Geometric Fiber Research Articles

A comparison of different geometrical elements to model fluid wicking in paper‐based microfluidic devices

AbstractRecently, microfluidic paper‐based analytical devices (μPADs) have outstripped polymeric microfluidic devices in the ease of fabrication and simplicity. Surface tension‐based fluid motion in the paper's porous structure has made the paper a suitable substrate for multiple biological assays by directing fluid into multiple assay zones. The widespread assumption in most works for modeling wicking in a paper is that the paper is a combination of capillaries with the same diameter equal to the effective pore diameter. Although assuming paper as a bundle of capillaries gives a good insight into pressure force that drives the fluid inside the paper, there are some difficulties using the effective pore radius. The effective pore radius is totally different from the average geometrical pore radius which makes it impossible to predict wicking in μPADs based on geometrical parameters. In this article, we introduce different analytical and numerical models to investigate the possibility of determining the permeability of the paper, based on geometrical parameters rather than effective parameters. The lattice Boltzmann method is used for numerical simulations. The permeability of each of the proposed models was compared with the experimental permeability. Results indicated that assuming paper as a combination of capillaries and annuluses leads to accurate results that totally depend on average geometrical values rather than effective values. This paves the way for prediction of the fluid wicking only by considering average geometrical pore and fiber diameters.

Subadditivity of Kodaira dimensions for fibrations of three-folds in positive characteristics

In this paper, we will prove subadditivity of Kodaira dimensions for a fibration with possibly singular geometric generic fiber, under certain nefness and relative semi-ampleness conditions. As an application, for a fibration f:X→Y of a smooth projective threefold over an algebraically closed field of characteristic p>5, under the assumption that Y is of general type and non-uniruled, we prove subadditivity of Kodaira dimensions when general fibers are smooth or when KX/Y is relatively big over Y.

Combined multiphoton imaging and biaxial tissue extension for quantitative analysis of geometric fiber organization in human reticular dermis

The geometric organization of collagen fibers in human reticular dermis and its relationship to that of elastic fibers remain unclear. The tight packing and complex intertwining of dermal collagen fibers hinder accurate analysis of fiber orientation. We hypothesized that combined multiphoton microscopy and biaxial extension could overcome this issue. Continuous observation of fresh dermal sheets under biaxial extension revealed that the geometry of the elastic fiber network is maintained during expansion. Full-thickness human thigh skin samples were biaxially extended and cleared to visualize the entire reticular dermis. Throughout the dermis, collagen fibers straightened with increased inter-fiber spaces, making them more clearly identifiable after extension. The distribution of collagen fibers was evaluated with compilation of local orientation data. Two or three modes were confirmed in all superficial reticular layer samples. A high degree of local similarities in the direction of collagen and elastic fibers was observed. More than 80% of fibers had directional differences of ≤15°, regardless of layer. Understanding the geometric organization of fibers in the reticular dermis improves the understanding of mechanisms underlying the pliability of human skin. Combined multiphoton imaging and biaxial extension provides a research tool for studying the fibrous microarchitecture of the skin.

Manufacturing-Induced Imperfections in Composite Parts Manufactured via Automated Fiber Placement

The automated fiber placement process (AFP) enables the manufacturing of large and geometrical complex fiber composite structures with high quality at low cycle times. Although the AFP process is highly accurate and reproducible, manufacturing induced imperfections in the produced composite structure occur. This review summarizes and classifies typical AFP-related manufacturing defects. Several methodologies for evaluating the effects of such manufacturing defects from the literature are reviewed. This review paper presents recent scientific contributions and discusses proposed experimental and simulation-based methodologies. Among the identified ten defect classes, gaps and overlaps are predominant. This paper focuses then on methods for modelling and assessing gaps and overlaps. The state of the art in modelling gaps and overlaps and assessing their influence on mechanical properties is presented. Finally, research gaps and remaining issues are identified.

Performance Comparison of Three Fibre-Based Reflective Optical Sensors for Aero Engine Monitorization.

Among the different available optical technologies, fibre bundle-based reflective optical sensors represent an interesting alternative for parameter monitorization in aero engines. Tip clearance is one of the parameters of great concern for engine designers and engineers. In the framework of this optical technology, three fibre-based reflective optical sensors have been compared. Two of them are custom designed and based on the same geometrical fibre arrangement, whereas the third one is commercially available and relies on a different geometrical arrangement of the fibres. Their performance has been compared in clearance measurements carried out during an experimental program followed at a transonic wind tunnel for aero turbines. The custom-designed solution that operates in the most sensitive part of its response curve proved to be by far the most reliable tool for clearance measurements. Its high resolution opens up the possibility to detect small blade features such as cracks, reflectivity changes, etc. that otherwise could not be tracked. These results show that the detection of unexpected features on blade tips may have an important effect on how the clearance is calculated, ultimately giving rise to corrective actions.

The boundary control problem of optical fiber drawing

In the paper a new approach to solving problem of optimal control of technological process for the optical fiber production is proposed. The process of optical fiber drawing from a preform are considered. The optimal control problem of this process is formulated as problem of controlling partial differential equation system. The problem of the geometric fiber shape optimization in controlling the winding speed of the resulted fiber is formulated and solved. The optimality system in the strong form is obtained with the help of an analog of the Lagrange method. The optimal control function is determined from solving of this system. To obtain optimality system the properties of convexity, lower semi-continuity and coercivity of objective functional are used. In conclusion, an algorithm for realizing the optimal control problem is proposed and the results are analyzed. The problem is solved for several types of initial conditions for the radius deviation function from its stationary (programmed) solution. In these cases, optimality systems are solved with the help of algorithms of multi-physical modeling, control functions are found. The obtained correction values for the winding speed of the resulted fiber correspond to the possibilities of real production.

On singularity properties of convolutions of algebraic morphisms

Let $K$ be a field of characteristic zero, $X$ and $Y$ be smooth $K$-varieties, and let $V$ be a finite dimensional $K$-vector space. For two algebraic morphisms $\varphi:X\rightarrow V$ and $\psi:Y\rightarrow V$ we define a convolution operation, $\varphi*\psi:X\times Y\to V$, by $\varphi*\psi(x,y)=\varphi(x)+\psi(y)$. We then study the singularity properties of the resulting morphism, and show that as in the case of convolution in analysis, it has improved smoothness properties. Explicitly, we show that for any morphism $\varphi:X\rightarrow V$ which is dominant when restricted to each irreducible component of $X$, there exists $N\in\mathbb{N}$ such that for any $n>N$ the $n$-th convolution power $\varphi^{n}:=\varphi*\dots*\varphi$ is a flat morphism with reduced geometric fibers of rational singularities (this property is abbreviated (FRS)). By a theorem of Aizenbud and Avni, for $K=\mathbb{Q}$, this is equivalent to good asymptotic behavior of the size of the $\mathbb{Z}/p^{k}\mathbb{Z}$-fibers of $\varphi^{n}$ when ranging over both $p$ and $k$. More generally, we show that given a family of morphisms $\{\varphi_{i}:X_{i}\rightarrow V\}$ of complexity $D\in\mathbb{N}$ (i.e. that the number of variables and the degrees of the polynomials defining $X_{i}$ and $\varphi_{i}$ are bounded by $D$), there exists $N(D)\in\mathbb{N}$ such that for any $n>N(D)$, the morphism $\varphi_{1}*\dots*\varphi_{n}$ is (FRS).

On Derived Equivalences of K3 Surfaces in Positive Characteristic

For an ordinary K3 surface over an algebraically closed field of positive characteristic we show that every automorphism lifts to characteristic zero. Moreover, we show that the Fourier-Mukai partners of an ordinary K3 surface are in one-to-one correspondence with the Fourier-Mukai partners of the geometric generic fiber of its canonical lift. We also prove that the explicit counting formula for Fourier-Mukai partners of the K3 surfaces with Picard rank two and with discriminant equal to minus of a prime number, in terms of the class number of the prime, holds over a field of positive characteristic as well. We show that the image of the derived autoequivalence group of a K3 surface of finite height in the group of isometries of its crystalline cohomology has index at least two. Moreover, we provide a conditional upper bound on the kernel of this natural cohomological descent map. Further, we give an extended remark in the appendix on the possibility of an F-crystal structure on the crystalline cohomology of a K3 surface over an algebraically closed field of positive characteristic and show that the naive F-crystal structure fails in being compatible with inner product.

Nonlinear aerothermoelastic analysis of composite laminated panels using a general higher-order shear deformation zig-zag theory

A general higher-order shear deformation zig-zag theory is proposed for predicting the nonlinear aerothermoelastic characteristics of composite laminated panels subjected to supersonic airflow. The von Kármán strains are employed to describe the structural nonlinearity of the panels, and the quasi-steady first-order piston theory is adopted to calculate the aerodynamic loads. The discretized equations governing the aerothermoelastic motion of the panels are established using the nonlinear finite element method. The proposed higher-order shear deformation zig-zag theory employs seven variables to represent the displacement field of the panel in a unified form, which is capable of accommodating various plate theories available in the literature, including the Kirchhoff plate theory, the Mindlin–Reissner plate theory and other higher-order shear deformation plate theories. The validity of the present model is confirmed by comparing the computed results with those solutions available in the literature. The aerothermoelastic behaviors (including the critical buckling, limit-cycle oscillation and flutter boundary) for composite laminated panels with different geometrical dimensions, temperature gradients and fiber orientations are examined. The discrepancies of the aerothermoelastic characteristics of composite laminated panels determined by different structural theories are discussed in detail. Physical insight into the mechanism of the differences among the aerothermoelastic behaviors of the panels determined by different plate theories is provided.

Thermally Responsive Microfibers Mediated Stem Cell Fate via Reversibly Dynamic Mechanical Stimulation

AbstractThe role of mechanical forces is crucial for stem cell adhesion, viability, proliferation, self‐renewal, and differentiation. The relationship between the natural extracellular matrix mechanics and cell behavior is dynamic, such as compressive stress from skeletal muscle contraction. Thus, relatively little is known about how stem cells respond to reversibly dynamic mechanical stimulation (RD‐MS) in a 3D fiber network. Here, thermosensitive electrospun microfibrous cross‐linked hydrogels are investigated from variants of polycaprolactone and poly(N‐isopropylacrylamide) in which the mechanosensing can be in situ thermo‐induced switched from stiff (37 °C) to soft (25 °C) for multiple cycles. It is found that human mesenchymal stem cells seeded in bioengineered fibrillar microenvironments with multicyclic RD‐MS result in an increased cell spreading area and polarization. This 3D cell shape deformation can ultimately alter the intracellular signaling related to the differentiation. Combining with mechanosensing computer simulations, a positive correlation between the elongated morphology and the cycles of RD‐MS is predicted, suggesting that the cell polarization is proportional to dynamic changes of local stiffness and geometric fiber density of the fiber network. This study reveals RD‐MS as a key design parameter for biomaterial scaffolds as well to control cell behavior in tissue engineering applications.

Specialization map between stratified bundles and pro-étale fundamental group

Given a projective family of semi-stable curves over a complete discrete valuation ring of characteristic p>0 with algebraically closed residue field, we construct a specialization functor between the category of continuous representations of the pro-étale fundamental group of the closed fibre and the category of stratified bundles on the geometric generic fibre. By Tannakian duality, this functor induces a morphism between the corresponding affine group schemes. We show that this morphism is a lifting of the specialization map, constructed by Grothendieck, between the étale fundamental groups.

Influence of micro-scale uncertainties on the reliability of fibre-matrix composites

This study investigates the effect of micro-scale geometric and material property uncertainties on the elastic properties and reliability of fibre reinforced composite materials. Composite materials are often designed using conservative design factors to account for a limited understanding of how multi-scale uncertainties effect reliability. Structural reliability analysis can produce more efficient designs, but requires an understanding of how all sources uncertainty effect probability of failure. Previous studies have not considered micro-scale geometrical uncertainties and their combinations in a multi-scale probabilistic-based reliability framework. Thus, this study will investigate the effect of numerous combinations of micro-scale material property and geometric uncertainties on the homogenised elastic properties. Furthermore, to account for the effect in a reliability-based framework, a novel surrogate modelling technique is developed to represent the uncertainties efficiently. The study concluded that the geometrical fibre stacking uncertainty is as influential as the widely investigated constituent material stiffness uncertainties. Consequently, representing the micro-scale geometric uncertainties within the developed multi-scale probabilistic-based framework improves the estimated stiffness. Thus probability of failure is reduced, compared with considering material property uncertainties only. Moreover, the framework clarified and highlighted the importance of representing fibre geometrical stacking uncertainty for a deeper understanding of their effect on composite stiffness properties.

On the Hodge, Tate and Mumford-Tate Conjectures for Fibre Products of Families of Regular Surfaces with Geometric Genus 1

The Hodge, Tate and Mumford-Tate conjectures are proved for the fibre product of two non-isotrivial 1-parameter families of regular surfaces with geometric genus 1 under some conditions on degenerated fibres, the ranks of the N\'eron - Severi groups of generic geometric fibres and representations of Hodge groups in transcendental parts of rational cohomology.Let \(\pi_i:X_i\to C\quad (i = 1, 2)\) be a projective non-isotrivial family (possibly with degeneracies) over a smooth projective curve \(C\). Assume that the discriminant loci \(\Delta_i=\{\delta\in C\,\,\vert\,\, Sing(X_{i\delta})\neq\varnothing\} \quad (i = 1, 2)\) are disjoint, \(h^{2,0}(X_{ks})=1,\quad h^{1,0}(X_{ks}) = 0\) for any smooth fibre \(X_{ks}\), and the following conditions hold:\((i)\) for any point \(\delta \in \Delta_i\) and the Picard-Lefschetz transformation \( \gamma \in GL(H^2 (X_{is}, Q)) \), associated with a smooth part \(\pi'_i: X'_i\to C\setminus\Delta_i\) of the morphism \(\pi_i\) and with a loop around the point \(\delta \in C\), we have \((\log(\gamma))^2\neq0\);\((ii)\) the variety \(X_i \, (i = 1, 2)\), the curve \(C\) and the structure morphisms \(\pi_i:X_i\to C\) are defined over a finitely generated subfield \(k \hookrightarrow C\).If for generic geometric fibres \(X_{1s}\) \, and \, \(X_{2s}\) at least one of the following conditions holds: \((a)\) \(b_2(X_{1s})- rank NS(X_{1s})\) is an odd prime number, \(\quad\,\,\) \(b_2(X_{1s})- rank NS(X_{1s})\neq b_2(X_{2s})- rank NS(X_{2s})\); \((b)\) the ring \(End_{ Hg(X_{1s})} NS_ Q(X_{1s})^\perp\) is an imaginary quadratic field, \(\quad\,\, b_2(X_{1s})- rank NS(X_{1s})\neq 4,\) \(\quad\,\, End_{ Hg(X_{2s})} NS_ Q(X_{2s})^\perp\) is a totally real field or \(\,\, b_2(X_{1s})- rank NS(X_{1s})\,>\, b_2(X_{2s})- rank NS(X_{2s})\) ; \((c)\) \([b_2(X_{1s})- rank NS(X_{1s})\neq 4, \, End_{ Hg(X_{1s})} NS_ Q(X_{1s})^\perp= Q\); \(\quad\,\,\) \(b_2(X_{1s})- rank NS(X_{1s})\neq b_2(X_{2s})- rank NS(X_{2s})\),then for the fibre product \(X_1 \times_C X_2\) the Hodge conjecture is true, for any smooth projective \(k\)-variety \(X_0\) with the condition \(X_1 \times_C X_2\) \(\widetilde{\rightarrow}\) \(X_0 \otimes_k C\) the Tate conjecture on algebraic cycles and the Mumford-Tate conjecture for cohomology of even degree are true.

Existence of supersingular reduction for families of $K3$ surfaces with large Picard number in positive characteristic

We study non-isotrivial families of $K3$ surfaces in positive characteristic $p$ whose geometric generic fibers satisfy $\rho \ge 21 - 2h$ and $h \ge 3$, where $\rho$ is the Picard number and $h$ is the height of the formal Brauer group. We show that, under a mild assumption on the characteristic of the base field, they have potential supersingular reduction. Our methods rely on Maulik’s results on moduli spaces of $K3$ surfaces and the construction of sections of powers of Hodge bundles due to van der Geer and Katsura. For large $p$ and each $2 \le h \le 10$, using deformation theory and Taelman’s methods, we construct non-isotrivial families of $K3$ surfaces satisfying $\rho = 22 - 2h$.

Field emission from carbon nanotube fibers in varying anode-cathode gap with the consideration of contact resistance

Abstract

On an inductive approach to the standard conjecture for a fibred complex variety with strong semistable degeneracies

We prove that Grothendieck's standard conjecture of Lefschetz type on the algebraicity of the operators and of Hodge theory holds for a 4-dimensional smooth projective complex variety fibred over a smooth projective curve provided that every degenerate fibre is a union of smooth irreducible components of multiplicity with normal crossings, the standard conjecture holds for a generic geometric fibre , there is at least one degenerate fibre and the rational cohomology rings and of the irreducible components of every degenerate fibre are generated by classes of algebraic cycles. We obtain similar results for -dimensional fibred varieties with algebraic invariant cycles (defined by the smooth part of the structure morphism ) or with a degenerate fibre all of whose irreducible components possess the property .

Calculation of flutter and dynamic behavior of advanced composite swept wings with tapered cross section in unsteady incompressible flow

ABSTRACTIn this study, the aeroelastic stability and response of a swept composite wing in subsonic incompressible flow are investigated. The wing is modeled as an anisotropic tapered thin-walled beam with the circumferentially asymmetric stiffness structural configuration to establish proper coupling between bending and torsion. The structural model considers a number of nonclassical effects, such as transverse shear, material anisotropy, warping inhibition, nonuniform torsion, rotary inertia and three-dimensional strain effects. The aerodynamic strip method based on two-dimensional Wagner function in unsteady incompressible flow is used. Following the analysis, the mass, stiffness and the damping matrices of the nonconservative aeroelastic system are formed such that the extended Galerkin method and the separation of variables method can be employed. As a result, the coupled and linear governing system of dynamic equations is obtained. Then, by transforming matrices into the state-space and state-vector forms, the problem under study is finally converted into an eigenvalue problem. The flutter and the divergence speeds for various layer configurations with different geometric and material properties and fiber orientations are obtained. By solving the aforementioned equations of motion in the time domain, the aeroelastic responses of the tapered swept composite wing are computed. The obtained results are compared with the available literature.

Quasi-plastic deformation mechanism and off-line secondary molding of four-step three-dimensional braided preform

The present curved-surface preform made by the process copying the mandrel is easy to appear quasi-plastic deformation. And this process with low-efficiency, high-cost is difficult to batch production. In this study, a tubular preform is obtained by the process of off-line secondary molding based on the plate preform. The deformation mechanism of the plate preform under different load conditions is analyzed. Establishing mathematical model based on the deformation of microstructure unit, the geometric dimensions and fiber volume fraction of the deformed preform are forecasted. Theoretical results show that the size of unit can govern the stability of preform in molding, the deformation of preform can increase the fiber volume fraction effectively when the units of plate three-dimensional braided material are cubic. The tubular preform made by the technology of molding the pre-designed plate preform which can be braided quickly has a more stable geometrical structure and better performance. This technology avoid the complex braiding process and equipment of the tubular preform, which is expect to product the tubular preform in batches effectively.

On the group of units and the Picard group of a product

Let S be a reduced scheme and let $$f:X\rightarrow S$$ and $$g:Y\rightarrow S$$ be faithfully flat morphisms locally of finite presentation with reduced and connected maximal geometric fibers. We discuss the canonical maps and induced by f and g. Under certain additional conditions on S, X, Y, f and g, we describe the kernel and cokernel of the preceding maps, thereby extending known results when S is the spectrum of a field.

ON -DIVISIBLE GROUPS WITH SATURATED NEWTON POLYGONS

This paper concerns the classification of isogeny classes of$p$-divisible groups with saturated Newton polygons. Let$S$be a normal Noetherian scheme in positive characteristic$p$with a prime Weil divisor$D$. Let${\mathcal{X}}$be a$p$-divisible group over$S$whose geometric fibers over$S\setminus D$(resp. over$D$) have the same Newton polygon. Assume that the Newton polygon of${\mathcal{X}}_{D}$is saturated in that of${\mathcal{X}}_{S\setminus D}$. Our main result (Corollary 1.1) says that${\mathcal{X}}$is isogenous to a$p$-divisible group over$S$whose geometric fibers are all minimal. As an application, we give a geometric proof of the unpolarized analogue of Oort’s conjecture (Oort, J. Amer. Math. Soc.17(2) (2004), 267–296; 6.9).