In experiments and simulations the force acting on a single biomolecular system has been observed as a fluctuating quantity if the system is driven under constant velocity. We ask the question that is analogous to transient state entropy production and work fluctuation relations whether the force fluctuations observed in the single biomolecular system satisfy a transient state fluctuationlike relation, and the answer is in the affirmative. Using a constant velocity pulling steered molecular dynamics simulation study for protein unfolding, we confirm that the force fluctuations of this single biomolecular system satisfy a transient-state fluctuationlike relation $\frac{1}{\gamma (T,v)}\ln \left[\frac{P_v(+f)}{P_v(-f)}\right]=f$. $P_v(\pm f)$ is the probability of positive and negative values of forces $f=\vec{f}·\widehat{n}$ for a given unfolding velocity of magnitude $v$ and the pulling direction $\vec{n}$, $\widehat{n}$ is the unit vector of $\vec{n}$, and $\gamma (T,v)$ is a factor that depends on initial equilibrium temperature $T$ and the unfolding velocity. For different unfolding velocities we find that the system in the nonequilibrium pulling region displays substantial negative fluctuation in its unfolding force when velocity decreases. A negative value of force may indicate the emergence of refolding behavior during protein unfolding. We also find that $\gamma (T,v)\sim T^{-\delta }{v}^{\alpha }$ and the system relaxation time $\tau (T,v)\sim T^{\delta }{v}^{-(1+\alpha )}$, where $\alpha$ and $\delta$ are scaling exponents.

In an asymmetric Szilard engine model of Maxwell's demon, we show the equivalence between information theoretical and thermodynamic entropies when the demon erases information optimally. The work gain by the engine can be exactly canceled out by the work necessary to reset the demon's memory after optimal data compression in the manner of Shannon before the erasure.

Nonequilibrium stationary fluctuations may exhibit a special symmetry called fluctuation relations (FRs). Here, we show that this property is always satisfied by the subtraction of two random and independent variables related by a thermodynamiclike change of measure. Taking one of them as a modulated Poisson process, it is demonstrated that intermittence and FRs are compatible properties that may coexist naturally. Strong non-Gaussian features characterize the probability distribution and its generating function. Their associated large deviation functions develop a “kink” at the origin and a plateau regime respectively. Application of this model in different stationary nonequilibrium situations is discussed.

An artificial molecular rotor system mounted in a biological membrane, which can unidirectionally rotate in response to weak pumping from a linearly polarized ac field, is modeled. The dynamics of the rotor unit are described by the Langevin equation for a particle in a two-dimensional bistable potential with a two-tooth ratchet structure. This model reveals effects due to the two-dimensionality of the ratchet and the polarization of the applied field. First, we demonstrate that a unidirectional rotation appears with stochastic resonance exhibiting a bell-shaped peak for noise intensity in the mean angular momentum (MAM) of the rotor. An analytical expression for the MAM, $\langle L\rangle$, is obtained on the basis of a four-state Markov approximation. Second, a significant effect due to torsional nonlinearity (representing the ratchet-like structure) in the potential geometry is quantified: in the absence of torsion, the MAM depends on the polarization angle $\phi$ of the applied field as $\langle L\rangle \propto \sin \left(2\phi \right)$, whereas in the presence of torsion, an additional bias appears in the MAM as $\langle L\rangle \propto \{\text{bias}+\sin (2\phi \left)\right\}$. It is found that this effect can be used to make the rotor system robustly maintain rotation in a single direction independent of the mounting conditions. Possible designs for an artificial molecular rotor system using the torsion effect are discussed.

Brownian motion in a simple shear flow has been experimentally investigated by using a different method for observation and analysis. A number of polystyrene spheres dispersed in sheared water were tracked with a confocal scanning laser microscope, and the time dependences of their coordinates were obtained. Since in the usual mean-square displacement in the flow direction the contribution from the Brownian motion is overwhelmed by that due to the convection, we considered an alternative displacement for which the convection effect could be removed. We found that the new mean-square displacement consists of the normal Einstein diffusion term, which is linear in $t$, and an anomalous $t^3$ term arising from the coupling between the diffusion along the velocity gradient and the convection.

We report a theoretical model based on Green's functions and averaging techniques that gives analytical estimates to the signal-to-noise ratio (SNR) near the first parametric instability zone in parametrically driven oscillators in the presence of added ac drive and added thermal noise. The signal term is given by the response of the parametrically driven oscillator to the added ac drive, while the noise term has two different measures: one is dc and the other is ac. The dc measure of noise is given by a time average of the statistically averaged fluctuations of the displacement from equilibrium in the parametric oscillator due to thermal noise. The ac measure of noise is given by the amplitude of the statistically averaged fluctuations at the frequency of the parametric pump. We observe a strong dependence of the SNR on the phase between the external drive and the parametric pump. For some range of the phase there is a high SNR, while for other values of phase the SNR remains flat or decreases with increasing pump amplitude. Very good agreement between analytical estimates and numerical results is achieved.

Detonation of a three-dimensional reactive nonisotropic molecular crystal is modeled using molecular dynamics simulations. The detonation process is initiated by an impulse, followed by the creation of a stable fast reactive shock wave. The terminal shock velocity is independent of the initiation conditions. Further analysis shows supersonic propagation decoupled from the dynamics of the decomposed material left behind the shock front. The dependence of the shock velocity on crystal nonlinear compressibility resembles solitary behavior. These properties categorize the phenomena as a weak detonation. The dependence of the detonation wave on microscopic potential parameters was investigated. An increase in detonation velocity with the reaction exothermicity reaching a saturation value is observed. In all other respects the model crystal exhibits typical properties of a molecular crystal.

When a voltage is applied across a thin layer of cholesteric liquid crystal, fingers of cholesteric alignment can form and propagate in the layer. In computer simulation, based on experimental laboratory results, we demonstrate that these cholesteric fingers can solve selected problems of computational geometry, logic, and arithmetics. We show that branching fingers approximate a planar Voronoi diagram, and nonbranching fingers produce a convex subdivision of concave polygons. We also provide a detailed blueprint and simulation of a one-bit half-adder functioning on the principles of collision-based computing, where the implementation is via collision of liquid crystal fingers with obstacles and other fingers.

Micro-objects propelled by whole cell actuators, such as flagellated bacteria, are being increasingly studied and considered for a wide variety of applications. In this work we present theoretical and experimental investigations of chemotactic motility of a 10 $\mu$m diameter microbead propelled by an ensemble of attached flagellated bacteria. The stochastic model presented here encompasses the behavior of each individual bacterium attached to the microbead in a spatiotemporally varying chemoattractant field. The computational model shows that in a chemotactic environment, the ensemble of bacteria, although constrained, propel the bead in a chemotactic manner with a 67$\%$ enhancement in displacement to distance ratio (defined as directionality) compared to nonchemotactic propulsion. The simulation results are validated experimentally. Close agreement between theory and experiments demonstrates the possibility of using the presented model as a predictive tool for other similar biohybrid systems.

There are a great many proteins that localize to and collectively generate curvature in biological fluid membranes. We study changes in the topology of fluid membranes due to the presence of highly anisotropic, curvature-inducing proteins. Generically, we find a surprisingly rich phase diagram with phases of both positive and negative Gaussian curvature. As a concrete example modeled on experiments, we find that a lamellar phase in a negative Gaussian curvature regime exhibits a propensity to form screw dislocations of definite Burgers scalar but of both chiralities.

Random heteropolymers do not display the typical equilibrium properties of globular proteins, but are the starting point to understand the physics of proteins and, in particular, to describe their non-native states. So far, they have been studied with mean-field models in the thermodynamic limit, or with computer simulations of very small chains on lattice. After describing a self-adjusting parallel-tempering technique to sample efficiently the low-energy states of frustrated systems without the need of tuning the system-dependent parameters of the algorithm, we apply it to random heteropolymers moving in continuous space. We show that if the mean interaction between monomers is negative, the usual description through the random-energy model is nearly correct, provided that it is extended to account for noncompact conformations. If the mean interaction is positive, such a simple description breaks out and the system behaves in a way more similar to Ising spin glasses. The former case is a model for the denatured state of globular proteins, the latter of naturally unfolded proteins, whose equilibrium properties thus result as qualitatively different.

Recent experiments on Brownian colloidal particles have been studied theoretically in terms of overdamped Langevin equations with multiplicative white noise using an unconventional stochastic interpretation. Complementary numerical simulations of the same system are well described using the conventional Stratonovich interpretation. Here we address this dichotomy from a more generic starting point: the underdamped Langevin equation and its corresponding Fokker-Planck equation.

Multiscale simulation of transport in disordered and porous media requires microstructures covering several decades in length scale. X-ray and synchrotron computed tomography are presently unable to resolve more than one decade of geometric detail. Recent advances in pore scale modeling [Biswal, Held, Khanna, Wang, and Hilfer, Phys. Rev. E 80, 041301 (2009)] provide strongly correlated microstructures with several decades in microstructural detail. A carefully calibrated microstructure model for Fontainebleau sandstone has been discretized into a suite of three-dimensional microstructures with resolutions from roughly 128 $\mu$m down to roughly 500 nm. At the highest resolution the three-dimensional image consists of $32{768}^3=35184372088832$ discrete cubic volume elements with gray values between 0 and 216. To the best of our knowledge, this synthetic image is the largest computed tomogram of a porous medium available at present.

Ventricular fibrillation is a life-threatening cardiac arrhythmia which deserves quick and reliable detection as well as prediction from human electrocardiogram time series. We constructed networks of human ventricular time series with the visibility graph approach to study the network subgraph phenomenon and motif ranks. Our results show that different dominant motifs exist as an effective indicator in distinguishing ventricular fibrillations from normal sinus rhythms of a subject. We verify the reliability of our findings in a large database with different time lengths and sampling frequencies, and design an onset predictor of ventricular fibrillations with reliable verifications.

In this paper we extend our previous work on the stochastic block model, a commonly used generative model for social and biological networks, and the problem of inferring functional groups or communities from the topology of the network. We use the cavity method of statistical physics to obtain an asymptotically exact analysis of the phase diagram. We describe in detail properties of the detectability-undetectability phase transition and the easy-hard phase transition for the community detection problem. Our analysis translates naturally into a belief propagation algorithm for inferring the group memberships of the nodes in an optimal way, i.e., that maximizes the overlap with the underlying group memberships, and learning the underlying parameters of the block model. Finally, we apply the algorithm to two examples of real-world networks and discuss its performance.

A chaotic network of size $N$ with delayed interactions which resembles a pseudoinverse associative memory neural network is investigated. For a load $\alpha =P/N<1$, where $P$ stands for the number of stored patterns, the chaotic network functions as an associative memory of $2P$ attractors with macroscopic basin of attractions which decrease with $\alpha$. At finite $\alpha$, a chaotic spin-glass phase exists, where the number of distinct chaotic attractors scales exponentially with $N$. Each attractor is characterized by a coexistence of chaotic behavior and freezing of each one of the $N$ chaotic units or freezing with respect to the $P$ patterns. Results are supported by large scale simulations of networks composed of Bernoulli map units and Mackey-Glass time delay differential equations.

Most real life bubble dynamics applications involve multiple bubbles, for example, in cavitation erosion prevention, ultrasonic baths, underwater warfare, and medical applications involving microbubble contrast agents. Most scientific dealings with bubble-bubble interaction focus on two similarly sized bubbles. In this study, the interaction between two oscillating differently sized bubbles (generated in tap water) is studied using high speed photography. Four types of bubble behavior were observed, namely, jetting toward each other, jetting away from each other, bubble coalescence, and a behavior termed the “catapult” effect. In-phase bubbles jet toward each other, while out-of-phase bubbles jet away from each other. There exists a critical phase difference that separates the two regimes. The behavior of the bubbles is fully characterized by their dimensionless separation distance, their phase difference, and their size ratio. It is also found that for bubbles with large size difference, the smaller bubble behaves similarly to a single bubble oscillating near a free surface.

An anisotropic shell model has been proposed for two-dimensional (2D) turbulence. It is similar to the 2D version of the Gledzer-Ohkitani-Yamada model but with the angular variable in wave-number space divided into three distinct directions representing structures elongated in different directions. In the case when the drive is isotropic the usual isotropic solution is recovered as the fixed point of this model. The Hasegawa-Mima limit of the model is considered in particular due to its relevance for 2D anisotropic systems such a quasigeostrophic and plasma turbulence. It is observed from this simple model that the anisotropy diminishes as a function of scale during the cascade process, and the maximum of the energy is not at the node that has maximum drive, but at a nearby node that is directly coupled to that one.

Droplets moving in meandering microchannels can serve as a passive and robust strategy to produce chaotic mixing of species in droplet-based microfluidics. In this paper, a simplified theoretical model is proposed for plug-shaped droplets moving in meandering microchannels at Stokes flow. With this model to provide the velocity field, particle tracking, which requires a large computation time, is performed directly and easily without interpolation. With this convenience, a broad survey of the parameter space is carried out to investigate chaotic mixing in plugs, including the channel curvature, the Peclet number, the viscosity ratio, and the plug length. The results show that in order to achieve rapid mixing in plugs in meandering microchannels, a large curvature, a small Peclet number, a moderate viscosity ratio, and a moderate plug length are preferred.

Local control of droplet formation with acoustic actuation in a microfluidic flow-focusing device is investigated, and the effects of acoustic voltage, frequency, flow-rate ratio, fluid viscosity, and flow vorticity are characterized. Acoustic actuation is provided to affect droplet breakup in the squeezing regime by imposing periodic oscillation to the fluid-fluid interface and, therefore, a periodic change in its curvature at the cross-junction of the device. Time reduction is observed for the three key stages of droplet breakup in the squeezing regime: dispersed phase flow-front advancement into the orifice, pressure buildup upstream and within the orifice together with liquid inflation downstream, and finally the thinning and pinch-off of the liquid thread. It is found that acoustic actuation has less of an effect on droplet size for the continuous phase with a higher viscosity due to the restrained interfacial vibration under a high shear stress environment. Periodic velocity flow fields within the dispersed phase at different phases of one oscillation cycle are calculated based on the results from phase-averaged microresolution-particle-image velocimetry (μPIV). The oscillation paths for the points of maximum vorticities of phase-averaged velocity components are traced, which reveals that the motion is mainly along the $y$ direction.