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Pengfei Guan

Publications and source records attributed to Pengfei Guan.

At least 37 records · Page 2Linked to original sources
arXiv2019

Elastic avalanches reveal marginal behaviour in amorphous solids

Mechanical deformation of amorphous solids can be described as consisting of an elastic part in which the stress increases linearly with strain, up to a yield point at which the solid either fractures or starts deforming plastically. It is well established, however, that the apparent linearity of stress with strain is actually a proxy for a much more complex behavior, with a microscopic plasticity that is reflected in diverging nonlinear elastic coefficients. Very generally, the complex structure of the energy landscape is expected to induce a singular response to small perturbations. In the athermal quasistatic regime, this response manifests itself in the form of a scale free plastic activity. The distribution of the corresponding avalanches should reflect, according to theoretical mean field calculations (Franz and Spigler, Phys. Rev. E., 2017, 95, 022139), the geometry of phase space in the vicinity of a typical local minimum. In this work, we characterize this distribution for simple models of glass forming systems, and we find that its scaling is compatible with the mean field predictions for systems above the jamming transition. These systems exhibit marginal stability, and scaling relations that hold in the stationary state are examined and confirmed in the elastic regime. By studying the respective influence of system size and age, we suggest that marginal stability is systematic in the thermodynamic limit.

cond-mat.dis-nn↗
arXiv2019

A class of curvature type equations

In this paper, we study the solvability of a general class of fully nonlinear curvature equations, which can be viewed as generalizations of the equations for Christoffel-Minkowski problem in convex geometry. We will also study the Dirichlet problem of the corresponding degenerate equations as an extension of the equations studied by Krylov.

math.AP↗
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

Local versus global stretched mechanical response in a supercooled liquid near the glass transition

Amorphous materials have a rich relaxation spectrum, which is usually described in terms of a hierarchy of relaxation mechanisms. In this work, we investigate the local dynamic modulus spectra in a model glass just above the glass transition temperature by performing a mechanical spectroscopy analysis with molecular dynamics simulations. We find that the spectra, at the local as well as on the global scale, can be well described by the Cole-Davidson formula in the frequency range explored with simulations. Surprisingly, the Cole-Davidson stretching exponent does not change with the size of the local region that is probed. The local relaxation time displays a broad distribution, as expected based on dynamic heterogeneity concepts, but the stretching is obtained independently of this distribution. We find that the size dependence of the local relaxation time and moduli can be well explained by the elastic shoving model.

cond-mat.dis-nn↗
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

A volume preserving flow and the isoperimetric problem in warped product spaces

In this article, we continue the work in \cite{GL} and study a normalized hypersurface flow in the more general ambient setting of warped product spaces. This flow preserves the volume of the bounded domain enclosed by a graphical hypersurface, and monotonically decreases the hypersurface area. As an application, the isoperimetric problem in warped product spaces is solved for such domains.

math.DG↗
arXiv2018

Role of thermal expansion heterogeneity in the cryogenic rejuvenation of metallic glasses

Cryogenic rejuvenation in metallic glasses reported in Ketov et al 's experiment (Nature(2015)524,200) has attracted much attention, both in experiments and numerical studies. The atomic mechanism of rejuvenation has been conjectured to be related to the heterogeneity of the glassy state, but the quantitative evidence is still elusive. Here we use molecular dynamics simulations of a model metallic glass to investigate the heterogeneity in the local thermal expansion. We then combine the resulting spatial distribution of thermal expansion with a continuum mechanics calculation to infer the internal stresses caused by a thermal cycle. Comparing the internal stress with the local yield stress, we prove that the heterogeneity in thermomechanical response has the potential to trigger local shear transformations, and therefore to induce rejuvenation during a cryogenic thermal cycling.

cond-mat.dis-nn↗
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

Interior C2 regularity of convex solutions to prescribing scalar curvature equations

We establish interior $C^2$ estimates for convex solutions of scalar curvature equation and $σ_2$-Hessian equation. We also prove interior curvature estimate for isometrically immersed hypersurfaces $(M^n,g)\subset \mathbb R^{n+1}$ with positive scalar curvature. These estimates are consequences of an interior estimate for these equations obtained under a weakened condition.

math.DG↗
arXiv2017

$L^p$ Christoffel-Minkowski problem: the case $1< p<k+1$

We consider a fully nonlinear partial differential equation associated to the intermediate $L^p$ Christoffel-Minkowski problem in the case $1<p<k+1$. We establish the existence of convex body with prescribed $k$-th even $p$-area measure on $\mathbb S^n$, under an appropriate assumption on the prescribed function. We construct examples to indicate certain geometric condition on the prescribed function is needed for the existence of smooth strictly convex body. We also obtain $C^{1,1}$ regularity estimates for admissible solutions of the equation when $ p\ge \frac{k+1}2$.

math.DG↗
arXiv2016

Curvature estimates for immersed hypersurfaces in Riemannian manifolds

We establish mean curvature estimate for immersed hypersurface with nonnegative extrinsic scalar curvature in Riemannian manifold $(N^{n+1}, \bar g)$ through regularity study of a degenerate fully nonlinear curvature equation in general Riemannian manifold. The estimate has a direct consequence for the Weyl isometric embedding problem of $(\mathbb S^2, g)$ in $3$-dimensional warped product space $(N^3, \bar g)$. We also discuss isometric embedding problem in spaces with horizon in general relativity, like the Anti-de Sitter-Schwarzschild manifolds and the Reissner-Nordström manifolds.

math.DG↗
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↗
arXiv2015

Flow by the power of the Gauss curvature

We prove that convex hypersurfaces in ${\mathbb R}^{n+1}$ contracting under the flow by any power $α>\frac{1}{n+2}$ of the Gauss curvature converge (after rescaling to fixed volume) to a limit which is a smooth, uniformly convex self-similar contracting solution of the flow. Under additional central symmetry of the initial body we prove that the limit is the round sphere.

math.DG↗
arXiv2015

Gigahertz Dielectric Polarization of Single-atom Niobium Substituted in Graphitic layers

We have synthesized two Nb@C composites with an order of magnitude difference in the density of single-atom niobium substituted into graphitic layers. The concentration and sites of single-atom Nb are identified using aberration-corrected scanning transmission electron microscopy and density functional theory. Comparing the complex permittivity spectra show that the representative dielectric resonance at ~16 GHz originates from the intrinsic polarization of single-atom Nb sites, confirmed by theoretical simulations. The single-atom dielectric resonance represents the physical limit of the electromagnetic response of condensed matter, and thus might open up a new avenue for designing electromagnetic wave absorption materials. Single-atom resonance also has important implications in understanding the correlation between the macroscopic dielectric behaviors and the atomic-scale structural origin.

cond-mat.mtrl-sci↗
arXiv2013

A mean curvature type flow in space forms

In this article, we introduce a new type of mean curvature flow for bounded star-shaped domains in space forms and prove its longtime existence, exponential convergence without any curvature assumption. Along this flow, the enclosed volume is a constant and the surface area evolves monotonically. Moreover, for a bounded convex domain in R n+1, the quermassintegrals evolve monotonically along the flow which allows us to prove a class of Alexandrov-Fenchel inequalities of quermassintegrals.

math.DG↗
arXiv2013

Entropy and a convergence theorem for Gauss curvature flow in high dimension

In this paper we prove uniform regularity estimates for the normalized Gauss curvature flow in higher dimensions. The convergence of solutions in $C^\infty$-topology to a smooth strictly convex soliton as $t$ approaches to infinity is obtained as a consequence of these estimates together with an earlier result of Andrews. The estimates are established via the study of a new entropy functional for the flow.

math.DG↗