Cosmology with torsion: An alternative to cosmic inflation

We propose a simple scenario which explains why our Universe appears spatially flat, homogeneous and isotropic. We use the Einstein–Cartan–Kibble–Sciama (ECKS) theory of gravity which naturally extends general relativity to include the spin of matter. The torsion of spacetime generates gravitational repulsion in the early Universe filled with quarks and leptons, preventing the cosmological singularity: the Universe expands from a state of minimum but finite radius. We show that the dynamics of the closed Universe immediately after this state naturally solves the flatness and horizon problems in cosmology because of an extremely small and negative torsion density parameter, ΩS≈−¹⁰⁻⁶⁹${\Omega }_S\approx -{10}^{-69}$. Thus the ECKS gravity provides a compelling alternative to speculative mechanisms of standard cosmic inflation. This scenario also suggests that the contraction of our Universe preceding the bounce at the minimum radius may correspond to the dynamics of matter inside a collapsing black hole existing in another universe, which could explain the origin of the Big Bang.     

MHD mixed convection flow near the stagnation-point on a vertical permeable surface

The steady magnetohydrodynamic (MHD) mixed convection boundary layer flow of a viscous and electrically conducting fluid near the stagnation-point on a vertical permeable surface is investigated in this study. The velocity of the external flow and the temperature of the plate surface are assumed to vary linearly with the distance from the stagnation-point. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions exist for both cases, and the range of the mixed convection parameter for which the solution exists increases with suction.     

On the 4-dissections of certain infinite products

In this note, we give a generalization of Hirschhorn’s formulas on the 4-dissections of Ramanujan’s continued fraction R(q) and R ^?1(q) which were conjectured by Hirschhorn and proved by Lewis and Liu.     

Analogues of Ramanujan’s partition identities

Ramanujan discovered that $$\sum_{n=0}^\infty p(5n+4)q^n=5 \prod_{j=1}^\infty \frac{(1-q^{5j})^5}{(1-q^j)^6}, $$ where p(n) is the number of partitions of n. Recently, H.-C. Chan and S. Cooper, and H.H. Chan and P.C. Toh established several analogues of Ramanujan’s partition identities by employing the theory of modular functions. Very recently, N.D. Baruah and K.K. Ojah studied the partition function $p_{[c^{l}d^{m}]}(n)$ which is defined by $$\sum_{n=0}^\infty p_{[c^ld^m]}(n)q^n= \frac{1}{\prod_{j=1}^\infty (1-q^{cj})^{l}(1-q^{dj})^m}. $$ They discovered some analogues of Ramanujan’s partition identities and deduced several interesting partition congruences. In this paper, we provide a uniform method to prove some of their results by utilizing an addition formula. In the process, we also establish some new analogues of Ramanujan’s partition identities and congruences for $p_{[c^{l}d^{m}]}(n)$ .     

Seasonal Minimum and Maximum Solar Ultraviolet Exposure Measurements of Classroom Teachers Residing in Tropical North Queensland,Australia

The risk of keratinocyte skin cancer, malignant melanoma and ultraviolet radiation (UVR)‐induced eye disease is disproportionately higher in Australia and New Zealand compared to equivalent northern hemisphere latitudes. While many teachers are aware of the importance of reinforcing sun safety messages to students, many may not be aware of the considerable personal exposure risk while performing outdoor duties in locations experiencing high to extreme ambient UVR year‐round. Personal erythemally effective exposure of classroom teachers in tropical Townsville (19.3°S) was measured to establish seasonal extremes in exposure behavior. Mean daily personal exposure was higher in winter (91.2 J m^‐2, 0.91 Standard Erythema Dose [SED]) than summer (63.3 J m^?2, 0.63 SED). The range of exposures represents personal exposures that approximate current national guidelines for Australian workers at the study latitude of approximately 1.2 SED (30 J m^?2 effective to the International Commission on Non‐Ionizing Radiation Protection). Similar proportions of teachers spent more than 1 h outdoors per day in winter (28.6%) and summer (23.6%) as part of their teaching duties with seasonal differences having little effect on the time of exposure. Personal exposures for teachers peaked during both seasons near school meal break times at 11:00 am and 1:00 pm, respectively.     

PEG–Anthracene Hydrogels as an On‐Demand Stiffening Matrix To Study Mechanobiology

There is a growing interest in materials that can dynamically change their properties in the presence of cells to study mechanobiology. Herein, we exploit the 365 nm light mediated [4+4] photodimerization of anthracene groups to develop cytocompatible PEG‐based hydrogels with tailorable initial moduli that can be further stiffened. A hydrogel formulation that can stiffen from 10 to 50 kPa, corresponding to the stiffness of a healthy and fibrotic heart, respectively, was prepared. This system was used to monitor the stiffness‐dependent localization of NFAT, a downstream target of intracellular calcium signaling using a reporter in live cardiac fibroblasts (CFbs). NFAT translocates to the nucleus of CFbs on stiffening hydrogels within 6 h, whereas it remains cytoplasmic when the CFbs are cultured on either 10 or 50 kPa static hydrogels. This finding demonstrates how dynamic changes in the mechanical properties of a material can reveal the kinetics of mechanoresponsive cell signaling pathways that may otherwise be missed in cells cultured on static substrates.     

Turbulent combined forced and natural convection of nanofluid in a 3D rectangular channel using two-phase model approach

Journal of Thermal Analysis and Calorimetry - The nanofluid is a mixture of base fluid and solid nanoparticles in nanosize. The heat transfer generated by the nanofluid is more than the base fluid...