Polymers with stickers-and-spacers architectures can drive phase-separation-aided bond percolation transitions. Here, we present a generalized mean-field model to enable the calculation of bond percolation thresholds for polymers with multiple types of stickers. Further, using graph-based Monte Carlo simulations we demonstrate how cooperativity in bond formation can give rise to reentrant phase behavior. When combined with recent advances for modeling phase separation, our approaches for calculating percolation lines could be useful for modeling hardening transitions for multivalent proteins.

Responsive particles, such as biomacromolecules or hydrogels, display a broad and polymodal distribution of conformations and have thus the ability to change their properties (e.g., size, shape, charge density, etc.) substantially in response to external fields or to their local environment (e.g., mediated by cosolutes or pH). Here we discuss the basic statistical mechanics for a model of responsive colloids (RCs) by introducing an additional “property” degree of freedom as a collective variable in a formal coarse-graining procedure. The latter leads to an additional one-body term in the coarse-grained (CG) free energy, defining a single-particle property distribution for an individual polydisperse RC. We argue that in the equilibrium thermodynamic limit such a CG system of RCs behaves like a conventional polydisperse system of nonresponsive particles. We then illustrate the action of external fields, which impose local (position-dependent) property distributions leading to nontrivial effects on the spatial one-body property and density profiles, even for an ideal (noninteracting) gas of RCs. We finally apply density-functional theory in the local density approximation to discuss the effects of particle interactions for specific examples of (i) a suspension of RCs in an external field linear in both position and property, (ii) a suspension of RCs with highly localized properties (sizes) confined between two walls, and (iii) a two-component suspension where an inhomogeneously distributed (nonresponsive) cosolute component, as found, e.g., in the studies of osmolyte- or salt-induced collapse or swelling transitions of thermosensitive polymers, modifies the local properties and density of the RC liquid.

We investigated the spontaneous deformation and fission of a tetradecane droplet containing palmitic acid (PA) on a stearyltrimethylammonium chloride (STAC) aqueous solution. In this system, the generation and rupture of the gel layer composed of PA and STAC induce the droplet deformation and fission. To investigate the characteristics of the droplet-fission dynamics, we obtained the time series of the number of the droplets produced by fission and confirmed that the number has a peak at a certain STAC concentration. Since the fission of the droplet should be led by the deformation, we analyzed four parameters which may relate to the fission dynamics from the spatiotemporal correlation of the droplet-boundary velocity. We found that the parameter which corresponds to the expansion speed had the strongest positive correlation among them, and thus we concluded that the faster deformation would be the key factor for the fission dynamics.

The polarized components of transmission spectrum of a multilayered photonic structure containing a nematic liquid crystal under the magnetic-field-induced torsion deformation have been investigated. Since the planarly twisted director structure of the nematic is unrelated to a decrease in its optical anisotropy, the control of the polarization and spectral characteristics of the eigenmodes is based on the occurrence of a geometric phase, whose contribution gradually increases upon nematic deformation. Along with the previously observed blue shift of the cavity $o$ modes, the anomalous shift of the cavity $e$ modes to the long-wavelength region (red shift) of the transmission spectrum has been detected. It has been shown that the countershift of the modes narrows the intermode interval. Remarkably, the extremal approaching of $e$ and $o$ modes in magnetic field $H_{ex}$ occurs below the avoided crossing phenomenon observed in the stronger equalization field $H_{eq}$ ($H_{ex}<H_{eq})$. The experimental results have been interpreted by the numerical simulation of the transmission spectra of the chiral photonic structure using the transfer matrix method.

Granular flows triggered by vibration below the avalanche angle are ubiquitous in nature. However, the mechanism of triggering and the nature of the resulting flow are not fully understood. Here we investigate the triggering of the shear instability of granular layers by nanometer-amplitude ultrasound close to the static threshold. We find that such small-amplitude and high-frequency sound waves provoke unjamming, resulting in a self-accelerated inertial flow or a creeplike regime which stops flowing after the removal of ultrasound. We show that these effects are due to the reduction of interparticle friction at grain contacts by the shear acoustic lubrication. Our observations are consistent with the bistability inherent to velocity-weakening friction models [e.g., Jaeger et al., Europhys. Lett. 11, 619 (1990)]. This work should help to understand the local and remote triggering of landslides and earthquakes by seismic waves.

When the Zeeman energy approaches the characteristic kinetic energy of electrons, Landau quantization becomes important. In the vicinity of magnetars, the Zeeman energy can even be relativistic. We start from the Dirac equation and derive a kinetic equation for electrons, focusing on the phenomenon of Landau quantization in such ultrastrong but constant magnetic fields, neglecting short-scale quantum phenomena. It turns out that the usual relativistic $\gamma$ factor of the Vlasov equation is replaced by an energy operator, depending on the spin state, and also containing momentum derivatives. Furthermore, we show that the energy eigenstates in a magnetic field can be computed as eigenfunctions of this operator. The dispersion relation for electrostatic waves in a plasma is computed, and the significance of our results is discussed.

We consider the problem of first-passage time for reaching a boundary of a particle which diffuses in one dimension and is confined to the region $x\in (0,L),$ with a diffusion coefficient that switches randomly between two states, having diffusivities that are different. Exact analytical expressions are found for the survival probability of the particle as a function of time. The survival probability has a multiexponential decay, and to characterize it, we use the average rate constant $k$, as well as the instantaneous rate $r\left(t\right)$. Our approach can easily be extended to the case where the diffusion coefficient takes $n$ different values. The model should be of interest to biological processes, in which a reactant searches for a target in a heterogeneous environment, making the diffusion coefficient a random function of time. The best example for this is a protein searching for a target site on the DNA.

The dynamics of an ensemble of $N$ weakly coupled limit-cycle oscillators can be captured by their $N$ phases using standard phase reduction techniques. However, it is a phenomenological fact that all-to-all strongly coupled limit-cycle oscillators may behave as “quasiphase oscillators,” evidencing the need of novel reduction strategies. We introduce, here, quasi phase reduction (QPR), a scheme suited for identical oscillators with polar symmetry ($\lambda -\omega$ systems). By applying QPR, we achieve a reduction to $N+2$ degrees of freedom: $N$ phase oscillators interacting through one independent complex variable. This “quasi phase model” is asymptotically valid in the neighborhood of incoherent states, irrespective of the coupling strength. The effectiveness of QPR is illustrated in a particular case, an ensemble of Stuart-Landau oscillators, obtaining exact stability boundaries of uniform and nonuniform incoherent states for a variety of couplings. An extension of QPR beyond the neighborhood of incoherence is also explored. Finally, a general QPR model with $N+2M$ degrees of freedom is obtained for coupling through the first $M$ harmonics.

The cell membrane is responsible for the transportation of heat between inside and outside the cell. Whether the thermal properties of the cell membrane are affected by the cholesterol concentration or the membrane proteins has not been investigated so far. Although the experimental measurement of the membrane thermal conductivity was not available until very recently, computational methods have been widely used for this purpose. In this study, we carry out molecular dynamics simulations to investigate the relation between the concentration of cholesterol and the thermal conductivity of a model membrane. Our results suggest an increase in the membrane thermal conductivity upon increasing the concentration of cholesterol in the membrane. Moreover, we find that the asymmetric distribution of cholesterol in the two membrane leaflets decreases thermal conductivity. We also find a rectification effect when heat flows in opposite directions through a model membrane decorated with the amyloid precursor protein. The results of this study apply to the advancement of selective treatment methods, as well as the development of new materials such as biological rectifiers.

In this work, we use the kinetic theory of gases (KTG) to develop a theoretical model to understand the role of internal motions of molecules on the maximum evaporation flux from a planar liquid surface. The kinetic theory is applied to study the evaporation of molecular fluids into a vacuum and predict the dimensionless maximum evaporation flux ($J_{R,\max }$, i.e., the ratio of the maximum evaporation flux to the molar flux emitted from a liquid surface). The key assumptions regarding the velocity distribution function (VDF) of polyatomic molecules in the highly nonequilibrium vapor near the evaporating surface are validated by the VDF obtained directly from molecular dynamics (MD) simulations. Our KTG-based analysis shows that $J_{R,\max }$ is affected by the specific heat ($c_{V,\mathrm{int}}$) associated with internal degrees of freedom of fluid molecules. When the maximum evaporation flux is reached, the isotropic evaporating vapor far from the liquid surface moves at its speed of sound regardless of whether it is a monatomic vapor or polyatomic vapor. To fundamentally understand the evaporation of a molecular fluid into a vacuum, we solve the Boltzmann transport equation (BTE) to obtain the temperature, density, and flow speed distributions in the highly nonequilibrium evaporating vapor flow. Our BTE solutions indicate that there are several universal features of the evaporating vapor when the maximum evaporation flux occurs. In particular, we find that the evaporating vapor flow speed reaches the maximum value of $\sqrt{1.5}$ times the most probable thermal speed in the vapor flow direction at the vacuum boundary, and this maximum value is independent of fluid properties. All theoretical predictions in this work are verified by the MD simulation results of the evaporation of the model liquid Ar and the model liquid $n$-dodecane into a vacuum, and existing experimental data.

In this paper, we propose a variational approach to estimate eddy viscosity using forward sensitivity method (FSM) for closure modeling in nonlinear reduced order models. FSM is a data assimilation technique that blends model's predictions with noisy observations to correct initial state and/or model parameters. We apply this approach on a projection based reduced order model (ROM) of the one-dimensional viscous Burgers equation with a square wave defining a moving shock, and the two-dimensional vorticity transport equation formulating a decay of Kraichnan turbulence. We investigate the capability of the approach to approximate an optimal value for eddy viscosity with different measurement configurations. Specifically, we show that our approach can sufficiently assimilate information either through full-field or sparse noisy measurements to estimate eddy viscosity closure to cure standard Galerkin reduced order model (GROM) predictions. Therefore, our approach provides a modular framework to correct forecasting error from a sparse observational network on a latent space. We highlight that the proposed GROM-FSM framework is promising for emerging digital twin applications, where real-time sensor measurements can be used to update and optimize surrogate model's parameters.

Extracting excited states from lattice gauge theory correlation functions can be achieved through ${\chi }^2$ minimization fits or algebraic approaches such as the variational method and Prony's method. Performing any kind of error analysis often leads to overlapping confidence regions of model parameters, even when the spectrum is not particularly dense. To correctly estimate errors, one must beware of mislabeling the states. In this work, we provide an algorithm that we call automated label flows which consistently and systematically identifies a deterministic labeling of states. This is a black-box approach in the sense that it gives a sensible set of labels without user guidance. As an example, we pair one black box method with another, analyzing a lattice correlation function from real data using automated label flows in the context of Prony's method.

At room temperature, micron-sized sheets of freestanding graphene are in constant motion, even in the presence of an applied bias voltage. We quantify the out-of-plane movement by collecting the displacement current using a nearby small-area metal electrode and present an Ito-Langevin model for the motion coupled to a circuit containing diodes. Numerical simulations show that the system reaches thermal equilibrium and the average rates of heat and work provided by stochastic thermodynamics tend quickly to zero. However, there is power dissipated by the load resistor, and its time average is exactly equal to the power supplied by the thermal bath. The exact power formula is similar to Nyquist's noise power formula, except that the rate of change of diode resistance significantly boosts the output power, and the movement of the graphene shifts the power spectrum to lower frequencies. We have calculated the equilibrium average of the power by asymptotic and numerical methods. Excellent agreement is found between experiment and theory.

Aspects of the phase coexistence behavior of the generalized exponential model (GEM-m) and bounded versions of inverse power potentials based on theory and molecular dynamics (MD) simulation data are reported. The GEM-m potential is $\varphi \left(r\right)=exp(-r^m)$, where $r$ is the pair separation and $m$ is an adjustable exponent. A simple analytic formula for the fluid-solid envelope of the Gaussian core model which takes account of the known low- and high-density limiting forms is proposed and shown to represent the simulation data well. The bounded inverse power (BIP) potential is $\varphi \left(r\right)=1/{(a^q+r^q)}^{n/q}$, where $a$, $n$, and $q$ are positive constants. The BIP potential multiple occupancy crystal or cluster crystals are predicted to form when $q>2$ and $a>0$, for $n>3$, which compares with the corresponding GEM-m condition of $m>2$. Reentrant melting should occur for the BIP potential when $q\le 2$ and $a>0$. MD simulations in which the system was gradually compressed at constant temperature using the BIP potential produced cluster states in the parameter domain expected but it was not possible to establish conclusively whether a multiply occupied crystal or a cluster fluid had formed owing to assembly structural fluctuations. The random phase approximation reproduces very well the BIP MD energy per particle without any discontinuities at the phase boundaries. The Lindemann melting rule is shown analytically to give a more rapidly decaying reentrant melting curve boundary than the so-called melting indicator (MI) empirical melting criterion which has also been investigated in this study. The MI model gives a better match to the high-density phase boundary for small $m$ and $q$ values.

We study the connection between transport phenomenon and escape rate statistics in two-dimensional standard map. For the purpose of having an open phase space, we let the momentum coordinate vary freely and restrict only angle with periodic boundary condition. We also define a pair of artificial holes placed symmetrically along the momentum axis where the particles might leave the system. As a consequence of the leaks the diffusion can be analyzed making use of only the ensemble of survived particles. We present how the diffusion coefficient depends on the size and position of the escape regions. Since the accelerator modes and, thus, the diffusion are strongly related to the system's control parameter, we also investigate effects of the perturbation strength. Numerical simulations show that the short-time escape statistics do not follow the well-known exponential decay especially for large values of perturbation parameters. The analysis of the escape direction also supports this picture as a significant amount of particles skip the leaks and leave the system just after a longtime excursion in the remote zones of the phase space.

Many real-world complex networks arise as a result of a competition between growth and rewiring processes. Usually the initial part of the evolution is dominated by growth while the later one rather by rewiring. The initial growth allows the network to reach a certain size while rewiring to optimize its function and topology. As a model example we consider tree networks which first grow in a stochastic process of node attachment and then age in a stochastic process of local topology changes. The ageing is implemented as a Markov process that preserves the node-degree distribution. We quantify differences between the initial and aged network topologies and study the dynamics of the evolution. We implement two versions of the ageing dynamics. One is based on reshuffling of leaves and the other on reshuffling of branches. The latter one generates much faster ageing due to nonlocal nature of changes.

Our theoretical work has shown that rotating a Rayleigh-Taylor-unstable two-layer stratification about a vertical axis slows the development of the instability under gravity and can stabilize axisymmetric modes indefinitely. Here we compare theoretical predictions directly with our experiments on a rotating two-layer system which is made unstable by magnetic forces applied using a superconducting magnet.

This work investigates the time-dependent physics of multipactor discharge on a single dielectric surface with a transverse rf electric field of two carrier frequencies using a multiparticle Monte Carlo simulation model with adaptive time steps. The effects of the relative strength and phase, and the frequency separation between the two carriers are studied. Closed Lissajous curves are obtained to describe the relationship between the rf electric field parallel to the surface and the normal surface charging field in the ac saturation state. It is found that two-frequency operation can reduce the multipactor strength compared to single-frequency operation with the same total rf power, though the effect of the frequency separation is not prominent on multipactor susceptibility. Formation of beat waves is observed in the temporal profiles of the normal electric field due to surface charging with a noninteger frequency ratio between the two carrier modes. Phase space evolution of multipactor electrons is examined, revealing a periodic bunching and debunching of electrons in the surface normal direction, but a gradual debunching effect in the direction tangential to the dielectric surface. Migration of the multipactor trajectory is also demonstrated for different configurations of the two-frequency rf fields.

This paper is devoted to the problem of obtaining high-intense circularly polarized terahertz radiation in a nonequilibrium xenon plasma channel in the presence of an external static magnetic field. The physical mechanism is based on the well-known cyclotron resonance effect which enables to provide effective plasma-electromagnetic wave interaction that can increase the gain in plasma proposed earlier by the authors. According to the suggested scheme, a static magnetic field is imposed on a gas target along the propagation direction of a femtosecond ultraviolet laser driver. Numerical simulations demonstrate that, by varying a magnetic field, one can control the range of amplified frequencies in plasmas at atmospheric and lower pressures. Moreover, a pressure decrease in the nonequilibrium rare gas plasma channel allows one to obtain a larger value of the gain factor. Thus, controlling the central frequency and bandwidth of the amplified terahertz signals leads to producing both ultrashort and rather long high-intense pulses at the output of nonequilibrium plasma channel.