyl foliation is complete, this condition implies the existence of a global transitive attractor. We describe the structure of complete Weyl foliations modelled on Riemannian manifolds.

Compact leaves of codimension one holomorphic foliations on projective manifolds

This article studies codimension one foliations on projective man-ifolds having a compact leaf (free of singularities). It explores the interplay between Ueda theory (order of flatness of the normal bundle) and the holo-nomy representation (dynamics of the foliation in the transverse direction). We address in particular the following problems: existence of foliation having as a leaf a given hypersurface with topologically torsion normal bundle, global structure of foliations having a compact leaf whose holonomy is abelian (resp. solvable), and factorization results.

Geochemistry and petrogenesis of the Eocene back arc mafic rocks in the Zagros suture zone, northern Noorabad, western Iran

The northern Noorabad area in western Iran contains several gabbro and basalt bodies which were emplaced along the Zagros suture zone. The basalts show pillow and flow structures with amygdaloidal textures, and the gabbroic rocks show massive and foliated structures with coarse to fine-grained textures. The SiO2 contents of the gabbros and basalts are similar and range from 46.1–51.0wt.%, and the Al2O3 contents vary from 12.3–18.8wt.%, with TiO2 contents of 0.4–3.0wt.%. The Nb concentrations of some gabbros and basalts are high and can be classified as Nb-enriched arc basalts. The positive εNd(t) values (+3.7 to +9.8) and low 87Sr/86Sr(initial) ratios (0.7031–0.7071) of both bodies strongly indicate a depleted mantle source and indicate that the rocks were formed by partial melting of a depleted lithospheric mantle and interaction with slab fluids/melts. The chemical composition of trace elements, REE pattern and initial 87Sr/86Sr-143Nd/144Nd ratios show that the rocks have affinities to tholeiitic magmatic series and suggest an extensional tectonic regime over the subduction zone for the evolution of these rocks. We propose an extensional tectonic regime due to the upwelling of metasomatized mantle after the late Cretaceous collision in the Harsin-Noorabad area. These rocks can be also considered as Eocene back arc magmatic activity along the Zagros suture zone in this area.

Heat kernel methods for Lifshitz theories

We study the one-loop covariant effective action of Lifshitz theories using the heat kernel technique. The characteristic feature of Lifshitz theories is an anisotropic scaling between space and time. This is enforced by the existence of a preferred foliation of space-time, which breaks Lorentz invariance. In contrast to the relativistic case, covariant Lifshitz theories are only invariant under diffeomorphisms preserving the foliation structure. We develop a systematic method to reduce the calculation of the effective action for a generic Lifshitz operator to an algorithm acting on known results for relativistic operators. In addition, we present techniques that drastically simplify the calculation for operators with special properties. We demonstrate the efficiency of these methods by explicit applications.

The Foliated Weinstein Conjecture

A foliation is said to admit a foliated contact structure if there is a codimension 1 distribution in the tangent space of the foliation such that the restriction to any leaf is contact. We prove a version of the Weinstein conjecture in the presence of an overtwisted leaf. The result is shown to be sharp.

Lifshitz anomalies, Ward identities and split dimensional regularization

We analyze the structure of the stress-energy tensor correlation functions in Lifshitz field theories and construct the corresponding anomalous Ward identities. We develop a framework for calculating the anomaly coefficients that employs a split dimensional regularization and the pole residues. We demonstrate the procedure by calculating the free scalar Lifshitz scale anomalies in 2 + 1 spacetime dimensions. We find that the analysis of the regularization dependent trivial terms requires a curved spacetime description without a foliation structure. We discuss potential ambiguities in Lifshitz scale anomaly definitions.

Submagmatic Fabric in the 2.6 Ga Bundelkhand Granitoid, India:Evidence from Microstructure

Primary foliations in igneous rocks are the key to understanding processes within the magma chamber, cooling history, paleostress regime and strain during emplacement of granitoid plutons. In the 2.6 Ga Bundelkhand granitoid rocks, weak to moderately strong regional fabric is the result of submagmatic grainsupported flow during syn-kinematic emplacement of the magma. Microstructural and outcrop-scale evidences provide an excellent record for interpreting the significance of this fabric development vis-a-vis rheological state during fabric formation. Preferentially oriented tabular feldspar phenocrysts in the granitoid show deformation such as reformed shape, marginal fragmentation and recrystallization, whereas the finer interstitial grains of quartz remain undeformed or mildly deformed. On the basis of the characteristic foliated structure of the Bundelkhand granitoid and the specific contrasting deformation characteristics of feldspar and quartz grains, we propose that the fabric is submagmatic in origin and perhaps formed during syn-emplacement deformation environment of the granitoid.

Vertical and horizontal lifts of multivector fields and applications

Let Q be a smoothmanifold of dimension n ≥ 1. In this paper,we define the vertical lift of multivector fields from Q to T Q and we give some applications in the Poisson geometry. In particular we describe the structure of singular foliation induced by the vertical lift of Poisson structures defined below. On the other hand, given a second order vector field on Q, we defined the horizontal lift of multivector fields from Q to TQ and we study some properties.

Isotrivial Unfoldings and Structural Theorems for Foliations on Projective Spaces

Following T. Suwa, we study unfoldings of algebraic foliations and their relationship with families of foliations, making focus on those unfoldings related to trivial families. The results obtained in the study of unfoldings are then applied to obtain information on the structure of foliations on projective spaces.

Infinitesimal moduli for the Strominger system and Killing spinors in generalized geometry

We construct the space of infinitesimal variations for the Strominger system and an obstruction space to integrability, using elliptic operator theory. We initiate the study of the geometry of the moduli space, describing the infinitesimal structure of a natural foliation on this space. The associated leaves are related to generalized geometry and correspond to moduli spaces of solutions of suitable Killing spinor equations on a Courant algebroid. As an application, we propose a unifying framework for metrics with holonomy $\SU(3)$ and solutions of the Strominger system.