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This paper investigates the coexistence of two competing species on random geometric graphs (RGGs) in continuous time. The species grow by occupying vacant sites according to Richardson's model, while simultaneously competing for occupied sites under the dynamics of the voter model. Coexistence is defined as the event in which both species occupy at least one site simultaneously at any given time. We prove that coexistence occurs with strictly positive annealed probability by applying results from moderate deviations in first-passage percolation and random walk theory, with a focus on specific regions of the space., Comment: 16 pages, 5 figures

Alkali metal intercalation of graphene layers has been of particular interest due to potential applications in electronics, energy storage, and catalysis. Rubidium (Rb) is one of the largest alkali metals and the one less investigated as intercalant. Here, we report a systematic investigation, with a multi-technique approach, of the phase formation of Rb under epitaxial monolayer graphene on SiC(0001). We explore a wide phase space with two control parameters: the Rb density (i.e., deposition time) and sample temperature (i.e., room- and low-temperature). We reveal the emergence of $(2 \times 2)$ and $(\sqrt{3} \times \sqrt{3})$R30{\deg} structures formed by a single alkali metal layer intercalated between monolayer graphene and the interfacial C-rich reconstructed surface, also known as buffer layer. Rb intercalation also results in a strong n-type doping of the graphene layer. Progressively annealing to high temperatures, we first reveal diffusion of Rb atoms which results in the enlargement of intercalated areas. As desorption sets in, intercalated regions progressively shrink and fragment. Eventually, at approximately 600{\deg}C the initial surface is retrieved, indicating the reversibility of the intercalation process.

The dynamics of small-scale structures in free-surface turbulence is crucial to large-scale phenomena in natural and industrial environments. Here we conduct experiments on the quasi-flat free surface of a zero-mean-flow turbulent water tank over the Reynolds number range $Re_{\lambda} = 207\textrm{--}312$. By seeding microscopic floating particles at high concentrations, the fine scales of the flow and the velocity gradient tensor are resolved. A kinematic relation is derived expressing the contribution of surface divergence and vorticity to the dissipation rate. The probability density functions of divergence, vorticity and strain-rate collapse once normalized by the Kolmogorov scales. Their magnitude displays strong intermittency and follows chi-square distributions with power-law tails at small values. The topology of high-intensity events and two-point statistics indicate that the surface divergence is characterized by dissipative spatial and temporal scales, while the high-vorticity and high-strain-rate regions are larger, long-lived, concurrent, and elongated. The second-order velocity structure functions obey the classic Kolmogorov scaling in the inertial range when the dissipation rate on the surface is considered, with a different numerical constant than in 3D turbulence. The cross-correlation among divergence, vorticity and strain-rate indicates that the surface-attached vortices are strengthened during downwellings and diffuse when those dissipate. Sources (sinks) in the surface velocity fields are associated with strong (weak) surface-parallel stretching and compression along perpendicular directions. The floating particles cluster over spatial and temporal scales larger than those of the sinks. These results demonstrate that, compared to 3D turbulence, in free-surface turbulence the energetic scales leave a stronger imprint on the small-scale quantities.

The small-scale velocity gradient is connected to fundamental properties of turbulence at the large scales. By neglecting the viscous and nonlocal pressure Hessian terms, we derive a restricted Euler model for the turbulent flow along an undeformed free surface and discuss the associated stable/unstable manifolds. The model is compared with the data collected by high-resolution imaging on the free surface of a turbulent water tank with negligible surface waves. The joint probability density function (PDF) of the velocity gradient invariants exhibits a distinct pattern from the one in the bulk. The restricted Euler model captures the enhanced probability along the unstable branch of the manifold and the asymmetry of the joint PDF. Significant deviations between the experiments and the prediction are evident, however, in particular concerning the compressibility of the surface flow. These results highlight the enhanced intermittency of the velocity gradient and the influence of the free surface on the energy cascade.

Two-dimensional (2D) materials are poised to revolutionize current solid-state technology with their extraordinary properties. Yet, the primary challenge remains their scalable production. While there have been significant advancements, much of the scientific progress has depended on the exfoliation of materials, a method that poses severe challenges for large-scale applications. With the advent of artificial intelligence (AI) in materials science, innovative synthesis methodologies are now on the horizon. This study explores the forefront of autonomous materials synthesis using an artificial neural network (ANN) trained by evolutionary methods, focusing on the efficient production of graphene. Our approach demonstrates that a neural network can iteratively and autonomously learn a time-dependent protocol for the efficient growth of graphene, without requiring pretraining on what constitutes an effective recipe. Evaluation criteria are based on the proximity of the Raman signature to that of monolayer graphene: higher scores are granted to outcomes whose spectrum more closely resembles that of an ideal continuous monolayer structure. This feedback mechanism allows for iterative refinement of the ANN's time-dependent synthesis protocols, progressively improving sample quality. Through the advancement and application of AI methodologies, this work makes a substantial contribution to the field of materials engineering, fostering a new era of innovation and efficiency in the synthesis process.

Run to run variability in parallel programs caused by floating-point non-associativity has been known to significantly affect reproducibility in iterative algorithms, due to accumulating errors. Non-reproducibility can critically affect the efficiency and effectiveness of correctness testing for stochastic programs. Recently, the sensitivity of deep learning training and inference pipelines to floating-point non-associativity has been found to sometimes be extreme. It can prevent certification for commercial applications, accurate assessment of robustness and sensitivity, and bug detection. New approaches in scientific computing applications have coupled deep learning models with high-performance computing, leading to an aggravation of debugging and testing challenges. Here we perform an investigation of the statistical properties of floating-point non-associativity within modern parallel programming models, and analyze performance and productivity impacts of replacing atomic operations with deterministic alternatives on GPUs. We examine the recently-added deterministic options in PyTorch within the context of GPU deployment for deep learning, uncovering and quantifying the impacts of input parameters triggering run to run variability and reporting on the reliability and completeness of the documentation. Finally, we evaluate the strategy of exploiting automatic determinism that could be provided by deterministic hardware, using the Groq accelerator for inference portions of the deep learning pipeline. We demonstrate the benefits that a hardware-based strategy can provide within reproducibility and correctness efforts.

We introduce a non-Markovian rumor model in the complete graph on $n$ vertices inspired by Daley and Kendall's model. For this model, we prove a functional law of large numbers (FLLN) and a functional central limit theorem (FCLT). We apply these results to a non-Markovian version of the rumor model introduced by Lebensztayn, Machado and Rodr\'{i}guez.

Nickel nanoparticles (Ni NPs), thanks to their peculiar properties, are interesting materials for many applications including catalysis, hydrogen storage, and sensors. In this work, Ni NPs are synthesized in aqueous solution by a simple and rapid procedure with cetyltrimethylammonium bromide (CTAB) as a capping agent, and are extensively characterized by dynamic light scattering (DLS), scanning electron microscopy (SEM), and atomic force microscopy (AFM). We investigated their shape, dimension, and their distribution on the surfaces of SiO2 and epitaxial graphene (EG) samples. Ni NPs have an average diameter of ~11 nm, with a narrow size dispersion, and their arrangement on the surface is strongly dependent on the substrate. EG samples functionalized with Ni NPs are further characterized by X-ray photoelectron spectroscopy (XPS), as made and after thermal annealing above 350{\deg}C to confirm the degradation of CTAB and the presence of metallic Ni(0). Moreover, high resolution scanning tunneling microscopy (STM) topographies reveal the structural stability of the NPs up to 550 {\deg}C.

We investigate the turbulence below a quasi-flat free surface, focusing on the energy transport in space and across scales. We leverage a large zero-mean-flow tank where homogeneous turbulence is generated by randomly actuated jets. A wide range of Reynolds number is spanned, reaching sufficient scale separation for the emergence of an inertial sub-range. Unlike previous studies, the forcing extends through the source layer, though the surface deformation remains millimetric. Particle image velocimetry along a surface-normal plane resolves from the dissipative to the integral scales. The contributions to turbulent kinetic energy from both vertical and horizontal components of velocity approach the prediction based on rapid distortion theory as the Reynolds number is increased, indicating that discrepancies among previous studies are likely due to differences in the forcing. At odds with the theory, however, the integral scale of the horizontal fluctuations grows as the surface is approached. This is rooted in the profound influence exerted by the surface on the inter-scale energy transfer: along horizontal separations, the direct cascade of energy in horizontal fluctuations is hindered, while an inverse cascade of that in vertical fluctuations is established. This is connected to the structure of upwellings and downwellings. The former, characterized by somewhat larger spatial extent and stronger intensity, are associated to extensional surface-parallel motions. They thus transfer energy to the larger horizontal scales, prevailing over downwellings which favour the compression (and concurrent vertical stretching) of the eddies. Both types of structures extend to depths between the integral and Taylor microscales.

Atomically thin materials offer multiple opportunities for layer-by-layer control of their electronic properties. While monolayer graphene (MLG) is a zero-gap system, Bernal-stacked bilayer graphene (BLG) acquires a finite band gap when the symmetry between the layers' potential energy is broken, usually, via a displacement electric field applied in double-gate devices. Here, we introduce a twistronic stack comprising both MLG and BLG, synthesized via chemical vapor deposition, showing a Bernal gap in the absence of external fields. Although a large ($\sim30^{\circ}$) twist angle decouples the MLG and BLG electronic bands near Fermi level, proximity-induced energy shifts in the outermost layers result in a built-in asymmetry, which requires a displacement field of $0.14$ V/nm to be compensated. The latter corresponds to a $\sim10$ meV intrinsic BLG gap, a value confirmed by our thermal-activation measurements. The present results highlight the role of structural asymmetry and encapsulating environment, expanding the engineering toolbox for monolithically-grown graphene multilayers., Comment: 25 pages, 4 figures and supplementary information

Intercalation of epitaxial graphene on SiC(0001) with Sn results in a well-ordered Sn $(1\times1)$ structure on the SiC surface with quasi-freestanding graphene on top. While the electronic properties of the individual layers have been studied in the past, emerging phenomena arising from possible inter-layer interactions between the 2D\,Sn layer and graphene remain unexplored. We use time- and angle-resolved photoemission spectroscopy to reveal a surprisingly short-lived non-equilibrium carrier distribution inside the Dirac cone of Sn-intercalated graphene. Further, we find that the graphene $\pi$-band exhibits a transient increase in binding energy that we attribute to charging of the graphene layer with holes. We interpret our results with support from density functional theory calculations of the graphene - 2D\,Sn heterostructure that reveal a substantial hybridization between the graphene $\pi$-bands and Sn states, providing a channel for efficient ultrafast charge transfer between the layers. Our results on the graphene - 2D\,Sn model system are expected to trigger similar investigations on related heterostructures obtained by intercalation of epitaxial graphene. Regarding the huge choice of materials that have been successfully intercalated in the past, we believe that the interlayer interactions revealed in the present work only represent the tip of the iceberg with many fascinating emerging phenomena to be discovered in the near future., Comment: 19 pages, 5 figures

Understanding and controlling the electronic properties of two-dimensional materials is crucial for their potential applications in nano- and optoelectronics. Monolayer transition metal dichalcogenides such as WS$_2$ have garnered significant interest due to their strong light-matter interaction and extreme sensitivity of the band structure to the presence of photogenerated electron-hole pairs. In this study, we investigate the transient electronic structure of monolayer WS$_2$ on a graphene substrate after resonant excitation of the A-exciton using time- and angle-resolved photoemission spectroscopy. We observe a pronounced band structure renormalization including a substantial reduction of the transient band gap that is in good quantitative agreement with our {\it ab initio} theory that reveals the importance of both intrinsic WS$_2$ and extrinsic substrate contributions to the transient band structure of monolayer WS$_2$. Our findings not only deepen the fundamental understanding of band structure dynamics in two-dimensional materials but also offer valuable insights for the development of novel electronic and optoelectronic devices based on monolayer TMDs and their heterostructures with graphene., Comment: 48 pages, 16 figures

We discuss a complementary asymptotic analysis of the so called minimal random walk. More precisely, we present a version of the almost sure central limit theorem as well as a generalization of the recently proposed quadratic strong laws. In addition, alternative demonstrations of the functional limit theorems will be supplied based on a P\'olya urn scheme instead of a martingale approach.

In this paper, we study an analytically tractable SIS model with a non-linear incidence rate for the number of infectious individuals described through a stochastic differential equation (SDE). We guarantee the existence of a positive solution, and we study its regularity. We study the persistence and extinction regimes, and we give sufficient conditions under which the disease-free equilibrium point is an asymptotically stable equilibrium point with probability one. We provide sufficient conditions under which the model admits a unique stationary measure. Finally, we illustrate our findings using simulations.

The widespread adoption of quadrotors for diverse applications, from agriculture to public safety, necessitates an understanding of the aerodynamic disturbances they create. This paper introduces a computationally lightweight model for estimating the time-averaged magnitude of the induced flow below quadrotors in hover. Unlike related approaches that rely on expensive computational fluid dynamics (CFD) simulations or drone specific time-consuming empirical measurements, our method leverages classical theory from turbulent flows. By analyzing over 16 hours of flight data from drones of varying sizes within a large motion capture system, we show for the first time that the combined flow from all drone propellers is well-approximated by a turbulent jet after 2.5 drone-diameters below the vehicle. Using a novel normalization and scaling, we experimentally identify model parameters that describe a unified mean velocity field below differently sized quadrotors. The model, which requires only the drone's mass, propeller size, and drone size for calculations, accurately describes the far-field airflow over a long-range in a very large volume which is impractical to simulate using CFD. Our model offers a practical tool for ensuring safer operations near humans, optimizing sensor placements and drone control in multi-agent scenarios. We demonstrate the latter by designing a controller that compensates for the downwash of another drone, leading to a four times lower altitude deviation when passing below., Comment: 7+1 pages

We use video footage of a water tunnel experiment to construct a two-dimensional reduced-order model of the flapping dynamics of an inverted flag in uniform flow. The model is obtained as the reduced dynamics on an attracting spectral submanifold (SSM) that emanates from the two slowest modes of the unstable fixed point of the flag. Beyond an unstable fixed point and a limit cycle expected from observations, our SSM-reduced model also confirms the existence of two unstable fixed points for the flag, which were found by previous studies. Importantly, the model correctly reconstructs the dynamics from a small number of general trajectories and no further information on the system. In the chaotic flapping regime, we construct a 4D SSM-reduced model that captures the system's chaotic attractor.

Within the nucleus, structural maintenance of chromosome protein complexes, namely condensin and cohesin, create an architecture to facilitate the organization and proper function of the genome. Condensin, in addition to performing loop extrusion, creates localized clusters of chromatin in the nucleolus through transient crosslinks. Large-scale simulations revealed three different dynamic behaviors as a function of timescale: slow crosslinking leads to no clusters, fast crosslinking produces rigid slowly changing clusters, while intermediate timescales produce flexible clusters that mediate gene interaction. By mathematically analyzing different relative scalings of the two sources of stochasticity, thermal fluctuations and the force induced by the transient crosslinks, we predict these three distinct regimes of cluster behavior. Standard time-averaging that takes the fluctuations of the transient crosslink force to zero predicts the existence of rigid clusters. Accounting for the interaction of both fluctuations from the crosslinks and thermal noise with an effective energy landscape predicts the timescale-dependent lifetimes of flexible clusters. No clusters are predicted when the fluctuations of the transient crosslink force are taken to be large relative to thermal fluctuations. This mathematical perturbation analysis illuminates the importance of accounting for stochasticity in local incoherent transient forces to predict emergent complex biological behavior., Comment: 9 pages, 6 figures

This study delves into the exploration of the limiting shape theorem for subadditive processes on finitely generated groups with polynomial growth, commonly referred to as virtually nilpotent groups. Investigating the algebraic structures underlying these processes, we present a generalized form of the asymptotic shape theorem within this framework. Extending subadditive ergodic theory in this context, we consider processes which exhibit both at most and at least linear random growth. We conclude with applications and illustrative examples., Comment: 36 pages, 1 figure; typos corrected, some lemmas revised

This rejoinder responds to discussions by of Caimo, Niezink, and Schweinberger and Fritz of ''A Tale of Two Datasets: Representativeness and Generalisability of Inference for Samples of Networks'' by Krivitsky, Coletti, and Hens, all published in the Journal of the American Statistical Association in 2023., Comment: 10 pages, 3 figures, 3 tables

Consider the following simple parking process on $\Lambda_n := \{-n, \ldots, n\}^d,d\ge1$: at each step, a site $i$ is chosen at random in $\Lambda_n$ and if $i$ and all its nearest neighbor sites are empty, $i$ is occupied. Once occupied, a site remains so forever. The process continues until all sites in $\Lambda_n$ are either occupied or have at least one of their nearest neighbors occupied. The final configuration (occupancy) of $\Lambda_n$ is called the jamming limit and is denoted by $X_{\Lambda_n}$. Ritchie (2006) constructed a stationary random field on $\mathbb Z^d$ obtained as a (thermodynamic) limit of the $X_{\Lambda_n}$'s as $n$ tends to infinity. As a consequence of his construction, he proved a strong law of large numbers for the proportion of occupied sites in the box $\Lambda_n$ for the random field $X$. Here we prove the central limit theorem, the law of iterated logarithm, and a gaussian concentration inequality for the same statistics. A particular attention will be given to the case $d=1$, in which we also obtain new asymptotic properties for the sequence $X_{\Lambda_n},n\ge1$ as well as a new proof to the closed-form formula for the occupation density of the parking process., Comment: 19 pages, 1 figure

Two-dimensional (2D) materials have received extensive research attentions over the past two decades due to their intriguing physical properties (such as the ultrahigh mobility and strong light-matter interaction at atomic thickness) and a broad range of potential applications (especially in the fields of electronics and optoelectronics). The growth of single-crystal 2D materials is the prerequisite to realize 2D-based high-performance applications. In this review, we aim to provide an in-depth analysis of the state-of-the-art technology for the growth and applications of 2D materials, with particular emphasis on single crystals. We first summarize the major growth strategies for monolayer 2D single crystals. Following that, we discuss the growth of multilayer single crystals, including the control of thickness, stacking sequence, and heterostructure composition. Then we highlight the exploration of 2D single crystals in electronic and optoelectronic devices. Finally, a perspective is given to outline the research opportunities and the remaining challenges in this field.

The potential of graphene for hydrogen storage, coupled with the established role of Platinum as a catalyst for the hydrogen evolution reaction and the spillover effect, makes Pt-functionalized graphene a promising candidate for near-ambient hydrogen storage. This paper focuses on examining the process of Pt cluster formation on epitaxial graphene and assesses the suitability of the system as hydrogen storage material. Scanning tunneling microscopy unveils two primary pathways for Pt cluster growth. In the initial phase, up to ~1 ML of Pt coverage, Pt tends to randomly disperse and cover the graphene surface, while the cluster height remains essentially unchanged. Beyond a coverage of 3 ML, the nucleation of new layers on existing clusters becomes predominant. Then, the clusters mainly grow in height. Thermal desorption spectroscopy on hydrogenated Pt-decorated graphene reveals the presence of multiple hydrogen adsorption mechanisms, manifested as two Gaussian peaks superimposed on a linearly increasing background. We attribute the first peak at 150{\deg}C to hydrogen physisorbed on the surface of Pt clusters. The second peak at 430{\deg}C is attributed to chemisorption of hydrogen on the surface of the clusters, while the linearly increasing background is assigned to hydrogen bonded in the bulk of the Pt clusters. These measurements demonstrate the ability of Pt-functionalized graphene to store molecular hydrogen at temperatures that are high enough for stable hydrogen binding at room temperature.

Graphene-hexagonal boron nitride (hBN) scalable heterostructures are pivotal for the development of graphene-based high-tech applications. In this work, we demonstrate the realization of high-quality graphene-hBN heterostructures entirely obtained with scalable approaches. hBN continuous films were grown via ion beam-assisted physical vapor deposition directly on commercially available $SiO_2/Si$ and used as receiving substrates for graphene single-crystal matrixes grown by chemical vapor deposition on copper. The structural, chemical, and electronic properties of the heterostructure were investigated by atomic force microscopy, Raman spectroscopy, and electrical transport measurements. We demonstrate graphene carrier mobilities exceeding $10,000 cm^2/Vs$ in ambient conditions, 30% higher than those directly measured on $SiO_{2}/Si$. We prove the scalability of our approach by measuring more than 100 transfer length method devices over a centimeter scale, which present an average carrier mobility of $7500 \pm 850 cm^{2}/Vs$. The reported high-quality all-scalable heterostructures are of relevance for the development of graphene-based high-performing electronic and optoelectronic applications.

The accurate prediction of the two-phase heat transfer coefficient (HTC) as a function of working fluids, channel geometries and process conditions is key to the optimal design and operation of compact heat exchangers. Advances in artificial intelligence research have recently boosted the application of machine learning (ML) algorithms to obtain data-driven surrogate models for the HTC. For most supervised learning algorithms, the task is that of a nonlinear regression problem. Despite the fact that these models have been proven capable of outperforming traditional empirical correlations, they have key limitations such as overfitting the data, the lack of uncertainty estimation, and interpretability of the results. To address these limitations, in this paper, we use a multi-output Gaussian process regression (GPR) to estimate the HTC in microchannels as a function of the mass flow rate, heat flux, system pressure and channel diameter and length. The model is trained using the Brunel Two-Phase Flow database of high-fidelity experimental data. The advantages of GPR are data efficiency, the small number of hyperparameters to be trained (typically of the same order of the number of input dimensions), and the automatic trade-off between data fit and model complexity guaranteed by the maximization of the marginal likelihood (Bayesian approach). Our paper proposes research directions to improve the performance of the GPR-based model in extrapolation., Comment: 7 pages, 2 figures, to be published in the proceedings of the 17th International Heat Transfer Conference 2023 (IHTC-17)

The quantum Hall effect is widely used for the investigation of fundamental phenomena, ranging from topological phases to composite fermions. In particular, the discovery of a room temperature resistance quantum in graphene is significant for compact resistance standards that can operate above cryogenic temperatures. However, this requires large magnetic fields that are accessible only in a few high magnetic field facilities. Here, we report on the quantum Hall effect in graphene encapsulated by the ferroelectric insulator CuInP2S6. Electrostatic gating of the graphene channel enables the Fermi energy to be tuned so that electrons in the localized states of the insulator are in equilibrium with the current-carrying, delocalized states of graphene. Due to the presence of strongly bound states in this hybrid system, a quantum Hall plateau can be achieved at room temperature in relatively modest magnetic fields. This phenomenon offers the prospect for the controlled manipulation of the quantum Hall effect at room temperature., Comment: 24 pages, 6 figures