We investigate the flow of spherical, bulk granular particles down an inclined plane mixed with small-sized spherical lubricant particles using discrete element method simulations. Predefined cohesive interaction is implemented between lubricant and bulk particles, enabling the coating of the former over the latter. The overall flow rate exhibits non-monotonic dependence on lubricant content. Initially, it increases with lubricant addition, reaches a maximum at an intermediate lubricant content, and decreases for even higher lubricant content. The increase in the flow rate is attributed to a lower inter-particle friction coefficient between lubricant-coated bulk particles. The decrease in the flow rate at higher lubricant content, on the other hand, is attributed to enhanced densification and increased damping between crowded particles. Both these occurrences are examined using various flow level characteristics. The simulation results are found to be in qualitative agreement with previous experimental results. Overall, the outcome integrates novel computational insights and prior experimental results to enhance the understanding of the powder lubrication phenomena.

This paper studies an integrated sensing and communication (ISAC) system where a multi-antenna base station (BS) communicates with multiple single-antenna users in the downlink and senses the unknown and random angle information of a target based on its prior distribution information and the received echo signals. We focus on a challenging scenario with heterogeneous unknown parameters where the target's reflection coefficient is also unknown with no prior information. We consider a general transmit beamforming structure with both communication beams and dedicated sensing beams, where the communication users can cancel the interference caused by the pre-determined sensing signals. By adopting the periodic posterior Cramer-Rao bound (PCRB) to quantify a lower bound of the mean-cyclic error (MCE) for sensing the periodic angle parameter, we optimize the transmit beamforming to minimize the periodic PCRB, subject to individual communication user rate constraints, which is a non-convex problem. By leveraging the semi-definite relaxation (SDR) technique and Lagrange duality theory, we derive the optimal solution and prove that at most one dedicated sensing beam is needed. Numerical results validate our analysis and effectiveness of the proposed beamforming design.

Spherical and cylindrical KdV-B equations have few known exact solutions, yet these solutions are hard to be interpreted physically. But these equations do have a family of diverging shock waves. Their properties such as asymptotic modes, stability, rules of their interactions/superposition are the subject of this paper. It gives a detailed asymptotic description of the one-parameter families of shock wave solutions and proves their stability using a conservation law. Based on these results, effective rules of superposition are obtained. Moreover these rules are applicable to a wide class of shock waves, in particular discontinuous. Typical examples are illustrated by graphs.

We prove that given two compact oriented $3$-manifolds $N$ and $M,$ with $M$ satisfying only a mild hypothesis, there is a hyperbolic $3$-manifold $N'$ arbitrarily ``closely related'' to $N,$ and such that $N'$ does not embed in $M.$ For instance, as a weak version of our main theorem, if $M$ is a rational homology sphere then for any $k\geq 1$ the $3$-manifold $N'$ can be chosen to be $Y_k$-equivalent to $N.$ Our techniques rely on the construction of $3$-manifolds with complicated Frohman--Kania-Bartoszyńska ideals, using the strong approximation for $\mathrm{SO}_3$-Witten-Reshetikhin-Turaev quantum representations of mapping class groups of surfaces.

We present Reelay, a unified online temporal logic monitoring framework designed for the rigorous analysis and runtime verification of cyber-physical systems. Reelay addresses the fragmentation of existing logical formalisms and tools by providing a single computational model and interface that supports a broad class of temporal logics. These include Linear Temporal Logic (LTL), Metric Temporal Logic (MTL), and Signal Temporal Logic (STL), along with their extensions for robustness semantics and first-order quantification over unbounded categorical data domains. At its core, Reelay translates temporal logic specifications into executable computation graphs operating as synchronous dataflow systems. This architecture ensures an efficient execution mechanism, making the framework ideal for high-frequency data streams regardless of behavior length. Uniquely, the framework supports both discrete and dense-time semantics, as well as delta-encoded temporal behaviors to minimize bandwidth usage in bandwidth-constrained environments. Reelay is implemented as a header-only C++ library with a high-level Python interface, facilitating integration across a wide range of deployment contexts, from resource-constrained embedded systems to autonomous robotic platforms. We demonstrate the practical applicability of the framework through a representative case study and performance experiments, illustrating how Reelay bridges the gap between expressive formal specifications and efficient runtime verification.

Real-time communications (RTC) is a core technology for emerging applications in 6G, such as cloud gaming, teleoperation, and extended reality (XR), which require consistently low latency and high bitrates. Existing RTC solutions fundamentally struggle to maintain low latency while supporting high bitrates due to their reliance on trial-and-error-based mechanisms. These mechanisms fail to probe the available bandwidth (ABW) promptly and accurately, leading to a trade-off between latency reliability and bandwidth utilization. The tension becomes extremely more critical as the cellular bandwidth and application's demand fluctuate with a larger range in cellular networks nowadays. To address this trade-off, we propose OCC, a novel approach that utilizes physical-layer information to explicitly obtain the ABW in real time, enabling rapid adaptation to dynamic wireless network conditions. However, the unique characteristics of RTC, including traffic bursts, application (APP) limits, and encoder lag, make the physical-layer informed control non-trivial. OCC effectively addresses these issues through three innovative strategies: frame-aware bandwidth measurement, APP-limit-aware bandwidth estimation, and encoder-friendly rate control. Extensive over-the-air experiments on an open-source cellular testbed demonstrate that OCC significantly enhances the performance of mobile RTC, reducing tail network latency by $13\%$ to $68\%$ and improving video frame bitrate by $1.2\times$ to $3.5\times$.

Solutions of the quark gap equation and the corresponding vacuum pressure are investigated within a modified Nambu-Jona-Lasinio model, which is a basic issue for studying the QCD equation of state (EOS) and the properties of hypothetical non-strange quark stars. In this study, the coupling strength $G$ is modified as $G=G_1+G_2\langle\barψψ\rangle$ to highlight the feedback effect of the quark condensate on the gluon propagator. Our analysis reveals that the influence of the vacuum pressure on EOS stiffness critically depends on whether the chiral phase transition is a first-order transition or a smooth crossover. A small ratio $G_1/G$ $(0.74\sim0.75)$ leads to a low vacuum pressure and a first-order chiral phase transition, a scenario favored by the existence of massive pulsars. Conversely, a large $G_1/G$ $(>0.96)$ leads to a high vacuum pressure and a crossover, but the corresponding EOS is ruled out by recent pulsar mass-radius observations. The model parameter space, restricted by four constraints, indicates the current quark mass is in the range $4.08\leq m\leq4.13$ MeV, with the quark condensate feedback contribution accounting for approximately 25\%. Furthermore, it is argued that the merging compact binary in GW170817 could be non-strange quark stars, and the tidal deformability is constrained to $Λ(1.4)\leq646$.

Gravitational-wave parameter estimation for binary neutron star (BNS) systems poses severe computational challenges due to the extended signal duration, which can reach several minutes in current detectors. Neural posterior estimation (NPE), a simulation-based inference approach, offers dramatic speedups but requires effective dimensionality reduction of the high-dimensional input data. We present a novel compression strategy based on likelihood-oriented summary statistics derived from the relative binning formalism of Zackay et al. (2018), which compresses raw frequency-domain data into the summary data. The summary data is based on a polynomial approximation of the waveform ratio using frequency banding grounded in post-Newtonian approximation, and directly evaluated with only $O(1000)$ sample points of the waveform. As a result, both the training and storage cost become more efficient than previously reported networks for BNS inference. We train a set of NPE networks on these summary statistics and validate a network against traditional nested sampling over 1024 BNS injections. The network produces well-calibrated posteriors across all source parameters we consider, with Jensen-Shannon divergences (JSD) consistent with numerical noise for most parameters. Although we find that the median JSD for the most inconsistent parameter exceeds $10^{-2}$ bits with current configurations, our results show potential for rapid parameter estimation of the BNS signal.

We propose a systematic method for constructing Wilf-Zeilberger (WZ) seeds and present seven WZ seeds. We also demonstrate how to construct WZ seeds from existing ones. With these WZ seeds, several hypergeometric identities are derived. The construction can be extended to the $q$-cases, leading to the $q$-analogues of the seven WZ seeds.

We study the thermodynamics of a quantum measurement-powered engine that converts energy injected by measurement backaction into work. We consider an engine with a finite-dimensional working substance, driven purely by quantum measurements, i.e., by bare quantum measurements, without feedback control or thermal contact in the thermodynamic cycle. On the basis of a Poincaré-like recurrence theorem for general quantum channels, we prove a no-go result for work extraction from such an engine in the steady regime. In the steady regime, quantum measurements become nondisturbing and do not inject energy into the working substance. Consequently, no work can be extracted. This result reveals the necessity of an entropy-decreasing process, such as feedback control or thermal contact, for work extraction in steady-cycle measurement-powered engines.

We study simplicity of Lie skew braces from both global and infinitesimal perspectives. After reviewing the correspondence between connected Lie skew braces, simply transitive affine actions, and post-Lie algebras, we investigate ideals and rigidity phenomena. Our main result concerns compact connected Lie skew braces. We prove that any compact connected simple Lie skew brace is either the trivial Lie skew brace on \(S^1\), or both of its underlying Lie groups are simple and the brace is trivial or almost trivial. Consequently, apart from the exceptional \(S^1\) case, simplicity of a compact connected Lie skew brace is equivalent to simplicity of either underlying Lie group. We also show that every connected compact solvable Lie skew brace is trivial. Finally, we construct a noncompact example demonstrating that this rigidity phenomenon does not hold in general: there exists a connected simply connected simple Lie skew brace whose additive and multiplicative Lie groups are both solvable.

The Onsager principle provides a variational route to the phenomenological equations of dissipative dynamics through the minimization of the Rayleighian. We develop a covariant formulation of the Onsager principle for active systems, ensuring geometric consistency under coordinate transformations. To further incorporate thermal fluctuations, we formulate the Onsager-Machlup principle for active systems by considering the Onsager-Machlup functional and the corresponding path probability for stochastic trajectories. Requiring that the path probability obeys the detailed fluctuation theorem, we show that the extended Onsager-Machlup theory is consistent with stochastic thermodynamics. Moreover, we incorporate inertia into the variational framework and show that the proper covariant equations follow when the covariant acceleration is held fixed during the variation.

We study the relationship between presheaf constructions and free cocompletions in the context of formal category theory, elucidating the coincidence between the two concepts in familiar settings. We show that, in a virtual equipment satisfying mild assumptions, free cocompletions under classes of weights are exhibited by presheaf constructions. We furthermore extend the theory of weighted colimits from enriched category theory to this setting, developing the concepts of atomicity and rank, and providing recognition theorems for presheaf objects, free cocompletions, and cocomplete objects. As an application of our methods, we construct free cocompletions, under arbitrary classes of colimit-small weights, of (possibly large) categories enriched in (not necessarily symmetric) monoidal categories and bicategories; this resolves a longstanding omission in the literature on enriched category theory.

Pinching of the driver beam in plasma wakefield acceleration is generally considered an unwanted effect that needs to be mitigated. Here, we propose that this effect can be utilized for the injection of spin-polarized electron beams from hydrogen halide targets into wakefields. Particle-in-cell simulations show that the electron spin is preserved on a level of 50% for a wide range of parameters due to the injection geometry. The presented injection scheme provides a possible pathway to alleviate some of the restrictions associated with pre-polarized hydrogen halide targets.

Entanglement has been proposed as a means to improve the sensitivity of sensing weak signals. While the degree of this quantum advantage is well understood in noiseless settings, the situation is more complex under realistic conditions, where the system is subject to decoherence. In this case, the enhancement depends on the specific noise characteristics. Previous treatments of colored noise typically assume that the noise is uncorrelated between successive experiments. Here, we consider the scenario in which the noise exhibits correlations across multiple shots. We derive a simple fundamental limit to the sensitivity based on the fact that the sensitivity cannot be better than the signal-to-noise ratio seen by the probe. Focusing on Ramsey spectroscopy with probes affected by pure classical dephasing, we show that, for suitable spatial and temporal noise correlations, entangled probes achieve a better scaling of the sensitivity with the number of probes than separable states. This demonstrates that entanglement can provide a substantial improvement for Ramsey spectroscopy subject to correlated noise.

We introduce and analyze a statistical estimator for Monge transport maps: solutions to the quadratic optimal transport problem in Euclidean space. For absolutely continuous source measures, this map is uniquely defined as the gradient of a convex function, a result known as Brenier's theorem. Without absolute continuity, the problem is relaxed, maps are replaced by coupling measures, and optimal couplings are supported on the subdifferential of a convex function, a Brenier potential. This characterization is the basis for our statistical estimator of Monge transport maps for measures known only through finite samples. The resulting Brenier potential has a simple closed-form expression based on the dual solution of the discrete sampled problem. In particular, our methodology does not rely on smoothness or continuity of the Monge transport map and requires no computation beyond primal-dual solutions of the discrete finite-dimensional problem. We exhibit convergence rates for this estimator based on a new error bound for the quadratic optimal transport problem. In the semi-discrete setting, where the target measure is finitely supported, our estimator enjoys sharper convergence rates. Finally, using similar proof techniques, we provide a novel convergence rate for empirical couplings.

Consider two planar graphs which are subject to edge insertions and deletions. We show that whether the two graphs are isomorphic can be maintained with first-order logic formulas and auxiliary data of polynomial size. This places the dynamic planar graph isomorphism problem into the dynamic descriptive complexity class DynFO. As a consequence, there is a dynamic constant-time parallel algorithm with polynomial-size auxiliary data which maintains whether two dynamic planar graphs are isomorphic.

Detecting copy number alterations (CNAs) from next-generation sequencing data remains challenging, particularly for short segments under noisy conditions. Existing segmentation methods often suffer from high false positive rates or fail to reliably detect short aberrations, especially in low-coverage data. In this study, we propose a modified tail-greedy unbalanced Haar (TGUHm) method that introduces a dual-thresholding strategy to improve segmentation accuracy. The proposed approach effectively suppresses spurious spikes while preserving sensitivity to both short and long CNA segments. Extensive simulation studies under Gaussian and heavy-tailed noise demonstrate that TGUHm consistently achieves higher true positive rates and lower false positive rates compared to state-of-the-art methods, including CBS, HaarSeg, and FDRSeg. In particular, the proposed method improves detection accuracy for short segments while maintaining competitive overall performance. Application to real cancer genomic data further confirms the practical utility of the method, revealing biologically meaningful CNAs associated with known cancer-related genes. These results suggest that TGUHm provides a robust and effective framework for CNA detection in challenging sequencing settings.

We introduce the notion of timed-Gromov--Hausdorff distance for timed-metric spaces. We prove that this distance is bi-Lipschitz equivalent to the intrinsic timed-Hausdorff distance of Sakovich--Sormani, and therefore induces the same notion of convergence. We establish a compactness theorem for the timed Gromov--Hausdorff distance, obtained as a straightforward consequence of Gromov's classical compactness theorem. We then investigate the causal structure of timed-metric spaces and the stability of causality under intrinsic timed-Hausdorff convergence. We further analyze causally-null timed-metric spaces and develop several of their basic properties. As a curiosity, we include in an appendix Gromov's original proof of his compactness theorem, as presented in his paper on groups of polynomial growth.

Tanaka et al. proposed a type system for verifying functional correctness properties of programs that use arrays and pointer arithmetic. Their system extends ConSORT -- a type system combining fractional ownership and refinement types for imperative program verification -- with support for pointer arithmetic. Their idea was to extend fractional ownership so that it can depend on an array index. Their formulation, however, does not handle nested arrays, which are essential for representing practical data structures such as matrices. We extend Tanaka et al.'s type system to support nested arrays by generalizing the notion of ownership to be able to refer to the indices of the outer arrays and prove the soundness of the extended type system. We have implemented a verifier based on the proposed type system and demonstrated that it can verify the correctness of programs that manipulate nested arrays, which were beyond the reach of Tanaka et al.

Within the framework of the one-boson-exchange model, we systematically investigate the interaction between the vector meson $K^{*}$ and the baryon $Σ^{*}$ with the aim of exploring the possibility of forming hadronic molecular states. The $K^{*}Σ^{*}$ interaction potential is constructed from $ρ$, $ω$, and $π$ meson exchanges, and the nonrelativistic Schrödinger equation is solved using the Gaussian expansion method. The binding energies are calculated for different total angular momenta $J^{P}$ and isospin channels $I=1/2$ and $I=3/2$. Our results show that $S$--$D$ wave mixed $K^{*}Σ^{*}$ molecular states with $J^{P}=1/2^{-}$ can be formed only in the $I=3/2$ channel, while no bound state appears in the $I=1/2$ channel due to destructive interference of the interaction potentials in isospin space. In addition, the $S$--$D$ wave mixed states with $J^{P}=3/2^{-}$ and $J^{P}=5/2^{-}$ are also found to support bound-state solutions. For higher partial-wave states, the binding mechanism is governed by the interplay of partial-wave mixing, tensor forces, and spin--orbit interactions. In particular, the $J^{P}=1/2^{+}$ channel does not support a bound state because the meson-exchange interaction is predominantly repulsive. Our analysis further supports the interpretation of the experimentally observed $N(2250)$ and $Δ(2200)$ states as $K^{*}Σ^{*}$ molecular states, corresponding to $I=1/2,\ J^{P}=9/2^{-}$ and $I=3/2,\ J^{P}=7/2^{-}$, respectively.

A sample of 139 young open star clusters closely associated with the Radcliffe wave is considered. Modeling their spatial distribution and kinematics over a time interval of 30 Myrs ago and 30 Myrs into the future revealed that they exhibit the main properties characteristic of a Radcliffe wave over the past 10-15 Myr. They are distributed on the galactic XY plane as a long and narrow chain inclined to the Y axis, and exhibit a wave-like behavior of their vertical coordinates up to 15 Myr in the past. This behavior of their vertical coordinates will persist over the interval of 15-20 Myr in the future. A new finding is the presence of vertical perturbations with an amplitude of deviation from the galactic symmetry plane of up to 200 pc over the entire time interval considered in the past, up to -30 Myr. This result calls into question the possibility of using a scenario in which the initial disturbance of the interstellar medium is assumed to be the Parker instability of the galactic magnetic field.

The conflict-free chromatic index of a graph $G$ is the minimum number of colours in an edge colouring of $G$ such that the neighbourhood of every edge contains a colour appearing exactly once. Its vertex analogue is the conflict-free chromatic number. These two parameters naturally coincide when the second is applied to the line graph of $G$. It is known that two variants of the latter parameter exhibit substantially different behaviour. For closed vertex neighbourhoods, where each vertex belongs to its own neighbourhood, it is known that $O(\ln^2 Δ)$ colours suffice, where $Δ$ denotes the maximum degree of $G$, and this bound is tight in order. In contrast, for open neighbourhoods, the corresponding parameter can be as large as $Δ+1$, but is bounded above by $O(\ln^{2+\varepsilon} Δ)$ for claw-free graphs. Since line graphs are claw-free, this yields the best known general upper bound for the edge analogue in the setting of open neighbourhoods. For closed edge neighbourhoods, a stronger general upper bound of $3\log_2 Δ+ 4$ is known. In this paper, we show that for both variants, the conflict-free chromatic index is bounded above by $(1+o(1))\log_2 Δ$. Since complete graphs require at least $(1 - o(1)) \log_2 Δ$ colours in the closed as well as the open setting, our result is asymptotically tight in order and in the leading constant. Moreover, we strengthen this conclusion by showing that $(1 - o(1)) \log_2 Δ$ colours are also typically necessary, as we prove this asymptotically almost surely for random graphs in both dense and relatively sparse regimes. Our proofs combine the probabilistic method with deterministic graph decomposition techniques, as well as new results relating the parameters under consideration with the chromatic number of a graph.

This study examined whether counterarguments generated by large language models (LLMs) influence the moral judgments of younger and older adults and whether these effects vary as a function of dilemma type, cognitive functioning, trust in AI, and prior experience using LLMs. Using the switch and footbridge trolley dilemmas, 130 participants (56 younger adults and 74 older adults) were presented with ChatGPT arguments that opposed their initial judgments. Results revealed that more than 30% of participants reversed their moral judgments in both dilemmas (32.31% in the switch dilemma and 36.92% in the footbridge dilemma), suggesting that LLMs possess substantial persuasive power. Older adults tended to be more likely than younger adults to reverse their judgments, and they showed a significantly greater degree of judgment change in the switch dilemma. Notably, in the emotionally aversive footbridge dilemma, older adults with lower cognitive functioning were significantly more likely to align with the LLM-generated counterargument. General trust in AI and prior experience with LLMs did not predict judgment reversal, supporting a disconnect between trust and persuasion. Instead, individual factors such as lower initial confidence and higher perceived task difficulty were associated with greater susceptibility to AI influence. These findings suggest that, although LLMs may serve as tools for cognitive offloading that compensate for age-related cognitive decline, they may also pose a risk of undue persuasion for cognitively vulnerable individuals.

Wave propagation can be observed in various nonequilibrium systems. In this study, we investigated the properties of several wave modes in active six-state Potts models using Monte Carlo simulations of square and hexagonal lattices. Disordered and spiral (SP) waves of six states are formed under weak and strong repulsions at nonflip contacts, respectively. The target (TG) and stripe (ST) waves were found to emerge under stronger repulsion. These three wave modes (SP, TG, and ST) can temporally coexist in small systems near the transition points but they do not switch in large systems or far from these transition points. During coarsening from randomly mixed states to ST waves, SP waves appear at an intermediate stage. The SP wave modes of three even- or odd-numbered states (states $s=0,2,4$ or $s=1,3,5$) emerge under two conditions: repulsion at the diagonal contact and attraction at nonflip contacts. Previously thought to be identical for both conditions, the wave types were found to differ, comprising forward and backward waves ($s=1\to 3\to 5\to 1$ or $s=1\to 5\to 3\to 1$), whose domain boundaries move by the two-step and four-step forward flips, respectively. The transition between the waves of the even- and odd-numbered states is first-order for both the forward and backward waves.

The equation of state (EoS) of strongly interacting matter at finite temperature and chemical potentials (baryon, charge, and strangeness) is a crucial input for hydrodynamic simulations of relativistic heavy-ion collisions. We construct a four-dimensional EoS using a deep-learning-assisted quasi-particle model (DLQPM) within a physics-informed neural network (PINN) framework, in which the masses of light quarks, strange quarks, and gluons are parameterized as functions of temperature and chemical potentials ($T, μ_B, μ_Q, μ_S$). The model is constrained by lattice QCD data at vanishing chemical potentials and provides a thermodynamically consistent extrapolation to finite $μ_{B,Q,S}$. The DLQPM accurately reproduces the lattice-calculated cumulants $χ^{B,Q,S}_{i,j,k}$ at $μ_{B,Q,S}=0$, and its predicted EoS at various chemical potentials agrees well with results from the generalized $T'$-expansion method in lattice QCD. Furthermore, the calculated baryon-strangeness correlation $C_{BS}$ is consistent, within uncertainties, with preliminary STAR data. This work offers a reliable EoS for exploring the QCD phase structure in the beam energy scan region.

We present preliminary results from a lattice-QCD study of the hadronic contributions to the running of the electromagnetic coupling, $Δα(Q^2)$, and the electroweak mixing angle, $Δ\sin^2θ_{W}(Q^2)$. Using $N_f = 2+1+1$ HISQ ensembles at physical quark masses, we discuss the challenges posed by strong statistical correlations in the time-momentum representation and propose a spectral-reconstruction strategy to obtain controlled continuum-extrapolated results across the full energy range.

Helium focused ion beam irradiation enables the fabrication of tunnel field-effect transistors based on two-dimensional electron systems (2DESs) at an oxide interface.High resolution scanning transmission electron microscopy and strain mapping reveal localized lattice deformation confined to the irradiated regions, which act as nanoscale potential barriers. The barrier profile can be continuously tuned by electrostatic backgating at low temperature without degrading the electronic properties of the 2DES electrodes. Transport measurements demonstrate controlled access to thermionic emission, direct tunneling, and Fowler-Nordheim tunneling within a single device architecture. These results establish He FIB irradiation as a powerful tool for nanoscale functional engineering of complex-oxide interfaces and provide a platform for exploring gate-tunable quantum tunneling phenomena.

We study a class of square matrices with non-negative elements which have cyclically monotone rows in the sense that each row of a matrix from the class consists of a cyclically non-increasing sequence of numbers starting from a maximal element on the diagonal. We prove that if every diagonal element is strictly larger than all other elements in the respective row, then the matrix is regular. This property enables us to solve an open problem that comes from the theory of non-standard numeration systems, also called Cantor numeration systems. The problem concerns a one-to-one relationship between Cantor real bases, which are supposed to be alternate, that is, periodic with a period p, and lists of p sequences of non-negative integers satisfying the so-called Parry condition.

Understanding the dynamical evolution of large-scale moiré systems is crucial for connecting theoretical predictions with experimental observations. Here we develop a machine-learning-based workflow, integrating DeePMD and DeepH frameworks with first-principles calculations, to efficiently investigate time-dependent structural and electronic responses in twisted bilayer transition metal dichalcogenides (TMDs) with experimentally relevant moiré supercells containing over 3000 atoms. Using $\mathrm{WS_2}$ as a representative system, we show that low-temperature lattice vibrations and relaxation deepen the moiré potential wells, narrow the lowest conduction band, and facilitate the formation of strongly localized electronic states. Based on DFT-derived moiré potentials that incorporate these dynamical effects, density-matrix-renormalization-group (DMRG) simulations reveal robust Wigner crystallization and a kagomé-patterned three-electron state, consistent with recent experimental observations. Our workflow provides a practical route for exploring large moiré supercells beyond static configurations and offers new insight into the interplay between lattice dynamics, electronic localization, and emergent correlated states in twisted two-dimensional materials.