The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is derived from the Wigner function formulation of the Feynman-Vernon influence functional theory. It is shown how the true self-energy for the equation of motion is connected with the influence functional for the path integral. Explicit expressions are derived in terms of the bare Wigner propagator. Finally, we show under which approximations the resulting equation of motion reduces to the Wigner-Boltzmann equation.

We performed a parametric study of the drag on vertical intruders with uniform cross sections of different sizes and shapes, from which we developed a semiempirical model. Baffling techniques were used to isolate the contributions of the intruder's different subsurfaces, and we observed size effects and force focusing on edges. We propose a boundary layer approach, whereby the drag is the surface integral of an effective stress over a monolayer of particles contacting the intruder. The stress has a simple lithostatic dependence and is a function of the orientation relative to the intruder's direction of motion. This approach is experimentally verified and is consistent with the semiempirical model.

The onset of large-scale connectivity in a network (i.e., percolation) often has a major impact on the function of the system. Traditionally, graph percolation is analyzed by adding edges to a fixed set of initially isolated nodes. Several years ago, it was shown that adding nodes as well as edges to the graph can yield an infinite order transition, which is much smoother than the traditional second-order transition. More recently, it was shown that adding edges via a competitive process to a fixed set of initially isolated nodes can lead to a delayed, extremely abrupt percolation transition with a significant jump in large but finite systems. Here we analyze a process that combines both node arrival and edge competition. If started from a small collection of seed nodes, we show that the impact of node arrival dominates: although we can significantly delay percolation, the transition is of infinite order. Thus, node arrival can mitigate the trade-off between delay and abruptness that is characteristic of explosive percolation transitions. This realization may inspire new design rules where network growth can temper the effects of delay, creating opportunities for network intervention and control.

We present a numerical determination of the scaling functions of the magnetization, the susceptibility, and the Binder's cumulant for two nonequilibrium model systems with varying range of interactions. We consider Monte Carlo simulations of the block voter model (BVM) on square lattices and of the majority-vote model (MVM) on random graphs. In both cases, the satisfactory data collapse obtained for several system sizes and interaction ranges supports the hypothesis that these functions are universal. Our analysis yields an accurate estimation of the long-range exponents, which govern the decay of the critical amplitudes with the range of interaction, and is consistent with the assumption that the static exponents are Ising-like for the BVM and classical for the MVM.

Recently, stochastic resonance was shown to occur in underdamped periodic potentials at frequencies (of the drive field) close to the natural frequency at the minima of the potentials. In these systems the particle trajectories are not arbitrary at low temperatures but follow the drive field with two definite mean phase differences depending on the initial conditions. The trajectories are thus found to be in only two stable dynamical states. The occurrence of stochastic resonance in the periodic potentials was explained as a consequence of the transitions between these two dynamical states as the temperature was increased. In the present work, we find the range of amplitudes of the drive field over which the dynamical states could be observed in a sinusoidal potential. The variation of the relative stability of the dynamical states as a function of drive-field amplitude is clarified by analyzing the nature of curves characterizing the stochastic resonance as the amplitude is varied within the range.

By treating both control parameters and dynamical variables as probabilistic variables, we develop a succinct theory of perpetual extraction of work from a generic classical nonequilibrium system subject to a heat bath via repeated measurements under a Markovian feedback control. It is demonstrated that a problem for perpetual extraction of work in a nonequilibrium system is reduced to a problem of Markov chain in the higher-dimensional phase space. We derive a version of the detailed fluctuation theorem, which was originally derived for classical nonequilibrium systems by Horowitz and Vaikuntanathan [Phys. Rev. E 82, 061120 (2010)], in a form suitable for the analyses of perpetual extraction of work. Since our theory is formulated for generic dynamics of probability distribution function in phase space, its application to a physical system is straightforward. As simple applications of the theory, two exactly solvable models are analyzed. The one is a nonequilibrium two-state system and the other is a particle confined to a one-dimensional harmonic potential in thermal equilibrium. For the former example, it is demonstrated that the observer on the transitory steps to the stationary state can lose energy and that work larger than that achieved in the stationary state can be extracted. For the latter example, it is demonstrated that the optimal protocol for the extraction of work via repeated measurements can differ from that via a single measurement. The validity of our version of the detailed fluctuation theorem, which determines the upper bound of the expected work in the stationary state, is also confirmed for both examples. These observations provide useful insights into exploration for realistic modeling of a machine that extracts work from its environment.

Kawai and Komatsuzaki [J. Chem. Phys. 134, 114523 (2011)] recently derived the nonequilibrium generalized Langevin equation (GLE) for a nonstationary system using the projection operator technique. In the limit when the environment is slowly changing (that is, a quasi-equilibrium bath), it should reduce to the irreversible GLE approach (iGLE) [J. Chem. Phys. 111, 7701 (1999)]. Kawai and Komatsuzaki, however, found that the driven harmonic oscillator, an example of a nonequilibrium system does not obey the iGLE presumably because it did not quite satisfy the limiting conditions of the latter. Notwithstanding the lack of a massive quasi-equilibrium bath (one of the conditions under which the iGLE had been derived earlier), we found that the temperature-driven iGLE (T-iGLE) [J. Chem. Phys. 126, 244506 (2007)] can reproduce the nonequilibrium dynamics of a driven dissipated pair of harmonic oscillators. It requires a choice of the function representing the coupling between the oscillator coordinate and the bath and shows that the T-iGLE representation is consistent with the projection operator formalism if only dominant bath modes are taken into account. Moreover, we also show that the more readily applicable phenomenological iGLE model is recoverable from the Kawai and Komatsuzaki model beyond the adiabatic limit used in the original T-iGLE theory.

We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving maps, with and without feedback control. Our results include the quantum Jarzynski equality and Crooks fluctuation theorem, and clarify the special role played by the thermodynamic work and thermal equilibrium states in previous studies. We show that for a specific class of generalized measurements, which include projective measurements, unitality replaces microreversibility as the condition for the physicality of the reverse process in our fluctuation theorems. We present an experimental application of our theory to the problem of extracting the system-bath coupling magnitude, which we do for a system of pairs of coupled superconducting flux qubits undergoing quantum annealing.

The specific heats of exactly solvable alternating layered planar Ising models with strips of width $m_1$ lattice spacings and “strong” couplings $J_1$ sandwiched between strips of width $m_2$ and “weak” coupling $J_2$, have been studied numerically to investigate the effects of connectivity and proximity. We find that the enhancements of the specific heats of the strong layers and of the overall or “bulk” critical temperature $T_c(J_1,J_2;m_1,m_2)$ arising from the collective effects reflect the observations of Gasparini and co-workers in experiments on confined superfluid helium. Explicitly, we demonstrate that finite-size scaling holds in the vicinity of the upper limiting critical point $T_{1c}$ ($\propto J_1/k_B$) and close to the corresponding lower critical limit $T_{2c}$ ($\propto J_2/k_B$) when $m_1$ and $m_2$ increase. However, the residual enhancement, defined via appropriate subtractions of leading contributions from the total specific heat, is dominated (away from $T_{1c}$ and $T_{2c}$) by a decay factor $1/(m_1+m_2)$ arising from the seams (or boundaries) separating the strips; close to $T_{1c}$ and $T_{2c}$ the decay is slower by a factor $\ln m_1$ and $\ln m_2$, respectively.

Part I of this article studied the specific heats of planar alternating layered Ising models with strips of strong coupling $J_1$ sandwiched between strips of weak coupling $J_2$, to illustrate qualitatively the effects of connectivity, proximity, and enhancement in analogy to those seen in extensive experiments on superfluid helium by Gasparini and co-workers. It was demonstrated graphically that finite-size scaling descriptions hold in a variety of temperature regions including in the vicinity of the two specific heat maxima. Here we provide exact theoretical analyses and asymptotics of the specific heat that support and confirm the graphical findings. Specifically, at the overall or bulk critical point, the anticipated (and always present) logarithmic singularity is shown to vanish exponentially fast as the width of the stronger strips increases.

Wrinkling and folding are examined experimentally for three distinct types of disordered films on polydimethylsiloxane (PDMS) substrates; diblock copolymers, glassy polymers, and single-wall carbon nanotubes. All three of these systems exhibit localization and length-scale doubling at small strains, and we qualitatively account for these observations with a simple physical argument related to the width of the stress correlation function and the interaction of localization sites. Our results have relevance to wrinkling and folding in a diverse array of disordered films on soft substrates, and the insights offered here should help guide the development of theoretical models for the influence of structural disorder on thin-film wrinkling instabilities.

We present a generic analytical scheme for the quantification of fluctuations due to bifunctionality-induced signal transduction within the members of a bacterial two-component system. The proposed model takes into account post-translational modifications in terms of elementary phosphotransfer kinetics. Sources of fluctuations due to autophosphorylation, kinase, and phosphatase activity of the sensor kinase have been considered in the model via Langevin equations, which are then solved within the framework of linear noise approximation. The resultant analytical expression of phosphorylated response regulators are then used to quantify the noise profile of biologically motivated single and branched pathways. Enhancement and reduction of noise in terms of extra phosphate outflux and influx, respectively, have been analyzed for the branched system. Furthermore, the role of fluctuations of the network output in the regulation of a promoter with random activation-deactivation dynamics has been analyzed.

The disappearance of the guanosine triphosphate- (GTP) tubulin cap is widely believed to be the forerunner event for the growth-shrinkage transition (“catastrophe”) in microtubule filaments in eukaryotic cells. We study a discrete version of a stochastic model of the GTP cap dynamics, originally proposed by Flyvbjerg, Holy, and Leibler [Phys. Rev. Lett. 73, 2372 (1994)]. Our model includes both spontaneous and vectorial hydrolysis, as well as dissociation of a nonhydrolyzed dimer from the filament after incorporation. In the first part of the paper, we apply this model to a single protofilament of a microtubule. A catastrophe transition is defined for each protofilament, similarly to the earlier one-dimensional models, the frequency of occurrence of which is then calculated under various conditions but without explicit assumption of steady-state conditions. Using a perturbative approach, we show that the leading asymptotic behavior of the protofilament catastrophe in the limit of large growth velocities is remarkably similar across different models. In the second part of the paper, we extend our analysis to the entire filament by making a conjecture that a minimum number of such transitions are required to occur for the onset of microtubule catastrophe. The frequency of microtubule catastrophe is then determined using numerical simulations and compared with analytical and semianalytical estimates made under steady-state and quasi-steady-state assumptions, respectively, for the protofilament dynamics. A few relevant experimental results are analyzed in detail and compared with predictions from the model. Our results indicate that loss of GTP cap in two to three protofilaments is necessary to trigger catastrophe in a microtubule.

To explain the differentiation of stem cells in terms of dynamical systems theory, models of interacting cells with intracellular protein expression dynamics are analyzed and simulated. Simulations were carried out for all possible protein expression networks consisting of two genes under cell-cell interactions mediated by the diffusion of a protein. Networks that show cell differentiation are extracted and two forms of symmetric differentiation based on Turing's mechanism and asymmetric differentiation are identified. In the latter network, the intracellular protein levels show oscillatory dynamics at a single-cell level, while cell-to-cell synchronicity of the oscillation is lost with an increase in the number of cells. Differentiation to a fixed-point-type behavior follows with a further increase in the number of cells. The cell type with oscillatory dynamics corresponds to a stem cell that can both proliferate and differentiate, while the latter fixed-point type only proliferates. This differentiation is analyzed as a saddle-node bifurcation on an invariant circle, while the number ratio of each cell type is shown to be robust against perturbations due to self-consistent determination of the effective bifurcation parameter as a result of the cell-cell interaction. Complex cell differentiation is designed by combing these simple two-gene networks. The generality of the present differentiation mechanism, as well as its biological relevance, is discussed.

We present numerical simulations of a two-dimensional (2D) nuclear magnetic resonance process, $T_2$-storage-$T_2$, on a simple mixed porosity system, the micrograin consolidation ($\mu$GC) model. The results of these calculations are compared with predictions based on the analytic two-site exchange model, for which we have independently established numerical values for all the input parameters. Although there is qualitative and semiquantitative agreement between the two models, we identify specific instances where the two-site model fails to properly describe the combined effects of relaxation and diffusion. Generally, these instances occur when a gradient in magnetization within the large pores of the $\mu$GC model is established during the initial phase of the 2D process. The two-site model assumes that the magnetization is spatially uniform within each of its subpore systems and thus cannot describe such effects.

A generalized Peregrine soliton moving on a fluctuating background is constructed. The agreement with the experimental results is improved compared to the standard Peregrine soliton. It has a deformed shape asymmetric with respect to time, and the peak values are not always 3.

Ferromagnetic microparticles suspended at the interface between immiscible liquids and energized by an external alternating magnetic field show a rich variety of self-assembled structures, from linear snakes to radial asters. In order to obtain insight into the fundamental physical mechanisms and the overall balance of forces governing self-assembly, we develop a modeling approach based on analytical solutions of the time-averaged Navier-Stokes equations. These analytical expressions for the self-consistent hydrodynamic flows are then employed to modify effective interactions between the particles, which in turn are formulated in terms of the time-averaged quantities. Our method allows effective computational verification of the mechanisms of self-assembly and leads to a testable prediction, e.g., on the transitions between various patterns versus viscosity of the solvent.

We describe the physical mechanism responsible for the rotation of Brownian metal nanowires suspended in an electrolyte exposed to a rotating electric field. The electric field interacts with the induced charge in the electrical double layer at the metal-electrolyte interface, causing rotation due to the torque on the induced dipole and to the induced-charge electro-osmotic flow around the particle. Experiments demonstrate that the primary driving mechanism is the former of these two. Our analysis contrasts with previous work describing the electrical manipulation of metallic particles with electric fields, which neglected the electrical double layer. Theoretical values for the rotation speed are calculated and good agreement with experiments is found.

In this study we report several experimental and numerical results on the influence of static pressure ($P_0$) over the main parameters in single bubble sonoluminescence (SBSL), using a sulfuric acid aqueous solution (SA) with low concentrations of argon gas dissolved. Bifrequency driving was used in the experiments to enhance spatial stability of the bubbles. The experimental results were compared with simulations provided by a numerical code that models the radial dynamics of the bubbles. The results showed that an increase on the static pressure of the system shifts the Bjerknes instability threshold, allowing the bubble to access higher acoustic pressures ($P_{\mathrm{Ac}}^{}$). Furthermore, a decrease in the measured ambient radius $R_0$ and the calculated relative gas concentration $c_{\infty }/c_0$ were observed. A notorious increment in the bubble collapse violence and energy focusing for $P_0$ above 1 bar was achieved. These were mainly indicated by the growth of the bubble expansion ratio ($R_{\max }/R_0$), the bubble mechanical energy density, and the maximum bubble wall velocity $dR/dt$. In agreement with the previous statement, the maximum temperature during the bubble collapse predicted by the model is augmented as well. The use of different harmonics in the ultrasound pressure field regarding energy focusing is also discussed. Finally, we analyzed the stability regions of the $R_0$-$P_{\mathrm{Ac}}^{}$ parameter space via numerical predictions for $P_0$ above the measured, identifying the shape instabilities as the main limiting agent to obtain further energy concentration in SA systems at high static pressures.

A microfluidic technique is proposed to produce microbubbles. A gaseous stream is injected through a $\mathsf{T}$ junction into a channel transporting a liquid current. The gas adheres to a hydrophobic strip printed on the channel surface. When the gas and liquid flow rates are set appropriately, a gaseous rivulet flows over that strip. The rivulet breaks up downstream due to a capillary pearling instability, which leads to a monodisperse collection of microbubbles that can be much smaller than the channel size. The physics of the process is theoretically investigated, using both full numerical simulation of the Navier-Stokes equations and a linear stability analysis of an infinite gaseous rivulet driven by a coflowing liquid stream. This stability analysis allows one to determine a necessary condition to get this effect in a $\mathsf{T}$ junction device. It also provides reasonably good predictions for the size of the produced microbubbles as obtained from numerical experiments.