External force-induced focus pattern of a flexible filament in a viscous fluid

In order to study the mechanism of wall attraction of micro-swimmers, this paper presents a numerical study on the external force-induced focus of a flexible filament in a quiescent viscous fluid. In the numerical model, the fluid is solved by the lattice Boltzmann method (LBM) and the moving filament is modeled with the immersed boundary (IB). The filament is parallel and adjacent to a near-wall initially. A periodic driving force is applied on it to induce a vibration motion which could lead to the wall attraction phenomenon of the vibrating filament. Furthermore, by adjusting the mean value of the periodic driving force, we can get a stable vibrating mode of the filament, which is called as focus pattern. The pattern is a special state of the wall attraction, which provides a convenient way to investigate the law of hydrodynamic balance. Simulations are conducted by varying the following parameters, including the boundary setting of the flow field, the magnitude, period and waveform of the external driving force, the bending modulus of the filament and the fluid viscosity. The laws of the focus pattern are discussed in detail. The results indicate that all the above parameters can affect the focus position remarkably. By analyzing the outputs of each item of the Navier–Stokes momentum conservation equation, we found that the focus is mainly caused by the balance of the joint force on the filament and the pressure effect from the flow. This finding may provide a novel way to uncover the hydrodynamic mechanism for wall attraction of waving propulsion.     

Approximating the minimum clique cover and other hard problems in subtree filament graphs

Subtree filament graphs are the intersection graphs of subtree filaments in a tree. This class of graphs contains subtree overlap graphs, interval filament graphs, chordal graphs, circle graphs, circular-arc graphs, cocomparability graphs, and polygon-circle graphs. In this paper we show that, for circle graphs, the clique cover problem is NP-complete and the h-clique cover problem for fixed h is solvable in polynomial time. We then present a general scheme for developing approximation algorithms for subtree filament graphs, and give approximation algorithms developed from the scheme for the following problems which are NP-complete on circle graphs and therefore on subtree filament graphs: clique cover, vertex colouring, maximum k-colourable subgraph, and maximum h-coverable subgraph.     

On the vortex filament in 3-spaces and its generalizations

Science China Mathematics - In this article, we devote to a mathematical survey on the theory of the vortex filament in 3-dimensional spaces and its generalizations. We shall present some effective...     

Convergence of the contour dynamics method

In this paper the contour dynamics method (CDM) is formulated and applied to the study of a two-dimensional incompressible and inviscid fluid flow. A result concerning the convergence of this method is proved. The foundation of the CDM is based on the study of the dynamic interaction between contours enclosing vortex regions. The idea of the analysis is to show that the CDM can be considered as a vortex filament method. Hence, the convergence for the contour dynamics method is proved by using some results in the theory of the vortex method.     

Motion of a vortex filament in the half-space

A model equation for the motion of a vortex filament immersed in three-dimensional, incompressible and inviscid fluid is investigated as a preliminary attempt to model the motion of a tornado. We solve an initial–boundary value problem in the half-space, where we impose a boundary condition in which the vortex filament is allowed to move on the boundary.     

测试屏幕上B、C两点所对应的聚焦现象及其亮度比初步分析

根据相对聚焦强度公式,分析了灯丝上发出的光线在通过旋转抛物面反射到测试屏幕上的B,C两点时所具有的完全聚焦现象,并说明了这种聚焦的现象是一阶的.进一步,我们还给出了相对聚光强度的各种比值,并据此给出了在满足B点亮度不小于C点亮度的两倍的条件下,灯丝的最短长度为3.122mm.     

Asymptotics of eigenfrequencies and eigenmodes of non‐homogeneous inextensible filament with an end load

We consider a class of non‐selfadjoint operators generated by the equation and the boundary conditions, which govern small vibrations of an ideal filament with non‐conservative boundary conditions at one end and a heavy load at the other end. The filament has a non‐constant density and is subject to a viscous damping with a non‐constant damping coefficient. The boundary conditions contain two arbitrary complex parameters. We derive the spectral asymptotics for the aforementioned two‐parameter family of non‐selfadjoint operators. In the forthcoming papers, based on the asymptotical results of the present paper, we will prove the Riesz basis property of the eigenfunctions. The spectral results obtained in the aforementioned papers will allow us to solve boundary and/or distributed controllability problems for the filament using the spectral decomposition method. Copyright © 2001 John Wiley & Sons, Ltd.     

Finite-Gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations

We study the topology of quasiperiodic solutions of the vortex filament equation in a neighborhood of multiply covered circles. We construct these solutions by means of a sequence of isoperiodic deformations, at each step of which a real double point is “unpinched” to produce a new pair of branch points and therefore a solution of higher genus. We prove that every step in this process corresponds to a cabling operation on the previous curve, and we provide a labelling scheme that matches the deformation data with the knot type of the resulting filament.     

Nonlinear micromechanical model of filament-wound composites considering fiber undulation

Flexible-matrix composites with highly anisotropic properties have successfully been used in numerous fields to improve the performance of conventional structures or to facilitate new innovations. Many of them are designed on the basis of tubes which are produced efficiently by the filament winding process. To predict the elastic behavior of filament-wound flexible-matrix composites, aspects of the nonlinear behavior of the flexible material have to be considered, as well as the features of the distinct fiber undulation geometry inherent to the filament winding process. The present study considers these characteristics in the micromechanical modeling of the elastic behavior by including a nonlinear material model to represent the strain-dependent moduli and manufacturing-dependent geometries. The structure is characterized by a unit cell and subcells, analyzed separately and combined based on different sets of isostress and isostrain assumptions that depend on the winding angle. On the basis of experimentally obtained nonlinear lamina properties, an iterative method of solution is chosen to calculate the axial stress–strain behavior of tubes with various winding parameters. The resulting predictions are validated by testing tubes in tension and compression. The model shows good agreement with the experiments. Predictions made using the model show a strong influence of filament winding parameters on the axial modulus of flexible-matrix composite tubes.     

Thermodynamic Equilibrium in the System of Chaotic Quantized Vortices in a Weakly Imperfect Bose Gas

In the example of a weakly imperfect Bose gas, we discuss the mechanism of establishing thermodynamic equilibrium for a chaotic set of quantum vortex filaments. We assume that the dynamics of the Bose condensate is described by the Gross–Pitaevsky equation with an additional noise satisfying the fluctuation–dissipation theorem. In considering a vortex filament as the intersection line of surfaces on which the real and imaginary parts of the order parameter (x,t) vanish, we obtain an equation of the Langevin type for elements of the vortex filament with an appropriately transformed random force. The Fokker–Planck equation for the probability density has a solution given by the Gibbs distribution at the temperature of the Bose condensate. In other words, when the Bose condensate is in thermal equilibrium and no other random actions exist, the system of vortices is also in thermal equilibrium.     

A major solar flare in a small δ-type active region

A small δ-type active region was observed on September 14-18, 2000 at Ganyu Station of the Purple Mountain Observatory. It developed rapidly during its passage through solar disk and there was a stereo-typed spiral filament near the magnetic inversion line on 15-17th, Sept. Its magnetic axis made an angle 85° to the equator. On Sept. 16 it produced a major flare, 3B importance, having more intense geophysical effects. Using the vector-magnetograms the distribution of magnetic field lines was deduced. The analysis of QSL stereo-map made a discovery that there is a null or separator about such spiral filament which can be used to explain the formation of this major flare and intense mass ejection.     

A major solar flare in a small δ-type active region

A small δ-type active region was observed on September 14–18, 2000 at Ganyu Station of the Purple Mountain Observatory. It developed rapidly during its passage through solar disk and there was a stereo-typed spiral filament near the magnetic inversion line on 15–17th, Sept. Its magnetic axis made an angle 85° to the equator. On Sept. 16 it produced a major flare, 3B importance, having more intense geophysical effects. Using the vector-magnetograms the distribution of magnetic field lines was deduced. The analysis of QSL stereo-map made a discovery that there is a null or separator about such spiral filament which can be used to explain the formation of this major flare and intense mass ejection.     

Vortex Filament Solutions of the Navier-Stokes Equations

We consider solutions of the Navier-Stokes equations in 3d with vortex filament initial data of arbitrary circulation, that is, initial vorticity given by a divergence-free vector-valued measure of arbitrary mass supported on a smooth curve. First, we prove global well-posedness for perturbations of the Oseen vortex column in scaling-critical spaces. Second, we prove local well-posedness (in a sense to be made precise) when the filament is a smooth, closed, non-self-intersecting curve. Besides their physical interest, these results are the first to give well-posedness in a neighborhood of large self-similar solutions of 3d Navier-Stokes, as well as solutions that are locally approximately self-similar. © 2023 Wiley Periodicals LLC.     

Remark on well-posedness for the fourth order nonlinear Schrödinger type equation

We consider the initial value problem for the fourth order nonlinear Schrödinger type equation (4NLS) related to the theory of vortex filament. In this paper we prove the time local well-posedness for (4NLS) in the Sobolev space, which is an improvement of our previous paper.

     

On the growth of filamentary structures in planar media

We analyse a mathematical model for the growth of thin filaments into a two dimensional medium. More exactly, we focus on a certain reaction/diffusion system, describing the interaction between three chemicals (an activator, an inhibitor and a growth factor), and including a fourth cell variable characterising irreversible incorporation to a filament. Such a model has been shown numerically to generate structures shaped like nets. We perform an asymptotical analysis of the behaviour of solutions, in the case when the system has parameters very large and very small, thereby allowing the onset of different time and space scales. In particular, we describe the motion of the tip of a filament, and the changes in the relevant chemical species nearby. Copyright © 2004 John Wiley & Sons, Ltd.     

Instability Paths in the Kirchhoff–Plateau Problem

The Kirchhoff–Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a soap film, with the filament being modeled as a Kirchhoff rod and the action of the spanning surface being solely due to surface tension. Adopting a variational approach, we define an energy associated with shape deformations of the system and then derive general equilibrium and (linear) stability conditions by considering the first and second variations of the energy functional. We analyze in detail the transition to instability of flat circular configurations, which are ground states for the system in the absence of surface tension, when the latter is progressively increased. Such a theoretical study is particularly useful here, since the many different perturbations that can lead to instability make it challenging to perform an exhaustive experimental investigation. We generalize previous results, since we allow the filament to possess a curved intrinsic shape and also to display anisotropic flexural properties (as happens when the cross section of the filament is noncircular). This is accomplished by using a rod energy which is familiar from the modeling of DNA filaments. We find that the presence of intrinsic curvature is necessary to obtain a first buckling mode which is not purely tangent to the spanning surface. We also elucidate the role of twisting buckling modes, which become relevant in the presence of flexural anisotropy.     

Analytical prediction of damage in the composite part of a type-3 hydrogen storage vessel

The damage behavior of a type-3 hydrogen storage vessel is modeled. The vessel consists of a metal envelop, called liner, coated with a filament winding. The model proposed allows simulating the mechanical response of the structure to a quasi-static loading. The model is based on a meso-macro approach and takes into account the damage behavior of the composite and the elastoplastic deformation of the liner. The results obtained are compared with experimental data. Finally, the effect of stacking sequence of filament layers on the damage level in the composite is investigated.     

Inhomogeneous Current States in a Gauged Two-Component Ginzburg-Landau Model

We consider the energy bounds of inhomogeneous current states in doped antiferromagnetic insulators in the framework of the two-component Ginzburg-Landau model. Using the formulation of this model in terms of the gauge-invariant order parameters (the unit vector n, spin stiffness field ρ², and particle momentum c), we show that this strongly correlated electron system involves a geometric small parameter that determines the degree of packing in the knots of filament manifolds of the order parameter distributions for the spin and charge degrees of freedom. We find that as the doping degree decreases, the filament density increases, resulting in a transition to an inhomogeneous current state with a free energy gain.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 1, pp. 182–189, July, 2005.     

丝条不匀率U与变异系数CV转换的数学推算

本文通过研究丝条的条干不匀，分析不匀的原因，从而达到改进的目的。