We present a methodology for quantifying biodiversity at the sequence level by developing the probability theory on a set of strings. Further, we apply our methodology to the problem of quantifying the population diversity of microorganisms in several extreme environments and digestive organs and reveal the relation between microbial diversity and various environmental parameters.

We study a continuous-space version of the totally asymmetric simple exclusion process (TASEP), consisting of interacting Brownian particles subject to a driving force in a periodic array of potential wells. Particles are inserted into the leftmost well at rate $\alpha$, hop to the right at unit rate, and are removed at the rightmost well at rate $\beta$. Our study is motivated by recent experiments on colloidal particles in a periodic potential generated by an optical tweezers array. Particles spend most of the time near potential minima, approximating the situation on the lattice; a short-range repulsive interaction prevents two particles from occupying the same potential well. A constant driving force, representing Stokes drag on particles suspended in a moving fluid, leads to biased motion. Our results for the density profile and current, obtained via numerical integration of the Langevin equation and dynamic Monte Carlo simulations, indicate that the continuous-space model exhibits phase transitions analogous to those observed in the lattice TASEP. The correspondence is not exact, however, due to the lack of particle-hole symmetry in our model.

Reaction-diffusion systems where transition rates exhibit quenched disorder are common in physical and chemical systems. We study pair reactions on a periodic two-dimensional lattice, including continuous deposition and spontaneous desorption of particles. Hopping and desorption are taken to be thermally activated processes. The activation energies are drawn from a binary distribution of well depths, corresponding to “shallow” and “deep” sites. This is the simplest nontrivial distribution, which we use to examine and explain fundamental features of the system. We simulate the system using kinetic Monte Carlo methods and provide a thorough understanding of our findings. We show that the combination of shallow and deep sites broadens the temperature window in which the reaction is efficient, compared to either homogeneous system. We also examine the role of spatial correlations, including systems where one type of site is arranged in a cluster or a sublattice. Finally, we show that a simple rate equation model reproduces simulation results with very good accuracy.

We consider the Potts model and the related bond, site, and mixed site-bond percolation problems on triangular-type and kagome-type lattices, and derive closed-form expressions for the critical frontier. For triangular-type lattices the critical frontier is known, usually derived from a duality consideration in conjunction with the assumption of a unique transition. Our analysis, however, is rigorous and based on an established result without the need of a uniqueness assumption, thus firmly establishing all derived results. For kagome-type lattices the exact critical frontier is not known. We derive a closed-form expression for the Potts critical frontier by making use of a homogeneity assumption. The closed-form expression is unique, and we apply it to a host of problems including site, bond, and mixed site-bond percolations on various lattices. It yields exact thresholds for site percolation on kagome, martini, and other lattices and is highly accurate numerically in other applications when compared to numerical determination.

In the preceding paper, one of us (F. Y. Wu) considered the Potts model and bond and site percolation on two general classes of two-dimensional lattices, the triangular-type and kagome-type lattices, and obtained closed-form expressions for the critical frontier with applications to various lattice models. For the triangular-type lattices Wu’s result is exact, and for the kagome-type lattices Wu’s expression is under a homogeneity assumption. The purpose of the present paper is twofold: First, an essential step in Wu’s analysis is the derivation of lattice-dependent constants $A,B,C$ for various lattice models, a process which can be tedious. We present here a derivation of these constants for subnet networks using a computer algorithm. Second, by means of a finite-size scaling analysis based on numerical transfer matrix calculations, we deduce critical properties and critical thresholds of various models and assess the accuracy of the homogeneity assumption. Specifically, we analyze the $q$-state Potts model and the bond percolation on the 3–12 and kagome-type subnet lattices $\left(n\times n\right):\left(n\times n\right)$, $n\le 4$, for which the exact solution is not known. Our numerical determination of critical properties such as conformal anomaly and magnetic correlation length verifies that the universality principle holds. To calibrate the accuracy of the finite-size procedure, we apply the same numerical analysis to models for which the exact critical frontiers are known. The comparison of numerical and exact results shows that our numerical values are correct within errors of our finite-size analysis, which correspond to 7 or 8 significant digits. This in turn infers that the homogeneity assumption determines critical frontiers with an accuracy of 5 decimal places or higher. Finally, we also obtained the exact percolation thresholds for site percolation on kagome-type subnet lattices $\left(1\times 1\right):\left(n\times n\right)$ for $1\le n\le 6$.

Brownian particles moving in a periodic potential with or without external load are often used as good theoretical models for the phenomenological studies of microscopic heat engines. The model that we propose here, assumes the particle to be moving in a nonequilibrium medium and we have obtained the exact expression for the stationary current density. We have restricted our consideration to the overdamped motion of the Brownian particle. We present here a self-consistent theory based on the system-reservoir coupling model, within a microscopic approach, of fluctuation induced transport in the semiclassical limit for a general system coupled with two heat baths kept at different temperatures. This essentially puts forth an approach to semiclassical state-dependent diffusion. We also explore the possibility of observing a current when the temperature of the two baths are different, and also envisage that our system may act as a Carnot engine even when the bath temperatures are the same. The condition for such a construction has been elucidated.

We study a model of “elastic” lattice polymer in which a fixed number of monomers $m$ is hosted by a self-avoiding walk with fluctuating length $l$. We show that the stored length density ${\rho }_m\equiv 1-⟨l⟩/m$ scales asymptotically for large $m$ as ${\rho }_m={\rho }_{\infty }\left(1-\theta /m+\dots \right)$, where $\theta$ is the polymer entropic exponent, so that $\theta$ can be determined from the analysis of ${\rho }_m$. We perform simulations for elastic lattice polymer loops with various sizes and knots, in which we measure ${\rho }_m$. The resulting estimates support the hypothesis that the exponent $\theta$ is determined only by the number of prime knots and not by their type. However, if knots are present, we observe strong corrections to scaling, which help to understand how an entropic competition between knots is affected by the finite length of the chain.

A nonlinear mathematical model is used to investigate the time evolution of the cell populations in colon crypts (stem, semidifferentiated and fully differentiated cells). To mimic pathological alteration of the biochemical pathways leading to abnormal proliferative activity of the population of semidifferentiated cells their renewal rate is assumed to be dependent on the population size. Then, the effects of such perturbation on the population dynamics are investigated theoretically. Using both theoretical methods and numerical simulations it is shown that the increase in the renewal rate of semidifferentiated cells strongly impacts the dynamical behavior of the cell populations.

We consider a simple Maier-Saupe statistical model with the inclusion of disorder degrees of freedom to mimic the phase diagram of a mixture of rodlike and disklike molecules. A quenched distribution of shapes leads to a phase diagram with two uniaxial and a biaxial nematic structure. A thermalized distribution, however, which is more adequate to liquid mixtures, precludes the stability of this biaxial phase. We then use a two-temperature formalism, and assume a separation of relaxation times, to show that a partial degree of annealing is already sufficient to stabilize a biaxial nematic structure.

In the literature, transport networks are usually treated as homogeneous networks, that is, every node has the same function, simultaneously providing and requiring resources. However, some real networks, such as power grids and supply chain networks, show a far different scenario in which nodes are classified into two categories: supply nodes provide some kinds of services, while demand nodes require them. In this paper, we propose a general transport model for these supply-demand networks, associated with a criterion to quantify their transport capacities. In a supply-demand network with heterogeneous degree distribution, its transport capacity strongly depends on the locations of supply nodes. We therefore design a simulated annealing algorithm to find the near optimal configuration of supply nodes, which remarkably enhances the transport capacity compared with a random configuration and outperforms the degree target algorithm, the betweenness target algorithm, and the greedy method. This work provides a start point for systematically analyzing and optimizing transport dynamics on supply-demand networks.

We study the statistical properties of ensembles of polymers in isotropic turbulence numerically in the one-way coupling regime. A linear polymer chain passively convected by turbulence is modeled by a line of beads, each of which is connected by a finitely extensible nonlinear elastic force and subject to Brownian motion. We find that when the Weissenberg number ${\text{Wi}}_{\eta }<1$, the polymer chain has a coiled configuration, while for ${\text{Wi}}_{\eta }>10$, it remains stretched for a much longer time than the typical time scale of the fluctuating turbulent velocity gradient. Various statistical quantities characterizing the ensemble of polymers, such as the mean, variance, autocorrelation time, and probability density function of the end-to-end vector distance, indicate that the coil-stretch transition occurs at ${\text{Wi}}_{\eta }=3–4$. We also find that this trend is insensitive to the number of beads $N_b$ ($N_b=20$ or $N_b=2$), provided that the parameters in the model with a small number of beads are properly generated from the one with a large number of beads (i.e., using the formula of Jin and Collins). Finally, the ${\text{Wi}}_{\eta }$ effects on the alignment of the end-to-end vector versus the principal axis of the rate of strain tensor and on the polymer elongation are examined from the viewpoint of local flow topology.

We study mixing of isothermal fluids by controlling the global hydrodynamic entropy $⟨s⟩$. In particular, based on the statistical coupling between the evolution of $⟨s⟩$ and the global viscous dissipation $⟨ϵ⟩$, we analyze stirring protocols such that $⟨s⟩\sim t^{\alpha }\iff ⟨ϵ⟩\sim t^{\alpha -1},$ with $0<\alpha \le 1$. For a model array of vortices [Fukuta and Murakami, Phys. Rev. E 57, 449 (1998)], we show that: (i) feedback control can be achieved via input-output linearization, (ii) mixing is monotonically enhanced for increasing entropy production, and (iii) the mixing time $t_m$ scales as $t_m\sim {⟨ϵ⟩}^{-1/2}$.

A three-dimensional model of a low-Reynolds-number swimmer is introduced and analyzed in this Brief Report. This model consists of two large and small spheres connected by two perpendicular thin rods. The geometry of this system is motivated by the microorganisms that use a single tail to swim; the large sphere represents the head of microorganism and the small sphere resembles its tail. Each rod changes its length and orientation in a nonreciprocal manner that effectively propels the system. Translational and rotational velocities of the swimmer are studied for different values of parameters. Our findings show that by changing the parameters we can adjust both the velocity and the direction of motion of the swimmer.

The dynamics of disclination defect lines in a nematic liquid crystal are measured experimentally and considered theoretically. An optical trap is used to deform the line, enabling the previously unexplored regime of large deformation to be accessed. The relaxation follows a linear decay at large amplitude, crossing over into the well understood exponential decay at small amplitude. Both regimes can be described by simple theoretical arguments. The crossover point is well described by the theory, but the experiments show a faster than expected dynamics, indicating that the effective viscosity in the models is overestimated.

Vesicles are becoming a quite popular model for the study of red blood cells. This is a free boundary problem which is rather difficult to handle theoretically. Quantitative computational approaches constitute also a challenge. In addition, with numerical studies, it is not easy to scan within a reasonable time the whole parameter space. Therefore, having quantitative analytical results is an essential advance that provides deeper understanding of observed features and can be used to accompany and possibly guide further numerical development. In this paper, shape evolution equations for a vesicle in a shear flow are derived analytically with precision being cubic (which is quadratic in previous theories) with regard to the deformation of the vesicle relative to a spherical shape. The phase diagram distinguishing regions of parameters where different types of motion (tank treading, tumbling, and vacillating breathing) are manifested is presented. This theory reveals unsuspected features: including higher order terms and harmonics (even if they are not directly excited by the shear flow) is necessary, whatever the shape is close to a sphere. Not only does this theory cure a quite large quantitative discrepancy between previous theories and recent experiments and numerical studies, but also it reveals a phenomenon: the VB mode band in parameter space, which is believed to saturate after a moderate shear rate, exhibits a striking widening beyond a critical shear rate. The widening results from excitation of fourth-order harmonic. The obtained phase diagram is in a remarkably good agreement with recent three-dimensional numerical simulations based on the boundary integral formulation. Comparison of our results with experiments is systematically made.

With a view to determining the distance between the two opposing duplexes in supercoiled DNA, we have measured small angle neutron scattering from pHSG298 plasmid (2675 base pairs) dispersed in saline solutions. Experiments were carried out under full and zero average DNA neutron scattering contrast using hydrogenated plasmid and a 1:1 mixture of hydrogenated and perdeuterated plasmid, respectively. In the condition of zero average contrast, the scattering intensity is directly proportional to the single DNA molecule scattering function (form factor), irrespective of the DNA concentration and without complications from intermolecular interference. The form factors are interpreted with Monte Carlo computer simulation. For this purpose, the many body problem of a dense DNA solution was reduced to the one of a single DNA molecule in a congested state by confinement in a cylindrical potential. It was observed that the interduplex distance decreases with increasing concentration of salt as well as plasmid. Therefore, besides ionic strength, DNA crowding is shown to be important in controlling the interwound structure and site juxtaposition of distal segments of supercoiled DNA. This first study exploiting zero average DNA contrast has been made possible by the availability of perdeuterated plasmid.

This paper is concerned with addressing how biological cells react to mechanical impulse. We propose a particle based model to numerically study the mechanical response of these cells with subcellular detail. The model focuses on a plant cell in which two important features are present: (1) the cell’s interior liquidlike phase inducing hydrodynamic phenomena, and (2) the cell wall, a viscoelastic solid membrane that encloses the protoplast. In this particle modeling framework, the cell fluid is modeled by a standard smoothed particle hydrodynamics (SPH) technique. For the viscoelastic solid phase (cell wall), a discrete element method (DEM) is proposed. The cell wall hydraulic conductivity (permeability) is built in through a constitutive relation in the SPH formulation. Simulations show that the SPH-DEM model is in reasonable agreement with compression experiments on an in vitro cell and with analytical models for the basic dynamical modes of a spherical liquid filled shell. We have performed simulations to explore more complex situations such as relaxation and impact, thereby considering two cell types: a stiff plant type and a soft animal-like type. Their particular behavior (force transmission) as a function of protoplasm and cell wall viscosity is discussed. We also show that the mechanics during and after cell failure can be modeled adequately. This methodology has large flexibility and opens possibilities to quantify problems dealing with the response of biological cells to mechanical impulses, e.g., impact, and the prediction of damage on a (sub)cellular scale.

The dynamics of Davydov-Scott monomer in a thermal bath with higher order amide-site’s displacement leads to anharmonic oscillation effect is investigated using full-quantum approach and the Lindblad formulation of master equation. The specific heat is calculated based on the thermodynamic partition function using the path integral method. The temperature dependence of the specific heat is studied. In the model the specific heat anomaly as pointed out in recent works by Ingold et al. [Phys. Rev. E 79, 061105 (2009)] is also observed. However, it is found that the anomaly occurs at high-temperature region, and the anharmonic oscillation restores the positivity of specific heat.

Cooperative clusters of $N$ parallel bonds confined to an anchoring surface by springs of stiffness $k_s$ are considered. The free energy of a cluster can be obtained from its force-displacement relation. The dissociation kinetics of the cluster can be modeled as the dissociation of an effective single bond. There is a critical force $F_c$ beyond which the barrier for the cluster dissociation vanishes. $F_c$ scales such as $k_s^{1/2}$ and $F_c/N$ is small compared to the critical force of a single bond. The theoretical predictions of free energy landscape and cluster lifetime are supported by numerical simulations for large number of bonds. Our study suggests that experiments measuring force-displacement relations could be useful in exploring the dynamics of adhesion clusters.