Mathématiques physiques

The use of the data assimilation technique to identify optimal topography is discussed in frames of time-dependent motion governed by nonlinear barotropic ocean model. As-similation of arti cially generated data allows to measure the in uence of various error sources and to classify the impact of noise that is present in observational data and model parameters. The choice of length of the assimilation window in 4DVar is discussed. It is shown that using longer window lengths would provide more accurate ocean topography. The topography de ned using this technique can be further used in other model runs that start from other initial conditions and are situated in other parts of the model's attractor.

In this paper we prove that Bose gas with weak pair interaction is nonergodic system. In order to prove this fact we consider the divergences in some nonequilibrium diagram technique. These divergences are analogous to the divergences in the kinetic equations discovered by Cohen and Dorfman. We develop the general theory of renormalization of such divergences and illustrate it with some simple examples. The fact that the system is nonergodic leads to the following consequence: to prove that the system tends to the thermal equilibrium we should take into account its behavior on its boundary. In this paper we illustrate this thesis with the Bogoliubov derivation of the kinetic equations.

By using the Hamiltonian form of the Maxwell equations, a biquaternionic model of electro-gravimagnetic (EGM) field is proposed. The EGM-field equations, generating different charges and currents, are constructed. The field analogs of three Newton’s laws are formulated for free and interacting charges and currents, as well as the total field of interaction. The Lorentz invariance of the EGM-field equations is investigated (in particular, the charge-current conservation law). It is shown that at the presence of field interaction, this law differs from the well-known one. A new modification of the Maxwell equations is proposed with the scalar resistance field in the biquaternion EGM-field tension. Relativistic transformations of mass and charge-current densities, forces, and their powers are constructed. The solution of the Cauchy problem is given for equation of charge-current transformations.

We consider several models of the damped oscillators in nonrelativistic quantum me-chanics in a framework of a general approach to the dynamics of the time-dependent Schr•odinger equation with variable quadratic Hamiltonians. The Green functions are explicitly found in terms of elementary functions and the corresponding gauge trans-formations are discussed. The factorization technique is applied to the case of a shifted harmonic oscillator. The time evolution of the expectation values of the energy-related operators is determined for two models of the quantum damped oscillators under con-sideration. The classical equations of motion for the damped oscillations are derived for the corresponding expectation values of the position operator.