The shape of the front of multidimensional branching Brownian motion

We study the shape of the outer envelope of a branching Brownian motion (BBM) in $\mathbb{R}^d$, $d\geq 2$. We focus on the extremal particles: those whose norm is within $O(1)$ of the maximal norm amongst the particles alive at time $t$. Our main result is a scaling limit, with exponent $3/2$, for the outer-envelope of the BBM around each extremal particle (the "front"); the scaling limit is a continuous random surface given explicitly in terms of a Bessel(3) process. Towards this end, we introduce a point process that captures the full landscape around each extremal particle and show convergence in distribution to an explicit point process. This complements the global description of the extremal process given in Berestycki et. al. (Ann. Probab., to appear), where the local behavior at directions transversal to the radial component of the extremal particles is not addressed.Comment: 26 pages, 2 figure

On level line fluctuations of SOS surfaces above a wall

We study the low temperature $(2+1)$D Solid-On-Solid model on $[[1, L]]^2$ with zero boundary conditions and non-negative heights (a floor at height $0$). Caputo et al. (2016) established that this random surface typically admits either $\mathfrak h$ or $\mathfrak h+1$ many nested macroscopic level line loops $\{\mathcal L_i\}_{i\geq 0}$ for an explicit $\mathfrak h\asymp \log L$, and its top loop $\mathcal L_0$ has cube-root fluctuations: e.g., if $\rho(x)$ is the vertical displacement of $\mathcal L_0$ from the bottom boundary point $(x,0)$, then $\max \rho(x) = L^{1/3+o(1)}$ over $x\in I_0:=L/2+[[-L^{2/3},L^{2/3}]]$. It is believed that rescaling $\rho$ by $L^{1/3}$ and $I_0$ by $L^{2/3}$ would yield a limit law of a diffusion on $[-1,1]$. However, no nontrivial lower bound was known on $\rho(x)$ for a fixed $x\in I_0$ (e.g., $x=\frac L2$), let alone on $\min\rho(x)$ in $I_0$, to complement the bound on $\max\rho(x)$. Here we show a lower bound of the predicted order $L^{1/3}$: for every $\epsilon>0$ there exists $\delta>0$ such that $\min_{x\in I_0} \rho(x) \geq \delta L^{1/3}$ with probability at least $1-\epsilon$. The proof relies on the Ornstein--Zernike machinery due to Campanino--Ioffe--Velenik, and a result of Ioffe, Shlosman and Toninelli (2015) that rules out pinning in Ising polymers with modified interactions along the boundary. En route, we refine the latter result into a Brownian excursion limit law, which may be of independent interest.Comment: 48 pages, 2 figure

On Orders of Elliptic Curves over Finite Fields

In this work, we completely characterize by $j$-invariant the number of orders of elliptic curves over all finite fields $F_{p^r}$ using combinatorial arguments and elementary number theory. Whenever possible, we state and prove exactly which orders can be taken on

The extremal point process of branching Brownian motion in Rd\mathbb{R}^d

We consider a branching Brownian motion in $\mathbb{R}^d$ with $d \geq 1$ in which the position $X_t^{(u)}\in \mathbb{R}^d$ of a particle $u$ at time $t$ can be encoded by its direction $\theta^{(u)}_t \in \mathbb{S}^{d-1}$ and its distance $R^{(u)}_t$ to 0. We prove that the {\it extremal point process} $\sum \delta_{\theta^{(u)}_t, R^{(u)}_t - m_t^{(d)}}$ (where the sum is over all particles alive at time $t$ and $m^{(d)}_t$ is an explicit centring term) converges in distribution to a randomly shifted decorated Poisson point process on $\mathbb{S}^{d-1} \times \mathbb{R}$. More precisely, the so-called {\it clan-leaders} form a Cox process with intensity proportional to $D_\infty(\theta) e^{-\sqrt{2}r} ~\mathrm{d} r ~\mathrm{d} \theta$, where $D_\infty(\theta)$ is the limit of the derivative martingale in direction $\theta$ and the decorations are i.i.d. copies of the decoration process of the standard one-dimensional branching Brownian motion. This proves a conjecture of Stasi\'nski, Berestycki and Mallein (Ann. Inst. H. Poincar\'{e} 57:1786--1810, 2021), and builds on that paper and on Kim, Lubetzky and Zeitouni (arXiv:2104.07698).Comment: 20 pages, 4 figure

Evaluation of simulated O-3 production efficiency during the KORUS-AQ campaign: Implications for anthropogenic NOx emissions in Korea

We examine O3 production and its sensitivity to precursor gases and boundary layer mixing in Korea by using a 3-D global chemistry transport model and extensive observations during the KORea-US cooperative Air Quality field study in Korea, which occurred in May–June 2016. During the campaign, observed aromatic species onboard the NASA DC-8 aircraft, especially toluene, showed high mixing ratios of up to 10 ppbv, emphasizing the importance of aromatic chemistry in O3 production. To examine the role of VOCs and NOx in O3 chemistry, we first implement a detailed aromatic chemistry scheme in the model, which reduces the normalized mean bias of simulated O3 mixing ratios from –26% to –13%. Aromatic chemistry also increases the average net O3 production in Korea by 37%. Corrections of daytime PBL heights, which are overestimated in the model compared to lidar observations, increase the net O3 production rate by ~10%. In addition, increasing NOx emissions by 50% in the model shows best performance in reproducing O3 production characteristics, which implies that NOx emissions are underestimated in the current emissions inventory. Sensitivity tests show that a 30% decrease in anthropogenic NOx emissions in Korea increases the O3 production efficiency throughout the country, making rural regions ~2 times more efficient in producing O3 per NOx consumed. Simulated O3 levels overall decrease in the peninsula except for urban and other industrial areas, with the largest increase (~6 ppbv) in the Seoul Metropolitan Area (SMA). However, with simultaneous reductions in both NOx and VOCs emissions by 30%, O3 decreases in most of the country, including the SMA. This implies the importance of concurrent emission reductions for both NOx and VOCs in order to effectively reduce O3 levels in Korea

Resource availability governs polyhydroxyalkanoate (PHA) accumulation and diversity of methanotrophic enrichments from wetlands

Aquatic environments account for half of global CH4 emissions, with freshwater wetlands being the most significant contributors. These CH4 fluxes can be partially offset by aerobic CH4 oxidation driven by methanotrophs. Additionally, some methanotrophs can convert CH4 into polyhydroxyalkanoate (PHA), an energy storage molecule as well as a promising bioplastic polymer. In this study, we investigate how PHA-accumulating methanotrophic communities enriched from wetlands were shaped by varying resource availability (i.e., C and N concentrations) at a fixed C/N ratio. Cell yields, PHA accumulation, and community composition were evaluated in high (20% CH4 and 10 mM NH4+) and low resource (0.2% CH4 and 0.1 mM NH4+) conditions simulating engineered and environmental settings, respectively. High resource availability decreased C-based cell yields, while N-based cell yields remained stable, suggesting nutrient exchange patterns differed between methanotrophic communities at different resource concentrations. PHA accumulation was only observed in high resource enrichments, producing approximately 12.6% ± 2.4% (m/m) PHA, while PHA in low resource enrichments remained below detection. High resource enrichments were dominated by Methylocystis methanotrophs, while low resource enrichments remained significantly more diverse and contained only a minor population of methanotrophs. This study demonstrates that resource concentration shapes PHA-accumulating methanotrophic communities. Together, this provides useful information to leverage such communities in engineering settings as well as to begin understanding their role in the environment

A review on boiling heat transfer enhancement with nanofluids

There has been increasing interest of late in nanofluid boiling and its use in heat transfer enhancement. This article covers recent advances in the last decade by researchers in both pool boiling and convective boiling applications, with nanofluids as the working fluid. The available data in the literature is reviewed in terms of enhancements, and degradations in the nucleate boiling heat transfer and critical heat flux. Conflicting data have been presented in the literature on the effect that nanofluids have on the boiling heat-transfer coefficient; however, almost all researchers have noted an enhancement in the critical heat flux during nanofluid boiling. Several researchers have observed nanoparticle deposition at the heater surface, which they have related back to the critical heat flux enhancement