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.     

Mildred Dresselhaus and Solid State Pedagogy at MIT

Mildred Dresselhaus is known for her influential research on the physics of carbon. Her wide‐ranging influence as a physics teacher, although well‐known to her students, has been less thoroughly examined. Exploring how Dresselhaus grew into her role teaching solid state physics at MIT reveals much about how that subfield evolved.     

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.     

An interview with Sam C. Saunders

Sam C. Saunders, the son of Elizabeth Cundiff and Winston E. Saunders, was born in Richland, OR, on February 24, 1931. The family moved to La Grande, OR, in 1944, where Sam completed high school and two years at Eastern Oregon College. He then received the BSc degree in Mathematics from the University of Oregon, Eugene, OR, in 1952, and he attended the University of Washington, Seattle, WA, receiving a PhD degree under Z. W. Birnbaum. After graduating, he accepted employment at the Boeing Company in its Mathematical Services Unit and, in 1972, a position as a Full Professor at Washington State University, Pullman, WA, from which he retired in 1996.     

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.     

LIMITATIONS ON PRESCRIBING THE HOPF DIFFERENTIAL FOR MINIMAL SURFACES IN H3

ABSTRACT

The Hopf map from minimal surfaces in H ³ to holomorphic quadratic differentials on H ² is considered. Whether or not a given quadratic differential is in the image of this map is determined by the global existence/non-existence of solutions to a certain quasi-linear PDE. It is shown that this map is not surjective.     

单轴拉伸对Nafion 结构及性能的影响

²H NMR 和PFG-NMR 用于研究拉伸过程中Nafion 结构的改变以及对溶剂分子运动性质的影响．²H 谱表明单轴拉伸Nafion 膜在拉伸比率较低情况下（L < 5），通道排列取向程度随着拉伸比率变大而增大，同时扩散实验表明水分子的运动能力也得到增强，表明取向化的通道网络有助于增强材料取向方向质子的导电能力，可以用于提高质子膜材料性能．在取向达到最大值后（L≥5）继续拉伸，膜内水分子的移动能力相比略有降低．溶胀实验表明取向膜的溶胀行为呈各向异性,拉伸作用致使膜内通道沿拉伸方向取向排列，通道的取向效应使得其在垂直拉伸方向（Y）和膜厚度方向（Z）溶胀更为显著．拉伸Nafion 膜对甲醇的吸附能力随着拉伸比率的增加而增强，同时甲醇的扩散数据显示，甲醇的运动能力在该通道网络中也随着拉伸比率的变大而不断增强，甲醇燃料在该类质子膜内的渗透效
应得以增强，不利于其在直接甲醇燃料电池中的应用．     

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.     

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.