arXiv subjects
Publications and source records attributed to A. Woszczyna.
General description of an on-line procedure of calibration for IGRT (Image Guided Radiotherapy) is given. The algorithm allows to improve targeting cancer by estimating its position in space and suggests appropriate correction of the position of the patient. The description is given in the Geometric Algebra language which significantly simplifies calculations and clarifies presentation.
In the present paper a general setup for determination of imperfect geometry of radiotherapeutic devices has been proposed that base on geometric algebra framework. To account for this imperfect geometry, two methods of a calibration were presented, consisting of determining for each angular position of a gantry a correction shift which must be applied to the origin of a laboratory frame of reference to place it along a radiation axis for this angular position. Closed form solutions for these corrections are provided.
In this paper, we briefly discuss the dynamic and functional approach to computer symbolic tensor analysis. The ccgrg package for Wolfram Language/Mathematica is used to illustrate this approach. Some examples of applications are attached.
The transition from acoustic noise in the radiation-dominated universe to the density structures in the matter dominated epoch is considered. The initial state is a stochastic field of sound waves moving in different directions. The construction of the initial state is compatible with the hyperbolic type of propagation equation for density perturbations, and parallel to the theory of stochastic background of gravitational waves. Instantaneous transition between the cosmological epochs is assumed, and Darmois-Israel joining conditions are applied to match solutions for sound waves with growing or decaying modes at the decoupling. As a result a substantial amplification of the low scale structures is obtained.
Nonlinear growth of one-dimensional density structures with a frozen-in magnetic field is investigated in Newtonian cosmology. A mechanism of magnetic field amplification is discussed. We discuss the relation between the initial conditions for the velocity field and the basic time-scales determining the growth of the magnetized structure.
Density perturbations in the flat (K=0) Robertson-Walker universe with radiation ($p=ε/3$) and positive cosmological constant ($Λ>0$) are investigated. The phenomenon of anomalous dispersion of acoustic waves on $Λ$ is discussed.