Using Monte Carlo simulations, we study the hysteresis in unzipping of a double-stranded block copolymer DNA with $-A_n{B}_n-$ repeat units. Here $A$ and $B$ represent two different types of base pairs having two and three bonds, respectively, and $2n$ represents the number of such base pairs in a unit. The end of the DNA are subjected to a time-dependent periodic force with frequency ($\omega$) and amplitude ($g_0$) keeping the other end fixed. We find that the equilibrium force-temperature phase diagram for the static force is independent of the DNA sequence. For a periodic force case, the results are found to be dependent on the block copolymer DNA sequence and on the base pair type on which the periodic force is acting. We observe hysteresis loops of various shapes and sizes and obtain the scaling of loop area both at low- and high-frequency regimes.

In this work, we provide experimental evidence of nonlinear wave propagation in a triangular lattice of repulsive magnets supported by an elastic foundation of thin pillars, and we interpret all the individual features of the nonlinear wave field through the lens of a phonon band calculation that precisely accounts for the interparticle repulsive forces. We confirm the coexistence of two spectrally distinct components (homogeneous and forced) in the wave response that is induced via second harmonic generation (SHG) as a result of the quadratic nonlinearity embedded in the magnetic interaction. The detection of the forced component, specifically, allows us to attribute unequivocally the generation of harmonics to the nonlinear mechanisms germane to the lattice. We show that the spatial characteristics of the second harmonic components are markedly different from those exhibited by the fundamental harmonic. This endows the lattice with a functionality enrichment capability, whereby additional modal characteristics and directivity patterns can be triggered and tuned by merely increasing the amplitude of excitation.

A chimeralike state is the spatiotemporal pattern in an ensemble of homogeneous coupled oscillators, described as the emergence of coexisting coherent (synchronized) and incoherent (unsynchronized) groups. We demonstrate the existence of these states in three active camphor ribbons, which are camphor infused rectangular pieces of paper. These pinned ribbons rotate on the surface of the water due to Marangoni effect driven forces generated by the surface tension gradients. The ribbons are coupled via a camphor layer on the surface of the water. In the minimal network of globally coupled camphor ribbons, chimeralike states are characterized by the coexistence of two synchronized and one unsynchronized ribbons. We present a numerical model, simulating the coupling between ribbons as repulsive Yukawa interactions, which was able to reproduce these experimentally observed states.

Complex problems of social interaction are usually studied within the framework of agent-based models. Some of these problems, such as issue alignment and opinion polarization, are better suited in the framework of $n$-dimensional opinion space. Although this kind of complex problem may be explored by numerical simulations, these simulations can hinder our ability to obtain general results. In this work, we show how, under certain conditions, a classical multidimensional opinion model such as the Axelrod model can give rise to a closed set of master equations in terms of vector similarities between agents. The analytical results fully agree with the simulations on complete networks, accurately predict the similarity distribution of the whole system in sparse topologies, and provide a good approximation of the similarity of physical links that improves when the mean degree of the system increases.

Polymers confined to a narrow channel are subject to strong entropic forces that tend to drive the molecules apart. In this study, we use Monte Carlo computer simulations to study the segregation behavior of two flexible hard-sphere polymers under confinement in a cylindrical channel. We focus on the effects of using polymers of different lengths. We measure the variation of the conformational free energy, $F$, with the center-of-mass separation distance, $\lambda$. The simulations reveal four different separation regimes, characterized by different scaling properties of the free energy with respect to the polymer lengths and the channel diameter, $D$. We propose a regime map in which the state of the system is determined by the values of the quantities $N_2/N_1$ and $\lambda /(N_1+N_2)D^{-\beta }$, where $N_1$ and $N_2$ are the polymer lengths, and where $\beta \approx 0.64$. The observed scaling behavior of $F\left(\lambda \right)$ in each regime is in reasonable agreement with predictions using a simple theoretical model. In addition, we use MC dynamics simulations to study the segregation dynamics of initially overlapping polymers by measurement of the incremental mean first-passage time with respect to $\lambda$. For systems characterized by a wide range of $\lambda$ in which a short polymer is nested within a longer one, the segregation dynamics are close to that expected for two noninteracting one-dimensional random walkers undergoing unbiased diffusion. When the free-energy gradient is large, segregation is rapid and characterized by out-of-equilibrium effects.

We determine the osmotic pressure of microgel suspensions using membrane osmometry and dialysis, for microgels with different softnesses. Our measurements reveal that the osmotic pressure of solutions of both ionic and neutral microgels is determined by the free ions that leave the microgel periphery to maximize their entropy and not by the translational degrees of freedom of the microgels themselves. Furthermore, up to a given concentration it is energetically favorable for the microgels to maintain a constant volume without appreciable deswelling. The concentration where deswelling starts weakly depends on the crosslinker concentration, which affects the microgel dimension; we explain this by considering the dependence of the osmotic pressure and the microgel bulk modulus on the particle size.

We present high-precision data for the time evolution of bubble area $A\left(t\right)$ and circularity shape parameter $C\left(t\right)$ for several bubbles in a quasi-two-dimensional foams consisting of bubbles squashed between parallel plates. In order to fully compare with earlier predictions, foam wetness is systematically varied by controlling the height of the sample above a liquid reservoir which in turn controls the radius $r$ of the inflation of the Plateau borders. For very dry foams, where the borders are very small, classic von Neumann behavior is observed where a bubble's growth rate depends only on its number $n$ of sides. For wet foams, the inflated borders impede gas exchange and cause deviations from von Neumann's law that are found to be in accord with the generalized coarsening equation. In particular, the overall growth rate varies linearly with the film height, which decrease as surface Plateau borders inflate. More interestingly, the deviation from $dA/dt\propto (n-6)$ von Neumann behavior grows in proportion to $nCr/\sqrt{A}$. This is highlighted definitively by data for six-sided bubbles, which are forbidden to grow or shrink except for the existence of this term. It is tested quantitatively by variation of all four relevant quantities: $n$, $C$, $r$, and $A$.

Mucin polymers in the tear film protect the corneal surface from pathogens and modulate the tear-film flow characteristics. Recent studies have suggested a relationship between the loss of membrane-associated mucins and premature rupture of the tear film in various eye diseases. This work aims to elucidate the hydrodynamic mechanisms by which loss of membrane-associated mucins causes premature tear-film rupture. We model the bulk of the tear film as a Newtonian fluid in a two-dimensional periodic domain, and the lipid layer at the air-tear interface as insoluble surfactants. Gradual loss of membrane-associated mucins produces growing areas of exposed cornea in direct contact with the tear fluid. We represent the hydrodynamic consequences of this morphological change through two mechanisms: an increased van der Waals attraction due to loss of wettability on the exposed area, and a change of boundary condition from an effective negative slip on the mucin-covered areas to the no-slip condition on exposed cornea. Finite-element computations, with an arbitrary Lagrangian-Eulerian scheme to handle the moving interface, demonstrate a strong effect of the elevated van der Waals attraction on precipitating tear-film breakup. The change in boundary condition on the cornea has a relatively minor role. Using realistic parameters, our heterogeneous mucin model is able to predict quantitatively the shortening of tear-film breakup time observed in diseased eyes.

Oceans and lakes sustain intense biological activity due to the motion of marine organisms, which has significant ecological and environmental impacts. The motion of individual organisms and their interactions with each other play a significant role in the collective motion of swimming organisms. However, ubiquitous vertical density stratification in these aquatic environments significantly alters the swimmer interactions as compared to in a homogeneous fluid. Furthermore, organisms have sizes varying over a wide range which results in finite inertia. To this end, we numerically investigate the interactions between a pair of model swimming organisms in two configurations: (1) approaching each other and (2) moving side by side with finite inertia in a linearly density stratified fluid. We use the archetypal reduced-order squirmer model to numerically model the swimming organisms. We present trajectories and the contact times of interacting squirmer (puller & pusher) pairs for different Re in the range 1–50 and Ri in the range 0–10. Depending on the squirmer Re and Ri we observe that the squirmer interactions can be categorized as (i) pullers getting trapped in circular loops at high Re and low Ri, (ii) pullers escaping each other with separating angle decreasing with increasing stratification at low Re and high Ri, (iii) pushers sticking to each other after the collision and deflecting away from the collision plane for either low Re or high Ri, (iv) pushers escaping otherwise with an angle of separation increasing with stratification. Stratification also increases the contact time for squirmer pairs. The presented results can be useful to understand the mechanisms behind the accumulation of planktonic organisms in horizontal layers in a stratified environment such as oceans and lakes.

The dynamics of low-energy electrons in general static strained graphene surface is modelled mathematically by the Dirac equation in curved space-time. In Cartesian coordinates, a parametrization of the surface can be straightforwardly obtained, but the resulting Dirac equation is intricate for general surface deformations. Two different strategies are introduced to simplify this problem: the diagonal metric approximation and the change of variables to isothermal coordinates. These coordinates are obtained from quasiconformal transformations characterized by the Beltrami equation, whose solution gives the mapping between both coordinate systems. To implement this second strategy, a least-squares finite-element numerical scheme is introduced to solve the Beltrami equation. The Dirac equation is then solved via an accurate pseudospectral numerical method in the pseudo-Hermitian representation that is endowed with explicit unitary evolution and conservation of the norm. The two approaches are compared and applied to the scattering of electrons on Gaussian shaped graphene surface deformations. It is demonstrated that electron wave packets can be focused by these local strained regions.

We introduce the notion of mixed symmetry quantum phase transition (MSQPT) as singularities in the transformation of the lowest-energy state properties of a system of identical particles inside each permutation symmetry sector $\mu$, when some Hamiltonian control parameters $\lambda$ are varied. We use a three-level Lipkin-Meshkov-Glick model, with $\text{U}\left(3\right)$ dynamical symmetry, to exemplify our construction. After reviewing the construction of $\text{U}\left(3\right)$ unitary irreducible representations using Young tableaux and the Gelfand basis, we first study the case of a finite number $N$ of three-level atoms, showing that some precursors (fidelity susceptibility, level population, etc.) of MSQPTs appear in all permutation symmetry sectors. Using coherent (quasiclassical) states of $\text{U}\left(3\right)$ as variational states, we compute the lowest-energy density for each sector $\mu$ in the thermodynamic $N\to \infty$ limit. Extending the control parameter space by $\mu$, the phase diagram exhibits four distinct quantum phases in the $\lambda \text{−}\mu$ plane that coexist at a quadruple point. The ground state of the whole system belongs to the fully symmetric sector $\mu =1$ and shows a fourfold degeneracy, due to the spontaneous breakdown of the parity symmetry of the Hamiltonian. The restoration of this discrete symmetry leads to the formation of four-component Schrödinger cat states.

Surface growth governed by the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher than two undergoes a roughening transition from smooth to rough phases with increasing the nonlinearity. It is also known that the KPZ equation can be mapped onto quantum mechanics of attractive bosons with a contact interaction, where the roughening transition corresponds to a binding transition of two bosons with increasing the attraction. Such critical bosons in three dimensions actually exhibit the Efimov effect, where a three-boson coupling turns out to be relevant under the renormalization group so as to break the scale invariance down to a discrete one. On the basis of these facts linking the two distinct subjects in physics, we predict that the KPZ roughening transition in three dimensions shows either the discrete scale invariance or no intrinsic scale invariance.

Based on a system-reservoir model and an appropriate choice of nonlinear coupling, we have explored the microscopic quantum generalization of classical Liénard systems. Making use of oscillator coherent states and canonical thermal distributions of the associated $c$ numbers, we have derived the quantum Langevin equation of the reduced system which admits single or multiple limit cycles. It has been shown that detailed balance in the form of the fluctuation-dissipation relation preserves the dynamical stability of the attractors even in the case of vacuum excitation. The quantum versions of Rayleigh, van der Pol, and several other variants of Liénard oscillators are derived as special cases in our theoretical scheme within a mean-field description.

I examine the fate of a kinetic Potts ferromagnet with a high ground-state degeneracy that undergoes a deep quench to zero temperature. I consider single spin-flip dynamics on triangular lattices of linear dimension $8\le L\le 128$ and set the number of spin states $q$ equal to the number of lattice sites $L\times L$. The ground state is the most abundant final state, and is reached with probability $\approx 0.71$. Three-hexagon states occur with probability $\approx 0.26$, and hexagonal tessellations with more than three clusters form with probabilities of $O\left({10}^{-3}\right)$ or less. Spanning stripe states—where the domain walls run along one of the three lattice directions—appear with probability $\approx 0.03$. “Blinker” configurations, which contain perpetually flippable spins, also emerge, but with a probability that is vanishingly small with the system size.

With conformal-invariance methods, Burkhardt, Guim, and Xue studied the critical Ising model, defined on the upper half plane $y>0$ with different boundary conditions $a$ and $b$ on the negative and positive $x$ axes. For $ab=-+$ and $f+$, they determined the one- and two-point averages of the spin $\sigma$ and energy $\epsilon$. Here $+,-$, and $f$ stand for spin-up, spin-down, and free-spin boundaries, respectively. The case $+-+-+\cdots$, where the boundary condition switches between $+$ and $-$ at arbitrary points, ${\zeta }_1,{\zeta }_2,\cdots$ on the $x$ axis was also analyzed. In the first half of this paper a similar study is carried out for the alternating boundary condition $+f+f+\cdots$ and the case $-f+$ of three different boundary conditions. Exact results for the one- and two-point averages of $\sigma ,\epsilon$, and the stress tensor $T$ are derived with conformal-invariance methods. From the results for $\langle T\rangle$, the critical Casimir interaction with the boundary of a wedge-shaped inclusion is derived for mixed boundary conditions. In the second half of the paper, arbitrary two-dimensional critical systems with mixed boundary conditions are analyzed with boundary-operator expansions. Two distinct types of expansions—away from switching points of the boundary condition and at switching points—are considered. Using the expansions, we express the asymptotic behavior of two-point averages near boundaries in terms of one-point averages. We also consider the strip geometry with mixed boundary conditions and derive the distant-wall corrections to one-point averages near one edge due to the other edge. Finally we confirm the consistency of the predictions obtained with conformal-invariance methods and with boundary-operator expansions, in the the first and second halves of the paper.

Surface growth processes can be significantly affected by long-range temporal correlations. In this work, we perform extensive numerical simulations of a (1+1)- and (2+1)-dimensional ballistic deposition (BD) model driven by temporally correlated noise, which is regarded as the temporal correlated Kardar-Parisi-Zhang universality class. Our results are compared with the existing theoretical predictions and numerical simulations. When the temporal correlation exponent is above a certain threshold, BD surfaces develop gradually faceted patterns. We find that the temporal correlated BD system displays nontrivial dynamic properties, and the characteristic roughness exponents satisfy $\alpha \simeq {\alpha }_{\mathrm{loc}}<{\alpha }_s$ in (1+1) dimensions, which is beyond the existing dynamic scaling classifications.

Random walks are fundamental models of stochastic processes with applications in various fields, including physics, biology, and computer science. We study classical and quantum random walks under the influence of stochastic resetting on arbitrary networks. Based on the mathematical formalism of quantum stochastic walks, we provide a framework of classical and quantum walks whose evolution is determined by graph Laplacians. We study the influence of quantum effects on the stationary and long-time average probability distribution by interpolating between the classical and quantum regime. We compare our analytical results on stationary and long-time average probability distributions with numerical simulations on different networks, revealing differences in the way resets affect the sampling properties of classical and quantum walks.

The hyperuniformity concept provides a unified means to classify all perfect crystals, perfect quasicrystals, and exotic amorphous states of matter according to their capacity to suppress large-scale density fluctuations. While the classification of hyperuniform point configurations has received considerable attention, much less is known about the classification of hyperuniform two-phase heterogeneous media, which include composites, porous media, foams, cellular solids, colloidal suspensions, and polymer blends. The purpose of this article is to begin such a program for certain two-dimensional models of hyperuniform two-phase media by ascertaining their local volume-fraction variances ${\sigma }_{{}_V}^2\left(R\right)$ and the associated hyperuniformity order metrics ${\overline{B}}_V$. This is a highly challenging task because the geometries and topologies of the phases are generally much richer and more complex than point-configuration arrangements, and one must ascertain a broadly applicable length scale to make key quantities dimensionless. Therefore, we purposely restrict ourselves to a certain class of two-dimensional periodic cellular networks as well as periodic and disordered or irregular packings of circular disks, some of which maximize their effective transport and elastic properties. Among the cellular networks considered, the honeycomb networks have minimal values of the hyperuniformity order metrics ${\overline{B}}_V$ across all volume fractions. On the other hand, for all packings of circular disks examined, the triangular-lattice packings have the smallest values of ${\overline{B}}_V$ for the possible range of volume fractions. Among all structures studied here, the triangular-lattice packing of circular disks have the minimal values of the order metric for almost all volume fractions. Our study provides a theoretical foundation for the establishment of hyperuniformity order metrics for general two-phase media and a basis to discover new hyperuniform two-phase systems with desirable bulk physical properties by inverse design procedures.

Cell type-specific gene expression patterns are represented as memory states of a Hopfield neural network model. It is shown that order parameters of this model can be interpreted as concentrations of master transcription regulators that form concurrent positive feedback loops with a large number of downstream regulated genes. The order parameter free energy then defines an epigenetic landscape in which local minima correspond to stable cell states. The model is applied to gene expression data in the context of hematopoiesis.

We find that a moderate intrinsic twisting rate (ITR) can induce a bistable state for a force-free two-dimensional intrinsically curved filament. There are two different configurations of equal energy in a bistable state so that the filament is clearly different from its three-dimensional counterpart. The smaller the ITR or the larger the intrinsic curvature (IC), the clearer the distinction between two isoenergetic configurations and the longer the filament. In bistable states, the relationship between length and ITR is approximately a hyperbola and relationship between IC and critical ITR is approximately linear. Thermal fluctuation can result in a shift between two isoenergetic configurations, but large bending and twisting rigidities can prevent the shift and maintain the filament in one of these two configurations. Moreover, a filament can have a metastable state and at a finite temperature such a filament has the similar property as that of a filament with bistable state.