Abstract : The goal of this STTR project is to develop a unified computational framework integrating adequate physical models for simulating complex non-equilibrium plasmas. The project aims to classify possible scenarios of plasma dynamics and develop general recipes for clustering phase space into sub-domains evolving at different scales and efficiently solve the dynamics for each scale. During Phase I, we developed a methodology to apply methods of Invariant Manifolds and the Renormalization Group for reduced description of plasma kinetics and the transition from micro to macro. We have tested state-of-the-art deterministic Eulerian and Lagrangian kinetic solvers (Vlasov, Pokker-Planck, Poltzmann) , investigated new algorithms (such as adaptive mesh in velocity space) and implemented basic plasma capabilities within the Adaptive Mesh and Algorithm Refinement framework. We prepared Phase II work plan where the proposed methodology could he fully developed and implemented in the next generation software for multi-scale plasma simulations. The new capabilities would be valuable for low-pressure weakly-collisional plasma systems with stochastic electron heating and anomalous skin effect, and for high-pressure discharges with runaway electrons, e-beams, sparks and streamers.

The book deals with so-called renormalization group symmetries considered in the framework of approximate transformation groups. Renormgroup symmetries provide a basis for the renormgroup algorithm for improving solutions to boundary value problems by converting "less applicable solutions" into "more applicable solutions". the algorithm is particularly useful for improving approximate solutions given by the perturbation theory.

We review the recent advances in constructing analytical solutions of self-consistent Vlasov-Poisson equations in plasma. These solutions describe different physical phenomena, such as the ion acceleration in the adiabatic expansion of a plasma bunch and the Coulomb explosion of cluster plasma. The particle distribution function, mean velocity, and density distribution, as well as the energy spectra for accelerated ions, are discussed.

The paper contains generalization of the renormgroup algorithm for boundary value problems of mathematical physics and related concept of the renormgroup symmetry, formulated earlier by authors with reference to models based on differential equations. These algorithm and symmetry are formulated now for models with non local (integral) equations. We discuss in detail and illustrate by examples applications of the generalized algorithm to models with not local terms which appear as linear functionals of the solution.

Experience is presented regarding the installation and operation of an observation system for the pile bed of a slab foundation at a site prone to karst formation using monitoring-measuring piles with special sensors, and also results of long-term observation of their readings. A procedure for validating the scheme used to deploy control piles and its probability assessment is described.

A singular solution of the boundary value problem for the system of equations describing wave beam self-focusing is investigated by constructing renormalization group symmetries. New analytic expressions are found that characterize the spatial evolution of a beam with an arbitrary initial profile in a medium with cubic nonlinearity. The behavior of a Gaussian beam is thoroughly analyzed up to the moment the solution singularity is formed, and a hypothesis is proposed for describing the solution structure after the singularity occurs.

An original approach to constructing special type symmetries for boundary value problems, RENORMGROUP SYMMETRIES, is reviewed here. It is applied to a system of geometric optics equations. New solutions to the laser beam self-focusing problem are presented.

where the charge density ρ and current density j are in turn governed by motion of particles:Equations ( 1)-( 3) are known as Vlasov-Maxwell equations [10].

On decrit une methode permettant de prevoir les vibrations d'un sol et de determiner les distances de securite par rapport aux batiments existants a partir des donnees de sondage statique. On presente des resultats experimentaux de determination des refus elastiques attendus des pieux et des vibrations elastiques du sol au voisinage immediat d'un pieu en utilisant un coefficient de glissement.

A method of predicting soil vibrations during pile driving and determining safe distances to existing buildings using static-penetration data is discussed. Experimental data on determination of expected elastic failures of piles and elastic vibrations of the soil in the immediate vicinty of the pile using the slip factor are cited.

It is shown that there is a set of oscillations with 0.5n(n + 1) periods against the background of a dependence of the efficiency of conversion of laser radiation into n≥2 harmonics that decays monotonically with increasing laser plasma temperature. The electron rest energy reduced by a factor (L / λ) ≫ 1 (L is the characteristic inhomogeneity scale of the plasma density, λ is the wavelength of the laser radiation) serves as the characteristic scale of the periods, which are an algebraic function of the harmonic number. In a hot laser plasma (T > 1 keV) with an inhomogeneity scale L = 50 μm exposed to the action of neodymium laser radiation, the flux density of the third harmonic oscillates with a period of the order of 0.5 keV.