In this paper, we develop a conservative phase-field method for interface-capturing among N $(N\ge 2)$ immiscible fluids, the evolution of the fluid-fluid interface is captured by conservative Allen-Cahn equation (CACE), and the interface force of N immiscible fluids is incorporated to Navier-Stokes equation (NSE) by chemical potential form. Accordingly, we propose a lattice Boltzmann equation (LBE) method for solving N $(N\ge 2)$ immiscible incompressible NSE and CACE at high density and viscosity contrasts. Numerical simulations including stationary droplets, Rayleigh-Taylor instability, spreading of liquid lenses, and spinodal decompositions are carried out to show the accuracy and capability of present LBE, and the results show that the predictions by use of the present LBE agree well with the analytical solutions and/or other numerical results.

In a recent paper, E. J. Janse van Rensburg has presented computational data enumerating the conformations of closed circular self-avoiding lattice polymers with knots confined in a cubic box, and claimed to have observed a negative osmotic pressure in the system. The purpose of this comment is to state that osmotic pressure by a self-avoiding polymer, knotted or otherwise, is positive, which means a polymer pushes confining walls outwards, and the statement of the opposite is a mistake.

The free energy of a model of uniformly weighted lattice knots of length $n$ and knot type $K$ confined to a lattice cube of side length $L-1$ is given by $F_L\left(\varphi \right)=-\frac{1}{V}log{p}_{n,L}\left(K\right)$, where $V=L^3$ and where $\varphi =n/V$ is the concentration of monomers of the lattice knot in the confining cube. The limiting free energy of the model is $F_{\infty }\left(\varphi \right)={lim}_{L\to \infty }{F}_L\left(\varphi \right)$ and the limiting osmotic pressure of monomers leaving the lattice knot to become solvent molecules is defined by ${\mathrm{\Pi }}_{\infty }\left(\varphi \right)={\varphi }^2\frac{d}{d\varphi }[F_{\infty }\left(\varphi \right)/\varphi ]$. I show that, under very mild assumptions, the functions $P_L\left(\varphi \right)={\varphi }^2\frac{d}{d\varphi }[F_L\left(\varphi \right)/\varphi ]{|}_n$ and ${\mathrm{\Pi }}_L\left(\varphi \right)={\varphi }^2\frac{d}{d\varphi }[F_L\left(\varphi \right)/\varphi ]{|}_L$ are finite-size approximations of ${\mathrm{\Pi }}_{\infty }\left(\varphi \right)$.

We examine a quantum Otto engine with a harmonic working medium consisting of two particles to explore the use of wave function symmetry as an accessible resource. It is shown that the bosonic system displays enhanced performance when compared to two independent single particle engines, while the fermionic system displays reduced performance. To this end, we explore the trade-off between efficiency and power output and the parameter regimes under which the system functions as engine, refrigerator, or heater. Remarkably, the bosonic system operates under a wider parameter space both when operating as an engine and as a refrigerator.

I study the equilibrium and nonequilibrium dynamics of a conservative and reversible Q2R cellular automata. This system exhibits a configuration space with $2^{2N}$ states, which grows with the size of the system. In this context, for small size, the phase space has fixed points and cycles. Through numerical studies and using a statistical approach, I can observe stable and unstable behaviors as well as a phase transition around a critical energy $E_c$. I introduce a coupling constant as a perturbation to the classic Q2R model and show through the phase diagram how this modified model exhibits three different phases.

Noise and fluctuations play vital roles in signal transduction in cells. Various numerical techniques for its simulation have been proposed, most of which are not efficient in cellular networks with a wide spectrum of timescales. In this paper, based on a recently developed variational technique, low-dimensional structures embedded in complex stochastic reaction dynamics are unfolded which sheds light on new design principles of efficient simulation algorithm for treating noise in the mesoscopic world. This idea is effectively demonstrated in several popular regulation models with an empirical selection of test functions according to their reaction geometry, which not only captures complex distribution profiles of different molecular species but also considerably speeds up the computation.

We examine the behavior of supercoiled DNA minicircles containing between 200 and 400 base-pairs, also named microDNA, in which supercoiling favors thermally assisted DNA denaturation bubbles of nanometer size and controls their lifetime. Mesoscopic modeling and accelerated dynamics simulations allow us to overcome the limitations of atomistic simulations encountered in such systems, and offer detailed insight into the thermodynamic and dynamical properties associated with the nucleation and closure mechanisms of long-lived thermally assisted denaturation bubbles which do not stem from bending- or torque-driven stress. Suitable tuning of the degree of supercoiling and size of specifically designed microDNA is observed to lead to the control of opening characteristic times in the millisecond range, and closure characteristic times ranging over well distinct timescales, from microseconds to several minutes. We discuss how our results can be seen as a dynamical bandwidth which might enhance selectivity for specific DNA binding proteins.

In the present paper, we theoretically study the drag force on nanoparticles in the free-molecule regime. It has been widely assumed that the particle temperature is equal to the gas media temperature in the open literature. However, this assumption can be invalid in some real applications. Based on the kinetic theory, we obtain the generalized formulas for the drag force on nanoparticles in the free-molecule regime. It is found that there exists a significant error induced by the assumption of equal temperature between the particle and the surrounding gas. Therefore, it is necessary to consider the effect of the particle temperature in the analysis of the particle transport properties.

We consider a formulation for the Hopf functional differential equation which governs statistical solutions of the Navier-Stokes equations. By introducing an exponential operator with a functional derivative, we recast the Hopf equation as an integro-differential functional equation by the Duhamel principle. On this basis we introduce a successive approximation to the Hopf equation. As an illustration we take the Burgers equation and carry out the approximations to the leading order. Scale invariance of the statistical Navier-Stokes equations in $d$ dimensions is formulated and contrasted with that of the deterministic Navier-Stokes equations. For the statistical Navier-Stokes equations, critical scale invariance is achieved for the characteristic functional of the $d\mathrm{th}$ derivative of the vector potential in $d$ dimensions. The deterministic equations corresponding to this choice of the dependent variable acquire the linear Fokker-Planck operator under dynamic scaling. In three dimensions it is the vorticity gradient that behaves like a fundamental solution (more precisely, source-type solution) of deterministic Navier-Stokes equations in the long-time limit. Physical applications of these ideas include study of a self-similar decaying profile of fluid flows. Moreover, we reveal typical physical properties in the late-stage evolution by combining statistical scale invariance and the source-type solution. This yields an asymptotic form of the Hopf functional in the long-time limit, improving the well-known Hopf-Titt solution. In particular, we present analyses for the Burgers equations to illustrate the main ideas and indicate a similar analysis for the Navier-Stokes equations.

Absorbing boundary conditions are presented for three-dimensional time-dependent Schrödinger-type of equations as a means to reduce the cost of the quantum-mechanical calculations. The boundary condition is first derived from a semidiscrete approximation of the Schrödinger equation with the advantage that the resulting formulas are automatically compatible with the finite-difference scheme and no further discretization is needed in space. The absorbing boundary condition is expressed as a discrete Dirichlet-to-Neumann map, which can be further approximated in time by using rational approximations of the Laplace transform to enable a more efficient implementation. This approach can be applied to domains with arbitrary geometry. The stability of the zeroth-order and first-order absorbing boundary conditions is proved. We tested the boundary conditions on benchmark problems. The effectiveness is further verified by a time-dependent Hartree-Fock model with Skyrme interactions. The accuracy in terms of energy and nucleon density is examined as well.

The article by Riera-Campeny, Mehboudi, Pons, and Sanpera [Phys. Rev. E 99, 032126 (2019)] studies heat rectification in a network of harmonic oscillators which is periodically driven. Both the title and introduction stress the quantum nature of the system. Here we show that the results are more general and are equally valid for a classical system, which broadens the interest of the paper and may suggest further pathways for a basic understanding of the phenomenon.

We propose a three-qubit setup for the implementation of a variety of quantum thermal machines where all heat fluxes and work production can be controlled. An important configuration that can be designed is that of an absorption refrigerator, extracting heat from the coldest reservoir without the need of external work supply. Remarkably, we achieve this regime by using only two-body interactions instead of the widely employed three-body interactions. This configuration could be more easily realized in current experimental setups. We model the open-system dynamics with both a global and a local master equation thermodynamic-consistent approach. Finally, we show how this model can be employed as a heat valve, in which by varying the local field of one of the two qubits allows one to control and amplify the heat current between the other qubits.

Brownian ratchets are shown to feature a nontrivial vanishing-noise limit where the dynamics is reduced to a stochastic alternation between two deterministic circle maps (quasideterministic ratchets). Motivated by cooperative dynamics of molecular motors, here we solve exactly the problem of two interacting quasideterministic ratchets. We show that the dynamics can be described as a random walk on a graph that is specific to each set of parameters. We compute point by point the exact velocity-force $V\left(f\right)$ function as a summation over all paths in the specific graph for each $f$, revealing a complex structure that features self-similarity and nontrivial continuity properties. From a general perspective, we unveil that the alternation of two simple piecewise linear circle maps unfolds a very rich variety of dynamical complexity, in particular the phenomenon of piecewise chaos, where chaos emerges from the combination of nonchaotic maps. We show convergence of the finite-noise case to our exact solution.

We develop a dynamic mean-field theory for polar active particles that interact through a self-generated field, in particular one generated through emitting a chemical signal. While being a form of chemotactic response, it is different from conventional chemotaxis in that particles discontinuously change their motility when the local concentration surpasses a threshold. The resulting coupled equations for density and polarization are linear and can be solved analytically for simple geometries, yielding inhomogeneous density profiles. Specifically, here we consider a planar and circular interface. Our theory thus explains the observed coexistence of dense aggregates with an active gas. There are, however, differences from the more conventional picture of liquid-gas coexistence based on a free energy, most notably the absence of a critical point. We corroborate our analytical predictions by numerical simulations of active particles under confinement and interacting through volume exclusion. Excellent quantitative agreement is reached through an effective translational diffusion coefficient. We finally show that an additional response to the chemical gradient direction is sufficient to induce vortex clusters. Our results pave the way to engineer motility responses in order to achieve aggregation and collective behavior even at unfavorable conditions.

Slow dynamic nonlinearity describes a poorly understood, creeplike phenomena that occurs in brittle composite materials such as rocks and cement. It is characterized by a drop in stiffness induced by a mechanical conditioning, followed by a log(time) recovery. A consensus theoretical understanding of the behavior has not been developed. Here we introduce an alternative experimental venue with which to inform theory. Unconsolidated glass bead packs are studied rather than rocks or cement because the structure and internal contacts of bead packs are less complex and better understood. Slow dynamics has been observed in such systems previously. However, the measurements to date tend to be irregular. Particular care is used here in the experimental design to overcome the difficulties inherent in bead pack studies. This includes the design of the bead pack support, the use of low-frequency conditioning, and the use of ultrasonic waves as a probe with coda wave interferometry to assess changes. Slow dynamics is observed in our system after three different methods for low-frequency conditioning, one of which has not been reported in the literature previously.

Slow dynamic nonlinearity is ubiquitous amongst brittle materials, such as rocks and concrete, with cracked microstructures. A defining feature of the behavior is the logarithmic-in-time recovery of stiffness after a mechanical conditioning. Materials observed to exhibit slow dynamics are sufficiently different in microstructure, chemical composition, and scale (ranging from the laboratory to the seismological) to suggest some kind of universality. A consensus of theoretical understanding of the universality in general and the log(time) recovery in particular is lacking. Seminal studies were focused on sandstones and other natural rocks, but in recent years other experimental venues have been introduced with which to inform theory. One such system is unconsolidated glass bead packs. However, bead packs still contain many contact points. The force distribution amongst the contacts is unknown. Here, we present slow dynamics measurements on a yet simpler system—a single glass bead confined between two large glass plates. The system is designed with a view towards rapid control of the contact zone environment. Ultrasonic waves are used as a probe of the system, and changes are assessed with coda wave interferometry. Three different methods of low-frequency conditioning are applied; all lead to slow dynamic recoveries. Results imply that force chains do not play an essential role in granular media slow dynamics, as they are absent in our system.

A viscoelastic solid sheet fed from a certain height towards a rigid horizontal plane folds on itself provided that there is no slip. This phenomenon commonly occurs in the manufacturing process of textile and paper products. In this paper we apply a particle dynamics model to investigate this phenomenon. At a low feeding velocity and low viscosity, the inertial effect and the viscous dissipation within the sheet are negligible, and our model successfully reproduces the existing quasistatic results in the gravitational regime. As the feeding velocity and the viscosity of the sheet increase, the folding process changes significantly. The length of the folds decrease and the “rolling back” motion of the sheet vanishes. In the inertial regime, a scaling law between the fold length and the feeding velocity is derived by balancing the kinetic energy and the elastic bending energy involved in folding, which is verified by the simulation. It is found that above a critical feeding velocity, the folding morphology transforms from line contact into point contact with the sheet exhibiting a lemniscate-like pattern. Finally, a phase diagram for the folding morphology is constructed. The results presented in this work may offer some insights into the high-speed manufacturing of paper and fabric sheets.

Transport of water in narrow nanochannels as a single-file chain is involved in various biological activities and nanofluidic applications. However, although the consistent dipole orientation of the water molecules is intensively studied, its effect upon the transport behavior is still unknown. In this Rapid Communication, we find two states of slow and fast transport coexist in the single-file water in the presence of channel defects that break the collective dipole orientation. A low diffusive mobility is found for the dipole orientation inconsistent configurations while mobility approximately two times higher is found for the consistent ones. The two-state diffusion process relies on the different hydrogen bond connections, which possess overlapped structures, enabling a spontaneous transition. The slow state is insensitive to the increased defect number while the fast state is reduced accordingly. The two states exhibit different lifetime and temperature dependences that demonstrate a possibility for manipulation. Our result implies the possibility of two-state diffusion process of water in nanofluid phenomena due to the common presence of defects in nanochannels.

By using transfer-matrix method we compute survival probabilities for the directed percolation problem on strips of a square lattice, and get very precise estimates of their Yang-Lee zeros lying closest to the real axis in the complex plane of occupation probability. This allows us to get accurate values for transverse-size critical exponent and percolation threshold.

Only recently has the essential role of the percolation critical point been considered on the dynamical properties of connected regions of aligned spins (domains) after a sudden temperature quench. In equilibrium, it is possible to resolve the contribution to criticality by the thermal and percolative effects (on finite lattices, while in the thermodynamic limit they merge at a single critical temperature) by studying the cluster size heterogeneity, $H_{\mathrm{eq}}\left(T\right)$, a measure of how different the domains are in size. We extend this equilibrium measure here and study its temporal evolution, $H\left(t\right)$, after driving the system out of equilibrium by a sudden quench in temperature. We show that this single parameter is able to detect and well-separate the different time regimes, related to the two timescales in the problem, namely the short percolative and the long coarsening one.