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Zhiwen Zhao

Publications and source records attributed to Zhiwen Zhao.

At least 37 records · Page 2Linked to original sources
arXiv2023

The Solenoidal Large Intensity Device (SoLID) for JLab 12 GeV

The Solenoidal Large Intensity Device (SoLID) is a new experimental apparatus planned for Hall A at the Thomas Jefferson National Accelerator Facility (JLab). SoLID will combine large angular and momentum acceptance with the capability to handle very high data rates at high luminosity. With a slate of approved high-impact physics experiments, SoLID will push JLab to a new limit at the QCD intensity frontier that will exploit the full potential of its 12 GeV electron beam. In this paper, we present an overview of the rich physics program that can be realized with SoLID, which encompasses the tomography of the nucleon in 3-D momentum space from Semi-Inclusive Deep Inelastic Scattering (SIDIS), expanding the phase space in the search for new physics and novel hadronic effects in parity-violating DIS (PVDIS), a precision measurement of $J/ψ$ production at threshold that probes the gluon field and its contribution to the proton mass, tomography of the nucleon in combined coordinate and momentum space with deep exclusive reactions, and more. To meet the challenging requirements, the design of SoLID described here takes full advantage of recent progress in detector, data acquisition and computing technologies. In addition, we outline potential experiments beyond the currently approved program and discuss the physics that could be explored should upgrades of CEBAF become a reality in the future.

nucl-ex↗
arXiv2022

Local regularity for nonlinear elliptic and parabolic equations with anisotropic weights

The main purpose of this paper is to capture the asymptotic behavior for solutions to a class of nonlinear elliptic and parabolic equations with the anisotropic weights consisting of two power-type weights of different dimensions near the degenerate or singular point, especially covering the weighted $p$-Laplace equations and weighted fast diffusion equations. As a consequence, we also establish the local Hölder estimates for their solutions in the presence of single power-type weights.

math.AP↗
arXiv2022

Gradient estimates for the insulated conductivity problem with inclusions of the general $m$-convex shapes

In this paper, the insulated conductivity model with two touching or close-to-touching inclusions is considered in $\mathbb{R}^{d}$ with $d\geq3$. We establish the pointwise upper bounds on the gradient of the solution for the generalized $m$-convex inclusions under these two cases with $m\geq2$, which show that the singular behavior of the gradient in the thin gap between two inclusions is described by the first non-zero eigenvalue of an elliptic operator of divergence form on $\mathbb{S}^{d-2}$. Finally, the sharpness of the estimates is also proved for two touching axisymmetric insulators, especially including curvilinear cubes.

math.AP↗
arXiv2022

Exact solutions for the insulated and perfect conductivity problems with concentric balls

The insulated and perfect conductivity problems arising from high-contrast composite materials are considered in all dimensions. The solution and its gradient, respectively, represent the electric potential and field. The novelty of this paper lies in finding exact solutions for the insulated and perfect conductivity problems with concentric balls. Our results show that there appears no electric field concentration for the insulated conductivity problem, while the electric field for the perfect conductivity problem exhibits sharp singularity with respect to the small distance between interfacial boundaries of the interior and exterior balls. This discrepancy reveals that concentric balls is the optimal structure of insulated composites, but not for superconducting composites.

math.AP↗
arXiv2022

Asymptotic analysis for hydrodynamic force acting on stiff particles

A three-dimensional mathematical model of a viscous incompressible fluid with two stiff particles is investigated in the near-contact regime. When one of the particles approaches the other motionless particle with prescribed translational and angular velocities, there always appears blow-up of hydrodynamic force exerted on the moving particle. In this paper, we construct explicit singular functions corresponding to the fluid velocity and pressure to establish precise asymptotic formulas for hydrodynamic force with respect to small interparticle distance, which show that its largest singularity is determined by squeeze motion between two particles. Finally, the primal-dual variational principle is employed to give a complete justification for these asymptotics.

math.AP↗
arXiv2022

Gradient estimates for the insulated conductivity problem: the case of $m$-convex inclusions

We consider an insulated conductivity model with two neighboring inclusions of $m$-convex shapes in $\mathbb{R}^{d}$ when $m\geq2$ and $d\geq3$. We establish the pointwise gradient estimates for the insulated conductivity problem and capture the gradient blow-up rate of order $\varepsilon^{-1/m+β}$ with $β=[-(d+m-3)+\sqrt{(d+m-3)^{2}+4(d-2)}]/(2m)\in(0,1/m)$, as the distance $\varepsilon$ between these two insulators tends to zero. In particular, the optimality of the blow-up rate is also demonstrated for a class of axisymmetric $m$-convex inclusions.

math.AP↗
arXiv2022

Stress concentration factors for the Stokes flow with two nearly touching rigid particles

In this paper, a mathematical model of two adjacent rigid particles immersed into a viscous incompressible fluid is considered. The main feature of the flow is that the Cauchy stress tensor consisting of the strain tensor and the pressure will appear blow-up as the distance between these two particles tends to zero. For the purpose of making clear this high concentration, a family of unified stress concentration factors are precisely captured in all dimensions, which determine whether the Cauchy stress tensor will blow up or not. As a direct application, we establish optimal gradient estimates and asymptotics of the Cauchy stress tensor for Stokes flow, which indicate that its maximal singularity comes from the pressure.

math.AP↗
arXiv2022

Stress concentration factors for the Lamé system arising from composites

For two neighbouring stiff inclusions, the stress, which is the gradient of a solution to the Lamé system of linear elasticity, may exhibit singular behavior as the distance between these two inclusions becomes arbitrarily small. In this paper, a family of stress concentration factors, which determine whether the stress will blow up or not, are accurately constructed in the presence of the generalized $m$-convex inclusions in all dimensions. We then use these stress concentration factors to establish the optimal upper and lower bounds on the stress blow-up rates in any dimension and meanwhile give a precise asymptotic expression of the stress concentration for interfacial boundaries of inclusions with different principal curvatures in dimension three. Finally, the corresponding results for the perfect conductivity problem are also presented.

math.AP↗
arXiv2022

Singular analysis of the stress concentration in the narrow regions between the inclusions and the matrix boundary

We consider the Lamé system arising from high-contrast composite materials whose inclusions (fibers) are nearly touching the matrix boundary. The stress, which is the gradient of the solution, always concentrates highly in the narrow regions between the inclusions and the external boundary. This paper aims to provide a complete characterization in terms of the singularities of the stress concentration by accurately capturing all the blow-up factor matrices and making clear the dependence on the Lamé constants and the curvature parameters of geometry. Moreover, the precise asymptotic expansions of the stress concentration are also presented in the presence of a strictly convex inclusion close to touching the external boundary for the convenience of application.

math.AP↗
arXiv2022

Asymptotic analysis for elliptic systems in a narrow region

This paper is concerned with investigating the asymptotic behavior of the gradients of solutions to a class of elliptic systems with general boundary data, especially covering the Lamé systems, in a narrow region. The novelty of this paper lies in finding the correction term to improve the previous gradient estimates to be a precise asymptotic formula. Through this justification, we capture all singular terms and thus give a fairly sharp characterization in terms of the singularities of the gradients.

math.AP↗
arXiv2021

Singularities of the stress concentration in the presence of $C^{1,α}$-inclusions with core-shell geometry

In high-contrast composites, if an inclusion is in close proximity to the matrix boundary, then the stress, which is represented by the gradient of a solution to the Lamé systems of linear elasticity, may exhibits the singularities with respect to the distance $\varepsilon$ between them. In this paper, we establish the asymptotic formulas of the stress concentration for core-shell geometry with $C^{1,α}$ boundaries in all dimensions by precisely capturing all the blow-up factor matrices, as the distance $\varepsilon$ between interfacial boundaries of a core and a surrounding shell goes to zero. Further, a direct application of these blow-up factor matrices gives the optimal gradient estimates.

math.AP↗
arXiv2021

Gradient asymptotics of solutions to the Lamé systems in the presence of two nearly touching $C^{1,γ}$-inclusions in all dimensions

In this paper, we establish the asymptotic expressions for the gradient of a solution to the Lamé systems with partially infinity coefficients as two rigid $C^{1,γ}$-inclusions are very close but not touching. The novelty of these asymptotics, which improve and make complete the previous results of Chen-Li (JFA 2021), lies in that they show the optimality of the gradient blow-up rate in dimensions greater than two.

math.AP↗
arXiv2021

Asymptotic analysis of the stress concentration between two adjacent stiff inclusions in all dimensions

In the region between two closely located stiff inclusions, the stress, which is the gradient of a solution to the Lamé system with partially infinite coefficients, may become arbitrarily large as the distance between interfacial boundaries of inclusions tends to zero. The primary aim of this paper is to give a sharp description in terms of the asymptotic behavior of the stress concentration, as the distance between interfacial boundaries of inclusions goes to zero. For that purpose we capture all the blow-up factor matrices, whose elements comprise of some certain integrals of the solutions to the case when two inclusions are touching. Then we are able to establish the asymptotic formulas of the stress concentration in the presence of two close-to-touching $m$-convex inclusions in all dimensions. Furthermore, an example of curvilinear squares with rounded-off angles is also presented for future application in numerical computations and simulations.

math.AP↗
arXiv2020

Blow-up analysis of hydrodynamic forces exerted on two adjacent $M$-convex particles

In a viscous incompressible fluid, the hydrodynamic forces acting on two close-to-touch rigid particles in relative motion always become arbitrarily large, as the interparticle distance parameter $\varepsilon$ goes to zero. In this paper we obtain asymptotic formulas of the hydrodynamic forces and torque in $2\mathrm{D}$ model and establish the optimal upper and lower bound estimates in $3\mathrm{D}$, which sharply characterizes the singular behavior of hydrodynamic forces. These results reveal the effect of the relative convexity between particles, denoted by index $m$, on the blow-up rates of hydrodynamic forces. Further, when $m$ degenerates to infinity, we consider the particles with partially flat boundary and capture that the largest blow-up rate of the hydrodynamic forces is $\varepsilon^{-3}$ both in 2D and 3D. We also clarify the singularities arising from linear motion and rotational motion, and find that the largest blow-up rate induced by rotation appears in all directions of the forces.

math.AP↗
arXiv2020

Asymptotics for the electric field when $M$-convex inclusions are close to the matrix boundary

In the perfect conductivity problem of composites, the electric field may become arbitrarily large as $\varepsilon$, the distance between the inclusions and the matrix boundary, tends to zero. The main contribution of this paper lies in developing a clear and concise procedure to establish a boundary asymptotic formula of the concentration for perfect conductors with arbitrary shape in all dimensions, which explicitly exhibits the singularities of the blow-up factor $Q[φ]$ introduced in [29] by picking the boundary data $φ$ of $k$-order growth. In particular, the smoothness of inclusions required for at least $C^{3,1}$ in [27] is weakened to $C^{2,α}$, $0<α<1$ here.

math.AP↗
arXiv2019

Boundary blow-up analysis of gradient estimates for Lamé systems in the presence of $M$-convex hard inclusions

In high-contrast elastic composites, it is vitally important to investigate the stress concentration from an engineering point of view. The purpose of this paper is to show that the blowup rate of the stress depends not only on the shape of the inclusions, but also on the given boundary data, when hard inclusions are close to matrix boundary. First, when the boundary of inclusion is partially relatively parallel to that of matrix, we establish the gradient estimates for Lamé systems with partially infinite coefficients and find that they are bounded for some boundary data $φ$ while some $φ$ will increase the blow-up rate. In order to identify such novel blowup phenomenon, we further consider the general $m$-convex inclusion cases and uncover the dependence of blow-up rate on the inclusion's convexity $m$ and the boundary data's order of growth $k$ in all dimensions. In particular, the sharpness of these blow-up rates is also presented for some prescribed boundary data.

math.AP↗
arXiv2018

Search for a hidden strange baryon-meson bound state from $ϕ$ production in a nuclear medium

We investigate the hidden strange light baryon-meson system. With the resonating-group method, two bound states, $η'-N$ and $ϕ-N$, are found in the quark delocalization color screening model. Focusing on the $ϕ-N$ bound state around 1950\,MeV, we obtain the total decay width of about 4\,MeV by calculating the phase shifts in the resonance scattering processes. To study the feasibility of an experimental search for the $ϕ-N$ bound state, we perform a Monte Carlo simulation of the bound state production with an electron beam and a gold target. In the simulation, we use the CLAS12 detector with the Forward Tagger and the BONUS12 detector in Hall B at Jefferson Lab. Both the signal and the background channels are estimated. We demonstrate that the signal events can be separated from the background with some momentum cuts. Therefore it is feasible to experimentally search for the $ϕ-N$ bound state through the near threshold $ϕ$ meson production from heavy nuclei.

hep-ph↗