The spatiotemporal evolutions of microstructure and motion in the transient relaxation toward the steady supercooled liquid state after quenching a dusty plasma Wigner liquid, formed by charged dust particles suspended in a low pressure discharge, are experimentally investigated through direct optical microscopy. It is found that the quenched liquid slowly evolves to a colder state with more heterogeneities in structure and motion. Hopping particles and defects appear in the form of clusters with multiscale cluster size distributions. Via the structure rearrangement induced by the reduced thermal agitation from the cold thermal bath after quenching, the temporarily stored strain energy can be cascaded through the network to different newly distorted regions and dissipated after transferring to nonlinearly coupled motions with different scales. It leads to the observed self-similar multiscale slowing down relaxation with power law increases of structural order and structural relaxation time, the similar power law decreases of particle motions at different time scales, and the stronger and slower fluctuations with increasing waiting time toward the new steady state.

In this work, the effect of the forcing term (or external force) in the multiple-relaxation-time lattice Boltzmann equation (MRTLBE) on the shear stress or the strain rate tensor is studied theoretically and numerically. Through a Chapman-Enskog analysis and numerical simulations, we show that the shear stress (or the strain rate tensor) derived from the MRTLBE is second-order accurate in space. We then examine the influence of the forcing term on the shear stress or the strain rate tensor, and demonstrate that the forcing term effect must be included when the shear stress or the strain rate tensor is computed with the nonequilibrium part of the distribution function.

In this paper, the lattice Boltzmann equation (LBE)-based framework is used to obtain the solution for the linear radiative or neutron transport equation. The LBE framework is devised for the integrodifferential forms of these equations which arise due to the inclusion of the scattering terms. The interparticle collisions are neglected, hence omitting the nonlinear collision term. Furthermore, typical representative examples for one-dimensional or two-dimensional geometries and inclusion or exclusion of the scattering term (isotropic and anisotropic) in the Boltzmann transport equation are illustrated to prove the validity of the method. It has been shown that the solution from the LBE methodology is equivalent to the well-known $P_n$ and $S_n$ methods. This suggests that the LBE can potentially provide a more convenient and easy approach to solve the physical problems of neutron and radiation transport.

The self-similarity of complex networks is typically investigated through computational algorithms, the primary task of which is to cover the structure with a minimal number of boxes. Here we introduce a box-covering algorithm that outperforms previous ones in most cases. For the two benchmark cases tested, namely, the E. coli and the World Wide Web (WWW) networks, our results show that the improvement can be rather substantial, reaching up to $15\%$ in the case of the WWW network.

Ordinary bond percolation (OP) can be viewed as a process where clusters grow by joining them pairwise, adding links chosen randomly one by one from a set of predefined virtual links. In contrast, in agglomerative percolation (AP) clusters grow by choosing randomly a target cluster and joining it with all its neighbors, as defined by the same set of virtual links. Previous studies showed that AP is in different universality classes from OP for several types of (virtual) networks (linear chains, trees, Erdös-Rényi networks), but most surprising were the results for two-dimensional (2D) lattices: While AP on the triangular lattice was found to be in the OP universality class, it behaved completely differently on the square lattice. In the present paper we explain this striking violation of universality by invoking bipartivity. While the square lattice is a bipartite graph, the triangular lattice is not. In conformity with this we show that AP on the honeycomb and simple cubic (3D) lattices—both of which are bipartite—are also not in the OP universality classes. More precisely, we claim that this violation of universality is basically due to a $Z_2$ symmetry that is spontaneously broken at the percolation threshold. We also discuss AP on bipartite random networks and suitable generalizations of AP on $k$-partite graphs.

Silicone fibers were synthesized by electrospinning, where 17 solvents with different chemical properties (boiling point, conductivity, viscosity, dielectric constant, and solubility parameter) were used to dissolve the silicone polymer for the formation of fibers through electrospinning. Previous reports on the miniaturization of fibers of polymers dissolved in a solvent suggested that the low viscosity and the high conductivity of the polymer solution were the key parameters to form thinner fibers when using a single solvent. Here we have found a powerful way to search for good solvents to reduce the fiber diameters as well as to dissolve the polymers. By considering different types of solvents, it was found that the solubility parameters conclusively determined the smallest fiber diameters of the silicone polymers. The solubility parameter of the silicone polymer should be lower than those of the solvents to make thinner fibers. The results have revealed the strong relationship between the diameters of the fibers and the solubility parameters of the solvents, and they indicate that the solubility parameter could be a good indicative parameter in selecting solvents during the fabrication of thinner fibers by electrospinning, especially for siloxane polymers.

The fundamental physical mechanisms of energy transfer in photosynthetic complexes is not yet fully understood. In particular, the degree of efficiency or sensitivity of these systems for energy transfer is not known given their realistic with surrounding photonic and phononic environments. One major problem in studying light-harvesting complexes has been the lack of an efficient method for simulation of their dynamics in biological environments. To this end, here we revisit the second order time-convolution (TC2) master equation and examine its reliability beyond extreme Markovian and perturbative limits. In particular, we present a derivation of TC2 without making the usual weak system-bath coupling assumption. Using this equation, we explore the long-time behavior of exciton dynamics of Fenna-Matthews-Olson (FMO) portein complex. Moreover, we introduce a constructive error analysis to estimate the accuracy of TC2 equation in calculating energy transfer efficiency, exhibiting reliable performance for system-bath interactions with weak and intermediate memory and strength. Furthermore, we numerically show that energy transfer efficiency is optimal and robust for the FMO protein complex of green sulfur bacteria with respect to variations in reorganization energy and bath correlation time scales.

We study the Bose-Hubbard model for three sites in a symmetric, triangular configuration and search for quantum signatures of the classical regime of oscillatory instabilities, known to appear through Hamiltonian Hopf bifurcations for the “single-depleted-well” family of stationary states in the discrete nonlinear Schrödinger equation. In the regimes of classical stability, single quantum eigenstates with properties analogous to those of the classical stationary states can be identified already for rather small particle numbers. On the other hand, in the instability regime the interaction with other eigenstates through avoided crossings leads to strong mixing, and no single eigenstate with classical-like properties can be seen. We compare the quantum dynamics resulting from initial conditions taken as perturbed quantum eigenstates and SU(3) coherent states, respectively, in a quantum-semiclassical transitional regime of 10–100 particles. While the perturbed quantum eigenstates do not show a classical-like behavior in the instability regime, a coherent state behaves analogously to a perturbed classical stationary state, and exhibits initially resonant oscillations with oscillation frequencies well described by classical internal-mode oscillations.

The spectral radiation of sonoluminescence (SL) from sulfuric acid doped with various Xe concentrations has been studied in a hydrochemical simulation, including radiation effects of both continuum and line emissions. The simulation considers the same temperature for both continuum and line parts of the SL spectrum and gives results in agreement with the experiment. Also, it can properly show period-doubling dynamics for a 50 torr bubble. For most of the allowable driving pressures, it is shown that both the temperature and the intensity of SL for a 4 torr bubble are greater than those of a 50 torr bubble. However, for the range of pressures near the maximum driving conditions of the 50 torr bubble, the SL intensity of this bubble can be up to three orders of magnitude greater than the 4 torr bubble. This case, which is in agreement with the experiment, is obtained when the light-emitting region of the 50 torr bubble is about three orders of magnitude greater than the 4 torr bubble.

We study the corrections to scaling for the mass of the watershed, the bridge line, and the optimal path crack in two and three dimensions (2D and 3D). We disclose that these models have numerically equivalent fractal dimensions and leading correction-to-scaling exponents. We conjecture all three models to possess the same fractal dimension, namely, $d_f=1.2168\pm 0.0005$ in 2D and $d_f=2.487\pm 0.003$ in 3D, and the same exponent of the leading correction, $\Omega =0.9\pm 0.1$ and $\Omega =1.0\pm 0.1$, respectively. The close relations between watersheds, optimal path cracks in the strong disorder limit, and bridge lines are further supported by either heuristic or exact arguments.

DNA polymerase (DNAP) is a dual-purpose enzyme that plays two opposite roles in two different situations during DNA replication. It plays its a normal role as a polymerase catalyzing the elongation of a new DNA molecule by adding a monomer. However, it can switch to the role of an exonuclease and shorten the same DNA by cleavage of the last incorporated monomer from the nascent DNA. Just as misincorporated nucleotides can escape exonuclease causing a replication error, the correct nucleotide may get sacrificed unnecessarily by erroneous cleavage. The interplay of polymerase and exonuclease activities of a DNAP is explored here by developing a minimal stochastic kinetic model of DNA replication. Exact analytical expressions are derived for a few key statistical distributions; these characterize the temporal patterns in the mechanical stepping and the chemical (cleavage) reaction. The Michaelis-Menten-like analytical expression derived for the average rates of these two processes not only demonstrate the effects of their coupling, but are also utilized to measure the extent of replication error and erroneous cleavage.

In recent years, significant progress in understanding the properties of supercoiled DNA has been obtained due to nanotechniques that made stretching and twisting of single molecules possible. Quantitative interpretation of such experiments requires accurate knowledge of torques inside manipulated DNA. This paper argues that it is not possible to transfer the entire magnitudes of external torques to the twisting stress of the double helix, and that a reducing torque transfer coefficient ($\text{TTC}<1$) should always be assumed. This assertion agrees with simple physical intuition and is supported by the results of all-atom molecular dynamics (MD) simulations. According to MD, the TTCs around 0.8 are observed in nearly optimal conditions. Reaching higher values requires special efforts and it should be difficult in practice. The TTC can be partially responsible for the persistent discrepancies between the twisting rigidity of DNA measured by different methods.

We theoretically derive the amplitude equations for a self-propelled droplet driven by Marangoni flow. As advective flow driven by surface tension gradient is enhanced, the stationary state becomes unstable and the droplet starts to move. The velocity of the droplet is determined from a cubic nonlinear term in the amplitude equations. The obtained critical point and the characteristic velocity are well supported by numerical simulations.

Dynamical modeling lies at the heart of our understanding of physical systems. Its role in science is deeper than mere operational forecasting, in that it allows us to evaluate the adequacy of the mathematical structure of our models. Despite the importance of model parameters, there is no general method of parameter estimation outside linear systems. A relatively simple method of parameter estimation for nonlinear systems is introduced, based on variations in the accuracy of probability forecasts. It is illustrated on the logistic map, the Henon map, and the 12-dimensional Lorenz96 flow, and its ability to outperform linear least squares in these systems is explored at various noise levels and sampling rates. As expected, it is more effective when the forecast error distributions are non-Gaussian. The method selects parameter values by minimizing a proper, local skill score for continuous probability forecasts as a function of the parameter values. This approach is easier to implement in practice than alternative nonlinear methods based on the geometry of attractors or the ability of the model to shadow the observations. Direct measures of inadequacy in the model, the “implied ignorance,” and the information deficit are introduced.

We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent $4-2\varepsilon$ of the forcing where real-space local interactions are relevant. In any spatial dimension $d$, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's $-5/3$ law is, thus, recovered for $\varepsilon =2$ as also predicted by perturbative renormalization. At variance with the perturbative prediction, the $-5/3$ law emerges in the presence of a saturation in the $\varepsilon$ dependence of the scaling dimension of the eddy diffusivity at $\varepsilon =3/2$ when, according to perturbative renormalization, the velocity field becomes infrared relevant.

An explicit expression is derived for the statistical description of small quantum systems, which are relatively weakly and directly coupled to only small parts of their environments. The derived expression has a canonical form, but is given by a renormalized self-Hamiltonian of the studied system, which appropriately takes into account the influence of the system-environment interaction. In the case that the system has a narrow spectrum and the environment is sufficiently large, the modification to the self-Hamiltonian usually has a mean-field feature, given by an environmental average of the interaction Hamiltonian. In other cases, the modification may be beyond the mean-field approximation.

We characterize the set of ground states that can be synthesized by classical two-body Ising Hamiltonians. We then construct simple Ising planar blocks that simulate efficiently a universal set of logic gates and connections, and hence any Boolean function. We therefore provide a new method of encoding universal computation in the ground states of Ising lattices and a simpler alternative demonstration of the known fact that finding the ground state of a finite Ising spin glass model is NP complete. We relate this with our previous result about emergent properties in infinite lattices.

If a suspension of magnetic micrometer-sized and nanosized particles is subjected to a homogeneous magnetic field, the nanoparticles are attracted to the microparticles and form thick anisotropic halos (clouds) around them. Such clouds can hinder the approach of microparticles and result in effective repulsion between them [M. T. López-López, A. Yu. Zubarev, and G. Bossis, Soft Matter 6, 4346 (2010)]. In this paper, we present detailed experimental and theoretical studies of nanoparticle concentration profiles and of the equilibrium shapes of nanoparticle clouds around a single magnetized microsphere, taking into account interactions between nanoparticles. We show that at a strong enough magnetic field, the ensemble of nanoparticles experiences a gas-liquid phase transition such that a dense liquid phase is condensed around the magnetic poles of a microsphere while a dilute gas phase occupies the rest of the suspension volume. Nanoparticle accumulation around a microsphere is governed by two dimensionless parameters—the initial nanoparticle concentration (${\phi }_0$) and the magnetic-to-thermal energy ratio (α)—and the three accumulation regimes are mapped onto a $\alpha -{\phi }_0$ phase diagram. Our local thermodynamic equilibrium approach gives a semiquantitative agreement with the experiments on the equilibrium shapes of nanoparticle clouds. The results of this work could be useful for the development of the bimodal magnetorheological fluids and of the magnetic separation technologies used in bioanalysis and water purification systems.

This article presents the study of the generic behavior of viscosity of liquids based on some simple theoretical models, the soft-spheres and Lennard-Jones systems. The use of these simple models allows us to investigate in detail the viscosity behavior in a wide range of temperatures and pressures including the high-temperature–high-pressure limits. Based on the simulation results, we discuss the shape of isoviscosity lines and analyze the glass transition at high temperatures and high pressures. Despite the fact that the viscosity drastically increases in the limit of high temperatures and high pressures along the melting line, the relaxation time rapidly decreases in this region, and the system becomes further from the glass transition.