In this work, we report an intriguing phenomenon: crowding-induced polymer trapping in a channel. Using Langevin dynamics simulations and analytical calculations, we find that for a polymer confined in a channel, crowding particles can push a polymer into the channel corner through inducing an effective polymer-corner attraction due to the depletion effect. This phenomenon is referred to as polymer trapping. The occurrence of polymer trapping requires a minimum volume fraction of crowders, ${\varphi }^{*}$, which scales as ${\varphi }^{*}\sim {\left(a_c/L_p\right)}^{1/3}$ for $a_c\gg a_m$ and ${\varphi }^{*}\sim {\left(a_c/L_p\right)}^{1/3}{\left(a_c/a_m\right)}^{1/2}$ for $a_c\ll a_m$, where $a_c$ is the crowder diameter, $a_m$ is the monomer diameter, and $L_p$ is the polymer persistence length. For DNA, ${\varphi }^{*}$ is estimated to be around 0.25 for crowders with $a_c=2\mathrm{nm}$. We find that ${\varphi }^{*}$ also strongly depends on the shape of the channel cross section, and ${\varphi }^{*}$ is much smaller for a triangle channel than a square channel. The polymer trapping leads to a nearly fully stretched polymer conformation along a channel corner, which may have practical applications, such as full stretching of DNA for the nanochannel-based genome mapping technology.

We study the avalanche statistics observed in a minimal random growth model. The growth is governed by a reproduction rate obeying a probability distribution with finite mean $\overline{a}$ and variance $v_a$. These two control parameters determine if the avalanche size tends to a stationary distribution (finite scale statistics with finite mean and variance, or power-law tailed statistics with exponent $\in (1,3]$), or instead to a nonstationary regime with log-normal statistics. Numerical results and their statistical analysis are presented for a uniformly distributed growth rate, which are corroborated and generalized by mathematical results. The latter show that the numerically observed avalanche regimes exist for a wide family of growth rate distributions, and they provide a precise definition of the boundaries between the three regimes.

The two-dimensional (2D) Ising model is the statistical physics textbook example for phase transitions and their kinetics. Quenched through the Curie point with Glauber rates, the late-time description of the ferromagnetic domain coarsening finds its place at the scalar sector of the Allen-Cahn (or Model A) class, which encompasses phase-ordering kinetics endowed with a nonconserved order parameter. Resisting exact results sought for theoreticians since Lifshitz's first account in 1962, the central quantities of 2D Model A—most scaling exponents and correlation functions—remain known up to approximate theories whose disparate outcomes urge experimental assessment. Here we perform such assessment based on a comprehensive study of the coarsening of 2D twisted nematic liquid crystals whose kinetics is induced by a superfast electrical switching from a spatiotemporally chaotic (disordered) state to a two-phase concurrent, equilibrium one. Tracking the dynamics via optical microscopy, we first show the sharp evidence of well-established Model A aspects, such as the dynamic exponent $z=2$ and the dynamic scaling hypothesis, to then move forward. We confirm the Bray-Humayun theory for Porod's regime describing intradomain length scales of the two-point spatial correlators and show that their nontrivial decay beyond the Porod's scale can be captured in a free-from-parameter fashion by Gaussian theories, namely the Ohta-Jasnow-Kawasaki (OJK) and Mazenko theories. Regarding time-related statistics, we corroborate the aging hypothesis in Model A systems, which includes the collapse of two-time correlators into a master curve whose format is, actually, best accounted for by a solution of the local scaling invariance theory: the same solution that fits the 2D nonconserved Ising model correlator along with the Fisher-Huse conjecture. We also suggest the true value for the local persistence exponent in Model A class, in disfavor of the exact outcome for the diffusion and OJK equations. Finally, we observe a fractal morphology for persistence clusters and extract their universal dimension. Given its accuracy and possibilities, this experimental setup may work as a prototype to address further universality issues in the realm of nonequilibrium systems.

One of the interesting phenomena due to the topological heterogeneities in complex networks is the friendship paradox, stating that your friends have on average more friends than you do. Recently, this paradox has been generalized for arbitrary nodal attributes, called a generalized friendship paradox (GFP). In this paper, we analyze the GFP for the networks in which the attributes of neighboring nodes are correlated with each other. The correlation structure between attributes of neighboring nodes is modeled by the Farlie-Gumbel-Morgenstern copula, enabling us to derive approximate analytical solutions of the GFP for three kinds of methods summarizing the neighborhood of the focal node, i.e., mean-based, median-based, and fraction-based methods. The analytical solutions are comparable to simulation results, while some systematic deviations between them might be attributed to the higher-order correlations between nodal attributes. These results help us get deeper insight into how various summarization methods as well as the correlation structure of nodal attributes affect the GFP behavior, hence better understand various related phenomena in complex networks.

We study a lattice model of a single magnetic polymer chain, where Ising spins are located on the sites of a lattice self-avoiding walk in $d=2$. We consider the regime where both conformations and magnetic degrees of freedom are dynamic, thus the Ising model is defined on a dynamic lattice and conformations generate an annealed disorder. Using Monte Carlo simulations, we characterize the globule-coil and ferromaget-to-paramagnet transitions, which occur simultaneously at a critical value of the spin-spin coupling. We argue that the transition is continuous—in contrast to $d=3$ where it is first order. Our results suggest that at the transition the metric exponent takes the $\theta$-polymer value $\nu =4/7$ but the crossover exponent $\varphi \approx 0.7$, which differs from the expected value for a $\theta$ polymer.

The elastic and viscous properties of lyotropic chromonic liquid crystals have a very sharp, often exponential temperature dependence. Self-propelled bacteria swimming in this viscoelastic medium induce director deformations which can strongly influence their velocity, and we study the temperature behavior of their motility in the whole range of the nematic phase. We observe experimentally that, with increasing temperature, while the viscosity drops exponentially and the frequency of the flagellum rotation grows linearly, the swimmers' speed first conventionally increases but then, above some crossover temperature, slows down and at the same time bacteria-induced director distortions become visible. It is shown that the physics behind this temperature-driven effect is in a sharp rise in the ability of the bacterium's flagellum to induce director deformations. As temperature increases, the splay and bend elastic constants sharply decrease and the anchoring extrapolation length of the flagellum surface gets shorter and shorter. At the crossover temperature the resulting effective anchoring effect dominates the fast dropping viscosity and the distortion strengthens. As a result, a fraction of the torque the flagellum applies for the propulsion is spent for the elastic degrees of freedom, which results in a bacterium slowdown. To find the director distortions, the flagellum is presented as a collection of anchoring-induced elastic monopoles, and the bacterium velocity is found from the balance of the energy spent for the propulsion and the viscous drag and nematodynamic dissipation.

It has been known for some time that when one uses the Lorentz force law, rather than Hamilton's equation, one can derive two basic algorithms for solving trajectories in a magnetic field formally similar to the velocity-Verlet (VV) and position-Verlet (PV) symplectic integrators independent of any finite-difference approximation. Because the Lorentz force law uses the mechanical rather than the canonical momentum, the resulting magnetic field algorithms are exact energy conserving, rather than symplectic. In general, both types of algorithms can only yield the exact trajectory in the limit of vanishing small time steps. This work shows that, for a constant magnetic field, both magnetic algorithms can be further modified so that their trajectories are exactly on the gyrocircle at finite time steps. The magnetic form of the PV integrator then becomes the well-known Boris solver, while the VV form yields a second, previously unknown Boris-type algorithm, unrelated to any finite-difference scheme. Remarkably, the modification needed for the trajectory to be exact is a reparametrization of the time step, reminiscent of the Ge-Marsden theorem.

Understanding time-dependent diffusion processes in multiphase media is of great importance in physics, chemistry, materials science, petroleum engineering, and biology. Consider the time-dependent problem of mass transfer of a solute between two phases and assume that the solute is initially distributed in one phase (phase 2) and absent from the other (phase 1). We desire the fraction of total solute present in phase 1 as a function of time, $\mathcal{S}\left(t\right)$, which we call the spreadability, since it is a measure of the spreadability of diffusion information as a function of time. We derive exact direct-space formulas for $\mathcal{S}\left(t\right)$ in any Euclidean space dimension $d$ in terms of the autocovariance function as well as corresponding Fourier representations of $\mathcal{S}\left(t\right)$ in terms of the spectral density, which are especially useful when scattering information is available experimentally or theoretically. These are singular results because they are rare examples of mass transport problems where exact solutions are possible. We derive closed-form general formulas for the short- and long-time behaviors of the spreadability in terms of crucial small- and large-scale microstructural information, respectively. The long-time behavior of $\mathcal{S}\left(t\right)$ enables one to distinguish the entire spectrum of microstructures that span from hyperuniform to nonhyperuniform media. For hyperuniform media, disordered or not, we show that the “excess” spreadability, $\mathcal{S}\left(\infty \right)-\mathcal{S}\left(t\right)$, decays to its long-time behavior exponentially faster than that of any nonhyperuniform two-phase medium, the “slowest” being antihyperuniform media. The stealthy hyperuniform class is characterized by an excess spreadability with the fastest decay rate among all translationally invariant microstructures. We obtain exact results for $\mathcal{S}\left(t\right)$ for a variety of specific ordered and disordered model microstructures across dimensions that span from hyperuniform to antihyperuniform media. Moreover, we establish a remarkable connection between the spreadability and an outstanding problem in discrete geometry, namely, microstructures with “fast” spreadabilities are also those that can be derived from efficient “coverings” of space. We also identify heretofore unnoticed, to our best knowledge, remarkable links between the spreadability $\mathcal{S}\left(t\right)$ and NMR pulsed field gradient spin-echo amplitude as well as diffusion MRI measurements. This investigation reveals that the time-dependent spreadability is a powerful, dynamic-based figure of merit to probe and classify the spectrum of possible microstructures of two-phase media across length scales.

Electrostatic two-stream instabilities play essential roles in an electrostatic collisionless shock formation. They are a key dissipation mechanism and result in ion heating and acceleration. Since the number and energy of the shock-accelerated ions depend on the instabilities, precise identification of the active instabilities is important. Two-dimensional particle-in-cell simulations in a multicomponent plasma reveal ion reflection and acceleration at the shock front, excitation of a longitudinally propagating electrostatic instability due to a nonoscillating component of the electrostatic field in the upstream region of the shock, and generation of up- and down-shifted velocity components within the expanding-ion components. A linear analysis of the instabilities for a ${\mathrm{C}}_2{\mathrm{H}}_3\mathrm{Cl}$ plasma using the one-dimensional electrostatic plasma dispersion function, which includes electron and ion temperature effects, shows that the most unstable mode is the electrostatic ion-beam two-stream instability (IBTI), which is weakly dependent on the existence of electrons. The IBTI is excited by velocity differences between the expanding protons and carbon-ion populations. There is an electrostatic electron-ion two-stream instability with a much smaller growth rate associated with a population of protons reflecting at the shock. The excitation of the fast-growing IBTI associated with laser-driven collisionless shock increases the brightness of a quasimonoenergetic ion beam.

Self-organized coherence-incoherence patterns, called chimera states, have first been reported in systems of Kuramoto oscillators. For coupled excitable units, similar patterns where coherent units are at rest are called bump states. Here, we study bumps in an array of active rotators coupled by nonlocal attraction and global repulsion. We demonstrate how they can emerge in a supercritical scenario from completely coherent Turing patterns: a single incoherent unit appears in a homoclinic bifurcation, undergoing subsequent transitions to quasiperiodic and chaotic behavior, which eventually transforms into extensive chaos with many incoherent units. We present different types of transitions and explain the formation of coherence-incoherence patterns according to the classical paradigm of short-range activation and long-range inhibition.

Geometric frustration arises whenever the constituents of a physical assembly locally favor an arrangement that cannot be realized globally. Recently, such frustrated assemblies were shown to exhibit filamentation, size limitation, large morphological variations and other exotic response properties. While these unique characteristics can be shown to be a direct outcome of the geometric frustration, some geometrically frustrated systems do not exhibit any of the above phenomena. In this work we exploit the intrinsic approach to provide a framework for directly addressing the frustration in physical assemblies. The framework highlights the role of the compatibility conditions associated with the intrinsic fields describing the physical assembly. We show that the structure of the compatibility conditions determines the behavior of small assemblies and in particular predicts their superextensive energy growth exponent. We illustrate the use of this framework to several well-known frustrated assemblies.

We measure by experiment and particle-based simulation the rheology of concentrated, non-Brownian droplet emulsions functionalized with surface-bound single-stranded (ss), “sticky,” DNA. In the absence of ssDNA, the emulsion viscosity increases with the dispersed phase volume fraction $\varphi$, before passing through a liquid-solid transition at a critical ${\varphi }_c$ related to random close packing. Introducing ssDNA leads to a liquid-solid transition at $\varphi <{\varphi }_c$, the onset being set by the droplet valency $N$ and the ssDNA concentration (or simulated binding strength $\epsilon$). Using insight from simulation, we identify three key behaviors: (i) jammed suspensions ($\varphi >{\varphi }_c\approx 0.64$) show weak effects of functionalization, with elastic rheology instead governed by droplet stiffness; (ii) suspensions with $\varphi <{\varphi }_c$ and $N=1$, 2 always exhibit viscous rheology, regardless of functionalization; and (iii) for $\varphi <{\varphi }_c$ and $N>3$, functionalization leads to a controllable viscous-elastic transition. We present state diagrams showing the range of rheological tuning attainable by these means.

A foldable cone, or f-cone, is a discrete vertex folded from flat with curved faces, and is an exemplar of nonrigid origami. We determine the exact equilibrium shape of a well-folded symmetrical f-cone by geometrical considerations alone, by treating as cones intersecting along original fold lines expressing equal fold angles. When moderate displacements prevail, the shape is found alternatively from the spherical image of the vertex, from deploying Gauss's mapping. The analytical working is much less compared to direct linearization of the exact solution framework; expressions for shape parameters are availed in closed form, and some of their variation is accurately retained compared to the exact case.

A model computational quantum thermodynamic network is constructed with two variable temperature baths coupled by a linker system, with an asymmetry in the coupling of the linker to the two baths. It is found in computational simulations that the baths come to “thermal equilibrium” at different bath energies and temperatures. In a sense, heat is observed to flow from cold to hot. A description is given in which a recently defined quantum entropy $S_{\mathrm{univ}}^Q$ for a pure state “universe” continues to increase after passing through the classical equilibrium point of equal temperatures, reaching a maximum at the asymmetric equilibrium. Thus, a second law account $\mathrm{\Delta }{S}_{\mathrm{univ}}^Q\ge 0$ holds for the asymmetric quantum process. In contrast, a von Neumann entropy description fails to uphold the entropy law, with a maximum near when the two temperatures are equal, then a decrease $\mathrm{\Delta }{S}^{vN}<0$ on the way to the asymmetric equilibrium.

This paper presents statistical analyses of random motions in a single layer of fluidized lightweight spherical particles. Foam polystyrene spheres were driven by an upward airflow through the sieve mesh, and their two-dimensional motion was acquired using image analysis. In the bulk region, the particle velocity distributions changed from Gaussian to heavy-tailed distribution as the bulk packing fraction ${\varphi }_b$ was increased. The mean square displacement of the particles exhibited transition to subdiffusion at much lower ${\varphi }_b$ than observed in previous studies using similar setup but with heavier particles. A slight superdiffusion and significant growth of the correlation length in the two-body velocity correlation was observed at further large ${\varphi }_b$. The effect of the wall on the dynamics of the particles was also investigated, and the anisotropy of the granular temperature was found to be a useful index to discriminate between the wall region and the bulk. The turbulence statistics in the wake of a particle indicated a strong wall-normal asymmetry of aerodynamic forcing as the “thermal” agitation in the wall region.

Widths of shocks are compared, under liquid and solid conditions, for a two-dimensional layer of charged microspheres levitated in a plasma. In this strongly coupled dusty plasma, a shock was launched as a blast wave by moving an exciter wire at a supersonic speed and then bringing it to a halt. Runs were repeated with the layer of microspheres prepared two ways: a crystallinelike solid and a liquid. The liquid was sustained using laser heating, with conditions that were otherwise the same as in the solid. The shock width was found to be less in a liquid than in a solid, where it was four to six lattice constants. These measurements were based on the high-gradient region of density profiles. The profiles were obtained from particle coordinates, measured by high-speed video imaging. The spatial resolution was improved by combining particle coordinates, in the shock's frame of reference, from a sequence of images.

We study the mutual information between two lattice blocks in terms of von Neumann entropies for one-dimensional infinite lattice systems. Quantum $q$-state Potts model and transverse-field spin-$1/2 XY$ model are considered numerically by using the infinite matrix product state approach. As a system parameter varies, block-block mutual information exhibit singular behaviors that enable us to identify the critical points for the quantum phase transitions. As happens with von Neumann entanglement entropy of single block, at critical points, block-block mutual information for two adjacent blocks show a logarithmic leading behavior with increasing the size of the blocks, which yields the central charge $c$ of the underlying conformal field theory, as it should be. It seems that two disjoint blocks show a similar logarithmic growth of the mutual information as a characteristic property of critical systems but the proportional coefficients of the logarithmic term are very different from the central charges. As the separation between the two lattice blocks increases, the mutual information reveals a consistent power-law decaying behavior for various truncation dimensions and lattice-block sizes. The critical exponent of block-block mutual information in the thermodynamic limit is estimated by extrapolating the exponents of power-law decaying regions for finite truncation dimensions. For a given lattice-block size $\ell$, the critical exponents for the same universality classes seem to have very close values each other. Whereas the critical exponents have different values to a degree of distinction for the different universality classes. As the lattice-block size becomes bigger, the critical exponent becomes smaller. We discuss a relation between the exponents of block-block mutual information and correlation with the Shatten one-norm of block-block correlation.

Bacterial division is an inherently stochastic process with effects on fluctuations of protein concentration and phenotype variability. Current modeling tools for the stochastic short-term cell-size dynamics are scarce and mainly phenomenological. Here we present a general theoretical approach based on the Chapman-Kolmogorov equation incorporating continuous growth and division events as jump processes. This approach allows us to include different division strategies, noisy growth, and noisy cell splitting. Considering bacteria synchronized from their last division, we predict oscillations in both the central moments of the size distribution and its autocorrelation function. These oscillations, barely discussed in past studies, can arise as a consequence of the discrete time displacement invariance of the system with a period of one doubling time, and they do not disappear when including stochasticity on either division times or size heterogeneity on the starting population but only after inclusion of noise in either growth rate or septum position. This result illustrates the usefulness of having a solid mathematical description that explicitly incorporates the inherent stochasticity in various biological processes, both to understand the process in detail and to evaluate the effect of various sources of variability when creating simplified descriptions.

Inertial cavitation in soft matter is an important phenomenon featured in a wide array of biological and engineering processes. Recent advances in experimental, theoretical, and numerical techniques have provided access to a world full of nonlinear physics, yet most of our quantitative understanding to date has been centered on a spherically symmetric description of the cavitation process in water. However, cavitation bubble growth and collapse rarely occur in a perfectly symmetrical fashion, particularly in soft materials. Predicting the onset of dynamically arising, nonspherical instabilities in soft matter has remained a significant, unresolved challenge, in part due to the additional constitutive complexities introduced by the surrounding nonlinear viscoelastic solid. Here, we provide a new theoretical framework capable of accurately predicting the onset of nonspherical instability shapes of a bubble in a soft material by explicitly accounting for all pertinent nonlinear interactions between the cavitation bubble and the solid surroundings. Comparison with high-resolution experimental images from laser-induced cavitation events in a polyacrylamide hydrogel show excellent agreement. Interestingly, and consistent with experimental findings, our model predicts the emergence of various dynamic instability shapes for circumferential bubble stretch ratios greater than 1, in contrast to most quasistatic investigations. Our new theoretical framework not only provides unprecedented insight into the cavitation dynamics in a soft, nonlinear solid, but also provides a quantitative means of interpreting bubble dynamics relevant to a wide array of engineering and medical applications as well as natural phenomena.

The dynamic cavity method provides the most efficient way to evaluate probabilities of dynamic trajectories in systems of stochastic units with unidirectional sparse interactions. It is closely related to sum-product algorithms widely used to compute marginal functions from complicated global functions of many variables, with applications in disordered systems, combinatorial optimization, and computer science. However, the complexity of the cavity approach grows exponentially with the in-degrees of the interacting units, which creates a defacto barrier for the successful analysis of systems with fat-tailed in-degree distributions. In this paper, we present a dynamic programming algorithm that overcomes this barrier by reducing the computational complexity in the in-degrees from exponential to quadratic, whenever couplings are chosen randomly from (or can be approximated in terms of) discrete, possibly unit-dependent, sets of equidistant values. As a case study, we analyze the dynamics of a random Boolean network with a fat-tailed degree distribution and fully asymmetric binary $\pm J$ couplings, and we use the power of the algorithm to unlock the noise-dependent heterogeneity of stationary node activation patterns in such a system.