Extending a model due to Derrida, Gardner, and Zippelius, we have studied the recognition ability of an extreme and asymmetrically diluted version of the Hopfield model for associative memory by including the effect of a stimulus in the dynamics of the system. We obtain exact results for the dynamic evolution of the average network superposition. The stimulus field was considered as proportional to the overlapping of the state of the system with a particular stimulated pattern. Two situations were analyzed, namely, the external stimulus acting on the initialization pattern (parallel stimulus) and the external stimulus acting on a pattern orthogonal to the initialization one (orthogonal stimulus). In both cases, we obtained the complete phase diagram in the parameter space composed of the stimulus field, thermal noise, and network capacity. Our results show that the system improves its recognition ability for parallel stimulus. For orthogonal stimulus two recognition phases emerge with the system locking at the initialization or stimulated pattern. We confront our analytical results with numerical simulations for the noiseless case $T=0$.

A low-Mach-number analysis is presented of the collapse of a bubble in an electric field, which is assumed to be homogeneous, but may be unsteady. Ellipsoidal shape deformations are accounted for in the analysis, but are assumed to be small. It is shown that the presence of an electric field leads to additional terms in a modified Rayleigh-Plesset equation. This differential equation for the bubble radius and a corresponding equation for ellipsoidal shape deformations have been integrated numerically. The results indicate that a bubble can be made to collapse by instantaneously switching on an electric field. Also, nonharmonic volumetric oscillations are observed for time-dependent electric fields of sufficiently large amplitude. It is shown that the rate of a collapse driven by external pressure variations due, for instance, to acoustic forcing can be accelerated.

The dispersion relation for plane waves in uniaxial metamaterials with indefinite dielectric tensors and scalar positive permeability is theoretically investigated. It is found, that the isofrequency surfaces of the plane extraordinary waves have a hyperbolic shape which allows the propagation of waves with infinitely long wave vectors. As an example a metallodielectric multilayer was considered and the dispersion relations were determined using an effective medium approximation and an analytically exact Bloch wave calculation. The extraordinary waves in this structure are identified as multilayer plasmons and the validity of the effective medium approximation is examined.

Nanomechanical resonators having small mass, high resonance frequency, and low damping rate are widely employed as mass detectors. We study the performance of such a detector when the resonator is driven into a region of nonlinear oscillations. We predict theoretically that in this region the system acts as a phase-sensitive mechanical amplifier. This behavior can be exploited to achieve noise squeezing in the output signal when homodyne detection is employed for readout. We show that mass sensitivity of the device in this region may exceed the upper bound imposed by thermomechanical noise upon the sensitivity when operating in the linear region. On the other hand, we show that the high mass sensitivity is accompanied by a slowing down of the response of the system to a change in the mass.

It is known that the Green’s function for nondissipative acoustic or elastic wave propagation can be extracted by correlating noise recorded at different receivers. This property is often related to the invariance for time reversal of the acoustic or elastic wave equations. The diffusion equation is not invariant for time reversal. It is shown in this work that the Green’s function of the diffusion equation can also be retrieved by correlating solutions of the diffusion equation that are excited randomly and are recorded at different locations. This property can be used to retrieve the Green’s function for diffusive systems from ambient fluctuations. Potential applications include the fluid pressure in porous media, electromagnetic fields in conducting media, the diffusive transport of contaminants, and the intensity of multiply scattered waves.

We show that the phase diagram of substances whose molecular structure changes upon varying the thermodynamic parameters can be mapped, through state-dependent scaling, onto the phase diagram of systems of molecules having fixed structure. This makes it possible to identify broad universality classes in the complex phase scenario exhibited by soft matter, and enlightens a surprisingly close connection between puzzling phase phenomena and familiar behaviors. The analysis presented provides a straightforward way for deriving the phase diagram of soft substances from that of simpler reference systems. This method is applied here to study the phase behavior exhibited by two significative examples of soft matter with temperature-dependent molecular structure: thermally responsive colloids and polymeric systems. A region of inverse melting, i.e., melting upon isobaric cooling, is predicted at relatively low pressure and temperature in polymeric systems.

The nonequilibrium critical dynamics of the Ising magnet on a fractal substrate, namely the Sierpinski carpet with Hausdorff dimension $d_H=1.7925$, has been studied within the short-time regime by means of Monte Carlo simulations. The evolution of the physical observables was followed at criticality, after both annealing ordered spin configurations (ground state) and quenching disordered initial configurations (high temperature state), for three segmentation steps of the fractal. We have obtained evidence showing that during these relaxation processes both the growth and the fragmentation of magnetic domains become influenced by the hierarchical structure of the substrate. In fact, the interplay between the dynamic behavior of the magnet and the underlying fractal leads to the emergence of a logarithmic-periodic oscillation, superimposed to a power law, which has been observed in the time dependence of both the decay of the magnetization and its logarithmic derivative. These oscillations have been carefully characterized in order to determine the critical temperature of the second-order phase transition and the critical exponents corresponding to the short-time regime. The effects of the substrate can also be observed from the dependence of the effective critical exponents on the segmentation step. The exponent $\theta$ of the initial increase of the magnetization has also been obtained and the results suggest that it would be almost independent of the fractal dimension of the susbstrate, provided that $d_H$ is close enough to $d=2$. The oscillations have been discussed within the framework of the discrete scale invariance of the substrate.

We present a detailed study of a model of close-packed dimers on the square lattice with an interaction between nearest-neighbor dimers. The interaction favors parallel alignment of dimers, resulting in a low-temperature crystalline phase. With large-scale Monte Carlo and transfer matrix calculations, we show that the crystal melts through a Kosterlitz-Thouless phase transition to give rise to a high-temperature critical phase, with algebraic decays of correlations functions with exponents that vary continuously with the temperature. We give a theoretical interpretation of these results by mapping the model to a Coulomb gas, whose coupling constant and associated exponents are calculated numerically with high precision. Introducing monomers is a marginal perturbation at the Kosterlitz-Thouless transition and gives rise to another critical line. We study this line numerically, showing that it is in the Ashkin-Teller universality class, and terminates in a tricritical point at finite temperature and monomer fugacity. In the course of this work, we also derive analytic results relevant to the noninteracting case of dimer coverings, including a Bethe ansatz (at the free fermion point) analysis, a detailed discussion of the effective height model, and a free field analysis of height fluctuations.

We study theoretically a generic scheme of programmable self-assembly of nanoparticles into clusters of desired geometry. The problem is motivated by the feasibility of highly selective DNA-mediated interactions between colloidal particles. By analyzing both a simple generic model and a more realistic description of a DNA-colloidal system, we demonstrate that it is possible to suppress the glassy behavior of the system, and to make the self-assembly nearly errorproof. This regime requires a combination of stretchable interparticle linkers (e.g., sufficiently long DNA), and a soft repulsive potential. The jamming phase diagram and the error probability are computed for several types of clusters. The prospects for the experimental implementation of our scheme are also discussed.

Two correlations concerning the isobaric and isochoric fragilities, $m_P$ and $m_V$, as well as the scaling exponent $\gamma$ reported by Casalini and Roland [Phys. Rev. E 72, 031503 (2005)] have been examined for several van der Waals and hydrogen-bonded glass formers. It has been pointed out that the correlations lead to some serious inconsistency with the exponent $\gamma$, which is expected to be a constant dependent only on material, but varies also on pressure if experimentally found pressure dependences of $m_P$ are taken into account. This problem could be solved in the case of van der Waals liquids, but then at least one of the correlations becomes dependent on thermodynamic conditions, and consequently, loses its universality. However, some H-bonded systems, due to properties of hydrogen bonding, have been well argued not to be included to determine the correlations independently of thermodynamic conditions. Furthermore, it has been noticed that another correlation concerning the fragility, between $m_P$ and the structural relaxation peak breadth, yields discrepancies in comparison with results of experiments under elevated pressure.

A theory of the formation of nanoscale porous structures in oxides of metals grown by anodization is developed. It is shown that a growing oxide layer can become unstable which yields the formation of a spatially irregular array of pores. The instability is shown to result from a nonlinear dependence of electrochemical kinetics at the metal-oxide and oxide-electrolyte interfaces on the overpotential which is governed by the Butler-Volmer relation. The conditions for the instability of the oxide layer are found. The dependence of the oxide conductivity on the electric field is taken into account and is shown to have a destabilizing effect. A weakly nonlinear analysis is performed and it shows that the system evolution near the instability threshold is described by the Kuramoto-Sivashinsky equation. Farther from threshold, in the long-wave approximation, a system of strongly nonlinear equations is derived and solved numerically; this system describes the formation of deep irregular pores. In a particular case, a self-similar solution describing the propagation of a pore with a paraboloidal shape is found.

It is shown that the critical properties of a recently studied model for nonequilibrium wetting are robust if one extends the dynamic rules by single-particle diffusion on terraces of the wetting layer. Examining the behavior at the critical point and along the phase transition line, we identify a special point in the phase diagram where detailed balance of the dynamical processes is partially broken.

Spatial intensity correlations between waves transmitted through random media are analyzed within the framework of the random matrix theory of transport. Assuming that the statistical distribution of transfer matrices is isotropic, we found that the spatial correlation function can be expressed as the sum of three terms, with distinctive spatial dependences. This result coincides with the one obtained in the diffusive regime from perturbative calculations, but holds all the way from quasiballistic transport to localization. While correlations are positive in the diffusive regime, we predict a transition to negative correlations as the length of the system decreases.

This paper reports 2D and 3D direct numerical simulations of the Rayleigh-Bénard convection in a fluid layer, ${}^3\mathrm{He}$, close to its gas-liquid critical point. The main quantity of interest is the time when the convective motion becomes appreciable after the heat current has been started. A space periodic, time-independent temperature perturbation is applied to the top plate aiming to represent the various sources of noise in the experiments. A single amplitude of this additional perturbation reproduces the noise level of the experiments for all the used combinations of the critical point proximity and of the heating power. Over four decades of the Rayleigh number, this simple operation removes the systematic discrepancy reported in an earlier paper and brings the simulations into good agreement with the measurements. Scaling of the exponential convection growth rate is presented and discussed.

Possible propagating longitudinal strain solitary waves in a plate are shown to be seriously altered when physical cubic nonlinearity is taken into account in the modeling. This also affects an amplification of the wave due to the transverse instability of plane-localized waves and due to the plane-wave interaction.

We study the statistical mechanics of multi-index matching problems where the quenched disorder is a geometric site disorder rather than a link disorder. A recently developed functional formalism is exploited that yields exact results in the finite-temperature thermodynamic limit. Particular attention is paid to the zero-temperature limit of maximal matching problems where the method allows us to obtain the average value of the optimal match and also sheds light on the algorithmic heuristics leading to that optimal match.

We study a mathematical model of a single neuron with self-coupling. The model is based on the FitzHugh-Nagumo oscillator and an equation describing synaptic properties of the neuron. The analysis of the model is focused on its dynamics, depending on parameters characterizing synaptic time constants and external signals that affect the neuron. Applying Lyapunov exponents and bifurcation analysis, we point out the occurrence of parameter regions with different behavior such as bursting (chaotic or periodic), spiking, and multistable phenomena. Moreover, we can describe the dynamics of the model using an analytical approximation of the one-dimensional Poincaré map extracted from the numerical simulations.

We study the effects of the degree distribution in mutual synchronization of two-layer neural networks. We carry out three coupling strategies: large-large coupling, random coupling, and small-small coupling. By computer simulations and analytical methods, we find that couplings between nodes with large degree play an important role in the synchronization. For large-large coupling, less couplings are needed for inducing synchronization for both random and scale-free networks. For random coupling, cutting couplings between nodes with large degree is very efficient for preventing neural systems from synchronization, especially when subnetworks are scale free.

We use an extended Gō model, in unfrustrated and frustrated variants, to study the energy landscape and the fluctuations of a model protein. The model exhibits two transitions, folding and dynamical transitions, when changing the temperature. The inherent structures corresponding to the minima of the landscape are analyzed and we show how their energy density can be obtained from simulations around the folding temperature. The scaling of this energy density is found to reflect the folding transition. Moreover, this approach allows us to build a reduced thermodynamics in the inherent structure landscape. Equilibrium studies, from full molecular dynamics (MD) simulations and from the reduced thermodynamics, detect the features of a dynamical transition at low temperature and we analyze the location and time scale of the fluctuations of the protein, showing the need of some frustration in the model to get realistic results. The frustrated model also shows the presence of a kinetic trap which strongly affects the dynamics of folding.