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Jianfeng Zhao

Publications and source records attributed to Jianfeng Zhao.

11 recordsLinked to original sources
arXiv2026

Prandtl--Batchelor and flux-expulsion selection for steady MHD flows in a disk

We study the simultaneous vanishing-viscosity and vanishing-resistivity limit of steady incompressible MHD flows in a disk. The boundary velocity is a small nonaxisymmetric perturbation of a rigid rotation with mean angular speed \(\alpha\), while the prescribed tangential magnetic trace has mean \(\beta\). Assuming \(\alpha\neq0\) and the non-Alfv\'enic condition \(|\alpha|\neq|\beta|\), we construct solutions converging on compact interior subdisks to a rigidly rotating ideal MHD core with constant vorticity and out-of-plane current density. A new MHD--Wood law determines the two core rotations from the boundary data: the velocity core is selected by a coupled kinetic--magnetic balance, whereas the magnetic core is fixed by the imposed mean circulation. Consequently, zero circulation gives complete interior magnetic expulsion, while nonzero circulation leaves a uniform magnetic rotation after the nonaxisymmetric modes are confined to a thin boundary layer. This provides a fully coupled realization of Prandtl--Batchelor selection and flux expulsion; unlike classical kinematic models, the magnetic field actively changes the flow and need not be weak. The proof combines a non-Alfv\'enic coercive theory for a periodic MHD boundary layer, global matching of the two fields, and a coupled stability estimate adapted to the magnetic boundary condition. A separate conditional rigidity argument, using exact viscous identities and local convergence but no interior asymptotic expansion, explains the same core structure for a broader single-eddy family.

math.AP↗
arXiv2025

Strengthening and toughening mechanisms in heterostructured laminates revealed by a phase field-enhanced crystal plasticity simulation

Heterostructured (HS) materials exhibit excellent mechanical properties, combining high strength and significant ductility. Hetero-deformation-induced (HDI) hardening and strain de-localization are key to their strength-ductility synergy. However, existing models often fall short in addressing these aspects. In this work, a coupled framework integrating strain gradient crystal plasticity and phase field damage models is developed. The interface dominated HDI hardening in HS laminates is handled by introducing a heterogeneity coefficient into the back stress. The phase field model accounts for defect energy-driven damage and accurately represents the materials ductile damage behavior by accounting for effects of microstructure on crack initiation and propagation. Simulation results on HS laminates align well with experimental results and reflect the distribution of geometrically necessary dislocations and back stresses at interfaces between regions with dissimilar microstructure. Crack initiation and propagation are accurately described, providing valuable insights into fracture behavior. The model can predict how strength and ductility change upon variations of the HS laminate microstructure, thus providing an essential tool for microstructure optimization. This work enhances the understanding of deformation mechanisms in HS laminates and provides valuable insights for design and optimization of this class of materials.

cond-mat.mtrl-sci↗
arXiv2025

Vanishing viscosity limit of the 2D stationary Navier-Stokes equations outside a rotating disc and its application

In this paper, we establish the vanishing viscosity limit result of the 2D stationary Navier-Stokes equations outside a rotating disc. On the boundary of the disc, the fluid is subjected to a small perturbation of a non zero rotation of rigid body. While at the spacial infinity, the fluid stays at rest. Due to the Prandtl-Batchelor theory, the limiting Euler solution is chosen to be the rotation flow $\frac{A}{r} e_θ$ for some suitable constant $A$, which is determined by the Batchelor-Wood formula. When the viscosity approaches to zero, we will construct a solution to the 2D Navier-Stokes equations by using higher order asymptotic approximation and show the validity of the boundary layer expansion. Also the asymptotic behavior of the solution at spacial infinity is obtained. Our result partially answers one of the open problems (Problem 11b) raised by V. I. Yudovich in [Eleven great problems of mathematical hydrodynamics, Mosc. Math. J. 3 (2003), no. 2, 711--737]. As an application, we can show an existence result to the 2D stationary Navier-Stokes equations with fixed viscosity outside a disc when the fluid is subjected to a large perturbation of a fast rotation of rigid body at the boundary.

math.AP↗
arXiv2025

A level-set structural approach for multi-physics joint inversion using full-waveform and gravity data

This paper presents a level-set based structural approach for the joint inversion of full-waveform and gravity data. The joint inversion aims to integrate the strengths of full-waveform inversion for high resolution imaging and gravity inversion for detecting density contrasts over extensive regions. Although common studies typically only observe full-waveform inversion assisting gravity inversion, we propose three key points that enable gravity data to complement full-waveform data in the joint inversion. (i) Based on the well-posedness theorem, we consider a volume mass distribution where the density-contrast value is imposed as a priori information, ensuring that the gravity data provide meaningful information. (ii) We utilize a level-set formulation to characterize the shared interface of wave velocity and density functions, connecting multi-physics datasets via the structural similarity of their inversion parameters. (iii) We develop a balanced and decaying weight to regulate the influence of multi-physics datasets during joint inversion. This weight comprises a balanced part that accounts for the differing scales of full-waveform and gravity data, and a decaying part designed to effectively utilize the features and advantages of each dataset.

physics.geo-ph↗
arXiv2025

T-CACE: A Time-Conditioned Autoregressive Contrast Enhancement Multi-Task Framework for Contrast-Free Liver MRI Synthesis, Segmentation, and Diagnosis

Magnetic resonance imaging (MRI) is a leading modality for the diagnosis of liver cancer, significantly improving the classification of the lesion and patient outcomes. However, traditional MRI faces challenges including risks from contrast agent (CA) administration, time-consuming manual assessment, and limited annotated datasets. To address these limitations, we propose a Time-Conditioned Autoregressive Contrast Enhancement (T-CACE) framework for synthesizing multi-phase contrast-enhanced MRI (CEMRI) directly from non-contrast MRI (NCMRI). T-CACE introduces three core innovations: a conditional token encoding (CTE) mechanism that unifies anatomical priors and temporal phase information into latent representations; and a dynamic time-aware attention mask (DTAM) that adaptively modulates inter-phase information flow using a Gaussian-decayed attention mechanism, ensuring smooth and physiologically plausible transitions across phases. Furthermore, a constraint for temporal classification consistency (TCC) aligns the lesion classification output with the evolution of the physiological signal, further enhancing diagnostic reliability. Extensive experiments on two independent liver MRI datasets demonstrate that T-CACE outperforms state-of-the-art methods in image synthesis, segmentation, and lesion classification. This framework offers a clinically relevant and efficient alternative to traditional contrast-enhanced imaging, improving safety, diagnostic efficiency, and reliability for the assessment of liver lesion. The implementation of T-CACE is publicly available at: https://github.com/xiaojiao929/T-CACE.

eess.IV↗
arXiv2024

Prandtl-Batchelor flows with a point vortex on a disk

We study steady two-dimensional incompressible Navier-Stokes flow in the unit disk in a high Reynolds number regime, driven by a localized central forcing and a nearly rigid rotating boundary. The forcing models a compact source of circulation that sustains a vortex core in a viscous flow. For sufficiently small viscosity and boundary perturbation, we construct a very weak steady solution on the whole disk and identify its inviscid limit: a point vortex embedded in a constant vorticity background and joined to the boundary motion by a thin boundary layer. The background vorticity is selected by the Batchelor-Wood formula. The singular core introduces non-coercive interactions in the linearized problem that are absent for regular Prandtl-Batchelor flows. To overcome this difficulty, we map the punctured disk to a semi-infinite cylinder by a logarithmic radial transformation and develop a Fourier-mode analysis that isolates the delicate first Fourier mode, yielding uniform stability and vorticity estimates in the presence of the point-vortex singularity.

math.AP↗
arXiv2024

Vanishing viscosity limit of the Navier-Stokes equations in a horizontally periodic strip

In this paper, we establish vanishing viscosity limit of the 2D Navier-Stokes equations in a horizontally periodic strip. On the vertical direction, the horizontal component of the velocity is subjected to two different types of boundary conditions: at the lower boundary, we give the degenerate zero boundary condition, while at the upper boundary, a small smooth perturbation of non-zero constant is prescribed. Due to this different boundary condition setting, the boundary layer effects are different near the lower and upper boundaries, which result in different thickness of boundary layer and different leading order boundary layer equations. We will construct an approximate solution to this 2D Navier-Stokes equations by using higher order asymptotic approximation and show the validity of the boundary layer expansion. The leading order of the Euler solution is the Couette flow $(Ay,0)$ for some suitable constant $A$, which is determined by using the principle of the Prandtl-Batchelor theory.

math.AP↗
arXiv2022

A higher speed type II blow-up for the 4-d Fujita equation

This paper is concerned with blow-up solutions of the 4-dimensional energy critical heat equation $u_t=Δu + u^3$. Our main result is to show that the existence of type II blowup solutions, and $\|u(\cdot,t)\|_\infty\sim(T-t)^{-k}|ln(T-t)|^{\frac{2k}{2k-1}}, (k=1,2,3\cdots)$.The inner-outer gluing method has been employed.

math.AP↗
arXiv2022

United adversarial learning for liver tumor segmentation and detection of multi-modality non-contrast MRI

Simultaneous segmentation and detection of liver tumors (hemangioma and hepatocellular carcinoma (HCC)) by using multi-modality non-contrast magnetic resonance imaging (NCMRI) are crucial for the clinical diagnosis. However, it is still a challenging task due to: (1) the HCC information on NCMRI is invisible or insufficient makes extraction of liver tumors feature difficult; (2) diverse imaging characteristics in multi-modality NCMRI causes feature fusion and selection difficult; (3) no specific information between hemangioma and HCC on NCMRI cause liver tumors detection difficult. In this study, we propose a united adversarial learning framework (UAL) for simultaneous liver tumors segmentation and detection using multi-modality NCMRI. The UAL first utilizes a multi-view aware encoder to extract multi-modality NCMRI information for liver tumor segmentation and detection. In this encoder, a novel edge dissimilarity feature pyramid module is designed to facilitate the complementary multi-modality feature extraction. Second, the newly designed fusion and selection channel is used to fuse the multi-modality feature and make the decision of the feature selection. Then, the proposed mechanism of coordinate sharing with padding integrates the multi-task of segmentation and detection so that it enables multi-task to perform united adversarial learning in one discriminator. Lastly, an innovative multi-phase radiomics guided discriminator exploits the clear and specific tumor information to improve the multi-task performance via the adversarial learning strategy. The UAL is validated in corresponding multi-modality NCMRI (i.e. T1FS pre-contrast MRI, T2FS MRI, and DWI) and three phases contrast-enhanced MRI of 255 clinical subjects. The experiments show that UAL has great potential in the clinical diagnosis of liver tumors.

eess.IV↗
arXiv2020

Constitutive modeling of the tension-compression behavior of gradient structured materials

Gradient structured (GS) metals processed by severe plastic deformation techniques can be designed to achieve simultaneously high strength and high ductility. Significant kinematic hardening is key to their excellent strain hardening capacity which results in a favorable strength-ductility combination. Unfortunately, no constitutive model has been established to simulate and analyze the characteristic kinematic hardening behavior of GS metal to understand the relationship between their microstructure and macroscopic response. In this work, we developed a deformation-mechanismbased strain gradient plasticity model considering the plasticity heterogeneities from the grain to the sample scale. A back stress model, which accounts for the dependency of dislocation pile-ups on grain size, is established to describe the cyclic deformation properties of GS materials. The established model unified the geometrically necessary dislocations accommodating internal plasticity heterogeneities, the resulting back stress and reversible dislocations during reverse loading into a strain gradient plasticity framework, without introducing excessive numbers of independent material parameters. A finite element implementation of the model quantitatively predicts the uniaxial tensile and tensile-compressive responses of a GS copper bar as well as of a reference sample with homogeneous grain size. It is found that GS copper exhibits enhanced kinematic hardening which results mainly from fine grains in the GS layer and contributes to the considerable ductility of the GS material. The model allows to investigate the mechanical response and optimize the properties of materials with various types of spatially heterogeneous grain microstructures.

cond-mat.mtrl-sci↗