We derive two principal components (PCs) of temporal magnetic field variations over the solar cycles 21–24 from full disk magnetograms covering about 39% of data variance, with σ = 0.67. These PCs are attributed to two main magnetic waves travelling from the opposite hemispheres with close frequencies and increasing phase shift. Using symbolic regeression analysis we also derive mathematical formulae for these waves and calculate their summary curve which we show is linked to solar activity index. Extrapolation of the PCs backward for 800 years reveals the two 350-year grand cycles superimposed on 22 year-cycles with the features showing a remarkable resemblance to sunspot activity reported in the past including the Maunder and Dalton minimum. The summary curve calculated for the next millennium predicts further three grand cycles with the closest grand minimum occurring in the forthcoming cycles 26–27 with the two magnetic field waves separating into the opposite hemispheres leading to strongly reduced solar activity. These grand cycle variations are probed by α − Ω dynamo model with meridional circulation. Dynamo waves are found generated with close frequencies whose interaction leads to beating effects responsible for the grand cycles (350–400 years) superimposed on a standard 22 year cycle. This approach opens a new era in investigation and confident prediction of solar activity on a millenium timescale.

A comprehensive spectral analysis of both the solar background magnetic field (SBMF) in cycles 21-23 and the sunspot magnetic field in cycle 23 reported in our recent paper showed the presence of two principal components (PCs) of SBMF having opposite polarity, e.g., originating in the northern and southern hemispheres, respectively. Over a duration of one solar cycle, both waves are found to travel with an increasing phase shift toward the northern hemisphere in odd cycles 21 and 23 and to the southern hemisphere in even cycle 22. These waves were linked to solar dynamo waves assumed to form in different layers of the solar interior. In this paper, for the first time, the PCs of SBMF in cycles 21-23 are analyzed with the symbolic regression technique using Hamiltonian principles, allowing us to uncover the underlying mathematical laws governing these complex waves in the SBMF presented by PCs and to extrapolate these PCs to cycles 24-26. The PCs predicted for cycle 24 very closely fit (with an accuracy better than 98%) the PCs derived from the SBMF observations in this cycle. This approach also predicts a strong reduction of the SBMF in cycles 25 and 26 and, thus, a reduction of the resulting solar activity. This decrease is accompanied by an increasing phase shift between the two predicted PCs (magnetic waves) in cycle 25 leading to their full separation into the opposite hemispheres in cycle 26. The variations of the modulus summary of the two PCs in SBMF reveals a remarkable resemblance to the average number of sunspots in cycles 21-24 and to predictions of reduced sunspot numbers compared to cycle 24: 80% in cycle 25 and 40% in cycle 26.

The aim of this paper is to derive the principal components (PCs) in variations of (i) the solar background magnetic field (SBMF), measured by the Wilcox Solar Observatory with low spatial resolution for solar cycles 21-23, and (ii) the sunspot magnetic field (SMF) in cycle 23, obtained by SOHO/MDI. For reduction of the component dimensions, principal component analysis (PCA) is carried out to identify global patterns in the data and to detect pairs of PCs and corresponding empirical orthogonal functions (EOFs). PCA reveals two main temporal PCs in the SBMF of opposite polarities originating in opposite hemispheres and running noticeably off-phase (with a delay of about 2.5 yr), with their maxima overlapping in the most active hemisphere for a given cycle. Their maximum magnitudes are reduced by a factor of 3 from cycle 21 to 23, and overlap in the Northern hemisphere for cycle 21, in the Southern one in cycle 22 and in the Northern one again in cycle 23. The reduction of magnitudes and slopes of the maxima of the SBMF waves from cycle 21 to cycle 23 leads us to expect lower magnitudes of the SBMF wave in cycle 24. In addition, PCA allowed us to detect four pairs of EOFs in the SBMF latitudinal components: the two main latitudinal EOFs attributed to symmetric types and another three pairs of EOFs assigned to asymmetric types of meridional flows. The results allow us to postulate the existence of dipole and quadruple (or triple-dipole) magnetic structures in the SBMF, which vary from cycle to cycle and take the form of two waves travelling off-phase, with a phase shift of one-quarter of the 11 yr period. Similar PC and EOF components were found in temporal and latitudinal distributions of the SMF for cycle 23, revealing polarities opposite to the SBMF polarities, and a double maximum in time or maxima in latitude corresponding to the maxima of the SBMF PC residuals or minima in the SBMF EOFs, respectively. This suggests that the SBMF waves modulate the occurrence and magnitude of the SMF in time and latitude.

Background: In recent years there has been renewed interest in the use of air ionisers to control of the spread of airborne infection. One characteristic of air ions which has been widely reported is their apparent biocidal action. However, whilst the body of evidence suggests a biocidal effect in the presence of air ions the physical and biological mechanisms involved remain unclear. In particular, it is not clear which of several possible mechanisms of electrical origin (i.e. the action of the ions, the production of ozone, or the action of the electric field) are responsible for cell death. A study was therefore undertaken to clarify this issue and to determine the physical mechanisms associated with microbial cell death.

Abstract-This paper addresses the problem of selecting the optimum training sequence for channel estimation in communication systems over time-dispersive channels. By processing in the frequency domain, a new explicit form of search criterion is found, the gain loss factor (GLF), which minimizes the variance of the estimation error and is easy to compute. Theoretical upper and lower bounds on the GLF are derived. An efficient directed search strategy and optimal sequences up to length 42 are given. These sequences are optimal only for frequency domain estimation, not for time domain estimation.