Existence and asymptotic properties of solutions for a nonlinear Schrödinger elliptic equation from geophysical fluid flows

In this paper, we study the existence and asymptotic behavior of radial solutions for a class of nonlinear Schrödinger elliptic equations on infinite domains describing the gyre of geophysical fluid flows. The existence theorem and asymptotic properties of radial positive solutions are established by using a new renormalization technique.     

Beyond direct simulation Monte Carlo (DSMC) modelling of collision environments

ABSTRACT

Direct simulation Monte Carlo (DSMC) models have been successfully adopted and adapted to describe gas flows in a wide range of environments since the method was first introduced by Bird in the 1960s. We propose a new approach to modelling collisions between gas-phase particles in this work – operating in a similar way to the DSMC model, but with one key difference. Particles move in a mean field, generated by all previously propagated particles, which removes the requirement that all particles be propagated simultaneously. This yields a significant reduction in computation effort and lends itself to applications for which DSMC becomes intractable, such as when a species of interest is only a minor component of a large gas mixture.     

Dynamic leg-motion and its effect on the aerodynamic performance of cyclists

In this wind-tunnel based experimental study, the flow topology of the near wake of a generic anatomically accurate model cyclist is mapped for a range of reduced pedalling frequencies. Wake flow fields for both static leg and pedalling cyclists are compared over the full 360° rotation of the crank using both time- and phase-averaging. The primary wake flow structures and aerodynamic forces are quantified and analysed under dynamic pedalling conditions representative of an elite-level time-trial cyclist. Over the range of reduced pedalling frequencies studied, only minor variation was detected between the instantaneous drag and primary vortical structures of a pedalling cyclist compared to a stationary cyclist with the pedals in the same position. A simplified model of the aerodynamic forces acting on the legs under motion is presented to provide insight into how the motion of the legs influences aerodynamic drag. A comparison of predicted forces from this model with those from experiments provides a new perspective on how the aerodynamics of cyclists may be optimised.     

On the Center of Continuous Maps of Dendrites

The structure and the depth of the center of a continuous map of a dendrite with a closed countable set of branch points of a finite order are studied. It is proved that the center of that map coincides with the closure of the set of periodic points. It is shown also that for an arbitrary natural number n S 2 there are the dendrite X n with a closed countable set of branch points of a finite order and the continuous map f n : X n M X n with n as the depth of the center.     

Global persistence of geometrical structures for the Boussinesq equation with no diffusion

Our main aim is to investigate the temperature patch problem for the two-dimensional incompressible Boussinesq system with partial viscosity: the initial temperature is the characteristic function of some simply connected domain with 𝒞^1,𝜀 Hölder regularity. Although recent results ensure that the 𝒞¹ regularity of the patch persists for all time, whether higher order regularity is preserved has remained an open question. In the present paper, we give a positive answer to that issue. We also study the higher dimensional case, after prescribing an additional smallness condition involving critical Lebesgue or weak-Lebesgue norms of the data, so as to get a global-in-time statement. All our results stem from general properties of persistence of geometrical structures (of independent interest), that we establish in the first part of the paper.     

Polypropylene/polystyrene/clay blends prepared by an innovative eccentric rotor extruder based on continuous elongational flow: Analysis of morphology,rheology property,and crystallization behavior

The polypropylene (PP)/polystyrene (PS)/montmorillonite (MMT) blends were prepared by an innovative eccentric rotor extruder based on continuous elongational flow. Addition of MMT nanoparticles was found to reduce the PS droplet size and improve the compatibility of PP/PS. The MMT nanoparticles had clear intercalation and/or exfoliation structures and were located mostly at the interface of PP/PS. It was found that the intercalation and exfoliation of MMT was finished under the synergy of interfacial interaction and tensile deformation so that we called the mechanism as “MMT exfoliation mechanism induced by synergy of interface and tensile deformation”. The rheological analysis showed that incorporation of MMT led to an increase in complex viscosity to an optimum level (5 wt%), after which any further increase in MMT concentration decreased the complex viscosity. Moreover, the degree of crystallinity of blends was controlled by the heterogeneous nucleation effect of MMT and the inhibition effect of PS.     

A sharp‐interface immersed boundary framework for simulations of high‐speed inviscid compressible flows

A new finite‐volume flow solver based on the hybrid Cartesian immersed boundary (IB) framework is developed for the solution of high‐speed inviscid compressible flows. The IB method adopts a sharp‐interface approach, wherein the boundary conditions are enforced on the body geometry itself. A key component of the present solver is a novel reconstruction approach, in conjunction with inverse distance weighting, to compute the solutions in the vicinity of the solid‐fluid interface. We show that proposed reconstruction leads to second‐order spatial accuracy while also ensuring that the discrete conservation errors diminish linearly with grid refinement. Investigations of supersonic and hypersonic inviscid flows over different geometries are carried out for an extensive validation of the proposed flow solver. Studies on cylinder lift‐off and shape optimisation in supersonic flows further demonstrate the efficacy of the flow solver for computations with moving and shape‐changing geometries. These studies conclusively highlight the capability of the proposed IB methodology as a promising alternative for robust and accurate computations of compressible fluid flows on nonconformal Cartesian meshes.     

Membrane-based microchannel device for continuous quantitative extraction of dissolved free sulfide from water and from oil

Underground fluids are important natural sources of drinking water, geothermal energy, and oil-based fuels. To facilitate the surveying of such underground fluids, a novel microchannel extraction device was investigated for in-line continuous analysis and flow injection analysis of sulfide levels in water and in oil. Of the four designs investigated, the honeycomb-patterned microchannel extraction (HMCE) device was found to offer the most effective liquid–liquid extraction. In the HMCE device, a thin silicone membrane was sandwiched between two polydimethylsiloxane plates in which honeycomb-patterned microchannels had been fabricated. The identical patterns on the two plates were accurately aligned. The extracted sulfide was detected by quenching monitoring of fluorescein mercuric acetate (FMA). The sulfide extraction efficiencies from water and oil samples of the HMCE device and of three other designs (two annular and one rectangular channel) were examined theoretically and experimentally. The best performance was obtained with the HMCE device because of its thin sample layer (small diffusion distance) and large interface area. Quantitative extraction from both water and oil could be obtained using the HMCE device. The estimated limit of detection for continuous monitoring was 0.05 μM, and sulfide concentrations in the range of 0.15–10 μM could be determined when the acceptor was 5 μM FMA alkaline solution. The method was applied to natural water analysis using flow injection mode, and the data agreed with those obtained using headspace gas chromatography-flame photometric detection. The analysis of hydrogen sulfide levels in prepared oil samples was also performed. The proposed device is expected to be used for real time survey of oil wells and groundwater wells.