H. P. Zhang

Collective motion and density fluctuations in bacterial colonies

Flocking birds, fish schools, and insect swarms are familiar examples of collective motion that plays a role in a range of problems, such as spreading of diseases. Models have provided a qualitative understanding of the collective motion, but progress has been hindered by the lack of detailed experimental data. Here we report simultaneous measurements of the positions, velocities, and orientations as a function of time for up to a thousand wild-type Bacillus subtilis bacteria in a colony. The bacteria spontaneously form closely packed dynamic clusters within which they move cooperatively. The number of bacteria in a cluster exhibits a power-law distribution truncated by an exponential tail. The probability of finding clusters with large numbers of bacteria grows markedly as the bacterial density increases. The number of bacteria per unit area exhibits fluctuations far larger than those for populations in thermal equilibrium. Such “giant number fluctuations” have been found in models and in experiments on inert systems but not observed previously in a biological system. Our results demonstrate that bacteria are an excellent system to study the general phenomenon of collective motion.

Jamming transition in emulsions and granular materials

We investigate the jamming transition in packings of emulsions and granular materials via molecular dynamics simulations. The emulsion model is composed of frictionless droplets interacting via nonlinear normal forces obtained using experimental data acquired by confocal microscopy of compressed emulsions systems. Granular materials are modeled by Hertz-Mindlin deformable spherical grains with Coulomb friction. In both cases, we find power-law scaling for the vanishing of pressure and excess number of contacts as the system approaches the jamming transition from high volume fractions. We find that the construction history parametrized by the compression rate during the preparation protocol has a strong effect on the micromechanical properties of granular materials but not on emulsions. This leads the granular system to jam at different volume fractions depending on the histories. Isostaticity is found in the packings close to the jamming transition in emulsions and in granular materials at slow compression rates and infinite friction. Heterogeneity of interparticle forces increases as the packings approach the jamming transition which is demonstrated by the exponential tail in force distributions and the small values of the participation number measuring spatial localization of the forces. However, no signatures of the jamming transition are observed in structural properties, like the radial distribution functions and the distributions of contacts.

Measuring Crowd Collectiveness

Collective motions of crowds are common in nature and have attracted a great deal of attention in a variety of multidisciplinary fields. Collectiveness, which indicates the degree of individuals acting as a union, is a fundamental and universal measurement for various crowd systems. By quantifying the topological structures of collective manifolds of crowd, this paper proposes a descriptor of collectiveness and its efficient computation for the crowd and its constituent individuals. The Collective Merging algorithm is then proposed to detect collective motions from random motions. We validate the effectiveness and robustness of the proposed collectiveness on the system of self-driven particles as well as other real crowd systems such as pedestrian crowds and bacteria colony. We compare the collectiveness descriptor with human perception for collective motion and show their high consistency. As a universal descriptor, the proposed crowd collectiveness can be used to compare different crowd systems. It has a wide range of applications, such as detecting collective motions from crowd clutters, monitoring crowd dynamics, and generating maps of collectiveness for crowded scenes. A new Collective Motion Database, which consists of 413 video clips from 62 crowded scenes, is released to the public.

Deadly competition between sibling bacterial colonies

Bacteria can secrete a wide array of antibacterial compounds when competing with other bacteria for the same resources. Some of these compounds, such as bacteriocins, can affect bacteria of similar or closely related strains. In some cases, these secretions have been found to kill sibling cells that belong to the same colony. Here, we present experimental observations of competition between 2 sibling colonies of Paenibacillus dendritiformis grown on a low-nutrient agar gel. We find that neighboring colonies (growing from droplet inoculation) mutually inhibit growth through secretions that become lethal if the level exceeds a well-defined threshold. In contrast, within a single colony developing from a droplet inoculation, no growth inhibition is observed. However, growth inhibition and cell death are observed if material extracted from the agar between 2 growing colonies is introduced outside a growing single colony. To interpret the observations, we devised a simple mathematical model for the secretion of an antibacterial compound. Simulations of this model illustrate how secretions from neighboring colonies can be deadly, whereas secretions from a single colony growing from a droplet are not.

Experimental study of internal gravity waves generated by supercritical topography

Oscillatory tides flowing over rough topography on the ocean floor generate internal gravity waves, which are a major source of ocean mixing. Linear inviscid theory can describe waves generated by gentle topography with slopes that are less steep than the propagation angle of the internal waves; such topography is termed subcritical. However, a clear physical picture of internal waves generated by topography with slopes steeper than the angle of internal waves (supercritical topography) is lacking. In this paper we present an experimental study at Reynolds number ∼O(100) of internal gravity waves generated by a circular cylinder that oscillates horizontally (at a frequency Ω), thus mimicking barotropic tidal flow over bottom topography. Fundamental waves of frequency Ω emanate from locations on the cylinder where the topographic slope equals the slope of internal waves. For small oscillating amplitude A (weak forcing), our experimental results compare well with predictions of the viscous linear theory of D. G. Hurley and G. Keady [J. Fluid Mech. 351, 119 (1997)]. The width of the wave beams is determined by competition between forcing and viscous smoothing, and hydrodynamic screening of the steep part of the topography extends the cylinder’s horizontal length scale. Beyond the weak forcing regime, harmonic waves of frequency nΩ (with integer n>1 and nΩ<N, where N is the buoyancy frequency) are generated mainly by nonlinear interaction involving the overlapping fundamental waves. For moderate forcing we find that the intensity of the fundamental and second harmonic waves scales linearly and quadratically with A, respectively.Oscillatory tides flowing over rough topography on the ocean floor generate internal gravity waves, which are a major source of ocean mixing. Linear inviscid theory can describe waves generated by gentle topography with slopes that are less steep than the propagation angle of the internal waves; such topography is termed subcritical. However, a clear physical picture of internal waves generated by topography with slopes steeper than the angle of internal waves (supercritical topography) is lacking. In this paper we present an experimental study at Reynolds number ∼O(100) of internal gravity waves generated by a circular cylinder that oscillates horizontally (at a frequency Ω), thus mimicking barotropic tidal flow over bottom topography. Fundamental waves of frequency Ω emanate from locations on the cylinder where the topographic slope equals the slope of internal waves. For small oscillating amplitude A (weak forcing), our experimental results compare well with predictions of the viscous linear theory of ...

Lethal protein produced in response to competition between sibling bacterial colonies

Sibling Paenibacillus dendritiformis bacterial colonies grown on low-nutrient agar medium mutually inhibit growth through secretion of a lethal factor. Analysis of secretions reveals the presence of subtilisin (a protease) and a 12 kDa protein, termed sibling lethal factor (Slf). Purified subtilisin promotes the growth and expansion of P. dendritiformis colonies, whereas Slf is lethal and lyses P. dendritiformis cells in culture. Slf is encoded by a gene belonging to a large family of bacterial genes of unknown function, and the gene is predicted to encode a protein of approximately 20 kDa, termed dendritiformis sibling bacteriocin. The 20 kDa recombinant protein was produced and found to be inactive, but exposure to subtilisin resulted in cleavage to the active, 12 kDa form. The experimental results, combined with mathematical modeling, show that subtilisin serves to regulate growth of the colony. Below a threshold concentration, subtilisin promotes colony growth and expansion. However, once it exceeds a threshold, as occurs at the interface between competing colonies, Slf is then secreted into the medium to rapidly reduce cell density by lysis of the bacterial cells. The presence of genes encoding homologs of dendritiformis sibling bacteriocin in other bacterial species suggests that this mechanism for self-regulation of colony growth might not be limited to P. dendritiformis.

Paenibacillus dendritiformis Bacterial Colony Growth Depends on Surfactant but Not on Bacterial Motion

Most research on growing bacterial colonies on agar plates has concerned the effect of genetic or morphotype variation. Some studies have indicated that there is a correlation between microscopic bacterial motion and macroscopic colonial expansion, especially for swarming strains, but no measurements have been obtained for a single strain to relate the microscopic scale to the macroscopic scale. We examined here a single strain (Paenibacillus dendritiformis type T; tip splitting) to determine both the macroscopic growth of colonies and the microscopic bacterial motion within the colonies. Our multiscale measurements for a variety of growth conditions revealed that motion on the microscopic scale and colonial growth are largely independent. Instead, the growth of the colony is strongly affected by the availability of a surfactant that reduces surface tension.

Tidal flow over three-dimensional topography in a stratified fluid

Our laboratory experiments and numerical simulations of stratified tidal flow past model topography (a half sphere on a horizontal plane) reveal several three-dimensional flow features, including an unexpected flow perpendicular to the forcing plane (the vertical plane through the center of the sphere, in the direction of the oscillating tide). This perpendicular flow has a time-independent component and a component oscillating at twice the tidal frequency. Our results show that the time-independent part of the perpendicular flow forms a large-scale horizontal circulation, which could enhance material transport and mixing near bottom topography in the oceans. In addition, for small forcing amplitude we find that the azimuthal dependence of the internal wave field is described by the functional form cos ϕ, as predicted by linear inviscid theory. At higher forcing amplitude, the internal wave energy is more concentrated in the forcing direction. Finally, we observe a wave intensity asymmetry in the polar di...

Harmonic generation by reflecting internal waves

The generation of internal gravity waves by tidal flow over topography is an important oceanic process that redistributes tidal energy in the ocean. Internal waves reflect from boundaries, creating harmonics and mixing. We use laboratory experiments and two-dimensional numerical simulations of the Navier–Stokes equations to determine the value of the topographic slope that gives the most intense generation of second harmonic waves in the reflection process. The results from our experiments and simulations agree well but differ markedly from theoretical predictions by S. A. Thorpe [“On the reflection of a train of finite amplitude waves from a uniform slope,” J. Fluid Mech. 178, 279 (1987)] and A. Tabaei et al. [“Nonlinear effects in reflecting and colliding internal wave beams,” J. Fluid Mech. 526, 217 (2005)], except for nearly inviscid, weakly nonlinear flow. However, even for weakly nonlinear flow (where the Dauxois–Young amplitude parameter value is only 0.01), we find that the ratio of the reflected ...

Dynamics of static friction between steel and silicon

We conducted experiments in which steel and silicon or quartz are clamped together. Even with the smallest tangential forces we could apply, we always found reproducible sliding motions on the nanometer scale. The velocities we study are thousands of times smaller than in previous investigations. The samples first slide and then lock up even when external forces hold steady. One might call the result “slip-stick” friction. We account for the results with a phenomenological theory that results from considering the rate and state theory of dynamic friction at low velocities. Our measurements lead us to set the instantaneous coefficient of static friction that normally enters rate and state theories to zero.