Tootfinder

2D Ultrasound Elasticity Imaging of Abdominal Aortic Aneurysms Using Deep Neural Networks
Utsav Ratna Tuladhar, Richard Simon, Doran Mix, Michael Richards
https://arxiv.org/abs/2508.19303

2D Ultrasound Elasticity Imaging of Abdominal Aortic Aneurysms Using Deep Neural Networks
Abdominal aortic aneurysms (AAA) pose a significant clinical risk due to their potential for rupture, which is often asymptomatic but can be fatal. Although maximum diameter is commonly used for risk assessment, diameter alone is insufficient as it does not capture the properties of the underlying material of the vessel wall, which play a critical role in determining the risk of rupture. To overcome this limitation, we propose a deep learning-based framework for elasticity imaging of AAAs with …

Scattering of Antiplane Shear Waves by Fractals in Strain Gradient Elasticity
E. Alevras, Th. Zisis, P. A. Gourgiotis
https://arxiv.org/abs/2507.18768 https://

Scattering of Antiplane Shear Waves by Fractals in Strain Gradient Elasticity
Wave manipulation is essential in various applications, including seismic wave protection, sound isolation, and acoustic device design. This study examines the scattering and trapping of antiplane SH waves in a microstructured solid embedded with rigid pins. The material's response is governed by the theory of strain gradient elasticity. A method is proposed for identifying the wavenumbers that induce resonance in the elastic body, based on specific material parameters and pin configurations. T…

Physics-Informed Kolmogorov-Arnold Networks for multi-material elasticity problems in electronic packaging
Yanpeng Gong, Yida He, Yue Mei, Xiaoying Zhuang, Fei Qin, Timon Rabczuk
https://arxiv.org/abs/2508.16999

Physics-Informed Kolmogorov-Arnold Networks for multi-material elasticity problems in electronic packaging
This paper proposes a Physics-Informed Kolmogorov-Arnold Network (PIKAN) method for analyzing elasticity problems in electronic packaging multi-material structures. The core innovation lies in replacing Multi-Layer Perceptrons (MLPs) with Kolmogorov-Arnold Networks (KANs) within the energy-based Physics-Informed Neural Networks (PINNs) framework. The method constructs admissible displacement fields that automatically satisfy essential boundary conditions and employs various numerical integratio…

On the asymptotic limit for the dynamic isotropic-nematic phase transition with anisotropic elasticity
Dong Huan, Ren Siqi, Wang Wei
https://arxiv.org/abs/2508.18800 https://

On the asymptotic limit for the dynamic isotropic-nematic phase transition with anisotropic elasticity
In this paper, we consider the isotropic-nematic phase transition with anisotropic elasticity governed by the Landau-de Gennes dynamics of liquid crystals. For $-\frac{3}{2}< L<0,$ we rigorously justify the limit from the Landau-de Gennes flow to a sharp interface system characterized by a two-phase flow: The interface evolves via motion by mean curvature; In the isotropic region, $Q=0$; In the nematic region, $Q=s_+(nn-\frac{1}{3}I)$ with $n\in \mathbb{S}^2$ and $s_+>0$, where the alignment ve…

Conservative yet constitutively odd elasticity in prestressed metamaterials
Tyler A. Engstrom, Daniel M. Sussman
https://arxiv.org/abs/2509.19560 https://a…

Conservative yet constitutively odd elasticity in prestressed metamaterials
We introduce a design principle for mechanical metamaterials based on "odd elasticity, once removed." By revisiting classic results relating the variation of Cauchy stress and Lagrangian strain around a prestressed reference state, we show how anisotropic, equilibrium prestress can generate a major anti-symmetry in the material's constitutive response. Tuning the system to such a state drives it to a critical instability, radically transforming its acoustic properties. We then inverse-design se…

Higher-order homogenization for equations of linearized elasticity using the operator-asymptotic approach
Yi-Sheng Lim, Josip \v{Z}ubrini\'c
https://arxiv.org/abs/2508.19388

Higher-order homogenization for equations of linearized elasticity using the operator-asymptotic approach
The operator-asymptotic approach was introduced by Lim-Žubrinić in [Asymptotic Analysis. 141(4), p. 211-256 (2025)] for the homogenization of an $\varepsilon\mathbb{Z}^d$-periodic composite media. In this article, we consider the setting of three-dimensional linearized elasticity, and extend the approach to obtain higher-order convergence rates. In particular, we consider the so-called ``Bloch approximation'' for vector-valued functions with compact Fourier support, and demonstrate that under…

Bridging Cloud Convenience and Protocol Transparency: A Hybrid Architecture for Ethereum Node Operations on Amazon Managed Blockchain
S M Mostaq Hossain, Amani Altarawneh, Maanak Gupta
https://arxiv.org/abs/2507.18774

Bridging Cloud Convenience and Protocol Transparency: A Hybrid Architecture for Ethereum Node Operations on Amazon Managed Blockchain
As blockchain technologies are increasingly adopted in enterprise and research domains, the need for secure, scalable, and performance-transparent node infrastructure has become critical. While self-hosted Ethereum nodes offer operational control, they often lack elasticity and require complex maintenance. This paper presents a hybrid, service-oriented architecture for deploying and monitoring Ethereum full nodes using Amazon Managed Blockchain (AMB), integrated with EC2-based observability, IA…

Momentum Equation-Based Regularization and Image Registration for Two-Dimensional Ultrasound Elasticity Imaging
Olalekan A. Babaniyi, Rebecca Rodrigues, Michael S. Richards
https://arxiv.org/abs/2508.19086

Momentum Equation-Based Regularization and Image Registration for Two-Dimensional Ultrasound Elasticity Imaging
Objective: Evaluate and compare multiple mechanics-based and traditional regularization strategies within a variational image registration framework for quasi-static ultrasound elastography. Methods:We reformulate a previously proposed momentum-equation-based post-processing method (SPREME) as a regularization term directly integrated into an image registration energy functional. Four regularization types are implemented and compared: a strain magnitude ($\R_ε$), a strain magnitude with incomp…

A continued fraction approximation for the effective elasticity tensor of two-dimensional polycrystals as a function of the crystal elasticity tensor
Graeme W. Milton
https://arxiv.org/abs/2510.10297

A continued fraction approximation for the effective elasticity tensor of two-dimensional polycrystals as a function of the crystal elasticity tensor
For two-dimensional polycrystals the effective elasticity tensor $C_*$ as a function $C_*(C_0)$ of the elasticity tensor $C_0$ of the constituent crystal is considered. It is shown that this function can be approximated by one with a continued fraction expansion resembling that associated with a class of microstructure known as sequential laminates. These are hierarchical microstructures defined inductively. Rank 0 sequential laminates are simply rotations of the pure crystal. Rank $j$ sequenti…

Channel flows of deformable nematics
Ioannis Hadjifrangiskou, Sumesh P. Thampi, Julia M. Yeomans
https://arxiv.org/abs/2508.19013 https://arxiv.org/pdf/250…

Channel flows of deformable nematics
We describe channel flows in a continuum model of deformable nematic particles. In a simple shear flow, deformability leads to a nonlinear coupling of strain rate and vorticity, and results in shape oscillations or flow alignment. The final steady state can depend on initial conditions, and we explain this behaviour by considering a phase space representation of the dynamics. In Poiseuille flow, particle deformability and nematic elasticity induce banding, where particles near the walls are ali…

High-order Multiscale Preconditioner for Elasticity of Arbitrary Structures
Sabit Mahmood Khan, Yashar Mehmani
https://arxiv.org/abs/2509.19777 https://arx…

High-order Multiscale Preconditioner for Elasticity of Arbitrary Structures
We present a two-level preconditioner for solving linear systems arising from the discretization of the elliptic, linear-elastic deformation equation, in displacement unknowns, over domains that have arbitrary geometric and topological complexity and heterogeneity in material properties (including fractures). The preconditioner is an algebraic translation of the high-order pore-level multiscale method (hPLMM) proposed recently by the authors, wherein a domain is decomposed into non-overlapping …

Defects in Wigner crystals: fracton-elasticity duality and vacancy proliferation
Pawe{\l} Matus
https://arxiv.org/abs/2509.14344 https://arxiv.org/pdf/2509…

Defects in Wigner crystals: fracton-elasticity duality and vacancy proliferation
We develop a low-energy field theory for electrically charged crystals. Using the tools of fracton-elasticity duality, generalized to accommodate the magnetic 1-form symmetry of electromagnetism, we show how the elastic and electromagnetic degrees of freedom couple to the different crystal defects and to one another. The resulting field theory is then used to calculate vacancy-vacancy interaction energy, and to study the consequences of vacancy proliferation. We find that the longitudinal mode,…

One-sided Fractional Integrals and Riesz Potentials on a Spherical Cap
Boris Rubin
https://arxiv.org/abs/2509.19584 https://arxiv.org/pdf/2509.19584…

One-sided Fractional Integrals and Riesz Potentials on a Spherical Cap
We introduce fractional integrals on the $n$-dimensional spherical cap, study their boundednes in weighted $L^p$ spaces and obtain explicit inversion formulas. The results are applied to the inversion problem for Riesz potentials on a spherical cap. In the case $n=2$, this problem arises in electrostatics, elasticity, and some other applied areas. The main tools are stereographic projection, hypersingular integrals of the Marchaud type, Poisson integrals, and spherical harmonic decompositions.

Replaced article(s) found for cs.CE. https://arxiv.org/list/cs.CE/new
[1/1]:
- A comparative analysis for different finite element types in strain-gradient elasticity simulatio...
B. Cagri Sarar, M. Erden Yildizdag, Francesco Fabbrocino, B. Emek Abali

Understanding the effect of wall elasticity in turbulent channel flows
M. Koseki, M. S. Aswathy, M. E. Rosti
https://arxiv.org/abs/2509.11142 https://arxiv…

Understanding the effect of wall elasticity in turbulent channel flows
This study compares turbulent channel flows over elastic walls with those over rough walls, to explore the role of the dynamic change of shape of the wall on turbulence. The comparison is made meaningful by generating rough walls from instantaneous configurations of the elastic cases. The aim of this comparison is to individually understand the role of fluid-structure interaction effects and the role of wall shape/undulations in determining the overall physics of flow near elastic walls. With a…

WAVE: Worm Gear-based Adaptive Variable Elasticity for Decoupling Actuators from External Forces
Moses Gladson Selvamuthu, Tomoya Takahashi, Riichiro Tadakuma, Kazutoshi Tanaka
https://arxiv.org/abs/2509.21878

WAVE: Worm Gear-based Adaptive Variable Elasticity for Decoupling Actuators from External Forces
Robotic manipulators capable of regulating both compliance and stiffness offer enhanced operational safety and versatility. Here, we introduce Worm Gear-based Adaptive Variable Elasticity (WAVE), a variable stiffness actuator (VSA) that integrates a non-backdrivable worm gear. By decoupling the driving motor from external forces using this gear, WAVE enables precise force transmission to the joint, while absorbing positional discrepancies through compliance. WAVE is protected from excessive loa…

The slender body free boundary problem
Laurel Ohm
https://arxiv.org/abs/2509.16800 https://arxiv.org/pdf/2509.16800…

The slender body free boundary problem
We consider the slender body free boundary problem describing the evolution of an inextensible, closed elastic filament immersed in a Stokes fluid in $\mathbb{R}^3$. The filament elasticity is governed by Euler-Bernoulli beam theory, and the coupling between this 1D elasticity law and the surrounding 3D fluid is governed by the slender body Neumann-to-Dirichlet (NtD) map, which treats the filament as a 3D object with constant cross-sectional radius $0<ε\ll1$. This map serves as a mathematical …

Generalized Clapeyron's theorem
Yury Grabovsky, Lev Truskinovsky
https://arxiv.org/abs/2508.12441 https://arxiv.org/pdf/2508.12441

Generalized Clapeyron's theorem
Clapeyron's Theorem in classical linear elasticity provides a way to explicitly express the energy stored in an equilibrium configuration in terms of the work of the forces applied on the boundary. We derive several new integral relations which can be viewed as nonlinear analogs of this classical result, reinterpreting them as rather general statements within Calculus of Variations. In the framework of nonlinear elasticity these relations reflect various partial symmetries of the material respo…

Self-similar collapse with elasticity
Jorge V. Rocha, Diogo L. F. G. Silva
https://arxiv.org/abs/2509.07136 https://arxiv.org/pdf/2509.07136

Self-similar collapse with elasticity
Critical collapse is a well-studied subject for a variety of self-gravitating matter. One of the most intensively examined models is that of perfect fluids, which have been used extensively to describe compact objects such as stars, as well as being of cosmological interest. However, neutron stars are believed to possess an elastic crust, thus departing from a perfect fluid body, and critical collapse with elastic materials is an entirely unexplored topic. In this work, we employ a scale-invari…

Anisotropic shrinkage and finite strains in confined frictional contacts
Marco Ceglie, Cosimo Mandriota, Giuseppe Carbone, Nicola Menga, Antoine Chateauminois
https://arxiv.org/abs/2509.20313

Anisotropic shrinkage and finite strains in confined frictional contacts
We report on an experimental investigation of the interplay between friction, adhesion, contact geometry, and finite strains for smooth frictional contacts between rigid spherical glass probes and flat silicone substrates. Using both bulk and layer substrates under various loading conditions (normal force, radius of the probe), we show that shear-induced anisotropic shrinkage of the adhesive contact area under steady-state sliding is an effect of finite-elasticity conditions and is drastically …

Low Complexity Elasticity Models for Cardiac Digital Twins
Sophia Ohnemus, Kristin Fullerton, Leto L. Riebel, Mary M. Maleckar, Andrew D. McCulloch, Viviane Timmermann, Gabriel Balaban
https://arxiv.org/abs/2508.09772

Low Complexity Elasticity Models for Cardiac Digital Twins
This article introduces CHESRA (Cardiac Hyperelastic Evolutionary Symbolic Regression Algorithm), a novel data-driven framework for automatically designing low-complexity hyperelastic strain energy functions (SEF) for cardiac digital twins. Cardiac digital twins require accurate yet personalized models of heart tissue elasticity, but existing SEF often suffer from high parameter variance, hindering personalization. CHESRA addresses this by using an evolutionary algorithm to derive SEF that bala…

Taming Serverless Cold Starts Through OS Co-Design
Ben Holmes, Baltasar Dinis, Lana Honcharuk, Joshua Fried, Adam Belay
https://arxiv.org/abs/2509.14292 https://

Taming Serverless Cold Starts Through OS Co-Design
Serverless computing promises fine-grained elasticity and operational simplicity, fueling widespread interest from both industry and academia. Yet this promise is undercut by the cold setart problem, where invoking a function after a period of inactivity triggers costly initialization before any work can begin. Even with today's high-speed storage, the prevailing view is that achieving sub-millisecond cold starts requires keeping state resident in memory. This paper challenges that assumption…

On the structure of length sets with maximal elasticity
Doniyor Yazdonov
https://arxiv.org/abs/2508.21383 https://arxiv.org/pdf/2508.21383

On the structure of length sets with maximal elasticity
Let $H$ be a Krull monoid with finite class group $G$ and suppose that each class contains a prime divisor. Then every non-unit $a \in H$ has a factorization into atoms, say $a=u_1 \cdot\ldots \cdot u_k$ where $k$ is the factorization length and $u_1, \ldots, u_k$ are atoms of $H$. The set $\mathsf L (a)$ of all possible factorizaton lengths is the length set of $a$, and $ρ(H) = \sup \{ \max \mathsf L (a)/\min \mathsf L (a) \colon a \in H \}$ is the elasticity of $H$. We study the structure of…

Active Learning and Explainable AI for Multi-Objective Optimization of Spin Coated Polymers
Brendan Young, Brendan Alvey, Andreas Werbrouck, Will Murphy, James Keller, Mattias J. Young, Matthew Maschmann
https://arxiv.org/abs/2509.08988

Active Learning and Explainable AI for Multi-Objective Optimization of Spin Coated Polymers
Spin coating polymer thin films to achieve specific mechanical properties is inherently a multi-objective optimization problem. We present a framework that integrates an active Pareto front learning algorithm (PyePAL) with visualization and explainable AI techniques to optimize processing parameters. PyePAL uses Gaussian process models to predict objective values (hardness and elasticity) from the design variables (spin speed, dilution, and polymer mixture), guiding the adaptive selection of sa…

Mathematical Modeling of Networks in Strength of Materials
Ioannis Dassios
https://arxiv.org/abs/2510.10132 https://arxiv.org/pdf/2510.10132

Mathematical Modeling of Networks in Strength of Materials
We study a material modeled as a network of nodes connected by edges. Using a discrete approach, we build a nonlinear algebraic system that connects applied forces to internal forces and node positions. The model can describe elasticity, plasticity, and possibly cracking. The goal is to solve this system and understand how the material responds. Students are asked to start with a simple triangle example and then apply the method to larger structures. The final aim is to solve the full system an…

Mathematical and numerical study of symmetry and positivity of the tensor-valued spring constant defined from P1-FEM for two- and three-dimensional linear elasticity
Oussama Ounissi, Masato Kimura, Hirofumi Notsu
https://arxiv.org/abs/2509.10335

Mathematical and numerical study of symmetry and positivity of the tensor-valued spring constant defined from P1-FEM for two- and three-dimensional linear elasticity
In this study, we consider a spring-block system that approximates a $d$-dimensional linear elastic body, where $d=2$ or $d=3$. We derive a $d\times d$ matrix as the spring constant using the P1 finite element method with a triangular mesh for the linear elasticity equations. We mathematically analyze the symmetry and positive-definiteness of the spring constant. Even if we assume full symmetry of the elasticity tensor, the symmetry of the matrix obtained as the spring constant is not trivial. …

Towards Energy-Efficient Serverless Computing with Hardware Isolation
Natalie Carl, Tobias Pfandzelter, David Bermbach
https://arxiv.org/abs/2510.08180 https://

Towards Energy-Efficient Serverless Computing with Hardware Isolation
Serverless computing provides just-in-time infrastructure provisioning with rapid elasticity and a finely-grained pricing model. As full control of resource allocation is in the hands of the cloud provider and applications only consume resources when they actually perform work, we believe that serverless computing is uniquely positioned to maximize energy efficiency. However, the focus of current serverless platforms is to run hundreds or thousands of serverless functions from different tenan…

Inferring Dynamic Physical Properties from Video Foundation Models
Guanqi Zhan, Xianzheng Ma, Weidi Xie, Andrew Zisserman
https://arxiv.org/abs/2510.02311 https://

Inferring Dynamic Physical Properties from Video Foundation Models
We study the task of predicting dynamic physical properties from videos. More specifically, we consider physical properties that require temporal information to be inferred: elasticity of a bouncing object, viscosity of a flowing liquid, and dynamic friction of an object sliding on a surface. To this end, we make the following contributions: (i) We collect a new video dataset for each physical property, consisting of synthetic training and testing splits, as well as a real split for real world …

Further testing the validity of generalized heterogeneous-elasticity theory for low-frequency excitations in structural glasses
Walter Schirmacher, Matteo Paoluzzi, Felix Cosmin Mocanu, Dmytro Khomenko, Grzegorz Szamel, Francesco Zamponi, Giancarlo Ruocco
https://arxiv.org/abs/2509.04988

Further testing the validity of generalized heterogeneous-elasticity theory for low-frequency excitations in structural glasses
In a recent paper E. Lerner and E. Bouchbinder, Phys. Rev. E {\bf 111}, L013402 (2025) raised concerns regarding the validity of the theory and the interpretation of the data, presented in our previous study on non-phononic vibrational excitations in glasses, W. Schirmacher {\it et al.}, Nature Comm. {\bf 15}, 3107 (2024). In that work, we presented evidence suggesting that the commonly observed low-frequency regime of the non-phononic vibrational density of states (DoS) is, in fact, high…

Compatible Instability: Gauge Constraints of Elasticity Inherited by Electronic Nematic Criticality
W. Joe Meese, Rafael M. Fernandes
https://arxiv.org/abs/2507.23753 https://…

Compatible Instability: Gauge Constraints of Elasticity Inherited by Electronic Nematic Criticality
Electronic nematicity is widely observed in quantum materials with varying degrees of electronic correlation, manifesting through charge, spin, orbital, or superconducting degrees of freedom. A phenomenological model capable of describing this broad set of systems must also account for nemato-elasticity, by which nematic and elastic degrees of freedom become intertwined. However, being a tensor gauge field theory, elasticity must satisfy the compatibility relations which guarantee the integrabi…

Shell energies derived from three-dimensional isotropic strain-gradient elasticity
C. Balitactac, Y. Canzani, R. S. Hallyburton, J. Mott, C. Rodriguez
https://arxiv.org/abs/2508.05453

Shell energies derived from three-dimensional isotropic strain-gradient elasticity
We derive a class of two-dimensional shell energies for thin elastic bodies exhibiting small-length scale effects modeled via strain-gradient elasticity. Building on the final author's earlier work on plate models, the kinetic and stored surface energies arise as the leading cubic order-in-thickness expressions for three-dimensional kinetic energies with velocity-gradient effects and a broad class of isotropic stored energies, each possessing an intrinsic length scale $\ell$. These include both…

Do We Need Pre-Processing for Deep Learning Based Ultrasound Shear Wave Elastography?
Sarah Grube, S\"oren Gr\"unhagen, Sarah Latus, Michael Meyling, Alexander Schlaefer
https://arxiv.org/abs/2508.03744

Do We Need Pre-Processing for Deep Learning Based Ultrasound Shear Wave Elastography?
Estimating the elasticity of soft tissue can provide useful information for various diagnostic applications. Ultrasound shear wave elastography offers a non-invasive approach. However, its generalizability and standardization across different systems and processing pipelines remain limited. Considering the influence of image processing on ultrasound based diagnostics, recent literature has discussed the impact of different image processing steps on reliable and reproducible elasticity analysis.…

A nonlinear homogenization-based perspective on the soft modes and effective energies of some conformal metamaterials
Xuenan Li, Robert V. Kohn
https://arxiv.org/abs/2509.16907 …

A nonlinear homogenization-based perspective on the soft modes and effective energies of some conformal metamaterials
There is a growing mechanics literature concerning the macroscopic properties of mechanism-based mechanical metamaterials. This amounts mathematically to a homogenization problem involving nonlinear elasticity. A key goal is to identify the "soft modes" of the metamaterial. We achieve this goal using methods from homogenization for some specific 2D examples -- including discrete models of the Rotating Squares metamaterial and the Kagome metamaterial -- whose soft modes are compressive conformal…

The Hu-Zhang element for linear elasticity on curved domains
Wei Chen, Xinyuan Du, Jun Hu
https://arxiv.org/abs/2508.10674 https://arxiv.org/pdf/2508.10674…

The Hu-Zhang element for linear elasticity on curved domains
This paper extends the Hu-Zhang element for linear elasticity problems to curved domains, preserving strong symmetry and H(div)-conformity. The non-polynomial structure of the curved Hu-Zhang element makes it difficult to analyze the stability result, which is overcome by establishing a novel inf-sup condition. Optimal convergence rates are achieved for all variables except the stress $L^2$-error. This suboptimality originates from the fact that the divergence space of the curved Hu-Zhang eleme…

A variational phase-field model for anisotropic fracture accounting for multiple cohesive lengths
Angela Maria Fajardo Lacave, Francesco Vicentini, Fabian Welschinger, Laura De Lorenzis
https://arxiv.org/abs/2510.11309

A variational phase-field model for anisotropic fracture accounting for multiple cohesive lengths
We propose a novel variational phase-field model for fracture in anisotropic materials. The model is specifically designed to allow a more flexible calibration of crack nucleation than existing anisotropic fracture formulations, while avoiding the introduction of multiple damage variables. In addition to the classical components of anisotropic phase-field models based on a single damage variable -- namely, anisotropic elasticity and the extension of the fracture energy density via a second-orde…

Odd elasticity in disordered chiral active materials
Cheng-Tai Lee, Tom Lubensky, Tomer Markovich
https://arxiv.org/abs/2508.04468 https://arxiv.org/pdf/25…

Odd elasticity in disordered chiral active materials
Chiral active materials are abundant in nature, including the cytoskeleton with attached motor proteins, rotary clusters of bacteria flagella, and self-spinning starfish embryos. These materials break both time reversal and mirror-image (parity) symmetries due to injection of torques at the microscale. Recently, it was found that chiral active materials may show a new type of elastic response termed `odd' elasticity. Currently, odd elasticity is understood microscopically only in ordered struct…

The problem of sharp notch in microstructured solids governed by dipolar gradient elasticity
P. A. Gourgiotis, M. D. Sifnaiou, H. G. Georgiadis
https://arxiv.org/abs/2508.03595 …

The problem of sharp notch in microstructured solids governed by dipolar gradient elasticity
In this paper, we deal with the asymptotic problem of a body of infinite extent with a notch (re-entrant corner) under remotely applied plane-strain or anti-plane shear loadings. The problem is formulated within the framework of the Toupin-Mindlin theory of dipolar gradient elasticity. This generalized continuum theory is appropriate to model the response of materials with microstructure. A linear version of the theory results by considering a linear isotropic expression for the strain-energy d…

Derivation of the Reissner-Mindlin model from nonlinear elasticity
Tamara Fastovska, Janusz Ginster, Barbara Zwicknagl
https://arxiv.org/abs/2508.08834 https://

Derivation of the Reissner-Mindlin model from nonlinear elasticity
We discuss how the Reissner-Mindlin plate model can be derived from three-dimensional finite elasticity in terms of $Γ$-convergence. The presence of transverse shear effects in the Reissner-Mindlin model requires to scale different components of the three-dimensional elastic strain differently. A main technical tool is then the combination of rigidity estimates for the deformation and suitably averaged versions.

Some geometrical aspects of gravitational waves using continuum mechanics analogy: State of the art and potential consequences
David Izabel, Yves Remond, Matteo Luca Ruggiero
https://arxiv.org/abs/2508.09279

Some geometrical aspects of gravitational waves using continuum mechanics analogy: State of the art and potential consequences
In this study, the authors employ the analogy between continuum mechanics and general relativity to investigate, from the perspective of elasticity and crystal plasticity, the deformations of space measured by LIGO/VIRGO interferometers during the passage of gravitational waves over Earth. The results of different innovative or existing mechanical models are compared with each other and compared with the observations in the framework of general relativity and Einstein-Cartan theory. Despite lim…

A Parallel Solver with Multiphysics Finite Element Method for Poroelasticity Coupled with Elasticity Model
Zhihao Ge, Chengxin Wang
https://arxiv.org/abs/2509.06673 https://

A Parallel Solver with Multiphysics Finite Element Method for Poroelasticity Coupled with Elasticity Model
In this paper, we propose a parallel solver for solving the quasi-static linear poroelasticity coupled with linear elasticity model in the Lagrange multiplier framework. Firstly, we reformulate the model into a coupling of the nearly incompressible elasticity and an unsteady affection-diffusion equations by setting new variable ``elastic pressure" and ``volumetric fluid content". And we introduce a Lagrange multiplier to guarantee the normal stress continuity on the interface. Then, we give the…

Mo-Re-W Alloys for High Temperature Applications: Phase Stability, Elasticity, and Thermal Property Insights via Multi-Cell Monte Carlo and Machine Learning
Tyler D. Dole\v{z}al, Nick A. Valverde, Jodie Yuwono, Ryan Kemnitz
https://arxiv.org/abs/2507.20085

Mo-Re-W Alloys for High Temperature Applications: Phase Stability, Elasticity, and Thermal Property Insights via Multi-Cell Monte Carlo and Machine Learning
The increasing demand for materials capable of withstanding high temperatures and harsh environments necessitates the discovery of advanced alloys. This study introduces a computational routine to predict solid-state phase stability and calculates elastic constants to determine high temperature viability. With it, machine learning models were trained on 1,014 Mo-Re-W structures to enable a large compilation of elastic and thermal properties over the complete Mo-Re-W compositional domain with ex…

Elasticity and plasticity of epithelial gap closure
Maryam Setoudeh, Pierre A. Haas
https://arxiv.org/abs/2509.05110 https://arxiv.org/pdf/2509.05110

Elasticity and plasticity of epithelial gap closure
Epiboly, during which a tissue closes around the surface of the egg, pervades animal development. This epithelial gap closure involves cell intercalations at the edge of the gap. Here, inspired by serosa closure in the beetle Tribolium, we study the interplay between these plastic cell rearrangements and the elasticity of the tissue in a minimal continuum model of the closure of a circular gap bounded by a contractile actomyosin cable. We discover two different closure mechanisms at the tissue …

Crosslisted article(s) found for math.CA. https://arxiv.org/list/math.CA/new
[1/1]:
- Constitutive properties for isotropic energies in ideal nonlinear elasticity for solid materials:...
Ionel-Dumitrel Ghiba, Robert Martin, Marius Apetrii, Patrizio Neff

A Keynesian Intertemporal Synthesis (KIS) Model: Towards a unified and empirically grounded framework for fiscal policy
Ricardo Alonzo Fern\'andez Salguero
https://arxiv.org/abs/2508.00224

A Keynesian Intertemporal Synthesis (KIS) Model: Towards a unified and empirically grounded framework for fiscal policy
This paper develops a new generation of the Keynesian Intertemporal Synthesis (KIS) Model, a macroeconomic framework designed to reconcile the empirical strengths of the Post-Keynesian (PK) and New Keynesian (NK) traditions. The central innovation of this work is the abandonment of the traditional Cobb-Douglas production function in favor of a Constant Elasticity of Substitution (CES) specification. This modification is directly motivated by the compelling evidence from the meta-analysis by Gec…

Replaced article(s) found for math.NA. https://arxiv.org/list/math.NA/new
[1/1]:
- Multi-phase-field elasticity model based on partial rank-one energy relaxation on pairwise interf...
Mohammad Sarhil, Oleg Shchyglo, Hesham Salama, Dominik Brands, Ingo Steinbach, J\"org Schr\"ode…

A Higher-Order Time Domain Boundary Element Formulation based on Isogeometric Analysis and the Convolution Quadrature Method
Thomas Kramer, Benjamin Marussig, Martin Schanz
https://arxiv.org/abs/2510.06804

A Higher-Order Time Domain Boundary Element Formulation based on Isogeometric Analysis and the Convolution Quadrature Method
An isogeometric boundary element method (BEM) is presented to solve scattering problems in an isotropic homogeneous medium. We consider wave problems governed by the scalar wave equation as in acoustics and the Lamé-Navier equations for elastodynamics considering the theory of linear elasticity. The underlying boundary integral equations imply time-dependent convolution integrals and allow us to determine the sought quantities in the bounded interior or the unbounded exterior after solving for…

Will Compute Bottlenecks Prevent an Intelligence Explosion?
Parker Whitfill, Cheryl Wu
https://arxiv.org/abs/2507.23181 https://arxiv.org/pdf/2507.23181

Will Compute Bottlenecks Prevent an Intelligence Explosion?
The possibility of a rapid, "software-only" intelligence explosion brought on by AI's recursive self-improvement (RSI) is a subject of intense debate within the AI community. This paper presents an economic model and an empirical estimation of the elasticity of substitution between research compute and cognitive labor at frontier AI firms to shed light on the possibility. We construct a novel panel dataset for four leading AI labs (OpenAI, DeepMind, Anthropic, and DeepSeek) from 2014 to 2024 an…

ElasWave: An Elastic-Native System for Scalable Hybrid-Parallel Training
Xueze Kang, Guangyu Xiang, Yuxin Wang, Hao Zhang, Yuchu Fang, Yuhang Zhou, Zhenheng Tang, Youhui Lv, Eliran Maman, Mark Wasserman, Alon Zameret, Zhipeng Bian, Shushu Chen, Zhiyou Yu, Jin Wang, Xiaoyu Wu, Yang Zheng, Chen Tian, Xiaowen Chu
https://arxiv.org/abs/2510.00…

ElasWave: An Elastic-Native System for Scalable Hybrid-Parallel Training
Large-scale LLM pretraining today spans $10^{5}$--$10^{6}$ accelerators, making failures commonplace and elasticity no longer optional. We posit that an elastic-native training system must simultaneously ensure (i) Parameter Consistency, (ii) low Mean Time to Recovery (MTTR), (iii) high post-change Throughput, and (iv) Computation Consistency. This objective set not has never been jointly attained by prior work. To achieve these goals, we present ElasWave, which provides per-step fault toleranc…

Multi-material structural optimization for additive manufacturing based on a phase field approach
Luise Blank, Maximilian Urmann
https://arxiv.org/abs/2508.02206 https://…

Multi-material structural optimization for additive manufacturing based on a phase field approach
A topology optimization problem in a phase field setting is considered to obtain rigid structures, which are resilient to external forces and constructable with additive manufacturing. Hence, large deformations of overhangs due to gravity shall be avoided during construction. The deformations depend on the stage of the construction and are modelled by linear elasticity equations on growing domains with height-dependent stress tensors and forces. Herewith, possible hardening effects can be inclu…

Elasto-viscous regime in coalescence of viscoelastic droplets
Pallavi Katre, Bimalendu Mahapatra, Manaswita Karmakar, Sarang Jagdish, Navin Kumar Chandra, Aloke Kumar
https://arxiv.org/abs/2510.06686

Elasto-viscous regime in coalescence of viscoelastic droplets
We report a regime transition in the coalescence of concentrated polymeric droplets in a pendant-pendant configuration. While Newtonian droplet coalescence has been extensively studied with distinct identification of viscous and inertial regimes, the presence of polymers introduces additional regimes governed by elasticity and molecular relaxation effects. The coalescence process is typically characterized by the neck radius, $R$, of the liquid bridge connecting the two droplets, following a po…

Frequency Response Data-Driven Disturbance Observer Design for Flexible Joint Robots
Deokjin Lee, Junho Song, Alireza Karimi, Sehoon Oh
https://arxiv.org/abs/2507.18979 https://…

Frequency Response Data-Driven Disturbance Observer Design for Flexible Joint Robots
Motion control of flexible joint robots (FJR) is challenged by inherent flexibility and configuration-dependent variations in system dynamics. While disturbance observers (DOB) can enhance system robustness, their performance is often limited by the elasticity of the joints and the variations in system parameters, which leads to a conservative design of the DOB. This paper presents a novel frequency response function (FRF)-based optimization method aimed at improving DOB performance, even in th…

Stress Response of Jammed Solids: Prestress and Screening
Surajit Chakraborty, Jishnu N. Nampoothiri, Subhro Bhattacharjee, Bulbul Chakraborty, Kabir Ramola
https://arxiv.org/abs/2509.14336

Stress Response of Jammed Solids: Prestress and Screening
Unlike classical elasticity, where stresses arise from deformations relative to a stress-free reference configuration, rigidity in amorphous systems is maintained by disordered force networks that generate internal prestress. Previously, we introduced a ''stress-only'' formulation, where mechanical equilibrium resembles Gauss's law in a rank-2 tensor electrostatics with vector charges, and demonstrated that the mechanical response of jammed solids is described by the dielectric response of this…

General expression for the energy and the equation of state for polycrystalline solids
O. Bystrenko (Frantsevich Institute for problems of materials science, Kyiv, Ukraine), B. Ilkiv (Frantsevich Institute for problems of materials science, Kyiv, Ukraine), S. Petrovska (Frantsevich Institute for problems of materials science, Kyiv, Ukraine), T. Bystrenko (Frantsevich Institute for problems of materials science, Kyiv, Ukraine), O. Foia (Frantsevich Institute for problems of materials sc…

General expression for the energy and the equation of state for polycrystalline solids
On the basis of the extended classical elasticity theory, we propose universal semi-empirical analytical expressions for the energy and the equation of state for poly-crystalline solids. The validation of the relations has been made by means of first principle density functional theory simulations with the use of pseudo-potential approach and generalized gradient approximation for the exchange-correlation energy. The calculations performed for a large number of inorganic crystalline compounds w…

Anomalous Critical Behavior of Driven Disordered Systems Beyond the Overdamped Limit
Giuseppe Petrillo, Eduardo Jagla, Eugenio Lippiello, Alberto Rosso
https://arxiv.org/abs/2508.09617

Anomalous Critical Behavior of Driven Disordered Systems Beyond the Overdamped Limit
We investigate the role of relaxation mechanisms in the driven response of elastic disordered interfaces in finite dimensions, focusing on the interplay between dimensionality and interaction range. Through extensive numerical simulations, we identify two distinct dynamical regimes. In two-dimensional systems with long-range interactions, we observe a regime of coexistence between pinned and flowing states. In contrast, for one-dimensional interfaces with long-range elasticity, as well as for s…

Permeability heterogeneity and bulk linear elasticity determine interfacial pattern morphologies during confined, miscible displacements of clay suspensions
Vaibhav Raj Singh Parmar, Ranjini Bandyopadhyay
https://arxiv.org/abs/2509.02335

Permeability heterogeneity and bulk linear elasticity determine interfacial pattern morphologies during confined, miscible displacements of clay suspensions
When a less viscous Newtonian fluid displaces an aging aqueous clay suspension in a confined space, a rich array of interfacial patterns emerges due to a predominantly viscous instability. In the present work, we controlled the mechanical properties of clay suspensions by incorporating additives and studied the interfacial instabilities that resulted when these suspensions were radially displaced by water in a Hele-Shaw cell. When the elasticity of clay was low, the interfacial dynamics exhibit…

The coherent structures of EVP Fluid Flow Past a Circular Cylinder
Adri\'an Corrochano, Kazi Tassawar Iqbal, Saeed Parvar, Soledad Le Clainche, Outi Tammisola
https://arxiv.org/abs/2508.03362

The coherent structures of EVP Fluid Flow Past a Circular Cylinder
This study investigates the impact of elasticity and plasticity on two-dimensional flow past a circular cylinder at Reynolds number $Re = 100$. Ten direct numerical simulations were performed using the Saramito-Herschel-Bulkley model to represent viscoelastic and elastoviscoplastic (EVP) fluids. The flow evolves from a periodic von Kármán vortex street to chaotic-like regimes. Proper Orthogonal Decomposition (POD) and Higher Order Dynamic Mode Decomposition (HODMD) are applied to extract domi…

Uniform estimates of Landau-de Gennes minimizers in the vanishing elasticity limit with line defects
Haotong Fu, Huaijie Wang, Wei Wang
https://arxiv.org/abs/2508.01811 https://…

Uniform estimates of Landau-de Gennes minimizers in the vanishing elasticity limit with line defects
For the Landau-de Gennes functional modeling nematic liquid crystals in dimension three, we prove that, if the energy is bounded by $C(\log\frac{1}{\varepsilon}+1)$, then the sequence of minimizers $\{\mathbf{Q}_{\varepsilon}\}_{\varepsilon\in (0,1)}$ is relatively compact in $W_{\operatorname{loc}}^{1,p}$ for every $1

Some semi-decoupled algorithms with optimal convergence for a four-field linear thermo-poroelastic model
Ziliang Li, Mingchao Cai, Jingzhi Li, Qiang Liu
https://arxiv.org/abs/2508.13109

Some semi-decoupled algorithms with optimal convergence for a four-field linear thermo-poroelastic model
We propose three semi-decoupled algorithms for efficiently solving a four-field thermo-poroelastic model. The first two algorithms adopt a sequential strategy: at the initial time step, all variables are computed simultaneously using a monolithic solver; thereafter, the system is split into a mixed linear elasticity subproblem and a coupled pressure-temperature reaction-diffusion subproblem. The two variants differ in the order in which these subproblems are solved. To further improve computati…

The roles of elasticity and dimension in liquid-gel phase separation
Shichen Wang, Peter D. Olmsted
https://arxiv.org/abs/2510.05415 https://arxiv.org/pdf/…

The roles of elasticity and dimension in liquid-gel phase separation
We compare six elastic models for polymer networks in the context of phase separation within a gel, including a new model that combines the finite extensible Arruda-Boyce model and the slip tube model for entangled chains. We study incompressible uniaxial stretch and compression, and three volume-changing constrained-dimension deformations, in which the material can only deform in the designated dimensions(s) while the constrained direction(s) remain(s) the same. Each model responds differently…

Crosslisted article(s) found for q-bio.TO. https://arxiv.org/list/q-bio.TO/new
[1/1]:
- Elasticity and plasticity of epithelial gap closure
Maryam Setoudeh, Pierre A. Haas

An inherent regularization approach to parameter-free preconditioning for nearly incompressible linear poroelasticity and elasticity
Weizhang Huang, Zhuoran Wang
https://arxiv.org/abs/2507.22334

An inherent regularization approach to parameter-free preconditioning for nearly incompressible linear poroelasticity and elasticity
An inherent regularization strategy and block Schur complement preconditioning are studied for linear poroelasticity problems discretized using the lowest-order weak Galerkin FEM in space and the implicit Euler scheme in time. At each time step, the resulting saddle point system becomes nearly singular in the locking regime, where the solid is nearly incompressible. This near-singularity stems from the leading block, which corresponds to a linear elasticity system. To enable efficient iterative…

Engineering Phonons in Compositionally Complex Carbide Ceramics
Linu Malakkal, Jarin C French, Lanh Trinh, Kaustubh K Bawane, Shuxiang Zhou, Zilong Hua, Lingfeng He, Yongfeng Lu, Bai Cui
https://arxiv.org/abs/2508.04812

Engineering Phonons in Compositionally Complex Carbide Ceramics
In the pursuit of advanced ceramic materials with exceptional irradiation-resistance and high-temperature tolerance for nuclear applications, compositionally complex carbides (CCCs) have emerged as a highly promising class of candidate materials for extreme environments. In such conditions, critical material properties such as thermal stability, elasticity, thermal conductivity and thermodynamics behavior are predominantly influenced by phonons. In CCCs, pronounced cation disorder can lead to s…

Homogenization of rate-independent elastoplastic spring network models with non-local random fields
Simone Hermann
https://arxiv.org/abs/2509.09872 https://

Homogenization of rate-independent elastoplastic spring network models with non-local random fields
We investigate the time-evolution of elastoplastic materials reinforced by randomly distributed long-range interactions. Starting from a rate-independent system on a discrete spring lattice that combines local linearized elasticity, gradient-regularized plasticity and stochastic non-local links modeling stiff fibers, we establish a discrete-to-continuum limit in the energetic formulation. We prove that as the lattice spacing tends to zero, an evolutionary solution of the discrete system converg…

Linear viscoelasticity: Mechanics, analysis and approximation
Michael Ortiz
https://arxiv.org/abs/2509.03485 https://arxiv.org/pdf/2509.03485

Linear viscoelasticity: Mechanics, analysis and approximation
The aim of this review is to highlight the connection between well-established physical and mathematical principles as they pertain to the theory of linear elasticity. We begin by examining the physical foundations of Boltzmann and Volterra's hereditary law formalism, and how those principles restrict the form of the hereditary law. We then turn to questions of material stability and continuous dependence on the stress history within the framework of the Lax-Milgram theorem, which we find to se…

Theory of Electronic Nematic Criticality Constrained by Elastic Compatibility
W. Joe Meese, Rafael M. Fernandes
https://arxiv.org/abs/2507.23754 https://ar…

Theory of Electronic Nematic Criticality Constrained by Elastic Compatibility
The defining property of electronic nematicity -- the spontaneous breaking of rotational symmetry -- implies an unavoidable coupling between the nematic order parameter and elastic strain fields, known as nemato-elasticity. While both quantities are rank-2 tensors, the strain tensor is constrained through the Saint Venant compatibility relations. These three coupled second-order partial differential equations arise from the lattice displacement vector's role as a potential field, and they refle…

A finite element model for thermomechanical stress-strain fields in transversely isotropic strain-limiting materials
Saugata Ghosh, Dambaru Bhatta, S. M. Mallikarjunaiah
https://arxiv.org/abs/2510.05704

A finite element model for thermomechanical stress-strain fields in transversely isotropic strain-limiting materials
This paper presents a comprehensive computational framework for investigating thermo-elastic fracture in transversely isotropic materials, where classical linear elasticity fails to predict physically realistic behavior near stress concentrations. We address the challenge of unphysical strain singularities at crack tips by employing a strain-limiting theory of elasticity. This theory is characterized by an algebraically nonlinear constitutive relationship between stress and strain, which intrin…

High-magnitude, spatially variable, and sustained strain engineering of 2D semiconductors
Boran Kumral, Peter Serles, Pedro Guerra Demingos, Shuo Yang, Da Bin Kim, Dian Yu, Akhil Nair, Akshat Rastogi, Nima Barri, Md Akibul Islam, Jane Howe, Cristina H Amon, Sjoerd Hoogland, Edward H. Sargent, Chandra Veer Singh, Tobin Filleter
https://arxi…

High-magnitude, spatially variable, and sustained strain engineering of 2D semiconductors
Crystalline two-dimensional (2D) semiconductors often combine high elasticity and in-plane strength, making them ideal for strain-induced tuning of electronic characteristics, akin to strategies used in silicon electronics. However, current techniques fall short in achieving high-magnitude (>1%), spatially resolved, and stable strain in these materials. Here, we apply biaxial tensile strain up to 2.2%, with +/-0.12% resolution over micrometre-scale regions in monolayer MoS2 via conformal transf…

Homogenization rates of beam lattices to micropolar continua
Eric T. Chung, Kuang Huang, Changqing Ye
https://arxiv.org/abs/2508.03512 https://arxiv.org/pd…

Homogenization rates of beam lattices to micropolar continua
As the size of a mechanical lattice with beam-modeled edges approaches zero, it undergoes homogenization into a continuum model, which exhibits unusual mechanical properties that deviate from classical Cauchy elasticity, named micropolar elasticity. Typically, the homogenization process is qualitative in the engineering community, lacking quantitative homogenization error estimates. In this paper, we rigorously analyze the homogenization process of a beam lattice to a continuum. Our approach is…

Nonreciprocal constitutive laws for oriented active solids
Bal\'azs N\'emeth, Takuya Kobayashi, Ronojoy Adhikari
https://arxiv.org/abs/2509.11430 https://

Nonreciprocal constitutive laws for oriented active solids
We present an overdamped continuum description of oriented active solids in which interactions respect the symmetries of space but do not obey the principle of action and reaction. Taking position and orientation as kinematic variables, we examine the conservation of the linear and angular momentum variables in an elementary volume. We find that nonreciprocal interactions yield, in addition to the areal stresses and moment stresses of classical elasticity, volumetric forces and torques that act…

Crosslisted article(s) found for math-ph. https://arxiv.org/list/math-ph/new
[1/2]:
- Constitutive properties for isotropic energies in ideal nonlinear elasticity for solid materials:...
Ionel-Dumitrel Ghiba, Robert Martin, Marius Apetrii, Patrizio Neff

Scattering theory for Stokes flow in complex branched structures
Haiyang Wang, Fredrik Fryklund, Samuel Potter, Leslie Greengard
https://arxiv.org/abs/2509.12500 https://…

Scattering theory for Stokes flow in complex branched structures
Slow, viscous flow in branched structures arises in many biological and engineering settings. Direct numerical simulation of flow in such complicated multi-scale geometry, however, is a computationally intensive task. We propose a scattering theory framework that dramatically reduces this cost by decomposing networks into components connected by short straight channels. Exploiting the phenomenon of rapid return to Poiseuille flow (Saint-Venant's principle in the context of elasticity), we compu…

The coupling of mixed and primal finite element methods for the coupled body-plate problem
Jun Hu, Zhen Liu, Rui Ma
https://arxiv.org/abs/2509.10827 https://

The coupling of mixed and primal finite element methods for the coupled body-plate problem
This paper considers the coupled problem of a three-dimensional elastic body and a two-dimensional plate, which are rigidly connected at their interface. The plate consists of a plane elasticity model along the longitudinal direction and a plate bending model with Kirchhoff assumptions along the transverse direction. The Hellinger-Reissner formulation is adopted for the body by introducing the stress as an auxiliary variable, while the primal formulation is employed for the plate. The well-pose…

Impact of elastic inhomogeneity on collective dynamical properties investigated by field theoretical description in real space
Cunyuan Jiang
https://arxiv.org/abs/2510.10928 htt…

Impact of elastic inhomogeneity on collective dynamical properties investigated by field theoretical description in real space
Interpreting the vibrational properties of amorphous solids beyond Debye's theory is challenging due to the presence of inhomogeneity on the mesoscopic scale. In this work, we model this inhomogeneity by real-space fluctuating elasticity with a spatially correlated distribution and calculate the dynamical properties using an exact real-space field theoretical approach. Our results clarify that the excess low-frequency density of states (DOS) originates from a selective scattering effect (strong…

Boson peak in covalent network glasses: Isostaticity and marginal stability
Hideyuki Mizuno, Tatsuya Mori, Giacomo Baldi, Emi Minamitani
https://arxiv.org/abs/2508.20481 https:/…

Boson peak in covalent network glasses: Isostaticity and marginal stability
The boson peak (BP) stands as a key feature in understanding glasses and amorphous materials. It directly underlies their anomalous material properties, including thermal behaviors such as excess specific heat and low thermal conductivity, as well as mechanical characteristics such as nonaffine elasticity and fragile plasticity. Despite its importance, understanding of the BP remains limited in covalent network glasses. The most promising concepts are isostaticity and marginal stability, which …

Fully mixed virtual element schemes for steady-state poroelastic stress-assisted diffusion
Isaac Bermudez, Bryan Gomez-Vargas, Andres E. Rubiano, Ricardo Ruiz-Baier
https://arxiv.org/abs/2510.12307

Fully mixed virtual element schemes for steady-state poroelastic stress-assisted diffusion
We propose a fully mixed virtual element method for the numerical approximation of the coupling between stress-altered diffusion and linear elasticity equations with strong symmetry of total poroelastic stress (using the Hellinger--Reissner principle). A novelty of this work is that we introduce a less restrictive assumption on the stress-assisted diffusion coefficient, requiring an analysis of the perturbed diffusion equation using Banach spaces. The solvability of the continuous and discrete …

Quantitative Gaffney and Korn inequalities
Wadim Gerner
https://arxiv.org/abs/2510.05870 https://arxiv.org/pdf/2510.05870

Quantitative Gaffney and Korn inequalities
We prove a homogeneous, quantitative version of Ehrling's inequality for the function spaces $H^1(Ω)\subset\subset L^2(\partialΩ)$, $H^1(Ω)\hookrightarrow L^2(Ω)$ which reflects geometric properties of a given $C^{1,1}$-domain $Ω\subset\mathbb{R}^n$. We use this result to derive quantitative homogeneous versions of Gaffney's inequality, of relevance in electromagnetism as well as Korn's inequality, of relevance in elasticity theory. The main difference to the corresponding classical re…

The Hidden Wheel-Within
Falko Ziebert, Igor M. Kuli\'c
https://arxiv.org/abs/2510.06830 https://arxiv.org/pdf/2510.06830…

The Hidden Wheel-Within
There is this old, eternal question: Why don't animals have wheels? In this perspective we show that they actually do. And they do so in a physically extraordinary way -- by combining incompatible elasticity, differential geometry and dissipative self-organization. Nature's wheel -- the ``wheel-within'' -- has been mysteriously concealed in plain sight, yet it spins in virtually every slender-body organism: in falling cats, crocodilians spinning to subdue their prey, rolling fruit-fly larvae, c…

Replaced article(s) found for math.AP. https://arxiv.org/list/math.AP/new
[1/2]:
- Strong existence for free discontinuity problems in linear elasticity
Manuel Friedrich, Camille Labourie, Kerrek Stinson

Dynamic micromagnetism a la Ericksen-Leslie, allowing the Einstein-de Haas and Barnett effects
Amit Acharya, Siladitya Pal
https://arxiv.org/abs/2510.04393 https://

Dynamic micromagnetism a la Ericksen-Leslie, allowing the Einstein-de Haas and Barnett effects
A model of dissipative micromagnetics coupled to elasticity is developed, following the procedures of the Ericksen-Leslie theory of nematic liquid crystals allowing for angular momentum due to magnetization. An outcome is the Landau-Lifshitz-Gilbert theory coupled to material spin. A further power-less augmentation to the angular momentum of the theory with classical kinetic energy density is also considered, which allows for plausible approaches to model the Einstein-de Haas and Barnett effect…

Bound-Preserving WENO Schemes for Temple-class systems
Wei Chen, Shumo Cui, Kailiang Wu, Tao Xiong, Baoyue Yu
https://arxiv.org/abs/2510.04123 https://arxi…

Bound-Preserving WENO Schemes for Temple-class systems
This paper explores numerical schemes for Temple-class systems, which are integral to various applications including one-dimensional two-phase flow, elasticity, traffic flow, and sedimentation. Temple-class systems are characterized by conservative equations, with different pressure function expressions leading to specific models such as the Aw-Rascle-Zhang (ARZ) traffic model and the sedimentation model. Our work extends existing studies by introducing a moving mesh approach to address the cha…

Convergence of two-scale expansions for elastic heterogeneous plates
Virginie Ehrlacher, Arthur Leb\'ee, Fr\'ed\'eric Legoll, Adrien Lesage
https://arxiv.org/abs/2507.20874

Convergence of two-scale expansions for elastic heterogeneous plates
The aim of this article is to prove strong convergence results on the difference between the solution to highly oscillatory problems posed in thin domains and its two-scale expansion. We first consider the case of the linear diffusion equation and establish such results in arbitrary dimensions, by using a straightforward adaptation of the classical arguments used for the homogenization of highly oscillatory problems posed on fixed (non-thin) domains. We next consider the linear elasticity probl…

Finite element conformal complexes in three dimensions
Xuehai Huang
https://arxiv.org/abs/2508.01238 https://arxiv.org/pdf/2508.01238

Finite element conformal complexes in three dimensions
This paper extends the Bernstein-Gelfand-Gelfand (BGG) framework to the construction of finite element conformal Hessian complexes and conformal elasticity complexes in three dimensions involving conformal tensors (i.e., symmetric and traceless tensors). These complexes incorporate higher-order differential operators, including the linearized Cotton-York operator, and require conformal tensor spaces with nontrivial smoothness and trace conditions. A novel application of the discrete BGG framewo…

Finite Element Complexes with Traces Structures: A unified framework for cohomology and bounded interpolation
Jun Hu, Yizhou Liang, Ting Lin
https://arxiv.org/abs/2509.23788 htt…

Finite Element Complexes with Traces Structures: A unified framework for cohomology and bounded interpolation
This paper considers the cohomology and bounded interpolation of nonstandard finite element complexes, e.g. Stokes, Hessian, Elasticity, divdiv. Compared to the standard finite element exterior calculus, the main challenge is the existence of extra smoothness. This paper provides a unified framework for finite element complexes with extra smoothness. The trace structure is introduced to derive the bubble complexes in different dimensions (vertices, edges, faces). It is shown that if the bubble …

Finite element discretizations of bending plates with prestrained microstructure
Klaus B\"ohnlein, Stefan Neukamm, Oliver Sander
https://arxiv.org/abs/2509.26438 https://…

Finite element discretizations of bending plates with prestrained microstructure
We investigate a finite element discretization of an elastic bending-plate model with an effective prestrain. The model has been obtained via homogenization and dimension reduction by Bönlein at al. (2023). Its energy functional is the $Γ$-limit of a three-dimensional nonlinear microstructured elasticity functional. In the derived effective model, the microstructure is incorporated as a local corrector problem, a system of linear elliptic partial differential equations posed on a three-dimens…

Stabilizing the singularity swap quadrature for near-singular line integrals
David Krantz, Alex H. Barnett, Anna-Karin Tornberg
https://arxiv.org/abs/2509.23881 https://

Stabilizing the singularity swap quadrature for near-singular line integrals
Singularity swap quadrature (SSQ) is an effective method for the evaluation at nearby targets of potentials due to densities on curves in three dimensions. While highly accurate in most settings, it is known to suffer from catastrophic cancellation when the kernel exhibits both near-vanishing numerators and strong singularities, as arises with scalar double layer potentials or tensorial kernels in Stokes flow or linear elasticity. This precision loss turns out to be tied to the interpolation ba…