The conformation of DNA inside bacteriophages is of paramount importance for understanding packaging and ejection mechanisms. Models describing the structure of the confined macromolecule have depicted highly ordered conformations, such as spooled or toroidal arrangements that focus on reproducing experimental results obtained by averaging over thousands of configurations. However, it has been seen that more disordered states, including DNA kinking and the presence of domains with different DNA orientation can also accurately reproduce many of the structural experiments. In this work we have compared the results obtained through different simulated filling rates. We find a rate dependence for the resulting constrained states showing different anisotropic configurations. We present a quantitative analysis of the density distribution and the DNA orientation across the capsid showing excellent agreement with structural experiments. Second, we have analyzed the correlations within the capsid, finding evidence of the presence of domains characterized by aligned segments of DNA characterized by the structure factor. Finally, we have measured the number and distribution of DNA defects such as the emergence of bubbles and kinks as function of the filling rate. We find the slower the rate the fewer kink defects that appear and they would be unlikely at experimental filling rates with our model parameters. DNA domains of various orientation get larger with slower rates.

The prevailing theories describing DNA confinement in a nanochannel are predicated on the assumption that wall-DNA electrostatic interactions are sufficiently short-ranged such that the problem can be mapped to an equivalent neutral polymer confined by hard walls with an appropriately reduced effective channel size. To determine when this hypothesis is valid, we leveraged a recently reported experimental data set for the fractional extension of DNA molecules in a 250-nm-wide poly(dimethyl siloxane) (PDMS) nanochannel with buffer ionic strengths between 0.075 and 48 mM. Evaluating these data in the context of the weakly correlated telegraph model of DNA confinement reveals that, at ionic strengths greater than 0.3 mM, the average fractional extension of the DNA molecules agree with theoretical predictions with a mean absolute error of 0.04. In contrast, experiments at ionic strengths below 0.3 mM produce average fractional extensions that are systematically smaller than the theoretical predictions with a larger mean absolute error of 0.15. The deviations between experiment and theory display a correlation coefficient of 0.82 with the decay length for the DNA-wall electrostatics, linking the deviations with a breakdown in approximating the DNA with an equivalent neutral polymer.

We analyze the flow curves of a two-dimensional assembly of granular particles which are interacting via frictional contact forces. For packing fractions slightly below jamming, the fluid undergoes a large scale instability, implying a range of stress and strain rates where no stationary flow can exist. Whereas small systems were shown previously to exhibit hysteretic jumps between the low and high stress branches, large systems exhibit continuous shear thickening arising from averaging unsteady, spatially heterogeneous flows. The observed large scale patterns as well as their dynamics are found to depend on strain rate: At the lower end of the unstable region, force chains merge to form giant bands that span the system in the compressional direction and propagate in the dilational direction. At the upper end, we observe large scale clusters which extend along the dilational direction and propagate along the compressional direction. Both patterns, bands and clusters, come in with infinite correlation length similar to the sudden onset of system-spanning plugs in impact experiments.

It has been observed that the direction in which a sand dune extends its crest line depends on seasonal variation of wind direction; when the variation is small, the crest line develops more or less perpendicularly to the mean wind direction to form a transverse dune with some undulation. In the case of bimodal wind with a large relative angle, however, the dune extends its crest along the mean wind direction and evolves into an almost straight longitudinal dune. Motivated by these observations, we investigate the dynamical stability of isolated dunes using the crest line model, where the dune dynamics is represented by its crest line motion. First, we extend the previous linear stability analysis under the unidirectional wind to the case with nonzero slant angle between the wind direction and the normal direction of the crest line, and show that the stability diagram does not depend on the slant angle. Second, we examine how the linear stability is affected by the seasonal changes of wind direction in the case of bimodal wind with equal strength and duration. For the transverse dune, we find that the stability is virtually the same with that for the unidirectional wind as long as the dune evolution during a season is small. On the other hand, in the case of the longitudinal dune, the dispersions of the growth rates for the perturbation are drastically different from those of the unidirectional wind, and we find that the largest growth rate is always located at $k=0$. This is because the growth of the perturbation with $k\ne 0$ is canceled by the alternating wind from opposite sides of the crest line even though it grows during each duration period of the bimodal wind. For a realistic parameter set, the system is in the wavy unstable regime of the stability diagram for the unidirectional wind, thus the straight transverse dune is unstable to develop undulation and eventually evolves into a string of barchans when the seasonal variation of wind direction is small, but the straight longitudinal dune is stabilized under the large variation of bimodal wind direction. We also perform numerical simulations on the crest line model, and find that the results are consistent with our linear analysis and the previous reports that show that the longitudinal dunes tend to have a straight ridge elongating over time.

The divergence of the correlation length $\xi$ at criticality is an important phenomenon of percolation in two-dimensional systems. Substantial speed-ups to the calculation of the percolation threshold and component distribution have been achieved by utilizing disjoint sets, but existing algorithms of this sort cannot measure the correlation length. Here we utilize the parallel axis theorem to track the correlation length as nodes are added to the system, allowing us to utilize disjoint sets to measure $\xi$ for the entire percolation process with arbitrary precision in a single sweep. This algorithm enables direct measurement of the correlation length in lattices as well as spatial network topologies and provides an important tool for understanding critical phenomena in spatial systems.

The kinetics of contact processes are determined by the interplay among local mass transfer mechanisms, spatial heterogeneity, and segregation. Determining the macroscopic behavior of a wide variety of phenomena across the disciplines requires linking reaction times to the statistical properties of spatially fluctuating quantities. We formulate the dynamics of advected agents interacting with segregated immobile components in terms of a chemical continuous-time random walk. The inter-reaction times result from the first-passage times of mobile species to and across reactive regions, and available immobile reactants undergo a restart procedure. Segregation leads to memory effects and enhances the role of concentration fluctuations in the large-scale dynamics.

For a quantum system in a macroscopically large volume $V$, prepared in a pure state and subject to maximally noisy or ergodic unitary dynamics, the reduced density matrix of any sub-system $v\ll V$ is almost surely totally mixed. We show that the fluctuations around this limiting value, evaluated according to the invariant measure of these unitary flows, are captured by the Gaussian unitary ensemble (GUE) of random matrix theory. An extension of this statement, applicable when the unitary transformations conserve the energy but are maximally noisy or ergodic on any energy shell, allows to decipher the fluctuations around canonical typicality. According to typicality, if the large system is prepared in a generic pure state in a given energy shell, the reduced density matrix of the sub-system is almost surely the canonical Gibbs state of that sub-system. We show that the fluctuations around the Gibbs state are encoded in a deformation of the GUE whose covariance is specified by the Gibbs state. Contact with the eigenstate thermalization hypothesis is discussed.

Mixing by cutting and shuffling can be mathematically described by the dynamics of piecewise isometries (PWIs), higher dimensional analogs of one-dimensional interval exchange transformations. In a two-dimensional domain under a PWI, the exceptional set, $\overline{E}$, which is created by the accumulation of cutting lines (the union of all iterates of cutting lines and all points that pass arbitrarily close to a cutting line), defines where mixing is possible but not guaranteed. There is structure within $\overline{E}$ that directly influences the mixing potential of the PWI. Here we provide computational and analytical formalisms for examining this structure by way of measuring the density and connectivity of $\varepsilon$-fattened cutting lines that form an approximation of $\overline{E}$. For the example of a PWI on a hemispherical shell studied here, this approach reveals the subtle mixing behaviors and barriers to mixing formed by invariant ergodic subsets (confined orbits) within the fractal structure of the exceptional set. Some PWIs on the shell have provably nonergodic exceptional sets, which prevent mixing, while others have potentially ergodic exceptional sets where mixing is possible since ergodic exceptional sets have uniform cutting line density. For these latter exceptional sets, we show the connectivity of orbits in the PWI map through direct examination of orbit position and shape and through a two-dimensional return plot to explain the necessity of orbit connectivity for mixing.

Optomagnonics supports optical modes with high-quality optical factors and strong photon-magnon interaction on the scale of micrometers. These novel features provide an effective way to modulate the electromagnetic field in optical microcavities. Here in this work, we studied the magnon-induced chaos in an optomagnonical cavity under the condition of parity-time symmetry, and the chaotic behaviors of electromagnetic field could be observed under ultralow thresholds. Even more, the existence optomagnetic interaction makes this chaotic phenomenon controllable through modulating the external field. This research will enrich the study of light matter interaction in the microcavity and provide a theoretical guidance for random number state generation and the realization of the chaotic encryption of information on chips.

The beneficial role of noise in promoting species coexistence and preventing extinction has been recognized in theoretical ecology, but previous studies were mostly concerned with low-dimensional systems. We investigate the interplay between noise and nonlinear dynamics in real-world complex mutualistic networks with a focus on species recovery in the aftermath of a tipping point. Particularly, as a critical parameter such as the mutualistic interaction strength passes through a tipping point, the system collapses and approaches an extinction state through a dramatic reduction in the species populations to near-zero values. We demonstrate the striking effect of noise: when the direction of parameter change is reversed through the tipping point, noise enables species recovery which otherwise would not be possible. We uncover an algebraic scaling law between the noise amplitude and the parameter distance from the tipping point to the recovery point and provide a physical understanding through analyzing the nonlinear dynamics based on an effective, reduced-dimension model. Noise, in the form of small population fluctuations, can thus play a positive role in protecting high-dimensional, complex ecological networks.

Centrality, which quantifies the importance of individual nodes, is among the most essential concepts in modern network theory. As there are many ways in which a node can be important, many different centrality measures are in use. Here, we concentrate on versions of the common betweenness and closeness centralities. The former measures the fraction of paths between pairs of nodes that go through a given node, while the latter measures an average inverse distance between a particular node and all other nodes. Both centralities only consider shortest paths (i.e., geodesics) between pairs of nodes. Here we develop a method, based on absorbing Markov chains, that enables us to continuously interpolate both of these centrality measures away from the geodesic limit and toward a limit where no restriction is placed on the length of the paths the walkers can explore. At this second limit, the interpolated betweenness and closeness centralities reduce, respectively, to the well-known current-betweenness and resistance-closeness (information) centralities. The method is tested numerically on four real networks, revealing complex changes in node centrality rankings with respect to the value of the interpolation parameter. Nonmonotonic betweenness behaviors are found to characterize nodes that lie close to intercommunity boundaries in the studied networks.

Direct observation of a rotating detonation engine combustion chamber has enabled the extraction of the kinematics of its detonation waves. These records exhibit a rich set of instabilities and bifurcations arising from the interaction of coherent wave fronts and global gain dynamics. We develop a model of the observed dynamics by recasting the Majda detonation analog as an autowave process. The solution fronts become attractors of the engine, i.e., mode-locked rotating detonation waves. We find that denotative energy release competes with dissipation and gain recovery to produce the observed dynamics and a bifurcation structure common to other driven-dissipative systems, such as mode-locked lasers.

We construct a multifidelity framework for the kinematic parameter optimization of flapping airfoil. We employ multifidelity Gaussian process regression and Bayesian optimization to effectively synthesize the aerodynamic performance of the flapping airfoil with the kinematic parameters under multiresolution numerical simulations. The objective of this work is to demonstrate that the multifidelity framework can efficiently discover the optimal kinematic parameters of the flapping airfoil with specific aerodynamic performance using a limited number of expensive high-fidelity simulations combined with a larger number of inexpensive low-fidelity simulations. We efficiently identify the optimal kinematic parameters of an asymmetrically flapping airfoil with various target aerodynamic forces in the design space of heaving amplitude, flapping frequency, angle of attack amplitude, and stroke angle. Notably, it is found that the angle of attack can significantly affect the magnitude of aerodynamic forces by facilitating the generation of the leading-edge vortex. In the meanwhile, its combination effect with the stroke angle can determine the attitude and trajectory of the flapping airfoil, thus further affect the direction of the aerodynamic forces. With the influence of the streamwise in-line motion, the asymmetrical vortex structures emerge in the wake fields because the streamwise velocities of shedding vortices are different in the upstroke and downstroke. Furthermore, we conduct the kinematic parameter optimization for a three-dimensional asymmetrically flapping wing. Compared to the two-dimensional simulations, we further investigate the flow induced by the vortex ring and its unsteady effects on the vortex structure and aerodynamic performance.

We analyze the annihilation of equally charged particles based on the Brownian motion model built by Dyson for $N$ particles with charge $q$ interacting via the log-Coulomb potential on the unitary circle at a reduced inverse temperature $\beta$, defined as $\beta =q^2/\left(k_{B}T\right)$. We derive an analytical approach to describe the large-$t$ asymptotic behavior for the number density decay, which can be described as a power law, $n\sim t^{-\nu }$. For a sufficiently large $\beta$, the power-law exponent $\nu$ behaves as ${(\beta +1)}^{-1}$, which was corroborated through several computational simulations. For small $\beta$, in the diffusive regime, we recover the exponent of 1/2 as predicted by single-species uncharged annihilation.

An approach was developed to describe the first passage time (FPT) in multistep stochastic processes with discrete states governed by a master equation (ME). The approach is an extension of the totally absorbing boundary approach given for calculation of FPT in one-step processes [N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier Science Publishers, North Holland, Amsterdam, 2007)] to include multistep processes where jumps are not restricted to adjacent sites. In addition, a Fokker-Planck equation (FPE) was derived from the multistep ME, assuming the continuity of the state variable. The developed approach and an FPE based approach [C. W. Gardiner, Handbook of Stochastic Methods, 3rd ed. (Springer-Verlag, New York, 2004)] were used to find the mean first passage time (MFPT) of the transition between the negative and positive stable macrostates of dust grain charge when the charging process was bistable. The dust was in a plasma and charged by collecting ions and electrons, and emitting secondary electrons. The MFPTs for the transitioning of grain charge from one macrostate to the other were calculated by the two approaches for a range of grain sizes. Both approaches produced very similar results for the same grain except for when it was very small. The difference between MFPTs of two approaches for very small grains was attributed to the failure of the charge continuity assumption in the FPE description. For a given grain, the MFPT for a transition from the negative macrostate to the positive one was substantially larger than that for a transition in a reverse order. The normalized MFPT for a transition from the positive to the negative macrostate showed little sensitivity to the grain radius. For a reverse transition, with the increase of the grain radius, it dropped first and then increased. The probability density function of FPT was substantially wider for a transition from the positive to the negative macrostate, as compared to a reverse transition.

Recent progress on multiplex networks has provided a powerful way to abstract the diverse interaction of a network system with multiple layers. In this paper, we show that a multiplex structure can greatly affect the spread of an epidemic driven by traffic dynamics. One of the interesting findings is that the multiplex structure could suppress the outbreak of an epidemic, which is different from the typical finding of spread dynamics in multiplex networks. In particular, one layer with dense connections can attract more traffic flow and eventually suppress the epidemic outbreak in other layers. Therefore, the epidemic threshold will be larger than the minimal threshold of the layers. With a mean-field approximation, we provide explicit expressions for the epidemic threshold and for the onset of suppressing epidemic spreading in multiplex networks. We also provide the probability of obtaining a multiplex configuration that suppresses the epidemic spreading when the multiplex is composed of: (i) two Erdős-Rényi layers and (ii) two scale-free layers. Therefore, compared to the situation of an isolated network in which a disease may be able to propagate, a larger epidemic threshold can be found in multiplex structures.

The influence of electrostatic conditions (salt concentration of the solution and vesicle surface charge density) on the size distribution of self-assembled giant unilamellar vesicles (GUVs) is considered. The membranes of GUVs are synthesized by a mixture of dioleoylphosphatidylglycerol and dioleoylphosphatidylcholine in a physiological buffer using the natural swelling method. The experimental results are presented in the form of a set of histograms. The log-normal distribution is used for statistical treatment of results. It is obtained that the decrease of salt concentration and the increase of vesicle surface charge density of the membranes increase the average size of the GUV population. To explain the experimental results, a theory using the Helmholtz free energy of the system describing the GUV vesiculation is developed. The size distribution histograms and average size of GUVs under various conditions are fitted with the proposed theory. It is shown that the variation of the bending modulus due to changing of electrostatic parameters of the system is the main factor causing a change in the average size of GUVs.

Apart from intrinsic stochastic variability, gene expression also involves stochastic reaction delay arising from heterogeneity and fluctuation processes, which can affect the efficiency of reactants (e.g., mRNA or protein) in exploring their environments. In contrast to the former that has been extensively investigated, the impact of the latter on gene expression remains not fully understood. Here, we analyze a non-Markovian model of bursty gene expression with general delay distribution. We analytically find that the effect of stochastic reaction delay is equivalent to the introduction of negative feedback, and stationary protein distribution only depends on the mean of the delay and is independent of its distribution. We numerically show that the stochastic reaction delay always slightly amplifies the mean protein level but remarkably reduces the protein noise (quantified by the ratio of the variance over the squared average). Our analysis indicates that stochastic reaction delay is an important factor affecting gene expression.

In this work, we model and simulate the shape evolution of critically charged droplets, from the initial spherical shape to the charge emission and back to the spherical shape. The shape deformation is described using the viscous correction for viscous potential flow model, which is a potential flow approximation of the Navier-Stokes equation for incompressible Newtonian fluids. The simulated shapes are compared to snapshots of experimentally observed drop deformations. We highlight the influence of the dimensionless viscosity and charge carrier mobility of the liquid on the shape evolution of droplets and discuss the observed trends. We give an explanation as to why the observed deformation pathways of positively and negatively charged pure water droplets differ and give a hint as to why negatively charged water droplets emit more charge during charge breakup than positively charged ones.