Different contact regimes between a spherical lens and a periodically patterned substrate are observed, when they are pressed against each other. Top contact occurs when only the highest substrate sections touch the lens, whereas mixed contact implies that both the highest and the lowest substrate sections come into contact with the lens. In this paper, we study how the pattern density of the substrate, along with its physical properties and those of the lens, determine the transition from top contact to mixed contact. Experiments and numerical simulations had been performed, as complementary approaches to obtain data, and a theoretical analysis has been developed to gain insight on the effect of the physical parameters on the contact transition. As a result, a phase diagram is presented, in terms of the load and the contact radius, that combines the observations of the three approaches (experimental, numerical, and theoretical), unveiling the boundaries of three contact regimes: (1) deterministic-driven contact, (2) top contact, and (3) mixed contact.

We compare quantum Otto engines based on two different cycle models: a two-bath model, with a standard heat source and sink, and a measurement-based protocol, where the role of heat source is played by a quantum measurement. We furthermore study these cycles using two different “working substances”: a single qutrit (spin-1 particle) or a pair of qubits (spin-1/2 particles) interacting via the $XXZ$ Heisenberg interaction. Although both cycle models have the same efficiency when applied on a single-qubit working substance, we find that both can reach higher efficiencies using these more complex working substances by exploiting the existence of “idle” levels, i.e., levels that do not shift while the spins are subjected to a variable magnetic field. Furthermore, with an appropriate choice of measurement, the measurement-based protocol becomes more efficient than the two-bath model.

We perform a multifractal detrended fluctuation analysis of the magnetoconductance data of two standard types of mesoscopic systems: a disordered nanowire and a ballistic chaotic billiard, with two different lattice structures. We observe in all cases that multifractality is generally present and that it becomes stronger in the quantum regime of conduction, i.e., when the number of open scattering channels is small. We argue that this behavior originates from correlations induced by the magnetic field, which can be characterized through the distribution of conductance increments in the corresponding “stochastic time series,” with the magnetic field playing the role of a fictitious time. More specifically, we show that the distributions of conductance increments are well fitted by $q$ Gaussians and that the value of the parameter $q$ is a useful quantitative measure of multifractality in magnetoconductance fluctuations.

We study in detail the interplay between chaos and entanglement in the Bohmian trajectories of three entangled qubits, made of coherent states of the quantum harmonic oscillator. We find that all the three-dimensional (3D) chaotic trajectories are ergodic; namely, they have a common long time distribution of points regardless of the initial conditions, and for any nonzero entanglement, their number is much larger than in the corresponding two-qubit system. Furthermore, the range of entanglements for which practically all the trajectories are chaotic and ergodic is much larger than in the two-qubit case. Thus, as the dimensionality of the system increases, Born's rule becomes accessible to a wider range of arbitrary initial distributions than in the 2D case. Our numerical results lead to the conjecture that, for multiqubit systems, Born's rule is the limit of almost all initial distributions of particles.

Nematode species are well-known for their invariant cell lineage pattern during development. Combining knowledge about the fate specification induced by asymmetric division and the anti-correlation between cell cycle length and cell volume in Caenorhabditis elegans, we propose a minimal model to simulate lineage initiation by altering cell volume segregation ratio in each division, and quantify the derived pattern's performance in proliferation speed, fate diversity, and space robustness. The stereotypic pattern in C. elegans embryo is found to be one of the most optimal solutions taking minimum time to achieve the cell number before gastrulation, by programming asymmetric divisions as a strategy.

Recently, it has been shown that in graded systems, thermal rectification (TR) effect may remain in the thermodynamical limit. Here, by taking the one-dimensional rotor lattice as an illustrating model, we investigate how the graded structure may affect the TR efficiency. In particular, we consider the case where the interaction is assigned with nonlinear polynomial functions. It is found that TR is robust in the thermodynamical limit and meanwhile its efficiency may considerably depend on the details of the graded structure. This finding suggests that it is possible to enhance the TR effect by taking into account the nonlinear graded structure even in large systems.

We study integrable spin chains and quantum and classical cellular automata with interaction range $\ell \ge 3$. This is a family of integrable models for which there was no general theory so far. We develop an algebraic framework for such models, generalizing known methods from nearest-neighbor interacting chains. This leads to a new integrability condition for medium-range Hamiltonians, which can be used to classify such models. A partial classification is performed in specific cases, including $U\left(1\right)$-symmetric three-site interacting models, and Hamiltonians that are relevant for interaction-round-a-face models. We find a number of models which appear to be new. As an application we consider quantum brickwork circuits of various types, including those that can accommodate the classical elementary cellular automata on light cone lattices. In this family we find that the so-called Rule150 and Rule105 models are Yang-Baxter integrable with three-site interactions. We present integrable quantum deformations of these models, and derive a set of local conserved charges for them. For the famous Rule54 model we find that it does not belong to the family of integrable three-site models, but we cannot exclude Yang-Baxter integrability with longer interaction ranges.

A stochastic process with movement, return, and rest phases is considered in this paper. For the movement phase, the particles move following the dynamics of the Gaussian process or the ballistic type of Lévy walk, and the time of each movement is random. For the return phase, the particles will move back to the origin with a constant velocity or acceleration or under the action of a harmonic force after each movement, so that this phase can also be treated as a noninstantaneous resetting. After each return, a rest with a random time at the origin follows. The asymptotic behaviors of the mean-squared displacements with different kinds of movement dynamics, returning, and random resting time are discussed. The stationary distributions are also considered when the process is localized. In addition, the mean first passage time is considered when the dynamic of the movement phase is Brownian motion.

Consider the short-time probability distribution $\mathcal{P}(H,t)$ of the one-point interface height difference $h(x=0,\tau =t)-h(x=0,\tau =0)=H$ of the stationary interface $h(x,\tau )$ described by the Kardar-Parisi-Zhang (KPZ) equation. It was previously shown that the optimal path, the most probable history of the interface $h(x,\tau )$ which dominates the upper tail of $\mathcal{P}(H,t)$, is described by any of two ramplike structures of $h(x,\tau )$ traveling either to the left, or to the right. These two solutions emerge, at a critical value of $H$, via a spontaneous breaking of the mirror symmetry $x\leftrightarrow -x$ of the optimal path, and this symmetry breaking is responsible for a second-order dynamical phase transition in the system. We simulate the interface configurations numerically by employing a large-deviation Monte Carlo sampling algorithm in conjunction with the mapping between the KPZ interface and the directed polymer in a random potential at high temperature. This allows us to observe the optimal paths, which determine each of the two tails of $\mathcal{P}(H,t)$, down to probability densities as small as ${10}^{-500}$. At short times we observe mirror-symmetry-broken traveling optimal paths for the upper tail, and a single mirror-symmetric path for the lower tail, in good quantitative agreement with analytical predictions. At long times, even at moderate values of $H$, where the optimal fluctuation method is not supposed to apply, we still observe two well-defined dominating paths. Each of them violates the mirror symmetry $x\leftrightarrow -x$ and is a mirror image of the other.

Nonlocally coupled oscillators with a phase lag exhibit various nontrivial spatiotemporal patterns such as the chimera states and the multitwisted states. We numerically study large-scale spatiotemporal patterns in a ring of oscillators with a repulsive coupling with a phase delay parameter $\alpha$. We find that the multichimera state disappears when $\alpha$ exceeds a critical value. Analysis of the fraction of incoherent regions shows that the transition is analogous to that of directed percolation with two absorbing states but that their critical behaviors are different. The multichimera state reappears when $\alpha$ is further increased, exhibiting nontrivial spatiotemporal patterns with a plateau in the fraction of incoherent regions. A transition from the multichimera to multitwisted states follows at a larger value of $\alpha$, resulting in five collective phases in total.

The outcome of an election depends not only on which candidate is more popular, but also on how many of their voters actually turn out to vote. Here we consider a simple model in which voters abstain from voting if they think their vote would not matter. Specifically, they do not vote if they feel sure their preferred candidate will win anyway (a condition we call complacency), or if they feel sure their candidate will lose anyway (a condition we call dejectedness). The voters reach these decisions based on a myopic assessment of their local network, which they take as a proxy for the entire electorate: voters know which candidate their neighbors prefer and they assume—perhaps incorrectly—that those neighbors will turn out to vote, so they themselves cast a vote if and only if it would produce a tie or a win for their preferred candidate in their local neighborhood. We explore various network structures and distributions of voter preferences and find that certain structures and parameter regimes favor unrepresentative outcomes where a minority faction wins, especially when the locally preferred candidate is not representative of the electorate as a whole.

The globular-stretch transition of a collapsed polymer in low strain rate elongational flow is studied using polymeric protrusion kinetics scaling laws and numerical simulation. Results demonstrate the influence of fluid flow on the occurrence probability of long-length thermally nucleated polymeric protrusions, which regulate collapsed polymer unfolding in low strain rate flows. Further, we estimate that the globular-stretch transition rate $\left(k_{\mathrm{s}}\right)$ in low strain rate $\left(\dot{\in }\right)$ elongational flows varies as $k_{\mathrm{s}}\sim e^{-\alpha {\dot{\in }}^{-1}}.$ Results here reveal that the existing approach of neglecting the effects of fluid flow on thermally nucleated protrusions distribution is not valid for analyzing polymer unfolding behavior in low strain rate flows. Neglecting such an effect overestimates the constant $\alpha$ in the scaling law of transition rate $\left(k_{\mathrm{s}}\sim e^{-\alpha {\dot{\in }}^{-1}}\right)$ by a factor of 2.

Amphiphilic lipid bilayers modify the friction properties of the surfaces on top of which they are deposited. In particular, the measured sliding friction coefficient can be significantly reduced compared with the native surface. We investigate in this work the friction properties of a numerical coarse-grained model of DSPC (1,2-distearoyl-sn-glycero-3-phosphocholine) lipid bilayer subject to longitudinal shear. The interleaflet friction coefficient is obtained from out-of-equilibrium pulling or from relaxation simulations. In particular, we gain access to the transient viscoelastic response of a sheared bilayer. The bilayer mechanical response is found to depend significantly on the membrane physical state, with evidence in favor of a linear response regime in the fluid but not in the gel region. The linear response validity domain is established, and the timescales appearing in the membrane response discussed.

We construct exact solutions for the Saffman-Taylor problem in a planar Hele-Shaw cell for the case of an isolated bubble near the tip of an expanding bubble in the limit of zero surface tension. This construction utilizes the integrability of the problem in the limit of vanishing surface tension. It exploits the connection, brought by the Schwarz function, between the constants of motion and the shape of the bubbles. The results of this paper provide a step toward the theoretical understanding of the dynamics of Saffman-Taylor problem in a Hele-Shaw cell with randomly distributed tiny bubbles.

We carry out extensive direct path integral Monte Carlo (PIMC) simulations of the uniform electron gas (UEG) at finite temperature for different values of the spin-polarization $\xi$. This allows us to unambiguously quantify the impact of spin effects on the momentum distribution function $n\left(\mathbf{k}\right)$ and related properties. We find that interesting physical effects like the interaction-induced increase in the occupation of the zero-momentum state $n\left(\mathbf{0}\right)$ substantially depend on $\xi$. Our results further advance the current understanding of the UEG as a fundamental model system, and are of practical relevance for the description of transport properties of warm dense matter in an external magnetic field. All PIMC results are freely available online and can be used as a benchmark for the development of methods and applications.

The smoothed particle hydrodynamics (SPH) method has been increasingly applied to simulate multiphase flows with large density ratios, but the method is computationally expensive when a high resolution is needed. Traditionally a uniform spatial resolution (USR) is used in an SPH simulation. In our previous work, an adaptive spatial resolution (ASR) method was developed for use in the SPH simulations of multiphase flows; the spatial resolution changes adaptively according to the distance to the interface between different phases. In this paper, the SPH-ASR method for multiphase flows is improved by introducing a particle shifting technique to improve the distribution of particles. This particle shifting technique considers the variable smoothing length. The present SPH-ASR method is further enhanced by optimizing the algorithm for adaptive resolution. In addition, the current SPH-ASR method is extended from two- to three-dimensional applications. The improved SPH-ASR method is validated by simulating the dam-break flows, liquid drop formation, and drop impact on a solid surface. Results show that the present SPH-ASR method can greatly reduce the computational cost while maintain the same accuracy to the uniform resolutions.

In this paper, we propose a family of parametric second-order boundary schemes for the vectorial finite-difference-based lattice Boltzmann method (FD-LBM), which consist of convex combinations. The FD-LBM unifies several different numerical schemes for the Navier-Stokes equations, and thereby these boundary schemes are naturally applicable for the standard LBM. The accuracy of the boundary schemes is independent of the boundary location, and it is validated by several numerical experiments, two- and three-dimensional flow problems, with straight and curved boundaries.