Two-dimensional Regime Research Articles

Weakly bound states of two- and three-boson systems in the crossover from two to three dimensions

The spectrum and properties of quantum bound states is strongly dependent on the dimensionality of space. How this comes about and how one may theoretically and experimentally study the interpolation between different dimensions is a topic of great interest in different fields of physics. In this paper we study weakly bound states of non-relativistic two and three boson systems when passing continuously from a three (3D) to a two-dimensional (2D) regime within a ‘squeezed dimension’ model. We use periodic boundary conditions to derive a surprisingly simple form of the three-boson Schrödinger equation in momentum space that we solve numerically. Our results show a distinct dimensional crossover as three-boson states will either disappear into the continuum or merge with a 2D counterpart, and also a series of sharp transitions in the ratios of three-body and two-body energies from being purely 2D to purely 3D.

Hybrid Vlasov-Maxwell simulations of two-dimensional turbulence in plasmas

Turbulence in plasmas is a very challenging problem since it involves wave-particle interactions, which are responsible for phenomena such as plasma dissipation, acceleration mechanisms, heating, temperature anisotropy, and so on. In this work, a hybrid Vlasov-Maxwell numerical code is employed to study local kinetic processes in a two-dimensional turbulent regime. In the present model, ions are treated as a kinetic species, while electrons are considered as a fluid. As recently reported in [S. Servidio, Phys. Rev. Lett. 108, 045001 (2012)], nearby regions of strong magnetic activity, kinetic effects manifest through a deformation of the ion velocity distribution function that consequently departs from the equilibrium Maxwellian configuration. Here, the structure of turbulence is investigated in detail in phase space, by evaluating the high-order moments of the particle velocity distribution, i.e., temperature, skewness, and kurtosis. This analysis provides quantitative information about the non-Maxwellian character of the system dynamics. This departure from local thermodynamic equilibrium triggers several processes commonly observed in many astrophysical and laboratory plasmas.

Volmer–Weber InAs quantum dot formation on InP (113)B substrates under the surfactant effect of Sb

We report on Sb surfactant growth of InAs nanostructures on GaAs0.51Sb0.49 layers deposited on InP (001) and on (113)B oriented substrates. On the (001) orientation, the presence of Sb significantly favors the two-dimensional growth regime. Even after the deposition of 5 mono-layers of InAs, the epitaxial film remains flat and InAs/GaAs0.51Sb0.49 type-II quantum wells are achieved. On (113)B substrates, same growth runs resulted in formation of high density InAs islands. Microscopic studies show that wetting layer is missing on (113)B substrates, and thus, a Volmer-Weber growth mode is concluded. These different behaviors are attributed to the surface energy changes induced by Sb atoms on surface.

Low-Reynolds-number wakes of elliptical cylinders: from the circular cylinder to the normal flat plate

AbstractWhile the wake of a circular cylinder and, to a lesser extent, the normal flat plate have been studied in considerable detail, the wakes of elliptic cylinders have not received similar attention. However, the wakes from the first two bodies have considerably different characteristics, in terms of three-dimensional transition modes, and near- and far-wake structure. This paper focuses on elliptic cylinders, which span these two disparate cases. The Strouhal number and drag coefficient variations with Reynolds number are documented for the two-dimensional shedding regime. There are considerable differences from the standard circular cylinder curve. The different three-dimensional transition modes are also examined using Floquet stability analysis based on computed two-dimensional periodic base flows. As the cylinder aspect ratio (major to minor axis) is decreased, mode A is no longer unstable for aspect ratios below 0.25, as the wake deviates further from the standard Bénard–von Kármán state. For still smaller aspect ratios, another three-dimensional quasi-periodic mode becomes unstable, leading to a different transition scenario. Interestingly, for the 0.25 aspect ratio case, mode A restabilises above a Reynolds number of approximately 125, allowing the wake to return to a two-dimensional state, at least in the near wake. For the flat plate, three-dimensional simulations show that the shift in the Strouhal number from the two-dimensional value is gradual with Reynolds number, unlike the situation for the circular cylinder wake once mode A shedding develops. Dynamic mode decomposition is used to characterise the spatially evolving character of the wake as it undergoes transition from the primary Bénard–von Kármán-like near wake into a two-layered wake, through to a secondary Bénard–von Kármán-like wake further downstream, which in turn develops an even longer wavelength unsteadiness. It is also used to examine the differences in the two- and three-dimensional near-wake state, showing the increasing distortion of the two-dimensional rollers as the Reynolds number is increased.

Emergent Kinetics and Fractionalized Charge in 1D Spin-Orbit Coupled Flatband Optical Lattices

Recent ultracold atomic gas experiments implementing synthetic spin-orbit coupling allow access to flatbands that emphasize interactions. We model spin-orbit coupled fermions in a one-dimensional flatband optical lattice. We introduce an effective Luttinger-liquid theory to show that interactions generate collective excitations with emergent kinetics and fractionalized charge, analogous to properties found in the two-dimensional fractional quantum Hall regime. Observation of these excitations would provide an important platform for exploring exotic quantum states derived solely from interactions.

Local transport measurements on epitaxial graphene

Growth of large-scale graphene is still accompanied by imperfections. By means of a four-tip scanning tunneling and electron microscope (4-tip STM/SEM), the local structure of graphene grown on SiC(0001) was correlated with scanning electron microscope images and spatially resolved transport measurements. The systematic variation of probe spacings and substrate temperature has clearly revealed two-dimensional transport regimes of Anderson localization as well as of diffusive transport. The detailed analysis of the temperature dependent data demonstrates that the local on-top nano-sized contacts do not induce significant strain to the epitaxial graphene films.

The influence of vibration on Marangoni waves in two-layer films

AbstractThe influence of time-periodic vibrations on long Marangoni waves in two-layer films is investigated. The problem is governed by a system of nonlinear equations obtained in the framework of the lubrication approximation. Periodic boundary conditions are applied on the boundaries of the computational region. The development of instabilities is investigated by means of nonlinear simulations. Excitation of two-dimensional and three-dimensional subharmonic wavy regimes is studied. A new phenomenon, the excitation of nonlinear waves with a temporal period that is four times larger than that of the gravity modulation, is revealed.

Designs for highly nonlinear ablative Rayleigh-Taylor experiments on the National Ignition Facility

We present two designs relevant to ablative Rayleigh-Taylor instability in transition from weakly nonlinear to highly nonlinear regimes at the National Ignition Facility [E. I. Moses, J. Phys.: Conf. Ser. 112, 012003 (2008)]. The sensitivity of nonlinear Rayleigh-Taylor instability physics to ablation velocity is addressed with targets driven by indirect drive, with stronger ablative stabilization, and by direct drive, with weaker ablative stabilization. The indirect drive design demonstrates the potential to reach a two-dimensional bubble-merger regime with a 20 ns duration drive at moderate radiation temperature. The direct drive design achieves a 3 to 5 times increased acceleration distance for the sample in comparison to previous experiments allowing at least 2 more bubble generations when starting from a three-dimensional broadband spectrum.

A water-balance drip-irrigation scheduling model

To conserve water, some form of irrigation scheduling should be used by the farming community. Most irrigation scheduling computer models in the United States are one-dimensional water balance models that may not be appropriate for a two-dimensional flow regime under drip irrigation. However, the one-dimensional water balance models have been applied to all forms of irrigation systems, from flood, to sprinkler to drip irrigation. The objective of the research was to develop an irrigation scheduling model that simulates two-dimensional water infiltration, drainage, and uptake for a surface-line source-drip irrigation system and to compare the results to the simpler one-dimensional model for a shallow-rooted onion crop and a deep-rooted chile pepper (Capsicum annuum) crop. Two experiments were conducted to evaluate the models. One was conducted during the 2006–2007 growing season for a shallow-rooted onion (Allium cepa L.) crop and the other for a deep-rooted chile pepper crop grown in 1995 and 1996. The one-dimensional model overestimates seasonal evapotranspiration (Et) compared to the measured values for onions by 20% and for chile by 12%. The two-dimensional model overestimates seasonal Et compared to the measured values for onion by 5% and for chile by 8%. Therefore, the two-dimensional model is recommended for scheduling irrigation for drip-irrigated shallow-rooted crops. For deep-rooted crops, both the one-dimensional and two-dimensional models give reasonable results, but the two-dimensional model simulates the seasonal water balance better than the one-dimensional model.

HOMOTOPY ANALYSIS OF TRANSIENT MAGNETO-BIO-FLUID DYNAMICS OF MICROPOLAR SQUEEZE FILM IN A POROUS MEDIUM: A MODEL FOR MAGNETO-BIO-RHEOLOGICAL LUBRICATION

The transient squeezing flow of a magneto-micropolar biofluid in a noncompressible porous medium intercalated between two parallel plates in the presence of a uniform strength transverse magnetic field is investigated. The partial differential equations describing the two-dimensional flow regime are transformed into nondimensional, nonlinear coupled ordinary differential equations for linear and angular momentum (micro-inertia). These equations are solved using the robust Homotopy Analysis Method (HAM) and also numerical shooting quadrature. Excellent correlation is achieved. The influence of magnetic field parameter (Ha) , micropolar spin gradient viscosity parameter (Γ) and unsteadiness parameter (S) on linear and angular velocity (micro-rotation) are presented graphically, for specified values of the micropolar vortex viscosity parameter (R), Darcy number (Da i.e. permeability parameter) and medium porosity parameter (ε). Increasing magnetic field (Ha) serves to decelerate both the linear and angular velocity i.e. enhances lubrication. The excellent potential of HAM in bio-lubrication flows is highlighted.

Transition from single-file to two-dimensional diffusion of interacting particles in a quasi-one-dimensional channel

Diffusive properties of a monodisperse system of interacting particles confined to a quasi-one-dimensional channel are studied using molecular dynamics simulations. We calculate numerically the mean-squared displacement (MSD) and investigate the influence of the width of the channel (or the strength of the confinement potential) on diffusion in finite-size channels of different shapes (i.e., straight and circular). The transition from single-file diffusion to the two-dimensional diffusion regime is investigated. This transition [regarding the calculation of the scaling exponent (α) of the MSD (Δx(2)(t) ∝ t(α)] as a function of the width of the channel is shown to change depending on the channel's confinement profile. In particular, the transition can be either smooth (i.e., for a parabolic confinement potential) or rather sharp (i.e., for a hard-wall potential), as distinct from infinite channels where this transition is abrupt. This result can be explained by qualitatively different distributions of the particle density for the different confinement potentials.

Momentum and heat transfer characteristics of a long parallelepiped submerged in power-law fluids in the laminar vortex shedding regime

The governing partial differential equations describing the flow and forced convection heat transfer characteristics of power-law fluids past a long parallelepiped at α=45° incidence have been solved numerically in the two-dimensional laminar flow regime. In particular, the major thrust of this work is to elucidate the influence of Reynolds number (Re), Prandtl number (Pr) and power-law index (n) on the detailed and macroscopic momentum and heat transfer characteristics in the laminar vortex shedding regime. The detailed features of the flow and heat transfer phenomena are visualized and analyzed in terms of the instantaneous streamlines, iso-vorticity and isotherm contours whereas the surface pressure and local Nusselt number distributions over the surface of the parallelepiped provide the next level of description of these phenomena. The gross features of the flow are captured in terms of the time-averaged drag coefficient, rms value of the lift coefficient, Strouhal number and Nusselt number. The trends seen here are qualitatively similar to that reported in the literature for a circular cylinder and a bar of square cross-section (with zero angle of incidence). Broadly, shear-thinning viscosity promotes heat transfer due to the lower effective viscosity of the fluid in the close proximity of the parallelepiped bar. As expected, shear-thickening behaviour shows the opposite effect. The ranges of the pertinent dimensionless groups spanned in this study are as follows: 0.3⩽n⩽1.8; 45⩽Re⩽120 and 0.7⩽Pr⩽80. Over this range of Reynolds number, the flow was found to be truly periodic. Finally, the numerical heat transfer results are correlated using a simple analytical form which facilitates the interpolation of the present results for the intermediate values of the parameters.

Analysis of a Two-dimensional Warranty Servicing Strategy with an Imperfect Repair Option

Items sold under warranty often require post sale support in terms of repair or replacement. Providence of such support costs the warrantor considerably and affects his profit margin. Thus reducing warranty servicing costs is an issue of great interest in warranty studies. In this paper, we look at two variations of a servicing strategy in two-dimensional warranty regimes involving minimal and imperfect repairs. Our work demonstrates the modeling and analysis of costs under these servicing strategies and compares their performance to other strategies present in the literature.

Bolgiano scale in confined Rayleigh–Taylor turbulence

AbstractWe investigate the statistical properties of Rayleigh–Taylor turbulence in a three-dimensional convective cell of high aspect ratio, in which one transverse side is much smaller that the others. By means of high-resolution numerical simulation we study the development of the turbulent mixing layer and the scaling properties of the velocity and temperature fields. We show that the system undergoes a transition from a three- to two-dimensional turbulent regime when the width of the turbulent mixing layer becomes larger than the scale of confinement. In the late stage of the evolution the convective flow is characterized by the coexistence of Kolmogorov–Obukhov and Bolgiano–Obukhov scaling at small and large scales, respectively. These regimes are separated by the Bolgiano scale, which is determined by the scale of confinement of the flow. Our results show that the emergence of the Bolgiano–Obukhov scaling in Rayleigh–Taylor turbulence is connected to the onset of an upscale energy transfer induced by the geometrical constraint of the flow.

Nonlinear oscillatory convective regimes in a three-layer system with an inclined temperature gradient

The influence of the horizontal component of the temperature gradient on nonlinear regimes of oscillatory convection developed under the joint action of buoyant and thermocapillary effects in a multilayer system is investigated. Two-dimensional convective regimes are studied by the finite difference method. Rigid heat-insulated lateral walls are considered. It is found that the region of nonlinear asymmetric oscillations is restricted by the Grashof number values, both from below and from above, by the steady states.

The Influence of the Horizontal Component of the Temperature Gradient on Nonlinear Oscillatory Convective Regimes in Multilayer System

The influence of the horizontal component of the temperature gradient on nonlinear regimes of oscillatory convection developed under the joint action of buoyant and thermocapillary effects in a multilayer system, is investigated. The nonlinear two-dimensional convective regimes are studied by the finite difference method. The interfaces are assumed to be non-deforming. The rigid heat-insulated lateral walls are considered. Transitions between different oscillatory and steady flow regimes have been studied. Specifically, it is shown that the horizontal component of the temperature gradient leads to the violation of the symmetry conditions and the appearance of the asymmetric oscillatory flows. The cavities with different lengths have been considered.

Momentum and heat transfer characteristics of a semi-circular cylinder immersed in power-law fluids in the steady flow regime

The continuity, momentum and energy equations describing the flow and heat transfer of power-law fluids over a semi-circular cylinder have been solved numerically in the two-dimensional steady flow regime. The influence of the Reynolds number ( Re), Prandtl number ( Pr) and power-law index ( n) on the local and global flow and heat characteristics have been studied over wide ranges of conditions as follows: 0.01 ⩽ Re ⩽ 30, 1 ⩽ Pr ⩽ 100 and 0.2 ⩽ n ⩽ 1.8. The variation of drag coefficient and Nusselt number with the Reynolds number, Prandtl number and power-law index is shown over the aforementioned ranges of conditions. In addition, streamline and isotherm profiles along with the recirculation length and distribution of pressure coefficient and Nusselt number over the surface of the semi-circular cylinder are also presented to gain further insights into the nature of the underlying kinematics. The wake size (recirculation length) shows almost linear dependence on the Reynolds number ( Re ⩾ 1) for all values of power-law index studied herein. The drag values show the classical inverse variation with the Reynolds number, especially for shear-thinning fluids at low Reynolds numbers. The point of maximum pressure coefficient is found slightly displaced from the front stagnation point for highly shear-thinning fluids, whereas for shear-thickening and Newtonian fluids, it coincides with the front stagnation point. For fixed values of the Prandtl number and Reynolds number, the rate of heat transfer decreases with the gradual increase in power-law index; this effect is particularly striking at high Prandtl numbers due to the thinning of the thermal boundary layer. Conversely, as expected, shear-thinning behavior facilitates heat transfer and shear-thickening impedes it. The effect of power-law index on both momentum and heat-transfer characteristics is seen to be appreciable at low Reynolds numbers and it gradually diminishes with the increasing Reynolds number.

Effect of power-law fluid behavior on momentum and heat transfer characteristics of an inclined square cylinder in steady flow regime

The governing equations describing the momentum and heat transfer phenomena of power-law non-Newtonian fluids over a heated square cylinder at 45° of incidence in the two-dimensional (2-D) steady flow regime are solved numerically. Extensive results on the detailed structure of the flow and temperature fields as well as on the gross engineering parameters are presented over the following ranges of conditions: 0.2 ⩽ n ⩽ 1; 0.1 ⩽ Re ⩽ 40 and 0.7 ⩽ Pr ⩽ 100. At low Reynolds numbers, the flow remains attached to the surface of the cylinder. This seems to occur for all values of power-law index, at least up to about Re = 1. On the other hand, twin standing vortices were seen to form at Re = 10 for all values of power-law index considered herein. The influence of the Reynolds number and power-law index is delineated on the detailed structure of the flow field (streamlines), wake characteristics and surface pressure distribution as well as on the value of drag coefficients. Similarly, the effect of Prandtl number is studied on forced convective heat transfer for the two commonly encountered boundary conditions, namely, constant temperature or constant heat flux prescribed on the surface of the cylinder. Using the computed numerical results, simple heat transfer correlations are obtained in terms of the Nusselt number as a function of the pertinent governing parameters thereby enabling the prediction of the rate of heat transfer between the fluid and the immersed cylinder. In addition, variation of the local Nusselt number on the surface of the inclined of square cylinder and representative isotherm plots are also presented to elucidate the effect of Reynolds number, Prandtl number and power-law index on the heat transfer phenomenon.

Different types of nonlinear convective oscillation in a multilayer system

The nonlinear development of oscillatory instability under the joint action of buoyant and thermocapillary effects in a multilayer system is investigated. The nonlinear two-dimensional convective regimes are studied by the finite-difference method. Rigid heat-insulated lateral walls are considered. Different types of nonlinear flow, symmetric and asymmetric oscillations, have been found. It is shown that the oscillatory motion takes place in an interval of the Grashof number values bounded both from below (by the mechanical equilibrium) and from above (by the steady state). Cavities with different lengths are considered.

Field Electron Emission Characteristics and Physical Mechanism of Individual Single-Layer Graphene

Due to its difficulty, experimental measurement of field emission from a single-layer graphene has not been reported, although field emission from a two-dimensional (2D) regime has been an attractive topic. The open surface and sharp edge of graphene are beneficial for field electron emission. A 2D geometrical effect, such as massless Dirac fermion, can lead to new mechanisms in field emission. Here, we report our findings from in situ field electron emission characterization on an individual singe-layer graphene and the understanding of the related mechanism. The measurement of field emission from the edges was done using a microanode probe equipped in a scanning electron microscope. We show that repeatable stable field emission current can be obtained after a careful conditioning process. This enables us to examine experimentally the typical features of the field emission from a 2D regime. We plot current versus applied field data, respectively, in ln(I/E(3/2)) ∼ 1/E and ln(I/E(3)) ∼ 1/E(2) coordinates, which have recently been proposed for field emission from graphene in high- and low-field regimes. It is observed that the plots all exhibit an upward bending feature, revealing that the field emission processes undergo from a low- to high-field transition. We discuss with theoretical analysis the physical mechanism responsible for the new phenomena.