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In this proceedings article we survey the results in [5] and their motivation, as presented at the 50th Journ\'ees EDP 2024. With the aim of quantifying turbulent behaviors of vortex filaments, we study the multifractality of a family of generalized Riemann's non-differentiable functions. These functions represent, in a certain limit, the trajectory of regular polygonal vortex filaments that evolve according to the binormal flow, the classical model for vortex filaments dynamics. We explain how we determined their spectrum of singularities through a careful design of Diophantine sets, which we study by using the Duffin-Schaeffer theorem and the Mass Transference Principle.

The structural and chemical properties of metal nanoparticles are often dictated by their interactions with molecular ligand shells. These interactions are highly material-specific and can vary significantly even among elements within the same group or materials with similar crystal structure. Precise characterization of ligand-metal interactions is crucial for the rational design of ligands and the functionalization of nanoparticles. In this study, we found that the ligation behavior with m-terphenyl isocyanide molecule differs significantly between Au and Ag nanoparticles, with distinct ligand extraction efficiencies and size dependencies. Surface-enhanced Raman spectroscopy measurements revealed unique enhancement factors for two molecular vibrational modes between two metal surfaces, indicating different ligand binding geometries. Molecular-level characterization using scanning tunneling microscopy allowed us to directly visualize these variations between Ag and Au surfaces, which we assign as two distinct binding mechanisms. This molecular-scale visualization provides clear insights into the different ligand-metal interactions, as well as the chemical behavior and spectroscopic characteristics of isocyanide-functionalized nanoparticles.

Several long-period binaries with a carbon-rich Wolf-Rayet star and an O star produce dust in their wind collisions. In eccentric binaries, this is seen most strongly near periastron passage. The exact conditions leading to dust creation require orbital properties to be determined, which is difficult owing to their long periods. Recently, the binary system WR 125 (WC7+O9III) began a dust creation episode seen through an infrared outburst first detected by NEOWISE-R, which was the first outburst detected since 1991. We present new near- and mid-infrared photometry, which we use to show consistency between the two outbursts and derive an orbital period of 28.12$^{+0.10}_{-0.05}$ yr. We use a long time-series of optical spectra to place the first constraints on its orbital elements, on the assumption that this system will produce dust near periastron. The orbit has a mild eccentricity of 0.29$\pm$0.12 and is only derived for the Wolf-Rayet component, as the O star's radial velocities have noise that is likely larger than the expected semi-amplitude of the orbit. We also present SOFIA/FORCAST grism spectroscopy to examine the infrared spectral energy distribution (SED) of the dust during this outburst, comparing its properties to other WCd binaries, deriving a dust temperature of 580 K in 2021. This collection of observations will allow us to plan future observations of this system and place the system in the context of dust-creating Wolf-Rayet binaries., Comment: accepted to ApJ

Virtual screening is a technique used in drug discovery to select the most promising molecules to test in a lab. To perform virtual screening, we need a large set of molecules as input, and storing these molecules can become an issue. In fact, extreme-scale high-throughput virtual screening applications require a big dataset of input molecules and produce an even bigger dataset as output. These molecules' databases occupy tens of TB of storage space, and domain experts frequently sample a small portion of this data. In this context, SMILES is a popular data format for storing large sets of molecules since it requires significantly less space to represent molecules than other formats (e.g., MOL2, SDF). This paper proposes an efficient dictionary-based approach to compress SMILES-based datasets. This approach takes advantage of domain knowledge to provide a readable output with separable SMILES, enabling random access. We examine the benefits of storing these datasets using ZSMILES to reduce the cold storage footprint in HPC systems. The main contributions concern a custom dictionary-based approach and a data pre-processing step. From experimental results, we can notice how ZSMILES leverage domain knowledge to compress x1.13 more than state of the art in similar scenarios and up to $0.29$ compression ratio. We tested a CUDA version of ZSMILES targetting NVIDIA's GPUs, showing a potential speedup of 7x.

With the aim of quantifying turbulent behaviors of vortex filaments, we study the multifractality and intermittency of the family of generalized Riemann's non-differentiable functions \begin{equation} R_{x_0}(t) = \sum_{n \neq 0} \frac{e^{2\pi i ( n^2 t + n x_0 ) } }{n^2}, \qquad x_0 \in [0,1]. \end{equation} These functions represent, in a certain limit, the trajectory of regular polygonal vortex filaments that evolve according to the binormal flow. When $x_0$ is rational, we show that $R_{x_0}$ is multifractal and intermittent by completely determining the spectrum of singularities of $R_{x_0}$ and computing the $L^p$ norms of its Fourier high-pass filters, which are analogues of structure functions. We prove that $R_{x_0}$ has a multifractal behavior also when $x_0$ is irrational. The proofs rely on a careful design of Diophantine sets that depend on $x_0$, which we study by crucially using the Duffin-Schaeffer theorem and the Mass Transference Principle., Comment: 43 pages, 3 figures. v2: Introduction rewritten. Overview rewritten in Section 2. Appendix B added. v3: Small corrections

We consider the 2D incompressible Euler equation on a bounded simply connected domain $\Omega$. We give sufficient conditions on the domain $\Omega$ so that for all initial vorticity $\omega_0 \in L^{\infty}(\Omega)$ the weak solutions are unique. Our sufficient condition is slightly more general than the condition that $\Omega$ is a $C^{1,\alpha}$ domain for some $\alpha>0$, with its boundary belonging to $H^{3/2}(\mathbb{S}^1)$. As a corollary we prove uniqueness for $C^{1,\alpha}$ domains for $\alpha >1/2$ and for convex domains which are also $C^{1,\alpha}$ domains for some $\alpha >0$. Previously uniqueness for general initial vorticity in $L^{\infty}(\Omega)$ was only known for $C^{1,1}$ domains with possibly a finite number of acute angled corners. The fundamental barrier to proving uniqueness below the $C^{1,1}$ regularity is the fact that for less regular domains, the velocity near the boundary is no longer log-Lipschitz. We overcome this barrier by defining a new change of variable which we then use to define a novel energy functional., Comment: 33 pages, comments welcome

In this note we further discuss the probabilistic scaling introduced by the authors in [21, 22]. In particular we do a case study comparing the stochastic heat equation, the nonlinear wave equation and the nonlinear Schrodinger equation., Comment: Expository paper, 14 pages

Direct imaging of single molecules at nanostructured interfaces is a grand challenge, with potential to enable new, precise material architectures and technologies. Of particular interest are the structural morphology and spectroscopic signatures of the adsorbed molecule, where modern probes are only now being developed with the necessary spatial and energetic resolution to provide detailed information at molecule-surface interface. Here, we directly visualize the binding of individual m-terphenyl isocyanide ligands to a reconstructed Au(111) surface through scanning tunneling microscopy (STM) and inelastic electron tunneling spectroscopy (IETS). The site-dependent steric pressure of the various surface features alters the vibrational fingerprints of the m-terphenyl isocyanides, which is characterized with single-molecule precision through joint experimental and theoretical approaches. This study for the first time provides molecular-level insights into the steric-pressure-enabled surface binding selectivity, as well as its effect on the chemical properties of individual surface-binding ligands.

Today digital revolution is having a dramatic impact on the pharmaceutical industry and the entire healthcare system. The implementation of machine learning, extreme-scale computer simulations, and big data analytics in the drug design and development process offers an excellent opportunity to lower the risk of investment and reduce the time to the patient. Within the LIGATE project, we aim to integrate, extend, and co-design best-in-class European components to design Computer-Aided Drug Design (CADD) solutions exploiting today's high-end supercomputers and tomorrow's Exascale resources, fostering European competitiveness in the field. The proposed LIGATE solution is a fully integrated workflow that enables to deliver the result of a virtual screening campaign for drug discovery with the highest speed along with the highest accuracy. The full automation of the solution and the possibility to run it on multiple supercomputing centers at once permit to run an extreme scale in silico drug discovery campaign in few days to respond promptly for example to a worldwide pandemic crisis., Comment: Paper Accepted to the 20th ACM International Conference on Computing Frontiers (CF'23)

COVID-19 has shown the importance of having a fast response against pandemics. Finding a novel drug is a very long and complex procedure, and it is possible to accelerate the preliminary phases by using computer simulations. In particular, virtual screening is an in-silico phase that is needed to filter a large set of possible drug candidates to a manageable number. This paper presents the implementations and a comparative analysis of two GPU-optimized implementations of a virtual screening algorithm targeting novel GPU architectures. The first adopts a traditional approach that spreads the computation required to evaluate a single molecule across the entire GPU. The second uses a batched approach that exploits the parallel architecture of the GPU to evaluate more molecules in parallel, without considering the latency to process a single molecule. The paper describes the advantages and disadvantages of the proposed solutions, highlighting implementation details that impact the performance. Experimental results highlight the different performance of the two methods on several target molecule databases while running on NVIDIA A100 GPUs. The two implementations have a strong dependency with respect to the data to be processed. For both cases, the performance is improving while reducing the dimension of the target molecules (number of atoms and rotatable bonds). The two methods demonstrated a different behavior with respect to the size of the molecule database to be screened. While the latency one reaches sooner (with fewer molecules) the performance plateau in terms of throughput, the batched one requires a larger set of molecules. However, the performances after the initial transient period are much higher (up to 5x speed-up). Finally, to check the efficiency of both implementations we deeply analyzed their workload characteristics using the instruction roof-line methodology.

We consider the Vlasov equation in any spatial dimension, which has long been known to be an infinite-dimensional Hamiltonian system whose bracket structure is of Lie-Poisson type. In parallel, it is classical that the Vlasov equation is a mean-field limit for a pairwise interacting Newtonian system. Motivated by this knowledge, we provide a rigorous derivation of the Hamiltonian structure of the Vlasov equation, both the Hamiltonian functional and Poisson bracket, directly from the many-body problem. One may view this work as a classical counterpart to arXiv:1908.03847, which provided a rigorous derivation of the Hamiltonian structure of the cubic nonlinear Schr\"odinger equation from the many-body problem for interacting bosons in a certain infinite particle number limit, the first result of its kind. In particular, our work settles a question of Marsden, Morrison, and Weinstein on providing a "statistical basis" for the bracket structure of the Vlasov equation., Comment: 54 pages

We prove the invariance of the Gibbs measure under the dynamics of the three-dimensional cubic wave equation, which is also known as the hyperbolic $\Phi^4_3$-model. This result is the hyperbolic counterpart to seminal works on the parabolic $\Phi^4_3$-model by Hairer '14 and Hairer-Matetski '18. The heart of the matter lies in establishing local in time existence and uniqueness of solutions on the statistical ensemble, which is achieved by using a para-controlled Ansatz for the solution, the analytical framework of the random tensor theory, and the combinatorial molecule estimates. The singularity of the Gibbs measure with respect to the Gaussian free field brings out a new caloric representation of the Gibbs measure and a synergy between the parabolic and hyperbolic theories embodied in the analysis of heat-wave stochastic objects. Furthermore from a purely hyperbolic standpoint our argument relies on key new ingredients that include a hidden cancellation between sextic stochastic objects and a new bilinear random tensor estimate., Comment: Added remarks and corrected typographical errors