We study a morphogen gradient formation under nonlinear degradation and subdiffusive transport. In the long-time limit, we obtain the nonlinear effect of degradation-enhanced diffusion, resulting from the interaction of non-Markovian subdiffusive transport with a nonlinear reaction. We find the stationary profile of power-law type, which has implications for robustness, with the shape of the profile being controlled by the anomalous exponent. Far away from the source of morphogens, any changes in the rate of production are not felt.

A nonequilibrium thermodynamic theory demonstrating an induction effect of a statistical nature is presented. We have shown that this thermodynamic induction can arise in a class of systems that have variable kinetic coefficients (VKC). In particular if a kinetic coefficient associated with a given thermodynamic variable depends on another thermodynamic variable then we have derived an expression that can predict the extent of the induction. The amount of induction is shown to be proportional to the square of the driving force. The nature of the intervariable coupling for the induction effect has similarities with the Onsager symmetry relations, though there is an important sign difference as well as the magnitudes not being equal. Thermodynamic induction adds nonlinear terms that improve the stability of stationary states, at least within the VKC class of systems. Induction also produces a term in the expression for the rate of entropy production that could be interpreted as self-organization. Many of these results are also obtained using a variational approach, based on maximizing entropy production, in a certain sense. Nonequilibrium quantities analogous to the free energies of equilibrium thermodynamics are introduced.

Prompted by results that showed that a simple protein model, the frustrated Gō model, appears to exhibit a transition reminiscent of the protein dynamical transition, we examine the validity of this model to describe the low-temperature properties of proteins. First, we examine equilibrium fluctuations. We calculate its incoherent neutron-scattering structure factor and show that it can be well described by a theory using the one-phonon approximation. By performing an inherent structure analysis, we assess the transitions among energy states at low temperatures. Then, we examine nonequilibrium fluctuations after a sudden cooling of the protein. We investigate the violation of the fluctuation-dissipation theorem in order to analyze the protein glass transition. We find that the effective temperature of the quenched protein deviates from the temperature of the thermostat, however it relaxes towards the actual temperature with an Arrhenius behavior as the waiting time increases. These results of the equilibrium and nonequilibrium studies converge to the conclusion that the apparent dynamical transition of this coarse-grained model cannot be attributed to a glassy behavior.

The effect of crowding on the run-and-tumble dynamics of swimmers such as bacteria is studied using a discrete lattice model of mutually excluding particles that move with constant velocity along a direction that is randomized at a rate $\alpha$. In stationary state, the system is found to break into dense clusters in which particles are trapped or stopped from moving. The characteristic size of these clusters predominantly scales as ${\alpha }^{-0.5}$ in both one and two dimensions. For a range of densities, due to cooperative effects, the stopping time scales as ${\mathcal{T}}_{1d}^{0.85}$ and as ${\mathcal{T}}_{2d}^{0.8}$, where ${\mathcal{T}}_d$ is the diffusive time associated with the motion of cluster boundaries. Our findings might be helpful in understanding the early stages of biofilm formation.

We study the escape of a chain of coupled units over the barrier of a metastable potential. It is demonstrated that a very weak external driving field with a suitably chosen frequency suffices to accomplish speedy escape. The latter requires passage through a transition state, the formation of which is triggered by permanent feeding of energy from a phonon background into humps of localized energy and elastic interaction of the arising breather solutions. In fact, cooperativity between the units of the chain entailing coordinated energy transfer is shown to be crucial for enhancing the rate of escape in an extremely effective and low-energy cost way where the effects of entropic localization and breather coalescence conspire.

Understanding flow properties and phase behavior of water confined to nanometer-sized pores and slits is central to a wide range of problems in science, such as percolation in geology, lubrication of future nano-machines, self-assembly and interactions of biomolecules, and transport through porous media in filtration processes. Experiments with different techniques in the past have reported that viscosity of nanoconfined water increases, decreases, or remains close to bulk water. Here we show that water confined to less than 20-nm-thick films exhibits both viscoelasticity and shear thinning. Typically viscoelasticity and shear thinning appear due to shearing of complex non-Newtonian mixtures possessing a slowly relaxing microstructure. The shear response of nanoconfined water in a range of shear frequencies (5 to 25 KHz) reveals that relaxation time diverges with reducing film thickness. It suggests that slow relaxation under confinement possibly arises due to existence of a critical point with respect to slit width. This criticality is similar to the capillary condensation in porous media.

For any branching process, we demonstrate that the typical total number $r_{\mathrm{mp}}\left(\nu \tau \right)$ of events triggered over all generations within any sufficiently large time window $\tau$ exhibits, at criticality, a superlinear dependence $r_{\mathrm{mp}}\left(\nu \tau \right)\sim {\left(\nu \tau \right)}^{\gamma }$ (with $\gamma >1$) on the total number $\nu \tau$ of the immigrants arriving at the Poisson rate $\nu$. In branching processes in which immigrants (or sources) are characterized by fertilities distributed according to an asymptotic power-law tail with tail exponent $1<\gamma ⩽2$, the exponent of the superlinear law for $r_{\mathrm{mp}}\left(\nu \tau \right)$ is identical to the exponent $\gamma$ of the distribution of fertilities. For $\gamma >2$ and for standard branching processes without power-law distribution of fertilities, $r_{\mathrm{mp}}\left(\nu \tau \right)\sim {\left(\nu \tau \right)}^2$. This scaling law replaces and tames the divergence $\nu \tau /(1-n)$ of the mean total number ${\overline{R}}_t\left(\tau \right)$ of events, as the branching ratio (defined as the average number of triggered events of first generation per source) tends to 1. The derivation uses the formalism of generating probability functions. The corresponding prediction is confirmed by numerical calculations, and an heuristic derivation enlightens its underlying mechanism. We also show that ${\overline{R}}_t\left(\tau \right)$ is always linear in $\nu \tau$ even at criticality ($n=1$). Our results thus illustrate the fundamental difference between the mean total number, which is controlled by a few extremely rare realizations, and the typical behavior represented by $r_{\mathrm{mp}}\left(\nu \tau \right)$.

We introduce a growing one-dimensional quenched spin model that bases on asymmetrical one-side Ising interactions in the presence of external field. Numerical simulations and analytical calculations based on Markov chain theory show that when the external field is smaller than the exchange coupling constant $J$ there is a nonmonotonous dependence of the mean magnetization on the temperature in a finite system. The crossover temperature $T_c$ corresponding to the maximal magnetization decays with system size, approximately as the inverse of the Lambert $W$ function. The observed phenomenon can be understood as an interplay between the thermal fluctuations and the presence of the first cluster determined by initial conditions. The effect exists also when spins are not quenched but fully thermalized after the attachment to the chain. By performing tests on real data we conceive the model is in part suitable for a qualitative description of online emotional discussions arranged in a chronological order, where a spin in every node conveys emotional valence of a subsequent post.

Recent results have shown the appearance of induced cooperative motions called dynamic heterogeneity during the isomerization of diluted azobenzene molecules in a host glass-former. In this paper, we raise the issue of the coupling between these “artificial” heterogeneities and the isomerization period. How do these induced heterogeneities differ in the saturation regime and in the linear response regime? Is there a maximum of the heterogeneous motion versus the isomerization rate, and why? Is the heterogeneity evolution with the isomerization rate connected with the diffusion or relaxation time evolution? We use out-of-equilibrium molecular dynamics simulations to answer these questions. We find that the heterogeneity increases in the linear response regime for large isomerization periods and small perturbations. In contrast, the heterogeneity decreases in the saturation regime, i.e., when the isomerization half-period (${\tau }_p/2$) is smaller than the relaxation time of the material (${\tau }_{\alpha }$). This result enables a test of the effect of cooperative motions on the dynamics using the chromophores as Maxwell demons that destroy or stimulate the cooperative motions. Because the heterogeneities increase in the linear regime and then decrease in the saturation regime, we find a maximum for ${\tau }_p/2\approx {\tau }_{\alpha }$. The induced excitation concentration follows a power-law evolution versus the isomerization rate and then saturates. As a consequence, the $\alpha$ relaxation time is related to the excitation concentration with a power law, a result in qualitative agreement with recent findings in constrained models. This result supports a common origin for the heterogeneities with constrained models and a similar relation to the excitation concentration.

We use an analog of nanoindentation on a colloidal glass to elucidate the incipient plastic deformation of glasses. By tracking the motion of the individual particles in three dimensions, we visualize the strain field and glass structure during the emerging deformation. At the onset of flow, we observe a power-law distribution of strain indicating strongly correlated deformation, and reflecting a critical state of the glass. At later stages, the strain acquires a Gaussian distribution, indicating that plastic events become uncorrelated. Investigation of the glass structure using both static and dynamic measures shows a weak correlation between the structure and the emerging strain distribution. These results indicate that the onset of plasticity is governed by strong power-law correlations of strain, weakly biased by the heterogeneous glass structure.

We consider a fiber made of a soft elastic material, encased in a stiff elastic shell (core-shell geometry). If the core and shell dimensions are mismatched, e.g., because the core shrinks while the shell does not, but the two remain attached, then an elastic instability is triggered whereby wrinkles may appear on the shell. The wrinkle orientation may be longitudinal (along the fiber axis), polar (along the fiber perimeter), or a mixture of both, depending on the fiber's geometrical and material parameters. Here we investigate under what conditions longitudinal or polar wrinkling will occur.

We have modeled stress concentration around small gaps in anisotropic elastic sheets, corresponding to the peptidoglycan sacculus of bacterial cells, under loading corresponding to the effects of turgor pressure in rod-shaped bacteria. We find that under normal conditions the stress concentration is insufficient to mechanically rupture bacteria, even for gaps up to a micron in length. We then explored the effects of stress-dependent smart autolysins, as hypothesized by A. L. Koch [Adv. Microb. Physiol. 24, 301 (1983); Res. Microbiol. 141, 529 (1990)]. We show that the measured anisotropic elasticity of the peptidoglycan (PG) sacculus can lead to stable circumferential propagation of small gaps in the sacculus. This is consistent with the recent observation of circumferential propagation of PG-associated MreB patches in rod-shaped bacteria. We also find a bistable regime of both circumferential and axial gap propagation, which agrees with behavior reported in cytoskeletal mutants of B. subtilis. We conclude that the elastic anisotropies of a bacterial sacculus, as characterized experimentally, may be relevant for maintaining rod-shaped bacterial growth.

The effect of confinement on the droplet formation in T junctions was studied for three configurations of fluid injection. The sizes of the main droplets and the satellite droplets were measured in the squeezing and dripping regimes. The evolution of droplet sizes with capillary number in the continuous phase is similar to that in flow-focusing junctions, i.e., the size of the main droplets decreases with an increase of this capillary number, while the size of the satellite droplets increases with an increase of this capillary number. While in the range of flow rates investigated the injection configuration does not exhibit a significant effect on the main droplet sizes, it does have an effect on the size of the satellite droplets. The latter ones are smaller when the neck rupture of the droplet occurs on an angle of the microsystem.

Using numerical simulations, we investigate the wave number and frequency dependent transverse current correlation function $C_T(k,\omega )$ of a single-component fluid with Yukawa interaction potential, also known as the Yukawa one-component plasma. The transverse current correlation function is an important quantity because it contains the microscopic details of the viscoelastic behavior of the fluid. We show that, in the region of densities and temperatures in which shear waves do not propagate, the dynamics of the system are in striking agreement with a simple model of generalized hydrodynamics. As either the density is increased or the temperature decreased, the transverse current correlation function shows additional structure that the simple models fail to capture.

The propagation and localization of transversal-rotational waves in a two-dimensional granular chain of equal masses are analyzed in this study. The masses are infinitely long cylinders possessing one translational and one rotational degree of freedom. Two dispersive propagating modes are predicted in this granular crystal. By considering the semi-infinite chain with a boundary condition applied at its beginning, the analytical study demonstrates the existence of localized modes, each mode composed of two evanescent modes. Their existence, position (either in the gap between the propagating modes or in the gap above the upper propagating mode), and structure of spatial localization are analyzed as a function of the relative strength of the shear and bending interparticle interactions and for different boundary conditions. This demonstrates the existence of a localized mode in a semi-infinite monatomic chain when transversal-rotational waves are considered, while it is well known that these types of modes do not exist when longitudinal waves are considered.

We present magneto-optical measurements on two liquid crystals that exhibit a wide temperature-range amorphous blue phase (BPIII). Magnetic fields up to 25 T are found to suppress the onset of BPIII in both materials by almost 1 °C. This effect appears to increase nonlinearly with the field strength. The effect of high fields on established BPIIIs is also reported, in which we find significant hysteresis and very slow dynamics. Possible explanations of these results are discussed.

Exact explicit rogue-wave solutions of intricate structures are presented for the long-wave–short-wave resonance equation. These vector parametric solutions feature coupled dark- and bright-field counterparts of the Peregrine soliton. Numerical simulations show the robustness of dark and bright rogue waves in spite of the onset of modulational instability. Dark fields originate from the complex interplay between anomalous dispersion and the nonlinearity driven by the coupled long wave. This unusual mechanism, not available in scalar nonlinear wave equation models, can provide a route to the experimental realization of dark rogue waves in, for instance, negative index media or with capillary-gravity waves.

The thermal properties of a system, comprising of a spinless noninteracting charged particle in the presence of a constant external magnetic field and confined in a parabolic quantum well are studied. The focus has been on the effects of a topological defect, of the form of conical disclination, with regard to the thermodynamic properties of the system. We have obtained the modifications to the traditional Landau-Fock-Darwin spectrum in the presence of conical disclination. The effect of the conical kink on the degeneracy structure of the energy levels is investigated. The canonical formalism is used to compute various thermodynamic variables. The study shows an interplay between magnetic field, temperature, and the degree of conicity by setting two scales for temperature corresponding to the frequency of the confining potential and the cyclotron frequency of external magnetic field. The kink parameter is found to affect the quantitative behavior of the thermodynamic quantities. It plays a crucial role in the competition between the external magnetic field and temperature in fixing the values of the thermal response functions. This study provides an important motivation for studying similar systems, however with nontrivial interactions in the presence of topological defects.

In this paper, the variation of permselectivity in the course of concentration polarization is systematically analyzed for a three-layer membrane system consisting of a nonperfectly permselective ion exchange membrane, homogeneous or heterogeneous, flanked by two diffusion layers of a binary univalent electrolyte. For a heterogeneous membrane, an ionic transport model is proposed, which is amenable to analytical treatment. In this model, assuming a constant fixed charge in the membrane and disregarding water splitting, the entire transport problem is reduced to solution of a single algebraic equation for the counterion transport number. It is concluded that for both types of membrane the concentration polarization may significantly affect the permselectivity of the system through the effects of the induced nonuniformity of the coion diffusion flux in the membrane (convexity of the coion concentration profile) and varying membrane-solution interface concentration. While the former is significant for low membrane fixed charge density, for a heterogeneous membrane, the latter might be considerably affected by the flux focusing effect at the permeable membrane segments.

Two kinds of electroconvection patterns in an ether-bridged bent-core nematic liquid crystal material (BCN), which appear in different frequency ranges, are examined and compared. One is a longitudinal pattern with the stripes parallel to the orientation of the BCN and with a periodicity of approximately the cell thickness, occurring in the high-frequency range of several hundreds Hz; the other one is oblique stripes, which results in a zigzag pattern, and appears in the low-frequency range of several tens Hz. In addition, within an intermediate-frequency range, transformations from oblique to longitudinal and then to normal stripes occur at increased ac voltages. In particular, we investigated the temperature behavior of longitudinal and oblique stripes: When the temperature $T$ increases and approaches the clearing temperature $T_c$, the contrast of the domains is enhanced and the frequency range of existence becomes wider, while the onset voltages increase only moderately instead of diverging, thus suggesting an isotropic mechanism of pattern formation.