Anisotropy of the permeability tensor in statistically uniform porous media of sizes used in typical computer simulations is studied. Although such systems are assumed to be isotropic by default, we show that de facto their anisotropic permeability can give rise to significant changes in transport parameters such as permeability and tortuosity. The main parameter controlling the anisotropy is $a/L$, being the ratio of the obstacle to system size. Distribution of the angle $\alpha$ between the external force and the volumetric fluid stream is found to be approximately normal, and the standard deviation of $\alpha$ is found to decay with the system size as ${\left(a/L\right)}^{d/2}$, where $d$ is the space dimensionality. These properties can be used to estimate both anisotropy-related statistical errors in large-scale simulations and the size of the representative elementary volume. For porous media types studied here, the anisotropy effect becomes negligible only if $a/L\lesssim 0.01$. This constraint was apparently violated in many previous computer simulations that need now to be recalculated.

A systematic procedure to derive shell models for magnetohydrodynamic turbulence is proposed. It takes into account the conservation of ideal quadratic invariants such as the total energy, the cross helicity, and the magnetic helicity, as well as the conservation of the magnetic energy by the advection term in the induction equation. This approach also leads to simple expressions for the energy exchanges as well as to unambiguous definitions for the energy fluxes. When applied to the existing shell models with nonlinear interactions limited to the nearest-neighbor shells, this procedure reproduces well-known models but suggests a reinterpretation of the energy fluxes.

Surface instabilities in vertically vibrated suspensions of various powders dispersed in silicone oil are investigated in quasi-two-dimensional (2D) and quasi-one-dimensional (1D) systems. As vibration acceleration exceeded a critical value, the flat surface became unstable against a finite-amplitude perturbation. We found an expanding hole or viscous fingerlike pattern in the quasi-2D system and segregation between dried and wet areas in the quasi-1D system. We show that these instabilities are accompanied by convectionlike flow at their rim and in the quasi-1D system, the height of the convectionlike flow can be scaled by acceleration, vibration frequency, diameter of the dispersed powder, mean density of the suspension, and viscosity of silicone oil. We propose a simple model that accounts for the scaling and concentric motion of the convectionlike flow.

The thresholds for the electron multiplication in both multipactor and the so-called collisional multipactor microwave discharges are calculated by means of an individual particle model. The simulations are restricted to low and intermediate gas pressures, where the collisional mean-free path of electrons is of the same order or larger than the characteristic dimension of the system. Thus, the charge multiplication is caused by both the electron impact ionization of the neutral gas and the secondary electron emission by electron collisions at the surfaces. The charge avalanche is simulated by the numerical integration of the trajectories of electrons up to the characteristic time for the space-charge buildup. The electron dynamics is described by the stochastic Langevin equations where the collisional scatter of electrons is incorporated by means of a random force, while the microwave electric field and the friction are deterministic forces. The physical properties of materials at the walls are considered by means of realistic models deduced from experimental data fitting, while the constant collision frequency model is used for elastic and inelastic electron collisions with neutral atoms. Previous results for low pressure electron multipactor are recovered, and for pressures corresponding to collisional multipactor the predictions of this simple model are in agreement with both the experimental results and particle in cell and Monte Carlo simulations. Finally, physical conditions under which the charge multiplication develops and the limitations for higher pressures of the proposed model are also discussed.

We consider geometric variational problems for a functional defined on a curve in a three-dimensional space. The functional is assumed to be written in a form invariant under the group of Euclidean motions. We present the Euler-Lagrange equations as equilibrium equations for the internal force and moment. Examples are discussed to illustrate our approach. This form of the equations particularly serves to promote the study of biofilaments and nanofilaments.

A family of smooth invariant tori of a Hamiltonian system can be parameterized by the values of the actions or the frequencies. These parameterizations are related by the action-frequency map. The purpose of this paper is to show that when the action-frequency map is degenerate, it signals a homoclinic bifurcation. Remarkably, the nonlinear properties of this homoclinic bifurcation to invariant tori are determined by the curvature of the action-frequency map. A homoclinic angle is also generated which is analogous to a Hannay-Berry phase shift. The theory is constructive and so can usefully be combined with computation. Some implications for quantization, and the generation of solitary waves are also discussed.

Microphase separation in poly($N$-isopropylacrylamide)(PNIPA)-clay nanocomposite hydrogels (NC gels) is investigated by means of contrast-variation small-angle neutron scattering (CV-SANS) and dynamic light scattering (DLS). By using CV-SANS, it is revealed that microphase separation occurs in NC gels above the lower-critical solution temperature (LCST) of PNIPA aqueous solutions. The observed partial scattering functions show that only the spatial distribution of PNIPA chains is highly distorted by microphase separation and PNIPA chains are preferentially adsorbed on the clay surfaces, where the PNIPA-rich phase forms nanoscaled bicontinuous structure mediated by the clay particles. Additional DLS measurements for dilute solutions with PNIPA and/or the clay nanoparticles confirm that aggregation of PNIPA above the LCST is dramatically suppressed by addition of clay particles. Based on these observations, we conclude that strong affinity between the polymer and clay has a significant effect on the phase separation in NC gels and allows one to tune the length scale of the phase separation phenomenon by clay concentration.

We examine numerically the yielding or failure of small granular packings subjected to an increasing deviatoric stress. As the load increases, the packing softens and the number of sliding contacts rises. When the packing fails, the kinetic energy starts to rise exponentially in time. It is always possible to identify a contact status change that triggers the collapse of the packing. Furthermore, by use of the stiffness matrix, we show that this change often causes a mechanical instability or a motion with neutral stability. In some cases, the status change provokes an oscillation and a second status change following shortly thereafter introduces an instability. Failure can also be considered from the perspective of energy flux: before failure, the energy injected by the load is stored as potential energy in the contacts. When this is no longer possible, failure occurs and the injected energy is converted to kinetic energy. However, the force disequilibrium then soon becomes the dominant energy source.

Sequential Bayesian filters, such as particle filters, are often presented as an ideal means of tracking the state of nonlinear systems. Here shadowing filters are demonstrated to perform better than sequential filters at tracking under specific circumstances. The success of shadowing filters is attributed to avoiding both well-known deficiencies of particle filters, and some newly identified problems.

Capillary cone jets are natural microfluidic structures arising in steady capillary tip streaming, whose paradigms are electrospray and flow focusing phenomena. In this work, we make a profound revision of the basic underlying physics of generic cone jets from thousands of experimental measurements, most of them reported in the literature. First, the boundaries of the stability region of steady jetting are calculated. We describe these limitations by instability mechanisms associated with the local flow structure in the tip and the issuing jet and with the global behavior of the meniscus. Second, to undertake a general physical treatment of cone jets in steady regime, we analyze the energy balance taking place in the tips of both flow focusing and electrospray. This analysis yields a fundamental result: if the electrospray data are expressed in terms of an effective pressure drop, both phenomena satisfy the same scaling law for the droplet size, which exhibits nearly complete similarity in the parameter window where quasimonodisperse sprays are produced. That effective pressure drop is a function of the liquid properties exclusively, i.e., it does not depend on the operational parameters (flow rate and applied voltage). Moreover, the stability limits of the operational regimes are analyzed in detail, finding fundamental coincidences between flow focusing and electrospray as well. These results provide most useful general description and predictive scaling laws for nearly monodisperse microspraying or nanospraying based on steady cone jets, of immediate applicability in analytical chemistry, chemical engineering, biochemistry, pharmaceutical and food technologies, painting, and many other technological fields.

A multitime probing of density fluctuations is introduced to investigate hidden time scales of heterogeneous dynamics in glass-forming liquids. Molecular-dynamics simulations for simple glass-forming liquids are performed and a three-time correlation function is numerically calculated for general time intervals. It is demonstrated that the three-time correlation function is sensitive to the heterogeneous dynamics and that it reveals couplings of correlated motions over a wide range of time scales. Furthermore, the time scale of the heterogeneous dynamics ${\tau }_{\text{hetero}}$ is determined by the change in the second time interval in the three-time correlation function. The present results show that the time scale of the heterogeneous dynamics ${\tau }_{\text{hetero}}$ becomes larger than the $\alpha$-relaxation time at low temperatures and large wavelengths. We also find a dynamical scaling relation between the time scale ${\tau }_{\text{hetero}}$ and the length scale $\xi$ of dynamical heterogeneity as ${\tau }_{\text{hetero}}\sim {\xi }^z$ with $z=3$.

Transverse sound velocity of cross-linked tetragonal hen egg-white (HEW) lysozyme crystals containing large amount of water in the crystal was measured using ultrasonic pulse-echo method. All elastic constants of cross-linked crystals were observed to be $C_{11}=C_{22}=5.50\text{GPa}$, $C_{12}=4.33\text{GPa}$, $C_{13}=C_{23}=3.94\text{GPa}$, $C_{33}=5.22\text{GPa}$, $C_{44}=C_{55}=0.68\text{GPa}$, and $C_{66}=0.84\text{GPa}$, respectively. We found that the elastic constants of the cross-linked crystals are identical to those of the intrinsic ones without cross-linking. Moreover, we found that tetragonal HEW lysozyme crystals that enclose large amount of water show decreased elastic constants (softening). In particular, the shear elastic constants $C_{44}=C_{55}$ and $C_{66}$ showed more softening effect comparing with other elastic components.

Molecular motors are essential components for the biophysical functions of the cell. Current quantitative understanding of how multiple motors move along a single track is not complete, even though models and theories for a single motor mechanochemistry abound. Recently, Müller et al. have developed a tug-of-war model to describe the bidirectional movement of the cargo [Proc. Natl. Acad. Sci. U.S.A. 105, 4609 (2008)]. They found that the tug-of-war model exhibits several qualitative different motility regimes, which depend on the precise value of single motor parameters, and they suggested that the sensitivity can be used by a cell to regulate its cargo traffic. In the present paper, we will carry out a detailed theoretical analysis of a special case of tug-of-war model: in which the numbers of the two different motor species which bound to the cargo tend to infinite. Through the analysis, all the stable, i.e., biophysically observable, steady states and their stability domains can be obtained. Depending on values of the several parameters, the tug-of-war model exhibits uni-, bi-, or tristability. The steady-state movement of the cargo, which is transported by two different molecular motor species, is determined by the initial numbers of the motors which bound to the track.

Optimization has been shown to be a driving force for the evolution of some biological structures, such as neural maps in the brain or transport networks. Here we show that insect networks also display characteristic traits of optimality. By using a graph representation of the chamber organization of termite nests and a disordered lattice model, it is found that these spatial nests are close to a percolation threshold. This suggests that termites build efficient systems of galleries spanning most of the nest volume at low cost. The evolutionary consequences are outlined.

We study numerically the coupling between a qubit and a Bose-Einstein condensate (BEC) moving in a kicked optical lattice using Gross-Pitaevskii equation. In the regime where the BEC size is smaller than the lattice period, the chaotic dynamics of the BEC is effectively controlled by the qubit state. The feedback effects of the nonlinear chaotic BEC dynamics preserve the coherence and purity of the qubit in the regime of strong BEC nonlinearity. This gives an example of an exponentially sensitive control over a macroscopic state by internal qubit states. At weak nonlinearity quantum chaos leads to rapid dynamical decoherence of the qubit. The realization of such coupled systems is within reach of current experimental techniques.

A combination of independent component analysis and empirical mode decomposition (ICA-EMD) is proposed in this paper to analyze low signal-to-noise ratio data. The advantages of ICA-EMD combination are these: ICA needs few sensory clues to separate the original source from unwanted noise and EMD can effectively separate the data into its constituting parts. The case studies reported here involve original sources contaminated by white Gaussian noise. The simulation results show that the ICA-EMD combination is an effective data analysis tool.

We develop a renormalization-group (RG) procedure that includes important system-specific features. The key ingredient is to systematize the coarse-graining procedure that generates the RG flow. The coarse-graining technology comes from the control and operator theoretic model reduction. The resulting “generalized” RG is a consistent generalization of the Wilsonian RG. We apply the procedure to a deterministic nonlinear wave equation (NLWE) with probabilistic initial conditions. We derive the form of the projection operator from the dynamics of the NLWE and then use it to generate the RG flow for the distribution of initial conditions. The probability density of the initial conditions is chosen to be a Boltzmann weight that is quartic in the field variables. In our calculation, we find that in contrast to conventional implementations of the RG, naïve power counting breaks down. We also show that the resulting RG equations are different from those derived from the conventional RG.

Collections of non-Brownian particles suspended in a viscous fluid and subjected to oscillatory shear at very low Reynolds number have recently been shown to exhibit a remarkable dynamical phase transition separating reversible from irreversible behavior as the strain amplitude or volume fraction are increased. We present a simple model for this phenomenon, based on which we argue that this transition lies in the universality class of the conserved directed percolation models. This leads to predictions for the scaling behavior of a large number of experimental observables. Non-Brownian suspensions under oscillatory shear may thus constitute the first experimental realization of an inactive-active phase transition which is not in the universality class of conventional directed percolation.