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Researcher profile

Chengjie Luo

Chengjie Luo contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
cond-mat.softcond-mat.stat-mechBiological Physics

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Published work

4 published item(s)

preprint2026arXiv

Coexistence of patterned phases in chemically active multicomponent mixtures

Chemically active mixtures exhibit complex patterns that emerge from the interplay of physical interactions and reactions among components. Individually, these two processes are well-understood: Physical interactions can give rise to phase separation, whereas reactions can form reaction-diffusion patterns. To understand the combination of both processes, we identify a Lyapunov functional for a class of chemical reactions. By minimizing this functional, we identify a generalized Gibbs phase rule that governs the number of coexisting patterns, and we demonstrate that complex patterns can be created by the modular combination of independent phases. Our theory unveils complex stationary patterns in chemically active mixtures and provides a framework for analyzing more complex systems.

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preprint2022arXiv

Dynamical Susceptibilities Near Ideal Glass Transitions

Building on the recently derived inhomogeneous mode-coupling theory, we extend the generalised mode-coupling theory of supercooled liquids to inhomogeneous environments. This provides a first-principles-based, systematic and rigorous way of deriving high-point dynamical susceptibilities from variations of the many-body dynamic structure factors with respect to their conjugate field. This new framework allows for a novel and fully microscopic possibility to probe for collective relaxation mechanisms in supercooled liquids near the mode-coupling glass transition.

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preprint2020arXiv

Generalized mode-coupling theory of the glass transition. II. Analytical scaling laws

Generalized mode-coupling theory (GMCT) constitutes a systematically correctable, first-principles theory to study the dynamics of supercooled liquids and the glass transition. It is a hierarchical framework that, through the incorporation of increasingly many particle density correlations, can remedy some of the inherent limitations of the ideal mode-coupling theory (MCT). However, despite MCT's limitations, the ideal theory also enjoys several remarkable successes, notably including the analytical scaling laws for the $α$- and $β$-relaxation dynamics. Here we mathematically derive similar scaling laws for arbitrary-order multi-point density correlation functions obtained from GMCT under arbitrary mean-field closure levels. More specifically, we analytically derive the asymptotic and preasymptotic solutions for the long-time limits of multi-point density correlators, the critical dynamics with two power-law decays, the factorization scaling laws in the $β$-relaxation regime, and the time-density superposition principle in the $α$-relaxation regime. The two characteristic power-law-divergent relaxation times for the two-step decay and the non-trivial relation between their exponents are also obtained. The validity ranges of the leading-order scaling laws are also provided by considering the leading preasymptotic corrections. Furthermore, we test these solutions for the Percus-Yevick hard-sphere system. We demonstrate that GMCT preserves all the celebrated scaling laws of MCT while quantitatively improving the exponents, rendering the theory a promising candidate for an ultimately quantitative first-principles theory of glassy dynamics.

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preprint2019arXiv

Generalized mode-coupling theory of the glass transition. I. Numerical results for Percus-Yevick hard spheres

Mode-coupling theory (MCT) constitutes one of the few first-principles-based approaches to describe the physics of the glass transition, but the theory's inherent approximations compromise its accuracy in the activated glassy regime. Here we show that microscopic generalized mode-coupling theory (GMCT), a recently proposed hierarchical framework to systematically improve upon standard MCT, provides a promising pathway toward a more accurate first-principles description of glassy dynamics. We present a comprehensive numerical analysis for Percus-Yevick hard spheres by performing explicitly wavenumber- and time-dependent GMCT calculations up to sixth order. Specifically, we calculate the location of the critical point, the associated non-ergodicity parameters, the time-dependent dynamics of the density correlators at both absolute and reduced packing fractions, and we test several universal scaling relations in the $α$- and $β$-relaxation regimes. It is found that higher-order GMCT can successfully remedy some of standard MCT's pathologies, including an underestimation of the critical glass transition density and an overestimation of the hard-sphere fragility. Furthermore, we numerically demonstrate that the celebrated scaling laws of standard MCT are preserved in GMCT at all closure levels, and that the predicted critical exponents manifestly improve as more levels are incorporated in the GMCT hierarchy. Although formally the GMCT equations should be solved up to infinite order to reach full convergence, our finite-order GMCT calculations unambiguously reveal a uniform convergence pattern for the dynamics. We thus argue that GMCT can provide a feasible and controlled means to bypass MCT's main uncontrolled approximation, offering hope for the future development of a quantitative first-principles theory of the glass transition.

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