We investigate the solution in rational form for the Sasa-Satsuma equation on a continuous background which describes a nonlinear fiber system with higher-order effects including the third-order dispersion, Kerr dispersion, and stimulated inelastic scattering. The W-shaped soliton in the system is obtained analytically. It is found that the height of hump for the soliton increases with decreasing the background frequency in certain parameter regime. The maximum height of the soliton can be three times the background's height and the corresponding profile is identical with the one for the well-known eye-shaped rogue wave with maximum peak. The numerical simulations indicate that the W-shaped soliton is stable with small perturbations. Particularly, we show that the W-shaped soliton corresponds to a stable supercontinuum pulse by performing exact spectrum analysis.

We show results of our high force (up to 1.8 nN) atomic force microscopy force spectroscopy measurements of a double stranded DNA. We have found that the force spectra of torsionally constrained molecules display a small plateau occurring at a force of approximately 1 nN. This transition is absent in molecules with rotational freedom. Based on all-atom molecular dynamics simulations, we suggest that this plateau is a result of reducing the diameter of a double helix through extreme stretching. The simulation suggests that the molecule is forced into a form resembling an underwound P-DNA, with bases protruding outside of the backbones. These results broaden our understanding of the fundamental aspects of DNA nanomechanics.

The hydrophobic interaction manifests two separate regimes in terms of size: Small nonpolar bodies exhibit a weak oscillatory force (versus distance) while large nonpolar surfaces exhibit a strong monotonic one. This crossover in hydrophobic behavior is typically explained in terms of water's tetrahedral structure: Its tetrahedrality is enhanced near small solutes and diminished near large planar ones. Here, we demonstrate that water's tetrahedral correlations signal this switch even in a highly simplified, isotropic, “core-softened” water model. For this task, we introduce measures of tetrahedrality based on the angular distribution of water's nearest neighbors. On a quantitative basis, the coarse-grained model of course is only approximate: (1) While greater than simple Lennard-Jones liquids, its bulk tetrahedrality remains lower than that of fully atomic models; and (2) the decay length of the large-scale hydrophobic interaction is less than has been found in experiments. Even so, the qualitative behavior of the model is surprisingly rich and exhibits numerous waterlike hydrophobic behaviors, despite its simplicity. We offer several arguments for the manner in which it should be able to (at least partially) reproduce tetrahedral correlations underlying these effects.

We present a theoretical and experimental study of light transport in disordered media with strongly heterogeneous distribution of scatterers formed via nonscattering regions. Step correlations induced by quenched disorder are found to prevent diffusivity from diverging with increasing heterogeneity scale, contrary to expectations from annealed models. Spectral diffusivity is measured for a porous ceramic where nanopores act as scatterers and macropores render their distribution heterogeneous. Results agree well with Monte Carlo simulations and a proposed analytical model.

Inspired by the flashing ratchet, Parrondo's game presents an apparently paradoxical situation. Parrondo's game consists of two individual games, game A and game B. Game A is a slightly losing coin-tossing game. Game B has two coins, with an integer parameter $M$. If the current cumulative capital (in discrete unit) is a multiple of $M$, an unfavorable coin $p_b$ is used, otherwise a favorable $p_g$ coin is used. Paradoxically, a combination of game A and game B could lead to a winning game, which is the Parrondo effect. We extend the original Parrondo's game to include the possibility of $M$ being either $M_1$ or $M_2$. Also, we distinguish between strong Parrondo effect, i.e., two losing games combine to form a winning game, and weak Parrondo effect, i.e., two games combine to form a better-performing game. We find that when $M_2$ is not a multiple of $M_1$, the combination of $B\left(M_1\right)$ and $B\left(M_2\right)$ has strong and weak Parrondo effect for some subsets in the parameter space $(p_b,p_g)$, while there is neither strong nor weak effect when $M_2$ is a multiple of $M_1$. Furthermore, when $M_2$ is not a multiple of $M_1$, a stochastic mixture of game A may cancel the strong and weak Parrondo effect. Following a discretization scheme in the literature of Parrondo's game, we establish a link between our extended Parrondo's game with the analysis of discrete Brownian ratchet. We find a relation between the Parrondo effect of our extended model to the macroscopic bias in a discrete ratchet. The slope of a ratchet potential can be mapped to the fair game condition in the extended model, so that under some conditions, the macroscopic bias in a discrete ratchet can provide a good predictor for the game performance of the extended model. On the other hand, our extended model suggests a design of a ratchet in which the potential is a mixture of two periodic potentials.

We use a hybrid Monte Carlo algorithm to simulate the shaking of spheres at different vibrational amplitudes and find that spontaneous crystallization occurs in specific dynamical regimes. Several crystallizing transitions are typically observed, leading to end states which can be fully or partially ordered, depending on the shaking amplitude, which we investigate using metrics of global and local order. At the lowest amplitudes, crystallization is incomplete, at least for our times of observation. For amplitude ranges where crystallization is complete, there is typically a competition between hcp and fcc ordering. It is seen that fcc ordering typically predominates; in fact for an optimal range of amplitudes, spontaneous crystallization into a pure fcc state is observed. An interesting feature is the breakdown of global order when there is juxtaposition of fully developed hcp and fcc order locally: we suggest that this is due to the interfaces between the different domains of order, which play the same role as dislocations.

Using molecular dynamics simulation with an angle-dependent Lennard-Jones potential, we study orientational glass with quadrupolar symmetry in mixtures of elliptic particles and circular impurities in two dimensions. With a mild aspect ratio $(=1.23$) and a mild size ratio $(=1.2$), we realize a plastic crystal at relatively high temperature $T$. With further lowering $T$, we find a structural phase transition for very small impurity concentration $c$ and pinned disordered orientations for not small $c$. The ellipses are anchored by the impurities in the planar alignment. With increasing $c$, the orientation domains composed of isosceles triangles gradually become smaller, resulting in orientational glass with crystal order. In our simulation, the impurity distribution becomes heterogeneous during quenching from liquid, which then produces rotational dynamic heterogeneities. We also examine rheology in orientational glass to predict a shape memory effect and a superelasticity effect, where a large fraction of the strain is due to collective orientation changes.

During a phase transition in a bulk material, heat is exchanged with matter to balance the changes in the internal energy and the entropy of the system. Here we report on the thermal detection of a surface-mediated anchoring transition, a spontaneous and discontinuous orientation change between planar (P) and homeotropic (H) alignments within a single nematic phase by changing temperature. In this case a stepwise change in the heat flow, similar to a glass transition, is observed by means of high-resolution differential scanning calorimetry. We found that the jump in the specific heat does not depend on the sample volume, although the contribution of molecules in the vicinity of surfaces, which trigger the transition, becomes less with increasing the sample volume. This means that different molecular orientations, H and P, with respect to surfaces have different thermodynamic free energies. We also address why the anchoring transition occurs by means of grazing-incidence x-ray diffraction measurements, which clearly reveal the formation of quasismectic layers parallel to surfaces in the nematic phase.

The results of many experiments on polymers such as polystyrene indicate that the polymer chains near a free surface exhibit enhanced dynamics when compared with the bulk. We have investigated whether this is the case for poly(tetrafluoroethylene) (PTFE) by using zero-field muon-spin-relaxation spectroscopy to characterize a local probe, the F–Mu${}^{+}$–F state, which forms when spin-polarized positive muons are implanted in PTFE. Low-energy muons (implantation energies from 2.0 to 23.0 keV) were used to study the F–Mu${}^{+}$–F state between $\sim$23 and 191 nm from the free surface of PTFE. Measurements were also made with surface muons (4.1 MeV) where the mean implantation depth is on the order of $\sim$0.6 mm. The relaxation rate of the F–Mu${}^{+}$–F state up to $\sim$150 K was found to be significantly higher for muons implanted at 2.0 keV than for higher implantation energies, which suggests that the polymer chains in a region on the order of a few tens of nanometers from the free surface are more mobile than those in the bulk.

Polymers exposed to shear flow exhibit a remarkably rich tumbling dynamics. While rigid rods rotate on Jeffery orbits, a flexible polymer stretches and coils up during tumbling. Theoretical results show that in both of these asymptotic regimes the corresponding tumbling frequency $f_c$ in a linear shear flow of strength $\gamma$ scales as a power law ${\mathrm{Wi}}^{2/3}$ in the Weissenberg number $\mathrm{Wi}=\gamma \tau$, where $\tau$ is a characteristic time of the polymer's relaxational dynamics. For a flexible polymer these theoretical results are well confirmed by a large body of experimental single molecule studies. However, for the intermediate semiflexible regime, especially relevant for cytoskeletal filaments like F-actin and microtubules, the situation is less clear. While recent experiments on single F-actin filaments are still interpreted within the classical ${\mathrm{Wi}}^{2/3}$ scaling law, theoretical results indicated deviations from it. Here we perform extensive Brownian dynamics simulations to explore the tumbling dynamics of semiflexible polymers over a broad range of shear strength and the polymer's persistence length $l_p$. We find that the Weissenberg number alone does not suffice to fully characterize the tumbling dynamics, and the classical scaling law breaks down. Instead, both the polymer's stiffness and the shear rate are relevant control parameters. Based on our Brownian dynamics simulations we postulate that in the parameter range most relevant for cytoskeletal filaments there is a distinct scaling behavior with $f_c{\tau }^{*}={\mathrm{Wi}}^{3/4}{\widehat{f}}_c\left(x\right)$ with $\mathrm{Wi}=\gamma {\tau }^{*}$ and the scaling variable $x=(l_p/L){\left(\mathrm{Wi}\right)}^{-1/3}$; here ${\tau }^{*}$ is the time the polymer's center of mass requires to diffuse its own contour length $L$. Comparing these results with experimental data on F-actin we find that the ${\mathrm{Wi}}^{3/4}$ scaling law agrees quantitatively significantly better with the data than the classical ${\mathrm{Wi}}^{2/3}$ law. Finally, we extend our results to single ring polymers in shear flow, and find similar results as for linear polymers with slightly different power laws.

The macroscopic responses of synthetic and natural filamentous networks are determined by a combination of microstructure and filament properties. Biofilament networks such as those of actin and fibrin have become vehicles for studying important concepts in mechanics such as rigidity percolation, linearity and nonlinearity, isotropy and anisotropy, affinity and nonaffinity, hardening and softening, bending and stretching transitions, etc. In this work, we consider generic fibrous network architectures to map out their mechanical responses over a wide range of filament properties. Using the finite element method, we perform two-dimensional simulations of discrete networks subjected to shear deformation. These simulations encompass stochastic effects arising from network topology (filament arrangement, orientation, and length distribution) and the thermally activated crosslink scission. We study the mechanics of these random networks up to a strain of 10%, including damage that is induced by crosslink scission. The response is nonlinear and the initial elastic modulus alone is not sufficient to give an understanding about the overall response. We show that the nonlinear elastic response of the network can be captured using a few parameters that depend on some well known length scales in network mechanics. For networks with filament density above the rigidity percolation threshold, by increasing filament density and bending stiffness, we observe a crossover from the bending dominated elastically compliant stiffening regime to a stretching dominated rigid nonstiffening regime. We show that in the bending dominated regime there are large deviations from the predictions of affine continuum theories. We also give a simple qualitative model for describing the contours of the incubation strain which marks the onset of damage in networks.

Some statistical features of steady states of a Kauffman-like model for prebiotic evolution are reported from computational studies. We postulate that the interesting “lifelike” states will be characterized by a nonequilibrium distribution of species and a time variable species self-correlation function. Selecting only such states from the population of final states produced by the model yields the probability of the appearance of such states as a function of a parameter $p$ of the model. $p$ is defined as the probability that a possible reaction in the the artificial chemistry actually appears in the network of chemical reactions. Small $p$ corresponds to sparse networks utilizing a small fraction of the available reactions. We find that the probability of the appearance of such lifelike states exhibits a maximum as a function of $p$: at large $p$, most final states are in chemical equilibrium and hence are excluded by our criterion. At very small $p$, the sparseness of the network makes the probability of formation of any nontrivial dynamic final state low, yielding a low probability of production of lifelike states in this limit as well. We also report results on the diversity of the lifelike states (as defined here) that are produced. Repeated starts of the model evolution with different random number seeds in a given reaction network lead to final lifelike states which have a greater than random likelihood of resembling one another. Thus a form of “convergence” is observed. On the other hand, in different reaction networks with the same $p$, lifelike final states are statistically uncorrelated. In summary, the main results are (1) there is an optimal $p$ or “sparseness” for production of lifelike states in our model—neither very dense nor very sparse networks are optimal—and (2) for a given $p$ or sparseness, the resulting lifelike states can be extremely different. We discuss some possible implications for studies of the origin of life.

The influence of absorption on the spectra of microwave graphs has been studied experimentally. The microwave networks were made up of coaxial cables and T junctions. First, absorption was introduced by attaching a $50\Omega$ load to an additional vertex for graphs with and without time-reversal symmetry. The resulting level-spacing distributions were compared with a generalization of the Wigner surmise in the presence of open channels proposed recently by Poli et al. [Phys. Rev. Lett. 108, 174101 (2012)]. Good agreement was found using an effective coupling parameter. Second, absorption was introduced along one individual bond via a variable microwave attenuator, and the influence of absorption on the length spectrum was studied. The peak heights in the length spectra corresponding to orbits avoiding the absorber were found to be independent of the attenuation, whereas, the heights of the peaks belonging to orbits passing the absorber once or twice showed the expected decrease with increasing attenuation.

It is well known that a velocity perturbation can travel through a mass spring chain with strongly nonlinear interactions as a solitary and antisolitary wave pair. In recent years, nonlinear wave propagation in 2D structures have also been explored. Here we first consider the propagation of such a velocity perturbation for cases where the system has a 2D “Y”-shaped structure. Here each of the three pieces that make up the “Y” are made of a small mass spring chain. In addition, we consider a case where multiple “Y”-shaped structures are used to generate a “tree.” We explore the early time dynamical behavior associated with the propagation of a velocity perturbation initiated at the trunk and at the extremities for both cases. We are looking for the energy transmission properties from one branch to another of these “Y”-shaped structures. Our dynamical simulations suggest the following broad observations: (i) for strongly nonlinear interactions, mechanical energy propagation resembles pulse propagation with the energy propagation being dispersive in the linear case; (ii) for strong nonlinear interactions, the tree-like structure acts as an energy gate showing preference for large perturbations in the system while the behavior of the linear case shows no such preference, thereby suggesting that such structures can possibly act as switches that activate at sufficiently high energies. The study aspires to develop insights into the nature of nonlinear wave propagation through a network of linear chains.

We analyze the solutions, on single network instances, of a recently introduced class of constraint-satisfaction problems (CSPs), describing feasible steady states of chemical reaction networks. First, we show that the CSPs generalize the scheme known as network expansion, which is recovered in a specific limit. Next, a full statistical mechanics characterization (including the phase diagram and a discussion of the physical origin of the phase transitions) for network expansion is obtained. Finally, we provide a message-passing algorithm to solve the original CSPs in the most general form.

We study the Poisson-Nernst-Planck (PNP) system with an arbitrary number of ion species with arbitrary valences in the absence of fixed charges. Assuming point charges and that the Debye length is small relative to the domain size, we derive an asymptotic formula for the steady-state solution by matching outer and boundary layer solutions. The case of two ionic species has been extensively studied, the uniqueness of the solution has been proved, and an explicit expression for the solution has been obtained. However, the case of three or more ions has received significantly less attention. Previous work has indicated that the solution may be nonunique and that even obtaining numerical solutions is a difficult task since one must solve complicated systems of nonlinear equations. By adopting a methodology that preserves the symmetries of the PNP system, we show that determining the outer solution effectively reduces to solving a single scalar transcendental equation. Due to the simple form of the transcendental equation, it can be solved numerically in a straightforward manner. Our methodology thus provides a standard procedure for solving the PNP system and we illustrate this by solving some practical examples. Despite the fact that for three ions, previous studies have indicated that multiple solutions may exist, we show that all except for one of these solutions are unphysical and thereby prove the existence and uniqueness for the three-ion case.

We analyze the problem of the helix-coil transition in explicit solvents analytically by using spin-based models incorporating two different mechanisms of solvent action: explicit solvent action through the formation of solvent-polymer hydrogen bonds that can compete with the intrinsic intra-polymer hydrogen bonded configurations (competing interactions) and implicit solvent action, where the solvent-polymer interactions tune biopolymer configurations by changing the activity of the solvent (non-competing interactions). The overall spin Hamiltonian is comprised of three terms: the background in vacuo Hamiltonian of the “Generalized Model of Polypeptide Chain” type and two additive terms that account for the two above mechanisms of solvent action. We show that on this level the solvent degrees of freedom can be explicitly and exactly traced over, the ensuing effective partition function combining all the solvent effects in a unified framework. In this way we are able to address helix-coil transitions for polypeptides, proteins, and DNA, with different buffers and different external constraints. Our spin-based effective Hamiltonian is applicable for treatment of such diverse phenomena as cold denaturation, effects of osmotic pressure on the cold and warm denaturation, complicated temperature dependence of the hydrophobic effect as well as providing a conceptual base for understanding the behavior of intrinsically disordered proteins and their analogues.

Due to the coupling between the plasma membrane and the actin cytoskeleton, membrane molecules such as receptor proteins can become immobilized by binding to cytoskeletal structures. We investigate the effect of immobile membrane molecules on the diffusion of mobile ones by modeling the membrane as a two-dimensional (2D) fluid composed of hard particles and performing event-driven molecular dynamics simulations at a particle density where the system is in an isotropic liquid state. We show that the diffusion coefficient sharply decreases with increasing immobile fraction, dropping by a factor of $\sim$3 as the fraction of immobile particles increases from 0 to 0.1, in a system-size dependent manner. By combining our results with earlier calculations, we estimate that a factor-of-$\sim$20 reduction in diffusion coefficients in live cell membranes, a puzzling finding in cell biology, can be accounted for when less than $\sim$22% of the particles in our model system is immobilized. Furthermore, we investigate the effects of confinement induced by a correlated distribution of immobile particles by calculating the distribution of the time it takes for particles to escape from a corral. In the regime where the particles can always escape from the corral, it is found that the escape times follow an exponential distribution, and the mean escape time grows exponentially with the density of obstacles at the corral boundary, increasing by a factor of 3–5 when immobile particles cover 50% of the boundary, and is approximately proportional to the area of the corral. We believe that our findings will be useful in interpreting (1) single molecule observations of membrane molecules and (2) results of particle based simulations that explore the effect of fluid dynamics on molecular transport in a 2D fluid.

We present and study a family of finite amplitude breathers on a genuinely anharmonic Klein-Gordon lattice embedded in a nonlinear site potential. The direct numerical simulations are supported by a quasilinear Schrodinger equation (QLS) derived by averaging out the fast oscillations assuming small, albeit finite, amplitude vibrations. The genuinely anharmonic interlattice forces induce breathers which are strongly localized with tails evanescing at a doubly exponential rate and are either close to a continuum, with discrete effects being suppressed, or close to an anticontinuum state, with discrete effects being enhanced. Whereas the D-QLS breathers appear to be always stable, in general there is a stability threshold which improves with spareness of the lattice.