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Dawei Wu

Publications and source records attributed to Dawei Wu.

8 recordsLinked to original sources
arXiv2026

Uniform asymptotics and entropy structure of the Bingham distribution in arbitrary dimensions

The Bingham distribution is widely used to model directional data with antipodal symmetry, and its normalizing constant $Z$ and moments play a central role in statistical inference and closure models. Their behavior becomes singular when one or more eigenvalue gaps of the parameter matrix become unbounded. In this work, we develop a uniform asymptotic framework for the Bingham distribution in arbitrary dimensions. Starting from an inverse-Laplace integral representation, we derive asymptotic expansions with explicit remainder estimates that are uniform with respect to arbitrary relative scales among multiple diverging eigenvalues. In a particular regime, the asymptotic series becomes absolutely convergent with an exponentially small remainder. These results yield precise asymptotic profiles of the Bingham moments and characterize the degeneration of higher-dimensional distributions to lower-dimensional counterparts. As an application to the Bingham closure, we prove that the entropy admits a decomposition into an explicit logarithmic leading term and a residual that is uniformly Lipschitz continuous on the moment simplex. Moreover, on each boundary face, the residual agrees with its lower-dimensional version up to an explicit additive constant. The results provide a unified description of the singular structure of the Bingham distribution and have implications for numerical closure and $Q$-tensor models of nematic liquid crystals.

math.PR↗
arXiv2026

From molecular model to tensor model of nematic liquid crystals through entropy decomposition

In the mathematical modeling of nematic liquid crystals, a practical and physically reliable $\mathbf{Q}$-tensor model can be derived from Onsager's molecular model with the Bingham closure. However, this procedure leads to a singular entropy term that implicitly depends on $\mathbf{Q}$, creating both computational and theoretical difficulties. In this paper, we characterize this entropy contribution by splitting it into a singular but explicit leading term and an implicit but regular correction term, the latter of which is proven to be sufficiently regular to be accurately approximated numerically, for example, by neural networks. This yields a computationally convenient free energy that can be used for the computation of nematic liquid crystals. Our numerical experiments demonstrate that the resulting free energy can capture the isotropic-nematic phase transition as well as the free-boundary droplet configurations.

cond-mat.soft↗
arXiv2026

A Landau-de Gennes Type Theory for Cholesteric-Helical Smectic-Smectic C* Liquid Crystal Phase Transitions

We present a rigorous mathematical analysis of a modified Landau-de Gennes (LdG) theory modeling temperature-driven phase transitions between cholesteric, helical smectic, and smectic C* phases. This model couples a tensor-valued order parameter (nematic orientational order) with a real-valued order parameter (smectic layer modulation). We establish the existence of energy minimizers of the modified LdG energy in three dimensions, subject to Dirichlet conditions, and rigorously analyze the energy minimizers in two asymptotic limits. First, in the Oseen--Frank limit, we show that the global minimizer strongly converges to a minimizer of the Landau-de Gennes bulk energy. Second, in the limit of dominant elastic constants, we prove that the global minimizers converge to a classical helical director profile. Finally, through stability analysis and bifurcation theory, we derive the complete sequence of symmetry-breaking transitions with decreasing temperature-from the cholesteric phase (with in-plane twist and no layering) to an intermediate helical smectic phase (with in-plane twist and layering), and ultimately to the smectic C* phase (with out-of-plane twist and layering). These theoretical results are supported by numerical simulations.

math.AP↗
arXiv2025

A diffuse-interface Landau-de Gennes model for free-boundary problems in the theory of nematic liquid crystals

We introduce a diffuse-interface Landau-de Gennes free energy for nematic liquid crystals (NLC) systems, with free boundaries, in three dimensions submerged in isotropic liquid, and a phase field is introduced to model the deformable interface. The energy consists of the original Landau-de Gennes free energy, three penalty terms and a volume constraint. We prove the existence and regularity of minimizers for the diffuse-interface energy functional. We also prove a uniform maximum principle of the minimizer under appropriate assumptions, together with a uniqueness result for small domains. Then, we establish a sharp-interface limit where minimizers of the diffuse-interface energy converge to a minimizer of a sharp-interface energy using methods from $Γ$-convergence. Finally, we conduct numerical experiments with the diffuse-interface model and the findings are compared with existing works.

math.AP↗
arXiv2023

Accelerating Unruh-DeWitt detectors coupled with a spinor field

The behavior of accelerating Unruh-DeWitt detectors coupled with a spinor field in (3+1)-dimensional spacetime is investigated. For a single point-like detector with Gaussian switching function, the transition probability increases with the acceleration and thus the antiUnruh effect effect cannot occur. Due to the spinor structure of the Dirac field, UV divergences are encountered in the calculation of the entanglement between the detectors. After introducing some UV cutoff $Λ$, the logarithmic negativity of detectors is shown to behave nonmonotonically with respect to the acceleration. Besides, the logarithmic negativity increases with the cutoff $Λ$ and decreases with the distance between the detectors. The mutual information between the two detectors is also discussed.

gr-qc↗
arXiv2023

Exact conditions for antiUnruh effect in (1+1)-dimensional spacetime

Exact conditions for antiUnruh effect in (1+1)-dimensional spacetime are obtained. For detectors with Gaussian switching functions, the analytic results are similar to previous ones, indicating that antiUnruh effect occurs when the energy gap matches the characteristic time scale. However, this conclusion does not hold for detectors with square wave switching functions, in which case the condition turns out to depend on both the energy gap and the characteristic time scale in some nontrivial way. We also show analytically that there is no antiUnruh effect for detectors with Gaussian switching functions in (3+1)-dimensional spacetime.

gr-qc↗
arXiv2022

A convergent numerical algorithm for the stochastic growth-fragmentation problem

The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain. The simulations of this stochastic process and its invariant measure are of interest. In this paper, we propose a numerical scheme for both the simulation of the process and the computation of the invariant measure, and show that under appropriate assumptions, the numerical chain converges to the continuous growth-fragmentation chain with an explicit error bound. With a triangle inequality argument, we are also able to quantitatively estimate the distance between the invariant measures of these two Markov chains.

math.NA↗