We use magnetic tweezers to study local viscoelastic response in filamentous actin networks. The choice of magnetic, colloidal particles of varying size allows us to explore properties on the relevant micron and submicron scales. At these scales the mechanical response is determined by the bending properties of individual filaments and described by an anomalous power-law behavior. In the absence of external forces the particles exhibit a subdiffusive motion. [S0031-9007(96)01627-4] Complex molecular systems, such as polymer solutions, polymer melts, gels, (micro)emulsions, and foams, often display a combination of the elastic properties of solids and the viscous properties of fluids. Using classical rheological methods [1], the viscoelastic properties of such materials have been described at scales much larger than the molecular dimensions, and the systems under study have mostly been treated as homogeneous media. In many situations, however, local mechanical properties are of critical importance. For instance, the shape and motility of living cells, as well as cytoplasmic transport, are strongly influenced by the mechanical properties of cytoskeleton networks [2] at submicron and micron scales.Actin filaments ( f-actin), formed upon polymerization of globular actin proteins, are major components of the cytoskeleton and are involved in both transport and motility [3]. Easily purified and polymerized in vitro, actin is a model system for the study of the mechanics and assembly of biopolymers [4,5]. In this paper we show, using the example of actin filaments, how micromechanical measurements can provide information about local viscoelastic properties of the medium.f-actin is a rigid polymer with a persistence length L p of the order of 15 mm [6]. At high enough concentrations, in the so-called semidilute regime, the polymers form a three-dimensional network with a mesh size L. L is typically of the order of a micron and thus much smaller than L p . Viscoelastic properties of this inhomogeneous medium can be locally studied by inserting colloidal magnetic beads and perturbing them with external magnetic forces. In fact, such simple methods have been used for many years to explore the cytoplasm [7]. For beads with diameter, d, much larger than L, the mechanical perturbation is macroscopic. On the other hand, if d is much smaller than the mesh size, the bead is expected to probe only the solvent viscosity and geometrical constraints introduced by polymers. Therefore, the regime that is relevant for exploring the local network mechanics is one for which d is comparable to L. In this case, the bead is moving inside a "cage" of typical linear size L. To move further, it has to perturb the polymers of the cage, either through the influence of an external force or via thermal fluctuations. In both cases, one can study the viscoelastic properties on micron scales by observing the motion of individual beads. We show below that this approach can be made quantitative, and that local mechanical properties of the network can be...

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Resonators driven into self-oscillation via active feedback often form the basis of clocks and other sensitive measurement instrumentation.The phase stability of such an oscillator is ultimately limited by the noise associated with the resonator s intrinsic losses. However, it is often the case that amplifier noise is the dominant cause of the oscillator's phase diffusion. Here it is shown that when the resonator possesses a suitable nonlinearity, the phase diffusion due to amplifier noise can be suppressed, allowing one to achieve a long-term phase stability comparable to the ultimate noise limit.PACS number(s): 42.50.Ne, 05.40. +j, 06.20.Dk, 03.65.Bz

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A magnetic micromanipulator capable of generating two-dimensional translational and rotational motions on a microscope stage is described. With 3 μm-diam paramagnetic beads, forces in the piconewton range and torques on the order of 10−14 N m are obtained and can be modulated in time at moderate frequencies (<5 Hz). Typical magnetic fields between 0.1 and 0.2 T, and gradients between 10 and 20 T m−1 are created by four independent feedback-controlled electromagnets. Video microscopy and computerized image analysis are used to locate the beads on each image with a resolution of 0.1 pixel (20 nm). The device is primarily designed to study, at a microscopic scale, the local mechanical properties of biological polymers such as actin in solution, and of cell cytoplasm. Possible applications include the in situ manipulation of intracellular organelles.

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Using a twisted nematic liquid crystal system exhibiting planar Ising model dynamics, we have measured the scaling exponent θ which characterizes the time evolution, p(t) ∼ t −θ , of the probability p(t) that the local order parameter has not switched its state by the time t. For 0.4 seconds to 200 seconds following the phase quench, the system exhibits scaling behavior and, measured over this interval, θ = 0.19 ± 0.031, in good agreement with theoretical analysis and numerical simulations. PACS: 82.20.Fd, 02.50.Ey, 05.40.+j, 05.50.+q There has been a recent surge of interest in determining the so-called nontrivial "persistence" exponent θ [1-11] associated with the dynamics of a phase ordering system following a quench from the high-temperature phase to zero temperature. This exponent describes the asymptotic power-law decay, p(t) ∼ t −θ , of the probability that the local order parameter φ(x, t) has not changed sign up to time t after the quench. For the Ising model, p(t) is simply the fraction of spins that have not flipped up to time t, or, equivalently, the probability that no interface has ever crossed a given spin. While there have been considerable theoretical and numerical efforts directed towards calculating θ, so far there has been no experimental measurement of this exponent in spin-like systems. A kind of persistence exponent was first introduced and measured in a breath figure experiment [1], and recently for soap bubbles [12] (in this latter example θ takes a rather trivial value, which can be inferred on simple physical grounds [12]). In this Letter, we present the first experimental measurement of the nontrivial persistence exponent for an Ising-like system, that we find in good agreement with a recent theoretical calculation.This power-law decay of persistence is quite ubiquitous and not just restricted to the phase ordering dynamics of the Ising or Potts models. For instance, a similar question arises in the study of Gaussian processes. Considering such a process m(t), the calculation of the probability that this Gaussian walker never crosses the origin (or changes sign) is a particularly difficult problem when this process is not Markovian [10,11]. For example, even for the simple diffusion equation, ∂ t φ = ∇ 2 φ, the probability that the Gaussian variable φ(x, t) does not change sign up to time t, decays algebraically with t with a nontrivial exponent θ [11]. This exponent θ also appears in other contexts such as reaction-diffusion systems [13][14][15] and driven diffusive systems [16]. For a quench to the critical point of spin systems, the persistence exponent θ associated with the total magnetization (another nonMarkovian Gaussian variable) has recently been argued to be a new non-equilibrium critical exponent [17].For the purpose of the experimental results presented below, we will restrict ourselves to the phase ordering dynamics of the Ising model at T = 0. The Ising model at T = 0 has two ordered states: either all spins are up or they are all down. Following a quench from the hig...