The wrinkled geometry of thin films is known to vary appreciably as the applied stresses exceed their buckling threshold. Here we derive and analyze a minimal, nonperturbative set of equations that captures the continuous evolution of radial wrinkles in the simplest axisymmetric geometry from threshold to the far-from-threshold limit, where the compressive stress collapses. This description of the growth of wrinkles is different from the traditional post-buckling approach and is expected to be valid for highly bendable sheets. Numerical analysis of our model predicts two surprising results. First, the number of wrinkles scales anomalously with the thickness of the sheet and the exerted load, in apparent contradiction with previous predictions. Second, there exists an invariant quantity that characterizes the mutual variation of the amplitude and number of wrinkles from threshold to the far-from-threshold regime.

The viscoelasticity of a two-dimensional (2D) liquid stronglycoupled dusty plasma is studied experimentally, without macroscopic shear. Positions and velocities of the dust particles, measured by video microscopy, are used as the inputs to the generalized Green-Kubo relation to obtain the complex viscosity $\eta \left(\omega \right)$. The real part of $\eta \left(\omega \right)$ (which corresponds to dissipation) diminishes gradually with frequency, while the imaginary part (which corresponds to elasticity) is peaked at a frequency below the 2D dusty plasma frequency. The viscoelastic approximation is found to accurately describe the 2D experimental results for $\eta \left(\omega \right)$, yielding the Maxwell relaxation time ${\tau }_M=0.10\mathrm{s}$. Results for $\eta \left(\omega \right)$ are compared to 2D molecular dynamics Yukawa simulations and to a previous experiment that was performed using an oscillating macroscopic shear.

A modified unified kinetic scheme for the prediction of fluid flow behaviors in all flow regimes is described. The time evolution of macrovariables at the cell interface is calculated with the idea that both free transport and collision mechanisms should be considered. The time evolution of macrovariables is obtained through the conservation constraints. The time evolution of local Maxwellian distribution is obtained directly through the one-to-one mapping from the evolution of macrovariables. These improvements provide more physical realities in flow behaviors and more accurate numerical results in all flow regimes especially in the complex transition flow regime. In addition, the improvement steps introduce no extra computational complexity.

We consider a directed Abelian sandpile on a strip of size $2\times n$, driven by adding a grain randomly at the left boundary after every $T$ timesteps. We establish the exact equivalence of the problem of mass fluctuations in the steady state and the number of zeros in the ternary-base representation of the position of a random walker on a ring of size $3^n$. We find that while the fluctuations of mass have a power spectrum that varies as $1/f$ for frequencies in the range $3^{-2n}\ll f\ll 1/T$, the activity fluctuations in the same frequency range have a power spectrum that is linear in $f$.

Response to small external forces is investigated in quasistationary states of Hamiltonian systems having long-range interactions. Quasistationary states are recognized as stable stationary solutions to the Vlasov equation, and, hence, the linear response theory to the Vlasov equation is proposed for spatially one-dimensional systems with periodic boundary condition. The proposed theory is applicable both to homogeneous and to inhomogeneous quasistationary states and is demonstrated in the Hamiltonian mean-field model. In the homogeneous case magnetic susceptibility is explicitly obtained, and the Curie-Weiss like law is suggested in a high-energy region. The linear response is also computed in the inhomogeneous case, and resonance absorption is investigated to extract nonequilibrium dynamics in the unforced system. Theoretical predictions are examined by direct numerical simulations of the Vlasov equation.

Two important assumptions are often made in the analysis of molecular self-assembly at equilibrium, viz., that sequential is preferred to random aggregation and that the equilibrium constants at each stage of aggregation are equal, though both assumptions have not been justified strictly. In the present work we show that molecular self-assembly leading to formation of linear polymers and proceeding in a random manner appears to be less entropically favored than sequential aggregation, which provides a physical background for assuming sequential aggregation when studying molecular self-assembly in solution. Exact equations for analysis of experimental data for molecular assembly proceeding in a sequential manner were derived by taking strict account of the profile of the equilibrium constant, which provides a physically more correct approach than that using the conventional indefinite equilibrium constant (EK) model.

The nonlinear dynamic behavior of microscopic bubbles near a rigid wall is investigated. Oscillations are driven by the ultrasonic pressure field that arises in various biomedical applications such as ultrasound imaging or targeted drug delivery. It is known that, when bubbles approach a blood-vessel wall, their linear dynamic response is modified. This modification may be very useful for real-time detection of bubbles that have found targets; in future therapeutic technologies, it may be useful for controlled release of medical agents encapsulating microbubbles. In this paper, the nonlinear response of microbubbles near a wall is studied. The Keller-Miksis-Parlitz equation is adopted, but modified to account for the presence of a rigid wall. This base model describes the time evolution of the bubble surface, which is assumed to remain spherical, and accounts for the effect of acoustic radiation losses owing to liquid compressibility in the momentum conservation. Two situations are considered: the base case of an isolated bubble in an unbounded medium, and a bubble near a rigid wall. In the latter case, the wall influence is modeled by including a symmetrically oscillating image bubble. The bubble dynamics is traced using a numerical solution of the model equation. Subsequently, Floquet theory is used to accurately detect the bifurcation point where bubble oscillations stop following the driving ultrasound frequency and undergo period-changing bifurcations. Of particular interest is the detection of the subcritical period-tripling and -quadrupling transition. The parametric bifurcation maps are obtained as functions of nondimensional parameters representing the bubble radius, the frequency and pressure amplitude of the driving ultrasound field, and the distance from the wall. It is shown that the presence of the wall generally stabilises the bubble dynamics, so that much larger values of the pressure amplitude are needed to generate nonlinear responses. Thus, a clinical protocol in which selected nonlinear harmonics are examined under varying insonation amplitudes may be useful in detecting microbubble proximity to walls.

We present a direct numerical simulation method for investigating the dynamics of dispersed particles in a compressible solvent fluid. The validity of the simulation is examined by calculating the velocity relaxation of an impulsively forced spherical particle with a known analytical solution. The simulation also gives information about the fluid motion, which provides some insight into the particle motion. Fluctuations are also introduced by random stress, and the validity of this case is examined by comparing the calculation results with the fluctuation-dissipation theorem.

We consider a finite number of particles with soft-core interactions, subjected to thermal fluctuations and confined in a box with excluded mutual passage. Using numerical simulations, we focus on the influence of the longitudinal confinement on the transient behavior of the longitudinal mean squared displacement. We exhibit several power laws for its time evolution according to the confinement range and to the rank of the particle in the file. We model the fluctuations of the particles as those of a chain of springs and point masses in a thermal bath. Our main conclusion is that actual system dynamics can be described in terms of the normal oscillation modes of this chain. Moreover, we obtain complete expressions for the physical observables, in excellent agreement with our simulations. The correct power laws for the time dependency of the mean squared displacement in the various regimes are recovered, and analytical expressions of the prefactors according to the relevant parameters are given.

Current limiters and constant current sources, which play important roles in electronic circuits, have been built up for many decades. Their thermal counterparts, heat current limiters and constant heat current sources, are still not available yet. By combining two typical nonlinear lattices, the Frenkel-Kontorova (FK) lattice and a coupled rotator lattice, together, we present by numerical simulation a model that displays complete negative differential thermal resistance (NDTR). Namely, in a wide regime, the heat current that flows through this model is always a decreasing function of the temperature drop applied to it, no matter whether the change in the temperature drop is due to a change in the high or the low temperature. We show that, upon being properly set up, a complete NDTR can work as either a heat current limiter or a constant heat current source.

Cuprates show multiphase and multiscale complexity that has hindered physicists search for the mechanism of high $T_c$ for many years. Recently the interest has been addressed to a possible optimum inhomogeneity of dopants, defects, and interstitials, and the structural scale invariance of dopants detected by scanning micro-x-ray diffraction has been reported to promote the critical temperature. In order to shed light on critical phenomena on granular materials, here we propose a stylized model capturing the essential characteristics of the superconducting-insulator transition of a highly dynamical, heterogeneous granular material: the random transverse Ising model (RTIM) on annealed complex network. We show that when the networks encode for high heterogeneity of the expected degrees described by a power-law distribution, the critical temperature for the onset of the superconducting phase diverges to infinity as the power-law exponent $\gamma$ of the expected degree distribution is less than 3, i.e., $\gamma <3$. Moreover we investigate the case in which the critical state of the electronic background is triggered by an external parameter $g$ that determines an exponential cutoff in the power-law expected degree distribution characterized by an exponent $\gamma$. We find that for $g=g_c$ the critical temperature for the superconducting-insulator transition has a maximum if $\gamma >3$ and diverges if $\gamma <3$.

The orientational order parameters $\langle P_2\rangle$ and $\langle P_4\rangle$ of the ferroelectric, de Vries–type liquid crystal 9HL have been determined in the Sm$A{}^{*}$ and Sm$C{}^{*}$ phases by means of polarized Raman spectroscopy, and in the Sm$A{}^{*}$ phase using x-ray diffraction. Quantum density functional theory predicts Raman spectra for 9HL that are in good agreement with the observations and indicates that the strong Raman band probed in the experiment corresponds to the uniaxial, coupled vibration of the three phenyl rings along the molecular long axis. The magnitudes of the orientational order parameters obtained in the Raman and x-ray experiments differ dramatically from each other, a discrepancy that is resolved by considering that the two techniques probe the orientational distributions of different molecular axes. We have developed a systematic procedure in which we calculate the angle between these axes and rescale the orientational order parameters obtained from x-ray scattering with results that are then in good agreement with the Raman data. At least in the case of 9HL, the results obtained by both techniques support a “sugar loaf” orientational distribution in the Sm$A{}^{*}$ phase with no qualitative difference to conventional smectics $A$. The role of individual molecular fragments in promoting de Vries–type behavior is considered.

The necklace model, which mimics the reptation of a chain of $N$ beads in a square lattice, is used to study the drift velocity of charged linear polymers in gels under an applied electric field that periodically changes its direction. The characteristics of the model allow us to determine the effects of the alternating electric field on the chains’ dynamics. We explain why chains of different $N$ can be made to move in opposite directions with a nonuniform electric field with certain values of intensity and frequency. The key point is that, when alternating electric fields are applied, longer chains spend more time out of the steady-state regime than lower chains. Numerical results are obtained by means of Monte Carlo simulations and they are qualitatively in agreement with experiments of DNA migration in gel electrophoresis.

We report on the debonding process of a double-sided adhesive tape sandwiched between two glass plates. When the glass plates are separated from each other at a constant rate, a highly asymmetric extension of top and bottom adhesive layers and bending of the inner film are observed first. As the separation proceeds, the elongation of both layers becomes symmetric, and the inner film becomes flat again. When this happens, there appears a local maximum in the force-displacement curve. We explain this asymmetry-symmetry transition and discuss the role of the bimodal force-displacement relation of each adhesive layer. We also discuss the effect of the inner film thickness and the separation rate on the debonding behavior, which causes undesirable early detachment of the double-sided adhesive tape in a certain condition.

Folded proteins have a modular assembly. They are constructed from regular secondary structures like $\alpha$ helices and $\beta$ strands that are joined together by loops. Here we develop a visualization technique that is adapted to describe this modular structure. In complement to the widely employed Ramachandran plot that is based on toroidal geometry, our approach utilizes the geometry of a two sphere. Unlike the more conventional approaches that describe only a given peptide unit, ours is capable of describing the entire backbone environment including the neighboring peptide units. It maps the positions of each atom to the surface of the two-sphere exactly how these atoms are seen by an observer who is located at the position of the central $C_{\alpha }$ atom. At each level of side-chain atoms we observe a strong correlation between the positioning of the atom and the underlying local secondary structure with very little if any variation between the different amino acids. As a concrete example we analyze the left-handed helix region of nonglycyl amino acids. This region corresponds to an isolated and highly localized residue independent sector in the direction of the $C_{\beta }$ carbons on the two-sphere. We show that the residue independent localization extends to $C_{\gamma }$ and $C_{\delta }$ carbons and to side-chain oxygen and nitrogen atoms in the case of asparagine and aspartic acid. When we extend the analysis to the side-chain atoms of the neighboring residues, we observe that left-handed $\beta$ turns display a regular and largely amino acid independent structure that can extend to seven consecutive residues. This collective pattern is due to the presence of a backbone soliton. We show how one can use our visualization techniques to analyze and classify the different solitons in terms of selection rules that we describe in detail.

The shape transformation induced by pulling or compressing a vesicle along the symmetric axis is discussed in light of the numerical solution to the bending energy model with fixed enclosing volume and surface area. A complete phase diagram in terms of the external force and reduced vesicle volume is investigated. Some experimental observations are explained by the solution.

We consider epidemics in metapopulations on different network topologies. Recent work on epidemics on networks has focused on epidemics of humans. In this work we present a model for epidemics on directed networks, which are found, for example, in the livestock trade. We show that the direction of edges and the modular structure of networks have an impact on the outbreak size and the time of the outbreak peak. In some circumstances, the outbreak size in directed networks can even be larger than in undirected systems. The results presented here could be useful for decision-making processes in directed modular systems.

In the study of the evolution of cooperation, resource limitations are usually assumed just to provide a finite population size. Recently, however, agent-based models have pointed out that resource limitation may modify the original structure of the interactions and allow for the survival of unconditional cooperators in well-mixed populations. Here, we present analytical simplified versions of two types of agent-based models recently published: one in which the limiting resource constrains the ability of reproduction of individuals but not their survival, and a second one where the limiting resource is necessary for both reproduction and survival. One finds that the analytical models display, with a few differences, the same qualitative behavior of the more complex agent-based models. In addition, the analytical models allow us to expand the study and identify the dimensionless parameters governing the final fate of the system, such as coexistence of cooperators and defectors, or dominance of defectors or of cooperators. We provide a detailed analysis of the occurring phase transitions as these parameters are varied.

We extend simple opinion models to obtain stable but continuously evolving communities. Our scope is to meet a challenge raised by sociologists of generating “structures that last from nonlasting entities.” We achieve this by introducing two kinds of noise on a standard opinion model. First, agents may interact with other agents even if their opinion difference is large. Second, agents randomly change their opinion at a constant rate. We show that for a large range of control parameters, our model yields stable and fluctuating polarized states, where the composition and mean opinion of the emerging groups is fluctuating over time.

Shock tube experiments are performed in order to study shock propagation along a two-gas layer in a confined geometry and to compare it to the case of a homogeneous density equivalent mixture. The analysis of the homogeneous case gives values for the adiabatic coefficient and density of the mixture of both gases, while the comparison between heterogeneous and homogeneous media with the same averaged density shows modifications of the shock front shape and velocity. In the two-gas layer, the shock propagates faster than in the homogeneous medium. The shock front is curved with a triple point which appears close to the shock-tube wall, in the slow medium, while it stays planar during its whole propagation in the homogeneous mixture. A correlation is found between the angle of curvature and the shock velocity increase. It is confirmed by two-dimensional Eulerian numerical calculations. Experiments and calculations exhibit very good agreement on all the measurements when molecular diffusion is taken into account in the numerical calculations. A sustained irregular refraction pattern of the shock front at the diffuse interface of both gases is obtained experimentally and confirmed by the calculations.