Understanding and manipulating work fluctuations in microscale and nanoscale systems are of both fundamental and practical interest. For example, aspects of work fluctuations will be an important factor in designing nanoscale heat engines. In this work, an optimal control approach directly exploiting Jarzynski's equality is proposed to effectively suppress the fluctuations in the work statistics, for systems (initially at thermal equilibrium) subject to a work protocol but isolated from a bath during the protocol. The control strategy is to minimize the deviations of individual values of $e^{-\beta W}$ from their ensemble average given by $e^{-\beta \Delta F}$, where $W$ is the work, $\beta$ is the inverse temperature, and $\Delta F$ is the free energy difference between two equilibrium states. It is further shown that even when the system Hamiltonian is not fully known, it is still possible to suppress work fluctuations through a feedback loop, by refining the control target function on the fly through Jarzynski's equality itself. Numerical experiments are based on linear and nonlinear parametric oscillators. Optimal control results for linear parametric oscillators are also benchmarked with early results based on shortcuts to adiabaticity.

We consider a quantum system $A\cup B$ made up of degrees of freedom that can be partitioned into spatially disjoint regions $A$ and $B$. When the full system is in a pure state in which regions $A$ and $B$ are entangled, the quantum mechanics of region $A$ described without reference to its complement is traditionally assumed to require a reduced density matrix on $A$. While this is certainly true as an exact matter, we argue that under many interesting circumstances expectation values of typical operators anywhere inside $A$ can be computed from a suitable pure state on $A$ alone, with a controlled error. We use insights from quantum statistical mechanics—specifically the eigenstate thermalization hypothesis (ETH)—to argue for the existence of such “representative states.”

Classical density functional theory (DFT) of fluids is a fast and efficient theory to compute the structure of the electrical double layer in the primitive model of ions where ions are modeled as charged, hard spheres in a background dielectric. While the hard-core repulsive component of this ion-ion interaction can be accurately computed using well-established DFTs, the electrostatic component is less accurate. Moreover, many electrostatic functionals fail to satisfy a basic theorem, the contact density theorem, that relates the bulk pressure, surface charge, and ion densities at their distances of closest approach for ions in equilibrium at a smooth, hard, planar wall. One popular electrostatic functional that fails to satisfy the contact density theorem is a perturbation approach developed by Kierlik and Rosinberg [Phys. Rev. A 44, 5025 (1991)] and Rosenfeld [J. Chem. Phys. 98, 8126 (1993)], where the full free-energy functional is Taylor-expanded around a bulk (homogeneous) reference fluid. Here, it is shown that this functional fails to satisfy the contact density theorem because it also fails to satisfy the known low-density limit. When the functional is corrected to satisfy this limit, a corrected bulk pressure is derived and it is shown that with this pressure both the contact density theorem and the Gibbs adsorption theorem are satisfied.

This article presents a theoretical prediction of stochastic resonance in spin-crossover materials. The analysis of stochastic resonance phenomenon in a spin-crossover system is performed in the framework of the phenomenological kinetic model with light-induced transition described by dynamical potential in terms of the Lyapunov functions. By using numerical simulation of stochastic trajectories with white- and colored-noise action, the evaluation of stochastic resonance is carried out by signal-to-noise ratio of the system output. The corresponding signal-to-noise ratio features a two-peak behavior which is related to the asymmetric shape of the dynamic potential. For the case of the Ornstein-Uhlenbeck process, the variations of resonance condition with respect to different autocorrelation times are additionally studied.

Athermal steady-state plastic flows were simulated for the Kob-Andersen binary Lennard-Jones system and its repulsive version in which the sign of the attractive terms is changed to a plus. Properties evaluated include the distributions of energy drops, stress drops, and strain intervals between the flow events. We show that simulations at a single density in conjunction with an equilibrium-liquid simulation at the same density allow one to predict the plastic flow-event statistics at other densities. This is done by applying the recently established “hidden scale invariance” of simple liquids to the glass phase. The resulting scaling of flow-event properties reveals quasiuniversality, i.e., that the probability distributions of energy drops, stress drops, and strain intervals in properly reduced units are virtually independent of the microscopic pair potentials.

An elegant simulation method, suitable for investigating the dewetting dynamics of thin and viscous liquid layers, is discussed. The efficiency of the method is exemplified by studying a two-parameter depinninglike model defined on inhomogeneous solid surfaces. The morphology and the statistical properties of the contact line are mapped in the relevant parameter space, and as a result critical behavior in the vicinity of the depinning transition is revealed. The model allows for the tearing of the layer, which leads to a new propagation regime resulting in nontrivial collective behavior. The large deformations observed for the interface are a result of the interplay between the substrate inhomogeneities and the capillary forces.

The contribution to the free energy of distortion of the ferroelectric smectic-$C^{*}$ due to the electrostatic interaction of polarization charges is calculated. These calculations are performed by accounting for the anisotropy of the permittivity, which is essential for smectic-$C^{*}$. Fluctuations of the $\mathbf{c}$ director in an external electric field are considered. It is shown that the anisotropy of the permittivity strongly affects the interaction of the polarization charges, the spectrum orientation fluctuations, and the angular dependence of the light scattering intensity.

We compute the effects of excluded volume on the probability for double-stranded DNA to form a loop. We utilize a Monte Carlo algorithm for generation of large ensembles of self-avoiding wormlike chains, which are used to compute the J factor for varying length scales. In the entropic regime, we confirm the scaling-theory prediction of a power-law drop off of $-1.92$, which is significantly stronger than the $-1.5$ power law predicted by the non-self-avoiding wormlike chain model. In the elastic regime, we find that the angle-independent end-to-end chain distribution is highly anisotropic. This anisotropy, combined with the excluded volume constraints, leads to an increase in the J factor of the self-avoiding wormlike chain by about half an order of magnitude relative to its non-self-avoiding counterpart. This increase could partially explain the anomalous results of recent cyclization experiments, in which short dsDNA molecules were found to have an increased propensity to form a loop.

This paper deals with the control of bias estimation when estimating mutual information from a nonparametric approach. We focus on continuously distributed random data and the estimators we developed are based on a nonparametric $k$-nearest-neighbor approach for arbitrary metrics. Using a multidimensional Taylor series expansion, a general relationship between the estimation error bias and the neighboring size for the plug-in entropy estimator is established without any assumption on the data for two different norms. The theoretical analysis based on the maximum norm developed coincides with the experimental results drawn from numerical tests made by Kraskov et al. [Phys. Rev. E 69, 066138 (2004)]. To further validate the novel relation, a weighted linear combination of distinct mutual information estimators is proposed and, using simulated signals, the comparison of different strategies allows for corroborating the theoretical analysis.

Mechanical deformability of cells is a key property that influences their ability to migrate and their contribution to tissue development and regeneration. We analyze here the possibility of characterizing the overall deformability of cells by their apparent viscosity, using a simplified method to estimate that parameter. The proposed method simplifies the quantitative analysis of micropipette-aspiration experiments. We have studied by this procedure the overall apparent viscosity of cardiac stem cells, which are considered a promising tool to regenerate damaged cardiac tissue. Comparison with the apparent viscosity of low-viscosity cells such as immune-system cells suggests that treatments to reduce the viscosity of these cells could enhance their ability to repair damaged cardiac tissue.

Toxic fibrillar aggregates of islet amyloid polypeptide (IAPP) appear as the physical outcome of a peptidic phase transition signaling the onset of type-2 diabetes mellitus in different mammalian species. In particular, experimentally verified mutations on the amyloidogenic segment 20-29 in humans, cats, and rats are highly correlated with the molecular aggregation propensities. Through a microcanonical analysis of the aggregation of ${\mathrm{IAPP}}_{20\text{−}29}$ isoforms, we show that a minimalist one-bead hydrophobic-polar continuum model for protein interactions properly quantifies those propensities from free-energy barriers. Our results highlight the central role of sequence-dependent hydrophobic mutations on hot spots for stabilization, and thus for the engineering, of such biological peptides.

We describe the complex global structure of giant components in directed multiplex networks that generalizes the well-known bow-tie structure, generic for ordinary directed networks. By definition, a directed multiplex network contains vertices of one type and directed edges of $m$ different types. In directed multiplex networks, we distinguish a set of different giant components based on the existence of directed paths of different types between their vertices such that for each type of edges, the paths run entirely through only edges of that type. If, in particular, $m=2$, we define a strongly viable component as a set of vertices in which for each type of edges each two vertices are interconnected by at least two directed paths in both directions, running through the edges of only this type. We show that in this case, a directed multiplex network contains in total nine different giant components including the strongly viable component. In general, the total number of giant components is $3^m$. For uncorrelated directed multiplex networks, we obtain exactly the size and the emergence point of the strongly viable component and estimate the sizes of other giant components.

Recent empirical studies using large-scale data sets have validated the Granovetter hypothesis on the structure of the society in that there are strongly wired communities connected by weak ties. However, as interaction between individuals takes place in diverse contexts, these communities turn out to be overlapping. This implies that the society has a multilayered structure, where the layers represent the different contexts. To model this structure we begin with a single-layer weighted social network (WSN) model showing the Granovetterian structure. We find that when merging such WSN models, a sufficient amount of interlayer correlation is needed to maintain the relationship between topology and link weights, while these correlations destroy the enhancement in the community overlap due to multiple layers. To resolve this, we devise a geographic multilayer WSN model, where the indirect interlayer correlations due to the geographic constraints of individuals enhance the overlaps between the communities and, at the same time, the Granovetterian structure is preserved.

Dynamic social opinion models have been widely studied on undirected networks, and most of them are based on spin interaction models that produce a consensus. In reality, however, many networks such as Twitter and the World Wide Web are directed and are composed of both unidirectional and bidirectional links. Moreover, from choosing a coffee brand to deciding who to vote for in an election, two or more competing opinions often coexist. In response to this ubiquity of directed networks and the coexistence of two or more opinions in decision-making situations, we study a nonconsensus opinion model introduced by Shao et al. [Phys. Rev. Lett. 103, 018701 (2009)] on directed networks. We define directionality $\xi$ as the percentage of unidirectional links in a network, and we use the linear correlation coefficient $\rho$ between the in-degree and out-degree of a node to quantify the relation between the in-degree and out-degree. We introduce two degree-preserving rewiring approaches which allow us to construct directed networks that can have a broad range of possible combinations of directionality $\xi$ and linear correlation coefficient $\rho$ and to study how $\xi$ and $\rho$ impact opinion competitions. We find that, as the directionality $\xi$ or the in-degree and out-degree correlation $\rho$ increases, the majority opinion becomes more dominant and the minority opinion's ability to survive is lowered.

We study the Krapivsky-Redner (KR) network growth model, but where new nodes can connect to any number of existing nodes, $m$, picked from a power-law distribution $p\left(m\right)\sim m^{-\alpha }$. Each of the $m$ new connections is still carried out as in the KR model with probability redirection $r$ (corresponding to degree exponent ${\gamma }_{\mathrm{KR}}=1+1/r$ in the original KR model). The possibility to connect to any number of nodes resembles a more realistic type of growth in several settings, such as social networks, routers networks, and networks of citations. Here we focus on the in-, out-, and total-degree distributions and on the potential tension between the degree exponent $\alpha$, characterizing new connections (outgoing links), and the degree exponent ${\gamma }_{\mathrm{KR}}\left(r\right)$ dictated by the redirection mechanism.

Through supervised learning in a binary perceptron one is able to classify an extensive number of random patterns by a proper assignment of binary synaptic weights. However, to find such assignments in practice is quite a nontrivial task. The relation between the weight space structure and the algorithmic hardness has not yet been fully understood. To this end, we analytically derive the Franz-Parisi potential for the binary perceptron problem by starting from an equilibrium solution of weights and exploring the weight space structure around it. Our result reveals the geometrical organization of the weight space; the weight space is composed of isolated solutions, rather than clusters of exponentially many close-by solutions. The pointlike clusters far apart from each other in the weight space explain the previously observed glassy behavior of stochastic local search heuristics.

During pattern formation in spatially extended systems, different mechanisms with different characteristic length scales, e.g., reaction-diffusion processes or molecular interactions, can be active. Such multiscale effects may generate new phenomena, which are not observed in systems where pattern formation occurs on a single scale. Here, we derive and analyze a reaction-diffusion model of the FitzHugh-Nagumo type with short-range attractive molecular interactions of the activator species. The model exhibits a wave instability. Simulations in one and two dimensions show traveling waves with a wavelength set by the parameters of the molecular interaction in the model. In two dimensions, simulations reveal a labyrinthine arrangement of the waves in systems with isotropic diffusion, whereas parallel bands of counterpropagating waves are formed in simulations of a model with anisotropic diffusion. The latter findings are in good qualitative agreement with experimental observation in the catalytic $\mathrm{NO}+{\mathrm{H}}_2$ reaction on an anisotropic Rh(110) surface. In addition we have identified a transition regime in the simulations, where a short scale instability triggers global oscillations in an excitable regime.

We analyze a delay differential equation for the amplitude of the electrical field in order to understand recent experimental observations of low-frequency oscillations in a QD laser. The laser contains no saturable absorber section and exhibits no relaxation oscillations. We investigate the problem both analytically and numerically. We show that there exists a homoclinic bifurcation from a cavity mode that is responsible for the generation of low-frequency pulsating oscillations. We discuss the role of optothermal effects in the formation of the pulsed dynamics.

We study the long-range electron and energy transfer mediated by solitons in a quasi-one-dimensional molecular chain (conjugated polymer, alpha-helical macromolecule, etc.) weakly bound to a donor and an acceptor. We show that for certain sets of parameter values in such systems an electron, initially located at the donor molecule, can tunnel to the molecular chain, where it becomes self-trapped in a soliton state, and propagates to the opposite end of the chain practically without energy dissipation. Upon reaching the end, the electron can either bounce back and move in the opposite direction or, for suitable parameter values of the system, tunnel to the acceptor. We estimate the energy efficiency of the donor-acceptor electron transport depending on the parameter values. Our calculations show that the soliton mechanism works for the parameter values of polypeptide macromolecules and conjugated polymers. We also investigate the donor-acceptor electron transport in thermalized molecular chains.

Control of flow around a circular cylinder is studied numerically aiming at minimization of the energy dissipation. First, we derive a mathematical relationship (i.e., identity) between the energy dissipation in an infinitely large volume and the surface quantities, so that the cost function can be expressed by the surface quantities only. Subsequently a control law to minimize the energy dissipation is derived by using the suboptimal control procedure [J. Fluid Mech. 401, 123 (1999)]. The performance of the present suboptimal control law is evaluated by a parametric study by varying the value of the arbitrary parameter contained. Two Reynolds numbers, $\mathrm{Re}=100$ and 1000, are investigated by two-dimensional simulations. Although no improvement is obtained at $\mathrm{Re}=100$, the present suboptimal control shows better results at $\mathrm{Re}=1000$ than the suboptimal controls previously proposed. With the present suboptimal control, the dissipation and the drag are reduced by 58% and 44% as compared to the uncontrolled case, respectively. The suction around the front stagnation point and the blowing in the rear half are found to be weakened as compared to those in the previous suboptimal control targeting at pressure drag reduction. A predetermined control based on the control input profile obtained by the suboptimal control is also performed. The energy dissipation and the drag are found to be reduced as much as those in the present suboptimal control. It is also found that the present suboptimal and predetermined controls have better energy efficiencies than the suboptimal control previously proposed. Investigation at different control amplitudes reveals an advantage of the present control at higher amplitude. Toward its practical implementation, a localized version of the predetermined control is also examined, and it is found to work as effectively as the continuous case. Finally, the present predetermined control is confirmed to work well in a three-dimensional flow too.