Global Solvability,Pattern Formation and Stability to a Chemotaxis-haptotaxis Model with Porous Medium Diffusion

In this paper,we deal with the following chemotaxis-haptotaxis system modeling cancer invasion with nonlinear diffusion,ut=Δum−χ∇·(u∇v)−ξ∇·(u∇ω)+μu(1−u−ω),inΩ×R^(+),vt−Δv+v=u,inΩ×R+,ωt=−vω,inΩ×R+,whereΩ⊂R^(N)is a bounded domain.We first supplement the results of global existence and uniform boundedness of solutions for the case m=2N N+2.Then for any m>0 and any spatial dimension,we consider the stability of equilibrium,and find that the chemotaxis has a destabilizing effect,that is for the ODEs,or the diffusion-ODE system without chemotaxis,the solutions tend to a linearly stable uniform steady state(1,1,0).When the chemotactic coefficientχis large,the equilibrium(1,1,0)become unstable.Then we study the existence of nontrivial stationary solutions via bifurcation techniques withχbeing the bifurcation parameter,and obtain nonhomogeneous patterns.At last,we also investigate the stability of these bifurcation solutions.

Spectral selective fluorescence molecular imaging with volume holographic imaging system

A compact volume holographic imaging(VHI)method that can detect fluorescence objects located in diffusive medium in spectral selective imaging manner is presented.The enlargement of lateralfield of view of the VHI system is realized by using broadband illumination and demagnification optics.Each target spectrum of°uorescence emitting from a di®usive medium is probed by tuning the inclination angle of the transmission volume holographic grating(VHG).With the use of the single transmission VHG,fluorescence images with different spectrum are obtained sequentially and precise three-dimensional(3D)information of deep fluorescent objects located in a diffusive medium can be reconstructed from these images.The results of phantom experiments demonstrate that two fluorescent objects with a sub-millimeter distance can be resolved by spectral selective imaging.

Ionization state of cosmic hydrogen by early stars and quasars

Cosmic hydrogen is reionized and maintained in its highly ionized state by the ultraviolet emission attributed to an early generation of stars and quasars. The Lyα opacity observed in absorption spectra of high-redshift quasars permits more stringent constraints on the ionization state of cosmic hydrogen. Based on density perturbation and structure formation theory, we develop an analytic model to trace the evolution of the ionization state in the post-overlap epoch of reionization, in which the bias factor is taken into account. For quasars, we represent an improved luminosity function by utilizing a hybrid approach for the halo formation rate that is in reasonable agreement with the published measurements at 2 ≤ z ≤ 6. Comparison with the classic Press-Schechter mass function of dark matter halos, we demonstrate that the biased mass distribution indeed enhances star formation efficiency in the overdense environment by more than 25 per cent following the overlap of ionized bubbles. In addition, an alternative way is introduced to derive robust estimates of the mean free path for ionizing photons. In our model, star-forming galaxies are likely to dominate the ionizing background radiation beyond z = 3, and quasars contribute equally above a redshift of z ～ 2.5. From 5 ≤ z ≤ 6, the lack of evolution in photoionization rate can thus be explained by the relatively flat evolution in star formation efficiency, although the mean free path of ionizing photons increases rapidly. Moreover, in the redshift interval z ～ 2 - 6, the expected mean free path and Gunn-Peterson optical depth obviously evolve by a factor of ～ 500 and ～50 respectively. We find that the relative values of critical overdensities for hydrogen ionization and collapse could be 430% at z ≈2 and 2% at z ≈6, suggesting a rapid overlap process in the overdense regions around instant quasars following reionization. We further illustrate that the absolute estimates of the fraction of neutral hydrogen computed from theoretical models may not be important because of comparable uncertainties in the computation.

Molecular dynamics simulation of diffusion of nanoparticles in mucus

The rapid diffusion of nanoparticles （NPs） through mucus layer is critical for efficient transportation of NPs-loaded drug delivery system. To understand how the physical and surface properties of NPs affect their diffusion in mucus, we have developed a coarse-grained molecular dynamics model to study the diffusion of NPs in modeled mucus layer. Both steric obstruction and hydrodynamic interaction are included in the model capable of capturing the key characteristics of NPs＇ diffusion in mucus. The results show that both particle size and surface properties significantly affect the diffusivities of NPs in mucus. Furthermore, we find rodlike NPs can gain a higher diffusivity than spherical NPs with the same hydrodynamic diameter. In addition, the disturbed environment can enhance the diffusivity of NPs. Our findings can be utilized to design mucus penetrating NPs for targeted drug delivery system.

ONE DIMENSIONAL FILTRATION PROBLEM IN PARTIALLY SATURATED LAYERED POROUS MEDIA

We study in this paper the first boundary value problem of one dimensional degenerate quasilinear elliptic-parabolic equation with discontinuous coefficients (layered media). The uniquenessof the weak solutions is proved under natural conditions.