arXiv subjects

Yu Mei

Publications and source records attributed to Yu Mei.

41 records · Page 3Linked to original sources

arXiv2019

Convergence of the Ginzburg-Landau approximation for the Ericksen-Leslie system

We establish the local well-posedness of the general Ericksen-Leslie system in liquid crystals with the initial velocity and director field in $H^1 \times H_b^2$. In particular, we prove that the solutions of the Ginzburg-Landau approximation system converge smoothly to the solution of the Ericksen-Leslie system for any $t \in (0,T^\ast)$ with a maximal existence time $T^\ast$ of the Ericksen- Leslie system.

math.AP↗

arXiv2017

Well-posedness of the Ericksen-Leslie System for the Oseen-Frank Model in L^3_{uloc}(\mathbb{R}^3)

We investigate the Ericksen-Leslie system for the Oseen-Frank model with unequal Frank elastic constants in $\mathbb{R}^3$. To generalize the result of Hineman-Wang \cite{HW}, we prove existence of solutions to the Ericksen-Leslie system with initial data having small $L^3_{uloc}$-norm. In particular, we use a new idea to obtain a local $L^3$-estimate through interpolation inequalities and a covering argument, which is different from the one in \cite{HW}. Moreover, for uniqueness of solutions, we find a new way to remove the restriction on the Frank elastic constants by using the rotation invariant property of the Oseen-Frank density. We combine this with a method of Li-Titi-Xin \cite{LTX} to prove uniqueness of the $L^3_{uloc}$-solutions of the Ericksen-Leslie system assuming that the initial data has a finite energy.

math.AP↗

arXiv2015

Lensfree Spectral Light-field Fusion Microscopy for Contrast- and Resolution-enhanced Imaging of Biological Specimens

A lensfree spectral light-field fusion microscopy (LSLFM) system is presented for enabling contrast- and resolution-enhanced imaging of biological specimens. LSLFM consists of a pulsed multispectral lensfree microscope for capturing interferometric light-field encodings at various wavelengths, and Bayesian-based fusion to reconstruct a fused object light-field from the encodings. By fusing unique object detail information captured at different wavelengths, LSLFM can achieve improved resolution, contrast, and signal-to-noise ratio (SNR) over a single-channel lensfree microscopy system. A five-channel LSLFM system was developed and quantitatively evaluated to validate the design. Experimental results demonstrated that the LSLFM system provided SNR improvements of 6-12 dB, as well as a six-fold improvement in the dispersion index (DI), over that achieved using a single-channel, resolution-enhancing lensfree deconvolution microscopy system or its multi-wavelength counterpart. Furthermore, the LSLFM system achieved an increase in numerical aperture (NA) of ~16% over a single-channel resolution-enhancing lensfree deconvolution microscopy system at the highest-resolution wavelength used in the study. Samples of Staurastrum paradoxum, a waterborne algae, and human corneal epithelial cells were imaged using the system to illustrate its potential for enhanced imaging of biological specimens.

physics.optics↗

arXiv2015

Uniform regularity for the free surface compressible Navier-Stokes equations with or without surface tension

In this paper, we investigate the uniform regularity of solutions to the 3-dimensional isentropic compressible Navier-Stokes system with free surfaces and study the corresponding asymptotic limits of such solutions to that of the compressible Euler system for vanishing viscosity and surface tension. It is shown that there exists an unique strong solution to the free boundary problem for the compressible Navier-Stokes system in a finite time interval which is independent of the viscosity and the surface tension. The solution is uniform bounded both in $W^{1,\infty}$ and a conormal Sobolev space. It is also shown that the boundary layer for the density is weaker than the one for the velocity field. Based on such uniform estimates, the asymptotic limits to the free boundary problem for the ideal compressible Euler system with or without surface tension as both the viscosity and the surface tension tend to zero, are established by a strong convergence argument.

math.AP↗

arXiv2014

Global Classical Solutions to the 2D Compressible MHD Equations with Large Data and Vacuum

In this paper, we study the global well-posedness of classical solutions to the 2D compressible MHD equations with large initial data and vacuum. With the assumption $μ=const.$ and $λ=ρ^β,~β>1$ (Vaǐgant-Kazhikhov Model) for the viscosity coefficients, the global existence and uniqueness of classical solutions to the initial value problem is established on the torus $\mathbb{T}^2$ and the whole space $\mathbb{R}^2$ (with vacuum or non-vacuum far fields). These results generalize the previous ones for the Vaǐgant-Kazhikhov model of compressible Navier-Stokes.

math.AP↗