We introduce an asymmetric noisy voter model to study the joint effect of immigration and a competition-dispersal tradeoff in the dynamics of two species competing for space in regular lattices. Individuals of one species can invade a nearest-neighbor site in the lattice, while individuals of the other species are able to invade sites at any distance but are less competitive locally, i.e., they establish with a probability $g\le 1$. The model also accounts for immigration, modeled as an external noise that may spontaneously replace an individual at a lattice site by another individual of the other species. This combination of mechanisms gives rise to a rich variety of outcomes for species competition, including exclusion of either species, monostable coexistence of both species at different population proportions, and bistable coexistence with proportions of populations that depend on the initial condition. Remarkably, in the bistable phase, the system undergoes a discontinuous transition as the intensity of immigration overcomes a threshold, leading to a half loop dynamics associated to a cusp catastrophe, which causes the irreversible loss of the species with the shortest dispersal range.

We theoretically investigate the problem of diffusive target search and mean first passage times (MFPTs) of a tracer in a three-dimensional (3D) polymer network with a particular focus on the effects of combined one-dimensional (1D) diffusion along the polymer chains and 3D diffusion within the network. For this, we employ computer simulations as well as limiting theories of a single diffusive tracer searching for a spherical target fixed at a cross-link of a homogeneous 3D cubic lattice network. The free parameters are the target size, the ratio of the 1D and 3D friction constants, and the transition probabilities between bound and unbound states. For a very strongly bound tracer on the chains, the expected predominant set of 1D lattice diffusion (LD) is found. The MFPT in the LD process significantly depends on the target size, yielding two distinct scaling behaviors for target sizes smaller and larger than the network mesh size, respectively. In the limit of a pointlike target, the LD search becomes a random walk process on the lattice, which recovers the analytical solution for the MFPT previously reported by S. Condamin, O. Bénichou, and M. Moreau [Phys. Rev. Lett. 95, 260601 (2005)]. For the very weakly bound tracer, the expected 3D free diffusion (FD) dominates, extrapolating to the well-known Smoluchowski limit. A critical target size is found above which the MFPT in the FD process is faster than in the LD process. For intermediate binding, i.e., a combination of LD and FD processes, the target search time can be minimized for an optimal range of target sizes and partitions between FD and LD, for which the MFPTs are substantially faster when compared to the limiting FD or LD processes. Our study may provide a theoretical basis to better understand and predict search and reaction processes in complex structured materials, thereby contributing to practical applications such as designing nanoreactors where catalytic targets are immobilized in polymer networks.

We study the statistical properties of active Ornstein-Uhlenbeck particles (AOUPs). In this simplest of models, the Gaussian white noise of overdamped Brownian colloids is replaced by a Gaussian colored noise. This suffices to grant this system the hallmark properties of active matter, while still allowing for analytical progress. We study in detail the steady-state distribution of AOUPs in the small persistence time limit and for spatially varying activity. At the collective level, we show AOUPs to experience motility-induced phase separation both in the presence of pairwise forces or due to quorum-sensing interactions. We characterize both the instability mechanism leading to phase separation and the resulting phase coexistence. We probe how, in the stationary state, AOUPs depart from their thermal equilibrium limit by investigating the emergence of ratchet currents and entropy production. In the small persistence time limit, we show how fluctuation-dissipation relations are recovered. Finally, we discuss how the emerging properties of AOUPs can be characterized from the dynamics of their collective modes.

For the classical problem of the rotation of a solid, we show a somehow surprising behavior involving large transient growth of perturbation energy that occurs when the moment of inertia associated to the unstable axis approaches the moment of inertia of one of the two stable axes. In that case, small but finite perturbations around this stable axis may induce a total transfer of energy to the unstable axis, leading to relaxation oscillations where the stable and unstable manifolds of the unstable axis play the role of a separatrix, an edge state. For a fluid in solid-body rotation, a similar linear and nonlinear dynamics apply to the transfer of energy between three inertial waves respecting the triadic resonance condition. We show that the existence of large transient energy growth and of relaxation oscillations may be physically interpreted as in the case of a solid by the existence of two quadratic invariants, the energy and the helicity in the case of a rotating fluid. They occur when two waves of the triad have helicities that tend towards each other, when their amplitudes are set such that they have the same energy. We show that this happens when the third wave has a vanishing frequency which corresponds to a nearly horizontal wave vector. An inertial wave, perturbed by a small-amplitude wave with a nearly horizontal wave vector, will then be periodically destroyed, its energy being transferred entirely to the unstable wave, although this perturbation is linearly stable, resulting in relaxation oscillations of wave amplitudes. In the general case we show that the dynamics described for particular triads of inertial waves is valid for a class of triadic interactions of waves in other physical problems, where the physical energy is conserved and is linked to the classical conservation of the so-called pseudomomentum, which singles out the role of waves with vanishing frequency.

Using the diagonal entropy, we analyze the dynamical signatures of the Lipkin-Meshkov-Glick model excited-state quantum phase transition (ESQPT). We first show that the time evolution of the diagonal entropy behaves as an efficient indicator of the presence of an ESQPT. We also compute the probability distribution of the diagonal entropy values over a certain time interval and we find that the resulting distribution provides a clear distinction between the different phases of ESQPT. Moreover, we observe that the probability distribution of the diagonal entropy at the ESQPT critical point has a universal form, well described by a beta distribution, and that a reliable detection of the ESQPT can be obtained from the diagonal entropy central moments.

During transcription, translation, or self-replication of DNA or RNA, information is transferred to the newly formed species from its predecessor. These processes can be interpreted as (generalized) biological copying mechanism as the new biological entities like DNA, RNA, or proteins are representing the information of their parent bodies uniquely. The accuracy of these copying processes is essential, since errors in the copied code can reduce the functionality of the next generation. Such errors might result from perturbations on these processes. Most important in this context is the temperature of the medium, i.e., thermal noise. Although a reasonable amount of experimental studies have been carried out on this important issue, theoretical understanding is truly sparse. In the present work, we illustrate a model study which is able to focus on the effect of the temperature on the process of biological copying mechanisms, as well as on mutation. We find for our paradigmatic models that, in a quite general scenario, the copying processes are most accurate at an intermediate temperature range; i.e., there exists an optimum temperature where mutation is most unlikely. This allows us to interpret the observations for some biological species with the aid of our model study.

The Maier-Saupe-Zwanzig model for the nematic phase transitions in liquid crystals is investigated in a diamond hierarchical lattice. The model takes into account a parameter to describe the biaxiality of the microscopic units. Also, a suitably chosen external field is added to the Hamiltonian to allow the determination of critical parameters associated with the nematic phase transitions. Using the transfer-matrix technique, the free energy and its derivatives are obtained in terms of recursion relations between successive generations of the hierarchical lattice. In addition, a real-space renormalization-group approach is developed to obtain the critical parameters of the same model system. Results of both methods are in excellent agreement. There are indications of two continuous phase transitions. One of them corresponds to a uniaxial-isotropic transition, in the class of universality of the three-state Potts model on the diamond hierarchical lattice. The transition between the biaxial and the uniaxial phases is in the universality class of the Ising model on the same lattice.

For Markov jump processes in out-of-equilibrium steady state, we present inequalities which link the average rate of entropy production with the timing of the site-to-site recurrences. Such inequalities are upper bounds on the average rate of entropy production. The combination with the finite-time thermodynamic uncertainty relation (a lower bound) yields inequalities of the pure kinetic kind for the relative precision of a dynamical output. After having derived the main relations for the discrete case, we sketch the possible extension to overdamped Markov dynamics on continuous degrees of freedom, treating explicitly the case of one-dimensional diffusion in tilted periodic potentials; an upper bound on the average velocity is derived, in terms of the average rate of entropy production and the microscopic diffusion coefficient, which corresponds to the finite-time thermodynamic uncertainty relation in the limit of vanishingly small observation time.

Agitated strings serve as macroscale models of spontaneous knotting, providing valuable insight into knotting dynamics at the microscale while allowing explicit analysis of the resulting knot topologies. We present an experimental setup for confined macroscale knot formation via tumbling along with a software interface to process complex knot data. Our setup allows characterization of knotting probability, knot complexity, and knot formation dynamics for knots with as many as 50 crossings. We find that the probability of knotting saturates below 80% within 100 s of the initiation of tumbling and that this saturation probability does not increase for chains above a critical length, an indication of nonequilibrium knot-formation conditions in our experiment. Despite the saturation in knot formation, we show that longer chains, while being more confined, will always tend to form knots of higher complexity since the free end can access a greater number of loops during tumbling.

We propose an approach to describe the effective microscopic dynamics of (power-law) nonlinear Fokker-Planck equations. Our formalism is based on a nonextensive generalization of the Wiener process. This allows us to obtain, in addition to significant physical insights, several analytical results with great simplicity. Indeed, we obtain analytical solutions for a nonextensive version of the Brownian free-particle and Ornstein-Uhlenbeck processes, and we explain anomalous diffusive behaviors in terms of memory effects in a nonextensive generalization of Gaussian white noise. Finally, we apply the developed formalism to model thermal noise in electric circuits.

We derive the distribution of the number of distinct sites visited by a random walker before hitting a target site of a finite one-dimensional (1D) domain. Our approach holds for the general class of Markovian processes with connected span—i.e., whose trajectories have no “holes.” We show that the distribution can be simply expressed in terms of splitting probabilities only. We provide explicit results for classical examples of random processes with relevance to target search problems, such as simple symmetric random walks, biased random walks, persistent random walks, and resetting random walks. As a by-product, explicit expressions for the splitting probabilities of all these processes are given. Extensions to reflecting boundary conditions, continuous processes, and an example of a random process with a nonconnected span are discussed.

We address the role of geometrical asymmetry in the occurrence of spin rectification in two-dimensional quantum spin chains subject to two reservoirs at the boundaries, modeled by quantum master equations. We discuss the differences in the rectification for some one-dimensional cases, and present numerical results of the rectification coefficient $R$ for different values of the anisotropy parameter of the $XXZ$ model, and different configurations of boundary drives, including both local and nonlocal dissipators. Our results also show that geometrical asymmetry, along with inhomogeneous magnetic fields, can induce spin current rectification even in the $XX$ model, indicating that the phenomenon of rectification due to geometry may be of general occurrence in quantum spin systems.

The Heider balance addresses three-body interactions with the assumption that triads are equally important in the dynamics of the network. In many networks, the relations do not have the same strength, so triads are differently weighted. Now, the question is how social networks evolve to reduce the number of unbalanced triangles when they are weighted? Are the results foreseeable based on what we have already learned from the unweighted balance? To find the solution, we consider a fully connected network in which triads are assigned with different random weights. Weights are coming from Gaussian probability distribution with mean $\mu$ and variance $\sigma$. We study this system in two regimes: (I) the ratio of $\frac{\mu }{\sigma }\ge 1$ corresponds to weak disorder (small variance) that triads' weight are approximately the same; (II) $\frac{\mu }{\sigma }<1$ counts for strong disorder (big variance) and weights are remarkably diverse. Investigating the structural evolution of such a network is our intention. We see disorder plays a key role in determining the critical temperature of the system. Using the mean-field method to present an analytic solution for the system represents that the system undergoes a first-order phase transition. For weak disorder, our simulation results display the system reaches the global minimum as temperature decreases, whereas for the second regime, due to the diversity of weights, the system does not manage to reach the global minimum.

In this paper we identify optimal swimming strategies for drag-dominated swimmers with a passive elastic joint. We use resistive force theory to obtain the dynamics of the system. We then use frequency-domain analysis to relate the motion of the passive joint to the motion of the actuated joint. We couple this analysis with elements of the geometric framework introduced in our previous work aimed at identifying useful gaits for systems in drag-dominated environments to identify speed-maximizing and efficiency-maximizing gaits for drag-dominated swimmers with a passive elastic joint.

The Stokes-Einstein (SE) relation has been widely applied to quantitatively describe the Brownian motion. Notwithstanding, here we show that even for a simple fluid, the SE relation may fail over a wide range of the Brownian particle's size. Namely, although the SE relation could be a good approximation for a large enough Brownian particle, a significant error may appear when decreasing the Brownian particle's size down to several hundred times the size of the fluid molecules, and the error increases with the decrease of the Brownian particle's size. The cause is rooted in the fact that the kinetic contribution to the diffusion coefficient is inversely proportional to the squared radius of the Brownian particle. After excluding the kinetic contribution, we show that the applicable range of the SE relation is expanded significantly.

We measure the upward force acting on a single, unconstrained, large particle in a granular medium of small particles flowing over inclined plane using discrete element method (DEM) simulation. Based on the computed force, we obtain an expression for the flux of large particles in a binary mixture of large and small particles and predict the equilibrium concentration profile and the velocity profile of the flowing layer. The theoretical predictions are in very good agreement with the DEM simulation results for a wide range of concentrations of large particles and inclination angles.

This work extends the domain of vibrational mechanics to higher dimensions, with fast vibrations applied to different directions. In particular, the presented analysis considers the case of a split biharmonic drive, where harmonics of frequency $\omega$ and $2\omega$ are applied to orthogonal directions in a two-dimensional setting. It is shown, both numerically and with analytic calculations, that this determines a highly tunable effective potential with the same symmetry as the original one. The driving allows one not only to tune the amplitude of the potential, but also to introduce an arbitrary spatial translation in the direction corresponding to the $2\omega$ driving. The setup allows for generalization to implement translations in an arbitrary direction within the two-dimensional landscapes. The same principles also apply to three-dimensional periodic potentials.

The sampling of conformations in the molecular simulations for systems with complicated free energy landscapes is always difficult. Here, we report a method for enhanced sampling based on the coarse-graining of conformational space. In this method, the locally converged region of the conformational space is coarse-grained with its population characterized by the related average residence time and visiting number, and at the same time, the direct simulations inside it are eliminated. The detailed balance is satisfied by updating the visiting number and generating outgoing trajectories of this region. This kind of coarse-graining operation can be further carried out by merging all the neighboring regions which are already converged together. The global equilibrium is achieved when the local equilibrated regions cover all the interested areas of the landscape. We tested the method by applying it to two model potentials and one protein system with multiple-basin energy landscapes. The sampling efficiency is found to be enhanced by more than three orders of magnitude compared to conventional molecular simulations, and are comparable with other widely used enhanced sampling methods. In addition, the kinetic information can also be well captured. All these results demonstrate that our method can help to solve the sampling problems efficiently and precisely without applying high temperatures or biasing potentials.