arXiv subjects
Publications and source records attributed to Dongxiao Zhao.
A word in a group is called a test element if any endomorphism fixing it is necessarily an automorphism. In this note, we give a sufficient condition in geometry to construct test elements for monomorphisms of a free group, by using the Whitehead graph and the action of the free group on its Cayley graph.
We investigate interfacial dynamics and multiscale energy transfer in immiscible Rayleigh-Taylor turbulence using numerical simulations with varying surface tension coefficients $σ$. Capillarity is shown to control characteristic length scales, interfacial area, and global energy and enstrophy budgets. The flow exhibits self-similar evolution with respect to surface tension, with the maximum kinetic energy scaling as $σ^{1/2}$ and the flow duration as $σ^{-1/4}$. A scale-by-scale budget shows that surface tension removes kinetic energy at large scales while injecting it at small scales, with the crossover occurring near the Hinze scale. We further recast and verify a local kinematic relationship between surface-tension power and interface stretching, up to conservative transport, $ \boldsymbol{f}^σ\cdot\boldsymbol{u} = - σ\mathcal{S}~|\nabla c| + \mathrm{Transport}$, where $\boldsymbol{f}^σ$ is the surface-tension force, $\boldsymbol{u}$ the velocity, $c$ the heavy-fluid volume fraction, and $\mathcal{S}$ the interface stretch rate. This relation links kinetic-energy transfer to the scalar-variance cascade and shows that energy transfer to the interface is governed by local strain. Statistics of individual bubbles and droplets reveal vertically elongated filaments with diameters of about three capillary scales, yielding a linear volume-area relation. Their vertical velocities scale with the square root of equivalent diameter, consistent with drag-buoyancy balance. These findings, particularly the direct link between surface tension power and resolved interface stretching, provide a rigorous physical framework for developing subgrid-scale closures for large eddy simulation of immiscible turbulent flows.
In dynamic flow fields, various animals exhibit remarkable odor search capabilities despite relying on stochastic detections. Interestingly, there exists an optimal time window for integrating these detections that maximizes search efficiency. To understand the underlying mechanism, we investigate the navigation performance of Reinforcement Learning (RL) agents in unsteady flows under varying memory lengths and flow conditions. Without any predefined models, the agents develop a flow-assisted casting strategy and adaptively adjust both the geometry of their search trajectories and the concentration threshold for initiating casting to maximize the success rate. The agent's average speed toward the odor source exhibits a non-monotonic dependence on memory length, which can be explained by the "sector-search" model.
Let $F \ast G$ be a free product of a free group $F$ and a LERF group $G$. In this note, we provide sufficient conditions for a subgroup $H$ of $F \ast G$ to be $\mathcal{A} \cup \mathcal{S}$-separable, that is, for any finite set $\{γ_1, \ldots, γ_n\} \subset (F \ast G) \setminus H$, there is a surjection $f$ from $F \ast G$ to an alternating or symmetric group such that $f(γ_i) \notin f(H)$ for all $i$. As a corollary, any finitely generated infinite-index subgroup of a free group is $\mathcal{A} \cup \mathcal{S}$-separable in the free product of the free group and an arbitrary LERF group, generalizing a result of Wilton.
The magneto-Rayleigh-Taylor instability (mRTI) is a key process in inertial confinement fusion and is thought to be widespread in the interstellar medium, where it can concentrate plasma into discrete structures. We present resistive MHD simulations of the nonlinear evolution of multi-mode mRTI in both two and three dimensions, examining the effects of uniform external magnetic fields oriented either parallel or perpendicular to the initial interface. In both 2-D and 3-D, weak parallel fields enhance mixing-zone growth, whereas stronger fields suppress it. For perpendicular fields, growth is initially inhibited but becomes enhanced at later times. These behaviors arise from magnetic tension, which modifies flow anisotropy, buoyancy, drag, and vortex dynamics. The interplay of these mechanisms governs the distinct ways in which magnetic fields influence mRTI evolution.
Diffusion models exhibit notable fragility when faced with adversarial prompts, and strengthening attack capabilities is crucial for uncovering such vulnerabilities and building more robust generative systems. Existing works often rely on white-box access to model gradients or hand-crafted prompt engineering, which is infeasible in real-world deployments due to restricted access or poor attack effect. In this paper, we propose CAHS-Attack , a CLIP-Aware Heuristic Search attack method. CAHS-Attack integrates Monte Carlo Tree Search (MCTS) to perform fine-grained suffix optimization, leveraging a constrained genetic algorithm to preselect high-potential adversarial prompts as root nodes, and retaining the most semantically disruptive outcome at each simulation rollout for efficient local search. Extensive experiments demonstrate that our method achieves state-of-the-art attack performance across both short and long prompts of varying semantics. Furthermore, we find that the fragility of SD models can be attributed to the inherent vulnerability of their CLIP-based text encoders, suggesting a fundamental security risk in current text-to-image pipelines.
In this paper, we first study the endomorphisms of free-abelian times surface groups and give a characterization of when they are injective and surjective. Then, we see that free-abelian times hyperbolic groups are Hopfian but not co-Hopfian. Moreover, we give a complete classification of fixed subgroups of endomorphisms in free-abelian times surface groups, which extends that of automorphisms. Finally, we study the endomorphisms of free-abelian times non-elementary torsion-free hyperbolic groups and give an equivalent condition for them to contain, up to isomorphism, finitely many end-fixed subgroups.
We investigate the role of small-scale structures in turbulent Rayleigh-Taylor (RT) flows through the application of preferential flow control targeting high vorticity or high strain-rate regions (Buzzicotti et al. 2020). Through numerical simulations, we analyze the effects of flow control on RT statistics, mixing, and anisotropy behavior. Our results reveal that eliminating intense small-scale motion leads to the formation of more organized and coherent flow structures, with reduced mixing and enhanced anisotropy. The alignment of vorticity and scalar gradient with the strain-rate eigen-frame is also altered by the flow control, reducing the downscale cascade of kinetic energy and the scalar variance. When the control threshold is set below the spatial mean of the vorticity or strain-rate field, turbulent motion in RT is significantly suppressed. Moreover, flow control eliminates regions of extreme vorticity and strain-rate, leading to overlapped high vorticity and high strain-rate regions with reduced turbulence intensity and more coherent structures. These findings provide a deeper understanding of the fundamental mechanisms played by small-scale structures in RT flows and their modulation through flow control. This work has broader implications for realistic scenarios, such as RT flows under magnetic fields or rotation, where suppression of small-scale motions plays a critical role.
We expand on the method of sequential filtering for calculating spectra of inhomogeneous fields. Sadek & Aluie [Phys. Rev. Fluids, 3, 124610 (2018)] showed that the kernel has to have at least $p$ vanishing moments to extract a power-law spectrum $k^{-α}$ with $α<p+2$ by low-pass filtering. Here, we show that sequential high-pass filtering allows for extracting steeper spectra with $α<2p+3$ using the same $p$-th order kernel. For example, any spectrum of a field that is shallower than $k^{-5}$ can be extracted by sequential high-pass filtering using any 1st order kernel such as a Gaussian or top-hat. Finally, we demonstrate how second-order structure functions fail to capture spectral peaks because they cannot detect scaling that is too shallow.
A group $G$ is called a Howson group if the intersection $H\cap K$ of any two finitely generated subgroups $H, K<G$ is again finitely generated, and called a strongly Howson group when a uniform bound for the rank of $H\cap K$ can be obtained from the ranks of $H$ and $K$. Clearly, every strongly Howson group is a Howson group, but it is unclear in the literature whether the converse is true. In this note, we show that the converse is not true by constructing the first Howson groups which are not strongly Howson.
We generalize the `filtering spectrum' [1] to probe scales along different directions by spatial coarse-graining. This multi-dimensional filtering spectrum quantifies the spectral content of flows that are not necessarily homogeneous. From multi-dimensional spectral information, we propose a simple metric for shape anisotropy at various scales. The method is applied to simulations of 2D and 3D Rayleigh-Taylor (RT) turbulence, which is inhomogeneous and anisotropic. We show that 3D RT has clear shape anisotropy at large scales with approximately $4:3$ vertical to horizontal aspect ratio, but tends toward isotropy at small scales as expected [2,3,4]. In sharp contrast, we find that RT in 2D simulations, which are still the main modeling framework for many applications, is isotropic at large scales and its shape anisotropy increases at smaller scales where structures tend to be horizontally elongated. While this may be surprising, it is consistent with recent results in [5]; large-scale isotropy in 2D RT is due to the generation of a large-scale overturning circulation via an upscale cascade, while small scale anisotropy is due to the stable stratification resultant from such overturning and the inefficient mixing in 2D.
We highlight the differing roles of vorticity and strain in the transport of coarse-grained scalars at length-scales larger than $\ell$ by smaller scale (subscale) turbulence. %subscale flux/stress which appear in the evolution of coarse-grained (resolved) scalars/momentum account for the effect of (subgrid) scales smaller than the coarse-graining length $\ell$. We use the first term in a multiscale gradient expansion due to Eyink \cite{Eyink06a}, which exhibits excellent correlation with the exact subscale physics when the partitioning length $\ell$ is any scale smaller than that of the spectral peak. We show that unlike subscale strain, which acts as an anisotropic diffusion/anti-diffusion tensor, subscale vorticity's contribution is solely a conservative advection of coarse-grained quantities by an eddy-induced non-divergent velocity, $\bv_*$, that is proportional to the curl of vorticity. Therefore, material (Lagrangian) advection of coarse-grained quantities is accomplished not by the coarse-grained flow velocity, $\OL\bu_\ell$, but by the effective velocity, $\OL\bu_\ell+\bv_*$, the physics of which may improve commonly used LES models.
We study energy scale-transfer in Rayleigh-Taylor (RT) flows by coarse-graining in physical space without Fourier transforms, allowing scale analysis along vertical direction. Two processes are responsible for kinetic energy flux across scales: baropycnal work $Λ$, due to large-scale pressure gradients acting on small-scales of density and velocity, and deformation work $Π$, due to multi-scale velocity. Our coarse-graining analysis shows how these fluxes exhibit self-similar evolution that is quadratic-in-time, similar to RT mixing layer. We find that $Λ$ is a conduit for potential energy, transferring energy non-locally from the largest scales to smaller scales in the inertial range where $Π$ takes over. In 3D, $Π$ continues a persistent cascade to smaller scales, whereas in 2D $Π$ re-channels the energy back to larger scales despite the lack of vorticity conservation in 2D variable density flows. This gives rise to a positive feedback loop in 2D-RT (absent in 3D) in which mixing layer growth and the associated potential energy release are enhanced relative to 3D, explaining the oft-observed larger $α$ values in 2D simulations. Despite higher bulk kinetic energy levels in 2D, small inertial scales are weaker than in 3D. Moreover, the net upscale cascade in 2D tends to isotropize the large-scale flow, in stark contrast to 3D. Our findings indicate the absence of net upscale energy transfer in 3D-RT as is often claimed; growth of large-scale bubbles and spikes is not due to "mergers" but solely due to baropycnal work $Λ$.
Growth of the single-fluid single-mode Rayleigh-Taylor instability (RTI) is revisited in 2D and 3D using fully compressible high-resolution simulations. We conduct a systematic analysis of the effects of perturbation Reynolds number ($Re_p$) and Atwood number ($A$) on RTI's late-time growth. Contrary to the common belief that single-mode RTI reaches a terminal bubble velocity, we show that the bubble re-accelerates when $Re_p$ is sufficiently large, consistent with [Ramaparabhu et al. 2006, Wei and Livescu 2012]. However, unlike in [Ramaparabhu et al. 2006], we find that for a sufficiently high $Re_p$, the bubble's late-time acceleration is persistent and does not vanish. Analysis of vorticity dynamics shows a clear correlation between vortices inside the bubble and re-acceleration. Due to symmetry around the bubble and spike (vertical) axes, the self-propagation velocity of vortices points in the vertical direction. If viscosity is sufficiently small, the vortices persist long enough to enter the bubble tip and accelerate the bubble [Wei and Livescu 2012]. A similar effect has also been observed in ablative RTI [Betti and Sanz 2006]. As the spike growth increases relative to that of the bubble at higher $A$, vorticity production shifts downward, away from the centerline and toward the spike tip. We modify the Betti-Sanz model for bubble velocity by introducing a vorticity efficiency factor $η=0.45$ to accurately account for re-acceleration caused by vorticity in the bubble tip. It had been previously suggested that vorticity generation and the associated bubble re-acceleration are suppressed at high $A$. However, we present evidence that if the large $Re_p$ limit is taken first, bubble re-acceleration is still possible. Our results also show that re-acceleration is much easier to occur in 3D than 2D, requiring smaller $Re_p$ thresholds.
The proper scale decomposition in flows with significant density variations is not as straightforward as in incompressible flows, with many possible ways to define a `length-scale.' A choice can be made according to the so-called \emph{inviscid criterion} \cite{Aluie13}. It is a kinematic requirement that a scale decomposition yield negligible viscous effects at large enough `length-scales.' It has been proved \cite{Aluie13} recently that a Favre decomposition satisfies the inviscid criterion, which is necessary to unravel inertial-range dynamics and the cascade. Here, we present numerical demonstrations of those results. We also show that two other commonly used decompositions can violate the inviscid criterion and, therefore, are not suitable to study inertial-range dynamics in variable-density and compressible turbulence. Our results have practical modeling implication in showing that viscous terms in Large Eddy Simulations do not need to be modeled and can be neglected.