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Ruobing Bai

Publications and source records attributed to Ruobing Bai.

At least 19 recordsLinked to original sources
arXiv2026

Morphology-Property Interplay in Chemo-Mechanics of Ion-Intercalation Active Particles

Morphology, material property, and mechanical constraint jointly govern the chemo-mechanical behavior of ion-intercalation particles, yet their coupled effects remain insufficiently understood. Here we establish a thermodynamically consistent single-particle framework and combine analytical solutions with multiphysics simulations to determine how these factors regulate lithiation and stress generation. We study hollow spherical, cylindrical, and ellipsoidal particles with isotropic or transversely isotropic material properties under fully constrained, inner-free, or unconstrained boundary conditions. We show that the transient lithiation pathway and the associated stress and strain fields are governed not by morphology, property, or constraint alone, but by their coupled interaction: isotropic particles are sensitive to the mechanical constraint, whereas transversely isotropic particles exhibit persistent heterogeneous lithiation dominated by anisotropic diffusivity. Flux decomposition analysis reveals that the mechanical contribution to Li flux is negligible in spheres but dominant in ellipsoids. Correlation analysis further shows that Li concentration and volumetric strain exhibit strong anti-correlation in unconstrained particles but weak correlation under full constraints. Bayesian optimization of hollow ellipsoids identifies Pareto-optimal morphologies that balance lithiation capacity against peak tensile stress. These results provide a unified framework for the morphology-property interplay in intercalation particles and offer morphology design principles for chemo-mechanical stability.

cond-mat.mtrl-sci↗
arXiv2026

Differentially Private Range Subgraph Counting

Subgraph counting is a fundamental problem in graph analysis. Motivated by practical scenarios where graph analytics are performed on subgraphs induced by selected vertices -- rather than on the entire graph -- and by growing privacy concerns, we initiate the study of differentially private range subgraph counting (DPRSC). The goal is to privately count occurrences of a fixed pattern graph within induced subgraphs defined by multi-dimensional attribute ranges. Unlike classical point counting, subgraph counting is inherently nonlinear and exhibits high sensitivity: a single edge modification can affect many subgraph occurrences. We present the first efficient algorithms for DPRSC with small additive error. Our approach introduces a subgraph projection that reduces DPRSC to weighted orthogonal range counting, enabling the use of range trees and local sensitivity estimation to achieve accurate private query answering. We complement our algorithms with matching lower bounds, obtained by reducing reconstruction attacks to DPRSC and leveraging discrepancy theory. In particular, we show that any differentially private algorithm for DPRSC must incur additive error exponential in the dimension. Empirical evaluations demonstrate that our algorithms significantly outperform baseline methods in accuracy and runtime while maintaining strong privacy guarantees.

cs.DS↗
arXiv2026

Thermoviscoelasticity of polydomain liquid crystal elastomers regulated by soft elasticity

Liquid crystal elastomers (LCEs) are elastomeric networks with rod-like mesogens that reorient under load. In polydomain LCEs, this reorientation drives a polydomain-to-monodomain transition that produces a soft-elastic plateau. Coupling between this soft elasticity and polymer-network viscoelasticity yields a path-dependent thermoviscoelastic response, central to applications in damping, impact protection, and tough adhesives. However, the physics governing this response under complex thermomechanical histories remains insufficiently studied. We present a combined experimental and theoretical study of polydomain LCEs under three uniaxial protocols: single-cycle loading-unloading, stress-free recovery from various pre-stretches, and multi-cycle loading with progressively increasing amplitude. We develop a finite-deformation constitutive model combining two parallel mechanisms: rate-independent, temperature-dependent soft elasticity from mesogen reorientation, and time- and temperature-dependent viscoelasticity. With a single parameter set, the model quantitatively reproduces all three protocols and resolves each mechanism's contribution. A temperature-dependent soft-elastic limit governs the low-rate response and the long-time recovered stretch, while viscoelasticity controls the rate-dependent deviation and the cycle-wise accumulation of residual stretch away from this limit. A thermal recovery test above the nematic-isotropic transition confirms that all hysteresis and residual deformation are reversible, ruling out irreversible damage. The framework provides mechanistic understanding and a predictive basis for designing polydomain LCE components under complex thermomechanical histories.

cond-mat.soft↗
arXiv2025

Regularization for the Schr\"{o}dinger equation with rough potential: one-dimensional case

In this work, we investigate the following Schr\"odinger equation with a spatial potential \begin{align*} i\partial_t u+\partial_x^2 u+\eta u=0, \end{align*} where $\eta$ is a given spatial potential (including the delta potential and $|x|^{-\gamma}$-potential). Our goal is to provide the regularization mechanism of this model when the potential $\eta\in L_x^r+L_x^\infty$ is rough. In this paper, we mainly focus on one-dimensional case and establish the following results: 1) When the potential $\eta \in L_x^1+L_x^\infty(\mathbb{R})$, then the solution is in $H_x^{\frac 32-}(\mathbb{R})$; however, there exists some $\eta \in L_x^1+L_x^\infty(\mathbb{R})$ such that the solution is not in $H_x^{\frac 32}(\mathbb{R})$; 2) When the potential $\eta \in L_x^r+L_x^\infty(\mathbb{R})$ for $1 2$, then the solution is in $H_x^{2}(\mathbb{R})$; however, there exists some $\eta \in L_x^r+L_x^\infty(\mathbb{R})$ such that the solution is not in $H_x^{2+}(\mathbb{R})$. Hence, we provide a complete classification of the regularity mechanism. Our proof is mainly based on the application of the commutator, local smoothing effect and normal form method. Additionally, we also discuss, without proof, the influence of the existence of nonlinearity on the regularity of solution.

math.AP↗
arXiv2025

Regularization for the Schr\"{o}dinger equation with rough potential: high-dimensional case

In this work, we investigate the regularization mechanisms of the Schr\"odinger equation with a spatial potential $$ i\partial_t u+\Delta u+\eta u =0, $$ where $\eta$ denotes a given spatial potential. The regularity of solutions constitutes one of the central problems in the theory of dispersive equations. Recent works \cite{Bai-Lian-Wu-2024, M-Wu-Z24} have established the sharp regularization mechanisms for this model in the whole space $\mathbb{R}$ and on the torus $\mathbb{T}$, with $\eta$ being a rough potential. The present paper extends the line of research to the high-dimensional setting with rough potentials $\eta \in L_x^r+L_x^{\infty}$. More precisely, we first show that when $1\leq r <\frac d2$, there exists some $\eta \in L_x^r+L_x^{\infty}$ such that the equation is ill-posed in $H_x^{\gamma}$ for any $\gamma \in \mathbb{R}$. Conversely, when $\frac d2 \leq r \leq \infty$, the expected optimal regularity is given by $$H_x^{\gamma_*}, \quad \gamma_*=\mbox{min}\{2+\frac d2-\frac dr, 2\}.$$ We establish a comprehensive characterization of the regularity, with the exception of two dimensional endpoint case $d=2, r=1$. Our novel theoretical framework combines several fundamental ingredients: the construction of counterexamples, the proposal of splitting normal form method, and the iterative Duhamel construction. Furthermore, we briefly discuss the effect of the interaction between rough potentials and nonlinear terms on the regularity of solutions.

math.AP↗
arXiv2025

Learning Reaction-Diffusion Kinetics from Mechanical Information

A central challenge in materials science is characterizing chemical processes that are elusive to direct measurement, particularly in functional materials operating under realistic conditions. Here, we demonstrate that mechanical strain fields contain sufficient information to reconstruct hidden chemical kinetics in coupled chemomechanical systems. Our partial differential equation-constrained learning framework decodes concentration-dependent diffusion kinetics, thermodynamic driving forces, and spatially heterogeneous reaction rates solely from mechanical observations. Using battery electrode materials as a model system, we demonstrate that the framework can accurately identify complex constitutive laws governing three distinct scenarios: classical Fickian diffusion, spinodal decomposition with pattern formation, and heterogeneous electrochemical reactions with spatial rate variations. The approach demonstrates robustness while maintaining accuracy with limited spatial data and reasonable experimental noise levels. Most significantly, the framework simultaneously infers multiple fundamental processes and properties, including diffusivity, reaction kinetics, chemical potential, and spatial heterogeneity maps, all from mechanical information alone. This method establishes a paradigm for materials characterization, enabling accurate learning of chemical processes in energy storage systems, catalysts, and phase-change materials where conventional diagnostics prove difficult. By revealing that mechanical deformation patterns serve as information-rich fingerprints of the underlying chemical processes, this work follows the pathway of inversely learning constitutive laws, with broad implications in materials science and engineering.

cond-mat.mtrl-sci↗
arXiv2025

Average Sensitivity of Hierarchical $k$-Median Clustering

Hierarchical clustering is a widely used method for unsupervised learning with numerous applications. However, in the application of modern algorithms, the datasets studied are usually large and dynamic. If the hierarchical clustering is sensitive to small perturbations of the dataset, the usability of the algorithm will be greatly reduced. In this paper, we focus on the hierarchical $k$ -median clustering problem, which bridges hierarchical and centroid-based clustering while offering theoretical appeal, practical utility, and improved interpretability. We analyze the average sensitivity of algorithms for this problem by measuring the expected change in the output when a random data point is deleted. We propose an efficient algorithm for hierarchical $k$-median clustering and theoretically prove its low average sensitivity and high clustering quality. Additionally, we show that single linkage clustering and a deterministic variant of the CLNSS algorithm exhibit high average sensitivity, making them less stable. Finally, we validate the robustness and effectiveness of our algorithm through experiments.

cs.LG↗
arXiv2024

Interfacial fatigue fracture of pressure sensitive adhesives

Pressure sensitive adhesives (PSAs) are viscoelastic polymers that can form fast and robust adhesion with various adherends under fingertip pressure. The rapidly expanding application domain of PSAs, such as healthcare, wearable electronics, and flexible displays, requires PSAs to sustain prolonged loads throughout their lifetime, calling for fundamental studies on their fatigue behaviors. However, fatigue of PSAs has remained poorly investigated. Here we study interfacial fatigue fracture of PSAs, focusing on the cyclic interfacial crack propagation due to the gradual rupture of noncovalent bonds between a PSA and an adherend. We fabricate a model PSA made of a hysteresis-free poly(butyl acrylate) bulk elastomer dip-coated with a viscoelastic poly(butyl acrylate-co-isobornyl acrylate) sticky surface, both crosslinked by poly(ethylene glycol) diacrylate. We adhere the fabricated PSA to a polyester strip to form a bilayer. The bilayer is covered by another polyester film as an inextensible backing layer. Using cyclic and monotonic peeling tests, we characterize the interfacial fatigue and fracture behaviors of the bilayer. From the experimental data, we obtain the interfacial fatigue threshold (4.6 J/m2) under cyclic peeling, the slow crack threshold (33.9 J/m2) under monotonic peeling, and the adhesion toughness (~ 400 J/m2) at a finite peeling speed. We develop a modified Lake-Thomas model to describe the interfacial fatigue threshold due to noncovalent bond breaking. The theoretical prediction (2.6 J/m2) agrees well with the experimental measurement (4.6 J/m2). Finally, we discuss possible additional dissipation mechanisms involved in the larger slow crack threshold and much larger adhesion toughness. It is hoped that this study will provide new fundamental knowledge for fracture mechanics of PSAs, as well as guidance for future tough and durable PSAs.

cond-mat.soft↗
arXiv2024

Strong and Highly Switchable Soft Sticky Adhesives

Many biological systems can form strong adhesion to various materials with complex shapes. The adhesion is further switchable between strongly adhering and completely non-adhering in a simple and fast manner. By contrast, no engineering system has yet achieved the same robust adherence and switching. This limitation severely hinders the advancement of several emerging technologies including biomimetic robots, assembly-based manufacturing, precision medicine, wearable and implantable devices, as well as on-demand material dismantling and recycling for sustainability. Here we present a design approach for strong and highly switchable adhesion by synergizing the surface stickiness, bulk energy dissipation, and stimuli-responsive polymer chains in a thermo-switchable soft sticky adhesive. The adhesive has a high adhesion strength of about 80 kPa with diverse materials at room temperature. The adhesion is highly switchable to near-vanishing (about 0.6 kPa) at an elevated temperature due to the thermo-responsive surface polymer chain retraction. This adhesion switching is reversible and repeatable for many cycles, enabling selective pick-and-release of objects with various materials, shapes, sizes, and weights. The switching time is around 10 s with an adhesive layer of 1 mm, governed by thermal conduction through the adhesive, faster than or comparable to most state-of-the-art methods. The adhesive is self-healing, and can be recycled, dried, stored, reswollen, and reused with nearly intact adhesion and switching properties. The synergistic design combining strong adhesion and stimuli-responsive switching can be potentially extended to various polymer systems, and further enhanced by optimized surface architectures.

cond-mat.soft↗
arXiv2023

Wave operator for the generalized derivative nonlinear Schr\"{o}dinger equation

In this work, we prove the existence of wave operator for the following generalized derivative nonlinear Schr\"odinger equation \begin{align*} i\partial_t u+\partial_x^2 u +i |u|^{2\sigma}\partial_x u=0, \end{align*} with $(t,x)\in\mathbb{R}\times\mathbb{R}$, $\sigma\in \mathbb{N}$, and $\sigma\geq 3$. The study of wave operators is an important part of the scattering theory, and it is useful in the construction of the nonlinear profile and the large data scattering. The previous argument for small data scattering in \cite{BaiWuXue-JDE}, which is based on the local smoothing effect and maximal function estimates, breaks down when considering the final data problem. The main reason is that the resolution space does not provide smallness near the infinite time. We overcome this difficulty by invoking the gauge transformation and the normal form method.

math.AP↗
arXiv2023

Finite time blow-up of non-radial solutions for some inhomogeneous Schr\"{o}dinger equations

This work studies the inhomogeneous Schr\"odinger equation $$ i\partial_t u-\mathcal{K}_{s,\lambda}u +F(x,u)=0 , \quad u(t,x):\mathbb{R}\times\mathbb{R}^N\to\mathbb{C}. $$ Here, $s\in\{1,2\}$, $N>2s$ and $\lambda>-\frac{(N-2)^2}{4}$. The linear Schr\"odinger operator reads $\mathcal{K}_{s,\lambda}:= (-\Delta)^s +(2-s)\frac{\lambda}{|x|^2}$ and the focusing source term is local or non-local $$F(x,u)\in\{|x|^{-2\tau}|u|^{2(q-1)}u,|x|^{-\tau}|u|^{p-2}(J_\alpha *|\cdot|^{-\tau}|u|^p)u\}.$$ The Riesz potential is $J_\alpha(x)=C_{N,\alpha}|x|^{-(N-\alpha)}$, for certain $0<\alpha 0$ gives a inhomogeneous non-linearity. One considers the inter-critical regime, namely $1+\frac{2(1-\tau)}N<q<1+\frac{2(1-\tau)}{N-2s}$ and $1+\frac{2-2\tau+\alpha}{N}<p<1+\frac{2-2\tau+\alpha}{N-2s}$. The purpose is to prove the finite time blow-up of solutions with datum in the energy space, non necessarily radial or with finite variance. The assumption on the data is expressed in terms of non-conserved quantities. This is weaker than the ground state threshold standard condition. The blow-up under the ground threshold or with negative energy are consequences. The proof is based on Morawetz estimates and a non-global ordinary differential inequality.

math.AP↗
arXiv2022

Temperature-Modulated Photomechanical Actuation of Photoactive Liquid Crystal Elastomers

Photoactive liquid crystal elastomers are polymer networks of liquid crystal mesogens embedded with chromophores like azobenzene. They undergo large deformation when illuminated by light of a certain wavelength through photochemical reaction, inspiring exciting new applications. However, despite the recent progresses in both the experiment and theory of these materials, the fundamental understanding of the temperature effect on their photomechanical actuation through various molecular-to-mesoscale processes have remained largely unexplored. This paper constructs a theoretical model to investigate this temperature-modulated photomechanical actuation, by integrating different temperature-dependent processes into a continuum framework. The model studies a special working condition where the material is subjected to a uniaxial tensile load, a prescribed temperature, and a polarized light illumination. We explore the free energy landscape of the system and the uniaxial stress-stretch responses under various conditions. We exploit the coupling between individual controls of temperature and light in a single photomechanical actuation for several working scenarios, including the temperature-modulated photomechanical snap-through instability, specific work, and blocking stress. We study the effect of the temperature-dependent backward isomerization of chromophores on the photomechanical actuation. These results are hoped to motivate future fundamental studies and new applications of various photomechanical material systems.

cond-mat.soft↗
arXiv2021

Large global solutions for energy-critical nonlinear Schrödinger equation

In this work, we consider the 3D defocusing energy-critical nonlinear Schrödinger equation $i\partial_t u+Δu =|u|^4 u,\quad (t,x)\in \mathbb{R}\times \mathbb{R}^3$. Applying the outgoing and incoming decomposition presented in the recent work \cite{BECEANU-DENG-SOFFER-WU-2021}, we prove that any radial function $f$ with $χ_{\leq1}f\in H^1$ and $χ_{\geq1}f\in H^{s_0}$ with $\frac{5}{6}<s_0<1$, there exists an outgoing component $f_+$ (or incoming component $f_-$) of $f$, such that when the initial data is $f_+$, then the corresponding solution is globally well-posed and scatters forward in time; when the initial data is $f_-$, then the corresponding solution is globally well-posed and scatters backward in time.

math.AP↗
arXiv2021

Finite time/Infinite time blow-up behaviors for the inhomogeneous nonlinear Schr\"{o}dinger equation

In this work, we consider the following focusing inhomogeneous nonlinear Schr\"odinger equation \begin{align*} i\partial_t u+\Delta u +|x|^{-b}|u|^p u=0,\quad (t, x)\in\mathbb{R}\times\mathbb{R}^N \end{align*} with $0 0. \end{equation*} To our knowledge, the statement (1) establishes the first finite time blow-up result for this equation in the intercritical case when the initial data $u_0$ doesn't have finite variance and is non-radial. The statement (2) gives the first result for the infinite time blow-up rate for this equation.

math.AP↗
arXiv2021

Photochemical-induced phase transitions in photoactive semicrystalline polymers

The emergent photoactive materials through photochemistry make it possible to directly convert photon energy to mechanical work. There is much recent work in developing appropriate materials and a promising new system is semi-crystalline polymers of the photoactive molecule azobenzene. We develop a phase field model with two order parameters for the crystal-melt transition and the trans-cis photo-isomerization to understand such materials, and the model describes the rich phenomenology. We find that the photo-reaction rate depends sensitively on temperature: at temperatures below the crystal-melt transition temperature, photoreaction is collective, requires a critical light intensity and shows an abrupt first order phase transition manifesting nucleation and growth; at temperatures above the transition temperature, photoreaction is independent and follows first order kinetics. Further, the phase transition depends significantly on the exact forms of spontaneous strain during the crystal-melt and trans-cis transitions. A non-monotonic change of photo-persistent cis ratio with increasing temperature is observed accompanied by a reentrant crystallization of trans below the melting temperature. A pseudo phase diagram is subsequently presented with varying temperature and light intensity along with the resulting actuation strain. These insights can assist the further development of these materials.

cond-mat.soft↗
arXiv2020

Collective behavior in the kinetics and equilibrium of solid-state photoreaction

There is current interest in developing photoactive materials that deform on illumination and can thus be used for photomechanical actuation. This is attractive since it can be affected at a distance, different frequencies can be used to actuate different modes and to sense, and corrosion-free lightweight fiber optic cables can deliver significant power over long distances. The strategy for developing new photomechanical materials is to first develop photoactive molecules in solution, and then to incorporate these in the solid-state either by crystallization or by inserting them into polymers. This letter shows that the kinetics and the nature of the photo-induced phase transitions are profoundly different in single molecules (solution) and in the solid state using a lattice spin model. In solution, where the molecules act independently, the photoreaction follows first-order kinetics. However, in the solid state where the photoactive molecules interact with each other and therefore behave collectively during reaction, photoreactions follow the sigmoidal kinetics of nucleation and growth as in a first-order phase transition. Further, we find that the exact nature of the photo-induced strain has a critical effect on the kinetics, equilibrium, and microstructure formation. These predictions agree qualitatively with experimental observations, and provide insights for the development of new photoactive materials.

cond-mat.mes-hall↗