The cumulative distribution transform (CDT) is a quantile-based transport representation that exactly linearizes one-dimensional translations of positive densities. We study how this structure behaves under additive perturbations and how it can be exploited for shift recovery. Under a local nondegeneracy condition, we derive a first-order expansion showing that additive noise in physical space induces a nonlocal perturbation in CDT space through the primitive of the noise, weighted by the reciprocal density. This yields an explicit description of transform-domain sensitivity and shows, in particular, that perturbations are amplified in low-density regions. When the physical-space perturbation is modeled as a centered Gaussian random field, the induced first-order CDT perturbation is again Gaussian, with an explicit covariance kernel. We then use this structure to study recovery in CDT coordinates. In the known-template setting, the transport shift is obtained by projection onto the constant mode, giving an explicit estimator together with exactness in the noiseless case and a stability bound under perturbations. In the unknown-template setting, multiple observations permit joint recovery of the shifts and a common template up to the natural constant-mode gauge, leading to a simple de-shift--and--average procedure. We also consider a signed-signal analogue based on the signed cumulative distribution transform (SCDT), where shifts are estimated numerically by feature matching and unknown templates are recovered by alternating alignment and averaging. Numerical experiments validate the perturbation analysis and illustrate effective recovery for both density-valued and signed signals.

We investigate repeated Bose-Einstein-condensate (BEC) formation and extraction in a dimple trap embedded in a reservoir of thermal atoms using a kinetic model. The model includes pulsed extraction, evaporation, three-body losses, and thermal-atom replenishment. Three extraction protocols are compared: extraction of all atoms from the dimple (BEC and thermal atoms), full and partial extractions of the BEC, but not of the thermal atoms. Residual atoms in the dimple after extraction seed subsequent Bose-stimulated growth and reduce the recovery time between extractions, but also enhance density-dependent losses. For all protocols, repeated extraction of BECs can be achieved without replenishment, but the number of BEC formations is limited by reservoir depletion and heating. With continuous replenishment, the system can reach a periodic steady-state regime, after an initial transient period, controlled by the externally imposed rates of extraction pulses and thermal-atom input. Within the explored parameter range, partial BEC extraction gives the highest efficiency, particularly for short extraction periods and high input rates. These results identify seeding by residual populations of BECs and thermal atoms as a kinetic mechanism for improving repeated condensate production in dimple traps.

Topological materials provide a new tool to direct wave energy with unprecedented precision and robustness. Three elastic topological phases, the valley Hall, Chern and spin Hall insulators, are currently studied, and they are achieved separately in rather distinct configurations. Here, we explore analytically various topological phase transitions for in-plane elastic wave in a unified mass-spring honeycomb lattice. It is demonstrated that the three elastic topological phases can be realized in this single lattice by designing mass, stiffness or introducing Coriolis' effect. In particular, the interface between valley Hall and Chern insulators is found to support topological interface mode for the first time. Perturbation method is used to derive the analytic effective continuum model in the neighbor of band degeneracy, and the physics in topological phase transitions are revealed through evaluation of topological invariants. The topologically protected interface states, their decaying profile as well as the pseudo-spin-indicating polarization specific for elastic wave are systematically analyzed, and these results are further confirmed numerically by Bloch wave analysis of domain wall strip and transient simulation of finite sized sample. This study offers a concise and unified analytical model to explore topology nature of elastic wave, and can provide intuitive guidance to design of continuum mechanical topological materials.

While long treated as empirical fits, Hill functions have been postulated to be the universal Hopfield barrier for sharpness of input-output responses by Martinez-Corral, Nam, DePace, and Gunawardena. A Hopfield barrier is a fundamental limit on how well biological systems can process information without expending energy. Their case rested on numerical findings for Hill coefficients $4$ and $6$. We give a precise formulation and proof of this: measuring sharpness by the supremum of the derivative in semi-log scale, any rational function $r(x)=(α_0+α_1 x+ \cdots +α_n x^n)/(β_0 + β_1 x+ \cdots + β_n x^n)$ with real coefficients $0\leq α_i\leq β_i$ has sharpness at most $n/4$, with equality if and only if $r$ is a Hill function with Hill coefficient $n$.

We recast Einstein's equations as ordinary integro-differential equations for the worldlines, integrating out the gravitational field by means of the Schwinger-Keldysh path integral. The same framework allows the gravitational waveform to be computed for unspecified orbits. The two computations are independent: solutions of the equations of motion can then be inserted to reconstruct the waveform for generic orbits. The derivation of the equations of motion does not require a map between scattering and bound-orbit observables. Thus, it could be implemented within an Effective One-Body-inspired framework, with the advantage that retardation and radiation effects are automatically included: no separation between potential and radiation modes is required. Conversely, the waveform computation may provide an alternative to the Effective One-Body approach, if supplemented by suitable resummation schemes. We emphasise that computations in this framework bypass the need for integration-by-parts identities, which are the main technical bottleneck in the computation of observables. In this paper, we outline the general framework and present a computational strategy at leading and next-to-leading order in the weak-field expansion.

For primes $p\geq 5$, we determine those $q$ for which the projective special linear group $\psl{2}{q}$ over the finite field of order $q$ is $(2,p)$-generated -- that is, there exist two elements of $\psl{2}{q}$ of orders $2$ and $p$, respectively, that generate $\psl{2}{q}$.

We prove that optimally weighted second-order least squares (SLS) and the degree-two generalized polynomial maximization method (PMM) are the same population estimating equation for linear regression with conditionally homoskedastic non-Gaussian errors: they choose the same optimal linear combination of the first two centered residual moments, solve one population normal system, share one influence function, and attain the common asymptotic variance $c_2g_2/N$ -- the ordinary-least-squares slope-variance factor $c_2$ scaled by the PMM variance-reduction coefficient $g_2=1-γ_3^2/(2+γ_4)$ (with $γ_3,γ_4$ the error skewness and excess kurtosis). Feasible plug-in implementations are therefore first-order equivalent, with only higher-order finite-sample differences. The identity is sharp: under heteroskedasticity the unconditional PMM body and the conditional SLS weighting separate, costing efficiency for symmetric errors and consistency for asymmetric errors. Beyond degree two, PMM holds an efficiency reserve that SLS cannot reach within its second-moment span. For symmetric platykurtic errors SLS collapses to ordinary least squares for the slope, while degree-three PMM exploits kurtosis information outside the SLS moment span through a closed-form coefficient $g_3$; for canonical asymmetric laws this reserve is $30$--$50\%$ within the degree-three polynomial moment class. The Lean 4 development machine-checks the degree-specific algebraic core -- the closed forms for $g_2$ and $g_3$, the $g_2\le1$ result, the design cancellations, and the symmetric collapse -- while the general monotonicity $g_{S+1}\le g_S\le1$ is proved analytically by nesting. A Monte Carlo study illustrates the equivalence, the reserve, and the heteroskedastic boundary at finite samples.

Zero modes, which are deformations that cost zero energy, underlie many exotic behaviors in elastic metamaterials. While classical linear Cauchy elasticity explains many of these modes, those linked to the rotations of metamaterial inner components often lie beyond its scope. Micropolar elasticity, which incorporates translation and rotation degrees of freedom, provides a framework for capturing these rotational modes. Herein, we present the first complete symmetry-based classification of zero modes in two-dimensional micropolar solids, with an emphasis on rotation-related modes. Guided by this classification, we construct threefold rotationally symmetric micropolar metamaterials and realize typical rotational micropolar zero modes. We further show that these metamaterials exhibit wave phenomena forbidden in Cauchy continua, including the emergence of three bulk waves in the long-wavelength limit and associated triple refraction, chiral acoustic modes, as well as strong wave anisotropy. All intriguing properties are quantitatively captured by micropolar continuum descriptions, whereas the classical Cauchy continuum theory fails to predict these behaviors, even at a qualitative level. Our results establish a general framework for engineering rotation-based zero modes, opening avenues for designing metamaterials with novel wave properties.

We propose a novel method that simultaneously determines the sample size for testing two survival probabilities at a pre-specified ltime while guaranteeing type I error control in both fixed and group-sequential trial designs. Simulations across varying hypothesized differences, failure distributions, censoring proportions, and nominal powers demonstrate consistent performance, while interim analyses highlight reduced type I error and increased power at each look, regardless of the underlying failure time distribution or spending function. Importantly, our method is especially useful for evaluating survival outcomes at a fixed time in randomized trials where one treatment arm includes neoadjuvant therapy prior to surgery while the other involves surgery alone. Furthermore, it is advantageous when the proportional hazards assumption is not satisfied, as often occurs in immunotherapy trials with delayed or time-varying treatment effects or crossing survival curves. The method is also applicable to randomized phase II trials, where smaller sample sizes and the use of intermediate or surrogate time-to-event endpoints demand efficient data use and robust error control. We illustrate the approach with motivating examples in renal and prostate cancer. An accompanying R Shiny application enables investigators to compute sample sizes interactively, facilitating practical trial planning in diverse settings.

Wormholes that are traversable in principle offer fascinating insights into general relativity, yet they typically require exotic matter and suffer from stability issues. We construct a thin-shell wormhole by gluing two copies of a quantum-corrected, regular spacetime obtained from string T-duality. This regularisation replaces the classical curvature singularity with a smooth core and introduces a fundamental length scale $l_0$. For the static configuration, we derive the surface stresses and show that, unlike the Schwarzschild case, the null and strong energy conditions can be satisfied for sufficiently large throat radii. A linearised stability analysis reveals a rich landscape: close to the minimum allowed throat radius the configuration is unstable; at intermediate radii ($a \sim l_0$) the geometric stability threshold becomes negative, yielding a window of \emph{unconditional stability} where any convex surface mass function suffices; at large radii the wormhole recovers Schwarzschild-like behaviour and stability requires a stiff equation of state. The T-duality scale $l_0$ is thus not merely a regulariser but a key physical parameter that opens a novel region of unconditional stability absent in classical thin-shell wormholes. Our results suggest that quantum-gravity-motivated modifications can simultaneously cure singularities and make traversable wormholes dynamically viable, providing new targets for gravitational-wave astronomy and theoretical studies of exotic compact objects.

For a commutative ring $R$ with unity, its algebraic $K$-theory space $K(R)$ may be obtained by group-completing the symmetric monoidal category of finitely generated free $R$-modules under direct sum. A natural question is what happens when one group-completes with respect to the tensor product structure instead. In this note, we give a direct proof of the folklore theorem that the resulting group-completion is the rationalization of $K(R)$, up to $π_0$. We also discuss how a similar group-completion would give the $p$-perfection and, more generally, the localization of $K(R)$ at any non-trivial multiplicatively closed subset $S \subseteq \mathbb{Z}_{> 0}$. The localization statement can be recovered from a localization theorem of May. We give a plus-construction proof without using the full machinery of multiplicative infinite loop space theory.

Charge-exchange (CEX) collisions can affect measurements of plasma plumes and neutralized ion flows in vacuum facilities, particularly when the background gas pressure increases and the CEX mean free path becomes comparable to the characteristic plume or facility dimension. Here, we investigate that regime in the plasma plume of a gridded ion source operating with a 400 eV argon ion beam. The fast-ion flux and low-energy ion flux were measured using a retarding potential analyzer (RPA) and planar probes, while the fast-neutral flux was inferred from deposited-power measurements with a thermal flux probe using a power-balance analysis. The low-energy ion flux increases with both background gas pressure and axial distance and its detection also depends on probe geometry. After the fast-ion component is isolated, its attenuation is described more accurately by an analytical reduced semi-empirical quasi-2D model that includes charge exchange and the experimentally observed plume divergence than by a one-dimensional attenuation law. The inferred fast-neutral flux also increases with pressure; however, the model underpredicts it at small axial distance and overpredicts it at elevated pressure and larger axial distance. This discrepancy suggests additional angular and collisional effects, as well as possible fast-neutral production near or inside the ion source, that are not captured by the present model. These results show that background gas pressure affects both the plasma plume and the diagnostic response, and that complementary electrostatic, thermal, and energy-selective diagnostics are required to distinguish source behavior from facility-induced effects.

For many trees $T$, the Ramsey number of $T$, denoted by ${\mathcal R}(T)$, is determined by the sizes of the partition classes in its unique bipartition. In 1976, Burr proved that when $T$ has partition classes of size $t_1$ and $t_2$ with $t_1 \le t_2$, the Ramsey number is at least $\max(2t_2-1,2t_1+t_2-1)$, and conjectured that this is tight. While counterexamples have been found for some pairs $(t_1, t_2)$, a main focus of research on this problem has been determining ratios $t_2/t_1$ or bounds on the maximum degree of $T$ for which Burr's bound is either exactly or asymptotically tight. We essentially resolve these questions for lopsided trees. Specifically, we show that (a) there are counterexamples whenever $t_2 \ge 2t_1$, with the order of magnitude of the difference between the largest Ramsey numbers and Burr's bound being $\max \left( t_1^2/t_2, \sqrt{t_1} \right)$, and (b) for $t_2 \ge 500 t_1$, Burr's bound is tight when $Δ(T) \le t_2 - t_1$, but is off by at least $C \log t_2$ (even when $t_2 \ge 2 t_1$) when $Δ(T) \gtrsim t_2 - t_1$. In particular, this shows that Burr's bound need not hold for $t$-vertex trees $T$ with $Δ(T) \approx t/3$.

We prove the Harish-Chandra isomorphism theorem for supersymmetric spaces, describing the polynomial algebra of eigenvalues of invariant differential operators. The polynomials obtained satisfy novel invariance conditions, which remain somewhat mysterious. We also prove the Harish-Chandra isomorphism for ghost distributions, which satisfy a `square root' of the invariance conditions coming from invariant differential operators. All proofs are algebraic, and rely on a rank-one reduction argument and the Chevalley restriction theorem.

Several recent works have addressed the problem of deconvolution under a linear model, where the goal is to estimate a completely unknown $G_0$ from a vector of noisy observations $\boldsymbol{Y} = X\boldsymbolβ + \boldsymbolε$, assuming the coefficients $β_j$ are i.i.d. unobserved realizations from $G_0$. Assuming $G_0$ has a density $g_0$, we study theoretically a Bayesian nonparametric method proposed in Weinstein et al. (2025) that postulates a Pólya tree prior $Π$ on $g_0$ and bases a deconvolution estimate on the posterior distribution $Π(\cdot|\boldsymbol{Y})$. Our main result asserts that under the true model (fixed and unknown $g_0$), and under a suitable condition on the minimum eigenvalue of $X^\top X$, the posterior $Π(\cdot|\boldsymbol{Y})$ concentrates around $g_0$ in sup-norm. The analysis presented builds on and extends results from Castillo (2017), where posterior consistency of Pólya trees was proved for density estimation, the simpler problem of estimating $g_0$ when observing the coefficients $β_j$ directly.

In survival studies, treatments can benefit patients through different mechanisms: a treatment may increase the probability of being cured or delay failure among patients who are not cured. Quantifying which mechanism is dominant, and whether it varies across subpopulations, is clinically important, yet there is limited work in the causal machine learning literature addressing this problem. Standard causal survival learners target finite-horizon survival or restricted mean survival time, while many cure models capture cure structures without estimating causal effects. In this work, we define meaningful causal effects in the presence of a cured subpopulation and introduce BartCure, a Bayesian causal machine learning approach for estimating them. The causal effects we recommend decompose the causal effect on restricted mean survival time into a stochastic cure and stochastic latency component, and we relate these new effects to both stochastic intervention effects and causal effects in principal strata. In simulations, BartCure is competitive for estimating average effects and is especially effective at conservatively detecting the direction of treatment-effect heterogeneity. We apply BartCure to estimate average and subgroup causal effects and to identify treatment effect heterogeneity in the CALGB 40101 breast cancer trial.

In the outer Solar System, for example in the Saturnian system, a planet's strong gravity attracts micrometeoroids and generates hypervelocity impacts on bodies such as rings and satellites. Micrometeoroids are seemingly non-icy, whereas the targets are typically icy, and both the impactor and the target may span a wide range of porosities. In this study, we perform three-dimensional iSALE simulations of hypervelocity impacts of rocky impactors onto icy targets, varying the impact angle and the porosities of the impactor and target ($ϕ_{\rm imp}$ and $ϕ_{\rm tar}$). We consider two end-member porosities (0% and 90%) for oblique ($45^\circ$) impacts. At an impact velocity of 30 km/s, characteristic of Saturn's rings, we find that the morphology of early-stage crater formation varies significantly with porosity, transitioning from deep-penetration, narrow-channel cavities ($ϕ_{\rm imp}=0$, $ϕ_{\rm tar}=90%$) to very shallow craters driven by near-surface vapor blowoff ($ϕ_{\rm imp}=90%$, $ϕ_{\rm tar}=0%$), with intermediate, more hemispherical cavity shapes when the porosities are comparable. Here, we focus on the thermodynamic fate of the impactor, which represents the exogenic material responsible for modifying the target surface. The impactor material is strongly heated and is efficiently vaporized regardless of the porosities of the impactor and target. However, the peak pressure and peak temperature experienced by the impactor vary by nearly an order of magnitude. These results imply that hypervelocity impacts occurring, for example, in Saturn's rings efficiently vaporize exogenic non-icy impactors upon impact, while the subsequent thermodynamic pathways $-$ such as condensation and chemical evolution $-$ may differ depending on the thermodynamic conditions. Our results are expected to be applicable to a variety of planetary systems.

Gaussian processes are a powerful tool for modeling continuous fields, but their naive $\mathcal{O}(N^3)$ computational cost and $\mathcal{O}(N^2)$ memory requirement often limit their practical use. Vecchia's approximation is a sparse precision matrix approximation for stationary, decaying kernels that conditions each point only on its $k$ nearest neighbors. We present GraphGP, a GPU algorithm for Vecchia's approximation that scales to nearly a billion parameters with linear time and memory requirements, handling arbitrary point distributions over a large dynamic range. Our key contributions are (1) a bit-reversed k-d tree ordering that allows efficient neighbor searches while also maximizing batch parallelism, and (2) a differentiable CUDA implementation, which is substantially faster and more memory efficient than our pure JAX baseline. GraphGP provides the building blocks for inference, including forward generation, inverse application, log-determinant, and kernel parameter derivatives.

We propose a low-complexity Chase decoder for optical interconnects that formulates test pattern selection as a generalized maximum coverage problem. For concatenated RS-BCH and oFEC codes, our decoder achieves the standard Chase decoding performance with 25% and 61.3% fewer test patterns, respectively.

Next generation wireless networks must sustain deterministic service levels for time-sensitive closed-loop applications. Flexible duplexing (FD) is an efficient solution to support these services, as it enables simultaneous uplink (UL) and downlink (DL) transmissions over orthogonal resources within the same band. However, simultaneous UL and DL transmissions can create conflicts that degrade performance due to interference from in-band emissions (IBE) and UL-to-DL cross-link interference (CLI). In this paper, we propose to use traffic forecasting and predictive scheduling to mitigate UL/DL conflicts in FD. Our proposal exploits traffic predictions to increase the likelihood of scheduling CLI-free UL and DL transmissions, and leverages spatial diversity to minimize the impact of unavoidable conflicts. Results show that the proposed scheme reduces UL/DL scheduling conflicts and improves the SINR of conflicted transmissions by more than 5 dB. This leads to gains of over 40% in the number of successfully completed transmissions compared to reference FD schemes.

The Price of Anarchy (PoA) is a popular measure of the costs of decentralization in terms of efficiency losses. Almost all PoA analyses operate within a framework assuming both Cardinal Full-Comparability (CFC) and smoothness, in which case any derived bounds conveniently extend beyond pure Nash to coarse correlated equilibria and no-regret learning outcomes. However, interpersonal utility comparability is an additional assumption that generally has to be justified. Without it, cardinal utilities (e.g. defined under classical von Neumann--Morgenstern framework) are unique only up to agent-specific affine transformations, rendering both the utilitarian PoA and the classical smoothness conditions representation-dependent. In this paper, we operate under a more general Cardinal Non-Comparability (CNC) framework, under which the weighted Nash welfare is a canonical admissible aggregator. We introduce multiplicative smoothness, a product-form condition matched to the multiplicative structure of Nash welfare, and obtain PoA bounds that are CNC-invariant and extend to coarse correlated equilibria. We demonstrate applicability of our framework on single-choice welfare games, deriving the bounds through simple proof relying on multiplicative retention envelope and geometric closure. The interpretation of this bound in terms of the true cost of decentralization depends crucially on interpersonal comparability of utilities.

High damage threshold gratings are in demand worldwide as critical components for next generation ultrahigh intensity lasers. Here we investigate the pulse-duration dependence of ultrafast laser-induced damage thresholds (LIDT) in hybrid multilayer dielectric gratings, touted to combine superior performance properties of both metallic and multilayer dielectric (MLD) gratings, using a dynamic finite-difference time-domain model incorporated with linear and non-linear absorption models. Simulations agree with reported experimental LIDT values for three representative designs and predict scaling exponents which vary with pulse durations ranging from 10 to 500 fs. The results reveal strong dependence on both material bandgap and grating field distribution, providing guidance for designing high LIDT gratings.

We present the first spatially contiguous study of the physical and chemical structure of the Helix Nebula (NGC~7293, PNG 036.1-57.1) based on integral-field spectroscopy from the SDSS-V Local Volume Mapper (LVM). The wide-field observations provide nearly complete spectroscopic coverage of the nebula, enabling a spaxel-by-spaxel analysis of extinction, electron density and temperature, ionisation structure, and chemical abundances. We reconstruct calibrated datacubes from the LVM row-stacked spectra and measure 41 optical emission lines, including hydrogen, helium, and collisionally excited metal lines. The resulting maps reveal a strongly stratified nebula, with highly ionised gas traced by \heii~concentrated toward the central cavity, low-ionisation material dominating the bright shell, and neutral or transition-zone gas enhanced in the outer regions. The Helix is a low-density object, with typical electron densities of $\sim10^{2}\mathrm{cm^{-3}}$, and exhibits a non-uniform temperature structure, with variations of several thousand Kelvin across different ionisation zones. We derive a near-solar oxygen abundance, $12+\log(\mathrm{O/H})\simeq8.7$, consistent with spatially complete sampling. The central abundance pattern indicates a significant contribution from unobserved O$^{3+}$, suggesting that apparent abundance variations are primarily driven by ionisation effects rather than true chemical inhomogeneities. We also find evidence for a sulfur deficit of $\sim$1 dex, consistent with the planetary-nebula sulfur anomaly. The helium and nitrogen abundances place the Helix near the classical boundary of Type~I planetary nebulae, suggesting moderate chemical enrichment by its progenitor star.

In this note, we derive a large-deviation-type scaling limit for a discretization of the Martingale Representation Theorem. Somewhat surprisingly, and to the best of our knowledge, this result has not been previously obtained in the literature.

Unitary time evolution of initially simple quantum many-body states rapidly generates entanglement and complex correlations, which limits direct numerical simulations. The late-time dynamics of physical observables, however, typically exhibits an effective simplicity in the form of hydrodynamics or kinetic theory. This leads to the question whether microscopic equations of motion can remain accurate and tractable up to long time scales by discarding irrelevant information in a controlled manner. Here, we introduce compressed minimum-purity time evolution (CoMPuTE) as an approach to keep track of a consistent set of reduced local density matrices, closing the hierarchical equations of motion using a minimum-purity principle. In benchmark applications we demonstrate (i) accurate description of energy diffusion in the one-dimensional mixed-field Ising model, (ii) the applicability to genuinely out-of-equilibrium Floquet dynamics starting from a pure state, and (iii) the limitations of the local reduced density matrix approximation when describing transport in the XXZ chain at $Δ=1$ that is governed by increasingly non-local integrals of motion. The CoMPuTE method enhances computational efficiency in comparison to the closely related local-information time evolution algorithm, opening a possible route towards an extension to systems in higher spatial dimensions.

Let $λ= λ(β,σ,a,b)$ denote the top Lyapunov exponent for the linearization along trajectories of the noisy damped non-linear oscillator $\ddot{x}+β\dot{x} + ax+bx^3 = σ\dot{W}_t$, where $a$, $b$ and $β$ are all positive and $σ\neq 0$. In 2004 Arnold, Imkeller and Sri Namachchivaya stated without proof that $λ(\varepsilon^2 β,\varepsilon σ,a,b) \sim \overlineλ \varepsilon^{2/3}$ as $\varepsilon \to 0$ with $\overlineλ > 0$. This paper contains a proof of this assertion.

The translation dynamics of two binary mixture droplets is investigated theoretically and is corroborated with experiments. The proposed model accounts for the effects of Marangoni stresses generated by evaporative cooling and concentration gradients, as well as vapour diffusion, for both components of the binary mixture. We consider thin droplets, allowing us to use the lubrication theory to derive the evolution equation for the droplet profiles. We numerically solve the evolution equations using the finite element method and examine various cases of pure and binary droplet pairs exhibiting translational behaviours like attraction, repulsion, and 'chasing'. The results show that the combined effect of solutal Marangoni, capillary effect, and thermal Marangoni determines the movement of the droplets. The non-uniform evaporation generated from 'vapour shielding' creates such effects. We observe that for droplets with the same initial composition, solutal Marangoni and capillary forces induce droplet attraction, while thermal Marangoni effects drive their repulsion. For droplets with different initial compositions, the drop with a higher concentration of the more volatile component pushes, or `chases', the drop with a lower initial concentration of this component, completely driven by the solutal Marangoni. We carried out experiments involving water-morpholine binary mixture droplets to validate the results predicted by our model.

Half-metallic ferromagnets exhibit a gap in the density of states for one spin projection while remaining gapless for the opposite spin. We show that in helimagnets an unusual half-metallic state can exist, where the spin projection that experiences the gap is determined by the direction of the wave vector. This state originates from the nontrivial topology of the band structure, specifically from the dispersion forming a multi-sheeted covering over the Brillouin zone. We present two-dimensional tight-binding models for $p$-wave and $f$-wave half metals. These structures can be realized in crystalline and van der Waals systems. The complex band structure of the unusual $p$-wave half metal in nanostructures is also discussed. In a quantum well, a standing wave with a helical spin structure is formed, and a persistent spin current exists.

Rolling stock planning is a complex optimization problem in railway management that involves assigning physical trains to scheduled trips while minimizing operational costs. In this work, we address a specific instance of this problem featuring 190 trips over two days, subject to constraints such as mandatory maintenance stops. We reformulate the problem as a Maximum-Weight Independent Set (MWIS) problem on a graph where nodes represent feasible train cycles. To handle the computational complexity of the large search space, we propose a hybrid divide-and-conquer algorithm. This approach iteratively selects subgraphs and solves the MWIS problem using various solvers, including exact classical methods and the Quantum Approximate Optimization Algorithm (QAOA). We evaluate the algorithm's performance by comparing these methods and analyzing the scaling with respect to subgraph size, with QAOA assessed through both classical simulation and execution on a quantum device (IQM Emerald). Our results indicate that increasing the subgraph size generally improves solution quality, demonstrating that the hybrid framework can effectively bridge the gap between polynomial-time approximate solvers and exponential-time exact methods.

The source of the optical/UV emission in tidal disruption events (TDEs) remains an enduring question in the field. Connecting the observed emission to the source is critical for both our understanding of these transients and for using TDEs to study the efficiency of super-Eddington accretion and black hole growth. To explore this connection, we ran time-dependent 1D radiation hydrodynamic simulations of TDE emission with the Sedona monte carlo radiative transfer code, focusing on the reprocessing paradigm. Our simulations follow a compact, evolving X-ray and EUV bright source and surrounding reprocessing outflow over multiple months, using luminosities and mass flow rates consistent with hydro simulations of tidal disruptions. We determine the efficiency of reprocessing as a function of time in this dramatically changing environment and reproduce key observables including timescales, luminosities, and color evolution. Notably, we see a strong wavelength-dependence in the emission timescale due to reprocessing effects. Early on there is an X-ray flare which quickly fades as material builds up and obscures the hot source. At the same time, the optical/UV luminosity begins to rise. Though the optical/UV light curve has a similar shape to the bolometric light curve, the optical peak is offset by $\sim$3 weeks from the bolometric peak due to the time required to build up the reprocessing layer. This implies that early time, high energy emission may be missed for TDEs discovered in optical surveys, and the initial disruption and mass return time to the black hole may occur earlier than optical light curves suggest.