Drop spreading with random viscosity

We examine theoretically the spreading of a viscous liquid drop over a thin film of uniform thickness, assuming the liquid's viscosity is regulated by the concentration of a solute that is carried passively by the spreading flow. The solute is assumed to be initially heterogeneous, having a spatial distribution with prescribed statistical features. To examine how this variability influences the drop's motion, we investigate spreading in a planar geometry using lubrication theory, combining numerical simulations with asymptotic analysis. We assume diffusion is sufficient to suppress solute concentration gradients across but not along the film. The solute field beneath the bulk of the drop is stretched by the spreading flow, such that the initial solute concentration immediately behind the drop's effective contact lines has a long-lived influence on the spreading rate. Over long periods, solute swept up from the precursor film accumulates in a short region behind the contact line, allowing patches of elevated viscosity within the precursor film to hinder spreading. A low-order model provides explicit predictions of the variances in spreading rate and drop location, which are validated against simulations

A Helson-Szeg\"o theorem for subdiagonal subalgebras with applications to Toeplitz operators

We formulate and establish a noncommutative version of the well known Helson-Szego theorem about the angle between past and future for subdiagonal subalgebras. We then proceed to use this theorem to characterise the symbols of invertible Toeplitz operators on the noncommutative Hardy spaces associated to subdiagonal subalgebras

Asymptotic Stability for Equilibria of Nonlinear Semiflows with Applications to Rotating Viscoelastic Rods, Part I

No Abstrac

Effective Maxwell equations from time-dependent density functional theory

The behavior of interacting electrons in a perfect crystal under macroscopic external electric and magnetic fields is studied. Effective Maxwell equations for the macroscopic electric and magnetic fields are derived starting from time-dependent density functional theory. Effective permittivity and permeability coefficients are obtained.Comment: 36 page

Quantum critical points of Helical Fermi Liquids

Following our previous work, we study the quantum phase transitions which spontaneously develop ferromagnetic spin order in helical fermi liquids which breaks continuous spin-space rotation symmetry, with application to the edge states of 3d topological band insulators. With finite fermi surface, the critical point has both z = 3 over-damped and z = 2 propagating quantum critical modes, and the z = 3 mode will lead to non-fermi liquid behavior on the entire fermi surface. In the ordered phase, the Goldstone mode is over-damped unless it propagates along special directions, and quasiparticle is ill defined on most parts of the fermi surface except for special points. Generalizations of our results to other systems with spin-orbit couplings are also discussed.Comment: 5 pages, 2 figure

miR-218 targets survivin and regulates resistance to chemotherapeutics in breast cancer

Multidrug resistance (MDR) remains one of the most significant obstacles in breast cancer treatment, and this process often involves dysregulation of a great number of microRNAs (miRNAs). Some miRNAs are indicators of drug resistance and confer resistance to chemotherapeutic drugs, although our understanding of this complex process is still incomplete. We have used a combination of miRNA profiling and real-time PCR in two drug-resistant derivatives of MCF-7 and Cal51 cells. Experimental modulation of miR expression has been obtained by retroviral transfection. Taxol and doxorubicin IC50 values were obtained by short-term drug sensitivity assays. Apoptosis was determined by flow cytometry after annexin V staining, by caspase 3/7 and caspase 9 activity assays and the levels of apoptosis-related proteins bcl-2 and bax by real-time PCR and Western blot. miR target was studied using transient transfection of luciferase constructs with the 3 untranslated regions (UTR) of target mRNAs. Small interfering RNA-mediated genetic knock-down was performed in MDR cells and its modulatory effect on apoptosis examined. The effect of miRNA on tumorigenicity and tumor drug response was studied in mouse xenografts. miRNA profiling of two drug-resistant breast cancer cell models indicated that miR-218 was down-regulated in both MCF-7/A02 and CALDOX cells. Ectopic expression of miR-218 resensitized both drug-resistant cell lines to doxorubicin and taxol due to an increase in apoptosis. miR-218 binds survivin (BIRC5) mRNA 3-UTR and down-regulated reporter luciferase activity. Experimental down-regulation of survivin by RNA interference in drug-resistant cells did mimic the sensitization observed when miRNA-218 was up-regulated. In addition, resensitization to taxol was also observed in mouse tumor xenografts from cells over-expressing miR-218. miR-218 is involved in the development of MDR in breast cancer cells via targeting survivin and leading to evasion of apoptosis. Targeting miR-218 and survivin may thus provide a potential strategy for reversing drug resistance in breast cancer