Folding and unfolding simulations of three-dimensional lattice proteins were analyzed using a simplified statistical mechanical model in which their amino acid sequences and native conformations were incorporated explicitly. Using this statistical mechanical model, under the assumption that only interactions between amino acid residues within a local structure in a native state are considered, the partition function of the system can be calculated for a given native conformation without any adjustable parameter. The simulations were carried out for two different native conformations, for each of which two foldable amino acid sequences were considered. The native and non-native contacts between amino acid residues occurring in the simulations were examined in detail and compared with the results derived from the theoretical model. The equilibrium thermodynamic quantities (free energy, enthalpy, entropy, and the probability of each amino acid residue being in the native state) at various temperatures obtained from the simulations and the theoretical model were also examined in order to characterize the folding processes that depend on the native conformations and the amino acid sequences. Finally, the free energy landscapes were discussed based on these analyses.

Pattern formation in spatiotemporal chaotic systems is investigated. Temporally chaotic and spatially ordered patterns are observed by varying the coupling strength. Spatial orderings emerge spontaneously due to self-organization of partial and nonlocal chaos synchronization, governed by various types of spatial symmetries. The first and secondary bifurcations from spatially disordered chaos to chaos with different levels of spatial orderings are observed and the scaling behaviors associated with these bifurcations are statistically analyzed.

Starting from a general ansatz, we show how community detection can be interpreted as finding the ground state of an infinite range spin glass. Our approach applies to weighted and directed networks alike. It contains the ad hoc introduced quality function from [J. Reichardt and S. Bornholdt, Phys. Rev. Lett. 93, 218701 (2004)] and the modularity $Q$ as defined by Newman and Girvan [Phys. Rev. E 69, 026113 (2004)] as special cases. The community structure of the network is interpreted as the spin configuration that minimizes the energy of the spin glass with the spin states being the community indices. We elucidate the properties of the ground state configuration to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study. Further, we show how hierarchies and overlap in the community structure can be detected. Computationally efficient local update rules for optimization procedures to find the ground state are given. We show how the ansatz may be used to discover the community around a given node without detecting all communities in the full network and we give benchmarks for the performance of this extension. Finally, we give expectation values for the modularity of random graphs, which can be used in the assessment of statistical significance of community structure.

A model of mobile, charged ion channels embedded in a biomembrane is investigated. The ion channels fluctuate between an opened and a closed state according to a simple two-state reaction scheme whereas the total number of ion channels is a conserved quantity. Local transport mechanisms suggest that the ion channel densities are governed by electrodiffusionlike equations that have to be supplemented by a cable-type equation describing the dynamics of the transmembrane voltage. It is shown that the homogeneous distribution of ion channels may become unstable to either a stationary or an oscillatory instability. The nonlinear behavior immediately above threshold of an oscillatory bifurcation occurring at finite wave number is analyzed in terms of amplitude equations. Due to the conservation law imposed on ion channels, large-scale modes couple to the finite-wave-number instability and have thus to be included in the asymptotic analysis near the onset of pattern formation. A modified Ginzburg-Landau equation extended by long-wavelength stationary excitations is established, and it is highlighted how the global conservation law affects the stability of traveling ion channel density waves.

We describe the dynamics of bound states of same-chirality spirals in a generic numerical model of an excitable medium. For each bound state, we analyze its tip trajectory patterns and determine its characteristic frequencies. We report two previously unidentified bound states: for spiral pairs, a state that exhibits alternating cycles of small and large distances between collisions $\left(A_2\right)$; for triplets, the first example of a meandering bound state $\left(M_3\right)$. In parameter space, $A_2$ lies in between the previously described oscillating pairs $\left(O_2\right)$ and master-slave pairs $\left(MS\right)$. We present numerical evidence that the transition $O_2\to A_2$ occurs via a supercritical period-doubling bifurcation, while the transition $A_2\to MS$ occurs via a symmetry breaking secondary Hopf bifurcation. A classification of all regimes according to dynamical systems theory exposes the wealth of phenomena exhibited by multiarmed spiral waves.

The chaotic behavior of a chemical reaction can be controlled perturbing periodically some of the parameters externally governing the reaction. Based on the resonance phenomenon, the method of external forcing can convert chaotic behavior into a periodical one through the application of a sinusoidal modulation. In this paper we analyze the effect of a periodical perturbation on room temperature in a model of cellular automaton that studies catalytic oxidation of $\mathrm{CO}$. This model considers the reaction of carbon monoxide and oxygen adsorbed on a surface allowing the variation of the surface temperature and analyzing the time oscillations in the reaction. The results of simulations of this model show quasiperiodical and chaotic behaviors. Then the strategy of control through periodical forcing is able to remove the chaotic dynamics by means of the stabilization of periodical solutions, there being enough of a perturbing harmonic function with only one frequency to transform a chaotic state of the system into a periodical state with periodicity 1.

Pairing together planar material slabs with opposite signs for the real parts of their constitutive parameters has been shown to lead in the steady-state regime to interesting and unconventional properties that are not otherwise observable for single slabs, such as resonance, anomalous tunneling, transparency, and subwavelength imaging through the reconstruction of evanescent waves [A. Alù and N. Engheta, IEEE Trans. Antennas Prop. 51, 2558 (2003)]. The mechanics of the phenomenon, however, and in particular how the steady-state resonant response is reached, has not been explored. Here we analyze how a transient sinusoidal signal that starts at $t=0$ interacts with such a complementary pair of finite size using a finite-difference time-domain (FDTD) technique. Multiple reflections and transmissions at each interface are shown to build up to the eventual steady-state response of the pair, and during this process one can observe how the “growing exponential” phenomenon may actually occur inside this bilayer. As with any resonant phenomena, the time response of this effect depends on the $Q$ of the system, which is related to the geometrical and electrical parameters of the bilayer. Transparency to finite beams and reconstruction of the subwavelength details of an image are shown in the transient and steady-state response of the setup through one-dimensional and two-dimensional FDTD simulations.

We investigate propagation of light pulses in photonic crystals in the vicinity of the zero diffraction point. We show that Gaussian pulses due to nonzero width of their temporal spectrum spread weakly in space and time during the propagation. We also find the family of nonspreading pulses, propagating invariantly in the vicinity of the zero diffraction point of photonic crystals.

We study a reaction model that presents stochastic resonance purely due to internal noise. This means that the only source of fluctuations comes from the discrete character of the reactants, and no more noises enter into the system. Our analysis reveals that the phenomenon is highly complex, and that is generated by the interplay of different stochasticity at the three fixed points of a bistable system.

We study the equilibrium states of energy functions involving a large set of real variables, defined on the links of sparsely connected networks, and interacting at the network nodes, using the cavity and replica methods. When applied to the representative problem of network resource allocation, an efficient distributed algorithm is devised, with simulations showing full agreement with theory. Scaling properties with the network connectivity and the resource availability are found.

We study the distributions of channel openings, local fluxes, and velocities in a two-dimensional random medium of nonoverlapping disks. We present theoretical arguments supported by numerical data of high precision and find scaling laws as functions of the porosity. For the channel openings we observe a crossover to a highly correlated regime at small porosities. The distribution of velocities through these channels scales with the square of the porosity. The fluxes turn out to be the convolution of velocity and channel width corrected by a geometrical factor. Furthermore, while the distribution of velocities follows a Gaussian form, the fluxes are distributed according to a stretched exponential with exponent $1∕2$. Finally, our scaling analysis allows us to express the tortuosity and pore shape factors from the Kozeny-Carman equation as direct average properties from microscopic quantities related to the geometry as well as the flow through the disordered porous medium.

The appearance of a convex dip in the microcanonical entropy of finite systems usually signals a first order transition. However, a convex dip also shows up in some systems with a continuous transition as, for example, in the Baxter-Wu model and in the four-state Potts model in two dimensions. We demonstrate that the appearance of a convex dip in those cases can be traced back to a finite-size effect. The properties of the dip are markedly different from those associated with a first order transition and can be understood within a microcanonical finite-size scaling theory for continuous phase transitions. Results obtained from numerical simulations corroborate the predictions of the scaling theory.

We study front propagation in the reversible reaction-diffusion system $A+A\leftrightarrow A$ on a one-dimensional lattice. Extending the idea of leading particle in studying the motion of the front we write a master equation in the stochastically moving frame attached to this particle. This approach provides a systematic way to improve on estimates of front speed obtained earlier. We also find that the leading particle performs a correlated random walk and this correlation needs to be taken into account to get the correct the value of the front diffusion coefficient.

We present a study, within a mean-field approach, of the stationary states of the kinetic spin-$3∕2$ Blume-Capel model in the presence of a time-dependent oscillating external magnetic field. We use the Glauber-type stochastic dynamics to describe the time evolution of the system. We have found that the behavior of the system strongly depends on the crystal-field interaction. We can identify two types of solutions: a symmetric one where the magnetization $\left(m\right)$ of the system oscillates in time around zero, which corresponds to a paramagnetic phase $\left(P\right)$, and an antisymmetric one where $m$ oscillates in time around a finite value different from zero, namely $\pm 3∕2$ and $\pm 1∕2$ that corresponds to the ferromagnetic-$3∕2$ $\left(F_{3∕2}\right)$ and the ferromagnetic-$1∕2$ $\left(F_{1∕2}\right)$ phases, respectively. There are coexistence regions of the phase space where the $F_{3∕2}$, $F_{1∕2}$ $(F_{3∕2}+F_{1∕2})$, $F_{3∕2}$, $P$ $(F_{3∕2}+P)$, $F_{1∕2}$, $P$ $(F_{1∕2}+P)$, and $F_{3∕2}$, $F_{1∕2}$, $P$ $(F_{3∕2}+F_{1∕2}+P)$ phases coexist, hence the system exhibits seven different phases. We obtain the dynamic phase transition points and find six fundamental phase diagrams which exhibit one or three dynamic tricritical points. We have also calculated the Liapunov exponent to verify the stability of the solutions and the dynamic phase transition points.

A combination of magnetic resonance imaging and x-ray microcomputed tomography has been used to visualize the development of the internal micro-structure within compressed tablets made from a combination of insoluble particles (Eudragit, a polymer) and soluble particles (diltiazem hydrochloride, a drug), during dissolution in water. Air voids in the tablet are seen to coarsen. The size distribution of the air voids is well fitted by a log-normal distribution with a mean size that grows linearly with time. There is evidence for both diffusion of voids and sudden collapse of individual voids, presumably as they coalesce. The behavior of the voids is studied and compared with models of coarsening; the implications for tablet dissolution are considered.

We derive a set of rotationally covariant amplitude equations for use in multiscale simulation of the two-dimensional phase-field crystal model by a variety of renormalization-group (RG) methods. We show that the presence of a conservation law introduces an ambiguity in operator ordering in the RG procedure, which we show how to resolve. We compare our analysis with standard multiple-scale techniques, where identical results can be obtained with greater labor, by going to sixth order in perturbation theory, and by assuming the correct scaling of space and time.

We present a combined experimental and Monte Carlo study of a nematic phase in the presence of quenched disorder. The turbidity of a nematic liquid crystal embedded in a porous polymer membrane is measured under different applied field conditions for field-cooled and zero-field-cooled samples. We find that a significant permanent alignment of the nematic can be induced by fields as low as $0.1\mathrm{V}∕\mathrm{\mu }\mathrm{m}$ applied during the isotropic to nematic transition. An analogous effect and dependence on sample history is found by studying the order parameter of a sprinkled disorder Lebwohl-Lasher spin model, indicating that dilute quenched randomness is sufficient to produce memory effects in nematics. The large memory induced by field cooling appears to be written in the system during the transition as a result of the field action on freely oriented nematic nuclei. At lower temperature the nuclei consolidate into permanent nematic textures developed from the interaction with quenched disorder.

We study evolutionary game dynamics in finite populations. We analyze an evolutionary process, which we call pairwise comparison, for which we adopt the ubiquitous Fermi distribution function from statistical mechanics. The inverse temperature in this process controls the intensity of selection, leading to a unified framework for evolutionary dynamics at all intensities of selection, from random drift to imitation dynamics. We derive a simple closed formula that determines the feasibility of cooperation in finite populations, whenever cooperation is modeled in terms of any symmetric two-person game. In contrast with previous results, the present formula is valid at all intensities of selection and for any initial condition. We investigate the evolutionary dynamics of cooperators in finite populations, and study the interplay between intensity of selection and the remnants of interior fixed points in infinite populations, as a function of a given initial number of cooperators, showing how this interplay strongly affects the approach to fixation of a given trait in finite populations, leading to counterintuitive results at different intensities of selection.

The transport process by which a T cell makes high-frequency encounters with antigen-presenting cells following infection is an important element of adaptive immunity. Recent experimental work has allowed in vivo cell motility to be characterized in detail. On the basis of experimental data we develop a quantitative model for encounters between T cells and antigen-presenting cells. We model this as a transport-limited chemical reaction with the dynamics dependent on physical contact between randomly moving reactants. We use asymptotic methods to calculate a time distribution which characterizes the delay before a T cell is activated and use Monte Carlo simulations to verify the analysis. We find that the density of antigen-primed dendritic cells within the lymph node paracortex must be greater than $35\mathrm{cells}∕{\mathrm{mm}}^3$ for a T cell to have a more than $50\%$ chance of encountering a dendritic cell within $24\mathrm{h}$. This density is much larger than existing estimates based on calculations which neglect the transport process. We also use simulations to compare a T cell which re-orients isotropically with a T cell which turns according to an experimentally observed distribution and find that the effects of anisotropy on the solution are small.

Using the continuous time Monte Carlo method, we simulated the translocation of a polynucleotide chain driven through a nanopore by an electric field. We have used two models of driven diffusion due to the electric field. The chain may have strong interaction with the pore, and depends on which end of the chain first enters the pore. Depending on this interaction, in both cases, the distribution of times for the chain to pass through the pore in our model is found to have three peaks, as observed in the experiment of Kasianowicz Brandin, Branton, and Deamer [Proc. Natl. Acad. Sci. USA 93, 13770 (1996)].