In this paper we present a detailed analytical study of the phase diagram and of the structural properties of a field theoretic model with a short-range attraction and a competing long-range screened repulsion. We provide a full derivation and expanded discussion and digression on results previously reported briefly in M. Tarzia and A. Coniglio, Phys. Rev. Lett. 96, 075702 (2006). The model contains the essential features of the effective interaction potential among charged colloids in polymeric solutions. We employ the self-consistent Hartree approximation and a replica approach, and we show that varying the parameters of the repulsive potential and the temperature yields a phase coexistence, a lamellar and a glassy phase. Our results suggest that the cluster phase observed in charged colloids might be the signature of an underlying equilibrium lamellar phase, hidden on experimental time scales, and emphasize that the formation of microphase structures may play a prominent role in the process of colloidal gelation.

Understanding the chemistry and physics of polyelectrolyte systems challenges scientists from a wide spectrum of research areas, ranging from colloidal science to biology. However, despite significant progress in the past decades, the calculation of large open polyelectrolyte systems on a detailed level remains computationally expensive, due to the highly polymeric nature of the macromolecules and/or long-range character of the intermonomer interactions. To cope with these difficulties, field-theoretic methodologies based on the mean-field approximation have emerged recently and have proven to provide useful results in the regime of high polyelectrolyte concentration. In this paper we present applications of a low-cost field-theoretic calculation approach based on the method of Gaussian equivalent representation, which has recently been proven useful for delivering accurate results in case of polymer solutions beyond the mean field level of approximation. Here we demonstrate its effectiveness on the example of a Gaussian effective potential, mimicking the effective interactions between weakly charged polyelectrolyte coils, and a screened Coulomb model, describing the effective intermonomer interactions of Debye-Hückel chains. Moreover, we show that the approach opens perspectives to extend the range of applicability of the grand canonical ensemble to dense liquid and solid phases of more sophisticated polyelectrolyte models. Finally, we demonstrate that our approach is also much more reliable for determining the phase boundaries of these models than conventional mean field and grand canonical Monte Carlo approaches.

Every sixth death in industrialized countries occurs because of cardiac arrhythmias such as ventricular tachycardia (VT) and ventricular fibrillation (VF). There is growing consensus that VT is associated with an unbroken spiral wave of electrical activation on cardiac tissue but VF with broken waves, spiral turbulence, spatiotemporal chaos and rapid, irregular activation. Thus spiral-wave activity in cardiac tissue has been studied extensively. Nevertheless, many aspects of such spiral dynamics remain elusive because of the intrinsically high-dimensional nature of the cardiac-dynamical system. In particular, the role of tissue heterogeneities in the stability of cardiac spiral waves is still being investigated. Experiments with conduction inhomogeneities in cardiac tissue yield a variety of results: some suggest that conduction inhomogeneities can eliminate VF partially or completely, leading to VT or quiescence, but others show that VF is unaffected by obstacles. We propose theoretically that this variety of results is a natural manifestation of a complex, fractal-like boundary that must separate the basins of the attractors associated, respectively, with spiral breakup and single spiral wave. We substantiate this with extensive numerical studies of Panfilov and Luo-Rudy I models, where we show that the suppression of spiral breakup depends sensitively on the position, size, and nature of the inhomogeneity.

We report a nonlinear acoustic system displaying excitability. The considered system is a magnetostrictive material where acoustic waves are parametrically generated. For a set of parameters, the system presents homoclinic and heteroclinic dynamics, whose boundaries define an excitability domain. The excitable behavior is characterized by analyzing the response of the system to different external stimuli. Single-spiking and bursting regimes have been identified. All these neuronlike properties are here predicted to occur in magnetostrictive materials, which are the basis of many smart systems and applications.

We present theoretical calculations of an argon bubble in a liquid solution of $85\%\mathrm{wt}$ sulfuric acid and $15\%\mathrm{wt}$ water in single-bubble sonoluminescence. We used a model without free parameters to be adjusted. We predict from first principles the region in parameter space for stable bubble evolution, the temporal evolution of the bubble radius, the maximum temperature, pressures, and the light spectra due to thermal emissions. We also used a partial differential equation based model (hydrocode) to compute the temperature and pressure evolutions at the center of the bubble during maximum compression. We found the behavior of this liquid mixture to be very different from water in several aspects. Most of the models in sonoluminescence were compared with water experimental results.

We consider the linear stability of two inviscid fluids, in the presence of gravity, sheared past each other and separated by a flexible plate. Conditions for exponential growth of velocity perturbations are found as functions of the flexural rigidity of the plate and the shear rate. This Kelvin-Helmholtz instability is then analyzed in the presence of plates with spatially periodic (with period $a$) flexural rigidity arising from, for example, a periodic material variation. The eigenvalues of this periodic system are computed using Bloch’s theorem (Floquet theory) that imposes specific Fourier decompositions of the velocity potential and plate deformations. We derive the non-Hermitian matrix whose eigenvalues determine the dispersion relation. Our dispersion relation shows that plate periodicity generally destabilizes the flow, compared to a uniform plate with the same mean flexural rigidity. However, enhanced destabilization and stabilization can occur for disturbances with wavelengths near an even multiple of the plate periodicity. The sensitivity of flows with such wavelengths arises from the nonpropagating, “Bragg reflected” modes coupled to the plate periodicity through the boundary condition at the plate.

We discuss localization phenomena in multilayer films doped with scattering particles. If the films exhibit a particular type of transmission resonance then above a critical frequency waves in the sample can decay as a power law rather than exponentially. This phenomenon is independent of the scattering strength of the particles, in stark contrast to previous work. We find that this phenomenon has many similarities to a second order phase transition. This work points to interesting avenues in the study of waves in anisotropic disordered media.

We present an optimistic synchronous relaxation algorithm for parallel kinetic Monte Carlo (KMC) simulations of thin film growth. This algorithm is based on spatial decomposition of the KMC lattice and it employs two measures aimed at improving the parallel efficiency: dynamic global updating and domain boundary shifting. We utilize this algorithm to simulate two different growth models, which represent the growth of Ag on Ag(111) and the heteroepitaxial growth of Ag on Pt(111). We show that these simulations can achieve good efficiency—especially for large domain sizes with a moderate number of processors. We find that domain boundary shifting can improve efficiency—especially for simulations of growth in the $\mathrm{Ag}∕\mathrm{Pt}\left(111\right)$ system, where the potential-energy surface topology creates areas of rapid, localized motion. We analyze the origins of parallel efficiency in these simulations.

Cardiac myocytes are excitable cells in which an external current stimulus depolarizes the membrane potential to elicit an action potential. This action potential then triggers calcium release from intracellular stores, which mediates contraction. Conversely, intracellular calcium also modulates membrane currents, affecting action potential morphology and action potential duration (APD). The interactions between action potential and calcium, termed excitation-contraction coupling, give rise to a rich spectrum of nonlinear dynamics, especially at rapid heart rates, which are important for cardiac contraction and the development of lethal arrhythmias. In this study, we developed a nonlinear iterated map model to investigate the dynamics of cardiac excitation-contraction coupling in a periodically stimulated cell. We first studied the nonlinear dynamics due to APD restitution, a functional relation between APD and its preceding diastolic interval. We then studied the nonlinear dynamics due to intracellular calcium cycling when total cell calcium is constant or varies at a beat-to-beat basis. Finally, we studied the nonlinear dynamics due to the bidirectional coupling of the two dynamical systems. Saddle-node bifurcations leading to bistability, period-doubling bifurcations leading to alternans, and period-doubling routes to chaos can independently occur in both action potential or intracellular calcium cycling subsystems as heart rate increases. A Hopf bifurcation leading to quasiperiodicity occurs when the two dynamical systems are coupled. Although these dynamics are predicted from low-dimensional iterated maps, the approach here provides valuable information which can be used as a basis to explore dynamical features of physiologically detailed ionic models, to illuminate experimental findings, and to design experimentally testable predictions for new biological experiments.

We propose a new model to approximate spatiotemporal noise covariance for use in neural electromagnetic source analysis, which better captures temporal variability in background activity. As with other existing formalisms, our model employs a Kronecker product of matrices representing temporal and spatial covariance. In our model, spatial components are allowed to have differing temporal covariances. Variability is represented as a series of Kronecker products of spatial component covariances and corresponding temporal covariances. Unlike previous attempts to model covariance through a sum of Kronecker products, our model is designed to have a computationally manageable inverse. Despite increased descriptive power, inversion of the model is fast, making it useful in source analysis. We have explored two versions of the model. One is estimated based on the assumption that spatial components of background noise have uncorrelated time courses. Another version, which gives closer approximation, is based on the assumption that time courses are statistically independent. The accuracy of the structural approximation is compared to an existing model, based on a single Kronecker product, using both Frobenius norm of the difference between spatiotemporal sample covariance and a model, and scatter plots. Performance of ours and previous models is compared in source analysis of a large number of single dipole problems with simulated time courses and with background from authentic magnetoencephalography data.

Reaction-diffusion systems with mass conservation are studied. In such systems, abrupt decays of stripes follow quasistationary states in sequence generally. We give a stability condition of steady state which the system reaches after long transient time. It is also shown that there exist systems in which a single-stripe pattern is solely steady state for an arbitrary size of the systems. The applicability to cell biology is discussed.

An analytical theory is developed to describe the dynamics of a closed lipid bilayer membrane (vesicle) freely suspended in a general linear flow. Considering a nearly spherical shape, the solution to the creeping-flow equations is obtained as a regular perturbation expansion in the excess area. The analysis takes into account the membrane fluidity, incompressibility, and resistance to bending. The constraint for a fixed total area leads to a nonlinear shape evolution equation at leading order. As a result two regimes of vesicle behavior, tank treading and tumbling, are predicted depending on the viscosity contrast between interior and exterior fluid. Below a critical viscosity contrast, which depends on the excess area, the vesicle deforms into a tank-treading ellipsoid, whose orientation angle with respect to the flow direction is independent of the membrane bending rigidity. In the tumbling regime, the vesicle exhibits periodic shape deformations with a frequency that increases with the viscosity contrast. Non-Newtonian rheology such as normal stresses is predicted for a dilute suspension of vesicles. The theory is in good agreement with published experimental data for vesicle behavior in simple shear flow.

We discuss the recoverable and irrecoverable energy densities associated with a pulse at a point in the propagation medium and derive easily computed expressions to calculate these quantities. Specific types of fields are required to retrieve the recoverable portion of the energy density from the point in the medium, and we discuss the properties that these fields must have. Several examples are given to illustrate these concepts.

Sieffert et al. [Phys. Rev. E 72, 066402 (2005)] have recently presented experimental results on optical emission enhancement at the front of shockwaves propagating in nitrogen afterglow. They claim that their results point to local heating of electrons at the shock front. In this Comment it is shown that the observed emission enhancement can be explained on the basis of a commonly accepted model of nitrogen discharge and afterglow, so that the use of unfounded assumption of local electron heating is not required.

We consider geometrical or Ising clusters (i.e., domains of parallel spins) in the square lattice random-field Ising model by varying the strength of the Gaussian random field $\Delta$. In agreement with the conclusion of a previous investigation [Phys. Rev. E 63, 066109 (2001)], the geometrical correlation length, i.e., the average size of the clusters $\xi$ is finite for $\Delta >{\Delta }_c\approx 1.65$ and divergent for $\Delta ⩽{\Delta }_c$. The scaling function of the distribution of the mass of the clusters as well as the geometrical correlation function are found to involve the scaling exponents of critical percolation. On the other hand, the divergence of the correlation length, $\xi \left(\Delta \right)\sim {(\Delta -{\Delta }_c)}^{-\nu }$, with $\nu \approx 2$, is related to that of tricritical percolation. It is verified numerically that critical geometrical correlations transform conformally.

We show how a large family of master equations, describing quantum Brownian motion of a harmonic oscillator with translationally invariant damping, can be derived within a phenomenological approach, based on the assumption that an environment can be simulated by two classical stochastic forces. This family is determined by three time-dependent correlation functions (besides the frequency and damping coefficients), and it includes as special cases the known master equations, whose dissipative part is bilinear with respect to the operators of coordinate and momentum.

The phase behavior and the orientational structure of polar model fluids confined to slit pores is investigated by means of density functional theory in a modified mean-field approximation. We focus on fluid states and further assume a uniform number density throughout the pore. Our results for spherical dipolar particles with additional van der Waals–like interactions (Stockmayer fluids) reveal complex fluid-fluid phase behavior involving condensation and first- and second-order isotropic-to-ferroelectric phase transitions, where the ferroelectric ordering occurs parallel to the confining walls. The relative importance of these phase transitions depends on two “tuning” parameters, that is the strength of the dipolar interactions (relative to the isotropic attractive ones) between fluid particles, and on the pore width. In particular, in narrow pores the condensation transition seen in bulk Stockmayer fluids is entirely suppressed. For dipolar hard spheres, on the other hand, the impact of confinement consists in a decrease of the isotropic-to-ferroelectric transition temperatures. We also demonstrate that the local orientational structure is inhomogeneous and anisotropic even in globally isotropic systems, in agreement with computer simulation results.

It has been established that a biological neuron reproduces the precise spike response to identical fluctuating input currents. We wish to predict the firing times of a given neuron for any input current. For this purpose, a mathematical model is introduced for mimicking the voltage response of the neuron to an input current. In predicting the firing times of a target neuron for a novel input current, we propose here the method of estimating the probability of spike occurrence, instead of naively thresholding an instantaneous value of the model voltage. The assessment is carried out maximally utilizing the information about the state space of the voltage and its time derivative(s) of the model, in advance of a possible spike, with a time lag that is determined by maximizing the mutual information. The prediction is significantly improved by the present method in comparison to the naive thresholding method.

Electronic detection of the specific recognition between complementary DNA sequences is investigated. DNA probes are immobilized at different lateral positions on a Poly($\mathrm{L}$-lysine)-coated surface of an integrated silicon transistor array. Hybridization and field effect detection are done with the solid surface immersed in electrolyte solutions. Differential measurements are performed, where DNA hybridization leads to surface potential shifts between the transistors of the array. We experimentally show that these differential signals of hybridization can be enhanced significantly by changing the salt concentration between hybridization and detection.