Compressing a rigid filament: Buckling and cyclization

We study elastic properties of rigid filaments modeled as stiff chains shorter than their persistence length. By rigid filaments we mean that fluctuations around the optimal filament shape are weak and that low-order expansions (quadratic or quartic) in the deviation from the optimal shape are sufficient to describe them. Our main interest lies in the profiles of force vs. projected filament length, closure probability and weakly buckled states. Results may be relevant to experiments on self-assembled biological (microtubules, actin filaments) and synthetic (organo-gelators) filaments, carbon nanotubes and polymers grafted with strongly repelling side chains, some of which are discussed here.     

Hydrodynamic induced deformation and orientation of a microscopic elastic filament

We describe simulations of an elastic filament immersed in a fluid and subjected to a body force. The coupling between the fluid flow and the friction that the filament experiences induces bending and alignment perpendicular to the force. With increasing force there are four shape regimes, ranging from slight distortion to an unsteady tumbling motion. We also find marginally stable structures. The instability of these shapes and the alignment are explained by induced bending and nonlocal hydrodynamic interactions. These effects are experimentally relevant for stiff microfilaments.     

Harmonically Confined, Semiflexible Polymer in a Channel: Response to a Stretching Force and Spatial Distribution of the Endpoints

We consider an inextensible, semiflexible polymer or worm-like chain which is confined in the transverse direction by a parabolic potential and subject to a longitudinal force at the ends, so that the polymer is stretched out and backfolding is negligible. Simple analytic expressions for the partition function, valid in this regime, are obtained for chains of arbitrary length with a variety of boundary conditions at the ends. The spatial distribution of the end points is also analyzed.     

Force distributions and force chains in random stiff fiber networks

We study the elasticity of random stiff fiber networks. The elastic response of the fibers is characterized by a central force stretching stiffness as well as a bending stiffness that acts transverse to the fiber contour. Previous studies have shown that this model displays an anomalous elastic regime where the stretching mode is fully frozen out and the elastic energy is completely dominated by the bending mode. We demonstrate by simulations and scaling arguments that, in contrast to the bending dominated elastic energy, the equally important elastic forces are to a large extent stretching dominated. By characterizing these forces on microscopic, mesoscopic and macroscopic scales we find two mechanisms of how forces are transmitted in the network. While forces smaller than a threshold F_c are effectively balanced by a homogeneous background medium, forces larger than F_c are found to be heterogeneously distributed throughout the sample, giving rise to highly localized force chains known from granular media.     

A General Random Walk Model of Molecular Motor

A general random walk model framework is presented which can be used to statistically describe the internal dynamics and external mechanical movement of molecular motors along filament track. The motion of molecular motor in a periodic potential and a constant force is considered. We show that the molecular motor‘s movement becomes slower with the potential barrier increasing, but if the force is increased, the molecular motor‘‘s movement becomes faster. The relation between the effective rate constant and the potential battler‘s height, and that between the effective rate constant and the value of the force are discussed. Our results are consistent with the experiments and relevant theoretical consideration, and can be used to explain some physiological phenomena.     

Elasticity of a Filament with Kinks

Using the wormlike chain model, we analytically study the elasticity of a filament with kinks. We calculate the position probability density function and the force constant of a kinked filament with a general kink angle. Then, using the mathematical induction, we obtain the positional-orientational probability density function of a filament with regular kinks. For this filament, we compute the force constant in two different directions. In longitudinal direction of the filament, the force constant is proportional to the inverse of the number of the segments, i.e., 1 / m, while in transverse direction, it is proportional to \(1/m^3\).     

A General Random Walk Model of Molecular Motor

A general random walk model framework is presented which can be used to statistically describe the internaldynamics and external mechanical movement of molecular motors along filament track. The motion of molecular motorin a periodic potential and a constant force is considered. We show that the molecular motor‘s movement becomesslower with the potential barrier increasing, but if the forceis increased, the molecular motor‘s movement becomesfaster. The relation between the effective rate constant and the potential barrier‘s height, and that between the effectiverate constant and the value of the force are discussed. Our results are consistent with the experiments and relevanttheoretical consideration, and can be used to explain some physiological phenomena.     

Entropy production of Brownian macromolecules with inertia

We investigate the nonequilibrium steady-state thermodynamics of single Brownian macromolecules with inertia under feedback control in an isothermal ambient fluid. With the control being represented by a velocity-dependent external force, we find such an open system can have a negative entropy production rate, and we develop a mesoscopic theory consistent with the second law. We propose an equilibrium condition and define a class of external force, which includes the transverse Lorentz force, leading to equilibrium.     

Transverse migration of a confined polymer driven by an external force

We demonstrate that a polymer confined to a narrow channel migrates towards the center when driven by an external force parallel to the channel walls. This migration results from asymmetric hydrodynamic interactions between polymer segments and the confining walls. A weak pressure-driven flow, applied in the same direction as the external force, enhances the migration. However, when the pressure gradient and the external force act in opposite directions the polymer can migrate towards the boundaries. Nevertheless, for sufficiently strong forces the polymer always migrates towards the center. A dumbbell kinetic theory explains these results qualitatively. A comparison of our results with experimental measurements on DNA suggests that hydrodynamic interactions in polyelectrolytes are only partially screened. We propose new experiments and analysis to investigate the extent of the screening in polyelectrolyte solutions.     

Convective terms and transversely driven charge-density waves

We derive the convective terms in the damping which determine the structure of the moving charge-density wave (CDW), and study the effect of a current flowing transverse to conducting chains on the CDW dynamics along the chains. In contrast to a recent prediction we find that the effect is orders of magnitude smaller, and that contributions from transverse currents of electron- and holelike quasiparticles to the force exerted on the CDW along the chains act in the opposite directions. We discuss recent experimental verification of the effect and demonstrate experimentally that geometry effects might mimic the transverse current effect.     

Dynamics of an ion flow in an electron layer

We study the acceleration of an ion flow in the electron layer formed by an electron flow moving in a transverse electric field and confined by the intrinsic magnetic field. The possibility of extraction of heavy ions with velocities lower than the ion sound velocity from the plasma, and the feasibility of their further acceleration by an external field is demonstrated.     

‘Confined coherence’ in strongly correlated anisotropic metals

We present a detailed discussion of both theoretical and experimental evidence in favour of the existence of states of ‘confined coherence’ in metals of sufficiently high anisotropy and with sufficiently strong correlations. The defining property of such a state is that single electron coherence is confined to lower dimensional subspaces (planes or chains) so that it is impossible to observe interference effects between histories which involve electrons moving between these subspaces. The most dramatic experimental manifestation of such a state is the coexistence of incoherent non-metallic transport in one or two directions (transverse to the lower dimensional subspaces) with coherent transport in at least one other direction (within the subspaces). The magnitude of the Fermi surface warping due to transverse (intersubspace) momentum plays the role of an order parameter (in a state of confined coherence, this order parameter vanishes) and the effect can occur in a pure system at zero temperature. Our theoretical approach is to treat an anisotropic two (2D)- or three (3D)-dimensional electronic system as a collection of one (1D)- or two-dimensional electron liquids coupled by weak interliquid single-particle hopping. We find that a necessary condition for the destruction of coherent interliquid transport is that the intraliquid state be a non-Fermi liquid. We present a very detailed discussion of coupled 1D Luttinger liquids and the reasons for believing in the existence of a phase of confined coherence in that model. This provides a paradigm for incoherent transport between weakly coupled 2D non-Fermi liquids, the case relevant to the experiments of which we are aware. Specifically, anomalous transport data in the (normal state of the) cuprate superconductors and in the low temperature metallic state of the highly anisotropic organic conductor (TMTSF)₂PF₆ cannot be understood within a Fermi liquid framework, and, we argue, the only plausible way to understand that transport is in terms of a state of confined coherence.     

Growth of attached actin filaments

In several studies of actin-based cellular motility, the barbed ends of actin filaments have been observed to be attached to moving obstacles. Filament growth in the presence of such filament-obstacle interactions is studied via Brownian dynamics simulations of a three-dimensional energy-based model. We find that with a binding energy greater than 24k _B T and a highly directional force field, a single actin filament is able to push a small obstacle for over a second at a speed of half of the free filament elongation rate. These results are consistent with experimental observations of plastic beads in cell extracts. Calculations of an external force acting on a single-filament-pushed obstacle show that for typical in vitro free-actin concentrations, a 3pN pulling force maximizes the obstacle speed, while a 4pN pushing force almost stops the obstacle. Extension of the model to treat beads propelled by many filaments suggests that most of the propulsive force could be generated by attached filaments.     

Soliton delay line based on a semiconductor superlattice

A new type of delay line intended for soliton pulses is proposed. As a nonlinear medium, a semiconductor superlattice is taken. Solitons that propagate along the superlattice layers are confined in cells bounded by transverse inhomogeneity layers. Solitons are confined and released with the help of an external electric current passing inside the cell.     

Confined space and effective interactions of multiple self-avoiding chains

We study the link between three seeming-disparate cases of self-avoiding polymers: strongly overlapping multiple chains in dilute solution, chains under spherical confinement, and the onset of semidilute solutions. Our main result is that the free energy for overlapping n chains is independent of chain length and scales as n9/4, slowly crossing over to n3, as n increases. For strongly confined polymers inside a spherical cavity, we show that rearranging the chains does not cost an additional free energy. Our results imply that, during cell cycle, global reorganization of eukaryotic chromosomes in a large cell nucleus could be readily achieved.     

VIBRATION SUPPRESSION OF A BEAM STRUCTURE BY INTERMEDIATE MASSES AND SPRINGS

A method based on the dynamic Green function has been proposed to determine the optimum values of masses and/or springs and their locations on a beam structure in order to confine the vibration at an arbitrary location. In the analysis, the beam is driven by a harmonic external excitation. The added masses on the beam and the springs attached are modelled as simple reactions that provide transverse forces to the beam. These forces act as secondary forces that reduce the response caused by the external force. Numerical simulation shows that the vibration of the beam can be confined in a certain region by the presence of masses and springs in best arrangement. This method is demonstrated for both a simply supported and a cantilever beam. An experimental set-up was designed in which a simply supported beam is excited by an electrodynamic shaker and the response of the beam is measured using an He-Ne laser system. This assures very accurate measurements and avoids any additional loading effects as in the case of accelerometers. Comparisons of the theoretical and the experimental results show good agreement.     

Self-healing femtosecond light filaments

A recent experiment [Appl. Phys. Lett. 83, 213 (2003)] indicated that filaments created in femtosecond high-power pulses propagating in air are surprisingly robust when interacting with microscopic water droplets. We present numerical modeling of the dynamics of the filament-droplet interaction. Our simulation results provide further insight into the interplay between the filament's core and the wide transverse pedestal of the pulse. It is shown that the robustness of the filament comes from the transverse low-intensity pedestal that controls the formation of the central hot spot. Implications for penetration of wide, high-power beams through obscurants are discussed.     

Coupling of transverse and longitudinal response in stiff polymers

The time-dependent transverse response of stiff inextensible polymers is well understood on the linear level, where transverse and longitudinal displacements evolve independently. We show that for times beyond a characteristic time tf, longitudinal friction considerably weakens the response compared to the widely used linear response predictions. The corresponding feedback mechanism is explained by scaling arguments and quantified by a systematic theory. Our scaling laws and exact solutions for the transverse response apply to cytoskeletal filaments as well as DNA under tension.     

外力驱动作用下高分子链在表面吸附性质的计算机模拟

采用退火法模拟研究受外力F驱动的高分子链在吸引表面的吸附特性.通过高分子链的平均表面接触数〈M〉与温度T之间的关系计算临界吸附温度T_c,并发现T_c随着F的增加而减小;进而通过高分子链的均方回转半径分析外力驱动作用对高分子链构象的影响,并从回转半径极小值或者垂直外力方向的y和z分量的变化交叉校验临界吸附点T_c.模拟计算了处于吸附状态的高分子链随着外力F的增加是否会发生吸附状态到脱附状态的相变以及发生相变所需施加的外力是否由温度所决定.模拟结果表明:两种不同温度下高分子链的吸附性质和构象性质受外力驱动作用而产生不同现象,在温度区间T*_cTT_c时会发生脱附现象,而在TT*_c时不会发生脱附现象.