We generalize the Green-Kubo approach, previously applied to bulk systems of spherically symmetric active particles [J. Chem. Phys. 145, 161101 (2016)], to include spatially inhomogeneous activity. The method is applied to predict the spatial dependence of the average orientation per particle and the density. The average orientation is given by an integral over the self part of the Van Hove function and a simple Gaussian approximation to this quantity yields an accurate analytical expression. Taking this analytical result as input to a dynamic density functional theory approximates the spatial dependence of the density in good agreement with simulation data. All theoretical predictions are validated using Brownian dynamics simulations.

The wetting of a charged wedgelike wall by an electrolyte solution is investigated by means of classical density functional theory. As in other studies on wedge wetting, this geometry is considered as the most simple deviation from a planar substrate, and it serves as a first step toward more complex confinements of fluids. By focusing on fluids containing ions and surface charges, features of real systems are covered that are not accessible within the vast majority of previous theoretical studies concentrating on simple fluids in contact with uncharged wedges. In particular, the filling transition of charged wedges is necessarily of first order, because wetting transitions of charged substrates are of first order and the barrier in the effective interface potential persists below the wetting transition of a planar wall; hence, critical filling transitions are not expected to occur for ionic systems. The dependence of the critical opening angle on the surface charge, as well as the dependence of the filling height, of the wedge adsorption, and of the line tension on the opening angle and on the surface charge are analyzed in detail.

The direct problem of optoacoustic signal generation in biological media consists of solving an inhomogeneous three-dimensional (3D) wave equation for an initial acoustic stress profile. In contrast, the more defiant inverse problem requires the reconstruction of the initial stress profile from a proper set of observed signals. In this article, we consider an effectively 1D approach, based on the assumption of a Gaussian transverse irradiation source profile and plane acoustic waves, in which the effects of acoustic diffraction are described in terms of a linear integral equation. The respective inverse problem along the beam axis can be cast into a Volterra integral equation of the second kind for which we explore here efficient numerical schemes in order to reconstruct initial stress profiles from observed signals, constituting a methodical progress of computational aspects of optoacoustics. In this regard, we explore the validity as well as the limits of the inversion scheme via numerical experiments, with parameters geared toward actual optoacoustic problem instances. The considered inversion input consists of synthetic data, obtained in terms of the effectively 1D approach, and, more generally, a solution of the 3D optoacoustic wave equation. Finally, we also analyze the effect of noise and different detector-to-sample distances on the optoacoustic signal and the reconstructed pressure profiles.

Synchrotron diffuse x-ray scattering data reveal a dramatic softening of the molecular tilt modulus $K_{\theta }$ of the model biomembrane composed of DMPC lipids as the temperature is lowered towards the main phase transition temperature at $T_M={24}^{\circ }\mathrm{C}$. Spontaneous tilt occurs below $T_M$, suggesting that tilt is a symmetry breaking order parameter. Consistent with this hypothesis, it is also found that a different lipid POPS has no spontaneous tilt below its $T_M$ at ${14}^{\circ }\mathrm{C}$ and correspondingly its tilt modulus did not soften as $T_M$ was approached from above. As previously known, the bending modulus $K_C$ of DMPC also softens close to $T_M$, but unlike the tilt modulus, $K_C$ has a maximum $3^{\circ }$ above $T_M$, which also marks the limit of the well-known anomalous swelling regime. Tilt adds a different perspective to our previous understanding of the main phase transition in lipid bilayers.

Expanding media are typical in many different fields, e.g., in biology and cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties such as the set of positional moments and the Green's function. Here, we focus on the characterization of such effects when the diffusion process is described by the continuous-time random-walk (CTRW) model. As is well known, when the medium is static this model yields anomalous diffusion for a proper choice of the probability density function (pdf) for the jump length and the waiting time, but the behavior may change drastically if a medium expansion is superimposed on the intrinsic random motion of the diffusing particle. For the case where the jump length and the waiting time pdfs are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including Lévy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. In the specific case of a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This “big crunch” effect, totally absent in the case of normal diffusion, stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model in an expanding medium. From this hierarchy, the full time evolution of the second-order moment is obtained for some specific types of expansion. In the case of an exponential expansion, exact recurrence relations for the Laplace-transformed moments are obtained, whence the long-time behavior of moments of arbitrary order is subsequently inferred. Our analytical and numerical results for both Lévy flights and subdiffusive CTRWs confirm the intuitive expectation that the medium expansion hinders the mixing of diffusive particles occupying separate regions. In the case of Lévy flights, we quantify this effect by means of the so-called “Lévy horizon.”

We derive the nonlinear equations that describe coupled drift waves and ion acoustic waves in a plasma. We show that when the coupling to ion acoustic waves is negligible, the reduced nonlinear equation is a generalization of the Hasegawa-Mima equation to the three-dimensional (3D) case. We find an exact analytical solution of this equation in the form of a 3D soliton drift wave (3D modon). By numerical simulations we study collisions between the modons and show that the collisions can be fully elastic.

In a wide range of complex networks, the links between the nodes are temporal and may sporadically appear and disappear. This temporality is fundamental to analyzing the formation of paths within such networks. Moreover, the presence of the links between the nodes is a random process induced by nature in many real-world networks. In this paper, we study random temporal networks at a microscopic level and formulate the probability of accessibility from a node $i$ to a node $j$ after a certain number of discrete time units $T$. While solving the original problem is computationally intractable, we provide an upper and two lower bounds on this probability for a very general case with arbitrary time-varying probabilities of the links' existence. Moreover, for a special case where the links have identical probabilities across the network at each time slot, we obtain the exact probability of accessibility between any two nodes. Finally, we discuss scenarios where the information regarding the presence and absence of links is initially available in the form of time duration (of presence or absence intervals) continuous probability distributions rather than discrete probabilities over time slots. We provide a method for transforming such distributions to discrete probabilities, which enables us to apply the given bounds in this paper to a broader range of problem settings.

We present a one-dimensional numerical model based on elastically coupled sliders on a frictional incline of variable tilt. This very simple approach makes it possible to study the precursors to the avalanche and to provide a rationalization of different features that have been observed in experiments. We provide a statistical description of the model leading to master equations describing the state of the system as a function of the angle of inclination. Our central results are the reproduction of large-scale regular events preceding the avalanche, on the one hand, and an analytical approach providing an internal threshold for the outbreak of rearrangements before the avalanche in the system, on the other hand.

Inspired by recent experiments on the organism Caenorhabditis elegans we present a stochastic problem to capture the adaptive dynamics of search in living beings, which involves the exploration-exploitation dilemma between remaining in a previously preferred area and relocating to new places. We assess the question of search efficiency by introducing a new magnitude, the mean valuable territory covered by a Browinan searcher, for the case where each site in the domain becomes valuable only after a random time controlled by a nonhomogeneous rate which expands from the origin outwards. We explore analytically this magnitude for domains of dimensions 1, 2, and 3 and discuss the theoretical and applied (biological) interest of our approach. As the main results here, we (i) report the existence of some universal scaling properties for the mean valuable territory covered as a function of time and (ii) reveal the emergence of an optimal diffusivity which appears only for domains in two and higher dimensions.

I study in detail the quantum Sherrington-Kirkpatrick (SK) model, i.e., the infinite-range Ising spin glass in a transverse field, by solving numerically the effective one-dimensional model that the quantum SK model can be mapped to in the thermodynamic limit. I find that the replica symmetric solution is unstable down to zero temperature, in contrast to some previous claims, and so there is not only a line of transitions in the (longitudinal) field-temperature plane (the de Almeida–Thouless, AT, line) where replica symmetry is broken, but also a quantum de Almeida–Thouless (QuAT) line in the transverse field-longitudinal field plane at $T=0$. If the QuAT line also occurs in models with short-range interactions its presence might affect the performance of quantum annealers when solving spin glass-type problems with a bias (i.e., magnetic field).

The one-dimensional pair contact process with diffusion (PCPD), an interacting particle system with diffusion, pair annihilation, and creation by pairs, has defied consensus about the universality class to which it belongs. An argument by Hinrichsen [Physica A 361, 457 (2006)] claims that freely diffusing particles in the PCPD should play the same role as frozen particles when it comes to the critical behavior. Therefore, the PCPD is claimed to have the same critical phenomena as a model with infinitely many absorbing states that belongs to the directed percolation (DP) universality class. To investigate if diffusing particles are really indistinguishable from frozen particles in the sense of the renormalization group, we study numerically a variation of the PCPD by introducing a nonorder field associated with infinitely many absorbing states. We find that a crossover from the PCPD to DP occurs due to the nonorder field. By studying a similar model, we exclude the possibility that the mere introduction of a nonorder field to one model can entail a nontrivial crossover to another model in the same universality class, thus we attribute the observed crossover to the difference of the universality class of the PCPD from the DP class.

We study the two-dimensional antiferromagnetic Ising model with a purely imaginary magnetic field, which can be thought of as a toy model for the usual $\theta$ physics. Our motivation is to have a benchmark calculation in a system which suffers from a strong sign problem, so that our results can be used to test Monte Carlo methods developed to tackle such problems. We analyze here this model by means of analytical techniques, computing exactly the first eight cumulants of the expansion of the effective Hamiltonian in powers of the inverse temperature, and calculating physical observables for a large number of degrees of freedom with the help of standard multiprecision algorithms. We report accurate results for the free energy density, internal energy, standard and staggered magnetization, and the position and nature of the critical line, which confirm the mean-field qualitative picture, and which should be quantitatively reliable, at least in the high-temperature regime, including the entire critical line.

Using molecular dynamics simulations and nonequilibrium thermodynamic-integration techniques we compute the Helmholtz free energies of the body-centered-cubic (bcc), face-centered-cubic (fcc), hexagonal close-packed, and fluid phases of the Uhlenbeck-Ford model (UFM) and use the results to construct its phase diagram. The pair interaction associated with the UFM is characterized by an ultrasoft, purely repulsive pair potential that diverges logarithmically at the origin. We find that the bcc and fcc are the only thermodynamically stable crystalline phases in the phase diagram. Furthermore, we report the existence of two reentrant transition sequences as a function of the number density, one featuring a fluid-bcc-fluid succession and another displaying a bcc-fcc-bcc sequence near the triple point. We find strong resemblances to the phase behavior of other soft, purely repulsive systems such as the Gaussian-core model (GCM), inverse-power-law, and Yukawa potentials. In particular, we find that the fcc-bcc-fluid triple point and the phase boundaries in its vicinity are in good agreement with the prediction supplied by a recently proposed corresponding-states principle [J. Chem. Phys. 134, 241101 (2011); Europhys. Lett. 100, 66004 (2012)]. The particularly strong resemblance between the behavior of the UFM and GCM models are also discussed.

Two-time correlation functions of a system of Bose particles are studied. We find a relation of zeros of the correlation functions with the Lee-Yang zeros of the partition function of the system. The obtained relation gives the possibility to observe the Lee-Yang zeros experimentally. A particular case of Bose particles on two levels is examined, and zeros of two-time correlation functions and Lee-Yang zeros of the partition function of the system are analyzed.

We study the transport and diffusion properties of passive inertial particles described by a six-dimensional dissipative bailout embedding map. The base map chosen for the study is the three-dimensional incompressible Arnold-Beltrami-Childress (ABC) map chosen as a representation of volume preserving flows. There are two distinct cases: the two-action and the one-action cases, depending on whether two or one of the parameters $(A,B,C)$ exceed 1. The embedded map dynamics is governed by two parameters ($\alpha ,\gamma$), which quantify the mass density ratio and dissipation, respectively. There are important differences between the aerosol $(\alpha <1)$ and the bubble $(\alpha >1)$ regimes. We have studied the diffusive behavior of the system and constructed the phase diagram in the parameter space by computing the diffusion exponents $\eta$. Three classes have been broadly classified—subdiffusive transport ($\eta <1$), normal diffusion ($\eta \approx 1$), and superdiffusion ($\eta >1$) with $\eta \approx 2$ referred to as the ballistic regime. Correlating the diffusive phase diagram with the phase diagram for dynamical regimes seen earlier, we find that the hyperchaotic bubble regime is largely correlated with normal and superdiffusive behavior. In contrast, in the aerosol regime, ballistic superdiffusion is seen in regions that largely show periodic dynamical behaviors, whereas subdiffusive behavior is seen in both periodic and chaotic regimes. The probability distributions of the diffusion exponents show power-law scaling for both aerosol and bubbles in the superdiffusive regimes. We further study the Poincáre recurrence times statistics of the system. Here, we find that recurrence time distributions show power law regimes due to the existence of partial barriers to transport in the phase space. Moreover, the plot of average particle kinetic energies versus the mass density ratio for the two-action case exhibits a devil's staircase–like structure for higher dissipation values. We explain these results and discuss their implications for realistic systems.

Recurrent networks are trained to memorize their input better, often in the hopes that such training will increase the ability of the network to predict. We show that networks designed to memorize input can be arbitrarily bad at prediction. We also find, for several types of inputs, that one-node networks optimized for prediction are nearly at upper bounds on predictive capacity given by Wiener filters and are roughly equivalent in performance to randomly generated five-node networks. Our results suggest that maximizing memory capacity leads to very different networks than maximizing predictive capacity and that optimizing recurrent weights can decrease reservoir size by half an order of magnitude.

Cell migration in morphogenesis and cancer metastasis typically involves interplay between different cell types. We construct and study a minimal, one-dimensional model composed of two different motile cells with each cell represented as an active elastic dimer. The interaction between the two cells via cadherins is modeled as a spring that can rupture beyond a threshold force as it undergoes dynamic loading from the interacting motile cells. We obtain a phase diagram consisting of chase-and-run dynamics and clumping dynamics as a function of the stiffness of the interaction spring and the threshold force and, therefore, posit that active rupture, or rupture via active forces, is a mechanosensitive means to regulate dynamics between cells. Since the parameters in the model differentiate between N- and E-cadherins, we make predictions for the interactions between a placodelike cell and a neural crestlike cell in a microchannel as well as discuss how our results inform chase-and-run dynamics found in a group of placode cells interacting with a group of neural crest cells. In particular, an argument was made in the latter case that the feedback between cadherins and cell-substrate interaction via integrins was necessary to obtain the chase-and-run behavior. Based on our two-cell results, we argue that this feedback accentuates, but is not necessary for, the chase-and-run behavior.

In the present work we have gone a step forward in the understanding of the DNA-cisplatin interaction, investigating the role of the ionic strength on the complexes formation. To achieve this task, we use optical tweezers to perform force spectroscopy on the DNA-cisplatin complexes, determining their mechanical parameters as a function of the drug concentration in the sample for three different buffers. From such measurements, we determine the binding parameters and study their behavior as a function of the ionic strength. The equilibrium binding constant decreases with the counterion concentration ([Na]) and can be used to estimate the effective net charge of cisplatin in solution. The cooperativity degree of the binding reaction, on the other hand, increases with the ionic strength, as a result of the different conformational changes induced by the drug on the double-helix when binding under different buffer conditions. Such results can be used to modulate the drug binding to DNA, by appropriately setting the ionic strength of the surrounding buffer. The conclusions drawn provide significant new insights on the complex cooperative interactions between the DNA molecule and the class of platinum-based compounds, much used in chemotherapies.

Bacterial species are known to show chemotaxis, i.e., the directed motions in the presence of certain chemicals, whereas the motion is random in the absence of those chemicals. The bacteria modulate their run time to induce chemotactic drift towards the attractant chemicals and away from the repellent chemicals. However, the existing theoretical knowledge does not exhibit a proper match with experimental validation, and hence there is a need for developing alternate models and validating experimentally. In this paper a more robust theoretical model is proposed to investigate chemotactic drift of peritrichous Escherichia coli under an exponential nutrient gradient. An exponential gradient is used to understand the steady state behavior of drift because of the logarithmic functionality of the chemosensory receptors. Our theoretical estimations are validated through the experimentation and simulation results. Thus, the developed model successfully delineates the run time, run trajectory, and drift velocity as measured from the experiments.