Thermal fluctuations renormalize the bending elasticity of lipid bilayers. This well-studied effect is a cornerstone in the study of several membrane biophysical phenomena. Analogously, nearly all membranes are endowed with an electromechanical coupling called flexoelectricity that admits membrane polarization due to curvature changes. Flexoelectricity is found to be important in a number of biological functions, including hearing, ion transport, and in some situations where mechanotransduction is necessary. Very little is known about the interplay between thermal fluctuations and flexoelectricity. In this work, we explore how the apparent flexoelectricity is altered due to thermal fluctuations and, further, how the elastic and dielectric properties are renormalized due to flexoelectricity. We find that the apparent bending rigidity is softened by flexoelectricity and discuss the ramifications for interpreting existing experimental work.

In experiments and in simulations, the free energy of a state of a system can be determined from the probability that the state is occupied. However, it is often necessary to impose a biasing potential on the system so that high energy states are sampled with sufficient frequency. The unbiased energy is typically obtained from the data using the weighted histogram analysis method (WHAM). Here we present differential energy surface analysis (DESA), in which the gradient of the energy surface, $dE/dx$, is extracted from data taken with a series of harmonic biasing potentials. It is shown that DESA produces a maximum likelihood estimate of the folding landscape gradient. DESA is demonstrated by analyzing data from a simulated system as well as data from a single-molecule unfolding experiment in which the end-to-end distance of a DNA hairpin is measured. It is shown that the energy surface obtained from DESA is indistinguishable from the energy surface obtained when WHAM is applied to the same data. Two criteria are defined which indicate whether the DESA results are self-consistent. It is found that these criteria can detect a situation where the energy is not a single-valued function of the measured reaction coordinate. The criteria were found to be satisfied for the experimental data analyzed, confirming that end-to-end distance is a good reaction coordinate for the experimental system. The combination of DESA and the optical trap assay in which a structure is disrupted under harmonic constraint facilitates an extremely accurate measurement of the folding energy surface.

Exact rogue wave solutions of the coupled Hirota equations are obtained by using a Darboux dressing transformation. An analysis of the spectral parameter condition shows that our coupled rogue waves, equal or unequal in background height, always exist no matter what parameters have been chosen for the starting plane waves. We demonstrate that, compared with the decoupled ones, the coupled rogue waves can appear in a rather striking way, i.e., one wave exhibits a centrally humped structure, while the other may feature one single hole in the center—a dark rogue wave structure. It is expected that these unusual rogue wave structures due to the two-wave coupling may help explain the extreme wave events in deep ocean or other nonlinear dispersive media.

In a recent Letter [P. K. Shukla and B. Eliasson, Phys. Rev. Lett. 108, 165007 (2012)] the discovery of a new attractive force between protons in a hydrogen plasma was reported that would be responsible for the formation of molecules and of a proton lattice. Here we show, based on ab initio density functional calculations and general considerations, that these predictions are not correct and caused by using linearized quantum hydrodynamics beyond the limits of its applicability.

A microscopic theory is adapted to compute the time-resolved terahertz (THz) probe response of a dynamically evolving, strong-field ionized electron-ion plasma. The numerical solutions show that the relaxation of the initially highly anisotropic carrier distributions leads to a polarization dependent short-time THz response. This THz polarization discrimination gradually vanishes as the plasma approaches a thermodynamic equilibrium configuration via electron-electron and electron-ion scattering. The detailed carrier-relaxation dynamics causes a strongly nonmonotonic time-development of the THz absorption.

We study the minimal thermodynamically consistent model for an adaptive machine that transfers particles from a higher chemical potential reservoir to a lower one. This model describes essentials of the inhomogeneous catalysis. It is supposed to function with the maximal current under uncertain chemical potentials: if they change, the machine tunes its own structure fitting it to the maximal current under new conditions. This adaptation is possible under two limitations: (i) The degree of freedom that controls the machine's structure has to have a stored energy (described via a negative temperature). The origin of this result is traced back to the Le Chatelier principle. (ii) The machine has to malfunction at a constant environment due to structural fluctuations, whose relative magnitude is controlled solely by the stored energy. We argue that several features of the adaptive machine are similar to those of living organisms (energy storage, aging).

We investigate the energy landscape of two- and three-dimensional $XY$ models with nearest-neighbor interactions by analytically constructing several classes of stationary points of the Hamiltonian. These classes are analyzed, in particular with respect to possible signatures of the thermodynamic phase transitions of the models. We find that, even after explicitly breaking the global $O\left(2\right)$ symmetry of the $XY$ spins, an exponentially large class of stationary points are singular and occur in continuous one-parameter families. This property may complicate the use of theoretical tools developed for the investigation of phase transitions based on stationary points of the energy landscape, and we discuss strategies to avoid these difficulties.

We study the critical behavior of the absorbing-state phase transition depicted by a contact process one-dimensional model system with power-law decaying interactions. The system dynamical processes include particle creation at a rate which decays with the distance from the nearest particle as $1/r^{\alpha }$. This model displays an absorbing-state phase transition with critical exponents varying continuously with the interaction exponent $\alpha$. Here, we provide a finite-size scaling analysis of the stationary order-parameter density, one of its moment ratio, its logarithmic derivative, and fluctuations. We also follow the short-time relaxation dynamic of these quantities to estimate their corresponding dynamical critical exponents. The estimated exponents are shown to be consistent with the hyperscaling relation. Further, we report an unconventional regime on which the critical order-parameter fluctuations vanish in the thermodynamic limit.

We investigate phase separation of near-critical binary mixtures between parallel symmetric walls in the strong adsorption regime. We take into account the renormalization effect due to the critical fluctuations using the recent local functional theory [Okamoto and Onuki, J. Chem. Phys. 136, 114704 (2012)]. In statics, a van der Waals loop is obtained in the relation between the average order parameter $\langle \psi \rangle$ in the film and the chemical potential when the temperature $T$ is lower than the film critical temperature $T_c^{\mathrm{ca}}$ (in the case of an upper critical solution temperature). In dynamics, we lower $T$ below the capillary condensation line from above $T_c^{\mathrm{ca}}$. We calculate the subsequent time development assuming no mass exchange between the film and the reservoir. In the early stage, the order parameter $\psi$ changes only in the direction perpendicular to the walls. For sufficiently deep quenching, such one-dimensional profiles become unstable with respect to the fluctuations varying in the lateral directions. The late-stage coarsening is then accelerated by the hydrodynamic interaction. A pancake domain of the phase disfavored by the walls finally appears in the middle of the film.

Dissipative particle dynamics (DPD) is becoming a popular particle-based method to study flow through microchannels due to the ease with which the presence of biological cells or DNA chains can be modeled. Many lab-on-a-chip devices require the ability to manipulate the transport of cells or DNA chains in the fluid flow. Microchannel surfaces coated with combinations of hydrophilic and hydrophobic materials have been found useful for this purpose. In this work we study numerically the hydrodynamics of a steady nonuniform developing flow between two infinite parallel plates with hydrophilic and hydrophobic surfaces using the DPD. The hydrophobic and hydrophilic surfaces are modeled using partial-slip and no-slip boundary conditions, respectively, in the simulations. We also propose a method to model the inflow and outflow boundaries for the DPD simulations. The simulation results of the developing flow are in good agreement with analytical solutions from continuum theory for no-slip and partial-slip surfaces. The entrance region constitutes a considerable fraction of the channel length in miniaturized devices. Thus it is desirable for the length of the developing region to be short as most microfluidic devices such as cell or DNA separators and mixers are designed for the developed flow field. We study the effect of a hydrophilic strip near the inlet of a hydrophobic microchannel on the developing length. We find that the presence of the hydrophilic strip significantly reduces the developing length.

We develop a method to infer log-normal random fields from measurement data affected by Gaussian noise. The log-normal model is well suited to describe strictly positive signals with fluctuations whose amplitude varies over several orders of magnitude. We use the formalism of the minimum Gibbs free energy to derive an algorithm that uses the signal's correlation structure to regularize the reconstruction. The correlation structure, described by the signal's power spectrum, is thereby reconstructed from the same data set. We show that the minimization of the Gibbs free energy, corresponding to a Gaussian approximation to the posterior marginalized over the power spectrum, is equivalent to the empirical Bayes ansatz, in which the power spectrum is fixed to its maximum a posteriori value. We further introduce a prior for the power spectrum that enforces spectral smoothness. The appropriateness of this prior in different scenarios is discussed and its effects on the reconstruction's results are demonstrated. We validate the performance of our reconstruction algorithm in a series of one- and two-dimensional test cases with varying degrees of nonlinearity and different noise levels.

Understanding the mechanisms responsible for the equilibration of isolated quantum many-body systems is a long-standing open problem. In this work we obtain a statistical relationship between the equilibration properties of Hamiltonians and the complexity of their eigenvectors, provided that a conjecture about the incompressibility of quantum circuits holds. We quantify the complexity by the size of the smallest quantum circuit mapping the local basis onto the energy eigenbasis. Specifically, we consider the set of all Hamiltonians having complexity $C$, and show that almost all such Hamiltonians equilibrate if $C$ is superquadratic in the system size, which includes the fully random Hamiltonian case in the limit $C\to \infty$, and do not equilibrate if $C$ is sublinear. We also provide a simple formula for the equilibration time scale in terms of the Fourier transform of the level density. Our results are statistical and, therefore, do not apply to specific Hamiltonians. Yet they establish a fundamental link between equilibration and complexity theory.

We examine the existence and stability of frozen waves in diblock copolymers with local conservation of the order parameter, which are described by the modified Cahn-Hilliard model. It is shown that a range of stable waves exists and each can emerge from a “general” initial condition (not only the one with the lowest density of free energy). We discuss the implications of these results for the use of block copolymers in templating nanostructures.

To keep the formation of colloidal crystal under a centrifugation in mind, we study ordering of Brownian particles under a uniform external force. When the force is added to Brownian particles distributing uniformly in the system, the particles drift and the density of particles near walls increases. Ordering of particles on the walls occurs at first and ordering in bulk occurs in succession. In bulk, both the clusters with face-centered cubic structure and those with the hexagonal close-packed structure appear. The distribution of cluster sizes changes with the direction of external force.

Ice lenses are formed by the migration and solidification of unfrozen water during soil freezing, which can lead to the upwards displacement of the ground surface known as frost heave. The complicated interplay between heat and mass transport that causes ice lens formation has been addressed by several theoretical models, but uncertainties remain that require further experimental constraints. In particular, the initiation of ice lenses has long posed theoretical difficulties. We performed a series of stepwise freezing experiments in fine granular materials to observe the initiation and growth of ice lenses. Our experiments demonstrate clear and systematic relationships between the behavior of ice lenses, and the particle size and cooling temperature. Ice lenses are thicker when formed in sediments with smaller particle sizes and the initial formation position is further from the cooled boundary when it is set to lower temperatures. Our temperature measurements and photographic documentation demonstrate that ice lenses are formed below the nominal melting temperature, at a location that is sufficiently distant for the freezing velocity to have slowed below a threshold. We compared our experimental results to numerical predictions of ice lens formation that were applied to our experimental conditions. Our experimental trends are consistent with predictions of our simple, initial model. However, important quantitative differences motivate a refined treatment that emphasizes the kinetics of liquid supply from the pore space through the thin films that separate ice lenses from particle surfaces. We obtained good quantitative agreement between our experimental measurements and the refined model predictions, emphasizing the importance of kinetic effects as a control in ice lens initiation and growth.

We investigate theoretically a diffusion-limited reaction between a reactant attached to a Rouse polymer and an external fixed reactive site in confinement. The present work completes and goes beyond a previous study [Guérin, Bénichou, and Voituriez, Nat. Chem. 4, 568 (2012)] that showed that the distribution of the polymer conformations at the very instant of reaction plays a key role in the reaction kinetics and its determination enables the inclusion of non-Markovian effects in the theory. Here we describe in detail this non-Markovian theory and compare it with numerical stochastic simulations and a Markovian approach, in which the reactive conformations are approximated by equilibrium ones. We establish the following results. Our analysis reveals a strongly non-Markovian regime in one dimension, where the Markovian and non-Markovian dependences of the reaction time on the initial distance are different. In this regime, the reactive conformations are so different from equilibrium conformations that the Markovian expressions of the reaction time can be overestimated by several orders of magnitudes for long chains. We also show how to derive qualitative scaling laws for the reaction time in a systematic way that takes into account the different behaviors of monomer motion at all time and length scales. Finally, we also give an analytical description of the average elongated shape of the polymer at the instant of the reaction and show that its spectrum behaves as a slow power law for large wave numbers.

We propose and study, by means of Monte Carlo numerical simulations, a minimal discrete model for avascular tumor growth, which can also be applied for the description of cell cultures in vitro. The interface of the tumor is self-affine and its width can be characterized by the following exponents: (i) the growth exponent $\beta =0.32\left(2\right)$ that governs the early time regime, (ii) the roughness exponent $\alpha =0.49\left(2\right)$ related to the fluctuations in the stationary regime, and (iii) the dynamic exponent $z=\alpha /\beta \simeq 1.49\left(2\right)$, which measures the propagation of correlations in the direction parallel to the interface, e.g., $\xi \propto t^{1/z}$, where $\xi$ is the parallel correlation length. Therefore, the interface belongs to the Kardar-Parisi-Zhang universality class, in agreement with recent experiments of cell cultures in vitro. Furthermore, density profiles of the growing cells are rationalized in terms of traveling waves that are solutions of the Fisher-Kolmogorov equation. In this way, we achieved excellent agreement between the simulation results of the discrete model and the continuous description of the growth front of the culture or tumor.

Lizards and insects can strongly attach to walls and then detach applying negligible additional forces. We propose a simple mechanical model of this phenomenon which implies active muscle control. We show that the detachment force may depend not only on the properties of the adhesive units, but also on the elastic interaction among these units. By regulating the scale of such cooperative interaction, the organism can actively switch between two modes of adhesion: delocalized (pull off) and localized (peeling).

We investigate bond percolation on the nonplanar Hanoi network (HN-NP), which was studied previously [Boettcher et al. Phys. Rev. E 80, 041115 (2009)]. We calculate the fractal exponent of a subgraph of the HN-NP, which gives a lower bound for the fractal exponent of the original graph. This lower bound leads to the conclusion that the original system does not have a nonpercolating phase, where only finite-size clusters exist for $p>0$, or equivalently, that the system exhibits either the critical phase, where infinitely many infinite clusters exist, or the percolating phase, where a unique giant component exists. Monte Carlo simulations support our conjecture.