We consider a one-dimensional lattice gas model of hardcore particles with nearest-neighbor interaction in presence of a time-periodic external potential. We investigate how attractive or repulsive interaction affects particle transport and determine the conditions for optimum transport, i.e., the conditions for which the maximum dc particle current is achieved in the system. We find that the attractive interaction in fact hinders the transport, while the repulsive interaction generally enhances it. The net dc current is a result of the competition between the current induced by the periodic external drive and the diffusive current present in the system. When the diffusive current is negligible, particle transport in the limit of low particle density is optimized for the strongest possible repulsion. But when the particle density is large, very strong repulsion makes particle movement difficult in an overcrowded environment and, in that case, the optimal transport is obtained for somewhat weaker repulsive interaction. Our numerical simulations show reasonable agreement with our mean-field calculations. When the diffusive current is significantly large, the particle transport is still facilitated by repulsive interaction, but the conditions for optimality change. Our numerical simulations show that the optimal transport occurs at the strongest repulsive interaction for large particle density and at a weaker repulsion for small particle density.

In coupled identical oscillators, complete synchronization has been well formulated; however, partial synchronization still calls for a general theory. In this work, we study the partial synchronization in a ring of $N$ locally coupled identical oscillators. We first establish the correspondence between partially synchronous states and conjugacy classes of subgroups of the dihedral group $D_N$. Then we present a systematic method to identify all partially synchronous dynamics on their synchronous manifolds by reducing a ring of oscillators to short chains with various boundary conditions. We find that partially synchronous states are organized into a hierarchical structure and, along a directed path in the structure, upstream partially synchronous states are less synchronous than downstream ones.

The advent of novel optogenetics technology allows the recording of brain activity with a resolution never seen before. The characterization of these very large data sets offers new challenges as well as unique theory-testing opportunities. Here we discuss whether the spatial and temporal correlations of the collective activity of thousands of neurons are tangled as predicted by the theory of critical phenomena. The analysis shows that both the correlation length $\xi$ and the correlation time $\tau$ scale as predicted as a function of the system size. With some peculiarities that we discuss, the analysis uncovers evidence consistent with the view that the large-scale brain cortical dynamics corresponds to critical phenomena.

Natural ecosystems, in particular on the microbial scale, are inhabited by a large number of species. The population size of each species is affected by interactions of individuals with each other and by spatial and temporal changes in environmental conditions, such as resource abundance. Here, we use a generic population dynamics model to study how, and under what conditions, a periodic temporal environmental variation can alter an ecosystem's composition and biodiversity. We demonstrate that using timescale separation allows one to qualitatively predict the long-term population dynamics of interacting species in varying environments. We show that the notion of Tilman's R* rule, a well-known principle that applies for constant environments, can be extended to periodically varying environments if the timescale of environmental changes (e.g., seasonal variations) is much faster than the timescale of population growth (doubling time in bacteria). When these timescales are similar, our analysis shows that a varying environment deters the system from reaching a steady state, and stable coexistence between multiple species becomes possible. Our results posit that biodiversity can in part be attributed to natural environmental variations.

The telegraph model is the standard model of stochastic gene expression, which can be solved exactly to obtain the distribution of mature RNA numbers per cell. A modification of this model also leads to an analytical distribution of nascent RNA numbers. These solutions are routinely used for the analysis of single-cell data, including the inference of transcriptional parameters. However, these models neglect important mechanistic features of transcription elongation, such as the stochastic movement of RNA polymerases and their steric (excluded-volume) interactions. Here we construct a model of gene expression describing promoter switching between inactive and active states, binding of RNA polymerases in the active state, their stochastic movement including steric interactions along the gene, and their unbinding leading to a mature transcript that subsequently decays. We derive the steady-state distributions of the nascent and mature RNA numbers in two important limiting cases: constitutive expression and slow promoter switching. We show that RNA fluctuations are suppressed by steric interactions between RNA polymerases, and that this suppression can in some instances even lead to sub-Poissonian fluctuations; these effects are most pronounced for nascent RNA and less prominent for mature RNA, since the latter is not a direct sensor of transcription. We find a relationship between the parameters of our microscopic mechanistic model and those of the standard models that ensures excellent consistency in their prediction of the first and second RNA number moments over vast regions of parameter space, encompassing slow, intermediate, and rapid promoter switching, provided the RNA number distributions are Poissonian or super-Poissonian. Furthermore, we identify the limitations of inference from mature RNA data, specifically showing that it cannot differentiate between highly distinct RNA polymerase traffic patterns on a gene.

The finite element method (FEM) based on a nonregular mesh is used to solve Hartree-Fock and Kohn-Sham equations for three atoms (hydrogen, helium, and beryllium) confined by finite and infinite potentials, defined in terms of piecewise functions or functions with a well-defined first derivative. This approach's reliability is shown when contrasted with Roothaan's approach, which depends on a basis set. Therefore, its exponents must be optimized for each confinement imposed over each atom, which is a monumental task. The comparison between our numerical approach and Roothaan's approach is made by using total and orbitals energies from the Hartree-Fock method, where there are several comparison sources. Regarding the Kohn-Sham method, there are few published data and consequently the results reported here can be used as a benchmark for future comparisons. The way to solve Hartree-Fock or Kohn-Sham equations by the FEM is entirely appropriate to study confined atoms with any form of confinement potential. This article represents a step toward developing a fully numerical quantum chemistry code free of basis sets to obtain the electronic structure of many-electron atoms confined by arbitrary confinement.

We investigate the fluctuating dynamics of colloidal particles in weakly crosslinked F-actin networks with optical-trap-based microrheology. Using the dual-feedback technology, embedded colloidal particles were stably forced beyond the linear regime in a manner that does not suppress spontaneous fluctuations of particles. Upon forcing, a particle that was stably confined in a cage made of the network's crosslinks started to intermittently jump to the next caging microenvironments. By investigating the statistics of the jump dynamics, we discuss how heterogeneous relaxations observed in equilibrium systems became homogeneous when similar jumps were activated under constant forcing beyond the linear regime.

Due to the presence of competing interactions, the square-well-linear fluid can exhibit either liquid-vapor equilibrium (macrophase separation) or clustering (microphase separation). Here we address the issue of determining the boundary between these two regimes, i.e., the Lifshitz point, expressed in terms of a relationship between the parameters of the model. To this aim, we carry out Monte Carlo simulations to compute the structure factor of the fluid, whose behavior at low wave vectors accurately captures the tendency of the fluid to form aggregates or, alternatively, to phase separate. Specifically, for a number of different combinations of attraction and repulsion ranges, we make the system go across the Lifshitz point by increasing the strength of the repulsion. We use simulation results to benchmark the performance of two theories of fluids, namely, the hypernetted chain (HNC) equation and the analytically solvable random phase approximation (RPA); in particular, the RPA theory is applied with two different prescriptions as for the direct correlation function inside the core. Overall, the HNC theory proves to be an appropriate tool to characterize the fluid structure and the low-wave-vector behavior of the structure factor is consistent with the threshold between microphase and macrophase separation established through simulation. The structural predictions of the RPA theory turn out to be less accurate, but this theory offers the advantage of providing an analytical expression of the Lifshitz point. Compared to simulation, both RPA schemes predict a Lifshitz point that falls within the macrophase-separation region of parameters: in the best case, barriers roughly twice higher than predicted are required to attain clustering conditions.

Jammed packings of granular materials display complex mechanical response. For example, the ensemble-averaged shear modulus $\langle G\rangle$ increases as a power law in pressure $p$ for static packings of soft spherical particles that can rearrange during compression. We seek to design granular materials with shear moduli that can either increase or decrease with pressure without particle rearrangements even in the large-system limit. To do this, we construct tessellated granular metamaterials by joining multiple particle-filled cells together. We focus on cells that contain a small number of bidisperse disks in two dimensions. We first study the mechanical properties of individual disk-filled cells with three types of boundaries: periodic boundary conditions (PBC), fixed-length walls (FXW), and flexible walls (FLW). Hypostatic jammed packings are found for cells with FLW, but not in cells with PBC and FXW, and they are stabilized by quartic modes of the dynamical matrix. The shear modulus of a single cell depends linearly on $p$. We find that the slope of the shear modulus with pressure ${\lambda }_c<0$ for all packings in single cells with PBC where the number of particles per cell $N\ge 6$. In contrast, single cells with FXW and FLW can possess ${\lambda }_c>0$, as well as ${\lambda }_c<0$, for $N\le 16$. We show that we can force the mechanical properties of multicell granular metamaterials to possess those of single cells by constraining the end points of the outer walls and enforcing an affine shear response. These studies demonstrate that tessellated granular metamaterials provide a platform for the design of soft materials with specified mechanical properties.

According to the manifold hypothesis, real data can be compressed to lie on a low-dimensional manifold. This paper explores the estimation of the dimensionality of this manifold with an interest in identifying independent degrees of freedom and possibly identifying state variables that would govern materials systems. The challenges identified that are specific to materials science are (i) accurate estimation of the number of dimensions of the data, (ii) coping with the intrinsic random and low-bit-depth nature of microstructure samples, and (iii) linking noncompressed domains such as processing to microstructure. Dimensionality estimates are made with the maximum-likelihood-estimation method with the Minkowski $p$-norms being used as a measure of the distance between microstructural images. It is found that, where dimensionality estimates are required to be accurate, it is necessary to use the Minkowski 1-norm (also known as the $L_1$-norm or Manhattan distance). This effect is found to be due to image quantification and proofs are given regarding the distortion produced by quantization. It is also found that homogenization is an effective way of estimating the dimension of random microstructure image sets. An estimate of 40 dimensions for the fibers of a SiC/SiC fiber composite is obtained. It is also found that, with images generated from a sparse domain (surrogate to the process domain), it is possible to infer the nature of the process manifold from images alone.

The properties of hydrogen at warm dense matter (WDM) conditions are of high importance for the understanding of astrophysical objects and technological applications such as inertial confinement fusion. In this work, we present extensive ab initio path integral Monte Carlo results for the electronic properties in the Coulomb potential of a fixed ionic configuration. This gives us unique insights into the complex interplay between the electronic localization around the protons with their density response to an external harmonic perturbation. We find qualitative agreement between our simulation data and a heuristic model based on the assumption of a local uniform electron gas model, but important trends are not captured by this simplification. In addition to being interesting in their own right, we are convinced that our results will be of high value for future projects, such as the rigorous benchmarking of approximate theories for the simulation of WDM, most notably density functional theory.

Advances in laser technology have led to ever-increasing laser intensities. As a result, in addition to the amplified spontaneous emission and pedestal, it has become necessary to accurately treat the relativistic rising edge component. This component has not needed much consideration in the past because of its not relativistic intensity. In the previous study, a thin contamination layer was blown away from the target by the rear sheath field due to the relativistic rising edge component, and the target bulk was accelerated by the sheath field due to the main pulse. These indicated that the proton acceleration is not efficient in the target normal sheath acceleration by the ultrahigh intense femtosecond laser if the proton-containing layer is as thin as the contamination layer. Here we employ a double-layer target, making the second (rear) layer thick enough not to be blown away by the rising edge, so that the second layer is accelerated by the main pulse. The first layer is composed of heavy ions to reduce the total thickness of the target for efficient proton acceleration. We investigate an optimal design of a double-layer target for proton acceleration by the ultrahigh intense femtosecond laser considering the relativistic rising edge using two-dimensional particle-in-cell simulations. We also discuss how to optimize the design of such a double-layer target and find that it can be designed with two conditions: the first layer is not penetrated by hole boring, and the second layer is not blown away by the rising edge.

The total cross section of binary collision is, in general, unbounded due to the long-range interations of molecules. It is conventional to truncate the small angle deflections of collisions. The present work suggests an alternative way of avoiding the difficulty of unboundedness. We employ the mean value theorem of definite integral over the deflection angle for the cross section. A series of numerical experiments were carried out to look for the representative collision cross section through which the single-angle simulation is amenable to the solution of the Boltzmann equation. Results show that the cross section should be $\langle \mathrm{\Sigma }\rangle ={\mathrm{\Sigma }}_D^2/(2{\mathrm{\Sigma }}_D-{\mathrm{\Sigma }}_{\mu })$, and the representative deflection for the single-angle simulation be $cos\langle \chi \rangle ={\mathrm{\Sigma }}_{\mu }/{\mathrm{\Sigma }}_D-1$, where ${\mathrm{\Sigma }}_D$ is the diffusion cross section and ${\mathrm{\Sigma }}_{\mu }$ is the viscosity cross section. The single-angle computations for the inverse power law and the Lennard-Jones force law perfectly reproduce the conventional scattering algorithms for one-dimensional (1D) simulations of transport coefficients and 1D shock thickness. The computation costs for Lennard-Jones molecules are comparable to the costs for inverse power-law models.

In a birth, death, and diffusion process, the extinction-survival transition occurs when the average net growth rate is zero. For instance, in the presence of normally distributed time-varying stochastic growth rates with no autocorrelation, the transition indeed occurs at zero net growth rates. In contrast, if the growth rates are constant in time, a large enough variance in the growth rate will systematically ensure the survival of the global population even in a small system and, more importantly, even with a negative net growth rate. We here show that, surprisingly, for any intermediate temporal autocorrelation, any length of correlation, and any negative average growth rate, the same result holds. We test this argument on exponential and power law autocorrelation models and propose a simple condition for the growth rate variance at the transition.

We develop a semiclassical approach for the statistics of the time delay in quantum chaotic systems in the presence of a tunnel barrier, for broken time-reversal symmetry. Results are obtained as asymptotic series in powers of the reflectivity of the barrier, with coefficients that are rational functions of the channel number. Exact expressions, valid for arbitrary reflectivity and channel number, are conjectured and numerically verified for specific families of statistical moments.

Many real-world time series exhibit both significant short- and long-range temporal correlations. Such correlations enhance the errors of linear trend analysis. In this paper, we provide a general framework for trend analysis under the consideration of such correlations. We propose a parsimonious model containing both a single short-range autoregressive parameter and long-range fractional parameter. We derive analytical closed-form results for the error bars of the least-squares estimate of the trend for such time series, highlighting the different effects of short- and of long-range correlations. We employ an ensemble method for the automated extraction of scaling regions to estimate the fractional parameter of the data model together with its error bar, and the Grünwald-Letnikov derivative for the identification of the autoregressive parameter. We apply this framework to the study of warming trends on gridded temperature data in central Europe. We make use of the redundancy of the trend signal in adjacent grid points using methods of spatial averaging and the first principal component of empirical orthogonal function analysis. We find good agreement between the results of these two methods. We find a statistically significant decadal warming trend in central Europe over the past 70 years, which shows a particularly dramatic increase over the past 20 years.

Stroke is one of the major causes of global death, which can occur due to blockage in a blood vessel by a clot. The immediate dissolving of the clot is essential to restore the blood flow and prevent tissue necrosis. Clot dissolution can be achieved via thrombolytic therapy using plasminogen activators. In this study, a clot dissolution model is developed for a three-dimensional patient-specific carotid artery that investigates the effect of different vessel wall models on clot dissolution. The lysis pattern of the clot and hemodynamics of blood flow are evaluated using three different models of the vessel wall, namely, rigid, linear elastic, and Mooney-Rivlin hyperelastic. The effect of flow condition is considered by solving the Navier-Stokes equations for the free flow domain and the Brinkman equation for the clot domain with the same pressure and velocity fields. This will result in continuous pressure and velocity over the interfaces of the free flow and clot domains. The blood inflow is assumed to be pulsatile. In addition, the species transport driven by diffusion and convection is considered to be different in the porous medium and plasma. The obtained results show that in all models, the starting time of clot volume decrease is almost the same and the clot starts dissolving from the inner curvature of the artery. However, in the hyperelastic model, dissolving the clot takes longer compared to the other two models. By monitoring the vessel wall deformation, the exact time of vessel recanalization is determined.

In this article, we simulate the translocation of a semiflexible homopolymer through an extended pore, driven by both a constant and a time-dependent end-pulled force, employing a model introduced in previous studies. The time dependence is simplistically modeled as a cosine function, and we distinguish between two scenarios for the driving—-longitudinal force and transversal force—depending on the relative orientation of the force, parallel or perpendicular, respectively, with respect to the pore axis. Besides some key differences between the two drivings, the mean translocation times present a large minimum region as a function of the frequency of the force that is typical of the resonant activation effect. The presence of the minimum is independent on the elastic characteristics of the polymeric chains and reveals a linear relation between the optimum mean translocation time and the corresponding period of the driving. The mean translocation times show different scaling exponents with the polymer length for different flexibilities. Lastly, we derive an analytical expression of the mean translocation time for low driving frequency, which clearly agrees with the simulations.

We study conformational properties of diluted dumbbell polymers composed of two rings attached to both ends of a linear spacer segment. Our investigation involves analytical methods of field theory and bead-spring coarse-grained molecular dynamics simulations. We focus on the influence of the relative length of the spacer segment to the length of side rings on the shape and the relative size of dumbbells as compared to linear polymers of equal mass. We find that dumbbells with short spacers exhibit a significantly more compact structure than linear polymers. Conversely, as the spacer length increases, the influence of the side rings on the size of the dumbbells becomes negligible. Consequently, dumbbell molecules with long spacers attain a size comparable to corresponding linear chains. Our analytical theory accurately predicts a quantitative conformational crossover between the behaviors of short-spacer and long-spacer dumbbells, which is further confirmed by our numerical simulations.