Constraints on the spectral distribution of energy and enstrophy dissipation in forced two-dimensional turbulence

We study two-dimensional (2D) turbulence in a doubly periodic domain driven by a monoscale-like forcing and damped by various dissipation mechanisms of the form νμ(−Δ)μ. By “monoscale-like” we mean that the forcing is applied over a finite range of wavenumbers kmin≤k≤kmax, and that the ratio of enstrophy injection η≥0 to energy injection ε≥0 is bounded by kmin2ε≤η≤kmax2ε. Such a forcing is frequently considered in theoretical and numerical studies of 2D turbulence. It is shown that for μ≥0 the asymptotic behaviour satisfies ∥u∥12≤kmax2∥u∥2, where ∥u∥2 and ∥u∥12 are the energy and enstrophy, respectively. If the condition of monoscale-like forcing holds only in a time-mean sense, then the inequality holds in the time mean. It is also shown that for Navier–Stokes turbulence (μ=1), the time-mean enstrophy dissipation rate is bounded from above by 2ν1kmax2. These results place strong constraints on the spectral distribution of energy and enstrophy and of their dissipation, and thereby on the existence of energy and enstrophy cascades, in such systems. In particular, the classical dual cascade picture is shown to be invalid for forced 2D Navier–Stokes turbulence (μ=1) when it is forced in this manner. Inclusion of Ekman drag (μ=0) along with molecular viscosity permits a dual cascade, but is incompatible with the log-modified −3 power law for the energy spectrum in the enstrophy-cascading inertial range. In order to achieve the latter, it is necessary to invoke an inverse viscosity (μ<0). These constraints on permissible power laws apply for any spectrally localized forcing, not just for monoscale-like forcing.

Unsteady flow simulation of a vertical axis augmented wind turbine: a two-dimensional study

As the integration of vertical axis wind turbines in the built environment is a promising alternative to horizontal axis wind turbines, a 2D computational investigation of an augmented wind turbine is proposed and analysed. In the initial CFD analysis, three parameters are carefully investigated: mesh resolution; turbulence model; and time step size. It appears that the mesh resolution and the turbulence model affect result accuracy; while the time step size examined, for the unsteady nature of the flow, has small impact on the numerical results. In the CFD validation of the open rotor with secondary data, the numerical results are in good agreement in terms of shape. It is, however, observed a discrepancy factor of 2 between numerical and experimental data. Successively, the introduction of an omnidirectional stator around the wind turbine increases the power and torque coefficients by around 30–35% when compared to the open case; but attention needs to be given to the orientation of the stator blades for optimum performance. It is found that the power and torque coefficients of the augmented wind turbine are independent of the incident wind speed considered.

Kraichnan–Leith–Batchelor similarity theory and two-dimensional inverse cascades

We study the scaling properties and Kraichnan–Leith–Batchelor (KLB) theory of forced inverse cascades in generalized two-dimensional (2D) fluids (α-turbulence models) simulated at resolution 8192x8192. We consider α=1 (surface quasigeostrophic flow), α=2 (2D Euler flow) and α=3. The forcing scale is well resolved, a direct cascade is present and there is no large-scale dissipation. Coherent vortices spanning a range of sizes, most larger than the forcing scale, are present for both α=1 and α=2. The active scalar field for α=3 contains comparatively few and small vortices. The energy spectral slopes in the inverse cascade are steeper than the KLB prediction −(7−α)/3 in all three systems. Since we stop the simulations well before the cascades have reached the domain scale, vortex formation and spectral steepening are not due to condensation effects; nor are they caused by large-scale dissipation, which is absent. One- and two-point p.d.f.s, hyperflatness factors and structure functions indicate that the inverse cascades are intermittent and non-Gaussian over much of the inertial range for α=1 and α=2, while the α=3 inverse cascade is much closer to Gaussian and non-intermittent. For α=3 the steep spectrum is close to that associated with enstrophy equipartition. Continuous wavelet analysis shows approximate KLB scaling ℰ(k)∝k−2 (α=1) and ℰ(k)∝k−5/3 (α=2) in the interstitial regions between the coherent vortices. Our results demonstrate that coherent vortex formation (α=1 and α=2) and non-realizability (α=3) cause 2D inverse cascades to deviate from the KLB predictions, but that the flow between the vortices exhibits KLB scaling and non-intermittent statistics for α=1 and α=2.

Two-dimensional electron states bound to an off-plane donor in a magnetic field

The states of an electron confined in a two-dimensional (2D) plane and bound to an off-plane donor impurity center, in the presence of a magnetic field, are investigated. The energy levels of the ground state and the first three excited states are calculated variationally. The binding energy and the mean orbital radius of these states are obtained as a function of the donor center position and the magnetic field strength. The limiting cases are discussed for an in-plane donor impurity (i.e. a 2D hydrogen atom) as well as for the donor center far away from the 2D plane in strong magnetic fields, which corresponds to a 2D harmonic oscillator.

Two-dimensional QSAR studies on arylpiperazines as high-affinity 5-HT(1A) receptor ligands

5-HT(1A) receptor plays an important role in the delayed onset of antidepressant action of a class of selective serotonin reuptake inhibitors. Moreover, 5-HT(1A) receptor levels have been shown to be altered in patients suffering from major depression. In this work, hologram quantitative structure-activity relationship (HQSAR) studies were performed on a series of arylpiperazine compounds presenting affinity to the 5-HT(1A) receptor. The models were constructed with a training set of 70 compounds. The most significant HQSAR model (q(2) = 0.81, r(2) = 0.96) was generated using atoms, bonds, connections, chirality, and donor and acceptor as fragment distinction, with fragment size of 6-9. Predictions for an external test set containing 20 compounds are in good agreement with experimental results showing the robustness of the model. Additionally, useful information can be obtained from the 2D contribution maps.

Effects of variation in modulator temperature during cryogenic modulation in comprehensive two-dimensional gas chromatography

Many modulation systems in comprehensive 2D GC (GC×GC) are based on cryogenic methods. High trapping temperatures in these systems can result in ineffective trapping of the more volatile compounds, whilst temperatures that are too low can prevent efficient remobilisation of some compounds. To better understand the trapping and release of compounds over a wide range of volatilities, we have investigated a number of different constant temperature modulator settings, and have also examined a constant temperature differential between the cryo-trap and the chromatographic oven. These investigations have led us to modify the temperature regulation capabilities of the longitudinally modulated cryogenic system (LMCS). In contrast to the current system, where the user sets a constant temperature for the cooling chamber, the user now sets the temperature difference between the cryo-trap and the chromatographic oven. In this configuration, the cooling chamber temperature increases during the chromatographic run, tracking the oven temperature ramp. This produces more efficient, volatility-dependent modulation, and increases the range of volatile compounds that can be analysed under optimal trap-and-release conditions within a single analytical run. This system also reduces cryogenic fluid consumption.

Two-dimensional string notation for representing video sequences

Most current work on video indexing concentrates on queries which operate over high level semantic information which must be entirely composed and entered manually. We propose an indexing system which is based on spatial information about key objects in a scene. These key objects may be detected automatically, with manual supervision, and tracked through a sequence using one of a number of recently developed techniques. This representation is highly compact and allows rapid resolution of queries specified by iconic example. A number of systems have been produced which use 2D string notations to index digital image libraries. Just as 2D strings provide a compact and tractable indexing notation for digital pictures, a sequence of 2D strings might provide an index for a video or image sequence. To improve further upon this we reduce the representation to the 2D string pair representing the initial frame, and a sequence of edits to these strings. This takes advantage of the continuity between frames to further reduce the size of the notation. By representing video sequences using string edits, a notation has been developed which is compact, and allows querying on the spatial relationships of objects to be performed without rebuilding the majority of the scene. Calculating ranks of objects directly from the edit sequence allows matching with minimal calculation, thus greatly reducing search time. This paper presents the edit sequence notation and algorithms for evaluating queries over image sequences. A number of optimizations which represent a considerably saving in search time is demonstrated in the paper.

Peak picking and the assessment of separation performance in two-dimensional high performance liquid chromatography

An algorithm was developed for 2DHPLC that automated the process of peak recognition, measuring their retention times, and then subsequently plotting the information in a two-dimensional retention plane. Following the recognition of peaks, the software then performed a series of statistical assessments of the separation performance, measuring for example, correlation between dimensions, peak capacity and the percentage of usage of the separation space. Peak recognition was achieved by interpreting the first and second derivatives of each respective one-dimensional chromatogram to determine the 1D retention times of each solute and then compiling these retention times for each respective fraction ‘cut’. Due to the nature of comprehensive 2DHPLC adjacent cut fractions may contain peaks common to more than one cut fraction. The algorithm determined which components were common in adjacent cuts and subsequently calculated the peak maximum profile by interpolating the space between adjacent peaks. This algorithm was applied to the analysis of a two-dimensional separation of an apple flesh extract separated in a first dimension comprising a cyano stationary phase and an aqueous/THF mobile phase as the first dimension and a second dimension comprising C18-Hydro with an aqueous/MeOH mobile phase. A total of 187 peaks were detected.

Improving peak shapes with counter gradients in two-dimensional high performance liquid chromatography

To achieve the greatest peak capacity in two-dimensional high performance liquid chromatography (2D-HPLC) a gradient should be operated in both separation dimensions. However, it is known that when an injection solvent that is stronger than the initial mobile phase composition is deleterious to peak performance, thus causing problems when cutting a portion from one gradient into another. This was overcome when coupling hydrophilic interaction with reversed phase chromatography by introducing a counter gradient that changed the solvent strength of the second dimension injection. It was found that an injection solvent composition of 20% acetonitrile in water gave acceptable results in one-dimensional simulations with an initial composition of 5% acetonitrile. When this was transferred to a 2D-HPLC separation of standards it was found that a marked improvement in peak shape was gained for the moderately retained analytes (phenol and dimethyl phthalate), some improvement for the weakly retained caffeine and very little change for the strongly retained n-propylbenzene and anthracene which already displayed good chromatographic profiles. This effect was transferred when applied to a 2D-HPLC separation of a coffee extract where the indecipherable retention profile was transformed to a successful application multidimensional chromatography with peaks occupying 71% of the separation space according to the geometric approach to factor analysis.

Determination of neurotransmitters and their metabolites using one- and two-dimensional liquid chromatography with acidic potassium permanganate chemiluminescence detection

High-performance liquid chromatography with chemiluminescence detection based on the reaction with acidic potassium permanganate and formaldehyde was explored for the determination of neurotransmitters and their metabolites. The neurotransmitters norepinephrine and dopamine were quantified in the left and right hemispheres of rat hippocampus, nucleus accumbens and prefrontal cortex, and the metabolites vanillylmandelic acid, 3,4-dihydrophenylacetic acid, 5-hydroxyindole-3-acetic acid and homovanillic acid were identified in human urine. Under optimised chemiluminescence reagent conditions, the limits of detection for these analytes ranged from 2.5 × 10−8 to 2.5 × 10−7 M. For the determination of neurotransmitter metabolites in urine, a two-dimensional high-performance liquid chromatography (2D-HPLC) separation operated in heart-cutting mode was developed to overcome the peak capacity limitations of the one-dimensional separation. This approach provided the greater separation power of 2D-HPLC with analysis times comparable to conventional one-dimensional separations.

General synthesis of two-dimensional patterned conducting polymer-nanobowl sheet via chemical polymerization

A general method for the generation of two-dimensional (2D) ordered, large-area, and liftable conducting polymer-nanobowl sheet has been demonstrated via chemical polymerization for the first time. The sheet is made using the monolayer self-assembled from polystyrene (PS) spheres at the aqueous/air interface as template, followed by depositing conducting polymer on the part of PS monolayer submerging in the aqueous phase via chemical polymerization, and core extraction. During the process of polymerization, no substrate is required, which caused the as-prepared patterned conducting polymer sheet can be easily lifted-off and deposited, in full size, on any flat substrate. Scanning electron microscopy (SEM), transmission electron microscopy (TEM), and Fourier transform infrared (FTIR) spectrum were used to characterize the products

Two-dimensional electron states bound to an off-plane donor in a magnetic field

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Non-Zeeman splitting for a spin-resolved STM with a Kondo adatom in a spin-polarized two-dimensional electron gas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dipolar Bose-Einstein condensate soliton on a two-dimensional optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Two-dimensional photonic crystals in antimony-based films fabricated by holography

In this work, we demonstrated the fabrication of two-dimensional (2D) photonic crystals layers (2D-PCLs) by combining holographic recording and the evaporation of antimony-based glasses. Such materials present high refractive indices that can be tuned from 1.8 to 2.4, depending on the film composition; thus, they are interesting dielectric materials for fabrication of 2D-PCLs. The good quality of the obtained samples allowed the measurement of their PC properties through the well-defined Fano resonances that appear in the transmittance spectrum measurements at different incidence angles. The experimental results are in good agreement with the calculated band diagram for the hexagonal asymmetric structure. (C) 2008 American Institute of Physics.