One of the main questions in planet formation theory is how to cross the metre-scale barrier. In this two-part series, we assess the merits of vortex-based theories by investigating the effect of backreacting dust on vortices. Specifically, this second paper focuses on the 'turbulent' vortex theory, according to which the streaming instability (SI) might be active in vortices. We re-purpose the dusty vortex models derived in paper I as background flows for a linear stability analysis. To simplify the perturbation equations, we build an analogue of the shearing box that follows vortex streamlines instead of Keplerian orbits. This allows us to study the evolution of small wavelength perturbations. We find that inertial waves and dust density waves can propagate in vortices, but that they are not sinusoidal in time. We then extend resonant drag instability theory to these non-modal waves. This allows us to demonstrate that a close cousin of the SI remains active in vortices, a result that greatly strengthens the case for vortex-induced planetesimal formation. Our results also complement past simulations - which showed that the dust's backreaction makes vortices unstable - by providing insights into the nature of (some of) the unstable modes. The caveat is that our work is restricted to the limit of dilute well-coupled dust and to the linear phase of the instability. Finally, our 'vortex SI' extends to 2D. We explain the mechanism of this 'zonal flow RDI', but remain unsure whether it is the unknown instability seen in 2D vortex simulations.

One of the main questions regarding planet formation is how to cross the metre-scale barrier. Several theories rely on the formation of dust clumps dense enough to collapse under their own gravity. Vortices are promising candidate sites of clump formation because they can concentrate dust 'laminarly' by capturing particles, and 'turbulently' by creating the ideal conditions for the streaming instability. In this two-part series, we assess the validity of both pathways by investigating the effect of backreacting dust on vortices. This first paper focuses on the laminar pathway. We use multiple timescale analysis to create two models of vortex evolution. They differ in their assumptions regarding how much gas crosses the vortex's boundary: the first one assumes that the vortex's mass is constant, whereas the second one assumes that the gas density is constant. These two options epitomize the two ways in which vortices can respond to dust concentration. Essentially, as dust gets closer to the vortex centre, it loses angular momentum. To compensate, the gas must either move away from the vortex centre or change its vorticity (and therefore its shape). This choice neatly emerges from the conservation of a quantity akin to potential vorticity. Interestingly, we find that vortices that adjust their vorticity all evolve towards elliptically unstable shapes. And since the elliptical instability destroys the vortex, we conclude that dust imposes an upper bound on vortex lifetimes. If vortex destruction happens before the dust reaches the Hill density, the 'laminar' vortex pathway to planetesimal formation fails.

Efficient, low-loss, and versatile optical modulators are a critical ingredient for practical integrated photonic systems. Modulators based on micro-electromechanical systems (MEMS) have unique advantages over more traditional thermal, electro-optic, or plasma dispersion modulators. In this work, we show that evanescent MEMS modulators (in which a dielectric slab is mechanically inserted into a waveguide's evanescent field) can exhibit anomalously dispersive modulation. That is, despite positive modulation of a waveguide mode's effective index, the modulator brings about a negative change in group index. We experimentally demonstrate these unique capabilities using a novel MEMS actuator design. The new theory and results here reveal that evanescent MEMS modulators possess a capability for control of wavelength dispersion not accessible to nearly any other type of modulator. These new capabilities may enable on-chip integration of systems for various optical applications, including broadband switching, photonic true time delay, pulse shaping, or phase matching of nonlinear processes.

Thermally activated delayed fluorescence (TADF) is a promising route towards high-efficiency, metal-free organic light-emitting diodes (OLEDs). However, the characterization of TADF kinetics in solid-state thin films is often complicated by pronounced multiexponential photoluminescence decays that prevent standard biexponential modeling. In this work, we introduce the 'Gamma-Fit' method, a streamlined analytical framework based on the gamma distribution that accounts for the continuous distribution of decay rates inherent in disordered molecular ensembles. By treating the decay as a result of conformational and kinetic heterogeneity, we accurately extract kinetic parameters for the benchmark emitters 4CzIPN and 5CzBN, as well as a series of novel diphenylamine (DPA)-based systems. Our results reveal that accounting for the local environment in thin films remains an important part in determining OLED efficiency. The experimental findings are complemented by a semiclassical Marcus-like computational approach. We evaluate the reliability of this conventional single-conformation rate calculation method and highlight the presence of conformational ensembles and multiple RISC-active triplet states as important factors for accurately describing the transition kinetics.

Deterrence coalitions that collectively own their deterrence technology, need an institutional design to decide when to retaliate against an attack or incident. This choice of institutional design, formalized through a social choice function, introduces a tradeoff between credible deterrence and escalation risk. We study this tradeoff via a simple signalling model, and use it to construct an associated binary classification problem to determine institutional designs that perform well in a variety of environments. For a small coalition of four members, we compute and study the statistics of the empirical ROC curves associated to a variety of choice functions and probability distributions for retaliation and false positives.

We study the topology of Lagrangian submanifolds in standard symplectic vector spaces $\mathbb{C}^n$ using ideas from open-closed string topology. Specifically, for a closed, oriented, spin Lagrangian $L$, we construct a (possibly curved) deformation of the dg associative algebra of chains on the based loop space of $L$. This is done via pushing forward moduli spaces of pseudo-holomorphic discs with boundaries on $L$, viewed as chains in the free loop space, along a string topology closed-open map. As an application, we prove that if $π_2(L)=0$, then $L$ has non-vanishing Maslov class, generalizing previous results due to Viterbo, Cieliebak-Mohnke, Fukaya, and Irie.

When a user sends a message over a wireless network, the message does not travel as-is. It is encrypted, authenticated, encapsulated, and transformed as it descends the protocol stack from the application layer to the physical medium. Each layer may apply its own cryptographic operations using its own algorithms, and these algorithms differ in their vulnerability to quantum computers. The security of the overall communication depends not on any single layer but on the \emph{composition} of transformations across all layers. We develop a preliminary formal framework for analyzing these cross-layer cryptographic transformations with respect to post-quantum cryptographic (PQC) readiness. We classify every per-layer cryptographic operation into one of four quantum vulnerability categories, define how per-layer PQC statuses compose across the full message transformation chain, and prove that this composition forms a bounded lattice with confidentiality composing via the join (max) operator and authentication via the meet (min). We apply the framework to five communication scenarios spanning Linux and iOS platforms, and identify several research challenges. Among our findings: WPA2-Personal provides strictly better PQC posture than both WPA3-Personal and WPA2-Enterprise; a single post-quantum layer suffices for payload confidentiality but \emph{every} layer must migrate for complete authentication; and metadata protection depends solely on the outermost layer.

The present work reports the parity ($\mathcal{P}$)-odd and time-reversal ($\mathcal{T}$)-odd interaction constants for the ground electronic state, X$^2Σ^{+}_{1/2}$, of YbX, X: Cu, Ag and Au molecules. The reported results have been calculated using the Kramers-restricted configuration interaction method limited to single and double excitations, in conjunction with relativistic core-valence double-, triple-, and quadruple-zeta quality basis sets, within a four-component relativistic framework. The computed results for the symmetry violating properties have been compared with the available results in the literature. Further, the parallel and perpendicular components of the hyperfine structure constants for the constituent atoms in YbX molecules are reported here for the first time.

Electro-optic (E/O) modulators are crucial for optical communication but face a trade-off between modulation bandwidth and efficiency. A small footprint could reduce the capacitance and increase the bandwidth, however, this usually results in a low modulation efficiency. Here, we present an integrated E/O modulator that simultaneously achieves wideband large bandwidth and high modu- lation efficiency operation by embedding a partially overlapped double-layer graphene on a compact silicon slot waveguide microring resonator. At 1550 nm, the graphene-silicon slot-waveguide demon- strates a high phase modulation efficiency of Vπ L = 220 V μm, and the corresponding microring modulator has a large bandwidth of over 70 GHz, a compact active length of 10 μm, and an optical modulation amplitude (OMA) of -1.97 dBm under a 3-V voltage swing. The modulator operates at a data rate of 50 Gbit/s with an open eye diagram under a 2-V Vpp RF drive voltage. The graphene modulator operation is broadband, and we also characterize its performance at 2 μm wavelength band. At 2 μm wavelength band, the microring modulator has a large bandwidth of over 20 GHz, an OMA of -3.36 dBm under a 6-V voltage swing, and an open eye diagram at 20 Gbit/s with a 2-V Vpp RF drive voltage. The difference in performance is caused by the bandwidth limit of the 2 μm wavelength band measurement setup. The broadband, large bandwidth, compact, highly effi- cient, and energy efficient graphene E/O modulator has the potential to enable large-scale graphene photonic integrated circuits, facilitating a broad range of applications such as optical interconnects, optical neural networks, and programmable photonic circuits.

We propose a flexible Bayesian approach for estimating the joint density of a multivariate outcome of interest in the presence of categorical covariates. Leveraging a Gaussian copula framework, our method effectively captures the dependence structure across different coordinates of the multivariate response. The conditional (on covariates) marginal (across outcomes) distributions are modeled as flexible mixtures with shared atoms across coordinates, while the mixture weights are allowed to vary with covariates through a novel Tucker tensor factorization-based structure, which enables the identification of coordinate-specific subsets of influential covariates. In particular, we replace the traditional mode matrices with coordinate-specific random partition models on the covariate levels, offering a flexible mechanism to aggregate covariate levels that exhibit similar effects on the response. Additionally, to handle settings with many covariates, we introduce a Markov chain Monte Carlo algorithm that scales with the number of aggregated levels rather than the original levels, significantly reducing memory requirements and improving computational efficiency. We demonstrate the method's numerical performance through simulation experiments and its practical applicability through the analysis of NHANES dietary data.

Quantum trajectory methods reduce the computational overhead of simulating noisy quantum systems, approximating them with $m$ stochastically sampled $2^n$-entry quantum statevectors rather than exact $2^{2n}$-entry density matrices. Recently, Pre-Trajectory Sampling with Batched Execution (PTSBE) has dramatically increased the data collection rate of these methods. While statevector PTSBE has demonstrated data collection speedups of over $10^6 \times$, tensor network implementations only achieved $\sim 15 \times$ speedup. This comparatively modest tensor network advantage stemmed from 1) contraction path recalculations, 2) sequential tensor network sampling, and 3) inflexible/unoptimized contraction hyperparameters. In this manuscript, we increase PTSBE's tensor network data collection rate to more than $10^8\times$ that of traditional trajectories methods by developing 1) error-independent unified path variation, 2) non-degenerate tensor network sampling, and 3) a flexible/optimized contraction framework. While our methods are particularly powerful for accelerating non-proportional sampling, we also demonstrate a more than $1000\times$ speedup for more general quantum simulations.

Impurity Hamiltonians are systems of $N$ fermionic modes where $O(1)$ of them interact among themselves via quartic (or higher order) fermion terms, while coupling quadratically with $O(N)$ bath modes. Without the quartic interactions, these systems are classically simulable with $O(N^3)$ resources. It was proved that the time-dependent evolution of these systems can perform universal quantum computation. The question of whether or not this remains true for time-independent evolution remains open. Here, we prove that the time evolution of generic time-independent impurity Hamiltonians on $O(N)$ qubits is universal on $N$ qubits if the input state is a product state of fermions in any single particle basis. In our proof we find that for a computation of depth $S$, the size of the impurity scales as $O(S\log S)$.

We study numerical invariants associated with the reduction of singularities of holomorphic foliation germs on $(\mathbb{C}^2, 0)$. Building on our previous work on generalized curve foliations, we extend explicit formulas for several fundamental invariants to arbitrary foliations. In particular, we provide general expressions for the discrepancy vector, the Milnor and intrinsic Milnor numbers, and classical indices along a separatrix as Camacho-Sad, Variation, Gómez-Mont-Seade-Verjovsky and also the Baum-Bott index. These extensions require a careful analysis of the contributions of saddle-nodes arising in the desingularization process. As applications, we recover results of Brunella and Cavalier-Lehmann, as well as a related statement appearing in [8], within a unified and purely numerical framework. Furthermore, we obtain intrinsic characterizations of generalized curve foliations in terms of indices and of second type foliations in terms of the discrepancy vector.

We present a novel, JAX-powered implementation of a parametric component-separation method for CMB polarization data, explicitly designed to handle spatially varying foreground Spectral Energy Distributions (SEDs). The approach models this variation across the sky by grouping sets of pixels that share common foreground spectral parameters, scanning over thousands of such configurations to evaluate the trade-off between model complexity and residual systematic contamination. Built within the FURAX framework -- a JAX-powered environment for CMB data analysis -- our pipeline extends the fgbuster parametric formalism. It enables fully vectorized, GPU-accelerated evaluation of the spectral likelihood, map reconstruction, and diagnostic metrics across tens of thousands of pixel subset configurations, noise realizations, and sky regions. Our implementation achieves up to $\sim 100\times$ speed-up over the scipy TNC optimizer used in fgbuster when running on GPUs, as well as giving more robust results. When applied to LiteBIRD-like simulations with spatially varying foreground SEDs, our optimized K-means configuration reduces the 68% upper limit on the tensor-to-scalar ratio $r$ by $\approx 30\%$ relative to a fixed, previously derived multi-resolution configuration, while maintaining competitive statistical uncertainties.

Consider critical Bernoulli percolation on $\mathbb{Z}^d$ for $d$ large; let $y_0, \dots, y_{k-1}$ be $k$ distinct points in $\mathbb{R}^d$. We prove that the probability that $\{\lfloor n y_i\rfloor\}_{i=0}^{k-1}$ all lie in the same open cluster, rescaled by an appropriate power of $n$, converges as $n \to \infty$ to an explicit constant. This confirms a conjecture of Aizenman and Newman.

We investigate the thermal properties of $\mathcal{PT}$-symmetric scalar field theories with purely imaginary couplings. The free energy governs the asymptotic density of states, providing an effective measure of the number of degrees of freedom, while thermal masses and one-point functions provide predictions for operator dimensions and three-point functions in the corresponding $d=2$ Conformal Field Theories. Naive finite-temperature perturbation theory near upper critical dimensions is spoiled by infrared divergences. To remove these divergences, we introduce a ''thermal normal-ordering'' scheme that resums these contributions and yields a systematic $ε$-expansion. This framework allows us to compute the free energy, thermal masses, and one-point functions in the cubic and quintic $O(N)$ models. We compare the thermal free energy density, thermal masses, and one-point function in two dimensions with exact results derived from the proposed Ginzburg-Landau descriptions of the non-unitary minimal models $M(2,5)$ and $M(3,8)_D$. Eventually, we employ two-sided Padé extrapolations to obtain estimates for the thermal free energy in $d=3,4,5$.

We investigate the size of fixed point sets of automorphisms of bounded domains in $\mathbb{C}^n$. In one complex variable, a nontrivial automorphism has at most two fixed points, but in higher dimensions fixed point sets need not be discrete. We show, under natural extension hypotheses, that discreteness forces finiteness. We also obtain a uniform bound for the number of fixed points of automorphisms in compact subgroups whose elements admit such extensions.

Advances in GPU compute throughput and memory capacity brings significant opportunities to a wide range of workloads. However, efficiently utilizing these resources remains challenging, particularly because diverse application characteristics may result in imbalanced utilization. Multi-Instance GPU (MIG) is a promising approach to improve utilization by partitioning GPU compute and memory resources into fixed-size slices with isolation. Yet, its effectiveness and limitations in supporting HPC workloads remain an open question. We present a comprehensive system-level characterization of different GPU sharing options using real-world scientific, AI, and data analytics applications, including NekRS, LAMMPS, Llama3, and Qiskit. Our analysis reveals that while GPU sharing via MIG can significantly reduce resource underutilization, and enable system-level improvements in throughput and energy, interference still occurs through shared resources, such as power throttling. Our performance-resource scaling results indicate that coarse-grained provisioning for tightly coupled compute and memory resources often mismatches application needs. To address this mismatch, we propose a memory-offloading scheme that leverages the cache-coherent Nvlink-C2C interconnect to bridge the gap between coarse-grained resource slices and reduce resource underutilization.

We define the probability of an equation in a finite algebra as the proportion of tuples in its domain that satisfy it. We call the probabilistic spectrum of an algebra the set of probability values obtained when the equation varies. We study fundamental properties of this spectrum, such as density and limit points, and show that its structure is related to several notions of primality of an algebra. We introduce a quantitative measure of primality $\Prim(\A)\in[0,1]$ that characterizes the functional approximation capacity. We show that the degree of primality is related to the size of the spectrum. We also prove that all non-primal two-element algebras satisfy the universal bound $\Prim(\A)\le 1/2$.

Memory Dependence Prediction (MDP) is a speculative technique to determine which stores, if any, a given load will depend on. Area-constrained cores are increasingly relevant in various applications such as energy-efficient or edge systems, and often have limited space for MDP tables. This leads to a high rate of false dependencies as memory independent loads alias with unrelated predictor entries, causing unnecessary stalls in the processor pipeline. The conventional way to address this problem is with greater predictor size or complexity, but this is unattractive on area-constrained cores. This paper proposes that targeting the predictor working set is as effective as growing the predictor, and can deliver performance competitive with large predictors while still using very small predictors. This paper introduces profile-guided memory dependence prediction (PG-MDP), a software co-design to label consistently memory independent loads via their opcode and remove them from the MDP working set. These loads bypass querying the MDP when dispatched and always issue as soon as possible. Across SPEC2017 CPU intspeed, PG-MDP reduces the rate of MDP queries by 79%, false dependencies by 77%, and improves geomean IPC for a small simulated core by 1.47% (to within 0.5% of using 16x the predictor entries), with no area cost and no additional instruction bandwidth.

We investigate an extended 3-4-1 model consisting of a new singly charged Higgs boson, implementing the minimal inverse seesaw mechanism to accommodate the large values of the $(g-2)_{e,μ}$ anomalies as well as the lepton-flavor-violating decay rates of charged leptons, the Standard Model-like Higgs boson, and the $Z$ boson, all consistent with current experimental data. Unlike the previously studied 3-4-1 realization, the model considered here predicts strong correlations among these observables that can be tested in future experiments. In particular, the current upper bound on Br$(τ\to μγ)$ imposes a stringent constraint compatible with the $1σ$ experimental range of $(g-2)_μ$, corresponding to a maximal deviation of $10^{-9}$ from the SM prediction. The forthcoming experimental sensitivity to Br$(τ\to μγ)$ will reduce this deviation to $5\times 10^{-10}$.

To elucidate how land surface state and soil moisture dynamics regulate moist convection, and how convective rainfall subsequently reshapes surface and root-zone hydrology, we develop a stochastic dynamical model that couples soil moisture, vegetation hydraulics, atmospheric boundary layer evolution, and convective available potential energy (CAPE). We show that CAPE depends not only on the free-tropospheric environment but also on soil moisture, through its control of surface fluxes, boundary-layer growth, and the timing of the intersection between the atmospheric boundary layer and the lifting condensation level (LCL). Soil texture and plant properties strongly modulate convective potential during dry-down. Loamy sand favors convection at relatively high soil moisture and maintains the largest CAPE at the time of LCL-ABL crossing across drying conditions. In contrast, sandy soils exhibit high CAPE when wet but lose convective potential rapidly as they dry. As matric potential becomes more negative, convection is increasingly suppressed in finer, loamy clay textures. Plant functional type further shapes dry-down dynamics: water-use-maximizing strategies can enhance dry persistence via stomatal closure during drying, whereas more conservative strategies can sustain convection for longer periods. On longer timescales, stochastic rainfall forcing with CAPE-dependent precipitation intensity produces persistent wet and dry soil moisture regimes, with switching times that depend on soil hydraulic properties, plant physiological traits, and atmospheric conditions.

The conventional power allocation strategy via water-filling relies on the premise that the power amplifier (PA) operates sufficiently below saturation such that a linear RF chain model holds. This work integrates the PA nonlinearity directly into the power allocation formulation, thereby removing the linearity assumption altogether and enabling operation in regimes where distortion noise is non-negligible. Leveraging the Bussgang theorem, we establish a statistical linearization of the PA's hard-limiting model to characterize the trade-off between signal gain and power-dependent distortion. We propose a projected gradient descent algorithm that optimizes power allocation while identifying an optimal spatial back-off strategy. We also derive a closed-form thermal noise variance threshold that separates the noise-limited and distortion-limited operating regimes as a function of the distortion noise variance and the channel Frobenius norm. Numerical simulations validate that our amplifier-aware strategy provides significant capacity gains in the saturation regime compared to standard water-filling.

We introduce the concept of deck transformations within the category of developable complexes of groups. Drawing inspiration from classical covering theory for topological spaces, we propose an alternative construction of the universal development of a developable complex of groups, formulated in terms of equivalence classes of paths. This framework allows us to provide a natural characterization of the group of deck transformations.

The placement of Kubernetes control-plane nodes is critical to ensuring cluster reliability, scalability, and performance, and therefore represents a significant deployment challenge in heterogeneous, multi-region environments. Existing initialisation procedures typically select control-plane hosts arbitrarily, without considering node resource capacity or network topology, often leading to suboptimal cluster performance and reduced resilience. Given Kubernetes's status as the de facto standard for container orchestration, there is a need to rigorously evaluate how control-plane node placement influences the overall performance of the cluster operating across multiple regions. This paper advances this goal by introducing an intelligent methodology for selecting control-plane node placement across dynamically selected Cloud-Edge resources spanning multiple regions, as part of an automated orchestration system. More specifically, we propose a reinforcement learning framework based on neural contextual bandits that observes operational performance and learns optimal control-plane placement policies from infrastructure characteristics. Experimental evaluation across several geographically distributed regions and multiple cluster configurations demonstrates substantial performance improvements over several baseline approaches.

The coherent pulse propagation of a Bessel beam resonant to the 8.4 eV nuclear clock transition in $^{229}$Th-doped crystals is investigated theoretically. Due to the magnetic dipole character of the clock transition, Bessel beams which present non-uniform transverse profiles and carry orbital angular momentum might enhance excitation channels or offer new control degrees of freedom compared to standard plane waves. We model the nuclear forward scattering of a resonant Bessel beam pulse propagating through the crystal, extending an formalism based on the iterative wave equation for plane waves. Thereby we take into account the nuclear quadrupole splitting in the crystal, considering the possibility of multiple quantization axes and present results for scenarios involving a single nuclear transition and multiple simultaneously driven transitions, analyzing temporal and spatial intensity patterns. Our findings show that the propagation of Bessel beams can be used to determine the relative distribution of different directions of quantization axes inside the crystal.

We develop a procedure to solve Einstein-dilaton-Maxwell models in quadratures using the potential reconstruction approach. We then apply this procedure to three distinct models, examining both the null energy condition (NEC) and the validity of the third law of thermodynamics in each case. The explicit knowledge of the blackening function -- as opposed to relying solely on numerical data -- allows us to discuss the validity of the third law in detail. The three models considered are: (I) a 5D model with two Maxwell fields, featuring anisotropy specified by a Gaussian function and a Lifshitz function; (II) the same 5D model as in (I), but with anisotropy parametrized by two Lifshitz parameters; and (III) a 6D model with one 2-form and one 3-form field, with the metric parametrized by two Lifshitz parameters. We show that for models I and II the parameter regions, where both the NEC and the third law are satisfied, exhibit no correlation between the two conditions. In contrast, for model III the validity of the NEC implies the validity of the third law.

More than one hundred years ago, physics has been revolutionized when people realized that electronic orbitals, or electromagnetic interactions in general, are quantized. Now, in this study, we are presenting evidence of quantization of planet orbits around stars. Confining a wave in spatial dimensions "quantizes" its wave number. Therefore, this study points to the evidence of the existence of long-range standing waves in the proto-planetary disks. Such waves, although being on a much larger scale of few tens of AU, have already been found by ALMA observation-so called ring-like structure. Now we see that it may exist within 1 AU, and may exert its effect on the existence and distribution of planets within this distance range to the host star. Careful analysis has been carried out to compare the results of different surveys.

Quantum reservoir computing is a promising paradigm for processing temporal data. So far, the primary focus has been on univariate time series. However, the most relevant and complex real-world data is multidimensional. In this paper, we establish an extensive framework for multivariate data processing in quantum reservoir computing. We propose and evaluate three multivariate encoding schemes and introduce the mixing capacity as a novel metric to evaluate the effectiveness with which a reservoir combines independent data streams. The computational performance of these proposed schemes is systematically assessed using this metric, as well as on the chaotic Lorenz-63 system prediction task, for two quantum reservoirs based on discrete and continuous-variable quantum systems. Furthermore, we relate the computational performance on these tasks to the underlying quantum properties of the reservoir. Our findings reveal that the optimal encoding method is highly dependent on the reservoir system and the specific task, underlining the importance of a task-specific input design. Moreover, we observe that peak computational performance coincides with the presence of non-classical effects, which indicates that quantum resources play a role in processing multivariate data.

We combine Gaia DR3 5-parameter astrometry with calibrated radial velocities for 23 nearby (<1 kpc) young (<60 Myr) clusters, with membership lists from Cantat-Gaudin et al. (2020). We characterise the plane-of-sky structure of the clusters using Q-Parameter and Angular Dispersion Parameter (ADP) methods. We measure plane-of-sky expansion using several methods. We determine plane-of-sky orientations along which expansion is maximised. We also estimate expansion timescales and traceback ages and compare to isochronal ages. We then look for correlations between cluster properties and discuss sample-wide trends. We find that most young clusters are more smoothly structured in their centers where the rate of dynamical interactions is highest, while hierarchical structure can survive in the sparse outskirts for >10 Myr. We also find that the majority of nearby young clusters exhibit clear signatures of expansion in the plane-of-sky, which in many cases is significantly anisotropic, even at ages >30 Myr. We find evidence that older clusters tend to have directions of maximum expansion oriented closer to parallel with the Galactic plane. The high degree of spatial structure and significant expansion anisotropy imply that the majority of these young clusters have formed with significant spatial and kinematic substructure and not as dense, monolithic clusters. Kinematic ages estimated from expansion timescales and on-sky traceback are generally in good agreement with estimates inferred from stellar evolution models for clusters <10 Myr old. However, many clusters with older isochronal ages appear to have significantly younger kinematic ages. We discuss potential reasons for this discrepancy, including a prolonged embedded and/or gravitationally bound phase in the early stages of the clusters.