Thermodiffusion or thermophoresis or Soret effect, i.e., mass-transport induced by thermal gradient, has immense application in segregation of species in two or multicomponent gaseous, liquid, or colloidal mixtures. Here, we show that an external thermal gradient can be effectively utilized in creation and modification of patterns in spatially extended systems. We consider Brusselator and chlorine-dioxide iodine malonic acid (CDIMA) reaction-diffusion systems, which follow activator-inhibitor kinetics subjected to an external thermal gradient. We find that the conspicuous interaction of emergent thermodiffusive flux with reaction kinetics and diffusion can lead to various spatiotemporal instabilities in these two models. Specifically, our result reveals formation of Turing-like spatial patterns even for equal diffusivities of the activator and inhibitor components in the Brusselator model under the influence of differential thermodiffusion, whereas formation of such stationary patterns in the CDIMA system from a homogenous stable steady state, which is also stable under differential diffusion, requires the same sign and magnitude of Soret coefficients. However, with equal diffusivities of the components of the CDIMA system and without starch in the medium, our result identifies formation of drifting spiral waves which finally disappears at longer times under the influence of thermodiffusion. We also show formation of propagating patterns of spotlike or stripelike heterogeneity in both the model systems under appropriate conditions. Our study provides a route to pattern formation beyond Turing space and reveals remarkable influence of thermodiffusion to modify the pattern types just by employing an external thermal gradient which also opens up the possibility to set up new related experiments.

We study experimentally the electrorotation (ROT) of semiconducting microspheres. ZnO microspheres obtained by a hydrothermal synthesis method are dispersed in KCl aqueous solutions and subjected to rotating electric fields. Two ROT peaks are found in experiments: a counterfield peak and a cofield peak at somewhat higher frequencies. These observations are in accordance with recent theoretical predictions for semiconducting spheres. The counterfield rotation is originated by the charging of the electrical double layer at the particle-electrolyte interface, while the cofield rotation is due to the Maxwell-Wagner relaxation. Additionally, we also found that some microspheres in the sample behaved differently and only showed counterfield rotation. We show that the behavior of these particles can be described by the so-called shell model. The microstructure of the microspheres is analyzed with electron microscope techniques and related to the ROT measurements.

Reduced models, mirroring self-similar, fractal nature of two-dimensional turbulence, are proposed, using logarithmic spiral chains, which provide a natural generalization of shell models to two dimensions. In a turbulent cascade, where each step can be represented by a rotation and a scaling of the interacting triad, the use of a spiral chain whose nodes can be obtained by scaling and rotating an original wave vector provides an interesting perspective. A family of such spiral chain models depending on the distance of interactions can be obtained by imposing a logarithmic spiral grid with a constant divergence angle and a constant scaling factor and imposing the condition of exact triadic interactions. Scaling factors in such sequences are given by the square roots of known ratios such as the plastic ratio, the super-golden ratio, or some small Pisot numbers. While spiral chains can represent monofractal models of a self-similar cascade, which can span a large range of wave numbers and have good angular coverage, it is also possible that spiral chains or chains of consecutive triads play an important role in the cascade. As numerical models, the spiral chain models based on decimated Fourier coefficients have the usual problems of shell models of two-dimensional turbulence such as the dual cascade being overwhelmed by statistical chain equipartition due to an almost stochastic evolution of the complex phases. A generic spiral chain model based on evolution of energy is proposed, which is shown to recover the dual cascade behavior in two-dimensional turbulence.

We study the detention statistics of self-propelling droplet microswimmers attaching to microfluidic pillars. These droplets show negative autochemotaxis: they shed a persistent repulsive trail of spent fuel that biases them to detach from pillars in a specific size range after orbiting them just once. We have designed a microfluidic assay recording microswimmers in pillar arrays of varying diameter, derived detention statistics via digital image analysis, and interpreted these statistics via the Langevin dynamics of an active Brownian particle model. By comparing data from orbits with and without residual chemical field, we can independently estimate quantities such as hydrodynamic and chemorepulsive torques, chemical coupling constants and diffusion coefficients, as well as their dependence on environmental factors such as wall curvature. This type of analysis is generalizable to many kinds of microswimmers.

Droplet wetting on solid surfaces is a ubiquitous phenomenon in nature and applications. The wetting behavior of droplets on homogeneous surfaces has been accurately elucidated by the quintessential Young's law. However, on heterogeneous substrates, due to the energy barriers and contact line pinning effect, more than one equilibrated droplet pattern exists, which is more close to reality. Here, we propose a concise mathematical-physical model to delineate the droplet patterns on chemically patterned surfaces: stripe, “chocolate,” and “chessboard.” The present concept is capable of predicting the number as well as the morphologies of the equilibrated droplets on chemically patterned surfaces. We anticipate that the current work can be applied to fabricate programmable surfaces involving droplet manipulation in integrated circuits, biochips, and smart microelectronics.

The two-dimensional (zero magnetic field) Ising model is known to undergo a second-order paraferromagnetic phase transition, which is accompanied by a correlated percolation transition for the Fortuin-Kasteleyn (FK) clusters. In this paper we uncover that there exists also a second temperature $T_{\text{eb}}<T_c$ at which the elastic backbone of FK clusters undergoes a second-order phase transition to a dense phase. The corresponding universality class, which is characterized by determining various percolation exponents, is shown to be completely different from directed percolation, which leads us to propose a new anisotropic universality class with $\beta =0.54\pm 0.02$, ${\nu }_{\left|\right|}=1.86\pm 0.01$, ${\nu }_{\perp }=1.21\pm 0.04$, and $d_f=1.53\pm 0.03$. All tested hyperscaling relations are shown to be valid.

In this paper, we introduce a model to describe the decay of the number of unobserved ordinal patterns as a function of the time series length in noisy chaotic dynamics. More precisely, we show that a stretched exponential model fits the decay of the number of unobserved ordinal patterns for both discrete and continuous chaotic systems contaminated with observational noise, independently of the noise level and the sampling time. Numerical simulations, obtained from the logistic map and the $x$ coordinate of the Lorenz system, both operating in a totally chaotic dynamics were used as test beds. In addition, we contrast our results with those obtained from pure stochastic dynamics. The fitting parameters, namely, the stretching exponent and the characteristic decay rate, are used to distinguish whether the dynamical nature of the data sequence is stochastic or chaotic. Finally, the analysis of experimental records associated with the hyperchaotic pulsations of an optoelectronic oscillator allows us to illustrate the applicability of the proposed approach in a practical context.

Chemical and electrical synapses shape the dynamics of neuronal networks. Numerous theoretical studies have investigated how each of these types of synapses contributes to the generation of neuronal oscillations, but their combined effect is less understood. This limitation is further magnified by the impossibility of traditional neuronal mean-field models—also known as firing rate models or firing rate equations—to account for electrical synapses. Here, we introduce a firing rate model that exactly describes the mean-field dynamics of heterogeneous populations of quadratic integrate-and-fire (QIF) neurons with both chemical and electrical synapses. The mathematical analysis of the firing rate model reveals a well-established bifurcation scenario for networks with chemical synapses, characterized by a codimension-2 cusp point and persistent states for strong recurrent excitatory coupling. The inclusion of electrical coupling generally implies neuronal synchrony by virtue of a supercritical Hopf bifurcation. This transforms the cusp scenario into a bifurcation scenario characterized by three codimension-2 points (cusp, Takens-Bogdanov, and saddle-node separatrix loop), which greatly reduces the possibility for persistent states. This is generic for heterogeneous QIF networks with both chemical and electrical couplings. Our results agree with several numerical studies on the dynamics of large networks of heterogeneous spiking neurons with electrical and chemical couplings.

The classical Debye-Hückel (DH) theory clearly accounts for the origin of screening in electrolyte solutions and works rather well for dilute electrolyte solutions. While the Debye screening length decreases with the ion concentration and is independent of ion size, recent surface-force measurements imply that for concentrated solutions, the screening length exhibits an opposite trend; it increases with ion concentration and depends on the ionic size. The screening length is usually defined by the response of the electrolyte solution to a test charge but can equivalently be derived from the charge-charge correlation function. By going beyond DH theory, we predict the effects of ion size on the charge-charge correlation function. A simple modification of the Coulomb interaction kernel to account for the excluded volume of neighboring ions yields a nonmonotonic dependence of the screening length (correlation length) on the ionic concentration, as well as damped charge oscillations for high concentrations.

Aiming at systematically correcting the non-Galilean-invariant thermal diffusivity in the previous multiple-relaxation-time Boltzmann equation collision model [Shan and Chen, Int. J. Mod. Phys. C 18, 635 (2007)], we show that by separately relaxing the central moments of the distribution function, Chapman-Enskog calculation leads to the correct hydrodynamic equations with mutually independent and Galilean invariant viscosity and thermal diffusivity, provided the velocity-space discretization preserves moments up to the fourth order. By transforming the central moments back to the absolute reference frame and evaluating using fixed discrete velocities, the efficient and accurate streaming-collision time-stepping algorithm is preserved. The lattice Boltzmann model is found to have excellent numerical stability in high-Reynolds-number simulations.

We study a cluster Ising model with multispin interactions which can be exactly solved in the framework of free fermions. The model can realize topological phases with any integer winding numbers; we study the critical and multicritical behaviors of the phase transitions between these topological phases. For the ordinary critical point, we find that the critical exponent that governs the divergence of the correlation length is $\nu =1$, and the critical exponent that describes the scaling behaviors of the order parameter is $\beta =\mathrm{\Delta }{N}_w/8$, with $\mathrm{\Delta }{N}_w$ the difference of the winding numbers of the two phases at the two sides of the critical point. However, these results are not applicable for some multicritical points which have much more complicated behaviors, such as path dependent scaling behaviors and quasicritical behaviors and so forth.

The cytoplasmic volume of cells is occupied and crowded by a variety of macromolecules, such as proteins and cytoskeleton structures. Such diverse macromolecules make the cell cytoplasm not only structurally heterogeneous but also dynamically heterogeneous: Some macromolecules may diffuse freely inside cell cytoplasm at certain timescales while others hardly diffuse. Studies on the effects of the dynamic heterogeneity on reaction kinetics have been limited even though the effects of the crowdedness and structural heterogeneity were investigated extensively. In this study, we employ a simple model of mixtures of mobile and immobile matrix particles, tune the degree of dynamic heterogeneity by changing the fraction of immobile matrix particles, and investigate reaction kinetics in such heterogeneous media. We employ the loop formation of a single polymer chain as a model reaction and perform Langevin dynamics simulations. We find that the free-energy barrier of the loop formation is decreased as the systems become more crowded with matrix particles. But the free-energy barrier is not sensitive to the dynamic heterogeneity. As dynamic heterogeneity increases with an increase in the fraction of immobile matrix particles, however, the diffusivity of the system decreases significantly. The decrease in the diffusion (due to the dynamic heterogeneity) and the decrease in the free-energy barrier (due to the crowdedness) lead together to a complicated trend of the loop formation kinetics. As the volume fraction of immobile matrix particles reaches a critical value at the percolation transition, the reaction kinetics becomes significantly heterogeneous and the survival probability distribution of the chain loop formation becomes stretched-exponential. We also illustrate that the heterogeneous reaction rate near the percolation transition relates closely to the structures of local pores in which the polymer is located.

The glass transition and the binodals of asymmetric binary mixtures are investigated from the effective fluid approach in the mode coupling theory and by molecular dynamics. Motivated by previous theoretical predictions, the hard-sphere mixture and the Asakura-Oosawa models are used to analyze experimental results from the literature, relative to polystyrene spheres mixed either with linear polymers or with dense microgel particles. In agreement with the experimental observations, the specificity of the depletant particles is shown to favor lower density gels. It further favors equilibrium gelation by reducing also the tendency of the system to phase separate. These results are confirmed by a phenomenological modification of the mode coupling theory in which the vertex functions are computed at an effective density lower than the actual one. A model effective potential in asymmetric mixtures of hard particles is used to further check this phenomenological modification against molecular dynamics simulation.

We present results on a mesoscale model for amorphous matter in athermal, quasistatic (a-AQS), steady-state shear flow. In particular, we perform a careful analysis of the scaling with the lateral system size $L$ of (i) statistics of individual relaxation events in terms of stress relaxation $S$, and individual event mean-squared displacement $M$, and the subsequent load increments $\mathrm{\Delta }\gamma$, required to initiate the next event; (ii) static properties of the system encoded by $x={\sigma }_y-\sigma$, the distance of local stress values from threshold; and (iii) long-time correlations and the emergence of diffusive behavior. For the event statistics, we find that the distribution of $S$ is similar to, but distinct from, the distribution of $M$. We find a strong correlation between $S$ and $M$ for any particular event, with $S\sim M^q$ with $q\approx 0.65$. The exponent $q$ completely determines the scaling exponents for $P\left(M\right)$ given those for $P\left(S\right)$. For the distribution of local thresholds, we find $P\left(x\right)$ is analytic at $x=0$, and has a value ${\left.P\left(x\right)\right|}_{x=0}=p_0$ which scales with lateral system length as $p_0\propto L^{-0.6}$. The size dependence of the average load increment $\langle \mathrm{\Delta }\gamma \rangle$ appears to be asymptotically controlled by the plateau behavior of $P\left(x\right)$ rather than by a subsequent apparent power-law behavior. Extreme value statistics arguments lead thus to a scaling relation between the exponents governing $P\left(x\right)$ and those governing $P\left(S\right)$. Finally, we study the long-time correlations via single-particle tracer statistics. The value of the diffusion coefficient is completely determined by $\langle \mathrm{\Delta }\gamma \rangle$ and the scaling properties of $P\left(M\right)$ (in particular from $\langle M\rangle$) rather than directly from $P\left(S\right)$ as one might have naively guessed. Our results (i) further define the a-AQS universality class, (ii) clarify the relation between avalanches of stress relaxation and diffusive behavior, and (iii) clarify the relation between local threshold distributions and event statistics.

Equilibrium molecular dynamics simulations are used to calculate the thermal conductivity of the one-component plasma via the Green-Kubo formalism over a broad range of Coulomb coupling strength, $0.1\le \mathrm{\Gamma }\le 180$. These simulations address previous discrepancies between computations using equilibrium versus nonequilibrium methods. Analysis of heat flux autocorrelation functions show that very long ($6\times {10}^5{\omega }_p^{-1}$) time series are needed to reduce the noise level to allow $\lesssim 2\%$ accuracy. The simulations provide accurate data for $\mathrm{\Gamma }\lesssim 1$. This enables a test of the traditional Landau-Spitzer theory, which is found to agree with the simulations for $\mathrm{\Gamma }\lesssim 0.3$. It also enables tests of theories to address moderate and strong Coulomb coupling. Two are found to provide accurate extensions to the moderate coupling regime of $\mathrm{\Gamma }\lesssim 10$, but none are accurate in the $\mathrm{\Gamma }\gtrsim 10$ regime where potential energy transport and coupling between mass flow and stress dominate thermal conduction.

The free-free opacity in dense systems is a property that both tests our fundamental understanding of correlated many-body systems, and is needed to understand the radiative properties of high energy-density plasmas. Despite its importance, predictive calculations of the free-free opacity remain challenging even in the condensed matter phase for simple metals. Here we show how the free-free opacity can be modelled at finite-temperatures via time-dependent density functional theory, and illustrate the importance of including local field corrections, core polarization, and self-energy corrections. Our calculations for ground-state Al are shown to agree well with experimental opacity measurements performed on the Artemis laser facility across a wide range of extreme ultraviolet wavelengths. We extend our calculations across the melt to the warm-dense matter regime, finding good agreement with advanced plasma models based on inverse bremsstrahlung at temperatures above 10 eV.

We investigate the dynamics of a two-dimensional biaxial next-nearest-neighbor Ising model following a quench to zero temperature. The Hamiltonian is given by $H=-J_0{\sum }_{i,j=1}^L[(S_{i,j}{S}_{i+1,j}+S_{i,j}{S}_{i,j+1})-\kappa (S_{i,j}{S}_{i+2,j}+S_{i,j}{S}_{i,j+2})]$. For $\kappa <1$, the system does not reach the equilibrium ground state and keeps evolving in active states forever. For $\kappa \ge 1$, though, the system reaches a final state, but it does not reach the ground state always and freezes to a striped state with a finite probability like a two-dimensional ferromagnetic Ising model and an axial next-nearest-neighbor Ising (ANNNI) model. The overall dynamical behavior for $\kappa >1$ and $\kappa =1$ is quite different. The residual energy decays in a power law for both $\kappa >1$ and $\kappa =1$ from which the dynamical exponent $z$ has been estimated. The persistence probability shows algebraic decay for $\kappa >1$ with an exponent $\theta =0.22\pm 0.002$ while the dynamical exponent for ordering $z=2.33\pm 0.01$. For $\kappa =1$, the system belongs to a completely different dynamical class with $\theta =0.332\pm 0.002$ and $z=2.47\pm 0.04$. We have computed the freezing probability for different values of $\kappa$. We have also studied the decay of autocorrelation function with time for a different regime of $\kappa$ values. The results have been compared with those of the two-dimensional ANNNI model.

In classical thermodynamics the work cost of control can typically be neglected. On the contrary, in quantum thermodynamics the cost of control constitutes a fundamental contribution to the total work cost. Here, focusing on quantum refrigeration, we investigate how the level of control determines the fundamental limits to cooling and how much work is expended in the corresponding process. We compare two extremal levels of control: first, coherent operations, where the entropy of the resource is left unchanged, and, second, incoherent operations, where only energy at maximum entropy (i.e., heat) is extracted from the resource. For minimal machines, we find that the lowest achievable temperature and associated work cost depend strongly on the type of control, in both single-cycle and asymptotic regimes. We also extend our analysis to general machines. Our work provides a unified picture of the different approaches to quantum refrigeration developed in the literature, including algorithmic cooling, autonomous quantum refrigerators, and the resource theory of quantum thermodynamics.

We examine a one-dimensional nonlinear (Kerr) waveguide array which contains a single “void” waveguide where the nonlinearity is identically zero. We uncover a family of nonlinear localized modes centered at or near the void, and their stability properties. Unlike a usual impurity problem, here the void acts like a repulsive impurity causing the center of the simplest mode to lie to the side of the void's position. We also compute the stability of extended nonlinear modes showing significant differences from the usual homogeneous nonlinear array. The transmission of a nonlinear pulse across the void shows three main regimes—transmission, reflection, and trapping at the void's position—and we identify a critical momentum for the pulse below (above) where the pulse gets reflected (transmitted), or trapped indefinitely at the void's position. For relatively wide pulses, we observe a steep increase from a regime of no transmission to a regime of high transmission, as the amplitude of the soliton increases beyond a critical wave-vector value. Finally, we consider the transmission of an extended nonlinear wave across the void impurity numerically, finding a rather complex structure of the transmission as a function of wave vector, with the creation of more and more transmission gaps as nonlinearity increases. The overall transmittance decreases and disappears eventually, where the boundaries separating passing from nonpassing regions are complex and fractal-like.

Estimation of the three-dimensional (3D) structure of a protein using cryo transmission electron microscopy (cryo-TEM) is an inverse problem, which aims to estimate the parameters of a specific physical process from observations. In general, we need to model the observation process to estimate a structure. However, the inconsistency between the model and a real observation process decreases the estimation accuracy. In cryo-TEM, the flexibility of a soft protein, including the bending of a helix, can lead to inconsistencies between the observations because of the assumption that there is a consistent 3D structure behind each observed image. In this paper, we propose a 3D reconstruction algorithm for helical structures using a parametric soft-body model that can represent continuous deformation. We performed an approximate Bayesian inference for unobservable (hidden) variables, such as the deformation parameters, projection angle, and two-dimensional origin offset (shift) of each protein in the 3D structure estimation problem. Our principled approach is not only beneficial to deal with the uncertainties in the estimation, but also beneficial to make the optimization algorithm convergent and efficient. Reconstructions with artificial molecules validated the advantage of the proposed method, particularly, when deformed helices were imaged under a low signal-to-noise ratio condition. Moreover, we confirmed that the proposed method successfully reconstructed a 3D structure from cryo-TEM images of the tobacco mosaic virus.