R-matrix-Floquet theory of multiphoton processes:VIII. A linear equations method

A new linear equations method for calculating the R-matrix, which arises in the R-matrix-Floquet theory of multiphoton processes, is introduced. This method replaces the diagonalization of the Floquet Hamiltonian matrix by the solution of a set of linear simultaneous equations which are solved, in the present work, by the conjugate gradient method. This approach uses considerably less computer memory and can be readily ported onto parallel computers. It will thus enable much larger problems of current interest to be treated. This new method is tested by applying it to three-photon ionization of helium at frequencies where double resonances with a bound state and autoionizing states are important. Finally, an alternative linear equations method, which avoids the explicit calculation of the R-matrix by incorporating the boundary conditions directly, is described in an appendix.

Experimental Moments: R.U.R. and the Birth of British Television Science Fiction

Drawing on material from the BBC Written Archive Centre, this article examines the earliest sf dramas broadcast by the BBC Television Service: two adaptations of Karel Capek's "R.U.R." ("Rossum's Universal Robots") from 1938 and 1948. These productions are used as sites of formal experimentation with the possibilities of the new medium, representing one aspect of contemporary debates about the purpose of television and the style it would assume.

Review: R. Bellamy, D. Castiglione and J. Shaw (eds.), Making European Citizens (Palgrave Macmillan, 2006)

Review of edited collection.

Hypercyclic tuples of operators on $C^n$ and $R^n$

A tuple $(T_1,\dots,T_n)$ of continuous linear operators on a topological vector space $X$ is called hypercyclic if there is $x\in X$ such that the the orbit of $x$ under the action of the semigroup generated by $T_1,\dots,T_n$ is dense in $X$. This concept was introduced by N.~Feldman, who have raised 7 questions on hypercyclic tuples. We answer those 4 of them, which can be dealt with on the level of operators on finite dimensional spaces. In
particular, we prove that the minimal cardinality of a hypercyclic tuple of operators on $\C^n$ (respectively, on $\R^n$) is $n+1$ (respectively, $\frac n2+\frac{5+(-1)^n}{4}$), that there are non-diagonalizable tuples of operators on $\R^2$ which possess an orbit being neither dense nor nowhere dense and construct a hypercyclic 6-tuple of operators on $\C^3$ such that every operator commuting with each member of the tuple is non-cyclic.

Atomic harmonic generation in time-dependent R-matrix theory

We have developed the capability to determine accurate harmonic spectra for multielectron atoms within time-dependent R-matrix (TDRM) theory. Harmonic spectra can be calculated using the expectation value of the dipole length, velocity, or acceleration operator. We assess the calculation of the harmonic spectrum from He irradiated by 390-nm laser light with intensities up to 4 x 10(14) W cm(-2) using each form, including the influence of the multielectron basis used in the TDRM code. The spectra are consistent between the different forms, although the dipole acceleration calculation breaks down at lower harmonics. The results obtained from TDRM theory are compared with results from the HELIUM code, finding good quantitative agreement between the methods. We find that bases which include pseudostates give the best comparison with the HELIUM code, but models comprising only physical orbitals also produce accurate results.