Continuum description of the cytoskeleton: ring formation in the cell cortex

Motivated by the formation of ringlike filament structures in the cortex of plant and animal cells, we study the dynamics of a two-dimensional layer of cytoskeletal filaments and motor proteins near a surface by a general continuum theory. As a result of active processes, dynamic patterns of filament orientation and density emerge via instabilities. We show that self-organization phenomena can lead to the formation of stationary and oscillating rings. We present state diagrams that reveal a rich scenario of asymptotic behaviors and discuss the role of boundary conditions.     

Evolution of filament structures during edge-localized modes in the MAST Tokamak

Edge-localized modes (ELMs) are repetitive instabilities that occur in the outer region of tokamak plasmas. This Letter provides new information on and the implications of the evolution of the filament structures observed during ELMs in the MAST tokamak. The filaments exist for the time over which particles are being released into the scrape off layer. They start off at the plasma edge rotating at the velocity of the pedestal, and then decelerate toroidally and accelerate radially outwards. As the filaments propagate radially they remain aligned with the local magnetic field line.     

Weibel-induced filamentation during an ultrafast laser-driven plasma expansion

The development of current instabilities behind the front of a cylindrically expanding plasma has been investigated experimentally via proton probing techniques. A multitude of tubelike filamentary structures is observed to form behind the front of a plasma created by irradiating solid-density wire targets with a high-intensity (I ~ 10(19) W/cm(2)), picosecond-duration laser pulse. These filaments exhibit a remarkable degree of stability, persisting for several tens of picoseconds, and appear to be magnetized over a filament length corresponding to several filament radii. Particle-in-cell simulations indicate that their formation can be attributed to a Weibel instability driven by a thermal anisotropy of the electron population. We suggest that these results may have implications in astrophysical scenarios, particularly concerning the problem of the generation of strong, spatially extended and sustained magnetic fields in astrophysical jets.     

Motor-driven bacterial flagella and buckling instabilities

Many types of bacteria swim by rotating a bundle of helical filaments also called flagella. Each filament is driven by a rotary motor and a very flexible hook transmits the motor torque to the filament. We model it by discretizing Kirchhoff’s elastic-rod theory and develop a coarse-grained approach for driving the helical filament by a motor torque. A rotating flagellum generates a thrust force, which pushes the cell body forward and which increases with the motor torque. We fix the rotating flagellum in space and show that it buckles under the thrust force at a critical motor torque. Buckling becomes visible as a supercritical Hopf bifurcation in the thrust force. A second buckling transition occurs at an even higher motor torque. We attach the flagellum to a spherical cell body and also observe the first buckling transition during locomotion. By changing the size of the cell body, we vary the necessary thrust force and thereby obtain a characteristic relation between the critical thrust force and motor torque. We present a elaborate analytical model for the buckling transition based on a helical rod which quantitatively reproduces the critical force-torque relation. Real values for motor torque, cell body size, and the geometry of the helical filament suggest that buckling should occur in single bacterial flagella. We also find that the orientation of pulling flagella along the driving torque is not stable and comment on the biological relevance for marine bacteria.     

Breather-induced quantised superfluid vortex filaments and their characterisation

We study and characterise the breather-induced quantised superfluid vortex filaments which correspond to the Kuznetsov-Ma breather and super-regular breather excitations developing from localised perturbations. Such vortex filaments, emerging from an otherwise perturbed helical vortex, exhibit intriguing loop structures corresponding to the large amplitude of breathers due to the dual action of bending and twisting of the vortex. The loop induced by the Kuznetsov-Ma breather emerges periodically as time increases, while the loop structure triggered by the super-regular breather—the loop pair—exhibits striking symmetry breaking due to the broken reflection symmetry of the group velocities of the super-regular breather. In particular, we identify explicitly the generation conditions of these loop excitations by introducing a physical quantity—the integral of the relative quadratic curvature—which corresponds to the effective energy of breathers. Despite the nature of nonlinearity, it is demonstrated that this physical quantity shows a linear correlation with the loop size. These results will deepen our understanding of breather-induced vortex filaments and be helpful for controllable ring-like excitations on the vortices.     

Unstable membrane outgrowth induced by filament tip spreading

We analyse the dynamics of a network of regularly spaced parallel filaments, growing perpendicularly against an elongating membrane which limits the diffusion of monomers in the half-space where filaments grow. When the membrane bulges, some filaments spread, so that less monomers are absorbed at the bulge periphery. It results in both a local increase of the free monomer concentration and an enhancement of the filament polymerisation rate, leading to an original growth instability. This one, stabilised here at short wavelengths by filament tip diffusion along the membrane and the drawback force exerted by a subjacent network of crosslinking molecules, may play a noticeable part in the initiation of neuritic and lamellipodial structures.     

Twist and writhe dynamics of stiff polymers

I consider the dynamics of a stiff filament, in particular the coupling of twist and bend via writhe. The time dependence of the writhe of a filament of length L is ([Wr(t) - Wr(0)]2) > approximately Lt(1/4). Simulations, on a simple model of a stiff polymer, are used to confirm scaling arguments. Fuller's theorem, and its relation with geometric phases, is reconsidered for open filaments.     

Growth induced buckling of morphoelastic rod in viscous medium

Biological growth is a common phenomenon in nature, and some organisms such as DNA molecules and bacterial filaments grow in viscous media. The growth induced instability of morphoelastic rod in a viscous medium is studied in this paper. Based on the Kirchhoff kinetic analogy method, the mechanical model for growing elastic thin rod in the viscous medium is established. A perturbation analysis is used to analyze the stability of the growing elastic rod in the viscous medium. We apply the results into planar growing ring and get its criterion of instability. Take the criterion into DNA ring to discuss the influence of viscous resistance on its instability.     

AC losses in multifilamentary Bi(2223) tapes with an interfilamentary resistive carbonate barrier

For the most common AC application frequencies, the main component of the AC losses in multifilamentary Bi(2223) tapes are caused by hysteresis- and coupling losses. These losses can be reduced enhancing the matrix resistivity and applying a twist to the filaments. We report on the AC loss properties of 37-filament tapes with AgAu (8 wt.%) matrix, and novel 19-filament tapes with SrCO₃ barriers between the filaments. We performed transport AC loss and magnetic AC loss measurements in parallel and perpendicular magnetic fields. Both kinds of tapes were also prepared with filament twists below a twist pitch of 20 mm. The influence of the different tape modifications on the AC loss behaviour is presented and compared with theoretical models to understand the effect of the resistive matrix. In the case of magnetic AC loss measurements, reduced AC losses due to decoupled filaments were observed for the twisted tapes with a resistive matrix in low parallel fields.     

Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation

Wave propagation in ventricular muscle is rendered highly anisotropic by the intramural rotation of the fiber. This rotational anisotropy is especially important because it can produce a twist of electrical vortices, which measures the rate of rotation (in degree/mm) of activation wavefronts in successive planes perpendicular to a line of phase singularity, or filament. This twist can then significantly alter the dynamics of the filament. This paper explores this dynamics via numerical simulation. After a review of the literature, we present modeling tools that include: (i) a simplified ionic model with three membrane currents that approximates well the restitution properties and spiral wave behavior of more complex ionic models of cardiac action potential (Beeler-Reuter and others), and (ii) a semi-implicit algorithm for the fast solution of monodomain cable equations with rotational anisotropy. We then discuss selected results of a simulation study of vortex dynamics in a parallelepipedal slab of ventricular muscle of varying wall thickness (S) and fiber rotation rate (theta(z)). The main finding is that rotational anisotropy generates a sufficiently large twist to destabilize a single transmural filament and cause a transition to a wave turbulent state characterized by a high density of chaotically moving filaments. This instability is manifested by the propagation of localized disturbances along the filament and has no previously known analog in isotropic excitable media. These disturbances correspond to highly twisted and distorted regions of filament, or "twistons," that create vortex rings when colliding with the natural boundaries of the ventricle. Moreover, when sufficiently twisted, these rings expand and create additional filaments by further colliding with boundaries. This instability mechanism is distinct from the commonly invoked patchy failure or wave breakup that is not observed here during the initial instability. For modified Beeler-Reuter-like kinetics with stable reentry in two dimensions, decay into turbulence occurs in the left ventricle in about one second above a critical wall thickness in the range of 4-6 mm that matches experiment. However this decay is suppressed by uniformly decreasing excitability. Specific experiments to test these results, and a method to characterize the filament density during fibrillation are discussed. Results are contrasted with other mechanisms of fibrillation and future prospects are summarized. (c)1998 American Institute of Physics.     

Viscoelastic suppression of gravity-driven counterflow instability

Attempts to achieve "top kill" of flowing oil wells by pumping dense drilling "muds," i.e., slurries of dense minerals, from above will fail if the Kelvin-Helmholtz instability in the gravity-driven counterflow produces turbulence that breaks up the denser fluid into small droplets. Here we estimate the droplet size to be submillimeter for fast flows and suggest the addition of a shear-thickening or viscoelastic polymer to suppress turbulence. We find in laboratory experiments a variety of new physical effects for a viscoelastic shear-thickening liquid in a gravity-driven counterstreaming flow. There is a progression from droplet formation to complete turbulence suppression at the relevant high velocities. Thick descending columns show a viscoelastic analogue of the viscous buckling instability. Thinner streams form structures resembling globules on a looping filament.     

Dynamic buckling and fragmentation in brittle rods

We present experiments on the dynamic buckling and fragmentation of slender rods axially impacted by a projectile. By combining the results of Saint-Venant and elastic beam theory, we derive a preferred wavelength lambda for the buckling instability, and experimentally verify the resulting scaling law for a range of materials including teflon, dry pasta, glass, and steel. For brittle materials, buckling leads to the fragmentation of the rod. Measured fragment length distributions show two peaks near lambda/2 and lambda/4. The nonmonotonic nature of the distributions reflect the influence of the deterministic buckling process on the more random fragmentation processes.     

Three-dimensional spiral waves in an excitable reaction system: initiation and dynamics of scroll rings and scroll ring pairs

We report experimental results on spiral and scroll waves in the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction. The propagating concentration waves are detected by two-dimensional photometry and optical tomography. Wave pulses can disappear in front-to-front and front-to-back collisions. This anomaly causes the nucleation of vortices from collisions of three nonrotating waves. In three-dimensional systems, these vortices are scroll rings that rotate around initially circular filaments. Depending on reactant concentrations, the filaments shrink or expand indicating positive and negative filament tensions, respectively. Shrinkage results in vortex annihilation. Expansion is accompanied by filament buckling and bending, which is interpreted as developing Winfree turbulence. We also describe the initiation of scroll ring pairs in four-wave collisions. The two filaments are stacked on top of each other and their motion suggests filament repulsion.     

Reduction of AC losses applying novel resistive interfilamentary carbonate barriers in multifilamentary Bi(2223) tapes

Hysteresis losses and coupling losses, a main component of the AC losses in Bi(2223) tapes, can effectively be reduced by enhancing the resistivity of the matrix material between the filaments and applying a filament twist. Since through alloying the sheath, as using AgAu(8 wt.%), the resistivity can only be raised by a factor <10 (77 K), a new conductor configuration with a quite novel composite matrix having resistive SrCO₃ barriers inside the Ag matrix between the filaments was developed. These new barriers, a cheap and commercial material, withstand the tape annealing, do not react with the superconductor, sinter dense and have a good bonding to Ag. Applying two different preparation techniques for 19 filament prototype tapes, critical current densities up to 20.7 kA cm⁻² were achieved. We report on tape preparation, the effect on the phase texture and the superconducting properties of such barrier tapes.     

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The high speed CCD visible-light camera system has been installed to detect the dynamic characteristics of ELMs filaments on EAST tokamak. In order to convert the CCD video imaging coordinates into real space coordinates, the CCD system has calibrated using Tsai’s two-stage calibration technique. A raised spike in the grayscale profile, drawn by selecting the grayscale value of the image in the vertical direction of the ELMs filament in the CCD image, represents an ELMs filament structure whose positional coordinates are determined by the apex of the spike. The Sobel edge detection operator was used to examine the edge profile of the filament to obtain the width of the filament. By analyzing the characteristics of the filament width of the ELMs, it is found that the width of ELMs filaments continuously decreases outward from the outermost magnetic surface. This indicates that the filaments continue to dissipate energy and particles as they propagate outward. The width of filaments of Type-I ELMs is greater than that of Type-III ELMs.     

EAST 装置边缘局域模细丝宽度的高速CCD可见光相机系统诊断

利用高速CCD 可见光相机系统研究了EAST 上的边缘局域模(ELMs)细丝动力学特性。采用Tsai 两步标定法对CCD 相机进行标定,以实现将CCD 图像坐标转换为真实空间坐标。选取CCD 图像中与边缘局域模细丝垂直方向上的图像灰度值,绘制了灰度分布图。灰度分布图中的一个凸起的尖峰代表了一条边缘局域模细丝结构,细丝的位置坐标由尖峰顶点确定。运用Sobel 边缘检测算子检测细丝边缘轮廓,从而得到细丝的宽度。通过对边缘局域模细丝宽度特性的分析,发现边缘局域模细丝在从最外层封闭磁面向外传播的过程中宽度不断减小。这表明细丝在向外传播的过程中其能量和粒子不断耗散。I-型边缘局域模的细丝宽度比III-型边缘局域模细丝的宽度更大。     

Limits of filopodium stability

Filopodia are long, fingerlike membrane tubes supported by cytoskeletal filaments. Their shape is determined by the stiffness of the actin filament bundles found inside them and by the interplay between the surface tension and bending rigidity of the membrane. Although one might expect the Euler buckling instability to limit the length of filopodia, we show through simple energetic considerations that this is in general not the case. By further analyzing the statics of filaments inside membrane tubes, and through computer simulations that capture membrane and filament fluctuations, we show under which conditions filopodia of arbitrary lengths are stable. We discuss several in vitro experiments where this kind of stability has already been observed. Furthermore, we predict that the filaments in long, stable filopodia adopt a helical shape.     

Quantized Superfluid Vortex Filaments Induced by the Axial Flow Effect

We report the quantized superfluid vortex filaments induced by the axial flow effect, which exhibit intriguing loop structures on helical vortexes. Such new vortex filaments correspond to a series of soliton excitations including the multipeak soliton, W-shaped soliton, and anti-dark soliton, which have no analogue when the axial flow effect is absent. In particular, we show that the vortex filaments induced by the multipeak soliton and W-shaped soliton arise from the dual action of bending and twisting of the vortex, while the vortex filament induced by the anti-dark soliton is caused only by the bending action, which is consistent with the case of the standard bright soliton. These results will deepen our understanding of breather-induced vortex filaments and will be helpful for controllable ring-like excitations on vortices.