We propose a generic model of driven DNA under the influence of an oscillatory force of amplitude $F$ and frequency $\nu$ and show the existence of a dynamical transition for a chain of finite length. We find that the area of the hysteresis loop, $A_{\mathrm{loop}}$, scales with the same exponents as observed in a recent study based on a much more detailed model. However, towards the true thermodynamic limit, the high-frequency scaling regime extends to lower frequencies for larger chain length $L$ and the system has only one scaling $\left(A_{\mathrm{loop}}\approx {\nu }^{-1}{F}^2\right)$. Expansion of an analytical expression for $A_{\mathrm{loop}}$ obtained for the model system in the low-force regime revealed that there is a new scaling exponent associated with force $\left(A_{\mathrm{loop}}\approx {\nu }^{-1}{F}^{2.5}\right)$, which has been validated by high-precision numerical calculation. By a combination of analytical and numerical arguments, we also deduce that for large but finite $L$, the exponents are robust and independent of temperature and friction coefficient.

The direct bond percolation process (Gribov process) is studied in the presence of random velocity fluctuations generated by the Gaussian self-similar ensemble with finite correlation time. We employ the renormalization group in order to analyze a combined effect of the compressibility and finite correlation time on the long-time behavior of the phase transition between an active and an absorbing state. The renormalization procedure is performed to the one-loop order. Stable fixed points of the renormalization group and their regions of stability are calculated in the one-loop approximation within the three-parameter $(\varepsilon ,y,\eta )$ expansion. Different regimes corresponding to the rapid-change limit and frozen velocity field are discussed, and their fixed points' structure is determined in numerical fashion.

We examine the existence and properties of certain discrete breathers for a discrete nonlinear Schrödinger model where all but one site are placed in a ring and coupled to the additional central site. The discrete breathers we focus on are stationary solutions mainly localized on one or a few of the ring sites and possibly also the central site. By numerical methods, we trace out and study the continuous families the discrete breathers belong to. Our main result is the discovery of a split bifurcation at a critical value of the coupling between neighboring ring sites. Below this critical value, families form closed loops in a certain parameter space, implying that discrete breathers with and without central-site occupation belong to the same family. Above the split bifurcation the families split up into several separate ones, which bifurcate with solutions with constant ring amplitudes. For symmetry reasons, the families have different properties below the split bifurcation for even and odd numbers of sites. It is also determined under which conditions the discrete breathers are linearly stable. The dynamics of some simpler initial conditions that approximate the discrete breathers are also studied and the parameter regimes where the dynamics remain localized close to the initially excited ring site are related to the linear stability of the exact discrete breathers.

Strong-coupling phenomena, such as like-charge macroion attraction, opposite-charged macroion repulsion, charge renormalization, and charge inversion, are known to be mediated by multivalent counterions. Most theories treat the counterions as point charges and describe the system by a single coupling parameter that measures the strength of the Coulomb interactions. In many biological systems, the counterions are highly charged and have finite sizes and can be well-described by polyelectrolytes. The shapes and orientations of these polymer counterions play a major role in the thermodynamics of these systems. In this work we apply a field-theoretic description in the strong-coupling regime to the polymer counterions in the presence of a fixed charge distribution. We work out the special cases of rodlike polymer counterions confined by one, and two charged walls, respectively. The effects of the geometry of the rodlike counterions and the excluded volume of the walls on the density, pressure, and free energy of the rodlike counterions are discussed.

Using a probabilistic approximation of a mean-field mechanistic model of sheared systems, we analytically calculate the statistical properties of large failures under slow shear loading. For general shear $F\left(t\right)$, the distribution of waiting times between large system-spanning failures is a generalized exponential distribution, ${\rho }_T\left(t\right)=\lambda (F\left(t\right))P(F\left(t\right))exp\left[-{\int }_0^{t}d\tau \lambda (F\left(\tau \right))P(F\left(\tau \right))\right]$, where $\lambda (F\left(t\right))$ is the rate of small event occurrences at stress $F\left(t\right)$ and $P(F\left(t\right))$ is the probability that a small event triggers a large failure. We study the behavior of this distribution as a function of fault properties, such as heterogeneity or shear rate. Because the probabilistic model accommodates any stress loading $F\left(t\right)$, it is particularly useful for modeling experiments designed to understand how different forms of shear loading or stress perturbations impact the waiting-time statistics of large failures. As examples, we study how periodic perturbations or fluctuations on top of a linear shear stress increase impact the waiting-time distribution.

We propose a theoretical framework within which a robust micromechanical definition of precursors to plastic instabilities, often termed soft spots, naturally emerges. They are shown to be collective displacements (modes) $\widehat{z}$ that correspond to local minima of a barrier function $b\left(\widehat{z}\right)$, which depends solely on inherent structure information. We demonstrate how some heuristic searches for local minima of $b\left(\widehat{z}\right)$ can a priori detect the locus and geometry of imminent plastic instabilities with remarkable accuracy, at strains as large as ${\gamma }_c-\gamma \sim {10}^{-2}$ away from the instability strain ${\gamma }_c$. Our findings suggest that the a priori detection of the entire field of soft spots can be effectively carried out by a systematic investigation of the landscape of $b\left(\widehat{z}\right)$.

We report the results of an experimental investigation of the spatiotemporal dynamics of stable imbibition fronts in a disordered medium, in the regime of capillary disorder, for a wide range of experimental conditions. We have used silicone oils of various viscosities $\mu$ and nearly identical oil-air surface tension and forced them to slowly invade a model open fracture at different constant flow rates $\mathrm{v}$. In this first part of the study we have focused on the local dynamics at a scale below the size of the quenched disorder. Changing $\mu$ and $\mathrm{v}$ independently, we have found that the dynamics is not simply controlled by the capillary number $\text{Ca}\sim \mu \mathrm{v}$. Specifically, we have found that the wide statistical distributions of local front velocities, and their large spatial correlations along the front, are indeed controlled by the capillary number $\text{Ca}$. However, local velocities exhibit also very large temporal correlations, and these correlations depend more strongly on the mean imposed velocity $\mathrm{v}$ than on the viscosity $\mu$ of the invading fluid. Correlations between local velocities lead to a burstlike dynamics. Avalanches, defined as clusters of large local velocities, follow power-law distributions—both in size and duration—with exponential cutoffs that diverge as $\text{Ca}\to 0$, the pinning-depinning transition of stable imbibition displacements. Large data sets have led to reliable statistics, from which we have derived accurate values of critical exponents of the relevant power-law distributions. We have investigated also the dependence of their cutoffs on $\mu$ and $\mathrm{v}$ and related them to the autocorrelations of local velocities in space and time.

We report the results of an experimental investigation of the spatiotemporal dynamics of stable imbibition fronts in a disordered medium, in the regime of capillary disorder, for a wide range of experimental conditions. We have used silicone oils of various viscosities $\mu$ and nearly identical oil-air surface tension, and forced them to slowly invade a model open fracture at very different flow rates $\mathrm{v}$. In this second part of the study we have carried out a scale-dependent statistical analysis of the front dynamics. We have specifically analyzed the influence of $\mu$ and $\mathrm{v}$ on the statistical properties of the velocity $V_{\ell }$, the spatial average of the local front velocities over a window of lateral size $\ell$. We have varied $\ell$ from the local scale defined by our spatial resolution up to the lateral system size $L$. Even though the imposed flow rate is constant, the signals $V_{\ell }\left(t\right)$ present very strong fluctuations which evolve systematically with the parameters $\mu$, $\mathrm{v}$, and $\ell$. We have verified that the non-Gaussian fluctuations of the global velocity $V_{\ell }\left(t\right)$ are very well described by a generalized Gumbel statistics. The asymmetric shape and the exponential tail of those distributions are controlled by the number of effective degrees of freedom of the imbibition fronts, given by $N_{\text{eff}}=\ell /{\ell }_c$ (the ratio of the lateral size of the measuring window $\ell$ to the correlation length ${\ell }_c\sim 1/\sqrt{\mu \mathrm{v}}$). The large correlated excursions of $V_{\ell }\left(t\right)$ correspond to global avalanches, which reflect extra displacements of the imbibition fronts. We show that global avalanches are power-law distributed, both in sizes and durations, with robustly defined exponents—independent of $\mu$, $\mathrm{v}$, and $\ell$. Nevertheless, the exponential upper cutoffs of the distributions evolve systematically with those parameters. We have found, moreover, that maximum sizes ${\xi }_S$ and maximum durations ${\xi }_T$ of global avalanches are not controlled by the same mechanism. While ${\xi }_S$ are also determined by $\ell /{\ell }_c$, like the amplitude fluctuations of $V_{\ell }\left(t\right)$, ${\xi }_T$ and the temporal correlations of $V_{\ell }\left(t\right)$ evolve much more strongly with imposed flow rate $\mathrm{v}$ than with fluid viscosity $\mu$.

Chimera states are dynamical patterns in networks of coupled oscillators in which regions of synchronous and asynchronous oscillation coexist. Although these states are typically observed in large ensembles of oscillators and analyzed in the continuum limit, chimeras may also occur in systems with finite (and small) numbers of oscillators. Focusing on networks of $2N$ phase oscillators that are organized in two groups, we find that chimera states, corresponding to attracting periodic orbits, appear with as few as two oscillators per group and demonstrate that for $N>2$ the bifurcations that create them are analogous to those observed in the continuum limit. These findings suggest that chimeras, which bear striking similarities to dynamical patterns in nature, are observable and robust in small networks that are relevant to a variety of real-world systems.

Many experimental and theoretical methods have been developed to calculate the coarse-grained continuum elastic properties of macromolecules. However, all of those methods assume uniform elastic properties. Following the continuum mechanics framework, we present a systematic way of calculating the nonuniform effective elastic properties from atomic thermal fluctuations obtained from molecular dynamics simulation at any coarse-grained scale using a potential of the mean-force approach. We present the results for a mutant of Sesbania mosaic virus capsid, where we calculate the elastic moduli at different scales and observe an apparent problem with the chosen reference configuration in some cases. We present a possible explanation using an elastic network model, where inducing random prestrain results in a similar behavior. This phenomenon provides a novel insight into the continuum nature of macromolecules and defines the limits on details that the elasticity theory can capture. Further investigation into prestrains could elucidate important aspects of conformational dynamics of macromolecules.

We investigate scaling of work and efficiency of a photonic Carnot engine with a number of quantum coherent resources. Specifically, we consider a generalization of the “phaseonium fuel” for the photonic Carnot engine, which was first introduced as a three-level atom with two lower states in a quantum coherent superposition by M. O. Scully, M. Suhail Zubairy, G. S. Agarwal, and H. Walther [Science 299, 862 (2003)], to the case of $N+1$ level atoms with $N$ coherent lower levels. We take into account atomic relaxation and dephasing as well as the cavity loss and derive a coarse-grained master equation to evaluate the work and efficiency analytically. Analytical results are verified by microscopic numerical examination of the thermalization dynamics. We find that efficiency and work scale quadratically with the number of quantum coherent levels. Quantum coherence boost to the specific energy (work output per unit mass of the resource) is a profound fundamental difference of quantum fuel from classical resources. We consider typical modern resonator set ups and conclude that multilevel phaseonium fuel can be utilized to overcome the decoherence in available systems. Preparation of the atomic coherences and the associated cost of coherence are analyzed and the engine operation within the bounds of the second law is verified. Our results bring the photonic Carnot engines much closer to the capabilities of current resonator technologies.

The interplay between geometrical frustration (GF) and inverse freezing (IF) is studied within a cluster approach. The model considers first-neighbor $\left(J_1\right)$ and second-neighbor $\left(J_2\right)$ intracluster antiferromagnetic interactions between Ising spins on a checkerboard lattice and long-range disordered couplings $\left(J\right)$ among clusters. We obtain phase diagrams of temperature versus $J_1/J$ in two cases: the absence of $J_2$ interaction and the isotropic limit $J_2=J_1$, where GF takes place. An IF reentrant transition from the spin-glass (SG) to paramagnetic (PM) phase is found for a certain range of $J_1/J$ in both cases. The $J_1$ interaction leads to a SG state with high entropy at the same time that can introduce a low-entropy PM phase. In addition, it is observed that the cluster size plays an important role. The GF increases the PM phase entropy, but larger clusters can give an entropic advantage for the SG phase that favors IF. Therefore, our results suggest that disordered systems with antiferromagnetic clusters can exhibit an IF transition even in the presence of GF.

We analyze the controllability of a two-layer network, where driver nodes can be chosen randomly only from one layer. Each layer contains a scale-free network with directed links and the node dynamics depends on the incoming links from other nodes. We combine the in-degree and out-degree values to assign an importance value $w$ to each node, and distinguish between peripheral nodes with low $w$ and central nodes with high $w$. Based on numerical simulations, we find that the controllable part of the network is larger when choosing low $w$ nodes to connect the two layers. The control is as efficient when peripheral nodes are driver nodes as it is for the case of more central nodes. However, if we assume a cost to utilize nodes that is proportional to their overall degree, utilizing peripheral nodes to connect the two layers or to act as driver nodes is not only the most cost-efficient solution, it is also the one that performs best in controlling the two-layer network among the different interconnecting strategies we have tested.

We study the interacting self-avoiding trail (ISAT) model on a Bethe lattice of general coordination $q$ and on a Husimi lattice built with squares and coordination $q=4$. The exact grand-canonical solutions of the model are obtained, considering that up to $K$ monomers can be placed on a site and associating a weight ${\omega }_i$ with an $i$-fold visited site. Very rich phase diagrams are found with nonpolymerized, regular polymerized, and dense polymerized phases separated by lines (or surfaces) of continuous and discontinuous transitions. For a Bethe lattice with $q=4$ and $K=2$, the collapse transition is identified with a bicritical point and the collapsed phase is associated with the dense polymerized (solidlike) phase instead of the regular polymerized (liquidlike) phase. A similar result is found for the Husimi lattice, which may explain the difference between the collapse transition for ISATs and for interacting self-avoiding walks on the square lattice. For $q=6$ and $K=3$ (studied on the Bethe lattice only), a more complex phase diagram is found, with two critical planes and two coexistence surfaces, separated by two tricritical and two critical end-point lines meeting at a multicritical point. The mapping of the phase diagrams in the canonical ensemble is discussed and compared with simulational results for regular lattices.

Inspired by recent experiments and simulations on pattern formation in biomolecules by optical tweezers, a theoretical description based on the reference interaction site model (RISM) is developed to calculate the equilibrium density profiles of small polyelectrolytes in an external potential. The formalism is applied to the specific case of a finite number of Gaussian and rodlike polyelectrolytes trapped in a harmonic potential. The density profiles of the polyelectrolytes are studied over a range of lengths and numbers of polyelectrolytes in the trap, and the strength of the trap potential. For smaller polymers we recover the results for point charges. In the mean field limit the longer polymers, unlike point charges, form a shell at the boundary layer. When the interpolymer correlations are included, the density profiles of the polymers show sharp shells even at weaker trap strengths. The implications of these results are discussed.

It is well known that the polymer glass transition temperature $T_g$ is dependent on molecular weight, but the role of molecular-weight polydispersity on $T_g$ is unclear. Using molecular-dynamics simulations, we clarify that for polymers with the same number-average molecular weight, the molecular-weight distribution profile (either in Schulz-Zimm form or in bimodal form) has very little influence on the glass transition temperature $T_g$, the average segment dynamics (monomer motion, bond orientation relaxation, and torsion transition), and the relaxation-time spectrum, which are related to the local nature of the glass transition. By analyzing monomer motions in different chains, we find that the motion distribution of monomers is altered by molecular-weight polydispersity. Molecular-weight polydispersity dramatically enhances the dynamic heterogeneity of monomer diffusive motions after breaking out of the “cage,” but it has a weak influence on the dynamic heterogeneity of the short time scales and the transient spatial correlation between temporarily localized monomers. The stringlike cooperative motion is also not influenced by molecular-weight polydispersity, supporting the idea that stringlike collective motion is not strongly correlated with chain connectivity.

A multiple-relaxation-time lattice Boltzmann model of Couette flow is developed to investigate the rarified gas flow through microchannels with roughness characterized by fractal geometry, especially to elucidate the coupled effects of roughness and rarefaction on microscale gas flow in the transition flow regime. The results indicate that the surface roughness effect on gas flow behavior becomes more significant in rarefied gas flow with the increase of Knudsen number. We find the gas flow behavior in the transition flow regime is more sensitive to roughness height than that in the slip flow regime. In particular, the influence of fractal dimension on rarefied gas flow behavior is less significant than roughness height.

We investigate a quasi-two-dimensional system composed of an initially circular ferrofluid droplet surrounded by a nonmagnetic fluid of higher density. These immiscible fluids flow in a rotating Hele-Shaw cell, under the influence of an in-plane radial magnetic field. We focus on the situation in which destabilizing bulk magnetic field effects are balanced by stabilizing centrifugal forces. In this framing, we consider the interplay of capillary and magnetic normal traction effects in determining the fluid-fluid interface morphology. By employing a vortex-sheet formalism, we have been able to find a family of exact stationary $N$-fold polygonal shape solutions for the interface. A weakly nonlinear theory is then used to verify that such exact interfacial solutions are in fact stable.

Rogue waves (RWs) are unexpectedly strong excitations emerging from an otherwise tranquil background. The nonlinear Schrödinger equation (NLSE), a ubiquitous model with wide applications to fluid mechanics, optics, plasmas, etc., exhibits RWs only in the regime of modulation instability (MI) of the background. For a system of multiple waveguides, the governing coupled NLSEs can produce regimes of MI and RWs, even if each component has dispersion and cubic nonlinearity of opposite signs. A similar effect is demonstrated here for a system of coupled derivative NLSEs (DNLSEs) where the special feature is the nonlinear self-steepening of narrow pulses. More precisely, these additional regimes of MI and RWs for coupled DNLSEs depend on the mismatch in group velocities between the components, and the parameters for cubic nonlinearity and self-steepening. RWs considered in this paper differ from those of the NLSEs in terms of the amplification ratio and criteria of existence. Applications to optics and plasma physics are discussed.