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Large-amplitude current-driven plasma instabilities, which can transition to the Buneman instability, were observed in one-dimensional (1D) simulations to generate high-energy backstreaming ions. We investigate the saturation of multi-dimensional plasma instabilities and its effects on energetic ion formation. Such ions directly impact spacecraft thruster lifetimes and are associated with magnetic reconnection and cosmic ray inception. An Eulerian Vlasov--Poisson solver employing the grid-based direct kinetic method is used to study the growth and saturation of 2D2V collisionless, electrostatic current-driven instabilities spanning two dimensions each in the configuration (D) and velocity (V) spaces supporting ion and electron phase-space transport. Four stages characterise the electric potential evolution in such instabilities: linear modal growth, harmonic growth, accelerated growth via quasi-linear mechanisms alongside non-linear fill-in, and saturated turbulence. Its transition and isotropisation process bears considerable similarities to the development of hydrodynamic turbulence. While a tendency to isotropy is observed in the plasma waves, followed by electron and then ion phase space after several ion-acoustic periods, the formation of energetic backstreaming ions is more limited in the 2D2V than in the 1D1V simulations. Plasma waves formed by two-dimensional electrostatic kinetic instabilities can propagate in the direction perpendicular to the net electron drift. Thus, large-amplitude multi-dimensional waves generate high-energy transverse-streaming ions and eventually limit energetic backward-streaming ions along the longitudinal direction. The multi-dimensional study sheds light on interactions between longitudinal and transverse electrostatic plasma instabilities, as well as fundamental characteristics of the inception and sustenance of unmagnetised plasma turbulence.

Large-amplitude current-driven instabilities in hollow cathode plumes can generate energetic ions responsible for cathode sputtering and spacecraft degradation. A 2D2V (two dimensions each in configuration [D] and velocity [V] spaces) grid-based Vlasov--Poisson (direct kinetic) solver is used to study their growth and saturation, which comprises four stages: linear growth, quasilinear resonance, nonlinear fill-in, and saturated turbulence. The linear modal growth rate, nonlinear saturation process, and ion velocity and energy distribution features in the turbulent regime are analyzed. Backstreaming ions are generated for large electron drifts, several ion acoustic periods after the potential field becomes turbulent. Interscale phase-space transfer and locality are analyzed for the Vlasov equation. The multidimensional study sheds light on the interactions between longitudinal and transverse plasma instabilities, as well as the inception of plasma turbulence., Comment: Center for Turbulence Research Proceedings of the Summer Program 2022

Breaking surface waves generate drops of a broad range of sizes that have a significant influence on regional and global climates, as well as the identification of ship movements. Characterizing these phenomena requires a fundamental understanding of the underlying mechanisms behind drop production. The interscale nature of these mechanisms also influences the development of models that enable cost-effective computation of large-scale waves. Interscale locality implies the universality of small scales and the suitability of generic subgrid-scale (SGS) models, while interscale nonlocality points to the potential dependence of the small scales on larger-scale geometry configurations and the corresponding need for tailored SGS models instead. A recently developed analysis toolkit combining theoretical population balance models, multiphase numerical simulations, and structure-tracking algorithms is used to probe the nature of drop production and its corresponding interscale mass-transfer characteristics above the surface of breaking waves. The results from the application of this toolkit suggest that while drop breakup is a somewhat scale-nonlocal process, its interscale transfer signature suggests that it is likely capillary-dominated and thus sensitive not to the specific nature of large-scale wave breaking, but rather to the specific geometry of the parent drops.

Laser ablation plasma thrusters are an emerging space propulsion concept that provides promise for lightweight payload delivery. Predicting the lifetime and performance of these thrusters hinges on a comprehensive characterization of the expansion dynamics of the ablated plasma plume. While state-of-the-art techniques for simulating plasmas are often particle-based, a grid-based direct kinetic solver confers advantages in such a transient and inhomogeneous problem by eliminating statistical noise. A direct kinetic solver including interparticle collisions is employed on a plume expansion model problem spanning one dimension each in configuration and velocity space. The high degree of thermodynamic nonequilibrium inherent in plume expansion is characterized, justifying the need for a kinetic rather than a hybrid or fluid solver. Thruster-relevant metrics such as the momentum flux are also computed. The plume dynamics are observed to be highly inhomogeneous in space with insufficient time for thermalization in the region preceding the expansion front, and the theoretical possibility of reducing the local grid resolution by up to two orders of magnitude at the far end of the domain is established. These grid-point requirements are verified via the employment of nonuniform grids of various expansion ratios, several of which also employ coarsening in velocity space. Longer domain lengths are explored to characterize thruster-scale phenomena and larger ambient pressures are simulated as a testbed to probe facility effects due to collisions with background particles., Comment: Please see also IEPC Article Repository at https://www.electricrocket.org/index.php?page=iepc-article-repository

Knowledge of bubble and drop size distributions in two-phase flows is important for characterizing a wide range of phenomena, including combustor ignition, sonar communication, and cloud formation. The physical mechanisms driving the background flow also drive the time evolution of these distributions. Accurate and robust identification and tracking algorithms for the dispersed phase are necessary to reliably measure this evolution and thereby quantify the underlying mechanisms in interface-resolving flow simulations. The identification of individual bubbles and drops traditionally relies on an algorithm used to identify connected regions. This traditional algorithm can be sensitive to the presence of spurious structures. A cost-effective refinement is proposed to maximize volume accuracy while minimizing the identification of spurious bubbles and drops. An accurate identification scheme is crucial for distinguishing bubble and drop pairs with large size ratios. The identified bubbles and drops need to be tracked in time to obtain breakup and coalescence statistics that characterize the evolution of the size distribution, including breakup and coalescence frequencies, and the probability distributions of parent and child bubble and drop sizes. An algorithm based on mass conservation is proposed to construct bubble and drop lineages using simulation snapshots that are not necessarily from consecutive time-steps. These lineages are then used to detect breakup and coalescence events, and obtain the desired statistics. Accurate identification of large-size-ratio bubble and drop pairs enables accurate detection of breakup and coalescence events over a large size range. Together, these algorithms enable insights into the mechanisms behind bubble and drop formation and evolution in flows of practical importance., Comment: Under review for the Journal of Computational Physics

Breaking waves generate a distribution of bubble sizes that evolves over time. Knowledge of how this distribution evolves is of practical importance for maritime and climate studies. The analytical framework developed in Part 1 examined how this evolution is governed by the bubble-mass flux from large to small bubble sizes, which depends on the rate of break-up events and the distribution of child bubble sizes. These statistics are measured in Part 2 as ensemble-averaged functions of time by simulating ensembles of breaking waves, and identifying and tracking individual bubbles and their break-up events. The break-up dynamics are seen to be statistically unsteady, and two intervals with distinct characteristics were identified. In the first interval, the dissipation rate and bubble-mass flux are quasi-steady, and the theoretical analysis of Part 1 is supported by all observed statistics, including the expected -10/3 power-law exponent for the super-Hinze-scale size distribution. Strong locality is observed in the corresponding bubble-mass flux, supporting the presence of a super-Hinze-scale break-up cascade. In the second interval, the dissipation rate decays, and the bubble-mass flux increases as small- and intermediate-sized bubbles become more populous. This flux remains strongly local with cascade-like behaviour, but the dominant power-law exponent for the size distribution increases to -8/3 as small bubbles are also depleted more quickly. This suggests the emergence of different physical mechanisms during different phases of the breaking-wave evolution, although size-local break-up remains a dominant theme. Parts 1 and 2 present an analytical toolkit for population balance analysis in two-phase flows., Comment: Under review for the Journal of Fluid Mechanics. Several figure placements were affected by arXiv's processing; contact authors for the original submitted manuscript

Breaking waves entrain gas beneath the surface. The wave-breaking process energizes turbulent fluctuations that break bubbles in quick succession to generate a wide range of bubble sizes. Understanding this generation mechanism paves the way towards the development of predictive models for large-scale maritime and climate simulations. Garrett et al. (2000) suggested that super-Hinze-scale turbulent breakup transfers entrained gas from large to small bubble sizes in the manner of a cascade. We provide a theoretical basis for this bubble-mass cascade by appealing to how energy is transferred from large to small scales in the energy cascade central to single-phase turbulence theories. A bubble break-up cascade requires that break-up events predominantly transfer bubble mass from a certain bubble size to a slightly smaller size on average. This property is called locality. In this paper, we analytically quantify locality by extending the population balance equation in conservative form to derive the bubble-mass transfer rate from large to small sizes. Using our proposed measures of locality, we show that scalings relevant to turbulent bubbly flows, including those postulated by Garrett et al. (2000) and observed in breaking-wave experiments and simulations, are consistent with a strongly local transfer rate, where the influence of non-local contributions decays in a power-law fashion. These theoretical predictions are confirmed using numerical simulations in Part 2, revealing key physical aspects of the bubble break-up cascade phenomenology. Locality supports the universality of turbulent small-bubble break-up, which simplifies the development of subgrid-scale models to predict oceanic small-bubble statistics of practical importance., Comment: Under review for the Journal of Fluid Mechanics

Fong et al. (The game chromatic index of some trees with maximum degree four and adjacent degree-four vertices, J. Comb Optim 36 (2018) 1-12) proved that the game chromatic index of any tree $T$ of maximum degree 4 whose degree-four vertices induce a forest of paths of length $l$ less than 2 is at most 5. In this paper, we show that the bound 5 is also valid for $l\leq 2$. This partially solves the problem of characterization of the trees whose game chromatic index exceeds the maximum degree by at most 1, which was proposed by Cai and Zhu (Game chromatic index of $k$-degenerate graphs, J. Graph Theory 36 (2001) 144-155)., Comment: 36 pages, 72 figures

Micro-bubbles are of significant interest due to the long-living signature they leave behind naval ships. In order to numerically model and predict these bubbles in naval applications, subgrid-scale models are required because of the extreme separation of length- and time-scales between the macroscopic geometries and the physical processes leading to the formation of these bubbles. Yet, there is much that is unknown about the mechanism behind the entrainment of such bubbles. Furthermore, quantitative information regarding their size distribution and dependence on flow parameters is very limited. Impact events are hypothesized to be the main contributor to the generation of micro-bubbles. This is due to a phenomenon known as Mesler entrainment, which has been observed in the context of the drop-pool impact problem. Namely, when a water droplet with diameter of $\mathcal{O}(1mm)$ impacts a deep water pool with an impact velocity of $\mathcal{O}(1m/s)$, hundreds of air micro-bubbles are entrained into the pool. These bubbles have been found to be remnants of a very thin air film entrapped between the two liquid bodies. These films have extremely high aspect ratios and after being punctured, shed micro-bubbles while retracting on time scales much shorter than the outer flow time scales. This separation of time-scales, along with a lacking of studies on retracting thin gas films has motivated us to study this fundamental problem with numerical simulations in two and three dimensions. Using a diffuse interface method, we perform two-phase simulations of retracting thin gas films in initially static liquid backgrounds to gain understanding regarding this problem and gather statistics that can be potentially used in a subgrid-scale model to predict micro-bubble shedding from a thin gas film. Coupling a model like this to a model that predicts the thin film characteristics ..., Comment: Proceedings of 32nd Symposium on Naval Hydrodynamics, Hamburg, Germany, 5-10 Aug. 2018

The generation of microbubbles upon the collision and interaction of liquid bodies in a gaseous environment is a ubiquitous process in two-phase flows, including large-scale phenomena like ship wakes, breaking waves and rain showers. These collision and interaction events involve the relative approach of pairs of liquid-gas interfaces. As these interfaces approach, the smallest length scales of the system are dynamically reduced. This evolving disparity in length scales is numerically challenging to resolve without the employment of subgrid-scale (SGS) impact and breakup models. In this study, a physics-based impact and breakup model for the generation of these microbubbles is developed and implemented. The objectives of this study are to develop a computational algorithm that identifies interface collision events that contribute to the formation of microbubbles, to formulate a physics-based breakup model that predicts the distribution of microbubble sizes using the characteristics of the originating gas film, and to integrate these modules into a two-phase flow solver that accurately captures the effects of bubbles of all sizes. In these proceedings, an SGS model suitable for the aforementioned problems is proposed, and the steps involved in implementing the proposed SGS model in a macroscale flow solver are outlined. Two aspects of the development of this SGS model are then discussed in detail. First, the formulation and implementation of the first step of the SGS model, the collision detection algorithm, is detailed. Second, preliminary findings of a numerical investigation intended to shed light on breakup processes in turbulent two-phase flows are presented., Comment: This is a low-resolution version submitted to meet the arXiv requirements. For a high-resolution version, please contact the authors directly

In this paper, we study the blowup phenomena for the regular solutions of the isentropic relativistic Euler-Poisson equations with a vacuum state in spherical symmetry. Using a general family of testing functions, we obtain new blowup conditions for the relativistic Euler-Poisson equations. We also show that the proposed blowup conditions are valid regardless of the speed requirement, which was one of the key constraints stated in "Y. Geng, Singularity Formation for Relativistic Euler and Euler-Poisson Equations with Repulsive Force, Commun. Pure Appl. Anal., 14 (2015), 549--564."., Comment: 14 Pages; Key Words: Relativistic Euler-Poisson Equations, Integration Method, Blowup, Initial Value Problem, Vacuum, Radial Symmetry

Semiquantum key distribution allows a quantum party to share a random key with a "classical" party who only can prepare and measure qubits in the computational basis or reorder some qubits when he has access to a quantum channel. In this work, we present a protocol where a secret key can be established between a quantum user and an almost classical user who only needs the quantum ability to access quantum channels, by securely delegating quantum computation to a quantum server. We show the proposed protocol is robust even when the delegated quantum server is a powerful adversary, and is experimentally feasible with current technology. As one party of our protocol is the most quantum-resource efficient, it can be more practical and significantly widen the applicability scope of quantum key distribution., Comment: 7 pages, 2 figures

Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent interactions according to two protocols where the total network quantity is conserved or variable. For both protocols, our focus is on asymmetric interactions between agents involving directed graphs. Specifically, we define how the dynamics of conservative and non-conservative networks relate to the weighted in-degree Laplacian and the weighted out-degree Laplacian. Our framework allows the addition and subtraction of the considered quantity to and from a set of nodes. This enables the modeling of stubborn agents with time-invariant quantities, and the process of dynamic learning. We highlight several stability and convergence characteristics of our framework, and define the conditions under which asymptotic convergence is guaranteed when the network topology is variable. In addition, we indicate how our framework accommodates external network control and targeted network design. We show how network diffusion can be externally manipulated by applying time-varying input functions at individual nodes. Desirable network structures can also be constructed by adjusting the dominant diffusion modes. To this purpose, we propose a Markov decision process that learns these network adjustments through a reinforcement learning algorithm, suitable for large networks. The presented network control and design schemes enable flow modifications that allow the alteration of the dynamic and stationary behavior of the network in conservative and non-conservative networks.

Quantum signature (QS) is used to authenticate the identity of the originator, ensure data integrity and provide non-repudiation service with unconditional security. Depending on whether a trusted third party named arbitrator is involved or not, QS is classified as arbitrated QS and true QS. This paper studies existence problem about the two kinds of QS and contributes to two points: 1) a basic framework is provided to analyze the possibility of arbitrated QS on signing quantum messages; 2) disagreement between the impossibility of true QS and an existing true QS scheme is solved., Comment: 7 pages, no figures