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The fundamental conception in physics of the propagation of the electromagnetic wave polarization in matter is newly understood as the cardinal keyword in free-space quantum communication technology and cosmology in astrophysics. Interactive visualization of the propagation mechanism of polarized electromagnetism in a medium with its helicity has accordingly received attention from scientists exploiting the protocol of quantum key distribution (QKD) to guarantee unconditional security in cryptography communication. We have provided a dynamic polarization platform for presenting the polarization modes of a transverse electromagnetic wave, converting the state of polarization through the arrangement of optical elements, using Jones vectors calculations in Methematica. The platform graphically simulates the mechanism of production and propagation of the polarized waves in a medium while satisfying Maxwell`s equations.

In this study we compare the temporal variations of the solar, interplanetary, and geomagnetic (SIG) parameters with that of open solar magnetic flux from 1976 to 2012 (from Solar Cycle 21 to the early phase of Cycle 24) for a purpose of identifying their possible relationships. By the open flux, we mean the average magnetic field over the source surface (2.5 solar radii) times the source area as defined by the potential field source surface (PFSS) model of the Wilcox Solar Observatory (WSO). In our result, most SIG parameters except the solar wind dynamic pressure show rather poor correlations with the open solar magnetic field. Good correlations are recovered when the contributions from individual multipole components are counted separately. As expected, solar activity indices such as sunspot number, total solar irradiance, 10.7 cm radio flux, and solar flare occurrence are highly correlated with the flux of magnetic quadrupole component. The dynamic pressure of solar wind is strongly correlated with the dipole flux, which is in anti-phase with Solar Cycle (SC). The geomagnetic activity represented by the A p index is correlated with higher order multipole components, which show relatively a slow time variation with SC. We also found that the unusually low geomagnetic activity during SC 23 is accompanied by the weak open solar fields compared with those in other SCs. It is argued that such dependences of the SIG parameters on the individual multipole components of the open solar magnetic flux may clarify why some SIG parameters vary in phase with SC and others show seemingly delayed responses to SC variation.

The atmospheric flow in the 3-Cell model of global atmosphere circulation is described by the Lagrange's equation of the non-inertial frame where pressure force, frictional force and fictitious force are mixed in complex form. The Coriolis force is an important factor which requires calculation of fictitious force effects on atmospheric flow viewed from the rotating Earth. We make new Mathematica platform to solve Lagrange's equation by numerical analysis in order to analyze dynamics of atmospheric general circulation in the non-inertial frame. It can simulate atmospheric circulation process anywhere on the earth. It is expected that this pedagogical platform can be utilized to help students studying the atmospheric flow understand the mechanisms of atmospheric global circulation.

The length of solar cycle 23 has been prolonged up to about 13 years. Many studies have speculated that the solar cycle 23/24 minimum will indicate the onset of a grand minimum of solar activity, such as the Maunder Minimum. We check the trends of solar (sunspot number, solar magnetic fields, total solar irradiance, solar radio flux, and frequency of solar X-ray flare), interplanetary (interplanetary magnetic field, solar wind and galactic cosmic ray intensity), and geomagnetic (Ap index) parameters (SIG parameters) during solar cycles 21-24. Most SIG parameters during the period of the solar cycle 23/24 minimum have remarkably low values. Since the 1970s, the space environment has been monitored by ground observatories and satellites. Such prevalently low values of SIG parameters have never been seen. We suggest that these unprecedented conditions of SIG parameters originate from the weakened solar magnetic fields. Meanwhile, the deep 23/24 solar cycle minimum might be the portent of a grand minimum in which the global mean temperature of the lower atmosphere is as low as in the period of Dalton or Maunder minimum.

Solar cycle (SC) 23 was extraordinarily long with remarkably low magnetic activity. We have investigated whether this is a common behavior of solar-type stars. From the Ca ii H and K line intensities of 111 stars observed at Mount Wilson Observatory from 1966 to 1991, we have retrieved data of all 23 G-type stars and recalculated their cycle lengths using the damped least-squares method for the chromospheric activity index S as a function of time. A regression analysis was performed to find relations between the derived cycle length, Pavg, and the index for excess chromospheric emission, . As a noteworthy result, we found a segregation between young and old solar-type stars in the cycle length-activity correlation. We incorporated the relation for the solar-type stars into the previously known rule for stellar chromospheric activity and brightness to estimate the variation of solar brightness from SC 22 to SC 23 as (0.12 ± 0.06)%, much higher than the actual variation of total solar irradiance (TSI) ≤0.02%. We have then examined solar spectral irradiance (SSI) to find a good phase correlation with a sunspot number in the wavelength range of 170–260 nm, which is close to the spectral range effective in heating the Earth's atmosphere. Therefore, it appears that SSI rather than TSI is a good indicator of the chromospheric activity, and its cycle length dependent variation would be more relevant to the possible role of the Sun in the cyclic variation of the Earth's atmosphere.