Reduction Approaches for Thermogasdynamic Lubrication Problems

Gas thrust bearings are often used in low-load applications, e.g. in air cycle machines, in micro gas turbines or in rotor systems for fuel cell applications, to support a shaft in axial direction. The pressure and temperature distribution in a gas thrust bearing pad are described by the generalized Reynolds equation according to Dowson and the 3D energy equation. In this paper, two different approaches are presented in order to reduce the dimension of the governing nonlinear integro-differential equation system and in order to stabilize the solution process. In the first reduction approach, the temperature in the fluid is averaged across the fluid film according to Lee and Kim. In the second approach, Legendre polynomials are used to approximate temperature, density and fluidity across the fluid film according to Elrod, Brewe and Moraru. The reduction techniques are compared with respect to numerical efficiency, accuracy and convergence behavior. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Existence,Non-existence,and Uniqueness for a Heat Equation with Exponential Nonlinearity in ℝ2

We consider a semilinear heat equation with exponential nonlinearity in ?². We prove that local solutions do not exist for certain data in the Orlicz space exp L ²(?²), even though a small data global existence result holds in the same space exp L ²(?²). Moreover, some suitable subclass of exp L ²(?²) for local existence and uniqueness is proposed.

     

Adjuvants that Empower the Action of Photodynamic Therapy

Compounds have been devised whose supportive actions make them important adjuvants in the priming of photosensitization to selectively target cancer cells. Here, we highlight the paper by Maytin and Hasan in this issue of Photochemistry & Photobiology, which describes adjuvants methotrexate, 5-fluorouracil, vitamin D and its analogs leading to improved photodynamic therapy outcome. These small molecule adjuvants act by different mechanisms to enhance the cytotoxicity in tumor cells and the therapeutic effect in cancers. These findings add to the list of strategies for enhancement of photodynamic therapy.     

Ultrahigh molecular weight alternating propene/ethene/carbon monoxide terpolymers with elastic properties

Soluble propene/ethene/CO terpolymers (EPEC) with ultrahigh molecular weight (up to 1.2 × 10⁶ g/mol) were prepared by the use of dicationic palladium(II) phosphine catalysts and an optimized amount of water as activator. When the molar ratio of ethene/CO to propene/CO is below 50 mol-%, the terpolymers are thermoplastic elastomers with excellent properties. Above this ratio the terpolymers are crystalline thermoplastics. The ultrahigh molecular weight elastomers are highly soluble in organic solvents such as CH₂Cl₂ and CHCl₃.     

Investigations of silicone breast implants with the NMR-MOUSE

Silicone breast implants are used for breast augmentation and breast reconstruction. The issues of concern associated with such implants are: (a) the quality control of each implant before implantation, and (b) the detection of implant bleeding after implantation. We have studied the use of the Nuclear Magnetic Resonance-MObile Universal Surface Explorer (NMR-MOUSE) for the nondestructive testing of (a) the quality of implant shells, and (b) changes in implant gel due to leakage of body fluid into the implant. Depth profiles measured nondestructively through implant shells at different positions of each implant by the Profile NMR-MOUSE assured good reproducibility of the quality and thickness of different shell layers. The leakage of implants upon rupture was mimicked by observing changes in the transverse NMR relaxation time of the implant gel upon ingress of physiological saline solution and safflower oil through the rupture. Results demonstrate that nondestructive testing with unilateral NMR is a potential method for use in the quality control of implants and for the screening of implants for rupture after implantation.     

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.