Multifilament Model Research Articles

Theoretical relationships between axoneme distortion and internal forces and torques in ciliary beating.

The axoneme is an intricate nanomachine responsible for generating the propulsive oscillations of cilia and flagella in an astonishing variety of organisms. New imaging techniques based on cryoelectron-tomography (cryo-ET) and subtomogram averaging have revealed the detailed structures of the axoneme and its components with sub-nm resolution, but the mechanical function of each component and how the assembly generates oscillations remains stubbornly unclear. Most explanations of oscillatory behavior rely on the dynamic regulation of dynein by some signal, but this may not be necessary if the system of dynein-driven slender filaments is dynamically unstable. Understanding the possibility of instability-driven oscillations requires a multifilament model of the axoneme that accounts for distortions of the axoneme as it bends. Active bending requires forces and bending moments that will tend to change the spacing and alignment of doublets. We hypothesize that components of the axoneme resist and respond to these loads in ways that are critical to beating. Specifically, we propose (i) that radial spokes provide torsional stiffness by resisting misalignment (as well as spacing) between the central pair and outer doublets, and (ii) that the kinematics of dynein arms affect the relationships between active forces and bending moments on deforming doublets. These proposed relationships enhance the ability of theoretical, multifilament models of axonemal beating to generate propulsive oscillatory waveforms via dynamic mechanical instability.

Generation of ciliary beating by steady dynein activity: the effects of inter-filament coupling in multi-filament models.

The structure of the axoneme in motile cilia and flagella is emerging with increasing detail from high-resolution imaging, but the mechanism by which the axoneme creates oscillatory, propulsive motion remains mysterious. It has recently been proposed that this motion may be caused by a dynamic 'flutter' instability that can occur under steady dynein loading, and not by switching or modulation of dynein motor activity (as commonly assumed). In the current work, we have built an improved multi-filament mathematical model of the axoneme and implemented it as a system of discrete equations using the finite-element method. The eigenvalues and eigenvectors of this model predict the emergence of oscillatory, wave-like solutions in the absence of dynein regulation and specify the associated frequencies and waveforms of beating. Time-domain simulations with this model illustrate the behaviour predicted by the system's eigenvalues. This model and analysis allow us to efficiently explore the potential effects of difficult to measure biophysical parameters, such as elasticity of radial spokes and inter-doublet links, on the ciliary waveform. These results support the idea that dynamic instability without dynamic dynein regulation is a plausible and robust mechanism for generating ciliary beating.

Optimization of finite-build stellarator coils

Finding coil sets with desirable physics and engineering properties is a crucial step in the design of modern stellarator devices. Existing stellarator coil optimization codes ultimately produce zero-thickness filament coils. However, stellarator coils have finite depth and thickness, which can make the single-filament model a poor approximation, particularly when coil build dimensions are relatively large compared to the coil–plasma distance. In this paper, we present a new method for designing coils with finite builds and present a mechanism to optimize the orientation of the winding pack. We approximate finite-build coils with a multi-filament model. A numerical implementation has been developed, and applications to the Helically Symmetric eXperiment stellarator and a new UW-Madison quasihelically symmetric configuration are shown.

Electrical model of multi-level bipolar Ta2O5/TaOx Bi-layered ReRAM

An electrical model of a multi-level Ta2O5/TaOx resistive random-access memory (ReRAM) has been presented. The model is based on tunnelling current which is the dominant conduction mechanism at 3–4 nm oxide layer thickness. The presented model is capable of multi-level switching with four resistance states (LRS≈10 kΩ, IRS-1≈13 kΩ, IRS-2≈20 kΩ, and HRS≈50 kΩ). IRS-1 is achieved between 1.5 V and 1.6 V, IRS-2 is achieved between 1.6 V and 1.8 V, and HRS is achieved above 1.8 V. A comparison with experimental results is conducted and IRS-1 differs by 30.35% while IRS-2 matches well. The simulation results of the presented model show that during RESET phase, the multifilament ReRAM has higher current than the single filament ReRAM. In addition, the presented model successfully displays multi-level behaviour under sine, triangular, and pulse input voltages. Two pulse schemes are analyzed for multi-level switching; an extra resistance state is successfully achieved in one while the other is unfeasible for multi-level applications in the multi-filament model.

Improved Methodology to Estimate the Power Transfer Efficiency in an Inductively Coupled Radio Frequency Ion Source

The International Thermonuclear Experimental Reactor neutral beam injector includes an ion source which can produce D− ion beams for 1 h, accelerated at the energy of 1 MeV. An ion source consists of a driver where the plasma is produced by the application of the radio frequency (RF) power to an inductive coil. This paper presents an improved methodology which provides an estimation of the power transfer efficiency to the plasma of the driver. The developed methodology is based on different mechanisms which are responsible for the plasma heating (ohmic and stochastic) and an electrical model describing the power transfer to the plasma. As a first approximation in a previous work, a transformer model was assumed as an electrical model. In this paper, a main improvement is introduced based on the development of a multi-filament model which takes into account the mutual coupling between the RF coil, the plasma, and the passive metallic structure. The methodology is applied to the negative ion optimization 1 (NIO1), a flexible negative ion source, currently in operation at Consorzio RFX, Italy. The results from the two models, transformer and multi-filament, are presented and compared in terms of plasma equivalent resistance and power transfer efficiency. It is found that results obtained from both the transformer and the multi-filament model follow the same trend in comparison with the applied frequency and the other plasma parameters like electron density, temperature, and gas pressure. However, lower values of the plasma equivalent resistance and power transfer efficiency are observed with the multi-filament model. The multi-filament model reproduces a more realistic experimental scenario where the power losses due to the generation of the eddy currents in the metallic structure are considered.

Effects of cross-bridge compliance on the force-velocity relationship and muscle power output.

Muscles produce force and power by utilizing chemical energy through ATP hydrolysis. During concentric contractions (shortening), muscles generate less force compared to isometric contractions, but consume greater amounts of energy as shortening velocity increases. Conversely, more force is generated and less energy is consumed during eccentric muscle contractions (lengthening). This relationship between force, energy use, and the velocity of contraction has important implications for understanding muscle efficiency, but the molecular mechanisms underlying this behavior remain poorly understood. Here we used spatially-explicit, multi-filament models of Ca2+-regulated force production within a half-sarcomere to simulate how force production, energy utilization, and the number of bound cross-bridges are affected by dynamic changes in sarcomere length. These computational simulations show that cross-bridge binding increased during slow-velocity concentric and eccentric contractions, compared to isometric contractions. Over the full ranges of velocities that we simulated, cross-bridge cycling and energy utilization (i.e. ATPase rates) increased during shortening, and decreased during lengthening. These findings are consistent with the Fenn effect, but arise from a complicated relationship between velocity-dependent cross-bridge recruitment and cross-bridge cycling kinetics. We also investigated how force production, power output, and energy utilization varied with cross-bridge and myofilament compliance, which is impossible to address under typical experimental conditions. These important simulations show that increasing cross-bridge compliance resulted in greater cross-bridge binding and ATPase activity, but less force was generated per cross-bridge and throughout the sarcomere. These data indicate that the efficiency of force production decreases in a velocity-dependent manner, and that this behavior is sensitive to cross-bridge compliance. In contrast, significant effects of myofilament compliance on force production were only observed during isometric contractions, suggesting that changes in myofilament compliance may not influence power output during non-isometric contractions as greatly as changes in cross-bridge compliance. These findings advance our understanding of how cross-bridge and myofilament properties underlie velocity-dependent changes in contractile efficiency during muscle movement.

Modeling circular inductors coupled to a semi-infinite magnetic medium considering the proximity effect

This paper presents a simple 2D electromagnetic model that solves the high-frequency current distribution, considering the proximity effect, in a planar spiral coil above a linear conductive or non-conductive semi-infinite magnetic medium. The conductive regions are divided into axisymmetric elements in which the current is assumed constant. The current flowing in each element depends on its complex impedance and is computed by Kirchhoff’s circuit law. To take the effect of the magnetic medium into account, a new set of mutual inductance formulas are presented. Those formulas are expressed in terms of elliptic integrals and the fast-converging arithmetic–geometric mean iteration of Gauss. The geometric mean distance method is used to deal with elements of arbitrarily shaped cross-section. Elliptic integrals are also used to express the magnetic flux density. The current distribution, the magnetic field and the equivalent impedance computed with the multifilament model agree well with the results obtained using commercial finite element software.

Numerical investigations on a yarn structure at the microscale towards scale transition

Since the beginning of the last decade, few examples of multifilament models for dry fabrics have been presented in literature. This work deals with the simulation of a single yarn subjected to transverse impact. Inspired by the models previously developed by other authors, a revisited form of Discrete Element Method has been adopted to perform microscopic analyses in a more efficient computational environment. Transverse impact analysis onto a single KEVLAR KM2 yarn has been performed using this approach. Truss elements have been adopted to discretize yarn filaments instead of heavy computational 3D finite elements. A good agreement with literature results has been achieved with an important reduction of computational resource. In the end, a proposed scale transition is discussed.

Filamentary model of bipolar resistive switching in capacitor-like memristive nanostructures on the basis of yttria-stabilised zirconia

A filamentary model of bipolar resistive switching has been developed for the Au/ZrO2(Y)/TiN/Ti memristive nanostructures by using kinetic Monte-Carlo approach for the migration of oxygen vacancies at the stages of electroforming, SET, and RESET processes observed experimentally in the current-voltage switching hysteresis. Statistics of the forming and switching voltages are collected and used to simulate current-voltage characteristics based on a simplified multi-filament model. It is demonstrated that both abrupt and gradual switching behaviours can be determined by the parameters of the statistical distribution of switching voltages of different conductive channels - filaments. The results can be used for the development of new-generation nonvolatile memory.

Magnetic susceptibility anisotropy of myocardium imaged by cardiovascular magnetic resonance reflects the anisotropy of myocardial filament α-helix polypeptide bonds.

BackgroundA key component of evaluating myocardial tissue function is the assessment of myofiber organization and structure. Studies suggest that striated muscle fibers are magnetically anisotropic, which, if measurable in the heart, may provide a tool to assess myocardial microstructure and function.MethodsTo determine whether this weak anisotropy is observable and spatially quantifiable with cardiovascular magnetic resonance (CMR), both gradient-echo and diffusion-weighted data were collected from intact mouse heart specimens at 9.4 Tesla. Susceptibility anisotropy was experimentally calculated using a voxelwise analysis of myocardial tissue susceptibility as a function of myofiber angle. A myocardial tissue simulation was developed to evaluate the role of the known diamagnetic anisotropy of the peptide bond in the observed susceptibility contrast.ResultsThe CMR data revealed that myocardial tissue fibers that were parallel and perpendicular to the magnetic field direction appeared relatively paramagnetic and diamagnetic, respectively. A linear relationship was found between the magnetic susceptibility of the myocardial tissue and the squared sine of the myofiber angle with respect to the field direction. The multi-filament model simulation yielded susceptibility anisotropy values that reflected those found in the experimental data, and were consistent that this anisotropy decreased as the echo time increased.ConclusionsThough other sources of susceptibility anisotropy in myocardium may exist, the arrangement of peptide bonds in the myofilaments is a significant, and likely the most dominant source of susceptibility anisotropy. This anisotropy can be further exploited to probe the integrity and organization of myofibers in both healthy and diseased heart tissue.

Insight into distribution and switching of resistive random-access memory filaments based on analysis of variations in memory characteristics

Two hypotheses were formulated to validate a multi-filament model (MFM) as a mechanism for the cycle-to-cycle dispersion of Vset in resistive random-access memory. The first is that the probability of Δ(1/Vset) > 0, P[Δ(1/Vset) > 0], increases with the number of filaments in one memory cell, Nfila, and decreases with increasing switching cycle, n. Here, Δ(1/Vset) is the difference between the inverse of the set voltages after the n-th and (n + 1)-th reset processes [1/Vset(n) − 1/Vset(n + 1)]. Thus, Vset decreases with increasing Nfila and increases with n. The second hypothesis is that the probability of Δ(1/R) > 0, P[Δ(1/R) > 0], agrees with P[Δ(1/Vset) > 0], assuming that vset depends on d in the MFM. Here, Δ(1/R) = 1/Rn − 1/Rn + 1, and Rn, vset, and d represent the resistance in the high-resistance state after the n-th reset process, the set voltage of each filament, and the thickness of a gap between the electrode and the end of the filament, respectively. The validity of these two hypotheses was confirmed by measuring the dependence of P[Δ(1/Vset) > 0], P[Δ(1/R) > 0], and the mean value of Vset on both n and the length of the perimeter for Pt/NiO/Pt structures into which filaments were introduced by etching the NiO layer.

Filament Compliance Influences Cooperative Activation of Thin Filaments and the Dynamics of Force Production in Skeletal Muscle

Striated muscle contraction is a highly cooperative process initiated by Ca2+ binding to the troponin complex, which leads to tropomyosin movement and myosin cross-bridge (XB) formation along thin filaments. Experimental and computational studies suggest skeletal muscle fiber activation is greatly augmented by cooperative interactions between neighboring thin filament regulatory units (RU-RU cooperativity; 1 RU = 7 actin monomers+1 troponin complex+1 tropomyosin molecule). XB binding can also amplify thin filament activation through interactions with RUs (XB-RU cooperativity). Because these interactions occur with a temporal order, they can be considered kinetic forms of cooperativity. Our previous spatially-explicit models illustrated that mechanical forms of cooperativity also exist, arising from XB-induced XB binding (XB-XB cooperativity). These mechanical and kinetic forms of cooperativity are likely coordinated during muscle contraction, but the relative contribution from each of these mechanisms is difficult to separate experimentally. To investigate these contributions we built a multi-filament model of the half sarcomere, allowing RU activation kinetics to vary with the state of neighboring RUs or XBs. Simulations suggest Ca2+ binding to troponin activates a thin filament distance spanning 9 to 11 actins and coupled RU-RU interactions dominate the cooperative force response in skeletal muscle, consistent with measurements from rabbit psoas fibers. XB binding was critical for stabilizing thin filament activation, particularly at submaximal Ca2+ levels, even though XB-RU cooperativity amplified force less than RU-RU cooperativity. Similar to previous studies, XB-XB cooperativity scaled inversely with lattice stiffness, leading to slower rates of force development as stiffness decreased. Including RU-RU and XB-RU cooperativity in this model resulted in the novel prediction that the force-[Ca2+] relationship can vary due to filament and XB compliance. Simulations also suggest kinetic forms of cooperativity occur rapidly and dominate early to get activation, while mechanical forms of cooperativity act more slowly, augmenting XB binding as force continues to develop.

Insight into Distribution and Switching of ReRAM Filaments Based on Variation Analysis of Memory Characteristics

ABSTRACTA hypothesis that probability giving Δ(1/Vset) [= 1/Vset(n) - 1/Vset(n+1)] > 0, P[Δ(1/Vset) > 0], increases with increasing the number of filaments contained in one memory cell, Nfila, and decreases with increasing switching cycle, n, was made to validate a multi-filament model (MFM) as a mechanism causing the cycle to cycle dispersion of Vset in ReRAM. Here, Δ(1/Vset) is the difference between the inverse of set voltages after n-th and (n+1)-th reset processes. This in turn means that Vset will decrease with increasing Nfila and will increase with increasing n. In addition, another hypothesis that probability giving Δ(1/R) [= 1/Rn - 1/Rn+1] > 0, P[Δ(1/R) > 0], agrees with P[Δ(1/Vset) > 0] was made by incorporating the assumption that vset depends on d with the MFM. Here, Rn, vset, and d represent resistance in high resistance state after the n-th reset process, the set voltage of each filament, and the thickness of a gap between the electrode and the edge of the filament. The validity of these two hypotheses were confirmed by measuring the dependence of P[Δ(1/Vset) > 0], P[Δ(1/R) > 0], and the mean value of Vset, <Vset>, on both the length of the perimeter, L, and n of Pt/NiO/Pt structures to which filaments were introduced by etching the NiO layer.

Opposing Theories and the Buckling Strength of Unequal-Leg Angle Columns

A structural engineer wishing to determine the buckling load of unequal-leg angle columns receives conflicting information from published literature because researchers offer two radically different models for their analyses of thin-walled open-profile bars. One model considers the bar to be a continuum whereas the American Institute of Steel Construction adopts a noncontinuum multifilament model. Furthermore, the continuum model defines the normal planes of the deflected bar with the line of centroids whereas the multifilament model uses the shear center line. A test program based on 5×3×1/4 in. (127×76×6 mm) steel angles is proposed to resolve the issue by determining which model produces computed buckling loads that better correlate with collapse loads obtained from tests. The possibility that neither method produces a buckling load that correlates with collapse loads is not ruled out.

Resistive Switching and Memory Effect Based on CuSCN Complex Layer Created Through Interface Reactions

The preparation of copper(I) thiocyanate composite layers through vacuum evaporation of potassium thiocyanate onto a copper layer was investigated. The formation of CuSCN composite film was characterized, and plausible interface reactions were suggested. The Cu/CuSCN composite layer/Al cell exhibited reversible electrical bistability, with an on/off ratio of 10 5 -10 6 . The resistive switch mechanism was interpreted with the formation-rupture multifilament model through electrochemical reactions. The low- and high-resistance states follow ohmic conduction and trap-charge-limited conduction, respectively. The CuSCN medium layer and the interface between CuSCN and Cu electrode are proposed to be responsible for nonvolatile memory effect.

Modeling of multifilament PET fiber melt‐spinning

AbstractA fundamental issue in the polymer fiber melt‐spinning process is the control of final properties. Most available melt‐spinning models simulate only a single fiber, providing an incomplete representation of the actual industrial multifilament process. Variations across the fiber bundle in cooling air velocity and temperature result in nonuniformity in fiber properties. Simulation can provide insight into this cause‐and‐effect relationship and lead to better process design to control differences between fibers. The few multifilament models in existence typically use a Newtonian constitutive model for the polymer, failing to capture nonlinear effects which often play a significant role in the process. Experimental validation of multifilament simulation is lacking. We present a nonisothermal multifilament spinning model, applicable for a variety of polymer and process conditions. The model combines the flow‐enhanced crystallization (FEC) fiber spinning model of McHugh et al. with a generalization of Dutta's multifilament model. The model predicts fiber properties such as stress, degree of crystallinity, fiber radius and temperature as a function of distance from the spinneret, along with quench air cross velocity and temperature throughout the fiber bundle region. The McHugh FEC model for single fiber spinning, based on a modified Giesekus constitutive model and Avrami‐type crystallization kinetics, has been experimentally validated. In this work we show that results of the multifilament quench air model compare favorably to experimental measurements. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008

Plasma reconstruction in tokamaks with linearized approaches

This paper deals with the problem of the equilibrium reconstruction in a tokamak. We firstly describe two approaches for the shape reconstruction: the former based on a nonlinear least square minimization with Finite Element Method modelling taking into account the Grad Shafranov equilibrium equation; the latter based on linear multifilament models accounting for the presence of iron, eddy currents in the passive structures, and plasma. A possible unified treatment for shape and current profile reconstruction using both internal and external measurements is then discussed: the nonlinear least square minimization procedure used for shape identification is modified to account for internal measurements and profile shape fitting. A linearized approach is finally analysed making use of Singular Value Decomposition theory. Some results on the JET tokamak are shown and discussed.

Sarcomere Lattice Geometry Influences Cooperative Myosin Binding in Muscle

In muscle, force emerges from myosin binding with actin (forming a cross-bridge). This actomyosin binding depends upon myofilament geometry, kinetics of thin-filament Ca2+ activation, and kinetics of cross-bridge cycling. Binding occurs within a compliant network of protein filaments where there is mechanical coupling between myosins along the thick-filament backbone and between actin monomers along the thin filament. Such mechanical coupling precludes using ordinary differential equation models when examining the effects of lattice geometry, kinetics, or compliance on force production. This study uses two stochastically driven, spatially explicit models to predict levels of cross-bridge binding, force, thin-filament Ca2+ activation, and ATP utilization. One model incorporates the 2-to-1 ratio of thin to thick filaments of vertebrate striated muscle (multi-filament model), while the other comprises only one thick and one thin filament (two-filament model). Simulations comparing these models show that the multi-filament predictions of force, fractional cross-bridge binding, and cross-bridge turnover are more consistent with published experimental values. Furthermore, the values predicted by the multi-filament model are greater than those values predicted by the two-filament model. These increases are larger than the relative increase of potential inter-filament interactions in the multi-filament model versus the two-filament model. This amplification of coordinated cross-bridge binding and cycling indicates a mechanism of cooperativity that depends on sarcomere lattice geometry, specifically the ratio and arrangement of myofilaments.

Multifilament Model of PET Melt Spinning and Prediction of As‐spun Fiber's Quality

Based on the multifilament model with cross air blowing proposed by Dutta (1987) and the assumption that the quench air temperature around the filament obeys an exponential distribution, a multifilament model suitable for the annular air blowing condition of PET staple fiber melt spinning is proposed. The quench air velocity, quench air temperature, filament velocity, filament temperature, etc. at different positions were predicted and the relation between birefringence and the important quality index of as‐spun fiber, Eys1.5 (elongation corresponding to 1.5 times the yielding stress in a stress‐strain curve) was obtained through experiment. The as‐spun fiber properties of PET staple and its variability were predicted and the effects of spinning conditions and spinneret design on as‐spun fiber properties were discussed and verified.

A Spatially Explicit Nanomechanical Model of the Half-Sarcomere: Myofilament Compliance Affects Ca2+-Activation

The force exerted by skeletal muscle is modulated by compliance of tissues to which it is connected. Force of the muscle sarcomere is modulated by compliance of the myofilaments. We tested the hypothesis that myofilament compliance influences Ca2+ regulation of muscle by constructing a computational model of the muscle half sarcomere that includes compliance of the filaments as a variable. The biomechanical model consists of three half-filaments of myosin and 13 thin filaments. Initial spacing of motor domains of myosin on thick filaments and myosin-binding sites on thin filaments was taken to be that measured experimentally in unstrained filaments. Monte-Carlo simulations were used to determine transitions around a three-state cycle for each cross-bridge and between two-states for each thin filament regulatory unit. This multifilament model exhibited less "tuning" of maximum force than an earlier two-filament model. Significantly, both the apparent Ca(2+)-sensitivity and cooperativity of activation of steady-state isometric force were modulated by myofilament compliance. Activation-dependence of the kinetics of tension development was also modulated by filament compliance. Tuning in the full myofilament lattice appears to be more significant at submaximal levels of thin filament activation.