We report simulations of a continuum model for (apolar, flow aligning) active fluids in two dimensions. Both free and anchored boundary conditions are considered, at parallel confining walls that are either static or moving at fixed relative velocity. We focus on extensile materials and find that steady shear bands, previously shown to arise ubiquitously in one dimension for the active nematic phase at small (or indeed zero) shear rate, are generally replaced in two dimensions by more complex flow patterns that can be stationary, oscillatory, or apparently chaotic. The consequences of these flow patterns for time-averaged steady-state rheology are examined.

We consider the exit problem for an overdamped Brownian particle in a potential undergoing dichotomic fluctuations. The system exhibits resonant activation. We compute the corresponding exit times distribution and show that the resonance is associated with the presence of a finite number of complex conjugate eigenvalue pairs in the spectrum of the evolution equation. The properties of these eigenvalues and their influence on the exit times distribution and on the possible dynamics of the system are discussed in detail.

Synchronous oscillatory dynamics is frequently observed in the human brain. We analyze the fine temporal structure of phase-locking in a realistic network model and match it with the experimental data from Parkinsonian patients. We show that the experimentally observed intermittent synchrony can be generated just by moderately increased coupling strength in the basal ganglia circuits due to the lack of dopamine. Comparison of the experimental and modeling data suggest that brain activity in Parkinson's disease resides in the large boundary region between synchronized and nonsynchronized dynamics. Being on the edge of synchrony may allow for easy formation of transient neuronal assemblies.

Signal detection is generally related to network structure in both biological and engineering systems, and enormous effort has been putting into understanding the mechanism of amplification of weak signals in the aspects of self-tuning and scale-free topology. Here, we show that a third way of signal amplification exists, which does not require the scale-free topology as a necessary condition. This approach can effectively amplify the signal at an arbitrary node in a complex network by adaptively adjusting the coupling weights between the signal node and its neighbors, and thus can be used in both the local and global areas of a complex network. A theory is provided to explain its mechanism.

Recent experiments in one- and two-dimensional microfluidic arrays of droplets containing Belousov-Zhabotinsky reactants show a rich variety of spatial patterns [M. Toiya et al., J. Phys. Chem. Lett. 1, 1241 (2010)]. The dominant coupling between these droplets is inhibitory. Motivated by this experimental system, we study repulsively coupled Kuramoto oscillators with nearest-neighbor interactions, on a linear chain as well as a ring in one dimension, and on a triangular lattice in two dimensions. In one dimension, we show using linear stability analysis as well as numerical study that the stable phase patterns depend on the geometry of the lattice. We show that a transition to the ordered state does not exist in the thermodynamic limit. In two dimensions, we show that the geometry of the lattice constrains the phase difference between two neighboring oscillators to $2\pi /3$. We report the existence of domains with either clockwise or anticlockwise helicity, leading to defects in the lattice. We study the time dependence of these domains and show that at large coupling strengths the domains freeze due to frequency synchronization. Signatures of the above phenomena can be seen in the spatial correlation functions.

The synchronized behaviors of a noisy small-world neuronal network with delay and diversity is numerically studied by calculating a synchronization measure and plotting firing pattern. We show that delay in the information transmission can induce fruitful synchronization transitions, including transition from phase locking to antiphase synchronization, and transition from antiphase synchronization to complete synchronization. Furthermore, the delay-induced complete synchronization can be changed by diversity, which causes the oscillatory-like transition between antiphase synchronization and complete synchronization.

Diffusion coefficients of particles can be defined as time integrals over velocity correlation functions, or as mean square displacements divided by time. In the present paper it is demonstrated that these two definitions are not equivalent. An exact relation between mean square displacements and velocity correlations is derived. As an example of the applicability of these results so-called drift coefficients of energetic particles are discussed. It is explained why different previous approaches in drift theory provided contradicting results.

We study equilibrium configurations of thin and elongated non-Euclidean elastic strips with hyperbolic two-dimensional reference metrics $\mathrm{ā}$ which are invariant along the strip. In the vanishing thickness limit energy minima are obtained by minimizing the integral of the mean curvature squared among all isometric embeddings of $\mathrm{ā}$. For narrow strips these minima are very close to minimal surfaces regardless of the specific form of the metric. We study the properties of these “almost minimal” surfaces and find a rich range of three-dimensional stable configurations. We provide some explicit solutions as well as a framework for the incorporation of additional forces and constraints.

It is shown both analytically and numerically that the suggested lattice Boltzmann model on rectangular grids [J. G. Zhou, Phys. Rev. E 81, 026705 (2010)] leads to anisotropic dissipation of fluid momentum and thus does not recover the Navier-Stokes equations. Hence, it cannot be used for the simulation of hydrodynamics.

We demonstrate depth-resolved viscosity measurements within a single object using polarized optical scattering from ensembles of freely tumbling plasmon resonant gold nanorods (GNRs) monitored with polarization-sensitive optical coherence tomography. The rotational diffusion coefficient of the GNRs is shown to correlate with viscosity in molecular fluids according to the Stokes-Einstein relation. The plasmon resonant and highly anisotropic properties of GNRs are favorable for microrheological studies of nanoscale properties.

We present exact calculations of the chromatic polynomial and resultant ground state entropy of the $q$-state Potts antiferromagnet on lattice strips that are homeomorphic expansions of a strip of the kagomé lattice. The dependence of the ground state entropy on the form of homeomorphic expansion is elucidated.

We simulate quasistatic flows of an ideal two-dimensional monodisperse foam around different obstacles, both symmetric and asymmetric, in a channel. We record both pressure and network contributions to the drag and lift forces and study them as a function of obstacle geometry. We show that the drag force increases linearly with the cross section of an obstacles. The lift on an asymmetric aerofoil-like shape is negative and increases with its arc length, mainly due to the pressure contribution.

We study the probability of multistability in a quadratic map driven repeatedly by a random signal of length $N$, where $N$ is taken as a measure of the signal complexity. We first establish analytically that the number of coexisting attractors is bounded above by $N$. We then numerically estimate the probability $p$ of a randomly chosen signal resulting in a multistable response as a function of $N$. Interestingly, with increasing drive signal complexity the system exhibits a paucity of attractors. That is, almost any drive signal beyond a certain complexity level will result in a single attractor response ($p=0$). This mechanism may play a role in allowing sensitive multistable systems to respond consistently to external influences.

A stochastic version of the Biham-Middleton-Levine model with random update rule is studied. It is shown that under periodic boundary condition, the system exhibits a sharp transition from moving phase to jamming phase. Under open boundary condition, the coexistence of moving phase and jamming phase can be observed. We have presented a mean-field analysis for the moving phase, which successfully takes into account the correlation and produces good agreement with simulation results.

The dynamics of proteins and biopolymers play a crucial role in their function. By using Brownian dynamics we show that polymer globules, which serve as a model system for proteins, undergo a size-dependent dynamical transition from a liquid-like state at high $T$ to a frozen state at low $T$ with a relaxation time that diverges at the transition point. Furthermore, a stretch-induced melting transition is shown to be readily controlled by external forces that exploit the polymer connectivity to modify the size of the globule. This pathway could be a general route to enhance the rate of conformational changes in naturally occurring biopolymers.

We apply a Langevin model by imposing additive and multiplicative noises to study thermally activated diffusion over a fluctuating barrier in underdamped dynamics. The barrier fluctuation is characterized by Gaussian colored noise with exponential correlation. We present the exact solutions for the first and second moments. Furthermore, we use direct simulations to calculate the asymptotic probability for a Brownian particle passing over the fluctuating barrier. The results indicate that the correlation of the fluctuating barrier is crucial for barrier crossing dynamics.

We have investigated strain-accelerated dynamics of soft glasses theoretically and experimentally. Mechanical rheology measurements performed on a variety of systems reveal evidence for the speeding-up of relaxation at modest shear strains in both step and oscillatory shear flows. Using the soft glassy rheology (SGR) model framework, we show that the observed behavior is a fundamental, but heretofore unexplored attribute of soft glasses.

We theoretically and numerically studied ordering of “colloidal ionic clusters” on periodic substrate potentials such as those generated by optical trapping. Each cluster consists of three charged spherical colloids: two negatively and one positively charged. The substrate is a square or rectangular array of traps, each confining one such cluster. By varying the lattice constant from large to small, the observed clusters are first rodlike and form ferro- and antiferrolike phases, then they bend into a bananalike shape, and finally they condense into a percolated structure. Remarkably, in a broad parameter range between single-cluster and percolated structures, we have found stable supercomplexes composed of six colloids forming grapelike or rocketlike structures. We investigated the possibility of macroscopic pattern switching by applying external electrical fields.

The dispersion relation on the Kerr constant ($K$) of a polymer-stabilized isotropic phase (PSIP) liquid-crystal (LC) composite is investigated. Our experimental results show that $K$ decreases as the wavelength (λ) increases. The single-band birefringence dispersion model is used to fit the λ$K$ values of the PSIP LC composite. Very good agreement between the experiment and physical model is obtained.

A comparative classification scheme provides a good basis for several approaches to understand proteins, including prediction of relations between their structure and biological function. But it remains a challenge to combine a classification scheme that describes a protein starting from its well-organized secondary structures and often involves direct human involvement, with an atomary-level physics-based approach where a protein is fundamentally nothing more than an ensemble of mutually interacting carbon, hydrogen, oxygen, and nitrogen atoms. In order to bridge these two complementary approaches to proteins, conceptually novel tools need to be introduced. Here we explain how an approach toward geometric characterization of entire folded proteins can be based on a single explicit elementary function that is familiar from nonlinear physical systems where it is known as the kink soliton. Our approach enables the conversion of hierarchical structural information into a quantitative form that allows for a folded protein to be characterized in terms of a small number of global parameters that are in principle computable from atomary-level considerations. As an example we describe in detail how the native fold of the myoglobin 1M6C emerges from a combination of kink solitons with a very high atomary-level accuracy. We also verify that our approach describes longer loops and loops connecting $\alpha$ helices with $\beta$ strands, with the same overall accuracy.