We propose a very simple one-dimensional swimmer consisting of three spheres that are linked by rigid rods whose lengths can change between two values. With a periodic motion in a nonreciprocal fashion, which breaks the time-reversal symmetry as well as the translational symmetry, we show that the model device can swim at low Reynolds number. This model system could be used in constructing molecular-sized machines.

Phase objects can become visible by slightly defocusing an optical microscope, a technique seldom used as a useful tool. We revisited the theory of defocusing and apply it to our optical microscope with optics corrected at infinity. In our approximation, we obtain that the image contrast is proportional to the two-dimensional (2D) Laplacian of the phase difference introduced by the phase object. If the index of refraction of the phase object is uniform the image obtained from defocusing microscopy is the image of curvature (Laplacian of the local thickness) of the phase object, while standard phase-contrast microscopy gives information about the thickness of the object. We made artificial phase objects and measured image contrasts with defocusing microscopy. Measured contrasts are in excellent agreement with our theoretical model. We use defocusing microscopy to study curvature fluctuations (ruffles) on the surface of macrophages (cell of the innate immune system), and try to correlate mechanical properties of macrophage surface and phagocytosis. We observe large coherent propagating structures: Their shape, speed, density are measured and curvature energy estimated. Inhomogeneities of cytoskeleton refractive index, curvature modulations due to thermal fluctuations and/or periodic changes in cytoskeleton-membrane interactions cause random fluctuations in image contrast. From the temporal and spatial contrast correlation functions, we obtain the decay time and correlation length of such fluctuations that are related to their size and the viscoelastic properties of the cytoskeleton. In order to associate the dynamics of cytoskeleton with the process of phagocytosis, we use an optical tweezers to grab a zymosan particle and put it into contact with the macrophage. We then measure the time for a single phagocytosis event. We add the drug cytochalasin D that depolymerizes the cytoskeleton F-actin network: It inhibits the large propagating coherent fluctuations on the cell surface, increases the relaxation time of cytoskeleton fluctuations, and increases the phagocytosis time. Our results suggest that the methods developed in this work can be of utility to assess the importance of cytoskeleton motility in the dynamics of cellular processes such as phagocytosis exhibited by macrophages.

The Ikeda, Parker, and Sawai river meandering model is reexamined using a physical approach employing an explicit equation of motion. For periodic river shapes as seen from above, a cross-stream surface elevation gradient creates a velocity shear that is responsible for the decay of small-wavelength meander bends, whereas secondary currents in the plane perpendicular to the downstream direction are responsible for the growth of large-wavelength bends. A decay length ${D=H/2C}_f$ involving the river depth H and the friction coefficient $C_f$ sets the scale for meandering, giving the downstream distance required for the fluid velocity profile to recover from changes in the channel curvature. Using this length scale and a time scale T, we explicitly trace the observed length scale invariance to the equations of motion, and predict similar time and velocity scale invariances. A general time-dependent nonlinear modal analysis for periodic rivers reveals that modes higher than the third mode are needed to describe upstream migration of bend apexes just before oxbow cutoff, and are important to accurate calculations of the time and sinuosity at cutoff.

In living cells, cytoskeletal filaments interact with the plasma membrane to form structures that play a key role in cell shape and mechanical properties. To study the interaction between these basic components, we designed an in vitro self-assembled network of actin filaments attached to the outer surface of giant unilamellar vesicles. Optical tweezers and single-particle tracking experiments are used to study the rich dynamics of these actin-coated membranes (ACM). We show that microrheology studies can be carried out on such an individual microscopic object. The principle of the experiment consists in measuring the thermally excited position fluctuations of a probe bead attached biochemically to the membrane. We propose a model that relates the power spectrum of these thermal fluctuations to the viscoelastic properties of the membrane. The presence of the actin network modifies strongly the membrane dynamics with respect to a fluid, lipid bilayer one. It induces first a finite (ω=0) two-dimensional (2D) shear modulus $G_{2\mathrm{D}}^0\sim 0.5$ to 5 μN/m in the membrane plane. Moreover, the frequency dependence at high frequency of the shear modulus $\left[G_{2\mathrm{D}}^{\prime }\right(f\left)\sim f^{0.85\pm 0.07}\right]$ and of the bending modulus $\left({\kappa }_{\mathrm{ACM}}\mathrm{}\right(f\left)\mathrm{}\sim f^{0.55\pm 0.21}\right)$ demonstrate the viscoelastic behavior of the composite membrane. These results are consistent with a common exponent of 0.75 for both moduli as expected from our model and from prior measurements on actin solutions.

We report on a series of measurements aimed to characterize the development and the dynamics of the rhythmic applause in concert halls. Our results demonstrate that while this process shares many characteristics of other systems that are known to synchronize, it also has features that are unexpected and unaccounted for in many other systems. In particular, we find that the mechanism lying at the heart of the synchronization process is the period doubling of the clapping rhythm. The characteristic interplay between synchronized and unsynchronized regimes during the applause is the result of a frustration in the system. All results are understandable in the framework of the Kuramoto model.

Application of time correlated single photon counting to pulsed Mie scattering enables one to resolve changes in light scattering to better than 50 ps. This technique is applied to the highly nonlinear motion of a sonoluminescing bubble. Physical processes, such as outgoing shock wave emission, that limit the interpretation of the data are measured with a streak camera and microscopy. Shock speeds about 6 km/s have been observed.

We present a model for the dynamics of a cerebral cortex in which inputs to neuronal assemblies are treated as random Gaussian fluctuations about a mean value. We incorporate the effect of general anesthetic agents on the cortex as a modulation of the inhibitory neurotransmitter rate constant. Stochastic differential equations are derived for the state variable $h_e,$ the average excitatory soma potential, coherent fluctuations of which are believed to be the source of scalp-measured electroencephalogram (EEG) signals. Using this stochastic approach we derive a stationary (long-time limit) fluctuation spectrum for $h_e.$ The model predicts that there will be three distinct stationary (equilibrium) regimes for cortical activity. In region I (“coma”), corresponding to a strong inhibitory anesthetic effect, $h_e$ is single valued, large, and negative, so that neuronal firing rates are suppressed. In region II for a zero or small anesthetic effect, $h_e$ can take on three values, two of which are stable; we label the stable solutions as “active” (enhanced firing) and “quiescent” (suppressed firing). For region III, corresponding to negative anesthetic (i.e., analeptic) effect, $h_e$ again becomes single valued, but is now small and negative, resulting in strongly elevated firing rates (“seizure”). If we identify region II as associated with the conscious state of the cortex, then the model predicts that there will be a rapid transit between the active-conscious and comatose unconscious states at a critical value of anesthetic concentration, suggesting the existence of phase transitions in the cortex. The low-frequency spectral power in the $h_e$ signal should increase strongly during the initial stage of anesthesia induction, before collapsing to much lower values after the transition into comatose-unconsciousness. These qualitative predictions are consistent with clinical measurements by Bührer et al. [Anaesthesiology 77, 226 (1992)], MacIver et al. [ibid. 84, 1411 (1996)], and Kuizenga et al. [Br. J. Anaesthesia 80, 725 (1998)]. This strong increase in EEG spectral power in the vicinity of the critical point is similar to the divergences observed during thermodynamic phase transitions. We show that the divergence in low-frequency power in our model is a natural consequence of the existence of turning points in the trajectory of stationary states for the cortex.

Cellular differentiation in a developing organism is studied via a discrete bistable reaction-diffusion model. A system of undifferentiated cells is allowed to receive an inductive signal emanating from its environment. Depending on the form of the nonlinear reaction kinetics, this signal can trigger a series of bifurcations in the system. Differentiation starts at the surface where the signal is received and either cells change type up to a given distance or, under other conditions, the differentiation process propagates throughout the whole domain. When the signal diminishes, hysteresis is observed.

We investigate fracture and fragmentation of solids due to impact at low energies using a two-dimensional dynamical model of granular solids. Simulating collisions of two solid disks, we show that, depending on the initial energy, the outcome of a collision process can be classified into two states: a damaged state and a fragmented state, with a sharp transition in between. We give numerical evidence that the transition point between the two states behaves as a critical point, and we discuss the possible mechanism of the transition.