Long-range ordering of velocity-aligned active polymers.

In this work, we study the effect of covalent bonding on the behavior of non-equilibrium systems with the active force acting on particles along their velocity. Self-ordering of single particles does not occur in this model. However, starting from some critical polymerization degree, the ordered state is observed. It is homogeneous and exhibits no phase separation. In the ordered state, the chains prefer a near-two-dimensional configuration and all move in one direction. Importantly, the self-ordering is obtained only at intermediate active force magnitudes. At high magnitudes, the transition from the disordered to ordered state is suppressed by the swelling of the chains during the transition, as we show by the transition kinetics analysis. We demonstrate the bistable behavior of the system in a particular range of polymerization degrees, amplitudes of active force, densities, and thermostat temperatures. Overall, we show that covalent bonding greatly aids the self-ordering in this active particle model, in contrast to active Brownian particles.

Negative diffusion of excitons in quasi-two-dimensional systems.

We show how two different mobile-immobile type models explain the observation of negative diffusion of excitons reported in experimental studies in quasi-two-dimensional semiconductor systems. The main reason for the effect is the initial trapping and a delayed release of free excitons in the area close to the original excitation spot. The density of trapped excitons is not registered experimentally. Hence, the signal from the free excitons alone includes the delayed release of not diffusing trapped particles. This is seen as the narrowing of the exciton density profile or decrease of mean-squared displacement which is then interpreted as a negative diffusion. The effect is enhanced with the increase of recombination intensity as well as the rate of the exciton-exciton binary interactions.

Features of DNA-Montmorillonite Binding Visualized by Atomic Force Microscopy.

In the present work, complexes of DNA with nano-clay montmorillonite (Mt) were investigated by means of atomic force microscopy (AFM) under various conditions. In contrast to the integral methods of analysis of the sorption of DNA on clay, AFM allowed us to study this process at the molecular level in detail. DNA molecules in the deionized water were shown to form a 2D fiber network weakly bound to both Mt and mica. The binding sites are mostly along Mt edges. The addition of Mg2+ cations led to the separation of DNA fibers into separate molecules, which bound mainly to the edge joints of the Mt particles according to our reactivity estimations. After the incubation of DNA with Mg2+, the DNA fibers were capable of wrapping around the Mt particles and were weakly bound to the Mt edge surfaces. The reversible sorption of nucleic acids onto the Mt surface allows it to be used for both RNA and DNA isolation for further reverse transcription and polymerase chain reaction (PCR). Our results show that the strongest binding sites for DNA are the edge joints of Mt particles.

Gradient dynamics in reinforcement learning.

Despite the success achieved by the analysis of supervised learning algorithms in the framework of statistical mechanics, reinforcement learning has remained largely untouched by physicists. Here we move towards closing the gap by analyzing the dynamics of the policy gradient algorithm. For a convex problem, namely the k-armed bandit, we show that the learning dynamics obeys a drift-diffusion motion described by a Langevin equation, the coefficients of which can be tuned by the learning rate. We explore the striking similarity between our Langevin equation and the Kimura equation, describing genotypes evolution. Furthermore, we propose a mapping between a nonconvex reinforcement learning setting describing multiple joints of a robotic arm and a disordered system, namely a p-spin glass. This mapping enables us to show how the learning rate acts as an effective temperature and thus is capable of smoothing rough landscapes, corroborating what is displayed by the drift-diffusive description and paving the way for physics-inspired algorithmic optimization based on annealing procedures in disordered systems.

Non-Markovian diffusion of excitons in layered perovskites and transition metal dichalcogenides.

The diffusion of excitons in perovskites and transition metal dichalcogenides shows clear anomalous, subdiffusive behaviour in experiments. In this paper we develop a non-Markovian mobile-immobile model which provides an explanation of this behaviour through paired theoretical and simulation approaches. The simulation model is based on a random walk on a 2D lattice with randomly distributed deep traps such that the trapping time distribution involves slowly decaying power-law asymptotics. The theoretical model uses coupled diffusion and rate equations for free and trapped excitons, respectively, with an integral term responsible for trapping. The model provides a good fitting of the experimental data, thus, showing a way for quantifying the exciton diffusion dynamics.

Parameter-free predictions of the viscoelastic response of glassy polymers from non-affine lattice dynamics.

We study the viscoelastic response of amorphous polymers using theory and simulations. By accounting for internal stresses and considering instantaneous normal modes (INMs) within athermal non-affine theory, we make parameter-free predictions of the dynamic viscoelastic moduli obtained in coarse-grained simulations of polymer glasses at non-zero temperatures. The theoretical results show very good correspondence with rheology data collected from molecular dynamics simulations over five orders of magnitude in frequency, with some instabilities that accumulate in the low-frequency part on approach to the glass transition. These results provide evidence that the mechanical glass transition itself is continuous and thus represents a crossover rather than a true phase transition. The relatively sharp drop of the low-frequency storage modulus across the glass transition temperature can be explained mechanistically within the proposed theory: the proliferation of low-eigenfrequency vibrational excitations (boson peak and nearly-zero energy excitations) is directly responsible for the rapid growth of a negative non-affine contribution to the storage modulus.

Nonmonotonic dependence of polymer-glass mechanical response on chain bending stiffness.

We investigate the mechanical properties of amorphous polymers by means of coarse-grained simulations and nonaffine lattice dynamics theory. A small increase of polymer chain bending stiffness leads first to softening of the material, while hardening happens only upon further strengthening of the backbones. This nonmonotonic variation of the storage modulus G^{'} with bending stiffness is caused by a competition between additional resistance to deformation offered by stiffer backbones and decreased density of the material due to a necessary decrease in monomer-monomer coordination. This counterintuitive finding suggests that the strength of polymer glasses may in some circumstances be enhanced by softening the bending of constituent chains.

The efficiency of driving chemical reactions by a physical non-equilibrium is kinetically controlled.

An out-of-equilibrium physical environment can drive chemical reactions into thermodynamically unfavorable regimes. Under prebiotic conditions such a coupling between physical and chemical non-equilibria may have enabled the spontaneous emergence of primitive evolutionary processes. Here, we study the coupling efficiency within a theoretical model that is inspired by recent laboratory experiments, but focuses on generic effects arising whenever reactant and product molecules have different transport coefficients in a flow-through system. In our model, the physical non-equilibrium is represented by a drift-diffusion process, which is a valid coarse-grained description for the interplay between thermophoresis and convection, as well as for many other molecular transport processes. As a simple chemical reaction, we consider a reversible dimerization process, which is coupled to the transport process by different drift velocities for monomers and dimers. Within this minimal model, the coupling efficiency between the non-equilibrium transport process and the chemical reaction can be analyzed in all parameter regimes. The analysis shows that the efficiency depends strongly on the Damköhler number, a parameter that measures the relative timescales associated with the transport and reaction kinetics. Our model and results will be useful for a better understanding of the conditions for which non-equilibrium environments can provide a significant driving force for chemical reactions in a prebiotic setting.

Polymer translocation: the first two decades and the recent diversification.

Probably no other field of statistical physics at the borderline of soft matter and biological physics has caused such a flurry of papers as polymer translocation since the 1994 landmark paper by Bezrukov, Vodyanoy, and Parsegian and the study of Kasianowicz in 1996. Experiments, simulations, and theoretical approaches are still contributing novel insights to date, while no universal consensus on the statistical understanding of polymer translocation has been reached. We here collect the published results, in particular, the famous-infamous debate on the scaling exponents governing the translocation process. We put these results into perspective and discuss where the field is going. In particular, we argue that the phenomenon of polymer translocation is non-universal and highly sensitive to the exact specifications of the models and experiments used towards its analysis.

Levy flights do not always optimize random blind search for sparse targets.

It is generally believed that random search processes based on scale-free, Lévy stable jump length distributions (Lévy flights) optimize the search for sparse targets. Here we show that this popular search advantage is less universal than commonly assumed. We study the efficiency of a minimalist search model based on Lévy flights in the absence and presence of an external drift (underwater current, atmospheric wind, a preference of the walker owing to prior experience, or a general bias in an abstract search space) based on two different optimization criteria with respect to minimal search time and search reliability (cumulative arrival probability). Although Lévy flights turn out to be efficient search processes when the target is far from the starting point, or when relative to the starting point the target is upstream, we show that for close targets and for downstream target positioning regular Brownian motion turns out to be the advantageous search strategy. Contrary to claims that Lévy flights with a critical exponent α = 1 are optimal for the search of sparse targets in different settings, based on our optimization parameters the optimal α may range in the entire interval (1, 2) and especially include Brownian motion as the overall most efficient search strategy.

Surface induced self-organization of comb-like macromolecules.

We present a review of the theoretical and experimental evidence for the peculiar properties of comb copolymers, demonstrating the uniqueness of these materials among other polymer architectures. These special properties include an increase in stiffness upon increasing side-chain length, the spontaneous curvature of adsorbed combs, rod-globule transition, and specific intramolecular self-assembly. We also propose a theory of chemically heterogeneous surface nanopattern formation in ultrathin films of comblike macromolecules containing two different types (A and B) of incompatible side chains (so-called binary combs). Side chains of the binary combs are strongly adsorbed on a surface and segregated with respect to the backbone. The thickness of surface domains formed by the B side chains is controlled by the interaction with the substrate. We predict the stability of direct and inverse disc-, torus- and stripelike nanostructures. Phase diagrams of the film are constructed.

Nematic ordering of rigid rod polyelectrolytes induced by electrostatic interactions: effect of discrete charge distribution along the chain.

Similar to the Debye-Hückel plasma, charged groups in solutions of rigid rod polyelectrolytes attract each other. We derive expression for the correlation free energy of electrostatic attraction of the rods within the random phase approximation. In this theory, we explicitly take into account positions of charged groups on the chains and examine both charge and polymer concentration fluctuations. The correlation free energies and the osmotic pressures are calculated for isotropic and completely ordered nematic phase. The results of the discrete model are compared with results of a continuous model. The discrete model gives rise to a stronger attraction between the charged groups both in the isotropic and nematic phases and to a stronger orienting action of the electrostatic forces.

Complexation of oppositely charged polyelectrolytes: effect of discrete charge distribution along the chain.

Similar to the Debye-Hückel plasma, charged groups of oppositely charged polyelectrolytes attract each other. We find exact expression for the correlation free energy of electrostatic attraction in polyelectrolytes within the random phase approximation. The obtained expression is shown to be valid in dilute, semidilute, concentrated solutions, and melts. In this theory we explicitly take into account positions of charged groups on the chains and examine both charge and polymer concentrations fluctuations. The existence of the critical point in theta solvent is demonstrated. The theory reproduces scaling results and describes the system beyond the scaling approximation.

Microphase separation of double-grafted copolymers (centipedes) with gradient, random, and regular sequence of the branch points.

We propose a theory of microphase separation of the double-grafted copolymer melts with different types of branch point distribution. It is shown that copolymers with gradient sequence of the branch points form a microstructure easier (at smaller values of the Flory-Huggins parameters) than equivalent copolymers with random or regular sequences. Two characteristic types of the microphase separation, "diblock-" and "comblike" are predicted. Due to the existence of the two characteristic length scales (the length of the backbone and the length of the side chains), the two-scale switching is possible.