An influential theory of increasing returns was proposed by the economist W. B. Arthur in the 1980s to explain the lock-in phenomenon between two competing commercial products. In the most simplified situation there are two competing products that gain customers according to a majority mechanism: each new customer arrives and asks which product they bought to a certain odd number of previous customers, and then buys the most shared product within this sample. It is known that one of these two companies becomes a monopoly almost surely in the limit of infinite customers. Here we consider a generalization [Dosi, Ermoliev, and Kaniovsky, J. Math. Econom. 23, 1 (1994)] in which the new customer follows the indication of the sample with some probability, and buys the other product otherwise. Other than economy, this model can be reduced to the urn of Hill, Lane, and Sudderth, and it includes several models of physical interest as special cases, such as the Elephant Random Walk, Friedman's urn, and other generalized urn models. We provide a large-deviation analysis of this model at the sample-path level, and we provide a formula that allows us to find the most likely trajectories followed by the market share variable. Interestingly, in the parameter range where the lock-in phase is expected, we observe a whole region of convergence where the entropy cost is sublinear. We also find a nonlinear differential equation for the cumulant-generating function of the market share variable, which can be studied with a suitable perturbation theory.

We study the target searches of interacting Brownian particles in a finite domain, focusing on the effect of interparticle interactions on the search time. We derive the integral equation for the mean first-passage time and acquire its solution as a series expansion in the orders of the Mayer function. We analytically obtain the leading order correction to the search time for dilute systems, which are most relevant to target search problems and prove a universal relation given by the particle density and the second virial coefficient. Finally, we validate our theoretical prediction by Langevin dynamics simulations for the various types of the interaction potential.

We study propagation of wave packets through the interface between two dissimilar harmonic chains with on-site potentials (e.g., chains lying on elastic foundations). An expression for the transmission coefficient, relating energies of the incident and transmitted wave packets is derived using two different approaches. Without elastic foundation, the transmission coefficient monotonically decreases with increasing wave frequency. We show that by adding elastic foundations, one can qualitatively change this dependence and make it nonmonotonic or even increasing. Moreover, in some cases, the interface is totally transparent (the transmission coefficient is equal to unity at some frequency) if at least one of the chains has the elastic foundation. Presented results may serve for manipulation of the transmission coefficient and corresponding interfacial thermal resistance in low-dimensional nanosystems.

We study the influence of gravity on the dynamics of upward propagating premixed flames. We show that the role of gravity on the dispersion relation is small, but that the nonlinear effects are large. Using a Michelson Sivashinsky equation modified with a gravity term, it can be observed that the nonlinear dynamics of the crests is greatly influenced by gravity, as well as the final amplitude of the flame. A simple model is proposed to explain the role of gravity on the amplitude.

In order to probe the dynamics of contact-line motion, we study the macroscopic properties of sessile drops deposited on and then aspirated from carefully prepared horizontal surfaces. By measuring the contact angle and drop width simultaneously during droplet removal, we determine the changes in the shape of the drop as it depins and recedes. Our data indicate that there is a force which opposes the motion of the contact line that depends both on the amount of time that the drop has been in contact with the surface and on the withdrawal rate. For water on silanized glass, we capture the experimentally observed behavior with an overdamped dynamical model of contact-line motion in which the phenomenological drag coefficient and the assumed equilibrium contact angle are the only inputs. In this case, the damping coefficient decreases with increasing velocity of the contact line. For other liquid-substrate pairs, the observed contact-line motion suggests that a maximum static friction force is important in addition to damping. The dependence on time of contact and withdrawal rate, reminiscent of rate-and-state friction between solid surfaces, is qualitatively consistent across three substrate-liquid pairs.

Optimal laser irradiation conditions for water-window (WW) x-ray emission (2.3–4.4 nm) from an Au plasma are investigated to develop a laboratory-scale WW x-ray source. A minimum Au target thickness of 1 $\mu \mathrm{m}$ is obtained for a laser intensity of ∼${10}^{13}$ W/${\mathrm{cm}}^2$ by observing the intensity drop in the WW spectra. Au targets produced by thermal evaporation are found to have a higher conversion efficiency than commercial foil targets for WW x-ray radiation. In addition, optimal laser spots for fixed laser energies (240 and 650 mJ) are found for an Au target ∼1 mm in front of the focal point, where suitable conditions for plasma temperature and plume volume coupling are achieved. The mechanism of the optimal target thickness and spot size can be well explained using a radiation hydrodynamic simulation code.

Translation-invariant low-dimensional systems are known to exhibit anomalous heat transport. However, there are systems, such as the coupled-rotor chain, where translation invariance is satisfied, yet transport remains diffusive. It has been argued that the restoration of normal diffusion occurs due to the impossibility of defining a global stretch variable with a meaningful dynamics. In this Letter, an alternative mechanism is proposed, namely, that the transition to anomalous heat transport can occur at a scale that, under certain circumstances, may diverge to infinity. To illustrate the mechanism, I consider the case of a composite chain that conserves local energy and momentum as well as global stretch, and at the same time obeys, in the continuum limit, Fourier's law of heat transport. It is shown analytically that for vanishing elasticity the stationary temperature profile of the chain is linear; for finite elasticity, the same property holds in the continuum limit.

The directed bond percolation is a paradigmatic model in nonequilibrium statistical physics. It captures essential physical information on the nature of continuous phase transition between active and absorbing states. In this paper, we study this model by means of the field-theoretic formulation with a subsequent renormalization group analysis. We calculate all critical exponents needed for the quantitative description of the corresponding universality class to the third order in perturbation theory. Using dimensional regularization with minimal subtraction scheme, we carry out perturbative calculations in a formally small parameter $\varepsilon$, where $\varepsilon =4-d$ is a deviation from the upper critical dimension $d_c=4$. We use a nontrivial combination of analytical and numerical tools in order to determine ultraviolet divergent parts of Feynman diagrams.

We investigate the evolution dynamics of inhomogeneous discrete-time one-dimensional quantum walks displaying long-range correlations in both space and time. The associated quantum coin operators of internal states are built to exhibit random inhomogeneity distribution of long-range correlations embedded in the time evolution protocol through a fractional Brownian motion with spectrum following a power-law behavior, $S\left(k\right)\sim 1/k^{\nu }$. From extensive numerical simulations with averages over a large number of independent realizations of the phases of quantum coins, the power-law correlated disorder encoded in the coin phases is shown to give rise to a wide variety of spreading patterns of the qubit states, from localized to subdiffusive, diffusive, and superdiffusive (including ballistic) behavior, depending on the relative strength of the parameters driving the correlation degree. Dispersion control is possible in one-dimensional discrete-time quantum walks by tuning the long-range correlation properties assigned to the inhomogeneous quantum coin operator.

We consider $N$ Brownian motions diffusing independently on a line, starting at $x_0>0$, in the presence of an absorbing target at the origin. The walkers undergo stochastic resetting under two protocols: (A) each walker resets independently to $x_0$ with rate $r$ and (B) all walkers reset simultaneously to $x_0$ with rate $r$. We derive an explicit analytical expression for the mean first-passage time to the origin in terms of an integral which is evaluated numerically using Mathematica. We show that, as a function of $r$ and for fixed $x_0$, it has a minimum at an optimal value $r^{*}>0$ as long as $N<N_c$. Thus resetting is beneficial for the search for $N<N_c$. When $N>N_c$, the optimal value occurs at $r^{*}=0$ indicating that resetting hinders search processes. We obtain different values of $N_c$ for protocols A and B; indeed, for $N\le 7$ resetting is beneficial in protocol A, while for $N\le 6$ resetting is beneficial for protocol B. Our theoretical predictions are verified in numerical Langevin simulations.

The cubic-quintic Swift-Hohenberg equation (SH35) has been proposed as an order parameter description of several convective systems with reflection symmetry in the layer midplane, including binary fluid convection. We use numerical continuation, together with extensive direct numerical simulations (DNSs), to study SH35 with an additional nonvariational quadratic term to model the effects of breaking the midplane reflection symmetry. The nonvariational structure of the model leads to the propagation of asymmetric spatially localized structures (LSs). An asymptotic prediction for the drift velocity of such structures, derived in the limit of weak symmetry breaking, is validated numerically. Next, we present an extensive study of possible collision scenarios between identical and nonidentical traveling structures, varying a temperaturelike control parameter. These collisions are inelastic and result in stationary or traveling structures. Depending on system parameters and the types of structures colliding, the final state may be a simple bound state of the initial LSs, but it can also be longer or shorter than the sum of the two initial states as a result of nonlinear interactions. The Maxwell point of the variational system, where the free energy of the global pattern state equals that of the trivial state, is shown to have no bearing on which of these scenarios is realized. Instead, we argue that the stability properties of bound states are key. While individual LSs lie on a modified snakes-and-ladders structure in the nonvariational SH35, the multipulse bound states resulting from collisions lie on isolas in parameter space, disconnected from the trivial solution. In the gradient SH35, such isolas are always of figure-eight shape, but in the present nongradient case they are generically more complex, although the figure-eight shape is preserved in a small subset of cases. Some of these complex isolas are shown to terminate in T-point bifurcations. A reduced model is proposed to describe the interactions between the tails of the LSs. The model consists of two coupled ordinary differential equations (ODEs) capturing the oscillatory nature of SH35 profiles at the linear level. It contains three parameters: two interaction amplitudes and a phase, whose values are deduced from high-resolution DNSs using gradient descent optimization. For collisions leading to the formation of simple bound states, the reduced model reproduces the trajectories of LSs with high quantitative accuracy. When nonlinear interactions lead to the creation or deletion of wavelengths, the model performs less well. Finally, we propose an effective signature of a given interaction in terms of net attraction or repulsion relative to free propagation. It is found that interactions can be attractive or repulsive in the net, irrespective of whether the two closest interacting extrema are of the same or opposite signs. Our findings highlight the rich temporal dynamics described by this bistable nonvariational SH35, and show that the interactions in this system can be quantitatively captured, to a significant extent, by a highly reduced ODE model.

Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems, and machine learning. We introduce a decimation scheme that maps it to neural network models of associative memory and provide a detailed theoretical analysis of its performance, showing that decimation is able to factorize extensive-rank matrices and to denoise them efficiently. In the case of binary prior on the signal components, we introduce a decimation algorithm based on a ground-state search of the neural network, which shows performances that match the theoretical prediction.

When two partially miscible systems are put in contact, one phase, A, can dissolve into the other one with a given solubility. Chemical reactions in the host phase can impact this dissolution by consuming A and by generating products that impact the solubility of A. Here, we study theoretically the optimal conditions for transfer of a reactant A in a host phase containing a species B when a bimolecular A $+$ B $\to$ C reaction generates a product C that linearly decreases the solubility of A. We have quantified numerically the influence of this variable solubility on the reaction-diffusion (RD) concentration profiles of all species in the host phase, on the temporal evolution of the position of the reaction front, and on the flux of A through the interface. We have also computed the analytical asymptotic concentration profiles, solutions at long times of the RD governing equations. For a fixed negative effect of C on the solubility of A, an increase in the initial concentration of reactant B or an increase in the diffusion rate of species B and C results in a larger flux of A and hence a larger amount of A dissolved in the host solution at a given time. However, when the influence of C on the solubility increases, the mass transfer decreases. Our results help understand to what extent a chemical reaction can optimize the reactive transfer of a solute to a host phase with application to, among other things, the geological sequestration of carbon dioxide in an aquifer.

Persistent nonequilibrium effects such as the memory of the initial state, the ballistic diffusion, and the break of the equipartition theorem and the ergodicity in Brownian motions are investigated by analytically solving the generalized Langevin equation of nonrelativistic Brownian particles with colored noise. These effects can also be observed in the Brownian motion of relativistic particles by numerically solving the generalized Langevin equation for specially chosen memory kernels. Our analyses give rise to think about the possible anomalous motion of heavy quarks in relativistic heavy-ion collisions.

This paper considers a sandpile model subjected to a sinusoidal external drive with the period $T$. We develop a theoretical model for the Green's function in a large $T$ limit, which predicts that the avalanches are anisotropic and elongated in the oscillation direction. We track the problem numerically and show that the system additionally shows a regime where the avalanches are elongated in the perpendicular direction with respect to the oscillations. We find a crossover between these two regimes. The power spectrum of avalanche size and the grains wasted from the parallel and perpendicular directions are studied. These functions show power-law behavior in terms of the frequency with exponents, which run with $T$.

We consider a system of $N$ noncrossing Brownian particles in one dimension. We find the exact rate function that describes the long-time large deviation statistics of their occupation fraction in a finite interval in space. Remarkably, we find that, for any general $N\ge 2$, the system undergoes $N-1$ dynamical phase transitions of second order. The $N-1$ transitions are the boundaries of $N$ phases that correspond to different numbers of particles which are in the vicinity of the interval throughout the dynamics. We achieve this by mapping the problem to that of finding the ground-state energy for $N$ noninteracting spinless fermions in a square-well potential. The phases correspond to different numbers of single-body bound states for the quantum problem. We also study the process conditioned on a given occupation fraction and the large-$N$ limiting behavior.

The standard Lipkin-Meshkov-Glick (LMG) model undergoes a second-order ground-state quantum phase transition (QPT) and an excited-state quantum phase transition (ESQPT). The inclusion of an anharmonic term in the LMG Hamiltonian gives rise to a second ESQPT that alters the static properties of the model [Gamito , Phys. Rev. E 106, 044125 (2022)]. In the present work, the dynamical implications associated to this new ESQPT are analyzed. For that purpose, a quantum quench protocol is defined on the system Hamiltonian that takes an initial state, usually the ground state, into a complex excited state that evolves on time. The impact of the new ESQPT on the time evolution of the survival probability and the local density of states after the quantum quench, as well as on the Loschmidt echoes and the microcanonical out-of-time-order correlator (OTOC) are discussed. The anharmonity-induced ESQPT, despite having a different physical origin, has dynamical consequences similar to those observed in the ESQPT already present in the standard LMG model.