TY - JOUR AB - We investigate high-dimensional nonlinear dynamical systems exhibiting multiple resonances under adiabatic parameter variations. Our motivations come from experimental considerations where time-dependent sweeping of parameters is a practical approach to probing and characterizing the bifurcations of the system. The question is whether bifurcations so detected are faithful representations of the bifurcations intrinsic to the original stationary system. Utilizing a harmonically forced, closed fluid flow system that possesses multiple resonances and solving the Navier-Stokes equation under proper boundary conditions, we uncover the phenomenon of the early effect. Specifically, as a control parameter, e.g., the driving frequency, is adiabatically increased from an initial value, resonances emerge at frequency values that are lower than those in the corresponding stationary system. The phenomenon is established by numerical characterization of physical quantities through the resonances, which include the kinetic energy and the vorticity field, and a heuristic analysis based on the concept of instantaneous frequency. A simple formula is obtained which relates the resonance points in the time-dependent and time-independent systems. Our findings suggest that, in general, any true bifurcation of a nonlinear dynamical system can be unequivocally uncovered through adiabatic parameter sweeping, in spite of a shift in the bifurcation point, which is of value to experimental studies of nonlinear dynamical systems. AU - Park, Youngyong AU - Do, Younghae AU - Altmeyer, Sebastian AU - Lai, Yingcheng AU - Lee, Gyuwon ID - 1868 IS - 2 JF - Physical Review E SN - 1539-3755 TI - Early effect in time-dependent, high-dimensional nonlinear dynamical systems with multiple resonances VL - 91 ER - TY - JOUR AB - We present a model of soft active particles that leads to a rich array of collective behavior found also in dense biological swarms of bacteria and other unicellular organisms. Our model uses only local interactions, such as Vicsek-type nearest-neighbor alignment, short-range repulsion, and a local boundary term. Changing the relative strength of these interactions leads to migrating swarms, rotating swarms, and jammed swarms, as well as swarms that exhibit run-and-tumble motion, alternating between migration and either rotating or jammed states. Interestingly, although a migrating swarm moves slower than an individual particle, the diffusion constant can be up to three orders of magnitude larger, suggesting that collective motion can be highly advantageous, for example, when searching for food. AU - van Drongelen, Ruben AU - Pal, Anshuman AU - Goodrich, Carl Peter AU - Idema, Timon ID - 7767 IS - 3 JF - Physical Review E SN - 1539-3755 TI - Collective dynamics of soft active particles VL - 91 ER - TY - JOUR AB - We use numerical simulations to compute the equation of state of a suspension of spherical self-propelled nanoparticles in two and three dimensions. We study in detail the effect of excluded volume interactions and confinement as a function of the system's temperature, concentration, and strength of the propulsion. We find a striking nonmonotonic dependence of the pressure on the temperature and provide simple scaling arguments to predict and explain the occurrence of such anomalous behavior. We explicitly show how our results have important implications for the effective forces on passive components suspended in a bath of active particles. AU - Mallory, S. A. AU - Šarić, Anđela AU - Valeriani, C. AU - Cacciuto, A. ID - 10383 IS - 5 JF - Physical Review E SN - 1539-3755 TI - Anomalous thermomechanical properties of a self-propelled colloidal fluid VL - 89 ER - TY - JOUR AB - We investigate the vibrational modes of quasi-two-dimensional disordered colloidal packings of hard colloidal spheres with short-range attractions as a function of packing fraction. Certain properties of the vibrational density of states (vDOS) are shown to correlate with the density and structure of the samples (i.e., in sparsely versus densely packed samples). Specifically, a crossover from dense glassy to sparse gel-like states is suggested by an excess of phonon modes at low frequency and by a variation in the slope of the vDOS with frequency at low frequency. This change in phonon mode distribution is demonstrated to arise largely from localized vibrations that involve individual and/or small clusters of particles with few local bonds. Conventional order parameters and void statistics did not exhibit obvious gel-glass signatures as a function of volume fraction. These mode behaviors and accompanying structural insights offer a potentially new set of indicators for identification of glass-gel transitions and for assignment of gel-like versus glass-like character to a disordered solid material. AU - Lohr, Matthew A. AU - Still, Tim AU - Ganti, Raman AU - Gratale, Matthew D. AU - Davidson, Zoey S. AU - Aptowicz, Kevin B. AU - Goodrich, Carl Peter AU - Sussman, Daniel M. AU - Yodh, A. G. ID - 7768 IS - 6 JF - Physical Review E SN - 1539-3755 TI - Vibrational and structural signatures of the crossover between dense glassy and sparse gel-like attractive colloidal packings VL - 90 ER - TY - JOUR AB - Particle tracking and displacement covariance matrix techniques are employed to investigate the phonon dispersion relations of two-dimensional colloidal glasses composed of soft, thermoresponsive microgel particles whose temperature-sensitive size permits in situ variation of particle packing fraction. Bulk, B, and shear, G, moduli of the colloidal glasses are extracted from the dispersion relations as a function of packing fraction, and variation of the ratio G/B with packing fraction is found to agree quantitatively with predictions for jammed packings of frictional soft particles. In addition, G and B individually agree with numerical predictions for frictional particles. This remarkable level of agreement enabled us to extract an energy scale for the interparticle interaction from the individual elastic constants and to derive an approximate estimate for the interparticle friction coefficient. AU - Still, Tim AU - Goodrich, Carl Peter AU - Chen, Ke AU - Yunker, Peter J. AU - Schoenholz, Samuel AU - Liu, Andrea J. AU - Yodh, A. G. ID - 7772 IS - 1 JF - Physical Review E SN - 1539-3755 TI - Phonon dispersion and elastic moduli of two-dimensional disordered colloidal packings of soft particles with frictional interactions VL - 89 ER - TY - JOUR AB - Athermal packings of soft repulsive spheres exhibit a sharp jamming transition in the thermodynamic limit. Upon further compression, various structural and mechanical properties display clean power-law behavior over many decades in pressure. As with any phase transition, the rounding of such behavior in finite systems close to the transition plays an important role in understanding the nature of the transition itself. The situation for jamming is surprisingly rich: the assumption that jammed packings are isotropic is only strictly true in the large-size limit, and finite-size has a profound effect on the very meaning of jamming. Here, we provide a comprehensive numerical study of finite-size effects in sphere packings above the jamming transition, focusing on stability as well as the scaling of the contact number and the elastic response. AU - Goodrich, Carl Peter AU - Dagois-Bohy, Simon AU - Tighe, Brian P. AU - van Hecke, Martin AU - Liu, Andrea J. AU - Nagel, Sidney R. ID - 7769 IS - 2 JF - Physical Review E SN - 1539-3755 TI - Jamming in finite systems: Stability, anisotropy, fluctuations, and scaling VL - 90 ER - TY - JOUR AB - Packings of frictionless athermal particles that interact only when they overlap experience a jamming transition as a function of packing density. Such packings provide the foundation for the theory of jamming. This theory rests on the observation that, despite the multitude of disordered configurations, the mechanical response to linear order depends only on the distance to the transition. We investigate the validity and utility of such measurements that invoke the harmonic approximation and show that, despite particles coming in and out of contact, there is a well-defined linear regime in the thermodynamic limit. AU - Goodrich, Carl Peter AU - Liu, Andrea J. AU - Nagel, Sidney R. ID - 7770 IS - 2 JF - Physical Review E SN - 1539-3755 TI - Contact nonlinearities and linear response in jammed particulate packings VL - 90 ER - TY - JOUR AB - In dynamical models of cortical networks, the recurrent connectivity can amplify the input given to the network in two distinct ways. One is induced by the presence of near-critical eigenvalues in the connectivity matrix W, producing large but slow activity fluctuations along the corresponding eigenvectors (dynamical slowing). The other relies on W not being normal, which allows the network activity to make large but fast excursions along specific directions. Here we investigate the trade-off between non-normal amplification and dynamical slowing in the spontaneous activity of large random neuronal networks composed of excitatory and inhibitory neurons. We use a Schur decomposition of W to separate the two amplification mechanisms. Assuming linear stochastic dynamics, we derive an exact expression for the expected amount of purely non-normal amplification. We find that amplification is very limited if dynamical slowing must be kept weak. We conclude that, to achieve strong transient amplification with little slowing, the connectivity must be structured. We show that unidirectional connections between neurons of the same type together with reciprocal connections between neurons of different types, allow for amplification already in the fast dynamical regime. Finally, our results also shed light on the differences between balanced networks in which inhibition exactly cancels excitation and those where inhibition dominates. AU - Hennequin, Guillaume AU - Vogels, Tim P AU - Gerstner, Wulfram ID - 8024 IS - 1 JF - Physical Review E SN - 1539-3755 TI - Non-normal amplification in random balanced neuronal networks VL - 86 ER -