Radical-ion-pair reactions were recently shown to represent a rich biophysical laboratory for the application of quantum measurement theory methods and concepts. Here we show that radical-ion-pair reactions essentially form a nonlinear biochemical double-slit interferometer. Quantum coherence effects are visible when “which-path” information is limited, and the incoherent limit is approached when measurement-induced decoherence sets in. Based on this analogy with the optical double-slit experiment we derive and elaborate on the fundamental master equation of spin-selective radical-ion-pair reactions that covers the continuous range from complete incoherence to maximum singlet-triplet coherence.

The effect of sonic waves, in particular, ultrasonic radiation, on immiscible displacement in porous media and enhanced oil recovery has been of interest for more than five decades. Attempts were made to investigate the effect through core scale experimental or theoretical models. Visual experiments are useful to scrutinize the reason for improved oil recovery under acoustic waves of different frequency but are not abundant in literature. In this paper, we report observations and analyses as to the effects of ultrasonic energy on immiscible displacement and interaction of the fluid matrix visually in porous media through two-dimensional (2D) sand pack experiments. 2D glass bead models with different wettabilities were saturated with different viscosity oils and water was injected into the models. The experiments were conducted with and without ultrasound. Dynamic water injection experiments were preferred as they had both viscous and capillary forces in effect. The displacement patterns were evaluated both in terms of their shape, size, and the interface characteristics quantitatively and qualitatively to account for the effects of ultrasonic waves on the displacement and the reason for increased oil production under this type of sonic wave. More compact clusters were observed when ultrasonic energy was present in water-wet systems. In the oil-wet cases, more oil was produced after breakthrough when ultrasound was applied and no compact clusters were formed in contrast to the water-wet cases.

We study the behavior of pressure-driven flow in a cylindrical nanochannel patterned with different wettability using molecular dynamics simulations. We consider the flow perpendicular or parallel to the periodic stripes of wetting and nonwetting materials. For both geometries, we observe a sharp increase in the longitudinal velocity of the flow as wetting stripe width decreases, which is clearly distinguishable from the case of shear-driven flow. When the channel wall is spirally patterned with distinct wetting stripes, the transverse velocity of the flow is generated in the channel and its generation depends strongly on the degree of molecular ordering above the wetting stripes, which can be controlled by helical angle, wetting stripe width, the relative area of the wetting region, and the strength of the fluid-wall interaction.

The pinch-off of an air bubble from an underwater nozzle ends in a singularity with a remarkable sensitivity to a variety of perturbations. I report on experiments that break both the axial (i.e., vertical) and azimuthal symmetry of the singularity formation. The density of the inner gas influences the axial asymmetry of the neck near pinch-off. For denser gases, flow through the neck late in collapse changes the pinch-off dynamics. Gas density is also implicated in the formation of satellite bubbles. The azimuthal shape oscillations described by Schmidt et al. can be initiated by anisotropic boundary conditions in the liquid as well as with an asymmetric nozzle shape. I measure the $n=3$ oscillatory mode and observe the nonlinear, highly three-dimensional outcomes of pinch-off with large azimuthal perturbations. These are consistent with prior theory.

We consider the problem of inferring the interactions between a set of $N$ binary variables from the knowledge of their frequencies and pairwise correlations. The inference framework is based on the Hopfield model, a special case of the Ising model where the interaction matrix is defined through a set of patterns in the variable space, and is of rank much smaller than $N$. We show that maximum likelihood inference is deeply related to principal component analysis when the amplitude of the pattern components $\xi$ is negligible compared to $\sqrt{N}$. Using techniques from statistical mechanics, we calculate the corrections to the patterns to the first order in $\xi /\sqrt{N}$. We stress the need to generalize the Hopfield model and include both attractive and repulsive patterns in order to correctly infer networks with sparse and strong interactions. We present a simple geometrical criterion to decide how many attractive and repulsive patterns should be considered as a function of the sampling noise. We moreover discuss how many sampled configurations are required for a good inference, as a function of the system size $N$ and of the amplitude $\xi$. The inference approach is illustrated on synthetic and biological data.

This paper presents an analytical study of the coexistence of different transport regimes in quasi-one-dimensional surface-disordered waveguides (or electron conductors). To elucidate main features of surface scattering, the case of two open modes (channels) is considered in great detail. Main attention is paid to the transmission in dependence on various parameters of the model with two types of rough-surface profiles (symmetric and antisymmetric). It is shown that depending on the symmetry, basic mechanisms of scattering can be either enhanced or suppressed. As a consequence, different transport regimes can be realized. Specifically, in the two-mode waveguide with symmetric rough boundaries, there are ballistic, localized and coexistence transport regimes. In the waveguide with antisymmetric roughness of lateral walls, another regime of the diffusive transport can arise. Our study allows to reveal the interplay between all relevant scattering mechanisms, in particular, the role of the so-called square-gradient scattering which is typically neglected in literature, however, can give a strong impact to the transmission.

Neural networks can learn flexible input-output associations by changing their synaptic weights. The representational performance and learning dynamics of neural networks are intensively studied in several fields. Neural networks face the “credit assignment problem” in situations in which only incomplete performance evaluations are available. The credit assignment problem is that a network should assign credit or blame for its behaviors according to the contribution to the network performance. In reinforcement learning, a scalar evaluation signal is delivered to a network. The two main types of credit assignment problems in reinforcement learning are structural and temporal, that is, which parameters of the network (structural) and which past network activities (temporal) are related to an evaluation signal given from an environment. In this study, we apply statistical mechanical analysis to the learning processes in a simple neural network model to clarify the effects of two kinds of credit assignments and their interactions. Our model is based on node perturbation learning with eligibility trace. Node perturbation is a stochastic gradient learning method that can solve structural credit assignment problems by introducing a perturbation into the system output. The eligibility trace preserves the past network activities with a temporal credit to deal with the delay of an instruction signal. We show that both credit assignment effects mutually interact and the optimal time constant of the eligibility trace varies not only for the evaluation delay but also the network size.

We present a minimal dynamical model for randomly branched isotropic polymers, and we study this model in the framework of renormalized field theory. For the swollen phase, we show that our model provides a route to understand the well-established dimensional-reduction results from a different angle. For the collapse $\theta$ transition, we uncover a hidden Becchi-Rouet-Stora supersymmetry, signaling the sole relevance of tree configurations. We correct the long-standing one-loop results for the critical exponents, and we push these results on to two-loop order. For the collapse ${\theta }^{\prime }$ transition, we find a runaway of the renormalization group flow, which lends credence to the possibility that this transition is a fluctuation-induced first-order transition. Our dynamical model allows us to calculate for the first time the fractal dimension of the shortest path on randomly branched polymers in the swollen phase as well as at the collapse transition and related fractal dimensions.

Networks composed from both connectivity and dependency links were found to be more vulnerable compared to classical networks with only connectivity links. Their percolation transition is usually of a first order compared to the second-order transition found in classical networks. We analytically analyze the effect of different distributions of dependencies links on the robustness of networks. For a random Erdös-Rényi (ER) network with average degree $k$ that is divided into dependency clusters of size $s$, the fraction of nodes that belong to the giant component $P_{\infty }$ is given by $P_{\infty }=p^{s-1}[1-\exp (-{\mathit{kpP}}_{\infty })]{}^s$, where $1-p$ is the initial fraction of removed nodes. Our general result coincides with the known Erd$\mathrm{ö}$s-Rényi equation for random networks for $s=1$. For networks with Poissonian distribution of dependency links we find that $P_{\infty }$ is given by $P_{\infty }=f_{k,p}(P_{\infty })e^{(\langle s\rangle -1)[{\mathit{pf}}_{k,p}(P_{\infty })-1]}$, where $f_{k,p}(P_{\infty })\equiv 1-\exp (-{\mathit{kpP}}_{\infty })$ and $\langle s\rangle$ is the mean value of the size of dependency clusters. For networks with Gaussian distribution of dependency links we show how the average and width of the distribution affect the robustness of the networks.

A previous paper [Y. Farjoun and J. C. Neu, Phys. Rev. E 78, 051402 (2008)] presents a simple kinetic model of the initial creation transient, starting from pure monomer. During this transient the majority of clusters are created, and the distribution of cluster sizes that emerges from it is predicted to be discontinuous at the largest cluster size. It is well known that the further evolution according to the Lifshitz-Slyozov model of coarsening preserves this discontinuity. The result is at odds with the original proposal of Lifshitz and Slyozov, that the physical late-stage coarsening distribution is the smooth one. The current paper presents an analytic-numerical solution of the Lifshitz-Slyozov equations, starting from the discontinuous creation distribution. Of course, this analysis selects the discontinuous late-stage coarsening distribution, but there is much more. It resolves the intermediate stages between the creation transient and late-state coarsening and provides specific scales of time and cluster size that characterize the onset of coarsening.

We present in this paper a detailed analysis of the flexoelectric instability of a planar nematic layer in the presence of an alternating electric field (frequency $\omega$), which leads to stripe patterns (flexodomains) in the plane of the layer. This equilibrium transition is governed by the free energy of the nematic, which describes the elasticity with respect to the orientational degrees of freedom supplemented by an electric part. Surprisingly the limit $\omega \to 0$ is highly singular. In distinct contrast to the dc case, where the patterns are stationary and time independent, they appear at finite, small $\omega$ periodically in time as sudden bursts. Flexodomains are in competition with the intensively studied electrohydrodynamic instability in nematics, which presents a nonequilibrium dissipative transition. It will be demonstrated that $\omega$ is a very convenient control parameter to tune between flexodomains and convection patterns, which are clearly distinguished by the orientation of their stripes.

We propose an alternate measure of information, called superinformation, which has been found to be very effective for analyzing the coding and noncoding regions of the DNA. This superinformation is actually a measure of the “randomness of randomness.” It has been found to be highly accurate in classifying coding and noncoding regions of human DNA. In the proposed method, no prior training is required. This technique exhibits higher accuracy than previously reported techniques in distinguishing between the coding and the noncoding portions of the DNA. Superinformation can also be used to analyze the untranslated regions in various genes.

Spiral waves in excitable systems decay to drifting defects if forced by high-frequency wave trains. Using the Barkley model we analyze the drift velocity in planar wave trains as a function of wave frequency. Within two antiparallel, planar wave trains of equal frequency a defect is pushed into the collision region where it stops. Within two circular wave fields, however, it continues its drift in a direction perpendicular to the axis connecting the pacemakers. Depending on the forcing frequency and the initial position, this motion occurs either away from or toward the pacemaker axis. Three circular wave fields can be used to position the defect at a unique point close to the center of the pacemaker triangle. The results are also observed in experiments with the Belousov-Zhabotinsky reaction.

This numerical study of an axisymmetric motion of a viscous incompressible fluid in an elongated cylindrical container explains how a swirling inflow develops the global meridional circulation and two U-shaped throughflows (TFs). For moderate values of the Reynolds (Re) number, there is a single U-shaped TF: The fluid moves from the peripheral annular inlet near the sidewall to the dead end, turns around, goes back near the axis, and leaves the container through the central exhaust. As Re increases, vortex breakdown occurs near the dead end. If the exhaust orifice is wide, the ambient fluid is sucked into the container near its axis, reaches the dead-end vicinity, merges with the U-shaped TF, and goes back inside an annular region. Thus, a double counterflow develops, where the fluid moves to the dead end near both the sidewall and the axis and goes back in between. The physical mechanism of the double counterflow is a swirl decay combined with the focused flow convergence near the dead end. This double counterflow is beneficial for combustion applications.

Transient dynamics of spiral waves in a two-dimensional Barkley model is shown to be governed by pattern formation processes resulting in regions of synchronized activity separated by moving interfaces. During the transient the number of internally synchronized regions decreases as synchronization fronts move to the boundary of the simulated area. This spatiotemporal transient dynamics in an excitable medium is detected and visualized by means of an analysis of the local periodicity and by evaluation of prediction errors across the spatial domain. During the (long) transient both analyses show patterns that must not be misinterpreted as any information about (spatial) structure of the underlying (completely homogeneous) system.

Sequences of events in noise-driven excitable systems with slow variables often show serial correlations among their intervals of events. Here, we employ a master equation for generalized non-renewal processes to calculate the interval and count statistics of superimposed processes governed by a slow adaptation variable. For an ensemble of neurons with spike-frequency adaptation, this results in the regularization of the population activity and an enhanced postsynaptic signal decoding. We confirm our theoretical results in a population of cortical neurons recorded in vivo.

DNA denaturation has been a subject of intense study due to its relationship to DNA transcription and its fundamental importance as a nonlinear structural transition. Many aspects of this phenomenon, however, remain poorly understood. Existing models fit quite well with experimental results on the fraction of unbound base pairs versus temperature, but yield incorrect results for other essential quantities such as the base pair fluctuation time scales. Here we demonstrate that nanoscale thermal transport can serve as a sensitive probe of the underlying microscopic physics responsible for the dynamics of DNA denaturation. Specifically, we show that the heat transport properties of DNA are altered significantly as it denatures, and this alteration encodes detailed information on the dynamics of thermal fluctuations and their interaction along the strand. This finding allows for the discrimination between models of DNA denaturation and will help shed new light on the nonlinear vibrational dynamics of this important molecule.

The problem of the boundary effect for the $k$-nearest-neighbor ($k$NN) estimation is addressed, and a correction method is suggested. The correction is proposed for bounded distributions, but it can be used for any set of bounded samples. We apply the proposed correction to entropy estimation of multidimensional distributions and time series, and this correction reduces considerably the bias and statistical errors in the estimation. For a small sample size or high-dimensional data, the corrected estimator outperforms the uncorrected estimator significantly. This advantage makes the $k$NN method applicable to more real-life situations, e.g., the analysis of biological and molecular data.

We propose a method to analyze couplings between two simultaneously measured time series. Our approach is based on conditional mutual sorting information. It is related to other concepts for detecting coupling directions: the old idea of Marko for directed information and the more recent concept of Schreiber’s transfer entropy. By setting suitable conditions we first of all consider momentary information in both time series. This enables the detection not only of coupling directions but also delays. Sorting information refers to ordinal properties of time series, which makes the analysis robust with respect to strictly monotonous distortions and thus very useful in the analysis of proxy data in climatology. Fortunately, ordinal analysis is easy and fast to compute. We consider also the problem of reliable estimation from finite time series.

We perform a molecular dynamics simulation study of the behavior of a lipid coating layer on an oscillating bubble surface. Micrometer sized bubbles, stabilized with a lipid monolayer coating, are used in acoustic imaging as a contrast agent. The coating layer is expected to be strongly influenced by the oscillation of the bubble in the high frequency sound field, with a period of a microsecond. The typical time scale of molecular motion, however, is of the order of femtoseconds. One of the challenges is to bridge this nine decade gap in time scales. To this end we have developed a model that is highly coarse grained, but still features the essential mechanisms determining lipid dynamics, with time scales of picoseconds. This approach allows us to severely restrict the computing times, although we make use of very modest computing equipment. We show in our simulation that the amphiphilic monolayer folds upon contraction of the bubble, and forms micellar aggregates at the air-water interface. Some micellar structures survive consecutive re-expansion and indeed remain persistent over several cycles. These structures may add to the anisotropic behavior of the bubbles under oscillating conditions. We also investigated temperature and frequency dependence.