Infinite planar string: cusps, braids and soliton exitations

We investigate infinite strings in $(2+1)D$ space-time, which may be considered as excitations of straight lines on the spatial plane. We also propose the hamiltonian description of such objects that differs from the standard hamiltonian description of the string. The hamiltonian variables are separated into two independent groups: the "internal" and "external" variables. The first ones are invariant under space-time transformations and are connected with the second form of the world-sheet. The "external" variables define the embedding of the world-sheet into space-time. The constructed phase space is nontrivial because the finite number of constraints entangles the variables from these groups. First group of the variables constitute the coefficients for the pair of first-order spectral problems; the solution of these problems is necessary for the reconstruction of the string world-sheet. We consider the excitations, which correspond to "N- soliton" solution of the spectral problem, and demonstrate that the reconstructed string has cuspidal points. World lines of such points form braids of various topologies.Comment: 16 pages, 4 figure

About the Poisson Structure for D4 Spinning String

The model of D4 open string with non-Grassmann spinning variables is considered. The non-linear gauge, which is invariant both Poincar\'e and scale transformations of the space-time, is used for subsequent studies. It is shown that the reduction of the canonical Poisson structure from the original phase space to the surface of constraints and gauge conditions gives the degenerated Poisson brackets. Moreover it is shown that such reduction is non-unique. The conseption of the adjunct phase space is introduced. The consequences for subsequent quantization are discussed. Deduced dependence of spin $J$ from the square of mass $\mu^2$ of the string generalizes the ''Regge spectrum`` for conventional theory.Comment: 23 page

Determination of kinetic parameters for a pyrotechnic mixture

A general approach is considered to covering formally kinetic parameters from experiments for ignition, firing, or combustion of condensed substances based on minimizing discrepancies in experimental and calculated values. Results are provided for determining kinetic constants of a pyrotechnic mixture from data of firing it by a heated surface at a constant temperature

Research of gas flow movement in flash smelting furnace of Nadezhda Metallurgical Plant by mathematical modeling methods

In the recent years, Polar Division of JSC "Norilsk Nikel" have defined the tendency to ore base impoverishment, which makes a significant influence on composition and volume of metal-bearing feed, treated in the flash smelting furnaces of Nadezhda Metallurgical Plant. The flash smelting furnaces' stable performance (or workability) depends on the feed composition and characteristics. In particular, changes in composition and characteristics of ore fed to the flash smelting furnaces led to serious build-up formation in uptakes and settlers of flash smelting furnace-1 and flash smelting furnace-2. The build-up became rather sizeable, blocking the uptake and settler joint cross-section, disrupting regular gas removal from the furnace. For the purpose of analysis of build-up formation causes (using mathematical simulation), the gas stream flow behaviour in the flash smelting furnaces' uptake and settler was investigated together with the factors, influencing the gas stream at various furnace operating conditions. The results of the studies of the gas phase flow in the flash smelting furnaces' uptake and settler obtained via mathematical simulation are presented. The mathematical model was developed on the basis of Navier-Stokes equations, using classic turbulence model. Gas composition changes within acceptable industrial limits did not exert any marked effect on the flash smelting furnace gases flow. The furnace design and off-gases volume are the principal factors influencing the gas phase flow

Autocatalysis in thermal decomposition of polymers

Possibility of replicating polymer decomposition by a single global reaction greatly simplifies pyrolysis modeling. Apparent kinetic parameters are normally derived from the microscale experiments with linear heating program, and the n-th order reaction is routinely assumed thereby strongly affecting the numerical values of the kinetic parameters. In this work, we demonstrate inconsistency of the n-th order reaction assumption and reveal the autocatalytic behavior in thermal degradation of polyethylene, polystyrene and polycarbonate. The autocatalysis manifests itself in non-monotonicity of the conversion function, which markedly increases in a wide range of conversions. Although the iso-conversional approach makes it possible to explicitly recover the conversion function from the measurements, this option has not been used in most of the previous studies. Meanwhile, proper approximation of the experimentally derived conversion function results in excellent replication of the measured reaction rates, with the same kinetic parameters, in a range of the heating rates. Thus developed thermal decomposition kinetic models are provided in this paper for three kinds of polyethylene (LDPE, HDPE, and UHMWPE), seven kinds of polystyrene, polycarbonate, and two kinds of polymethylmethacrylate with different molecular weights. Although the pyrolysis of the polymers with different molecular weights proceeds differently, no systematic correlation of the pyrolysis characteristics (conversion-averaged apparent activation energy, heat of combustion, peak reaction rates and temperatures etc.) with the molecular weight has been observed for polystyrene. Peak reaction rates and temperatures varied in opposite directions for polyethylene and polymethylmethacrylate

Advancement in turbulent spray modelling:The effect of internal temperature gradient in droplets

Two simple and yet sufficiently accurate approaches to predict surface temperature of a vaporizing droplet (higher order polynomial approximation and the heat balance integral method) are proposed. Being computationally inexpensive these approaches are tested as candidates for use in high-resolution LES spray modelling. Robust and efficient numerical algorithm for solving inherently stiff equations of droplet heating and evaporation has been developed. Robustness and computational efficiency of the proposed algorithm is achieved by use of unconditionally stable strongly implicit integration scheme and appropriate adaptation of the time step. The above methodology has been implemented in CFD spray model included in the in-house Fire3D code. The spray model has been applied to replicate three essentially different experimental scenarios in which turbulent sprays of water, acetone, and diesel fuel were investigated. Reasonable agreement has been demonstrated for predicted and measured droplet sizes and velocities as well as for the spray tip penetration dynamics. New numerical algorithms used to calculate surface temperatures of evaporating droplets with non-uniform internal temperature did not incur observable increase of CPU time in turbulent spray simulations