Работы Ю.С. Колесова по дифференциальным уравнениям

The article describes the most interesting, in the author's opinion, results obtained by Yu.S. Kolesov, devoted to differential equations (common, functional-differential, with partial derivatives) and their applications to the mathematical ecology, radiophysics, automatic regulation, mechanics.Описываются наиболее интересные, по мнению автора, результаты Ю.С. Колесова, посвященные дифференциальным уравнениям (обыкновенным, функционально-дифференциальным, с частными производными) и их приложениям к математической экологии, радиофизике, автоматическому регулированию, механике

Snowmelt onset hinders bromine monoxide heterogeneous recycling in the Arctic

Reactive bromine radicals (bromine atoms, Br, and bromine monoxide, BrO) deplete ozone and alter tropospheric oxidation chemistry during the Arctic springtime (February–June). As spring transitions to summer (May–June) and snow begins to melt, reactive bromine events cease and BrO becomes low in summer. In this study, we explore the relationship between the end of the reactive bromine season and snowmelt timing. BrO was measured by Multi‐AXis Differential Optical Absorption Spectrometer at Utqiaġvik (Barrow), AK, from 2012 to 2016 and on drifting buoys deployed in Arctic sea ice from 2011 to 2016, a total of 13 site and year combinations. The BrO seasonal end date (SED) was objectively determined and was compared to surface‐air‐temperature‐derived melt onset date (MOD). The SED was highly correlated with the MOD (N = 13, R2 = 0.983, RMS = 1.9 days), and BrO is only observed at subfreezing temperatures. In subsets of these sites and years where ancillary data were available, we observed that snowpack depth reduced and rain precipitation occurred within a few days of the SED. These data are consistent with snowpack melting hindering BrO recycling, which is necessary to maintain enhanced BrO concentrations. With a projected warmer Arctic, a shift to earlier snowmelt seasons could alter the timing and role of halogen chemical reactions in the Arctic with impacts on ozone depletion and mercury deposition.Plain Language SummaryReactive bromine events in the Arctic are common in spring and deplete ozone and cause mercury deposition. These events are affected by snow and ice, which are changing in the Arctic; therefore, we need to understand how environmental conditions affect reactive bromine chemistry. We find that the reactive bromine season ends when snowpack begins to melt. Through these full seasonal observations, we find that reactive bromine events occur to warmer temperatures than previously reported, with 0°C being the observed threshold above which reactive bromine is absent. We also find that snow appears necessary for reactive bromine chemistry and rain stops this chemistry. Earlier snowmelt in a warmer Arctic would end the reactive bromine season earlier, decreasing late springtime ozone depletion and mercury deposition.Key PointsSnowmelt onset hinders reactive bromine heterogeneous recycling and ends season of reactive bromine eventsReactive bromine events occur at subfreezing air temperatures but not at higher temperaturesSnow appears necessary for reactive bromine heterogeneous recycling, and rainwater can terminate this chemistryPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138295/1/jgrd53947_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138295/2/jgrd53947.pd

Chaotic Friedmann-Robertson-Walker Cosmology

We show that the dynamics of a spatially closed Friedmann - Robertson - Walker Universe conformally coupled to a real, free, massive scalar field, is chaotic, for large enough field amplitudes. We do so by proving that this system is integrable under the adiabatic approximation, but that the corresponding KAM tori break up when non adiabatic terms are considered. This finding is confirmed by numerical evaluation of the Lyapunov exponents associated with the system, among other criteria. Chaos sets strong limitations to our ability to predict the value of the field at the Big Crunch, from its given value at the Big Bang. (Figures available on request)Comment: 28 pages, 11 figure

Exponential-Potential Scalar Field Universes I: The Bianchi I Models

We obtain a general exact solution of the Einstein field equations for the anisotropic Bianchi type I universes filled with an exponential-potential scalar field and study their dynamics. It is shown, in agreement with previous studies, that for a wide range of initial conditions the late-time behaviour of the models is that of a power-law inflating FRW universe. This property, does not hold, in contrast, when some degree of inhomogeneity is introduced, as discussed in our following paper II.Comment: 16 pages, Plain LaTeX, 1 Figure to be sent on request, to appear in Phys. Rev.

Axially Symmetric Bianchi I Yang-Mills Cosmology as a Dynamical System

We construct the most general form of axially symmetric SU(2)-Yang-Mills fields in Bianchi cosmologies. The dynamical evolution of axially symmetric YM fields in Bianchi I model is compared with the dynamical evolution of the electromagnetic field in Bianchi I and the fully isotropic YM field in Friedmann-Robertson-Walker cosmologies. The stochastic properties of axially symmetric Bianchi I-Einstein-Yang-Mills systems are compared with those of axially symmetric YM fields in flat space. After numerical computation of Liapunov exponents in synchronous (cosmological) time, it is shown that the Bianchi I-EYM system has milder stochastic properties than the corresponding flat YM system. The Liapunov exponent is non-vanishing in conformal time.Comment: 18 pages, 6 Postscript figures, uses amsmath,amssymb,epsfig,verbatim, to appear in CQ

On the Cosmology of Massive Vector Fields with SO(3) Global Symmetry

A relevant reference ([14]) has been added.Comment: 19 pages, plain tex, DF/IST-3/92 and DFFCUL 03-5/199

Qualitative Analysis of Viscous Fluid Cosmological Models satisfying the Israel-Stewart theory of Irreversible Thermodynamics

Isotropic and spatially homogeneous viscous fluid cosmological models are investigated using the truncated Israel-Stewart theory of irreversible thermodynamics to model the bulk viscous pressure. The governing system of differential equations is written in terms of dimensionless variables and a set of dimensionless equations of state is then utilized to complete the system. The resulting dynamical system is analyzed using geometric techniques from dynamical systems theory to find the qualitative behaviour of the Friedmann-Robertson-Walker models with bulk viscosity. In these models there exists a free parameter such that the qualitative behaviour of the models can be quite different (for certain ranges of values of this parameter) from that found in models satisfying the Eckart theory studied previously. In addition, the conditions under which the models inflate are investigated.Comment: 29 pages, 8 Encapsulated PostScript Figures, uses the IOP style file

On the Stability of the Einstein Static Universe

We show using covariant techniques that the Einstein static universe containing a perfect fluid is always neutrally stable against small inhomogeneous vector and tensor perturbations and neutrally stable against adiabatic scalar density inhomogeneities so long as c_{s}^2>1/5, and unstable otherwise. We also show that the stability is not significantly changed by the presence of a self-interacting scalar field source, but we find that spatially homogeneous Bianchi type IX modes destabilise an Einstein static universe. The implications of these results for the initial state of the universe and its pre-inflationary evolution are also discussed.Comment: some additional comments and references; version to appear in Class. Quant. Gra

Evolution of the Bianchi I, the Bianchi III and the Kantowski-Sachs Universe: Isotropization and Inflation

We study the Einstein-Klein-Gordon equations for a convex positive potential in a Bianchi I, a Bianchi III and a Kantowski-Sachs universe. After analysing the inherent properties of the system of differential equations, the study of the asymptotic behaviors of the solutions and their stability is done for an exponential potential. The results are compared with those of Burd and Barrow. In contrast with their results, we show that for the BI case isotropy can be reached without inflation and we find new critical points which lead to new exact solutions. On the other hand we recover the result of Burd and Barrow that if inflation occurs then isotropy is always reached. The numerical integration is also done and all the asymptotical behaviors are confirmed.Comment: 22 pages, 12 figures, Self-consistent Latex2e File. To be published in Phys. Rev.