We present the results of exact numerical studies of the energy landscape and the dynamics of a 12-monomer chain with contact interactions encoding the ground state on a square lattice. In spite of its simplicity, the model is shown to exhibit behavior at odds with the standard picture of proteins.

The soft glassy rheology (SGR) model is a mesoscopic framework which proved to be very successful in describing flow and deformation of various amorphous materials phenomenologically (e.g., pastes, slurries, foams, etc.). In this paper, we cast SGR in a general, model-independent framework for nonequilibrium thermodynamics called general equation for the nonequilibrium reversible-irreversible coupling. This leads to a formulation of SGR which clarifies how it can properly be coupled to hydrodynamic fields, resulting in a thermodynamically consistent, local, continuum version of SGR. Additionally, we find that compliance with thermodynamics imposes the existence of a modification to the stress tensor as predicted by SGR.

Current understanding of neuronal growth is mostly qualitative, as the staggering number of physical and chemical guidance cues involved prohibit a fully quantitative description of axonal dynamics. We report on a general approach that describes axonal growth in vitro, on poly-D-lysine–coated glass substrates, as diffusion in an effective external potential, representing the collective contribution of all causal influences on the growth cone. We use this approach to obtain effective growth rules that reveal an emergent regulatory mechanism for axonal pathfinding on these substrates.

We develop a simple physical model that captures the large-scale lamellipodia dynamics in crawling cells and explains the observed spectrum of fish keratocytes behavior. The main ingredients in this description are the geometrical evolution of the lamellipodium leading edge, the dynamic remodeling of the actin network, and the interconnection between them. We deviate from existing theoretical works and consider the lamellipodium leading edge as a propagating front. The agreement of our model with experimental works suggests that the large-scale morphological and migration features exhibited by keratocyte cells are a direct consequence of the closed feedback loop between the shape of the leading edge and the density of the actin network.

A simple mechanism for the emergence of complexity in cellular automata out of predictable dynamics is described. This leads to introduce the concept of conditional predictability for systems whose trajectory can only be piecewise known. The mechanism is used to construct a cellular automaton model for discrete chimeralike states, where synchrony and incoherence in an ensemble of identical oscillators coexist. The incoherent region is shown to have a periodicity that is three orders of magnitude longer than the period of the synchronous oscillation.

Most network formation analysis studies are centered on edge addition. However, edges in real world networks often have a rapid turnover with a large number of edges added and removed between each node addition or removal steps. In such a case, quasiequilibrium is obtained between edge addition and deletion. Edges have been shown to be added to nodes with a high degree and between pairs of nodes with a high number of common neighbors. If not balanced by a degree dependent edge removal, the preference for high degree nodes and node pairs with many common neighbors is expected to increase the average degree of high degree nodes and their clustering coefficient until very large cliques will be formed. Since such large cliques are not formed in real world networks, we conclude that the edge removal probability around high degree nodes and between node pairs with many common neighbors should be higher than around other nodes. We here show the existence of such a balancing mechanism through the relation between the future edge removal probability around nodes and their degree and a similar relation between the edge removal probability and the number of common neighbors of node pairs. In some networks, this preferential detachment process represents an explicit saturation process, and in others, it represents a random deletion process accompanied by a sublinear edge preferential attachment process. A more complex mechanism emerges in directed networks where the preferential detachment can be proportional to the in and out degrees of the nodes involved. In such networks, preferential detachment is stronger for the incoming edges than for the outgoing edges. We hypothesize multiple possible mechanisms that could explain this phenomenon.

Experimental evidence of the use of a circularly polarized electric field to control the spiral turbulence in a reaction-diffusion system is presented. The spiral turbulence obtained in the Belousov-Zhabotinsky reaction is shown to be forced into ordered stable spiral waves or “targetlike” waves by a circularly polarized electric field with appropriate frequency and intensity. An Arnold's-tongue-shaped control phase diagram is obtained, illustrating the resonance essence of the control.

We investigate the relationship between the emergence of chaos synchronization and the information flow in dynamical systems possessing homogeneous or heterogeneous global interactions whose origin can be external (driven systems) or internal (autonomous systems). By employing general models of coupled chaotic maps for such systems, we show that the presence of a homogeneous global field, either external or internal, for all times is not indispensable for achieving complete or generalized synchronization in a system of chaotic elements. Complete synchronization can also appear with heterogeneous global fields; it does not requires the simultaneous sharing of the field by all the elements in a system. We use the normalized mutual information and the information transfer between global and local variables to characterize complete and generalized synchronization. We show that these information measures can characterize both types of synchronized states and also allow us to discern the origin of a global interaction field. A synchronization state emerges when a sufficient amount of information provided by a field is shared by all the elements in the system, on the average over long times. Thus, the maximum value of the top-down information transfer can be used as a predictor of synchronization in a system, as a parameter is varied.

In two-phase microfluidics, droplets often undergo deformations that drive them away from their circular equilibrium shape. Herein we concentrate on the relaxation of symmetrical deformations to a circle driven by surface tension effects, which are predominant at the micrometer scales. Working in a Hele-Shaw cell, we report a generic pathway for these types of relaxations. We simulate numerically the interface shape evolution and investigate it using linear stability analysis. Finally, we characterize this universal aspect of relaxation using a purely geometrical model that is tested in experiments.

Drainage is typically understood as a process where the pore space is invaded by a nonwetting phase pore-by-pore, the controlling parameters of which are represented by capillary number and mobility ratio. However, what is less understood and where experimental data are lacking is direct knowledge of the dynamics of pore drainage and the associated intrinsic time scales since the rate dependencies often observed with displacement processes are potentially dependent on these time scales. Herein, we study pore drainage events with a high speed camera in a micromodel system and analyze the dependency of interfacial velocity on bulk flow rate and spatial fluid configurations. We find that pore drainage events are cooperative, meaning that capillary pressure differences which extend over multiple pores directly affect fluid topology and menisci dynamics. Results suggest that not only viscous forces but also capillarity acts in a nonlocal way. Lastly, the existence of a pore morphological parameter where pore drainage transitions from capillary to inertial and/or viscous dominated is discussed followed by a discussion on capillary dispersion and time scale dependencies. We show that the displacement front is disperse when volumetric flow rate is less than the intrinsic time scale for a pore drainage event and becomes sharp when the flow rate is greater than the intrinsic time scale (i.e., overruns the pore drainage event), which clearly shows how pore-scale parameters influence macroscale flow behavior.

We describe a Monte Carlo renormalization group approach to the calculation of critical behavior for percolation models. This approach can be utilized to determine the renormalized bond probabilities and the values of the critical exponents. We illustrate the method for two-dimensional bond percolation, but the method is also applicable to other percolation models and other dimensions.

Consider a dynamical many-body system with a random initial state subsequently evolving through stochastic dynamics. What is the relative importance of the initial state (“nature”) versus the realization of the stochastic dynamics (“nurture”) in predicting the final state? We examined this question for the two-dimensional Ising ferromagnet following an initial deep quench from $T=\infty$ to $T=0$. We performed Monte Carlo studies on the overlap between “identical twins” raised in independent dynamical environments, up to size $L=500$. Our results suggest an overlap decaying with time as $t^{-{\theta }_h}$ with ${\theta }_h=0.22\pm 0.02$; the same exponent holds for a quench to low but nonzero temperature. This “heritability exponent” may equal the persistence exponent for the two-dimensional Ising ferromagnet, but the two differ more generally.

We investigate the diffusive motion of micron-sized spherical tracers in a viscoelastic actin filament network over the time span of 8 orders of magnitude using optical-tweezers single-particle tracking. The hydrodynamic interactions of a tracer with the surrounding fluid are shown to dominate at microsecond time scales, while subdiffusive scaling due to viscoelastic properties of the medium emerges at millisecond time scales. The transition between these two regimes is analyzed in the frame of a minimal phenomenological model which combines the Basset force and the generalized Stokes force. The resulting Langevin equation accounts for various dynamical features of the thermal motion of endogenous or exogenous tracers in viscoelastic media such as inertial and hydrodynamic effects at short times, subdiffusive scaling at intermediate times, and eventual optical trapping at long times. Simple analytical formulas for the mean-square displacement and velocity autocorrelation function are derived.

We solve an inverse problem for fluid particle pair statistics: we show that a time sequence of probability density functions (PDFs) of separations can be exactly reproduced by solving the diffusion equation with a suitable time-dependent diffusivity. The diffusivity tensor is given by a time integral of a conditional Lagrangian velocity structure function, weighted by a ratio of PDFs. Physical hypotheses for hydrodynamic turbulence (sweeping, short memory, mean-field) yield simpler integral formulas, including one of Kraichnan and Lundgren (K-L). We evaluate the latter using a space-time database from a numerical Navier-Stokes solution for driven turbulence. The K-L formula reproduces PDFs well at root-mean-square separations, but growth rate of mean-square dispersion is overpredicted due to neglect of memory effects. More general applications of our approach are sketched.

Based on accurate Lennard-Jones-type interaction potentials, we derive a closed set of state equations for the description of warm atomic gases in the presence of ionization processes. The specific heat is predicted to exhibit peaks in correspondence to single and multiple ionizations. Such kinetic analog in atomic gases of the Schottky anomaly in solids is enhanced at intermediate and low atomic densities. The case of adiabatic compression of noble gases is analyzed in detail and the implications on sonoluminescence are discussed. In particular, the predicted plasma electron density in a sonoluminescent bubble turns out to be in good agreement with the value measured in recent experiments.

We study driven flow with exclusion in graphenelike structures. The totally asymmetric simple exclusion process (TASEP), a well-known model in its strictly one-dimensional (chain) version, is generalized to cylinder (nanotube) and ribbon (nanoribbon) geometries. A mean-field theoretical description is given for very narrow ribbons (“necklaces”) and nanotubes. For specific configurations of bond transmissivity rates, and for a variety of boundary conditions, theory predicts equivalent steady-state behavior between (sublattices on) these structures and chains. This is verified by numerical simulations, to excellent accuracy, by evaluating steady-state currents. We also numerically treat ribbons of general width. We examine the adequacy of this model to the description of electronic transport in carbon nanotubes and nanoribbons or specifically designed quantum-dot arrays.

We use Brownian dynamics simulations of a binary mixture of highly charged spherical colloidal particles to test some of the predictions of the random first-order transition (RFOT) theory [Phys. Rev. Lett. 58, 2091 (1987); Phys. Rev. A 40, 1045 (1989)]. In accord with mode-coupling theory and RFOT, we find that as the volume fraction of the colloidal particles $\varphi$ approaches the dynamical transition value ${\varphi }_A$, three measures of dynamics show an effective ergodic to nonergodic transition. First, there is a dramatic slowing down of diffusion, with the translational diffusion constant decaying as a power law as $\varphi \to {\varphi }_A^{-}$. Second, the energy metric, a measure of ergodicity breaking in classical many-body systems, shows that the system becomes effectively nonergodic as ${\varphi }_A$ is approached. Finally, the time $t^{*}$, at which the four-point dynamical susceptibility achieves a maximum, also increases as a power law near ${\varphi }_A$. Remarkably, the translational diffusion coefficients, ergodic diffusion coefficient, and ${\left(t^{*}\right)}^{-1}$ all vanish as ${({\varphi }^{-1}-{\varphi }_A^{-1})}^{\gamma }$ with both ${\varphi }_A(\approx$$0.1)$ and $\gamma$ being the roughly the same for all three quantities. Above ${\varphi }_A$, transport involves crossing free energy barriers. In this regime, the density-density correlation function decays as a stretched exponential [$\exp -{\left(\frac{t}{{\tau }_{\alpha }}\right)}^{\beta }$] with $\beta \approx 0.45$. The $\varphi$ dependence of the relaxation time ${\tau }_{\alpha }$ could be fit using the Vogel-Tamman-Fulcher law with the ideal glass transition at ${\varphi }_K\approx 0.47$. By using a local entropy measure, we show that the law of large numbers is not obeyed above ${\varphi }_A$, and gives rise to subsample to subsample fluctuations in all physical observables. We propose that dynamical heterogeneity is a consequence of violation of law of large numbers.

We derive coefficients of the electrokinetic coupling matrix (${\chi }_{11}$, ${\chi }_{12}$, and ${\chi }_{21}$) for the flow of an ionic solution through a parallel-plate geometry having porous and charged layers grafted onto a solid surface with a known potential and demonstrate Onsager reciprocity for the cross terms (i.e., ${\chi }_{12}={\chi }_{21}$). Our results enable the prediction of system outputs in the solid-porous-fluid system from parameters that are either known or may be measured and inferred. These electrokinetic coupling coefficients are in terms of the potential, $\varphi$, and fixed charge, ${\rho }_f$, only, removing dependence on field gradients and fluid velocity. Additionally, we present simplified expressions of these coupling coefficients in limiting regions of the parameter space. Away from these limits, we present numerical results demonstrating the facility of our functional form for facile numerical approximation and report the utility and accuracy of our analytical approximations.

We present an analytic and stochastic simulation study of a molecular engine working with a flux of particles as a turbine. We focus on the physical observables of velocity, flux, power, and efficiency. The control parameters are the external conservative force and the particle densities. We revise a simpler previous study by using a more realistic model containing multiple equidistant vanes complemented by stochastic simulations of the particles and the turbine. Here we show that the effect of the thermal fluctuations into the flux and the efficiency of these nanometric devices are relevant to the working scale of the system. The stochastic simulations of the Brownian motion of the particles and turbine support the simplified analytical calculations performed.

Mammalian cells are restricted from proliferating indefinitely. Telomeres at the end of each chromosome are shortened at cell division and when they reach a critical length, the cell will enter permanent cell cycle arrest—a state known as senescence. This mechanism is thought to be tumor suppressing, as it helps prevent precancerous cells from dividing uncontrollably. Stem cells express the enzyme telomerase, which elongates the telomeres, thereby postponing senescence. However, unlike germ cells and most types of cancer cells, stem cells only express telomerase at levels insufficient to fully maintain the length of their telomeres, leading to a slow decline in proliferation potential. It is not yet fully understood how this decline influences the risk of cancer and the longevity of the organism. We here develop a stochastic model to explore the role of telomere dynamics in relation to both senescence and cancer. The model describes the accumulation of cancerous mutations in a multicellular organism and creates a coherent theoretical framework for interpreting the results of several recent experiments on telomerase regulation. We demonstrate that the longest average cancer-free lifespan before cancer onset is obtained when stem cells start with relatively long telomeres that are shortened at a steady rate at cell division. Furthermore, the risk of cancer early in life can be reduced by having a short initial telomere length. Finally, our model suggests that evolution will favor a shorter than optimal average cancer-free lifespan in order to postpone cancer onset until late in life.