Thermal convection in fluidized granular systems

Thermal convection is observed in molecular dynamic simulations of a fluidized granular system of nearly elastic hard disks moving under gravity, inside a square box. Boundaries introduce no shearing or time dependence, but the energy injection comes from a slip (shear-free) thermalizing base. The top wall is perfectly elastic and lateral boundaries are either elastic or periodic. The spontaneous temperature gradient appearing in the system due to the inelastic collisions, combined with gravity, produces a buoyancy force that, when dissipation is large enough, triggers convection.     

Stokes eigenmodes in square domain and the stream function–vorticity correlation

The Stokes eigenmodes in the square are numerically determined and their symmetry properties are identified. The spectra evolution laws are in excellent qualitative agreement with the theoretical asymptotic predictions proposed by Constantin and Foias (in “Navier–Stokes equations”, University of Chicago Press, 1988), . The slopes are reported here and are found to be specific to the eigenmodes symmetry family. The dynamic equilibria are analyzed and show a linear relationship between the vorticity and the stream function in the core of the eigenmodes. These features of the Stokes eigenmodes confined in the square are shared by the fully periodic Stokes eigenmodes.     

Transition to chaos in a confined two-dimensional fluid flow

For a two-dimensional fluid in a square domain with no-slip walls, new direct numerical simulations reveal that the transition from steady to chaotic flow occurs through a sequence of various periodic and quasiperiodic flows, similar to the well-known Ruelle-Takens-Newhouse scenario. For all solutions beyond the ground state, the phenomenology is dominated by a domain-filling circulation cell, whereas the associated symmetry is reduced from the full symmetry group of the square to rotational symmetry over an angle pi. The results complement both laboratory experiments in containers with rigid walls and numerical simulations on double-periodic domains.     

The energy and structure of (0 0 1) twist grain boundary in noble metals

The relaxed energy and structure of (0 0 1) twist grain boundary (GB) in noble metals Au, Ag and Cu are simulated by the MAEAM. In-boundary translation between two adjacent grains results in a periodic energy variation and the period is a square with the side length L_Σ/Σ. The lowest energy appears when the two grains are translated relatively to either corner or center of the periodic square. The relaxed GB energy increases smoothly for low-angle boundaries and levels off for larger-angle boundaries except a cusp appeared at θ = 36.87° (Σ = 5). After relaxation, the symmetry of the GB structure is not changed but the displacement of the atoms parallel to the GB plane decreases with increasing the distance of the atoms from the GB plane.     

Modeling the self-assembly of copolymer-nanoparticle mixtures confined between solid surfaces

Using numerical calculations, we undertake the first morphological studies of mixtures of AB diblocks and nanoparticles that are confined between two hard walls. A complex interplay of entropic and enthalpic interactions drives the nonselective particles to localize at the hard walls and A/B interfaces, causing the mixture to spontaneously self-assemble into particle-decorated lamellae that are oriented perpendicular to the surfaces. The film reveals a periodic array of particle "nanowires" that are separated by the nanoscale polymer domains, yielding a vital material for nanodevice fabrication.     

Behavior of vertical-Bloch-line chains of hard domains in garnet bubble films

As a main micromagnetic structure of domain walls in garnet bubble films, vertical-Bloch-line (VBL) chains play an important role in the characteristics of hard domains. In the 1970s, their study progressed rapidly during the period in which bubble devices were developed. When ultra-high-density Bloch line memory (BLM) was proposed in 1983, VBL chain behavior again attracted attention. This review will introduce the early achivements focusing primarily on the results of the last decade. A convenient method of forming VBL chains, a new classification scheme of hard domains and the unsolved “number effect” of VBLs will be discussed. Various behaviors of VBL chains under static compression, and in-plane magnetic fields will also be presented. Finally, the temperature stability of VBL chains will be reported.     

The red queen's walk

We study a new type of walk with memory which might serve as a toy model for the behavior one must adopt to avoid exhaustion of resources and attraction of parasites and predators. The walk takes place on a regular square lattice with periodic boundary conditions. Although the walk is completely deterministic, it mimics a “true” self-avoiding walk, i.e. a random walk with weak autocorrelation. This shows that the Red Queen effect can lead to aperiodic behavior. In addition to the case of single walkers in a flat landscape we also study the cases of hilly landscapes and of several walkers performing simultaneous walks.     

Gaps and eigenfrequencies in the spectrum of a periodic acoustic waveguide

Sufficient conditions are found for the existence of eigenfrequencies within the spectral gaps which occur as a result of local regular perturbation of the hard walls of a periodic acoustic waveguide. Asymptotic formulas are derived and error estimates shown.     

Internal transverse fluctuation waves in a viscous liquid at a hard boundary

A liquid layer resting on a hard bottom and bounded by hard walls is considered. Analysis of the dispersion relation shows that both slowly decaying solitary waves and rapidly decaying periodic waves may arise inside the layer at the interface between stratified ～100-nm-thick near-surface regions of low-viscous liquids. Stratification is due to the orienting influence of the hard bottom and to fluctuation forces. The dispersion laws for the waves are characteristic of purely capillary waves in both a deep and shallow liquid.     

Propagative Sine-Gordon solitons in the spatially forced Kelvin-Helmholtz instability

The spatio-temporal evolution of the vortex sheet separating two finite-depth layers of immiscible fluids is examined in the vicinity of threshold when spatially periodic forcing is imposed at the horizontal boundaries. As a result of the Galilean invariance of the problem, the interface deformation is shown to satisfy a coupled system of evolution equations involving not only the usual “short-wave” at the critical wavenumber but also a shallow-water “long-wave” associated with the mean elevation of the interface. The weakly nonlinear model is further studied in the Boussinesq approximation where it reduces to a forced Klein-Gordon equation. Thus, the secondary Benjamin-Feir instability of nonlinear Stokes wavetrains is analysed in the absence of forcing. When spatial forcing is reintroduced, the competition between the imposed external length scale and the natural length scale of the interface is shown analytically to give rise to one-dimensional propagating Sine-Gordon phase solitons. Numerical simulations of the Klein-Gordon evolution model fully confirm this prediction and also lead to the determination of the range of stability of phase solitons.     

Pressure boundary conditions for computing incompressible flows with SPH

In Smoothed Particle Hydrodynamics (SPH) methods for fluid flow, incompressibility may be imposed by a projection method with an artificial homogeneous Neumann boundary condition for the pressure Poisson equation. This is often inconsistent with physical conditions at solid walls and inflow and outflow boundaries. For this reason open-boundary flows have rarely been computed using SPH. In this work, we demonstrate that the artificial pressure boundary condition produces a numerical boundary layer that compromises the solution near boundaries. We resolve this problem by utilizing a “rotational pressure-correction scheme” with a consistent pressure boundary condition that relates the normal pressure gradient to the local vorticity. We show that this scheme computes the pressure and velocity accurately near open boundaries and solid objects, and extends the scope of SPH simulation beyond the usual periodic boundary conditions.     

Reentrant surface melting of colloidal hard spheres

Concentrated suspensions of model colloidal hard spheres at a wall were studied in real space by means of time-resolved fluorescence confocal scanning microscopy. Both structure and dynamics of these systems differ dramatically from their bulk analogs (i.e., far away from a wall). In particular, systems that are a glass in the bulk show significant hexagonal order at a wall. Upon increasing the volume fraction of the colloids, a reentrant melting transition involving a hexatic structure is observed. The last observation points to two-dimensional behavior of matter at walls.     

Different types of nonlinear convective oscillations in a multilayer system under the joint action of buoyancy and thermocapillary effect

The nonlinear development of oscillatory instability under the joint action of buoyant and thermocapillary effects in a multilayer system, is investigated. The nonlinear convective regimes are studied by the finite difference method. Two different types of boundary conditions – periodic boundary conditions and rigid heat-insulated lateral walls, are considered. It is found that in the case of periodic boundary conditions, the competition of both mechanisms of instability may lead to the development of specific types of flow: buoyant-thermocapillary traveling wave and pulsating traveling wave. In the case of rigid heat-insulated boundaries, various types of nonlinear flows – symmetric and asymmetric oscillations, have been found.     

Mechanism of Strain-Induced Breaking the Long-Range Atomic Order in Alloys with the L12 Superlattice Caused by Accumulation of Dislocation Walls

The mechanism of strain-induced breaking the long-range atomic order in alloys with the L1₂ superlattice caused by rearrangement of dislocations in dislocation walls is examined. A mathematical model of strain-induced breaking the long-range atomic order caused by accumulation of dislocation walls is constructed. The dependence of the long-range order parameter on the strain degree is calculated for alloys with high- and low-energy antiphase boundaries.     

On the Role of Supercritical Water in Laser-Induced Backside Wet Etching of Glass

The features and mechanisms of microcrater formation in optical silicate glass by laser-induced backside wet etching (LIBWE) are determined in a wide range of energy densities (Φ) from 4 to 10³ J/cm² for laser pulses of 5 ns length and 1 kHz repetition rate. The existence of two different mechanisms of laserinduced microcrater formation is revealed: (i) chemical etching in supercritical water (SCW), and (ii) cavitation. At Φ > 10² J/cm² irregular craters of 1–20 μm in depth with rough walls and distinct cracks around microcrater are formed testifying that in such mode (“hard”) laser induced cavitation plays a dominant role in glass removal. At Φ < J/cm² neat glass craters with smooth walls are formed, their size and shape are easily reproducible, cracks are not formed, and the processing area is limited to the laser spot area. In this mode (“soft mode with active cavitation”), a microcirculation of water is stimulated by cavitation without causing undesirable shock breakage. The latter is achieved thanks to the fast removal of glass etching products by microcirculation, and the inflow of “fresh” etchant (SCW) to the glass surface in the vicinity of the formed microcraters. Such mode is optimal for highly controlled laser microstructuring of glass and other optically transparent materials.     

Curved two-dimensional electron gases

A method is introduced which makes it possible to fabricate non-planar two-dimensional electron gases. Making use of the “epitaxial lift-off” process, patterned, gated and contacted heterostructures are transferred from their crystalline substrate onto small glass tubes with diameters of a few millimeters. The transport properties of two-dimensional electron gases inside these curved semiconductor films are characterized by low-temperature magnetoresistance measurements. In the longitudinal resistance we find weak Shubnikov–de Haas oscillations, which are periodic in B⁻¹. The transverse resistance exhibits well-developed quantum Hall plateaus at low magnetic fields. At high fields, we observe a pronounced breakdown of the Hall effect. The experimental results are compared with simple theoretical models.     

Entropic bona fide stochastic resonance with periodic modulation

In this paper, we study the stochastic resonance (SR) in a geometrically confined system, where the irregular boundaries yield entropic barriers. When the boundaries are subjected to periodic modulation, the output signal-to-noise ratio (SNR) is calculated. The effects of the noise strength, the strength of the transversal force, the frequency and strength of modulation of the walls of the enclosure are discussed. Our results show that: (i) it is interesting to observe a resonance peak in the SNR as a function of the frequency of modulation, and therefore to the appearance of the entropic bona fide SR phenomenon; and (ii) the resonance peak is more pronounced with decreasing strength of the transversal force and increasing strength of modulation.     

Fabrication of microchannels in glass using focused femtosecond laser radiation and selective chemical etching

We use the combination of femtosecond laser dielectric modification and selective chemical etching to fabricate high-quality microchannels in glass. The photoinduced modification morphology has been studied in fused silica and in borosilicate glass BK7, using ultra-high spatial resolution techniques of selective chemical etching followed by atomic force or scanning electron microscopy. The analysis shows that the high differential etch rate inside the modified regions, is determined by the presence of polarization-dependent self-ordered periodic nanocracks or nanoporous structures. We also investigate the optimum irradiation conditions needed to produce high-aspect ratio microchannels with small symmetric cross-sections and smooth walls. PACS 42.62.-b; 42.65.Re; 81.05.Kf; 87.80.Mj     

Numerical Simulation of Grain-Boundary Grooving by Level Set Method

A numerical investigation of grain-boundary grooving by means of a level set method is carried out. An idealized polycrystalline interconnect which consists of grains separated by parallel grain boundaries aligned normal to the average orientation of the surface is considered. Initially, the surface diffusion is the only physical mechanism assumed. The surface diffusion is driven by surface-curvature gradients, while a fixed surface slope and zero atomic flux are assumed at the groove root. The corresponding mathematical system is an initial boundary value problem for a two-dimensional equation of Hamilton–Jacobi type. The results obtained are in good agreement with both Mullins analytical “small-slope” solution of the linearized problem (W. W. Mullins, 1957, j. Appl. Phys. 28, 333) (for the case of an isolated grain boundary) and with the solution for a periodic array of grain boundaries (S. A. Hackney, 1988, Scripta Metall. 22, 1731). Incorporation of an electric field changes the problem to one of electromigration. Preliminary results of electromigration drift velocity simulations in copper lines are presented and discussed.     

Vortex statistics for turbulence in a container with rigid boundaries

The evolution of vortex statistics for decaying two-dimensional turbulence in a square container with rigid no-slip walls is compared with a few available experimental results and with the scaling theory of two-dimensional turbulent decay as proposed by Carnevale et al. Power-law exponents, computed from an ensemble average of several numerical runs, coincide with some experimentally obtained values, but not with data obtained from numerical simulations of decaying two-dimensional turbulence with periodic boundary conditions.