Quantum manifestations of the dynamics around resonant tori in perturbed Hamiltonian systems, dictated by the Poincaré-Birkhoff theorem, are shown to exist. They are embedded in the interactions involving states which differ in a number of quanta equal to the order of the classical resonance. Moreover, the associated classical phase space structures are mimicked in the quasiprobability density functions and their zeros.

Deformation, orientation and internal flow of lipid bilayer vesicles in linear shear flows are investigated using phase contrast microscopy. We construct a rotating-cylinder apparatus, which can generate a linear shear flow with constant shear rates. Vesicles are prepared from 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) by the gentle hydration method. When visualizing internal flows, polystyrene tracer particles are mixed with the hydration water solution. In our observation, vesicles deform to steady ellipsoidal shapes and show constant orientations given by ${\theta }_{\mathrm{i}}$, which is the angle between the major axis and the flow direction. The tracer particles inside a vesicle rotate around the center of the vesicle along ellipsoidal orbits, which are homothetic to the shape of the vesicle. It is shown that the relationship between ${\theta }_{\mathrm{i}}$ and the swelling ratio (volume/surface ratio) $S_w$ agrees quantitatively with the experimental result of Abkarian et al. [Biophys. J.89, 1055 (2005)], which was obtained with vesicles in wall-bounded shear flows. It also agrees with a theoretical analysis of Keller and Skalak [J. Fluid Mech.120, 27 (1982)] and other numerical simulations. It is also shown that angular velocities of the particles near the membrane change periodically and agree quantitatively with the experimental result for the motion of a particle adhering to the membrane of a tank-treading vesicle [Kantsler and Steinberg, Phys. Rev. Lett.95, 258101 (2005)]. A statistical analysis indicates that the velocity of the internal fluid close to the membrane is not constant along the circumference, which implies the possibility of a three-dimensional flow field of the lipid molecules or an apparent stretching motion of the membrane by the effect of hidden surface area due to thermal fluctuation.

We derive an upper bound on the difference between the long-time average and the microcanonical ensemble average of observables in isolated quantum systems. We propose, numerically verify, and analytically support a new hypothesis, the eigenstate randomization hypothesis (ERH), which implies that in the energy eigenbasis the diagonal elements of observables fluctuate randomly. We show that ERH includes the eigenstate thermalization hypothesis (ETH) and makes the aforementioned bound vanishingly small. Moreover, ERH is applicable to integrable systems for which ETH breaks down. We argue that the range of the validity of ERH determines that of the microcanonical description.

Large deviation functions for an exactly solvable lattice gas model of diffusing particles on a ring, subject to pair annihilation and creation, are obtained analytically using exact free-fermion techniques. Our findings for the large deviation function for the current are compared to recent results of Appert-Rolland et al. [Phys. Rev. E 78, 021122 (2008)] for diffusive systems with conserved particle number. Unlike conservative dynamics, our nonconservative model has no universal finite-size corrections for the cumulants. However, the leading Gaussian part has the same variance as in the conservative case. We also elucidate some properties of the large deviation functions associated with particle creation and annihilation.

The study of selection and gating in potassium channels is a very important issue in modern biology. Indeed, such structures are known in essentially all types of cells in all organisms where they play many important functional roles. The mechanism of gating and selection of ionic species is not clearly understood. In this paper we study a model in which gating is obtained via an affinity-switching selectivity filter. We discuss the dependence of selectivity and efficiency on the cytosolic ionic concentration and on the typical pore open state duration. We demonstrate that a simple modification in the way in which the selectivity filter is modeled yields larger channel efficiency.

We put forward a nonlinear wave model describing the fundamental dynamical features of an aggressive type of brain tumors. Our model accounts for the invasion of normal tissue by a proliferating and propagating rim of active glioma cancer cells in the tumor boundary and the subsequent formation of a necrotic core. By resorting to numerical simulations, phase space analysis, and exact solutions we prove that bright solitary tumor waves develop in such systems. Possible implications of our model as a tool to extract relevant patient specific tumor parameters in combination with standard preoperative clinical imaging are also discussed.

We study the tagged-particle dynamics by solving equations of the mode-coupling theory (MCT). The numerical solutions are compared with results obtained by the molecular dynamics (MD) simulations from a unified point of view proposed by Tokuyama [Phys. Rev. E 80, 031503 (2009)]. We propose a way of comparison in which the reduced long-time self-diffusion coefficient is used to characterize states of the system. The comparison reveals that the tagged-particle dynamics calculated from MCT qualitatively deviates from that obtained by MD. Our results suggest that the deviation originates from the starting equation of MCT.

Effects of Darrieus-Landau (DL) instability on the structure and propagation of turbulent premixed flame fronts are considered. By first hypothesizing separation of time scales of instability and turbulence, we estimate whether the instability can develop in the presence of turbulence of given flow rms-velocity and integral length scale. As a result, we modify the standard turbulent premixed combustion regime diagram by introducing new boundaries, limiting the domain where the instability influences the global flame shape and speed. Based on this analysis, a “turbulence-induced DL cutoff” as a function of turbulence and instability parameters is introduced, which when combined with a turbulent flame speed without DL instability yields the turbulent flame speed accounting for the instability. The consumption turbulent flame speed for no DL instability is formulated from the spectral closure of the $G$ equation, thus accounting for the scale-dependent “turbulent” nature of the problem. Finally, an analytical form of the turbulent flame speed is derived, which is found to agree well with the corresponding experimentally measured turbulent flame speed from literature over wide ranges of normalized turbulence intensities and length scales.

Numerical simulations of convection in a layer filled with ideal gas are presented. The control parameters are chosen such that there is a significant variation of density of the gas in going from the bottom to the top of the layer. The relations between the Rayleigh, Peclet, and Nusselt numbers depend on the density stratification. It is proposed to use a data reduction which accounts for the variable density by introducing into the scaling laws an effective density. The relevant density is the geometric mean of the maximum and minimum densities in the layer. A good fit to the data is then obtained with power laws with the same exponent as for fluids in the Boussinesq limit. Two relations connect the top and bottom boundary layers: The kinetic energy densities computed from free fall velocities are equal at the top and bottom, and the products of free fall velocities and maximum horizontal velocities are equal for both boundaries.

We apply first-principles methodology to study the spatial localization of electric field enhancement at plasmonic resonance and magnetic field enhancement at gyroresonance in a self-similar chain of magnetoplasmonic core-shell nanostructures (MCSNs). Localized regions of high electric and magnetic fields in the vicinity of metal nanostructures can be created in a controlled manner by adjusting the physical parameters characterizing this system and the polarization of the external harmonic excitations. We demonstrate the high degree of control achieved on electric field confinement, of the order of 10${}^3$, down to a feature size of λ/1000 in self-similar chains of MCSNs, where λ denotes the free space wavelength of the resonant excitation. We also compare our findings with recent investigations in related plasmonic nanostructures.

Interactions between quiescent solitons in Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity are systematically investigated. In a previous work two disjoint families of solitons were identified in this model. One family can be viewed as the generalization of the Bragg grating solitons in Kerr nonlinearity with dispersive reflectivity (Type 1). On the other hand, the quintic nonlinearity is dominant in the other family (Type 2). For weak to moderate dispersive reflectivity, two in-phase solitons will attract and collide. Possible collision outcomes include merger to form a quiescent soliton, formation of three solitons including a quiescent one, separation after passing through each other once, asymmetric separation after several quasielastic collisions, and soliton destruction. Type 2 solitons are always destroyed by collisions. Solitons develop sidelobes when dispersive reflectivity is strong. In this case, it is found that the outcome of the interactions is strongly dependent on the initial separation of solitons. Solitons with sidelobes will collide only if they are in-phase and their initial separation is below a certain critical value. For larger separations, both in-phase and $\pi$-out-of-phase Type 1 and Type 2 solitons may either repel each other or form a temporary bound state that subsequently splits into two separating solitons. Additionally, in the case of Type 2 solitons, for certain initial separations, the bound state disintegrates into a single moving soliton.

Monte Carlo simulations of finite-size effects for continuum percolation in three-dimensional, rectangular sample spaces filled with spherical particles were performed. For samples with any dimension less than 10–20 times the particle diameter, finite-size effects were observed. For thin films in the finite-size regime, percolation across the thin direction of the film gave critical volume fraction ($p_c$) values that differed from those along the plane of the film. Simulations perpendicular to the film for very thin samples resulted in $p_c$ values lower than the classical limit of ∼29% (for spheres in a three-dimensional matrix) which increased with film thickness. For percolation along thin films, while holding film thickness constant, $p_c$ increased with increasing sample size, which is a modification of the finite-sized scaling effect for cubic samples. For samples with a large aspect ratio (fibers) and a finite-sized cross-sectional area, the critical volume fraction increased with sample length, as the sample became quasi-one-dimensional. The results are discussed in the context of adding volume along or perpendicular to the percolation direction. From an experimental perspective, these findings indicate that sample shape, as well as relative size, influences percolation in the finite-size regime.

Motivated by recent work [D. Cubero et al., Phys. Rev. E 82, 041116 (2010)], we examine the mechanisms which determine current reversals in rocking ratchets as observed when varying the frequency of the drive. We found that a class of these current reversals in the frequency domain is precisely determined by dissipation-induced symmetry breaking. Our experimental and theoretical work thus extends and generalizes the previously identified relationship between dynamical and symmetry-breaking mechanisms in the generation of current reversals.

We develop an approximate theoretical method to study discrete stochastic birth and death models that include a delay time. We analyze the effect of the delay in the fluctuations of the system and obtain that it can qualitatively alter them. We also study the effect of distributed delay. We apply the method to a protein-dynamics model that explicitly includes transcription and translation delays. The theoretical model allows us to understand in a general way the interplay between stochasticity and delay.

We estimate the exceedance probability $W(x,\alpha ;L)$ that, in a long-term correlated Gaussian-distributed (sub) record of length $L$ characterized by a fluctuation exponent $\alpha$ between 0.5 and 1.5, a relative increase $\Delta /{\sigma }_t$ of size larger than $x$ occurs, where $\Delta$ is the total observed increase measured by linear regression and ${\sigma }_t$ is the standard deviation around the regression line. We consider $L$ between 500 and 2000, which is the typical length scale of monthly local and reconstructed annual global temperature records. We use scaling theory to obtain an analytical expression for $W(x,\alpha ;L)$. From this expression, we can determine analytically, for a given confidence probability $Q$, the boundaries $\pm x_Q(\alpha ,L)$ of the confidence interval. In the presence of an external linear trend, the total observed increase is the sum of the natural and the external increase. An observed relative increase $\Delta /{\sigma }_t$ is considered unnatural when it is above $x_Q(\alpha ,L)$. In this case, the size of the external relative increase is bounded by $\Delta /{\sigma }_t\pm x_Q(\alpha ,L)$. We apply this approach to various global and local climate data and discuss the different results for the significance of the observed trends.

A postulate that ergodicity and entropy continuously decrease to zero on cooling a liquid to a glassy state was used to support the view that glass has $no$ residual entropy, and the features of mechanical relaxation spectra were cited as proof for the decrease. We investigate whether such spectra and the relaxation isochrones can serve as the proof. We find that an increase in the real component of elastic moduli with an increase in spectral frequency does not indicate continuous loss of ergodicity and entropy, and the spectra do not confirm isothermal glass transition or loss of entropy. Variation in ergodicity and entropy with the spectral frequency has untenable consequences for both thermodynamics and molecular dynamics and implies that, despite a broad distribution of its relaxation times, an equilibrium liquid can be considered as always ergodic. Perturbation from equilibrium used to obtain a spectrum does not have the effect of dynamic freezing and unfreezing, and Maxwell-Voigt models for the mechanical response function have neither the characteristic irreversibility of liquid-glass transition nor are commutable to ergodicity or entropy.

We introduce and study random bipartite networks with hidden variables. Nodes in these networks are characterized by hidden variables that control the appearance of links between node pairs. We derive analytic expressions for the degree distribution, degree correlations, the distribution of the number of common neighbors, and the bipartite clustering coefficient in these networks. We also establish the relationship between degrees of nodes in original bipartite networks and in their unipartite projections. We further demonstrate how hidden variable formalism can be applied to analyze topological properties of networks in certain bipartite network models, and verify our analytical results in numerical simulations.

The breakup of alkaline glass and alumina plates due to planar impacts on one of their lateral sides is studied. Particular attention is given to investigating the spatial location of the cracks within the plates. Analysis based on a phenomenological model suggests that bifurcations along the cracks’ paths are more likely to take place closer to the impact region than far away from it, i.e., the bifurcation probability seems to lower as the perpendicular distance from the impacted lateral increases. It is also found that many observables are not sensitive to the plate material used in this work, as long as the fragment multiplicities corresponding to the fragmentation of the plates are similar. This gives support to the universal properties of the fragmentation process reported in previous experiments. However, even under the just mentioned circumstances, some spatial observables are capable of distinguishing the material of which the plates are made, which therefore suggests that this universality should be carefully investigated.

The flow of two superimposed Newtonian layers in a channel is investigated numerically in this study. The two-layer film flows inside a long channel due to a pressure gradient. The scaled conservation equations for two-layer incompressible Newtonian film flow are first introduced. The weighted residual approach first proposed by Amaouche et al. [Phys. Fluids 19, 084106 (2007)] is used for finding the suitable weight functions before depth averaging. Subsequently, a linear stability analysis of thin-film equations for two-layer Poiseuille flow is carried out. The formulas which give the asymptotic stability with respect to long-wave perturbations obtained with Navier-Stokes equations [J. Non-Newtonian Fluid Mech. 71, 1 (1997)] are recovered with our averaging equations. In order to mimic the disturbance effect on the coextrusion flow, the steady flow, which is simply the uniform flow of two layers of fluid inside a channel, is then perturbed at inception. Following a finite difference based scheme, two types of boundary conditions are considered at the channel inception, namely a Dirac-type pulse and periodic forcing. The perturbation takes the form of a wave packet which may or may not be amplified as it moves downstream, depending on the values of the parameters involved in the problem. Furthermore, Gaster's relation is used to calculate the spatial growth rate of perturbation. The values obtained from this relation are in good quantitative agreement with those coming from the numerical simulations of thin-film equations. Then, our averaging equations also describe the nonlinear behavior of the interfacial instabilities occurring for the Poiseuille flow of two thin layers.

The growth rate of the dynamo instability as a function of the magnetic Reynolds number $R_{{}_M}$ is investigated by means of numerical simulations for the family of the Arnold-Beltrami-Childress (ABC) flows and for two different forcing scales. For the ABC flows that are driven at the largest available length scale, it is found that, as the magnetic Reynolds number is increased: (a) The flow that results first in a dynamo is the $2\frac{1}{2}$-dimensional flow for which $A=B$ and $C=0$ (and all permutations). (b) The second type of flow that results in a dynamo is the one for which $A=B\simeq 2C/5$ (and permutations). (c) The most symmetric flow, $A=B=C$, is the third type of flow that results in a dynamo. (d) As $R_{{}_M}$ is increased, the $A=B=C$ flow stops being a dynamo and transitions from a local maximum to a third-order saddle point. (e) At larger $R_{{}_M}$, the $A=B=C$ flow reestablishes itself as a dynamo but remains a saddle point. (f) At the largest examined $R_{{}_M}$, the growth rate of the $2\frac{1}{2}$-dimensional flows starts to decay, the $A=B=C$ flow comes close to a local maximum again, and the flow $A=B\simeq 2C/5$ (and permutations) results in the fastest dynamo with growth rate $\gamma \simeq 0.12$ at the largest examined $R_{{}_M}$. For the ABC flows that are driven at the second largest available length scale, it is found that (a) the 2$\frac{1}{2}$-dimensional flows $A=B,C=0$ (and permutations) are again the first flows that result in a dynamo with a decreased onset. (b) The most symmetric flow, $A=B=C$, is the second type of flow that results in a dynamo. It is, and it remains, a local maximum. (c) At larger $R_M$, the flow $A=B\simeq 2C/5$ (and permutations) appears as the third type of flow that results in a dynamo. As $R_{{}_M}$ is increased, it becomes the flow with the largest growth rate. The growth rates appear to have some correlation with the Lyapunov exponents, but constructive refolding of the field lines appears equally important in determining the fastest dynamo flow.