We study ensembles of continuous-time Markov chains evolving independently under a common transition rate matrix in some finite state space. A diffusion approximation, composed of two specifically coupled Ornstein-Uhlenbeck processes in stochastic differential equation representation, is formulated to deduce how the number of chains in a given particular state evolves in time. This particular form of the formulation builds upon a theoretical argument adduced here. The formulation is minimal in the sense that it is always a two-dimensional stochastic process regardless of the state space size or the transition matrix density, and that it requires no matrix square root operations. A set of criteria, put forward here as to be necessarily captured by any consistent approximation scheme, is used together with the master equation to determine uniquely the parameter values and noise variances in the formulation. The model is applied to the gating dynamics in ion channel clusters.

Using filter-space techniques, we study the spatial structure of the turbulent stress that couples motion on different length scales in a quasi-two-dimensional laboratory flow. As the length scale increases, we observe the appearance of long-range, system-spanning spatial order of this stress, even though the flow field remains disordered. Suggestively, this ordering occurs only in the range of scales over which we find net inverse energy transfer to larger scales. However, we find that a field built from wave vectors with random phases also displays ordering, suggesting that at least some of the ordering we observe is purely kinematic. Our results help to clarify the role played by geometric alignment in the turbulent energy cascade and highlight the importance of the scale-dependent rate of strain in the energy-transfer process.

The turbulent wake of a square-back body exhibits a strong bimodal behavior. The wake randomly undergoes symmetry-breaking reversals between two mirror asymmetric steady modes [reflectional symmetry-breaking (RSB) modes]. The characteristic time for reversals is about 2 or 3 orders of magnitude larger than the natural time for vortex shedding. Studying the effects of the proximity of a ground wall together with the Reynolds number, it is shown that the bimodal behavior is the result of an imperfect pitchfork bifurcation. The RSB modes correspond to the two stable bifurcated branches resulting from an instability of the stable symmetric wake. An attempt to stabilize the unstable symmetric wake is investigated using a passive control technique. Although the controlled wake still exhibits strong fluctuations, the bimodal behavior is suppressed and the drag reduced. This promising experiment indicates the possible existence of an unstable solution branch corresponding to a reflectional symmetry preserved (RSP) mode. This work is encouraging to develop a control strategy based on a stabilization of this RSP mode to reduce mean drag and lateral force fluctuations.

We study out-of-equilibrium conditions in recent x-ray Thomson scattering experiments performed in warm dense matter. We use an effective one-component plasma model to characterize the states in which electron and ion temperatures are different. An estimation of the ion temperature is obtained. This method is tested against two recent experiments. Strong out-of-equilibrium conditions are found.

We propose an efficient procedure to obtain Green's functions by combining the shifted conjugate orthogonal conjugate gradient (shifted COCG) method with the nonequilibrium Green's function (NEGF) method based on a real-space finite-difference (RSFD) approach. The bottleneck of the computation in the NEGF scheme is matrix inversion of the Hamiltonian including the self-energy terms of electrodes to obtain the perturbed Green's function in the transition region. This procedure first computes unperturbed Green's functions and calculates perturbed Green's functions from the unperturbed ones using a mathematically strict relation. Since the matrices to be inverted to obtain the unperturbed Green's functions are sparse, complex-symmetric, and shifted for a given set of sampling energy points, we can use the shifted COCG method, in which once the Green's function for a reference energy point has been calculated the Green's functions for the other energy points can be obtained with a moderate computational cost. We calculate the transport properties of a ${\mathrm{C}}_{60}$@(10,10) carbon nanotube (CNT) peapod suspended by (10,10)CNTs as an example of a large-scale transport calculation. The proposed scheme opens the possibility of performing large-scale RSFD-NEGF transport calculations using massively parallel computers without the loss of accuracy originating from the incompleteness of the localized basis set.

In this work, we investigate the classical loop models doped with monomers and dimers on a square lattice, whose partition function can be expressed as a tensor network (TN). In the thermodynamic limit, we use the boundary matrix product state technique to contract the partition function TN, and determine the thermodynamic properties with high accuracy. In this monomer-dimer-loop model, we find a second-order phase transition between a trivial monomer-condensation and a loop-condensation (LC) phase, which cannot be distinguished by any local order parameter, while nevertheless the two phases have distinct topological properties. In the LC phase, we find two degenerate dominating eigenvalues in the transfer-matrix spectrum, as well as a nonvanishing (nonlocal) string order parameter, both of which identify the topological ergodicity breaking in the LC phase and can serve as the order parameter for detecting the phase transitions.

The $\text{O}\left(n\right) {\varphi }^4$ model on a strip bounded by a pair of planar free surfaces at separation $L$ can be solved exactly in the large-$n$ limit in terms of the eigenvalues and eigenfunctions of a self-consistent one-dimensional Schrödinger equation. The scaling limit of a continuum version of this model is considered. It is shown that the self-consistent potential can be eliminated in favor of scattering data by means of appropriately extended methods of inverse scattering theory. The scattering data (Jost function) associated with the self-consistent potential are determined for the $L=\infty$ semi-infinite case in the scaling regime for all values of the temperature scaling field $t=(T-T_{\mathrm{c}})/T_{\mathrm{c}}$ above and below the bulk critical temperature $T_{\mathrm{c}}$. These results are used in conjunction with semiclassical and boundary-operator expansions and a trace formula to derive exact analytical results for a number of quantities such as two-point functions, universal amplitudes of two excess surface quantities, the universal amplitude difference associated with the thermal singularity of the surface free energy, and potential coefficients. The asymptotic behaviors of the scaled eigenenergies and eigenfunctions of the self-consistent Schrödinger equation as function of $x=t{(L/{\xi }_{+})}^{1/\nu }$ are determined for $x\to -\infty$. In addition, the asymptotic $x\to -\infty$ forms of the universal finite-size scaling functions $\mathrm{\Theta }\left(x\right)$ and $\vartheta \left(x\right)$ of the residual free energy and the Casimir force are computed exactly to order $1/x$, including their $x^{-1}ln\left|x\right|$ anomalies.

By means of a unitary transformation, we propose an ansatz to study quantum phase transitions in the ground state of a two-qubit system interacting with a dissipative reservoir. First, the ground-state phase diagram is analyzed in the presence of the Ohmic and sub-Ohmic bath using an analytic ground-state wave function that takes into account the competition between intrasite tunneling and intersite correlation. The quantum critical point is determined as the transition point from a nondegenerate to a degenerate ground state, and our calculated critical coupling strength ${\alpha }_c$ agrees with that from the numerical renormalization-group method. Moreover, by computing the entanglement entropy between the qubits and the bath as well as the qubit-qubit correlation function in the ground state, we explore the nature of the quantum phase transition between the delocalized and localized states.

We consider the density of states of granular media in which each grain-grain contact is damped with a damping force proportional to the relative velocity of the two grains, in addition to the usual spring constant. Under the assumption that the so-called criterion of proportional damping is only weakly violated we are able to deduce the density of states for undamped frequencies from the measured complex-valued frequencies of damped oscillations. We deduce a quantitative estimate of the deviation from the proportional criterion. We consider, specifically, numerical simulations of cases in which the grains are frictionless spheres that interact via Hertz central forces and all the nonzero contacts are damped with the same damping constant. We show how these ideas can be applied to data on real granular systems.

We combine computer simulations and analytical theory to investigate the glassy dynamics in dense assemblies of athermal particles evolving under the sole influence of self-propulsion. Our simulations reveal that when the persistence time of the self-propulsion is increased, the local structure becomes more pronounced, whereas the long-time dynamics first accelerates and then slows down. We explain these surprising findings by constructing a nonequilibrium microscopic theory that yields nontrivial predictions for the glassy dynamics. These predictions are in qualitative agreement with the simulations and reveal the importance of steady-state correlations of the local velocities to the nonequilibrium dynamics of dense self-propelled particles.

Frontal photopolymerization (FPP) is a versatile directional solidification process that can be used to rapidly fabricate polymer network materials by selectively exposing a photosensitive monomer bath to light. A characteristic feature of FPP is that the monomer-to-polymer conversion profiles take on the form of traveling waves that propagate into the unpolymerized bulk from the illuminated surface. Practical implementations of FPP require detailed knowledge about the conversion profile and speed of these traveling waves. The purpose of this theoretical study is to (i) determine the conditions under which FPP occurs and (ii) explore how optical attenuation and mass transport can be used to finely tune the conversion profile and propagation kinetics. Our findings quantify the strong optical attenuation and slow mass transport relative to the rate of polymerization required for FPP. The shape of the traveling wave is primarily controlled by the magnitude of the optical attenuation coefficients of the neat and polymerized material. Unexpectedly, we find that mass diffusion can increase the net extent of polymerization and accelerate the growth of the solid network. The theoretical predictions are found to be in excellent agreement with experimental data acquired for representative systems.

Synaptic unreliability is one of the major sources of biophysical noise in the brain. In the context of neural information processing, it is a central question how neural systems can afford this unreliability. Here we examine how synaptic noise affects signal transmission in cortical circuits, where excitation and inhibition are thought to be tightly balanced. Surprisingly, we find that in this balanced state synaptic response variability actually facilitates information transmission, rather than impairing it. In particular, the transmission of fast-varying signals benefits from synaptic noise, as it instantaneously increases the amount of information shared between presynaptic signal and postsynaptic current. Furthermore we show that the beneficial effect of noise is based on a very general mechanism which contrary to stochastic resonance does not reach an optimum at a finite noise level.

We study the dynamics of phase synchronization in growing populations of discrete phase oscillatory systems when the division process is coupled to the distribution of oscillator phases. Using mean-field theory, linear-stability analysis, and numerical simulations, we demonstrate that coupling between population growth and synchrony can lead to a wide range of dynamical behavior, including extinction of synchronized oscillations, the emergence of asynchronous states with unequal state (phase) distributions, bistability between oscillatory and asynchronous states or between two asynchronous states, a switch between continuous (supercritical) and discontinuous (subcritical) transitions, and modulation of the frequency of bulk oscillations.

Thermophoresis is the movement of molecules in a temperature gradient. For aqueous solutions its microscopic basis is debated. Understanding thermophoresis for this case is, however, important since it proved very useful to detect the binding affinity of biomolecules and since thermophoresis could have played an important role in early molecular evolution. Here we discuss why the thermophoresis of single- and double-stranded oligonucleotides - DNA and RNA - is surprisingly similar. This finding is understood by comparing the spherical capacitor model for single-stranded species with the case of a rod-shaped model for double-stranded oligonucleotides. The approach describes thermophoresis of DNA and RNA with fitted effective charges consistent with electrophoresis measurements and explains the similarity between single- and double-stranded species. We could not confirm the sign change for the thermophoresis of single- versus double-stranded DNA in crowded solutions containing polyethylene glycol [Y. T. Maeda, T. Tlusty, and A. Libchaber, Proc. Natl. Acad. Sci. USA 109, 17972 (2012)], but find a salt-independent offset while the Debye length dependence still satisfies the capacitor model. Overall, the analysis documents the continuous progress in the microscopic understanding of thermophoresis.

The well-known Knudsen paradox observed in pressure driven rarefied gas flows through long capillaries is quantitatively explored by decomposing the particle distribution function into its ballistic and collision parts. The classical channel, tube, and duct Poiseuille flows are considered. The solution is obtained by a typical direct simulation Monte Carlo algorithm supplemented by a suitable particle decomposition indexation process. It is computationally confirmed that in the free-molecular and early transition regimes the reduction rate of the ballistic flow is larger than the increase rate of the collision flow deducing the Knudsen minimum of the overall flow. This description interprets in a precise, quantitative manner the appearance of the Knudsen minimum and verifies previously reported qualitative physical arguments.

We investigate multicritical phenomena in $\mathrm{O}\left(N\right)+\mathrm{O}\left(M\right)$ models by means of nonperturbative renormalization group equations. This constitutes an elementary building block for the study of competing orders in a variety of physical systems. To identify possible multicritical points in phase diagrams with two ordered phases, we compute the stability of isotropic and decoupled fixed point solutions from scaling potentials of single-field models. We verify the validity of Aharony's scaling relation within the scale-dependent derivative expansion of the effective average action. We discuss implications for the analysis of multicritical phenomena with truncated flow equations. These findings are an important step towards studies of competing orders and multicritical quantum phase transitions within the framework of functional renormalization.

The stochastic properties of a Langevin-type Markov process can be extracted from a given time series by a Markov analysis. Also processes that obey a stochastically forced second-order differential equation can be analyzed this way by employing a particular embedding approach: To obtain a Markovian process in $2N$ dimensions from a non-Markovian signal in $N$ dimensions, the system is described in a phase space that is extended by the temporal derivative of the signal. For a discrete time series, however, this derivative can only be calculated by a differencing scheme, which introduces an error. If the effects of this error are not accounted for, this leads to systematic errors in the estimation of the drift and diffusion functions of the process. In this paper we will analyze these errors and we will propose an approach that correctly accounts for them. This approach allows an accurate parameter estimation and, additionally, is able to cope with weak measurement noise, which may be superimposed to a given time series.

The orientational order in vertically agitated granular-rod monolayers is investigated experimentally and compared quantitatively with equilibrium Monte Carlo simulations and density functional theory. At sufficiently high number density, short rods form a tetratic state and long rods form a uniaxial nematic state. The length-to-width ratio at which the order changes from tetratic to uniaxial is around $7.3$ in both experiments and simulations. This agreement illustrates the universal aspects of the ordering of rod-shaped particles across equilibrium and nonequilibrium systems. Moreover, the assembly of granular rods into ordered states is found to be independent of the agitation frequency and strength, suggesting that the detailed nature of energy injection into such a nonequilibrium system does not play a crucial role.