arXiv subjects

Xue Fan

Publications and source records attributed to Xue Fan.

6 recordsLinked to original sources

arXiv2026

Worst-Case Win Ratios Under Partially Specified Outcome Hierarchies

Win statistics require a prespecified outcome hierarchy. Clinical teams sometimes agree only on the highest priority outcome, leaving the order of lower priority outcomes unresolved, and clinically meaningful thresholds may be specified as ranges. Separate sensitivity analyses describe how the results change. A single inference for the full set of planned analyses is generally absent. We define the estimand as the smallest net benefit among the comparison rules allowed by the protocol or statistical analysis plan. Each rule uses the usual two-sample U-statistic. Large-sample results are developed for a finite list of rules and for a continuous threshold range. Inversion of an intersection-union test gives a one-sided lower confidence bound, with no multiplicity adjustment for the single claim that every individual net benefit is positive. Simulations show valid one-sided coverage and illustrate the gap between a favorable result for one selected hierarchy and a favorable result across all prespecified hierarchies. An application to ACTG 175 shows how the ordering of laboratory outcomes can affect the strength of the conclusion. A further example identifies an unfavorable threshold that is missed by a sparse grid.

stat.ME↗

arXiv2025

Physical Signatures of Supercritical Fluid Boundaries

In the supercritical fluid (SCF) region, at temperatures and pressures above the critical point, the thermodynamic singularity separating liquids and gases no longer exists. Recent arguments based on thermodynamics and critical scalings have revived the proposal that the SCF constitutes an intermediate state of matter, separated from the liquid and gas by two supercritical boundaries, the $L^\pm$ lines. However, until now, the nature of the supercritical state and the physical signatures of these boundaries have remained elusive. Here, we demonstrate that the SCF is characterized by distinct structural, transport, and dynamical behavior. Specifically, the spatial arrangement of particles-captured by the radial distribution function-as well as the diffusion coefficient, shear viscosity, and velocity autocorrelation function in the SCF regime are qualitatively different from those in both the liquid and gas states and exhibit clear physical signatures upon crossing the $L^\pm$ lines. Our theoretical predictions are validated by molecular dynamics simulations of argon and are further supported by existing experimental evidence. These results provide a clear physical foundation for a refined phase diagram of matter in the supercritical region, comprising three distinct states-gas, supercritical fluid, and liquid-separated by two crossover boundaries obeying universal scaling laws.

cond-mat.stat-mech↗

arXiv2024

Thermal Nanoquakes: Terahertz Frequency Surface Rayleigh Waves in Diamond Nanocrystals

Mechanical THz vibrations in nanocrystals have recently been harnessed for quantum sensing and thermal management. The free boundaries of nanocrystals introduce new surface wave solutions, analogous to the seismic waves on Earth, yet the implications of these surface waves on nanocrystals have remained largely unexplored. Here, we use atomistic molecular dynamics simulations and experimental neutron spectroscopy to elucidate these THz-scale features in nanodiamond. Our key insight is that thermally induced Rayleigh surface phonons, which have a low group velocity and an amplitude that decays exponentially away from the surface, are responsible for the previously observed but unexplained linear scaling of the low-energy vibrational density of states in nanocrystals. Large thermal atomic displacements, relative to the nanoparticle radius, induce perpetual surface quakes, even at ambient conditions. Normalised to the radius, the surface displacement ratio in diamond nanocrystals exceeds that of the largest recorded earthquakes by a factor of $10^{5\pm1}$. We explicate how these dramatic Rayleigh waves coexist with other distinctive features including confined lattice phonons, soft surface modes, the acoustic gap, Love waves, and Lamb modes, thereby offering a complete framework for the vibrational dynamics of nanocrystals.

cond-mat.mes-hall↗

arXiv2024

Revisiting the question of what instantaneous normal modes tell us about liquid dynamics

The lack of a well-defined equilibrium reference configuration has long hindered a comprehensive atomic-level understanding of liquid dynamics and properties. The Instantaneous Normal Mode (INM) approach, which involves diagonalizing the Hessian matrix of potential energy in instantaneous liquid configurations, has emerged as a promising framework in this direction. However, several conceptual challenges remain, particularly related to the approach's inability to capture anharmonic effects. In this study, we present a set of "experimental facts" through a comprehensive INM analysis of simulated systems, including Ar, Xe, N$_2$, CS$_2$, Ga, and Pb, across a wide temperature range from the solid to gas phase. First, we examine the INM density of states (DOS) and compare it to the DOS obtained from the velocity auto-correlation function. We then analyze the temperature dependence of the fraction of unstable modes and the low-frequency slope of the INM DOS in search of potential universal behaviors. Furthermore, we explore the relationship between INMs and other properties of liquids, including the liquid-like to gas-like dynamical crossover and the momentum gap of collective shear waves. In addition, we investigate the INM spectrum at low temperatures as the system approaches the solid phase, revealing a significant fraction of unstable modes even in crystalline solids. Finally, we confirm the existence of a recently discussed cusp-like singularity in the INM eigenvalue spectrum and uncover its complex temperature-dependent behavior, challenging current theoretical models.

cond-mat.soft↗

arXiv2023

Emergence of Debye scaling in the density of states of liquids under nanoconfinement

In the realm of nanoscience, the dynamic behaviors of liquids at scales beyond the conventional structural relaxation time, $\tau$, unfold a fascinating blend of solid-like characteristics, including the propagation of collective shear waves and the emergence of elasticity. However, in classical bulk liquids, where $\tau$ is typically of the order of 1 ps or less, this solid-like behavior remains elusive in the low-frequency region of the density of states (DOS). Here, we provide evidence for the emergent solid-like nature of liquids at short distances through inelastic neutron scattering measurements of the low-frequency DOS in liquid water and glycerol confined within graphene oxide membranes. In particular, upon increasing the strength of confinement, we observe a transition from a liquid-like DOS (linear in the frequency $\omega$) to a solid-like behavior (Debye law, $\sim\omega^2$) in the range of $1$-$4$ meV. Molecular dynamics simulations confirm these findings and reveal additional solid-like features, including propagating collective shear waves and a reduction in the self-diffusion constant. Finally, we show that the onset of solid-like dynamics is pushed towards low frequency along with the slowing-down of the relaxation processes upon confinement. This nanoconfinement-induced transition, aligning with k-gap theory, underscores the potential of leveraging liquid nanoconfinement in advancing nanoscale science and technology, building more connections between fluid dynamics and materials engineering.

cond-mat.soft↗

arXiv2023

On the temperature dependence of the density of states of liquids at low energies

We report neutron-scattering measurements of the density of states (DOS) of water and liquid Fomblin in a wide range of temperatures. In the liquid phase, we confirm the presence of a universal low-energy linear scaling of the experimental DOS as a function of the frequency, $g(\omega)= a(T) \omega$, which persists at all temperatures. The low-frequency scaling of the DOS exhibits a sharp jump at the melting point of water, below which the standard Debye's law, $g(\omega) \propto \omega^2$, is recovered. On the contrary, in Fomblin, we observe a continuous transition between the two exponents reflecting its glassy dynamics, which is confirmed by structure measurements. More importantly, in both systems, we find that the slope $a(T)$ grows with temperature following an exponential Arrhenius-like form, $a(T) \propto \exp(-\langle E \rangle /T)$. We confirm this experimental trend using molecular dynamics simulations and show that the prediction of instantaneous normal mode (INM) theory for $a(T)$ is in qualitative agreement with the experimental data.

cond-mat.soft↗