We present a simple new method to systematically identify all topological structures (e.g., positive feedback loops) potentially leading to locally unstable steady states: ICSA—The instability causing structure analysis. Systems without any instability causing structure (i.e., not fulfilling the necessary topological condition for instabilities) cannot have unstable steady states. It follows that common bistability or multistability and Hopf bifurcations are excluded and sustained oscillations and deterministic chaos are most unlikely. The ICSA leads to new insights into the topological organization of chemical and biochemical systems, such as metabolic, gene regulatory, and signal transduction networks.

We present a method for modeling phase transitions and morphological evolution of binary lipid membranes with approximately planar geometries. The local composition and the shape of the membrane are coupled through composition-dependent spontaneous curvature in a Helfrich free energy. The evolution of the composition field is described by a Cahn-Hilliard-type equation, while shape changes are described by relaxation dynamics. Our method explicitly treats the full nonlinear form of the geometrical scalars, tensors, and differential operators associated with the curved shape of the membrane. The model is applied to examine morphological evolution and stability of lipid membranes initialized in a variety of compositional and geometric configurations. Specifically, we investigate the dynamics of systems which have a lamellar structure as their lowest energy state. We find that evolution is very sensitive to initial conditions; only membranes with sufficiently large lamellar-type compositional perturbations or ripple-type shape perturbations in their initial configuration can deterministically evolve into a lamellar equilibrium morphology. We also observe that rigid topographical surface patterns have a strong effect on the phase separation and compositional evolution in these systems.

Networks of living neurons exhibit an avalanche mode of activity, experimentally found in organotypic cultures. Moreover, experimental studies of morphology indicate that neurons develop a network of small-world-like connections, with the possibility of a very high connectivity degree. Here we study a recent model based on self-organized criticality, which consists of an electrical network with threshold firing and activity-dependent synapse strengths. We study the model on a scale-free network, the Apollonian network. The system exhibits an avalanche activity with a power law distribution of sizes and durations. The analysis of the power spectra of the electrical signal reproduces very robustly the power law behavior with the exponent 0.8, experimentally measured in electroencephalogram spectra. The exponents are found to be quite stable with respect to initial configurations and strength of plastic remodeling, indicating that universality holds for a wide class of neural network models.

We study the dynamics of the bent Fermi-Pasta-Ulam (FPU) chain, incorporating the complicated effects of geometry, long-range interactions, as well as nonlinear dispersion. Within the rotating wave approximation, we obtain several exact discrete breather (DB) solutions, such as the odd-parity and even-parity discrete breathers, compactlike discrete breathers and moving discrete breathers for various geometries of the chain. In presence of long-range nonlinear dispersive interactions, we show that DBs exist in the discrete curved lattice for next-nearest-neighbor interactions as well. For all neighbors interactions, we treat the problem in the long-wavelength (continuum) and weakly nonlinear limit of the system and obtain exact static breather solutions and large-amplitude, traveling kink-soliton solutions. The curved FPU chain also admits finite amplitude discrete nonlinear sinusoidal wave solutions with short commensurate as well as incommensurate wavelengths. The usefulness of these solutions for energy localization and transport in various physical systems are discussed.

We study the susceptible-infected-recovered model of epidemics in the vicinity of the threshold infectivity. We derive the distribution of total outbreak size in the limit of large population size $N$. This is accomplished by mapping the problem to the first passage time of a random walker subject to a drift that increases linearly with time. We recover the scaling results of Ben-Naim and Krapivsky that the effective maximal size of the outbreak scales as $N^{2∕3}$, with the average scaling as $N^{1∕3}$, with an explicit form for the scaling function.

We implement a standard Monte Carlo algorithm to study the slow, equilibrium dynamics of a silica melt in a wide temperature regime, from $6100\mathrm{K}$ down to $2750\mathrm{K}$. We find that the average dynamical behavior of the system is in quantitative agreement with results obtained from molecular dynamics simulations, at least in the long-time regime corresponding to the $\alpha$-relaxation. By contrast, the strong thermal vibrations related to the boson peak present at short times in molecular dynamics are efficiently suppressed by the Monte Carlo algorithm. This allows us to reconsider silica dynamics in the context of mode-coupling theory, because several shortcomings of the theory were previously attributed to thermal vibrations. A mode-coupling theory analysis of our data is qualitatively correct, but quantitative tests of the theory fail, raising doubts about the very existence of an avoided singularity in this system. We discuss the emergence of dynamic heterogeneity and report detailed measurements of a decoupling between translational diffusion and structural relaxation, and of a growing four-point dynamic susceptibility. Dynamic heterogeneity appears to be less pronounced than in more fragile glass-forming models, but not of a qualitatively different nature.

Simple observations of evaporating solutions reveal a complex hierarchy of spatiotemporal instabilities. We analyze one such instability suggested by the qualitative observations of Du and Stone and find that it is driven by a variant of the classical morphological instability in alloy solidification. In the latter case a moving solid-liquid interface is accompanied by a solutally enriched boundary layer that is thermodynamically metastable due to constitutional supercooling. Here, we consider the evaporation of an impure film adjacent to a solid composed of the nonvolatile species. In this case, constitutional supercooling within the film is created by evaporation at the solution-vapor interface and this drives the corrugation of the solid-solution interface across the thickness of the film. The principal points of this simple theoretical study are to suggest an instability mechanism that is likely operative across a broad range of technological and natural systems and to focus future quantitative experimental searches.

The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The mean-field level of description allows one to highlight the delicate interplay between the different time-scale processes in the resulting complex dynamics of the system. We clarify the influence of the amplitude and period of the environmental changes on the critical value of the selection pressure corresponding to a phase-transition “extinct-alive” of the population. However, the intrinsic stochasticity and the dynamically-built in correlations among the individuals, as well as the role of the mutation-induced variety in population’s evolution are not appropriately accounted for. A more refined level of description, which is an individual-based one, has to be considered. The inherent fluctuations do not destroy the phase transition “extinct-alive,” and the mutation amplitude is strongly influencing the value of the critical selection pressure. The phase diagram in the plane of the population’s parameters—selection and mutation are discussed as a function of the environmental variation characteristics. The differences between a smooth variation of the environment and an abrupt, catastrophic change are also addressed.

We present single-molecule measurements of the opening rate of DNA hairpins under mechanical tension and compare with the results obtained from a reduced-degrees-of-freedom statistical mechanics model. We extract the apparent position of the transition state $s$ and find that the model, with no fitting parameters, reproduces the experimental measurements surprisingly well. Our values for $s$ are different from the ones obtained in previous experiments, where, however, the experimental conditions were different (different force fields, different salt concentrations). Thus it appears that the values of $s$ measured for relatively short hairpins are strongly affected by these experimental conditions.

Synchronization among neurons is critical for many processes in the nervous system, ranging from the processing of sensory information to the onset of pathological conditions such as epilepsy. Here, we study synchronization in an array of neurons, each modeled by a set of nonlinear ordinary differential equations. We find that an array of $20\times 20$ coupled neurons undergoes a series of alternating low and high synchronization states, as measured by phase-locking and frequency entrainment, as the coupling constant is tuned. The role of long-range connections in inducing “small-world networks” has recently been of great interest in many physical and biological problems. Since long-range connections do exist in the brain, we investigated the role of such connections in our neural array. Introducing a biologically realistic percentage of long-range connections has no significant effect on synchronization. We find that it is rather the type of coupling and the total number of connections that determine the synchronization state of the array. We also show that some coupling conditions can lead to frustration in the system, resulting from an inability to simultaneously satisfy conflicting phase requirements. This frustration leads to a drift in the overall behavior of the network, which may offer an explanation for transitions between different types of neural oscillations observed experimentally.

In mesoscopic systems, conductance fluctuations are a sensitive probe of electron dynamics and chaotic phenomena. We show that the conductance of a purely classical chaotic system, with either fully chaotic or mixed phase space, generically exhibits fractal conductance fluctuations unrelated to quantum interference. This might explain the unexpected dependence of the fractal dimension of the conductance curves on the (quantum) phase breaking length observed in experiments on semiconductor quantum dots.

Marangoni instabilities in binary mixtures in the presence of the Soret effect and evaporation are different from those in pure liquids. In contrast to a large amount of experimental work on Marangoni convection in pure liquids, such experiments in binary mixtures are not available in the literature, to our knowledge. Using binary mixtures of NaCl/water in an open system, evaporation of water molecules at the liquid-vapor interface is inevitable. We have systematically investigated the pattern formation for a set of substrate temperatures and solute concentrations in an open system. The flow patterns evolve with time, driven by surface-tension fluctuations due to evaporation and the Soret effect, while the air-liquid interface does not deform. A shadow-graph method is used to follow the pattern formation in time. The patterns are mainly composed of polygons and rolls. The mean pattern size first decreases slightly, and then gradually increases during the evolution. Evaporation affects the pattern formation mainly at the early stages and the local evaporation rate tends to become spatially uniform at the film surface. The Soret effect becomes important at the later stages and affects the mixture for a large mean solute concentration where the Soret number is significantly above zero. The strength of convection increases with the initial solute concentration and the substrate temperature. Our findings differ from the theoretical predictions in which evaporation is neglected.

Based on our previous experimental study, we present a one-dimensional phenomenological model of a thermal blanket floating on the upper surface of a thermally convecting fluid. The model captures the most important interactions between the floating solid and the fluid underneath. By the thermal blanketing effect, the presence of the solid plate modifies the flow structure below; in turn, the flow exerts a viscous drag that causes the floating boundary to move. An oscillatory state and a trapped state are found in this model, which is in excellent agreement with experimental observations. The model also offers details on the transition between the states, and gives useful insights on this coupled system without the need for full-scale simulations.

Phase resonances in transmission compound structures with subwavelength slits produce sharp dips in the transmission response. For all equal slits, the wavelengths of these sharp transmission minima can be varied by changing the width or the length of all the slits. In this paper we show that the width of the dip, i.e., the frequency range of minimum transmittance, can be controlled by making at least one slit different from the rest within a compound unit cell. In particular, we investigate the effect that a change in the dielectric filling, or in the length of a single slit, produces in the transmission response. We also analyze the scan angle behavior of these structures by means of band diagrams and compare them with previous results for all-equal slit structures.

Simulated tempering is a method to enhance simulations of complex systems by periodically raising and lowering the temperature. Despite its advantages, simulated tempering has been overshadowed by its parallel counterpart, replica exchange (also known as parallel tempering), due to the difficulty of weight determination in simulated tempering. Here we propose a simple and fast method to obtain near-optimal weights for simulated tempering, and demonstrate its effectiveness in a molecular dynamics simulation of $\mathrm{Al}{\mathrm{a}}_{10}$ polypeptide in explicit solvent. We believe simulated tempering now deserves another look.

Experimental conditions have recently been reported [G. Andresen et al., Phys. Rev. Lett. 98, 023402 (2007)] that are relevant to the prospect of trapping antihydrogen atoms. An analysis of the experimental conditions indicates that positron space charge can have an important effect. The fraction of antiprotons that have an energy suitable for antihydrogen trapping can be reduced by drifts caused by the presence of positron space charge.

The translocation dynamics of a polymer chain through a nanopore in the absence of an external driving force is analyzed by means of scaling arguments, fractional calculus, and computer simulations. The problem at hand is mapped on a one-dimensional anomalous diffusion process in terms of the reaction coordinate $s$ (i.e., the translocated number of segments at time $t$) and shown to be governed by a universal exponent $\alpha =2∕(2\nu +2-{\gamma }_1)$, where $\nu$ is the Flory exponent and ${\gamma }_1$ is the surface exponent. Remarkably, it turns out that the value of $\alpha$ is nearly the same in two and three dimensions. The process is described by a fractional diffusion equation which is solved exactly in the interval $0<s<N$ with appropriate boundary and initial conditions. The solution gives the probability distribution of translocation times as well as the variation with time of the statistical moments $⟨s\left(t\right)⟩$ and $⟨s^2\left(t\right)⟩-{⟨s\left(t\right)⟩}^2$, which provide a full description of the diffusion process. The comparison of the analytic results with data derived from extensive Monte Carlo simulations reveals very good agreement and proves that the diffusion dynamics of unbiased translocation through a nanopore is anomalous in its nature.

We examine the thermal conductivity of a one-dimensional ${\varphi }^4$ lattice with strong on-site harmonic potential. The expression for the thermal conductivity in terms of different parameters is derived from the effective phonon theory. Numerical calculations using nonequilibrium molecular dynamics are compared with the predictions of the effective phonon theory and the theory of the Peierls-Boltzmann transport equation. It is found that the numerical results are consistent with the prediction of the effective phonon theory in the intermediate parameter range and approach the predictions of Peierls-Boltzmann transport theory in the strongly pinned limit.

We propose a numerical integration scheme to solve stochastic differential equations driven by Poissonian white shot noise. Our formula, which is based on an integral equation, which is equivalent to the stochastic differential equation, utilizes a discrete time approximation with fixed integration time step. We show that our integration formula approaches the Euler formula if the Poissonian noise approaches the Gaussian white noise. The accuracy and efficiency of the proposed algorithm are examined by studying the dynamics of an overdamped particle driven by Poissonian white shot noise in a spatially periodic potential. We find that the accuracy of the proposed algorithm only weakly depends on the parameters characterizing the Poissonian white shot noise; this holds true even if the limit of Gaussian white noise is approached.

The behavior of the excess entropy of Morse and Lennard-Jones liquids is examined as a function of temperature, density, and the structural order metrics. The dominant pair correlation contribution to the excess entropy is estimated from simulation data for the radial distribution function. The pair correlation entropy $\left(S_2\right)$ of these simple liquids is shown to have a threshold value of $(-3.5\pm 0.3)k_B$ at freezing. Moreover, $S_2$ shows a $T^{-2∕5}$ temperature dependence. The temperature dependence of the pair correlation entropy as well as the behavior at freezing closely correspond to earlier predictions, based on density functional theory, for the excess entropy of repulsive inverse power and Yukawa potentials [Rosenfeld, Phys. Rev. E 62, 7524 (2000)]. The correlation between the pair correlation entropy and the local translational and bond orientational order parameters is examined, and, in the case of the bond orientational order, is shown to be sensitive to the definition of the nearest neighbors. The order map between translational and bond orientational order for Morse liquids and solids shows a very similar pattern to that seen in Lennard-Jones-type systems.