Shape transition and propulsive force of an elastic rod rotating in a viscous fluid

The deformation of an elastic rod rotating in a viscous fluid is considered, with applications related to flagellar motility. The rod is tilted relative to the rotation axis, and experiments and theory are used to study the shape transition when driven either at constant torque or at constant speed. At low applied torque, the rod bends gently and generates small propulsive force. At a critical torque, the rotation speed increases abruptly, and the rod forms a helical shape with increased propulsive force. We find good agreement between theory and experiment. A simple physical model is presented to capture and explain the essential behavior.     

Fluid transport at low Reynolds number with magnetically actuated artificial cilia

By numerical modeling we investigate fluid transport in low-Reynolds-number flow achieved with a special elastic filament or artifical cilium attached to a planar surface. The filament is made of superparamagnetic particles linked together by DNA double strands. An external magnetic field induces dipolar interactions between the beads of the filament which provides a convenient way of actuating the cilium in a well-controlled manner. The filament has recently been used to successfully construct the first artificial micro-swimmer (R. Dreyfus et al., Nature 437, 862 (2005)). In our numerical study we introduce a measure, which we call pumping performance, to quantify the fluid transport induced by the magnetically actuated cilium and identify an optimum stroke pattern of the filament. It consists of a slow transport stroke and a fast recovery stroke. Our detailed parameter study also reveals that for sufficiently large magnetic fields the artificial cilium is mainly governed by the Mason number that compares frictional to magnetic forces. Initial studies on multi-cilia systems show that the pumping performance is very sensitive to the imposed phase lag between neighboring cilia, i.e., to the details of the initiated metachronal wave.     

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.     

Elasticity,fracture and thermoreversible gelation of highly filled physical gels<Superscript>⋆</Superscript>

We describe a physically associating triblock copolymer-based gel that exhibits a reversible transition between solid and liquid states at a temperature of approximately 55^°C. The thermal transition of the gel enables us to compare the properties of liquid suspensions and elastic composites with identical particle loadings, with particle volume fractions as large as 0.55. The suspension viscosity and the composite elasticity scale in a similar manner with the overall particle volume fraction, a result that is rationalized in terms of an effective strain amplification factor that depends only on the particle loading. Measured values of the strain amplification factor are in good agreement with the expected form for well-dispersed spheres. We also find that the elastic composites are exceptionally strong, with fracture strengths that exceed the modulus of the base gel by a factor of 100 or more. Deviations from purely elastic behavior became important for high particle volume fractions, and were probed by stress relaxation experiments.     

Disorder driven roughening transitions of elastic manifolds and periodic elastic media

The simultaneous effect of both disorder and crystal-lattice pinning on the equilibrium behavior of oriented elastic objects is studied using scaling arguments and a functional renormalization group technique. Our analysis applies to elastic manifolds, e.g., interfaces, as well as to periodic elastic media, e.g., charge-density waves or flux-line lattices. The competition between both pinning mechanisms leads to a continuous, disorder driven roughening transition between a flat state where the mean relative displacement saturates on large scales and a rough state with diverging relative displacement. The transition can be approached by changing the impurity concentration or, indirectly, by tuning the temperature since the pinning strengths of the random and crystal potential have in general a different temperature dependence. For D dimensional elastic manifolds interacting with either random-field or random-bond disorder a transition exists for 2<D<4, and the critical exponents are obtained to lowest order in . At the transition, the manifolds show a superuniversal logarithmic roughness. Dipolar interactions render lattice effects relevant also in the physical case of D=2. For periodic elastic media, a roughening transition exists only if the ratio p of the periodicities of the medium and the crystal lattice exceeds the critical value . For p<p _c the medium is always flat. Critical exponents are calculated in a double expansion in and and fulfill the scaling relations of random field models. Received 28 August 1998     

Elastic rod model of a supercoiled DNA molecule

We study the elastic behaviour of a supercoiled DNA molecule. The simplest model is that of a rod-like chain, involving two elastic constants, the bending and the twist rigidities. Writing this model in terms of Euler angles, we show that the corresponding Hamiltonian is singular and needs a small distance cut-off, which is a natural length scale giving the limit of validity of the model, of the order of the double-helix pitch. The rod-like chain in the presence of the cut-off is able to reproduce quantitatively the experimentally observed effects of supercoiling on the elongation-force characteristics, in the small supercoiling regime. An exact solution of the model, using both transfer matrix techniques and its mapping to a quantum mechanics problem, allows to extract, from the experimental data, the value of the twist rigidity. We also analyse the variation of the torque and the writhe-to-twist ratio versus supercoiling, showing analytically the existence of a rather sharp crossover regime which can be related to the excitation of plectoneme-like structures. Finally we study the extension fluctuations of a stretched and supercoiled DNA molecule, both at fixed torque and at fixed supercoiling angle, and we compare the theoretical predictions to some preliminary experimental data. Received 1 April 1999 and Received in final form 4 January 2000     

Multicanonical Monte Carlo simulations on intramolecular micelle formation in copolymers

The formation of intramolecular micelles in copolymers with periodic sequence, where hydrophobic units (stickers) are periodically placed along the chain, is studied by using multicanonical Monte Carlo computer simulations for an off-lattice bead-rod model in three dimensions. With decreasing the temperature, a transition from random-coil conformations to micelles occurs and flower-type micelles are formed via the transition. The number of stickers forming a micelle core is limited by the excluded-volume effect of loop chains around micelle cores. By this effect, two intramolecular micelles are formed for long polymer chains with 60 bonds via the coil-to-micelle transition. By further decreasing the temperature, we find that another transition, i.e., a micelle-to-micelle transition, takes place. At this transition point, the two intramolecular micelles merge into one micelle. Furthermore, we extend the multicanonical MC method to study elastic properties of single polymer chains with strong attractive interactions under external force fields, and study how the intramolecular micellization affects the elastic property of single polymer chains.     

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.     

c-director relaxation around a vortex of strength +1 in free-standing smectic-C films

The relaxation of director fields in freely suspended smectic films is studied experimentally by means of polarizing microscopy, and analyzed by solving the torque balance equation under appropriate initial and boundary conditions. We consider in particular the role of anchoring conditions of the c-director at particles and defects in the film. The structure of regular relaxation patterns allows to determine the elastic anisotropy of smectic materials. The splay elastic constant can exceed the bend constant by a factor of two and more. A remarkable consequence of this anisotropy is the stick-slip-like relaxation around a central defect of topological strength s = + 1.     

DMRG studies on interchain coupling model for quasi-one-dimensional organic magnet

We introduce a solid-on-solid growth process which evolves by random deposition of dimers, surface diffusion, and evaporation of monomers from the edges of plateaus. It is shown that the model exhibits a robust transition from a smooth to a rough phase. The roughening transition is driven by an absorbing phase transition at the bottom layer of the interface, which displays the same type of critical behavior as the pair contact process with diffusion 2A↦3A, 2A↦. Received 14 October 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: Haye.Hinrichsen@physik.uni-wuppertal.de     

Large momenta fluctuations of charm quarks in the Quark-Gluon Plasma<Superscript>⋆</Superscript>

We show that large fluctuations of D-mesons kinetic-energy (or momentum) distributions might be a signature of a phase transition to the Quark-Gluon Plasma (QGP). In particular, a jump in the variance of the momenta or kinetic energy, as a function of a control parameter (temperature or Fermi energy at finite baryon densities) might be a signature for a first-order phase transition to the QGP. This behavior is completely consistent with the order parameter defined for a system of interacting quarks both at zero temperature (and finite baryon densities) or at finite temperatures which shows a jump in correspondence with a first-order phase transition to the QGP. The J/Ψ displays exactly the same behavior of the order parameter and of the variance of the D-mesons. We discuss implications for relativistic heavy-ion collisions within the framework of a transport model and possible hints for experimental search.     

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.     

Absence of dynamical crossover in the vortex creep near by the second peak effect in superconducting Hg-1201 single crystals

DC magnetic relaxation measurements in HgBa₂CuO₄ single crystals are analyzed nearby the fishtail line. It is found that in this case, it is not necessary to introduce any crossover from plastic creep to elastic creep models at the fishtail line. This type of fishtail effect comes only from a competition between a critical current at low temperature which increases versus field and the activation energy, which decreases versus field. According to the doping level of the compound, the fishtail effect can be observed or not, without any correlation with a vortex phase transition. Moreover, in this type of fishtail effect, there is no history effects as recently observed in YBaCu₂O₃ by the partial magnetization loop technique, suggesting that the transition from plastic to elastic flow is here hidden by the disorder of these materials. Received 11 January 2000     

Shear modulus of polydomain, mono-domain and non-mesomorphic side-chain elastomers: Influence of the nematic order

We investigate the behavior of the complex shear modulus of a series of elastomers including mono-domain and poly-domain liquid crystal samples, and a non-mesomorphic sample. We find that the dynamics of the glass transition are strongly modified by the nematic order. This result explains why the truly elastic response of liquid crystal elastomers can only be observed in the isotropic phase at very high temperatures and at very low frequencies. Between the elastic regime and the glassy state, the elastomers have a visco-elastic regime, which is characterized by a Rouse-like behavior for mono-domain and poly-domain samples, and by a Zimm-like behavior for the non-mesomorphic sample. We also show that the mono-domain sample exhibits marked anisotropy of the shear-modulus G ^′. This anisotropy, which is observed for the first time, is a function of frequency and is inverted between low and high frequencies, due to relaxation effects of the orientational order. Received 28 January 2000 and Received in final form 16 October 2000     

Energetics of 2D colloids in free-standing smectic-C films

The formation of regular colloid patterns in free-standing smectic films at the transition from the smectic-C to the isotropic or nematic phase is well known experimentally. The self-organization of isotropic or nematic droplets is caused by their mutual interaction, mediated by elastic distortions of the local director in the surrounding liquid crystal. These distortions are related to the anchoring conditions of the director at the droplet border. We describe analytically the energetics of the liquid crystal environment of a single droplet in one-constant approximation. A method of complex analysis, Conformal Mapping, is employed. Following a suggestion of Dolganov et al. (Phys. Rev. E. 73, 041706 (2006)), energetics of chain and grid patterns built from the colloids are investigated numerically in order to explain experimentally observed formations and their director fields.     

Twist of growing bacterial colonies

Twist observed in growing bacterial colonies at the macrolevel is explained in terms of the self-assembly (self-organization) of film-forming protein clusters, since the in vitro and in vivo behavior and symmetry properties of protein in an open thermodynamically nonequilibrium system are identical. The self-assembly of elastic protein films in the course of condensation in the protein-water system obeys the laws of the elasticity theory. As the viscosity of the system grows, the transition of the protein from the liquid-crystal to the solid phase occurs. This transition has a nonlinear dynamics, which also shows up at the macrolevel. Opposite vorticities (twist) appear in the system. Such a modification of protein has been named protos. It is hypothesized that the formation of an elastic nonequilibrium protos film is consistent with the behavior and orientation of elastic forces and magnetic fields in the presence of unlike electric charges.     

Two-neutron elastic transfer 4He(6He,4He)6He at E = 151 MeV

Using the framework of the coupled reaction channels (CRC) the elastic scattering and the elastic transfer in the system ⁶He + ⁴He measured at E = 151 MeV have been analysed. It is shown that the structure observed in the backward range of the angular distributions is influenced by the interference of the elastic 2n-transfer with a two-step process passing through the 2⁺ excitation in ⁶He. The two-neutron transfer mechanism is studied in the microscopic approach and it is found that for the ground-state transition the one step dominates by a factor 10 over the two-step mechanism at this energy. Received: 29 October 2001 / Accepted: 4 December 2001     

Torque equations for spin and orbital angular momenta of radiation fields and Faraday effect

The spin angular momentum S of light has never been linked to the Faraday rotation of light traveling in an optically active medium possessing a rotational invariance of a crystal, because there was no helicity term associated with the phase shift in the previous torque equation for S. In order to relate the change in S with time to the Faraday rotation, therefore, we derived an exact torque equation for S. As a result, a magnetic helicity term appeared in a new torque equation for S, so that one-half of the phase shift derived from the helicity term was equivalent to the Faraday rotation angle. However, the orbital angular momentum L had no relation to the Faraday rotation. It was thus clarified that the change in S with time is related to the Faraday rotation angle of light traveling in an optically active medium, owing to the appearance of the helicity term without a rotational invariance around the optical axis. It was also demonstrated theoretically that the Faraday rotation is accompanied by a torque acting on the crystal so that the total angular momentum of light and matter is conserved.     

He-Na2体系低温下的冷碰撞研究

在已经拟合好的He-Na₂体系势能面上,根据原子-双原子分子的非反应性碰撞动力学的相关基本理论,在空间固定坐标系下,采用严格的密耦方法求解了He原子和Na₂分子的转动非弹性碰撞动力学方程.并对He-Na₂体系的微分散射截面、积分截面作了详细的分析,结果与实验符合得比较好.结果表明：（1）弹性散射（Δj=0）截面远大于非弹性截面;（2）较小Δj的跃迁主要产生前向散射,随着Δj的增加,后向散射的几率增加 关键词： 2体系')" href="#">He-Na₂体系 密耦方法 微分散射截面 积分截面     

Electrostatic and electrokinetic contributions to the elastic moduli of a driven membrane

We discuss the electrostatic contribution to the elastic moduli of a cell or artificial membrane placed in an electrolyte and driven by a DC electric field. The field drives ion currents across the membrane, through specific channels, pumps or natural pores. In steady state, charges accumulate in the Debye layers close to the membrane, modifying the membrane elastic moduli. We first study a model of a membrane of zero thickness, later generalizing this treatment to allow for a finite thickness and finite dielectric constant. Our results clarify and extend the results presented by D. Lacoste, M. Cosentino Lagomarsino, and J.F. Joanny (EPL 77, 18006 (2007)), by providing a physical explanation for a destabilizing term proportional to k _⊥ ³ in the fluctuation spectrum, which we relate to a nonlinear (E²) electrokinetic effect called induced-charge electro-osmosis (ICEO). Recent studies of ICEO have focused on electrodes and polarizable particles, where an applied bulk field is perturbed by capacitive charging of the double layer and drives the flow along the field axis toward surface protrusions; in contrast, we predict “reverse” ICEO flows around driven membranes, due to curvature-induced tangential fields within a nonequilibrium double layer, which hydrodynamically enhance protrusions. We also consider the effect of incorporating the dynamics of a spatially dependent concentration field for the ion channels.