An Eulerian approach for computing the finite time Lyapunov exponent

We propose efficient Eulerian methods for approximating the finite-time Lyapunov exponent (FTLE). The idea is to compute the related flow map using the Level Set Method and the Liouville equation. There are several advantages of the proposed approach. Unlike the usual Lagrangian-type computations, the resulting method requires the velocity field defined only at discrete locations. No interpolation of the velocity field is needed. Also, the method automatically stops a particle trajectory in the case when the ray hits the boundary of the computational domain. The computational complexity of the algorithm is O(Δx^?(d+1)) with d the dimension of the physical space. Since there are the same number of mesh points in the x–t space, the computational complexity of the proposed Eulerian approach is optimal in the sense that each grid point is visited for only O(1) time. We also extend the algorithm to compute the FTLE on a co-dimension one manifold. The resulting algorithm does not require computation on any local coordinate system and is simple to implement even for an evolving manifold.     

Photo-activated pheophorbide a inhibits the growth of prostate cancer cells

Pheophorbide a (PhA) was identified as a photosensitizer to exert cytotoxicity on tumor cells. However, the efficacy of this compound on the treatment of prostate cancer remains unknown. The aim of this study was to evaluate the photodynamic effect of PhA on prostate cancer cells. Cellular uptake of PhA and cell viability after photo-activation was studied in LNCaP prostate cancer cells. The corresponding production of reactive oxygen species within cells was determined after photodynamic therapy (PDT). Our results showed that the uptake of PhA into LNCaP cells was in a time-dependent manner and the cytotoxicity of PhA-PDT was photosensitizer dose- and light dose-dependent. The intracellular reactive oxygen species was remarkably induced after PDT treatment, which was responsible for the inhibition effect on prostate cancer cells. This is the first report to evaluate the photodynamic effect of PhA on prostate cancer. Our findings demonstrate that PhA-PDT may be a potentially promising treatment for localized prostate cancer, which can be a therapeutic option after the failures of radiotherapy and hormone therapy.     

Photonic gap vanishing in one-dimensional photonic crystals with single-negative metamaterials

The properties of photonic band gap in one-dimensional photonic crystals composed of single-negative metamaterials are studied theoretically. Our study shows that the photonic gap will vanish at a certain incident angle when both the phase-match and impedance-match conditions are satisfied simultaneously, suggesting that the bandwidth and location of the photonic gap are strongly dependent on the incident angle and polarization. However, the photonic gap will not vanish and may become insensitive to the incident angle when the two match conditions cannot be met. Our study also shows that losses in metamaterials have little effect on the properties of the photonic gap.     

Effect of blue light radiation on curcumin-induced cell death of breast cancer cells

In the present study, we have successfully set up a novel blue light source with the power density of 9 mW/cm² and the wavelength of 435.8 nm and then the novel light source was used to investigate the effect of light radiation on curcumin-induced cell death. The cytotoxicity was investigated 24 h after the treatment of curcumin and blue light radiation together using MTT reduction assay. Nuclear chromatin was observed using a fluorescent microscopy with Hoechst33258 staining. The results showed blue light radiation could significantly enhance the cytotoxicity of curcumin on the MCF-7 cells and apoptosis induction. These findings demonstrated that blue light radiation could enhance curcumin-induced cell death of breast cancer cells, suggesting light radiation may be an efficient enhancer of curcumin in the management of breast cancer.     

Equilibrium charge-state fractions for 2.7–31 keV deuterium atoms and ions in strontium vapor

Equilibrium charge-state fractions of 2.7–31 keV deuterium in strontium vapor are reported. The energy dependence of the D^- equilibrium yield is discussed. The results are compared with the D^- yield in cesium and magnesium vapors.     

Diffraction effects in the Josephson tunneling between type II superconductors near Hc2

When the lattice of vortices on one side of a SIS tunneling junction moves with respect to that of the other side, we point out that the Josephson current should oscillate in magnitudes and directions as a function of time. The oscillatory behaviour is caused mainly by the diffraction effects of the variation of the order parameter in the mixed state with vortex motion.     

A calibrated model of local food system of Hawaii: What are the economic implications of the state's food goals and policies?

We develop a fully calibrated positive mathematical programming model for Hawaii's local food systems—which captures the production and the consumer sides of the market. Then we use the model to assess two proposed policies—a general excise tax (GET) exemption on locally produced foods, and an investment in agricultural infrastructure. For the GET exemption case, our results indicate an economic gain of $118 per $100 cost. On the other hand, an investment in 1,200 acres of land injected to support local production may generate an economic gain of up to $357 per $100 annual cost of the investment. However, these estimates should be considered preliminary, and thus viewed with caution. Although the model is used to capture Hawaii's local food systems, we believe that our model is generalizable and can be adopted by other economies to assess their respective food localization policies. Recommendations for Resource Managers

• Local food policies need to be based on quantitative terms instead of mere armchair speculation because often their potential outcomes may vary significantly.

• The current modeling framework demonstrates the potential of using positive mathematical programming (PMP) in capturing the intricacies of local food systems. However, this exploratory exercise should be viewed as preliminary in nature and the ensuing results were taken with caution because many important factors such as labor availability may have been left out.

• Thus, further model refinements are necessary to better capture the complexities of local food systems such as farm heterogeneity, availability of farm labor, water availability, and interisland transportation of farm products in the case of Hawaii.

     

On Lander’s conjecture for difference sets whose order is a power of 2 or 3

Let p be a prime and let b be a positive integer. If a (v, k, λ, n) difference set D of order n = p ^b exists in an abelian group with cyclic Sylow p-subgroup S, then \({p\in\{2,3\}}\) and |S| = p. Furthermore, either p = 2 and v ≡ λ ≡ 2 (mod 4) or the parameters of D belong to one of four families explicitly determined in our main theorem.     

On closedness of convex sets in Banach lattices

Positivity - Let X be a Banach lattice. A well-known problem arising from the theory of risk measures asks when order closedness of a convex set in X implies closedness with respect to the topology...     

A molecular dynamics method for simulations in the canonical ensemble

A molecular dynamics simulation method which can generate configurations belonging to the canonical (T, V, N) ensemble or the constant temperature constant pressure (T, P, N) ensemble, is proposed. The physical system of interest consists of N particles (f degrees of freedom), to which an external, macroscopic variable and its conjugate momentum are added. This device allows the total energy of the physical system to fluctuate. The equilibrium distribution of the energy coincides with the canonical distribution both in momentum and in coordinate space. The method is tested for an atomic fluid (Ar) and works well.