arXiv subjects

Lijin Wang

Publications and source records attributed to Lijin Wang.

At least 19 recordsLinked to original sources

arXiv2025

Correlation between the boson peak frequency and transverse Ioffe-Regel limit in four-dimensional structural glasses

The emergence of excess vibrational modes over the Debye prediction, typically manifested as the well-known boson peak in the plot of vibrational density of states scaled by the Debye prediction, has become a hallmark of various amorphous solids. The origin of the boson peak has been attracting considerable attention but is still under debate. A popular view is that the position of the boson peak coincides well with that of the Ioffe-Regel limit for transverse modes in both two- and three-dimensional glasses, which is primarily derived from simulation studies of model structural glasses. However, it remains unknown whether the proposed coincidence could be generalized to higher spatial dimensions, and addressing this could contribute to the advancement of relevant phenomenological theories. Here, we find that the transverse Ioffe-Regel limit frequency is higher than and not proportional to the boson peak frequency in our studied four-dimensional glasses. Our findings therefore suggest that the proposed coincidence between the boson peak frequency and the transverse Ioffe-Regel limit depends on spatial dimensions, which was not anticipated previously.

cond-mat.soft↗

arXiv2025

Learning Stochastic Hamiltonian Systems via Stochastic Generating Function Neural Network

In this paper we propose a novel neural network model for learning stochastic Hamiltonian systems (SHSs) from observational data, termed the stochastic generating function neural network (SGFNN). SGFNN preserves symplectic structure of the underlying stochastic Hamiltonian system and produces symplectic predictions. Our model utilizes the autoencoder framework to identify the randomness of the latent system by the encoder network, and detects the stochastic generating function of the system through the decoder network based on the random variables extracted from the encoder. Symplectic predictions can then be generated by the stochastic generating function. Numerical experiments are performed on several stochastic Hamiltonian systems, varying from additive to multiplicative, and from separable to non-separable SHSs with single or multiple noises. Compared with the benchmark stochastic flow map learning (sFML) neural network, our SGFNN model exhibits higher accuracy across various prediction metrics, especially in long-term predictions, with the property of maintaining the symplectic structure of the underlying SHSs.

math.DS↗

arXiv2025

Learning Hamiltonian Systems with Pseudo-symplectic Neural Network

In this paper, we introduces a Pseudo-Symplectic Neural Network (PSNN) for learning general Hamiltonian systems (both separable and non-separable) from data. To address the limitations of existing structure-preserving methods (e.g., implicit symplectic integrators restricted to separable systems or explicit approximations requiring high computational costs), PSNN integrates an explicit pseudo-symplectic integrator as its dynamical core, achieving nearly exact symplecticity with minimal structural error. Additionally, the authors propose learnable Padé-type activation functions based on Padé approximation theory, which empirically outperform classical ReLU, Taylor-based activations, and PAU. By combining these innovations, PSNN demonstrates superior performance in learning and forecasting diverse Hamiltonian systems (e.g., modified pendulum, galactic dynamics), surpassing state-of-the-art models in accuracy, long-term stability, and energy preservation, while requiring shorter training time, fewer samples, and reduced parameters. This framework bridges the gap between computational efficiency and geometric structure preservation in Hamiltonian system modeling.

math.NA↗

arXiv2025

Structure-Preserving Implicit Runge-Kutta Methods for Stochastic Poisson Systems with Multiple Noises

In this paper, we propose the diagonal implicit Runge-Kutta methods and transformed Runge-Kutta methods for stochastic Poisson systems with multiple noises. We prove that the first methods can preserve the Poisson structure, Casimir functions, and quadratic Hamiltonian functions in the case of constant structure matrix. Darboux-Lie theorem combined with coordinate transformation is used to construct the transformed Runge-Kutta methods for the case of non-constant structure matrix that preserve both the Poisson structure and the Casimir functions. Finally, through numerical experiments on stochastic rigid body systems and linear stochastic Poisson systems, the structure-preserving properties of the proposed two kinds of numerical methods are effectively verified.

math.NA↗

arXiv2024

Numerical integrations of stochastic contact Hamiltonian systems via stochastic contact Hamilton-Jacobi equation

Stochastic contact Hamiltonian systems are a class of important mathematical models, which can describe the dissipative properties with odd dimensions in the stochastic environment. In this article, we investigate the numerical dynamics of the stochastic contact Hamiltonian systems via structure-preserving methods. The contact structure-preserving schemes are constructed by the stochastic contact Hamilton-Jacobi equation. A general numerical approximation method of the stochastic contact Hamilton-Jacobi equation is devised, and the convergent order theorem is provided, too. Numerical tests are shown to confirm the theoretical results and the usability of proposed approach.

math.NA↗

arXiv2022

Purifier: Defending Data Inference Attacks via Transforming Confidence Scores

Neural networks are susceptible to data inference attacks such as the membership inference attack, the adversarial model inversion attack and the attribute inference attack, where the attacker could infer useful information such as the membership, the reconstruction or the sensitive attributes of a data sample from the confidence scores predicted by the target classifier. In this paper, we propose a method, namely PURIFIER, to defend against membership inference attacks. It transforms the confidence score vectors predicted by the target classifier and makes purified confidence scores indistinguishable in individual shape, statistical distribution and prediction label between members and non-members. The experimental results show that PURIFIER helps defend membership inference attacks with high effectiveness and efficiency, outperforming previous defense methods, and also incurs negligible utility loss. Besides, our further experiments show that PURIFIER is also effective in defending adversarial model inversion attacks and attribute inference attacks. For example, the inversion error is raised about 4+ times on the Facescrub530 classifier, and the attribute inference accuracy drops significantly when PURIFIER is deployed in our experiment.

cs.LG↗

arXiv2022

Scaling of the Non-Phononic Spectrum of Two-Dimensional Glasses

Low-frequency vibrational harmonic modes of glasses are frequently used to understand their universal low-temperature properties. One well studied feature is the excess low-frequency density of states over the Debye model prediction. Here we examine the system size dependence of the density of states for two-dimensional glasses. For systems of fewer than 100 particles, the density of states scales with the system size as if all the modes were plane-wave-like. However, for systems greater than 100 particles we find a different system-size scaling of the cumulative density of states below the first transverse sound mode frequency, which can be derived from the assumption that these modes are quasi-localized. Moreover, for systems greater than 100 particles, we find that the cumulative density of states scales with frequency as a power law with the exponent that leads to the exponent $β=3.5$ for the density of states independent of system size.

cond-mat.dis-nn↗

arXiv2022

Scaling of the Non-Phononic Spectrum of Two-Dimensional Glasses

The scaling of the non-phononic spectrum for 2D systems has been recently debated. Here we provide evidence that the non-phononic spectrum $D_{ex}(ω) \sim ω^β$ where $β\approx 3.5$ and there is no clear evidence of a finite size effect in beta for systems greater than 100 particles.

cond-mat.dis-nn↗

arXiv2022

Density of States below the First Sound Mode in 3D Glasses

Glasses feature universally low-frequency excess vibrational modes beyond Debye prediction, which could help rationalize, e.g., the glasses' unusual temperature dependence of thermal properties compared to crystalline solids. The way the density of states of these low-frequency excess modes $D(ω)$ depends on the frequency $ω$ has been debated for decades. Recent simulation studies of 3D glasses suggest that $D(ω)$ scales universally with $ω^4$ in a low-frequency regime below the first sound mode. However, no simulation study has ever probed as low frequencies as possible to test directly whether this quartic law could work all the way to extremely low frequencies. Here, we calculated $D(ω)$ below the first sound mode in 3D glasses over a wide range of frequencies. We find $D(ω)$ scales with $ω^β$ with $β<4.0$ at very low frequencies examined, while the $ω^4$ law works only in a limited intermediate-frequency regime in some glasses. Moreover, our further analysis suggests our observation does not depend on glass models or glass stabilities examined. The $ω^4$ law of $D(ω)$ below the first sound mode is dominant in current simulation studies of 3D glasses, and our direct observation of the breakdown of the quartic law at very low frequencies thus leaves an open but important question that may attract more future numerical and theoretical studies.

cond-mat.soft↗

arXiv2021

Low-frequency excess vibrational modes in two-dimensional glasses

Glasses possess more low-frequency vibrational modes than predicted by Debye theory. These excess modes are crucial for the understanding the low temperature thermal and mechanical properties of glasses, which differ from those of crystalline solids. Recent simulational studies suggest that the density of the excess modes scales with their frequency $ω$ as $ω^4$ in two and higher dimensions. Here, we present extensive numerical studies of two-dimensional model glass formers over a large range of glass stabilities. We find that the density of the excess modes follows $D_\text{exc}(ω)\sim ω^2 $ up to around the boson peak, regardless of the glass stability. The stability dependence of the overall scale of $D_\text{exc}(ω)$ correlates with the stability dependence of low-frequency sound attenuation. However, we also find that in small systems, where the first sound mode is pushed to higher frequencies, at frequencies below the first sound mode there are excess modes with a system size independent density of states that scales as $ω^3$.

cond-mat.dis-nn↗

arXiv2020

Structure-preserving numerical methods for stochastic Poisson systems

We propose a class of numerical integration methods for stochastic Poisson systems (SPSs) of arbitrary dimensions. Based on the Darboux-Lie theorem, we transform the SPSs to their canonical form, the generalized stochastic Hamiltonian systems (SHSs), via canonical coordinate transformations found by solving certain PDEs defined by the Poisson brackets of the SPSs. An a-generating function approach with α\in [0,1] is then used to create symplectic discretizations of the SHSs, which are then transformed back by the inverse coordinate transformation to numerical integrators for the SPSs. These integrators are proved to preserve both the Poisson structure and the Casimir functions of the SPSs. Applications to a three-dimensional stochastic rigid body system and a three-dimensional stochastic Lotka-Volterra system show efficiency of the proposed methods.

math.NA↗

arXiv2020

Sound attenuation in finite-temperature stable glasses

The temperature dependence of the thermal conductivity of amorphous solids is markedly different from that of their crystalline counterparts, but exhibits universal behaviour. Sound attenuation is believed to be related to this universal behaviour. Recent computer simulations demonstrated that in the harmonic approximation sound attenuation $Γ$ obeys quartic, Rayleigh scattering scaling for small wavevectors $k$ and quadratic scaling for wavevectors above the Ioffe-Regel limit. However, simulations and experiments do not provide a clear picture of what to expect at finite temperatures where anharmonic effects become relevant. Here we study sound attenuation at finite temperatures for model glasses of various stability, from unstable glasses that exhibit rapid aging to glasses whose stability is equal to those created in laboratory experiments. We find several scaling laws depending on the temperature and stability of the glass. First, we find the large wavevector quadratic scaling to be unchanged at all temperatures. Second, we find that at small wavectors $Γ\sim k^{1.5}$ for an aging glass, but $Γ\sim k^2$ when the glass does not age on the timescale of the calculation. For our most stable glass, we find that $Γ\sim k^2$ at small wavevectors, then a crossover to Rayleigh scattering scaling $Γ\sim k^4$, followed by another crossover to the quadratic scaling at large wavevectors. Our computational observation of this quadratic behavior reconciles simulation, theory and experiment, and will advance the understanding of the temperature dependence of thermal conductivity of glasses.

cond-mat.soft↗

arXiv2019

Energy Transport in Glasses

The temperature dependence of the thermal conductivity is linked to the nature of the energy transport at a frequency omega, which is quantified by thermal diffusivity d(omega). Here we study d(omega) for a poorly annealed glass and a highly stable glass prepared using the swap Monte Carlo algorithm. To calculate d(omega), we excite wave packets and find that the energy moves diffusively for high frequencies up to a maximum frequency, beyond which the energy stays localized. At intermediate frequencies, we find a linear increase of the square of the width of the wave packet with time, which allows for a robust calculation of d(omega), but the wave packet is no longer well described by a Gaussian as for high frequencies. In this intermediate regime, there is a transition from a nearly frequency independent thermal diffusivity at high frequencies to d(omega) ~ omega^(-4) at low frequencies. For low frequencies the sound waves are responsible for energy transport and the energy moves ballistically. The low frequency behavior can be predicted using sound attenuation coefficients.

cond-mat.soft↗

arXiv2019

Sound attenuation in stable glasses

Understanding the difference between universal low-temperature properties of amorphous and crystalline solids requires an explanation of the stronger damping of long-wavelength phonons in amorphous solids. A longstanding sound attenuation scenario, resulting from a combination of experiments, theories, and simulations, leads to a quartic scaling of sound attenuation with the wavevector, which is commonly attributed to Rayleigh scattering of the sound. Modern computer simulations offer conflicting conclusions regarding the validity of this picture. We simulate glasses with an unprecedentedly broad range of stabilities to perform the first microscopic analysis of sound damping in model glass formers across a range of experimentally relevant preparation protocols. We present a convincing evidence that quartic scaling is recovered for small wavevectors irrespective of the glass's stability. With increasing stability, the wavevector where the quartic scaling begins increases by approximately a factor of three and the sound attenuation decreases by over an order of magnitude. Our results uncover an intimate connection between glass stability and sound damping.

cond-mat.soft↗

arXiv2019

Low-frequency vibrational modes of stable glasses

We numerically study the evolution of the vibrational density of states $D(ω)$ of zero-temperature glasses when their kinetic stability is varied over an extremely broad range, ranging from poorly annealed glasses obtained by instantaneous quenches from above the onset temperature, to ultrastable glasses obtained by quenching systems thermalised below the experimental glass temperature. The low-frequency part of the density of states splits between extended and quasi-localized modes. Extended modes exhibit a boson peak crossing over to Debye behaviour ($D(ω) \sim ω^2$) at low-frequency, with a strong correlation between the two regimes. Quasi-localized modes instead obey $D(ω) \sim ω^4$, irrespective of the glass stability. However, the prefactor of this quartic law becomes smaller in more stable glasses, and the corresponding modes become more localized and sparser. Our work is the first numerical observation of quasi-localized modes in a regime relevant to experiments, and it establishes a direct connection between glass stability and soft vibrational motion in amorphous solids.

cond-mat.soft↗

arXiv2018

Revealing the Link between Structural Relaxation and Dynamic Heterogeneity in Glass-Forming Liquids

Despite the use of glasses for thousands of years, the nature of the glass transition is still mysterious. On approaching the glass transition, the growth of dynamic heterogeneity has long been thought to play a key role in explaining the abrupt slowdown of structural relaxation. However, it still remains elusive whether there is an underlying link between structural relaxation and dynamic heterogeneity. Here we unravel the link by introducing a characteristic time scale hiding behind an identical dynamic heterogeneity for various model glass-forming liquids. We find that the time scale corresponds to the kinetic fragility of liquids. Moreover, it leads to scaling collapse of both the structural relaxation time and dynamic heterogeneity for all liquids studied, together with a characteristic temperature associated with the same dynamic heterogeneity. Our findings imply that studying the glass transition from the viewpoint of dynamic heterogeneity is more informative than expected.

cond-mat.soft↗

arXiv2017

Exponential Discrete Gradient Schemes for Stochastic Differential Equations

In this paper, we propose a class of stochastic exponential discrete gradient schemes for SDEs with linear and gradient components in the coefficients. The root mean-square errors of the schemes are analyzed, and the structure-preserving properties of the schemes for SDEs with special structures are investigated. Numerical tests are performed to verify the theoretical results and illustrate the numerical behavior of the proposed methods.

math.NA↗

arXiv2016

The correlation between fragility, density and atomic interaction in glass-forming liquids

The fragility, that controls the temperature-dependent viscous properties of liquids as the glass transition is approached, in various glass-forming liquids with different atomic interactions and densities is investigated by molecular dynamic simulations. We show the landscape of fragility in purely repulsive systems can be separated into three regions with qualitatively disparate dynamic behaviors, suggesting that the density plays an unexpected role for understanding the repulsive steepness dependence of fragility. Furthermore, the vastly dissimilar influences of attractive interaction on fragility could be estimated from the structural properties of related zero-temperature glasses

cond-mat.soft↗