Performance Evaluation of PGM-Free Catalysts in Hydrogen Fuel Cells: Towards Sustainable and Cost-Effective Energy Solutions

The research presented in this report focuses on evaluating the performance of hydrogen fuel cells using platinum-group-metal (PGM)-free catalysts and optimizing their operation by varying cathode back pressure. The objective was to achieve similar or better performance compared to conventional platinum-based membrane electrode assemblies (MEAs) while reducing the reliance on rare earth materials. A series of experiments were conducted using synthetically fabricated PGM-free MEAs, with results indicating that higher input pressures led to a significant increase in power output, reaching nearly 70% of the performance of the conventional platinum, ruthenium, and carbon-based MEAs. This research contributes to the overall understanding and optimization of hydrogen fuel cell technology, which is essential for a more sustainable energy future. By exploring the potential of PGM-free catalysts, this study paves the way for more efficient, affordable, and environmentally friendly energy solutions in hydrogen fuel cell applications

Dynamics of Unipotent Subgroups on Infinite Volume Space

This thesis consists of five separate projects. They are organized into the following sections: 1. Orbit closures of unipotent flows for hyperbolic manifolds with Fuchsian ends. In joint work with Oh, we establish an analogue of Ratner\u27s orbit closure theorem for any connected closed subgroup generated by unipotent elements in $\mathrm{SO}(d, 1)$ acting on the space $\Gamma\backslash\mathrm{SO}(d, 1)$, assuming that the associated hyperbolic manifold $M=\Gamma\backslash\mathbb H^d$ is a convex cocompact manifold with Fuchsian ends. 2. Topological proof of Benoist-Quint. Let $G=\mathrm{SO}^\circ(d,1)$, $\Delt

Ergodic decompositions of geometric measures on Anosov homogeneous spaces

Let $G$ be a connected semisimple real algebraic group and $\Gamma$ a Zariski dense Anosov subgroup of $G$. Let $N$ be a maximal horospherical subgroup of $G$ and $P$ the normalizer of $N$ with a fixed Langlands decomposition $P=MAN$. We prove that for any non-trivial $NM$-invariant ergodic and $P$-quasi invariant measure $\mu$ on $\Gamma\backslash G$, $\mu=\sum_{\cal{E}_0\in \mathfrak Y_\Gamma} \mu|_{\cal{E}_0}$ describes the $N$-ergodic decomposition, where $\mathfrak Y_\Gamma$ denotes the collection of all $P^\circ$-minimal subsets of $\Gamma\backslash G$. As a consequence, we deduce that the space of all non-trivial $N$-invariant ergodic and $P^\circ$-quasi-invariant Radon measures on $\Gamma\backslash G$, up to positive constant multiples, is homeomorphic to ${\mathbb R}^{\text{rank}\,G-1}\times \{1,\cdots, \#\mathfrak Y_\Gamma\}$.Comment: 30 pages, new title, main result strengthene

Cold gas kinematics of star forming galaxies at high-z cluster forming epoch

I present recent results of ALMA observations toward protocluster z=2.49. With the observations of 1.1 mm dust continuum, CO(3-2) at 0".7-0".9 resolution allowed us to derive global ISM mass for the massive-end (>4.e10 Msun) of the star forming galaxies on the main sequence. We find a tentative, intriguing trend of changing SFE with respect to the increasing stellar mass that increases at higher rate than what is expected from (or opposed to) the results in field galaxies, which also correlates with the local density. Higher resolution imaging with CO(4-3) down to 0".3 gives some hints on this trend. With similarly higher resolution (~0".2) in 2 mm dust detection, we study the cold gas kinematics of galaxies. Our results suggest that major mergers play a crucial role for the evolution of the massive galaxies during the cluster forming epoch in the protocluster. 'Talk presented at the conference Galaxy evoltion Across Time, 12-16 June, Paris, France

Invariant measures for horospherical actions and Anosov groups

Let $\Gamma$ be an Anosov subgroup of a connected semisimple real linear Lie group $G$. For a maximal horospherical subgroup $N$ of $G$, we show that the space of all non-trivial $NM$-invariant ergodic and $A$-quasi-invariant Radon measures on $\Gamma\backslash G$, up to proportionality, is homeomorphic to ${\mathbb R}^{\text{rank}\,G-1}$, where $A$ is a maximal real split torus and $M$ is a maximal compact subgroup which normalizes $N$.Comment: 51 pages, 1 figur

Orbit closures of unipotent flows for hyperbolic manifolds with Fuchsian ends

We establish an analogue of Ratner's orbit closure theorem for any connected closed subgroup generated by unipotent elements in $\operatorname{SO}(d,1)$ acting on the space $\Gamma\backslash \operatorname{SO}(d,1)$, assuming that the associated hyperbolic manifold $M=\Gamma\backslash \mathbb H^d$ is a convex cocompact manifold with Fuchsian ends. For $d=3$, this was proved earlier by McMullen, Mohammadi and Oh. In a higher dimensional case, the possibility of accumulation on closed orbits of intermediate groups causes very serious obstacles, and surmounting these via the avoidance theorem (Theorem 7.13) is the heart of this paper. Our results imply the following: for any $k\ge 1$, (1) the closure of any $k$-horosphere in $M$ is a properly immersed submanifold; (2) the closure of any geodesic $(k+1)$-plane in $M$ is a properly immersed submanifold; (3) any infinite sequence of maximal properly immersed geodesic $(k+1)$-planes intersecting $\operatorname{core} M$ becomes dense in $M$.Comment: 101 pages, 3 figures, new abstract and revision on notation

Torus counting and self-joinings of Kleinian groups

For any $d\geq 1$, we obtain counting and equidistribution results for tori with small volume for a class of $d$-dimensional torus packings, invariant under a self-joining $\Gamma_\rho<\prod_{i=1}^d\mathrm{PSL}_2(\mathbb{C})$ of a Kleinian group $\Gamma$ formed by a $d$-tuple of convex cocompact representations $\rho=(\rho_1, \cdots, \rho_d)$. More precisely, if $\mathcal P$ is a $\Gamma_\rho$-admissible $d$-dimensional torus packing, then for any bounded subset $E\subset \mathbb{C}^d$ with $\partial E$ contained in a proper real algebraic subvariety, we have $$\lim_{s\to 0} { s^{\delta_{L^1}({\rho}) }} \cdot \#\{T\in \mathcal{P}: \mathrm{Vol} (T)> s,\, T\cap E\neq \emptyset \}= c_{\mathcal P}\cdot \omega_{\rho} (E\cap \Lambda_\rho).$$ Here $0<\delta_{L^1}(\rho)\le 2/\sqrt d$ is the critical exponent of $\Gamma_\rho$ with respect to the $L^1$-metric on the product $\prod_{i=1}^d \mathbb{H}^3$, $\Lambda_\rho\subset (\mathbb{C}\cup\{\infty\})^d$ is the limit set of $\Gamma_\rho$, and $\omega_{\rho}$ is a locally finite Borel measure on $\mathbb{C}^d\cap \Lambda_\rho$ which can be explicitly described. The class of admissible torus packings we consider arises naturally from the Teichm\"{u}ller theory of Kleinian groups. Our work extends previous results of Oh-Shah on circle packings (i.e. one-dimensional torus packings) to $d$-torus packings.Comment: 36 pages, 2 figures, To appear in Crelle's journa

Adaptive detrending to accelerate convolutional gated recurrent unit training for contextual video recognition

Video image recognition has been extensively studied with rapid progress recently. However, most methods focus on short-term rather than long-term (contextual) video recognition. Convolutional recurrent neural networks (ConvRNNs) provide robust spatio-temporal information processing capabilities for contextual video recognition, but require extensive computation that slows down training. Inspired by normalization and detrending methods, in this paper we propose "adaptive detrending" (AD) for temporal normalization in order to accelerate the training of ConvRNNs, especially of convolutional gated recurrent unit (ConvGRU). For each neuron in a recurrent neural network (RNN), AD identifies the trending change within a sequence and subtracts it, removing the internal covariate shift. In experiments testing for contextual video recognition with ConvGRU, results show that (1) ConvGRU clearly outperforms feed-forward neural networks, (2) AD consistently and significantly accelerates training and improves generalization, (3) performance is further improved when AD is coupled with other normalization methods, and most importantly, (4) the more long-term contextual information is required, the more AD outperforms existing methods

Improved Pill Splitter: An Analysis of 3&4-Point Bending to Split Pills

There is a niche in the pill splitting industry for a more efficient pill splitter. To fill this niche we explore various applications of 3-Point and 4-Point bending to pill splitting. All designs are 3D printed. Due to the elastic nature of PLA plastic, the reality that 3-Point bending may cause pills to fail in compression (as revealed by FEM analysis), and the difficulty in managing volume constraints in a 3-Point bending design, 4-Point bending is considered as a viable option for pill splitting. However, after testing and analysis, the 4-Point bending prototypes generated were able to break pills, but not split in half, which is unacceptable