We introduce an innovative numerical technique based on convex optimization to solve a range of infinite-dimensional variational problems arising from the application of the background method to fluid flows. In contrast to most existing schemes, we do not consider the Euler-Lagrange equations for the minimizer. Instead, we use series expansions to formulate a finite-dimensional semidefinite program (SDP) whose solution converges to that of the original variational problem. Our formulation accounts for the influence of all modes in the expansion, and the feasible set of the SDP corresponds to a subset of the feasible set of the original problem. Moreover, SDPs can be easily formulated when the fluid is subject to imposed boundary fluxes, which pose a challenge for the traditional methods. We apply this technique to compute rigorous and near-optimal upper bounds on the dissipation coefficient for flows driven by a surface stress. We improve previous analytical bounds by more than 10 times and show that the bounds become independent of the domain aspect ratio in the limit of vanishing viscosity. We also confirm that the dissipation properties of stress-driven flows are similar to those of flows subject to a body force localized in a narrow layer near the surface. Finally, we show that SDP relaxations are an efficient method to investigate the energy stability of laminar flows driven by a surface stress.

Relay synchronization is a collective state, originally found in chains of interacting oscillators, in which uncoupled dynamical units synchronize through the action of mismatched inner nodes that relay the information but do not synchronize with them. It is demonstrated herein that relay synchronization is not limited to such simple motifs, rather it can emerge in larger and arbitrary network topologies. In particular, we show how this phenomenon can be observed in networks of chaotic systems in the presence of some mismatched units, the relay nodes, and how it is actually responsible for an enhancement of synchronization in the network.

A general two-layer network consists of two networks $G_1$ and $G_2$, whose interconnection pattern is specified by the interconnectivity matrix $B$. We deduce desirable properties of $B$ from a dynamic process point of view. Many dynamic processes are described by the Laplacian matrix $Q$. A regular topological structure of the interconnectivity matrix $B$ (constant row and column sum) enables the computation of a nontrivial eigenmode (eigenvector and eigenvalue) of $Q$. The latter eigenmode is independent from $G_1$ and $G_2$. Such a regularity in $B$, associated to equitable partitions, suggests design rules for the construction of interconnected networks and is deemed crucial for the interconnected network to show intriguing behavior, as discovered earlier for the special case where $B=wI$ refers to an individual node to node interconnection with interconnection strength $w$. Extensions to a general $m$-layer network are also discussed.

The adaptation of prevertebra size to embryo size is investigated in the framework of a reaction-diffusion model involving a Turing pattern. The reaction scheme and Fick's first law of diffusion are modified in order to take into account the departure from dilute conditions induced by confinement in smaller embryos. In agreement with the experimental observations of scaling in somitogenesis, our model predicts the formation of smaller prevertebrae or somites in smaller embryos. These results suggest that models based on Turing patterns cannot be automatically disregarded by invoking the question of maintaining proportions in embryonic development. Our approach highlights the nontrivial role that the solvent can play in biology.

The kinetic preference of actin-binding proteins to actin filaments is altered by external forces on the filament. Such an altered kinetic preference is largely responsible for remodeling the actin cytoskeletal structure in response to intracellular forces. During remodeling, actin-binding proteins and actin filaments interact under isothermal conditions, because the cells are homeostatic. In such a temperature homeostatic state, we can rigorously and thermodynamically link the chemical potential of actin-binding proteins to stresses on the actin filaments. From this relationship, we can construct a physical model that explains the force-dependent kinetic preference of actin-binding proteins to actin filaments. To confirm the model, we have analyzed the mechanosensitive alternation of the kinetic preference of Arp2/3 and cofilin to actin filaments. We show that this model captures the qualitative responses of these actin-binding proteins to the forces, as observed experimentally. Moreover, our theoretical results demonstrate that, depending on the structural parameters of the binding region, actin-binding proteins can show different kinetic responses even to the same mechanical signal tension, in which the double-helix nature of the actin filament also plays a critical role in a stretch-twist coupling of the filament.

Mechanical properties of cells and their mechanical interaction with the extracellular environments are main factors influencing cellular function, thus indicating the progression of cells in different disease states. By considering the mechanical interactions between cell adhesion molecules and the extracellular environment, we developed a cell mechanical model that can characterize the mechanical changes in cells during cell spreading. A cell model was established that consisted of various main subcellular components, including cortical cytoskeleton, nuclear envelope, actin filaments, intermediate filaments, and microtubules. We demonstrated the structural changes in subcellular components and the changes in spreading areas during cell spreading driven by traction forces. The simulation of nanoindentation tests was conducted by integrating the indenting force to the cell model. The force-indentation curve of the cells at different spreading states was simulated, and the results showed that cell stiffness increased with increasing traction forces, which were consistent with the experimental results. The proposed cell mechanical model provides a strategy to investigate the mechanical interactions of cells with the extracellular environments through the adhesion molecules and to reveal the cell mechanical properties at the subcellular level as cells shift from the suspended state to the adherent state.

We study the dynamics of a double-stranded DNA (dsDNA) segment, as a semiflexible polymer, in a shear flow, the strength of which is customarily expressed in terms of the dimensionless Weissenberg number Wi. Polymer chains in shear flows are well known to undergo tumbling motion. When the chain lengths are much smaller than the persistence length, one expects a (semiflexible) chain to tumble as a rigid rod. At low Wi, a polymer segment shorter than the persistence length does indeed tumble as a rigid rod. However, for higher Wi the chain does not tumble as a rigid rod, even if the polymer segment is shorter than the persistence length. In particular, from time to time the polymer segment may assume a buckled form, a phenomenon commonly known as Euler buckling. Using a bead-spring Hamiltonian model for extensible dsDNA fragments, we first analyze Euler buckling in terms of the oriented deterministic state (ODS), which is obtained as the steady-state solution of the dynamical equations by turning off the stochastic (thermal) forces at a fixed orientation of the chain. The ODS exhibits symmetry breaking at a critical Weissenberg number ${\mathrm{Wi}}_{\text{c}}$, analogous to a pitchfork bifurcation in dynamical systems. We then follow up the analysis with simulations and demonstrate symmetry breaking in computer experiments, characterized by a unimodal to bimodal transformation of the probability distribution of the second Rouse mode with increasing Wi. Our simulations reveal that shear can cause strong deformation for a chain that is shorter than its persistence length, similar to recent experimental observations.

The effect of superposed dc and ac applied voltages on two types of spatially periodic instabilities in nematic liquid crystals, flexoelectric domains (FD), and electroconvection (EC) was studied. The onset characteristics, threshold voltages, and critical wave vectors were determined. We found that in general the superposition of driving with different time symmetries inhibits the pattern forming mechanisms for FD and EC as well. As a consequence, the onset extends to much higher voltages than the individual dc or ac thresholds. A dc-bias-induced reduction of the crossover frequency from the conductive to the dielectric EC regimes and a peculiar transition between two types of flexodomains with different wavelengths were detected. Direct measurements of the change of the electrical conductivity and its anisotropy, induced by the applied dc voltage component, showed that the dc bias substantially affects both parameters. Taking into account the experimentally detected variations of the conductivity in the linear stability analysis of the underlying nematohydrodynamic equations, a qualitative agreement with the experimental findings on the onset behavior of spatially periodic instabilities was obtained.

Many microorganisms swim in a highly heterogeneous environment with obstacles such as fibers or polymers. To better understand how this environment affects microorganism swimming, we study propulsion of a cylinder or filament in a fluid with a sparse, stationary network of obstructions modeled by the Brinkman equation. The mathematical analysis of swimming speeds is investigated by studying an infinite-length cylinder propagating lateral or spiral displacement waves. For fixed bending kinematics, we find that swimming speeds are enhanced due to the added resistance from the fibers. In addition, we examine the work and the torque exerted on the cylinder in relation to the resistance. The solutions for the torque, swimming speed, and work of an infinite-length cylinder in a Stokesian fluid are recovered as the resistance is reduced to zero. Finally, we compare the asymptotic solutions with numerical results for the Brinkman flow with regularized forces. The swimming speed of a finite-length filament decreases as its length decreases and planar bending induces an angular velocity that increases linearly with added resistance. The comparisons between the asymptotic analysis and computation give insight on the effect of the length of the filament, the permeability, and the thickness of the cylinder in terms of the overall performance of planar and helical swimmers.

We demonstrate that an inverse Monte Carlo approach allows one to reconstruct effective interaction potentials from real-space images. The method is exemplified on monomolecular ethanol-water films imaged with scanning force microscopy, which provides the spatial distribution of the molecules. Direct Monte Carlo simulations with the reconstructed potential allow for obtaining characteristics of the system which are unavailable in the experiment, such as the heat capacity of the monomolecularly thin film, and for a prediction of the critical temperature of the demixing transition.

We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the composition of independent systems, in the context of a recently proposed generalization of the Shannon-Khinchin axioms. We associate to each member of a large class of entropies a generalized information measure, satisfying the additivity property on a set of independent systems as a consequence of the underlying group law. At the same time, we also show that Einstein's likelihood function naturally emerges as a byproduct of our informational interpretation of (generally nonadditive) entropies. These results confirm the adequacy of composable entropies both in physical and social science contexts.

We consider several one-dimensional driven lattice-gas models that show a phase transition in the stationary state between a high-density fluid phase in which the typical length of a hole cluster is of order unity and a low-density jammed phase where a hole cluster of macroscopic length forms in front of a particle. Using a hydrodynamic equation for an interface growth model obtained from the driven lattice-gas models of interest here, we find that in the fluid phase, the roughness exponent and the dynamic exponent that, respectively, characterize the scaling of the saturation width and the relaxation time of the interface with the system size are given by the Kardar-Parisi-Zhang exponents. However, at the critical point, we show analytically that when the equal-time density-density correlation function decays slower than inverse distance, the roughness exponent varies continuously with a parameter in the hop rates, but it is one-half otherwise. Using these results and numerical simulations for the density-density autocorrelation function, we further find that the dynamic exponent $z=3/2$ in all cases.

In renormalized field theories there are in general one or few fixed points that are accessible by the renormalization-group flow. They can be identified from the fixed-point equations. Exceptionally, an infinite family of fixed points exists, parameterized by a scaling exponent $\zeta$, itself a function of a nonrenormalizing parameter. Here we report a different scenario with an infinite family of fixed points of which seemingly only one is chosen by the renormalization-group flow. This dynamical selection takes place in systems with an attractive interaction $\mathcal{V}\left(\varphi \right)$, as in standard ${\varphi }^4$ theory, but where the potential $\mathcal{V}$ at large $\varphi$ goes to zero, as, e.g., the attraction by a defect.

We consider the diffusive properties of Brownian motion in a biased periodic potential. We relate the effective diffusion coefficient to the solution of two coupled time-independent partial differential equations and solve these equations numerically by the matrix-continued-fraction (MCF) method for intermediate values of the temperature and friction coefficient. The weak-noise limit is explored by numerical simulations of the Langevin equations. Here, we identify the regions of parameters for which the diffusion coefficient exponentially grows with inverse temperature. In particular, we demonstrate that there is a finite range of bias forces for which such a growth is observed (region of giant enhancement of diffusion). We also show that at small forces close to the critical range, the diffusion coefficient possesses a pronounced maximum as a function of temperature. All results can be interpreted in the framework of a simple two-state theory incorporating the transition rates between the locked and running solutions.

Evolutionary games on networks traditionally involve the same game at each interaction. Here we depart from this assumption by considering mixed games, where the game played at each interaction is drawn uniformly at random from a set of two different games. While in well-mixed populations the random mixture of the two games is always equivalent to the average single game, in structured populations this is not always the case. We show that the outcome is, in fact, strongly dependent on the distance of separation of the two games in the parameter space. Effectively, this distance introduces payoff heterogeneity, and the average game is returned only if the heterogeneity is small. For higher levels of heterogeneity the distance to the average game grows, which often involves the promotion of cooperation. The presented results support preceding research that highlights the favorable role of heterogeneity regardless of its origin, and they also emphasize the importance of the population structure in amplifying facilitators of cooperation.

An analysis of an electron spectrometer used to characterize fast electrons generated by ultraintense (${10}^{20}\mathrm{W}{\mathrm{cm}}^{-2}$) laser interaction with a preformed plasma of scale length measured by shadowgraphy is presented. The effects of fringing magnetic fields on the electron spectral measurements and the accuracy of density scale-length measurements are evaluated. 2D EPOCH PIC code simulations are found to be in agreement with measurements of the electron energy spectra showing that laser filamentation in plasma preformed by a prepulse is important with longer plasma scale lengths ($>8 \mu \mathrm{m}$).

The nonlocal dielectric approach has led to new models and solvers for predicting electrostatics of proteins (or other biomolecules), but how to validate and compare them remains a challenge. To promote such a study, in this paper, two typical nonlocal dielectric models are revisited. Their analytical solutions are then found in the expressions of simple series for a dielectric sphere containing any number of point charges. As a special case, the analytical solution of the corresponding Poisson dielectric model is also derived in simple series, which significantly improves the well known Kirkwood's double series expansion. Furthermore, a convolution of one nonlocal dielectric solution with a commonly used nonlocal kernel function is obtained, along with the reaction parts of these local and nonlocal solutions. To turn these new series solutions into a valuable research tool, they are programed as a free fortran software package, which can input point charge data directly from a protein data bank file. Consequently, different validation tests can be quickly done on different proteins. Finally, a test example for a protein with 488 atomic charges is reported to demonstrate the differences between the local and nonlocal models as well as the importance of using the reaction parts to develop local and nonlocal dielectric solvers.

A conserved generalized zero-range process is considered in which two sites interact such that particles hop from the more populated site to the other with a probability $p$. The steady-state particle distribution function $P\left(n\right)$ is obtained using both analytical and numerical methods. The system goes through several phases as $p$ is varied. In particular, a condensate phase appears for $p_l<p<p_c$, where the bounding values depend on the range of interaction, with $p_c<0.5$ in general. Analysis of $P\left(n\right)$ in the condensate phase using a known scaling form shows there is universal behavior in the short-range process while the infinite range process displays nonuniversality. In the noncondensate phase above $p_c$, two distinct regions are identified: $p_c<p\le 0.5$ and $p>0.5$; a scale emerges in the system in the latter and this feature is present for all ranges of interaction.

Feedback loops are known as a versatile tool for controlling transport in small systems, which usually have large intrinsic fluctuations. Here we investigate the control of a temporal correlation function, the waiting-time distribution, under active and passive feedback conditions. We develop a general formalism and then specify to the simple unidirectional transport model, where we compare costs of open-loop and feedback control and use methods from optimal control theory to optimize waiting-time distributions.