Trace Element Uptake Assessment in the Planktonic Biofiltration System

Oceanology - The concentration of trace elements (Fe, Mn, Cr, Co, Ni, Cu, Pb, Cd, and As) through the planktonic food chain of the White Sea have been studied with an experimental approach. The...     

Classification of orbits in the plane isosceles three-body problem

The general plane isosceles three-body problem is considered for different ratios of the central body mass to the masses of other bodies. The central body goes through the middle of the segment connecting the other bodies along the perpendicular to this segment. The initial conditions are chosen by two parameters: the virial ratio k and the parameter     , where r˙ is the relative velocity of the 'outer' bodies, and R˙ is the velocity of the 'central' body with respect to the mass centre of the 'outer' bodies. The equations of motion are numerically integrated until one of three times: the time of escape of the central body, its time of ejection with   R >100 d   , or 1000 τ (here d is the mean size, and τ is the mean crossing time of the triple system). The regions corresponding to escapes of the central body after different numbers of triple approaches are found at the plane of parameters   k ∈(0,1)  and   μ ∈(-1,1)  . The regions of stable motions are revealed. The zones of regular and stochastic orbits are outlined. The fraction of stochastic trajectories increases with the central mass. The fraction of stable orbits is highest for equal masses of the bodies.     

Analysis of the neighborhood of the 2: 1 resonance in the equal-mass three-body problem

We consider the trajectories in the neighborhood of a 2: 1 resonance (in periods of osculating motions of the outer and inner binaries) in the plane equal-mass three-body problem. We identified the zones of motions that are stable on limited time intervals. All of them correspond to the retrograde motions of the outer and inner subsystems. The prograde motions are unstable: the triple system breaks up into a final binary and an escaping component. In the barycentric nonrotating coordinate system, the trajectories occasionally form symmetric structures composed of several leaves. These structures persist for a long time, and, subsequently, the trajectories of the bodies fill compact regions in coordinate space.     

Annual Variations in the Moisture Content of Gray Silts in a Reservoir

Relations between annual variations in sediment moisture content in the channel section of the Mozhaisk Reservoir, on the one hand, and bottom temperature and reservoir water level, on the other hand, are discussed. Exchange adsorption, as well as compaction and decompaction of bottom sediments under the effect of reservoir water level fluctuations are considered as the main mechanisms forming the above relations.     

Iron compound occurrence forms in freshwater deposits: Analytical review

Data on the occurrence forms and concentrations of crystalline, amorphous, and organic Fe in the solid phase of silts in lakes and reservoirs, as well as data on concentrations of Fe forms in the pore solution of deposits are analyzed. The major mechanisms of Fe compound transformations are briefly considered.     

Periodic orbits in the general three-body problem and the relationship between them

We study the regions of finite motions in the vicinity of three simple stable periodic orbits in the general problem of three equal-mass bodies with a zero angular momentum. Their distinctive feature is that one of the moving bodies periodically passes through the center of mass of the triple system. We consider the dynamical evolution of plane nonrotating triple systems for which the initial conditions are specified in such a way that one of the bodies is located at the center of mass of the triple system. The initial conditions can then be specified by three parameters: the virial coefficient k and the two angles, φ₁ and φ₂, that characterize the orientation of the velocity vectors for the bodies. We scanned the region of variation in these parameters k∈(0, 1); φ₁, φ₂∈(0, π) at steps of δk=0.01; δφ₁=δφ₂=1° and identified the regions of finite motions surrounding the periodic orbits. These regions are isolated from one another in the space of parameters (k, φ₁, φ₂). There are bridges that correspond to unstable orbits with long lifetimes between the regions. During the evolution of these metastable systems, the phase trajectory can “stick” to the vicinity of one of the periodic orbits or move from one vicinity to another. The evolution of metastable systems ends with their breakup.     

The decay of triple systems

Numerical simulations have been carried out in the general three-body problem with equal masses with zero initial velocities, to investigate the distribution of the decay times T based on a representative sample of initial conditions. The distribution has a power-law character on long time scales, f(T) ∝ T ^?α , with α = 1.74. Over small times T < 30T _cr (T _cr is the mean crossing time for a component of the triple system), a series of local maxima separated by about 1.0T _cr is observed in the decay-time distribution. These local peaks correspond to zones of decay after one or a few triple encounters. Figures showing the arrangement of these zones in the domain of the initial conditions are presented.