Stability in Cosmology, from Einstein to Inflation

I investigate the role of stability in cosmology through two episodes from the recent history of cosmology: (1) Einstein’s static universe and Eddington’s demonstration of its instability, and (2) the flatness problem of the hot big bang model and its claimed solution by inflationary theory. These episodes illustrate differing reactions to instability in cosmological models, both positive ones and negative ones. To provide some context to these reactions, I also situate them in relation to perspectives on stability from dynamical systems theory and its epistemology. This reveals, for example, an insistence on stability as an extreme position in relation to the spectrum of physical systems which exhibit degrees of stability and fragility, one which has a pragmatic rationale, but not any deeper one

Internal flows and energy circulation in light beams

We review optical phenomena associated with the internal energy redistribution which accompany propagation and transformations of monochromatic light fields in homogeneous media. The total energy flow (linear-momentum density, Poynting vector) can be divided into spin part associated with the polarization and orbital part associated with the spatial inhomogeneity. We give general description of the internal flows in the coordinate and momentum (angular spectrum) representations for both nonparaxial and paraxial fields. This enables one to determine local densities and integral values of the spin and orbital angular momenta of the field. We analyse patterns of the internal flows in standard beam models (Gaussian, Laguerre-Gaussian, flat-top beam, etc.), which provide an insightful picture of the energy transport. The emphasize is made to the singular points of the flow fields. We describe the spin-orbit and orbit-orbit interactions in the processes of beam focusing and symmetry breakdown. Finally, we consider how the energy flows manifest themselves in the mechanical action on probing particles and in the transformations of a propagating beam subjected to a transverse perturbation.Comment: 50 pages, 21 figures, 173 references. This is the final version of the manuscript (v1) modified in accord to the referee's remarks and with allowance for the recent development. The main changes are: additional discussion of the energy flows in Bessel beams (section 4.1), a lot of new references are added and the Conclusion is shortened and made more accurat

Stability in Cosmology, from Einstein to Inflation

I investigate the role of stability in cosmology through two episodes from the recent history of cosmology: (1) Einstein’s static universe and Eddington’s demonstration of its instability, and (2) the flatness problem of the hot big bang model and its claimed solution by inflationary theory. These episodes illustrate differing reactions to instability in cosmological models, both positive ones and negative ones. To provide some context to these reactions, I also situate them in relation to perspectives on stability from dynamical systems theory and its epistemology. This reveals, for example, an insistence on stability as an extreme position in relation to the spectrum of physical systems which exhibit degrees of stability and fragility, one which has a pragmatic rationale, but not any deeper one

Theory of oscillators

Theory of Oscillators presents the applications and exposition of the qualitative theory of differential equations. This book discusses the idea of a discontinuous transition in a dynamic process. Organized into 11 chapters, this book begins with an overview of the simplest type of oscillatory system in which the motion is described by a linear differential equation. This text then examines the character of the motion of the representative point along the hyperbola. Other chapters consider examples of two basic types of non-linear non-conservative systems, namely, dissipative systems and self

Diversity Indices of Plant Communities and Their Rhizosphere Microbiomes: An Attempt to Find the Connection

The rhizosphere community represents an “ecological interface” between plant and soil, providing the plant with a number of advantages. Despite close connection and mutual influence in this system, the knowledge about the connection of plant and rhizosphere diversity is still controversial. One of the most valuable factors of this uncertainty is a rough estimation of plant diversity. NGS sequencing can make the estimations of the plant community more precise than classical geobotanical methods. We investigate fallow and crop sites, which are similar in terms of environmental conditions and soil legacy, yet at the same time are significantly different in terms of plant diversity. We explored amplicons of both the plant root mass (ITS1 DNA) and the microbial communities (16S rDNA); determined alpha- and beta-diversity indices and their correlation, and performed differential abundance analysis. In the analysis, there is no correlation between the alpha-diversity indices of plants and the rhizosphere microbial communities. The beta-diversity between rhizosphere microbial communities and plant communities is highly correlated (R = 0.866, p = 0.01). ITS1 sequencing is effective for the description of plant root communities. There is a connection between rhizosphere communities and the composition of plants, but on the alpha-diversity level we found no correlation. In the future, the connection of alpha-diversities should be explored using ITS1 sequencing, even in more similar plant communities—for example, in different synusia

Dynamic of the Soil Microbiota in Short-Term Crop Rotation

Crop rotation is one of the oldest and most effective methods of restoring soil fertility, which declines when the same plant is grown repeatedly. One of the reasons for a reduction in fertility is the accumulation of pathogenic and unfavorable microbiota. The modern crop rotation schemes (a set of plant species and their order in the crop rotation) are highly effective but are designed without considering soil microbiota dynamics. The main goal of this study was to perform a short-term experiment with multiple plant combinations to access the microbiological effects of crop rotation. It could be useful for the design of long-term crop rotation schemes that take the microbiological effects of the crop rotation into account. For the analysis, five plants (legumes: vetch, clover, and cereals: oats, wheat, and barley) were used. These five plants were separately grown in pots with soil. After the first phase of vegetation, the plants were removed from the soil and a new crop was planted. Soil samples from all 25 possible combinations of primary and secondary crops were investigated using v4-16S rDNA gene sequencing. It was shown that the short-term experiments (up to 40 days of growing) are effective enough to find microbial shifts in bulk soil from different plants. Both primary and secondary cultures are significant factors for the microbial composition of microbial soil communities. Changes are the most significant in the microbial communities of vetch soils, especially in the case of vetch monoculture. Growing clover also leads to changes in microbiota, especially according to beta-diversity. Data obtained can be used to develop new crop rotation schemes that take into account the microbiological effects of various crops