Riesz-type inequalities and maximum flux exchange flow

Let $D$ stand for the open unit disc in $\mathbb{R}^d$ ($d\geq 1$) and $(D,\,\mathscr{B},\,m)$ for the usual Lebesgue measure space on $D$. Let $\mathscr{H}$ stand for the real Hilbert space $L^2(D,\,m)$ with standard inner product $(\cdot,\,\cdot)$. The letter $G$ signifies the Green operator for the (non-negative) Dirichlet Laplacian $-\Delta$ in $\mathscr{H}$ and $\psi$ the torsion function $G\,\chi_D$. We pose the following problem. Determine the optimisers for the shape optimisation problem $$\alpha_t:=\sup\Big\{(G\chi_A,\chi_A):\,A\subseteq D\text{is open and}(\psi,\chi_A)\leq t\,\Big\}$$ where the parameter $t$ lies in the range $0<t<(\psi,1)$. We answer this question in the one-dimensional case $d=1$. We apply this to a problem connected to maximum flux exchange flow in a vertical duct. We also show existence of optimisers for a relaxed version of the above variational problem and derive some symmetry properties of the solutions

Computation of flow behind three side-by-side cylinders of unequal/equal spacing

This paper aims to simulate unstable gap flows of three side-by-side cylinders unequally/equally spaced at T1/d = 1.5 and T2/d = 1.6 in a uniform cross flow (Re=300). The simulation is carried out using ANSYS Flotran 7.0. A mesh-independent study is conducted on a single cylinder at Re=100. The Strouhal number and wake flow characteristics compare well with experimental results. Simulation of three side-by-side cylinders in uniform cross flow has revealed that the gap flows are unstable and constantly re-orientating, which has the effect of restructuring the wake flows behind the cylinders. The flow field for unequal spacing of the cylinders is similar to the equal spacing case for some period of time with a symmetrical near wake. However, at other times, the wake flow is asymmetrical. This agrees well with the visualisation of Wang et al. (2002), in which the gap flows and the wake flow are constantly in transition

Cellular interactions with polystyrene nanoplastics-The role of particle size and protein corona.

Plastic waste is ubiquitously spread across the world and its smaller analogs-microplastics and nanoplastics-raise particular health concerns. While biological impacts of microplastics and nanoplastics have been actively studied, the chemical and biological bases for the adverse effects are sought after. This work explores contributory factors by combining results from in vitro and model mammalian membrane experimentation to assess the outcome of cell/nanoplastic interactions in molecular detail, inspecting the individual contribution of nanoplastics and different types of protein coronae. The in vitro study showed mild cytotoxicity and cellular uptake of polystyrene (PS) nanoplastics, with no clear trend based on nanoplastic size (20 and 200 nm) or surface charge. In contrast, a nanoplastic size-dependency on bilayer disruption was observed in the model system. This suggests that membrane disruption resulting from direct interaction with PS nanoplastics has little correlation with cytotoxicity. Furthermore, the level of bilayer disruption was found to be limited to the hydrophilic headgroup, indicating that transmembrane diffusion was an unlikely pathway for cellular uptake-endocytosis is the viable mechanism. In rare cases, small PS nanoplastics (20 nm) were found in the vicinity of chromosomes without a nuclear membrane surrounding them; however, this was not observed for larger PS nanoplastics (200 nm). We hypothesize that the nanoplastics can interact with chromosomes prior to nuclear membrane formation. Overall, precoating PS particles with protein coronae reduced the cytotoxicity, irrespective of the corona type. When comparing the two types, the extent of reduction was more apparent with soft than hard corona

I owe you: age-related similarities and differences in associative memory for gains and losses

Older adults often experience associative memory impairments but can sometimes remember important information. The current experiments investigate potential age-related similarities and differences associate memory for gains and losses. Younger and older participants were presented with faces and associated dollar amounts, which indicated how much money the person “owed” the participant, and were later given a cued recall test for the dollar amount. Experiment 1 examined face-dollar amount pairs while Experiment 2 included negative dollar amounts to examine both gains and losses. While younger adults recalled more information relative to older adults, both groups were more accurate in recalling the correct value associated with high value faces compared to lower value faces and remembered gist-information about the values. However, negative values (losses) did not have a strong impact on recall among older adults versus younger adults, illustrating important associative memory differences between younger and older adults