arXiv subjects

Jinjie Liu

Publications and source records attributed to Jinjie Liu.

At least 19 recordsLinked to original sources

arXiv2026

Entropy-Driven Initiation and Cellular Uptake Mediated by Viscoelastic Cytoskeleton: A Kinetic Phase Diagram from Onsager Variational Principle

A fundamental question in receptor-mediated endocytosis remains unanswered: what initial driving force brings ligands and receptors into close proximity? While previous models assume pre-existing contact and overlook this initiation problem, we propose that entropic forces from nanoscale biomolecules in crowded cellular environments provide the essential driving mechanism. We develop a unified continuum model rooted in the Onsager variational principle, where engulfment depth serves as the generalized coordinate and the driving force derives from a free energy landscape of entropic, binding, membrane, and cytoskeleton contributions. The framework naturally incorporates: (i) entropy-driven adhesion as initiation; (ii) ligand-receptor binding as the sustaining force; (iii) membrane deformation via the Helfrich-Canham Hamiltonian; and (iv) cytoskeleton viscoelasticity through the elastic-viscoelastic correspondence principle. The kinetic phase diagram predicts a critical biomolecule concentration for initiation, a lower bound of ligand density for complete engulfment, a finite size window for engulfable particles, and an optimal virus radius of 30--60 nm that decreases with increasing binding energy. The Onsager solubility condition naturally yields the phase boundaries. The model exhibits asymptotic consistency with the classic Asakura-Oosawa result in the large-particle flat-surface limit. Stiffer cells lead to longer engulfment times and narrower size windows. Strikingly, the optimal size matches HIV-1 dimensions under physiologically realistic parameters. This work provides a variational foundation for cellular uptake with implications for virology, nanotechnology, and drug delivery.

cond-mat.soft↗

arXiv2026

Energy-superconvergent Explicit Runge--Kutta Time Discretizations

This paper investigates the energy conservation properties of explicit Runge--Kutta (RK) time discretizations for autonomous skew-symmetric systems. For linear problems, we present a general framework for constructing RK methods in which the energy-accuracy order significantly exceeds the number of stages. Specifically, for an $s$-stage, $p$-th order RK method (where $p$ is even), we prove that the energy accuracy can reach up to order $2s-p+1$. Utilizing this framework, we derive several energy-superconvergent methods, including five- to seven-stage algorithms with energy accuracy up to the eleventh order, and establish their corresponding strong stability criteria. The methods are validated on a range of benchmark problems, including harmonic oscillators, integro-differential equations in peridynamics, and the Maxwell equations. Furthermore, we extend the energy-superconvergent framework to autonomous nonlinear systems with amplitude-dependent frequencies. By deriving fifth-order energy conditions for three-stage, second-order methods, we develop the RK325 algorithm. The performance of RK325 is demonstrated for a broad range of problems, including Euler's equations for rigid body dynamics, the nonlinear Schrödinger equation, the Korteweg--de Vries (KdV) equation, Burgers' equation, and the Landau--Lifshitz equation. Additionally, we develop four-stage, second-order methods (RK427) and five-stage, fourth-order methods (RK547), all of which achieve seventh-order energy accuracy for the cubic nonlinear case. Finally, the performance of RK547 method is illustrated using the nonlinear Maxwell--Kerr system.

math.NA↗

arXiv2026

BugScope: Learn to Find Bugs Like Human

Software auditing is an increasingly critical task in the era of rapid code generation. While LLM-based auditors have demonstrated strong potential, their effectiveness remains limited by misalignment with the highly complex, domain-specific nature of bug detection. In this work, we introduce BugScope, a framework that mirrors how human auditors learn specific bug patterns from representative examples and apply this knowledge during code auditing. BugScope structures auditing into three steps: seed identification, context retrieval, and bug detection, and aligns LLMs to each step by analyzing real bug reports and mutated examples, and distilling concise, reusable guidelines. On a curated dataset of 33 real-world bugs from 21 widely used open-source projects, BugScope achieves 86.05\% precision and 87.88\% recall, corresponding to an F1 score of 0.87. By comparison, leading industrial tools such as Claude Code (with Claude Opus 4.6) and Cursor BugBot achieve F1 scores of only 0.51 and 0.43, respectively. Beyond benchmarks, large-scale evaluation on real-world projects such as the Linux kernel uncovered 184 previously unknown bugs, of which 78 have already been fixed and 7 explicitly confirmed by developers. Our code is available at https://github.com/jinyaoguo/BugScope

cs.SE↗

arXiv2024

FluidML: Fast and Memory Efficient Inference Optimization

Machine learning models deployed on edge devices have enabled numerous exciting new applications, such as humanoid robots, AR glasses, and autonomous vehicles. However, the computing resources available on these edge devices are not catching up with the ever-growing number of parameters in these models. As the models become bigger and more complicated, the novel yet sophisticated structure challenges the inference runtime optimization. We present FluidML, a generic runtime memory management and optimization framework that can flexibly transform the model execution blueprint to achieve faster and more memory-efficient inference. Evaluations across different platforms show that FluidML can consistently reduce the end-to-end inference latency by up to 25.38% for popular language models and reduce peak memory usage by up to 41.47%, compared to state-of-the-art approaches. FluidML is of ~30K line of codes, built for general-purpose usage, and will be released as an open-source inference runtime optimization framework to the community.

cs.LG↗

arXiv2024

Copositivity criteria of a class of fourth order 3-dimensional symmetric tensors

In this paper, we mainly dicuss the non-negativity conditions for quartic homogeneous polynomials with 3 variables, which is the analytic conditions of copositivity of a class of 4th order 3-dimensional symmetric tensors. For a 4th order 3-dimensional symmetric tensor with its entries $1$ or $-1$, an analytic necessary and sufficient condition is given for its strict copositivity with the help of the properties of strictly semi-positive tensors. And by means of usual maxi-min theory, a necessary and sufficient condition is established for copositivity of such a tensor also. Applying these conclusions to a general 4th order 3-dimensional symmetric tensor, the analytic conditions are successfully obtained for verifying the (strict) copositivity, and these conditions can be very easily parsed and validated. Moreover, several (strict) inequalities of ternary quartic homogeneous polynomial are established by means of these analytic conditions.

math.OC↗

arXiv2023

AutoPCF: Efficient Product Carbon Footprint Accounting with Large Language Models

The product carbon footprint (PCF) is crucial for decarbonizing the supply chain, as it measures the direct and indirect greenhouse gas emissions caused by all activities during the product's life cycle. However, PCF accounting often requires expert knowledge and significant time to construct life cycle models. In this study, we test and compare the emergent ability of five large language models (LLMs) in modeling the 'cradle-to-gate' life cycles of products and generating the inventory data of inputs and outputs, revealing their limitations as a generalized PCF knowledge database. By utilizing LLMs, we propose an automatic AI-driven PCF accounting framework, called AutoPCF, which also applies deep learning algorithms to automatically match calculation parameters, and ultimately calculate the PCF. The results of estimating the carbon footprint for three case products using the AutoPCF framework demonstrate its potential in achieving automatic modeling and estimation of PCF with a large reduction in modeling time from days to minutes.

cs.AI↗

arXiv2021

ST-SVD Factorization and s-Diagonal Tensors

A third order real tensor is mapped to a special f-diagonal tensor by going through Discrete Fourier Transform (DFT), standard matrix SVD and inverse DFT. We call such an f-diagonal tensor an s-diagonal tensor. An f-diagonal tensor is an s-diagonal tensor if and only if it is mapped to itself in the above process. The third order tensor space is partitioned to orthogonal equivalence classes. Each orthogonal equivalence class has a unique s-diagonal tensor. Two s-diagonal tensors are equal if they are orthogonally equivalent. Third order tensors in an orthogonal equivalence class have the same tensor tubal rank and T-singular values. Four meaningful necessary conditions for s-diagonal tensors are presented. Then we present a set of sufficient and necessary conditions for s-diagonal tensors. Such conditions involve a special complex number. In the cases that the dimension of the third mode of the considered tensor is $2, 3$ and $4$, we present direct sufficient and necessary conditions which do not involve such a complex number.

math.NA↗

arXiv2021

Strengthening and Weakening by Dislocations in Monolayer MoS2

Dislocations govern the properties of any crystals. Yet, how dislocation of pentagonheptagon (5|7) in grain boundaries (GBs) affects the mechanical properties of two-dimensional MoS2 crystals remains poorly known. Using atomistic simulations and continuum disclination dipole model, we show that, depending on the tilt angle and 5|7 dislocation arrangement, MoS2 GB strength can be enhanced or reduced with tilt angle. For zigzag-tilt GBs primarily composed of Mo5|7+S5|7 dislocations, GB strength monotonically increases as the square of tilt angle. For armchair-tilt GBs with Mo5|7 or S5|7 dislocations, however, the trend of GB strength breaks down as 5|7 dislocations are non-evenly spaced. Moreover, mechanical failure initiates at the bond shared by 5|7 rings, in contrast to graphene where failure occurs at the bond shared by 6|7 rings. This work provides new insights into mechanical design of synthetic transition metal dichalcogenide crystals via dislocation engineering.

cond-mat.mtrl-sci↗

arXiv2021

Mechanical Ductile Detwinning in CH3NH3PbI3 Perovskite

Twin boundaries (TBs) were identified to show conflicting positive/negative effects on the physical properties of CH3NH3PbI3 perovskite, but their roles on the mechanical properties are pending. Herein, tensile characteristics of a variety of TB-dominated bicrystalline CH3NH3PbI3 perovskites are explored using molecular simulations. TB-contained CH3NH3PbI3 are classified into four types from their tensile ductile detwinning characteristics. Type I is characterized by smooth loading flow stressstrain responses, originating from relatively uniform stress distribution induced gradual amorphization at TB region. Types II and III are represented by sudden drop of loading stresses but then distinct ductile flow stress-strain curves, resulting from limited and large-area amorphizations of TB-involved structures, respectively. However, Type IV is highlighted by double apparent peaks in the loading curve followed by ductile flow response, coming from stress-concentration of localization-to-globalization at TB structure, as well as amorphization. This study provides critical insights into mechanics of CH3NH3PbI3 perovskites, and offers that TB engineering is a promising strategy to design mechanically robust hybrid organic-inorganic perovskites-based device systems

cond-mat.mtrl-sci↗

arXiv2019

Elasticity $\mathscr{M}$-tensors and the Strong Ellipticity Condition

In this paper, we establish two sufficient conditions for the strong ellipticity of any fourth-order elasticity tensor and investigate a class of tensors satisfying the strong ellipticity condition, the elasticity $\mathscr{M}$-tensor. The first sufficient condition is that the strong ellipticity holds if the unfolding matrix of this fourth-order elasticity tensor can be modified into a positive definite one by preserving the summations of some corresponding entries. Second, an alternating projection algorithm is proposed to verify whether an elasticity tensor satisfies the first condition or not. Besides, the elasticity $\mathscr{M}$-tensor is defined with respect to the M-eigenvalues of elasticity tensors. We prove that any nonsingular elasticity $\mathscr{M}$-tensor satisfies the strong ellipticity condition by employing a Perron-Frobenius-type theorem for M-spectral radii of nonnegative elasticity tensors. Other equivalent definitions of nonsingular elasticity $\mathscr{M}$-tensors are also established.

math-ph↗

arXiv2018

A New Class of Positive Semi-definite Tensors

In this paper, a new class of positive semi-definite tensors, the MO tensor, is introduced. It is inspired by the structure of Moler matrix, a class of test matrices. Then we focus on two special cases in the MO-tensors: Sup-MO tensor and essential MO tensor. They are proved to be positive definite tensors. Especially, the smallest H-eigenvalue of a Sup-MO tensor is positive and tends to zero as the dimension tends to infinity, and an essential MO tensor is also a completely positive tensor.

math.SP↗

arXiv2018

An Irreducible Function Basis of Isotropic Invariants of A Third Order Three-Dimensional Symmetric Tensor

In this paper, we present an eleven invariant isotropic irreducible function basis of a third order three-dimensional symmetric tensor. This irreducible function basis is a proper subset of the Olive-Auffray minimal isotropic integrity basis of that tensor. The octic invariant and a sextic invariant in the Olive-Auffray integrity basis are dropped out. This result is of significance to the further research of irreducible function bases of higher order tensors.

math-ph↗

arXiv2018

Isotropic Polynomial Invariants of the Hall Tensor

The Hall tensor emerges from the study of the Hall effect, an important magnetic effect observed in electric conductors and semiconductors. The Hall tensor is third order and three dimensional, whose first two indices are skew-symmetric. In this paper, we investigate the isotropic polynomial invariants of the Hall tensor by connecting it with a second order tensor via the third order Levi-Civita tensor. We propose a minimal isotropic integrity basis with 10 invariants for the Hall tensor. Furthermore, we prove that this minimal integrity basis is also an irreducible isotropic function basis of the Hall tensor.

math-ph↗

arXiv2018

Scattering of a short electromagnetic pulse from a Lorentz-Duffing film: theoretical and numerical analysis

We combine scattering theory, Fourier, traveling wave and asymptotic analyses together with numerical simulations to present interesting and practically useful properties of femtosecond pulse interaction with thin films. The dispersive material is described by a single resonance Lorentz model and its nonlinear extension with a cubic Duffing-type nonlinearity. A key feature of the Lorentz dielectric function is that its real part becomes negative between its zero and its pole, generating a forbidden region. We illustrate numerically the linear interaction of the pulse with the film using both scattering theory and Fourier analysis. Outside this region we show the generation of a sequence of pulses separated by round trips in the Fabry-Perot cavity due to multiple reflections. When the pulse spectrum is inside the forbidden region, we observe total reflection. Near the pole of the dielectric function, we demonstrate the slowing down of the pulse (group velocity tending to zero) in the medium that behaves as a high-Q cavity. We use the combination of analysis and simulations in the linear regime to validate the delta function approximation of the thin layer; this collapses the forbidden region to a single resonant point of the spectrum. We also study the single cycle pulse interaction with a thin film and show three distinct types of reflection: half-pulse, sinusoidal wave train and cosine wavelet. Finally we analyze the influence of a strong nonlinearity and observe that the film switches from reflecting to trasparent.

physics.optics↗

arXiv2016

Modified Iterated Crank-Nicolson Method with Improved Accuracy

The iterated Crank-Nicolson (ICN) method is a successful numerical algorithm in numerical relativity for solving partial differential equations. The $θ$-ICN method is the extension of the original ICN method where $θ$ is the weight when averaging the predicted and corrected values. It has better stability when $θ$ is chosen to be larger than 0.5, but the accuracy is reduced since the $θ$-ICN method is second order accurate only when $θ$ = 0.5. In this paper, we propose two modified $θ$-ICN algorithms that have second order of convergence rate when $θ$ is not 0.5, based on two different ways to choose the weight $θ$. The first approach employs two geometrically averaged $θ$s in two iterations within one time step, and the second one uses arithmetically averaged $θ$s for two consecutive time steps while $θ$ remains the same in each time step. The stability and second order accuracy of our methods are verified using stability and truncation error analysis and are demonstrated by numerical examples on linear and semi-linear hyperbolic partial differential equations and Burgers' equation.

math.NA↗

arXiv2014

Finite-Difference Time-Domain simulation of spacetime cloak

In this work, we present a numerical method that remedies the instabilities of the conventional FDTD approach for solving Maxwell's equations in a space-time dependent magneto-electric medium with direct application to the simulation of the recently proposed spacetime cloak. We utilize a dual grid FDTD method overlapped to the time domain to provide a stable approach for the simulation of magneto-electric medium with time and space varying permittivity, permeability and coupling coefficient. The developed method can be applied to explore other new physical possibilities offered by spacetime cloaking, metamaterials, and transformation optics.

physics.optics↗

arXiv2012

Classical theory of second-harmonic generation from magnetic metamaterials

Strong second-harmonic generation has recently been experimentally observed from metamaterials consisting of periodic arrays of metal split ring resonators with an effective negative magnetic permeability [Science, 313, 502 (2006)]. To explore the underlying physical mechanism, a classical model derived from microscopic theory is employed here. The quasi-free electrons inside the metal are approximated as a classical Coulomb-interacting electron gas, and their motion under the excitation of an external electromagnetic field is described by the cold-plasma wave equations. Through numerical simulations, it is demonstrated that the microscopic theory includes the dominant physical mechanisms bothqualitatively and quantitatively.

cond-mat.mtrl-sci↗

arXiv2011

General Properties of Two-dimensional Conformal Transformation in Electrostatics

Electrostatic properties of two-dimensional nanosystems can be described by their geometry resonances. In this paper we prove that these modes as well as the corresponding eigenvalues are invariant under any conformal transformation. This invariance further leads to a new way to studying the transformed structures. Namely, transforming a geometry is equivalent to modifying the strengths of these invariant eigenmodes excited by the external excitations.

physics.class-ph↗