Living in The Matrix: Virtual Reality Systems and Hyperspatial Representation in Architecture

In the digital age, the hyperspace of virtual reality systems stands out as a new spatial concept creating a parallel realm to "real" space. Virtual reality influences one’s experience of and interaction with architectural space. This "otherworld" brings up the criticism of the existing conception of space, time and body. Hyperspaces are relatively new to designers but not to filmmakers. Their cinematic representations help the comprehension of the outcomes of these new spaces. Visualisation of futuristic ideas on the big screen turns film into a medium for spatial experimentation. Creating a possible future, The Matrix (Andy and Larry Wachowski, 1999) takes the concept of hyperspace to a level not-yet-realised but imagined. With a critical gaze at the existing norms of architecture, the film creates new horizons in terms of space. In this context, this study introduces science fiction cinema as a discussion medium to understand the potentials of virtual reality systems for the architecture of the twenty first century. As a "role model" cinema helps to better understand technological and spatial shifts. It acts as a vehicle for going beyond the spatial theories and designs of the twentieth century, and defining the conception of space in contemporary architecture.

Combined R-matrix eigenstate basis set and finite-difference propagation method for the time-dependent Schrodinger equation: The one-electron case

In this work we present the theoretical framework for the solution of the time-dependent Schrödinger equation (TDSE) of atomic and molecular systems under strong electromagnetic fields with the configuration space of the electron’s coordinates separated over two regions; that is, regions I and II. In region I the solution of the TDSE is obtained by an R-matrix basis set representation of the time-dependent wave function. In region II a grid representation of the wave function is considered and propagation in space and time is obtained through the finite-difference method. With this, a combination of basis set and grid methods is put forward for tackling multiregion time-dependent problems. In both regions, a high-order explicit scheme is employed for the time propagation. While, in a purely hydrogenic system no approximation is involved due to this separation, in multielectron systems the validity and the usefulness of the present method relies on the basic assumption of R-matrix theory, namely, that beyond a certain distance (encompassing region I) a single ejected electron is distinguishable from the other electrons of the multielectron system and evolves there (region II) effectively as a one-electron system. The method is developed in detail for single active electron systems and applied to the exemplar case of the hydrogen atom in an intense laser field.

Eigenvalues of the time-delay matrix in overlapping resonances

We discuss the properties of the lifetime or the time-delay matrix Q(E) for multichannel scattering, which is related to the scattering matrix S(E) by Q = i?S(dS†/dE). For two overlapping resonances occurring at energies E with widths G(? = 1, 2), with an energy-independent background, only two eigenvalues of Q(E) are proved to be different from zero and to show typical avoided-crossing behaviour. These eigenvalues are expressible in terms of the four resonance parameters (E , G) and a parameter representing the strength of the interaction of the resonances. An example of the strong and weak interaction in an overlapping double resonance is presented for the positronium negative ion. When more than two resonances overlap (? = 1, ..., N), no simple representation of each eigenvalue has been found. However, the formula for the trace of the Q-matrix leads to the expression d(E) = -?arctan[(G/2)/(E - E)] + d(E) for the eigenphase sum d(E) and the background eigenphase sum d(E), in agreement with the known form of the state density. The formulae presented in this paper are useful in a parameter fitting of overlapping resonances. © 2006 IOP Publishing Ltd.

Form Follows Media::What is The Matrix as Film, Animation, Game and Comics?

In the digital age, the hyperspace of virtual reality systems stands out as a new spatial notion creating a parallel world to the space we live in. In this alternative realm, the body transforms into a hyperbody, and begins to follow the white rabbit. Not only in real world but also in the Matrix world. The Matrix project of Andy and Larry Wachowski started with a feature film released in 1999. However, The Matrix is not only a film (trilogy). It is a concept, a universe that brings real space and hyperspace together. It is a world represented not only in science fiction films but also in The Animatrix that includes nine animated Matrix films directed by Peter Chung, Andy Jones, Yoshiaki Kawajiri and others, four of which are written by the Wachowskis. The same universe is used in Enter the Matrix, a digital game whose script was written and directed by the brothers and a comic book, The Matrix Comics, which includes twelve different stories by artists like Neil Gaiman and Goef Darrow. The Wachowskis played an active role in the creation and realization of all these “products” of different media. The comic book came last (November 2003), however it is possible to argue that everything came out of comics – the storyboards of the original film. After all the Wachowskis have a background in comics.

In this study, I will focus on the formal analysis of the science fiction world of The Matrix - as a representation of hyperspace - in different media, feature film, animated film, digital game and comic book, focusing on diverse forms of space that come into being as a result of medium differences. To unfold the different formal characters of film, animation, game and comics, concepts and features including framing, flattening, continuity, movement, montage, sound/text, light and color will be discussed. An analysis of these products will help to open up a discussion on the relation of form, media and representation.

Liouville-space R-matrix-Floquet description of atomic radiative processes involving autoionizing states in the presence of intense electromagnetic fields

A reduced-density-operator description is developed for coherent optical phenomena in many-electron atomic systems, utilizing a Liouville-space, multiple-mode Floquet–Fourier representation. The Liouville-space formulation provides a natural generalization of the ordinary Hilbert-space (Hamiltonian) R-matrix-Floquet method, which has been developed for multi-photon transitions and laser-assisted electron–atom collision processes. In these applications, the R-matrix-Floquet method has been demonstrated to be capable of providing an accurate representation of the complex, multi-level structure of many-electron atomic systems in bound, continuum, and autoionizing states. The ordinary Hilbert-space (Hamiltonian) formulation of the R-matrix-Floquet method has been implemented in highly developed computer programs, which can provide a non-perturbative treatment of the interaction of a classical, multiple-mode electromagnetic field with a quantum system. This quantum system may correspond to a many-electron, bound atomic system and a single continuum electron. However, including pseudo-states in the expansion of the many-electron atomic wave function can provide a representation of multiple continuum electrons. The 'dressed' many-electron atomic states thereby obtained can be used in a realistic non-perturbative evaluation of the transition probabilities for an extensive class of atomic collision and radiation processes in the presence of intense electromagnetic fields. In order to incorporate environmental relaxation and decoherence phenomena, we propose to utilize the ordinary Hilbert-space (Hamiltonian) R-matrix-Floquet method as a starting-point for a Liouville-space (reduced-density-operator) formulation. To illustrate how the Liouville-space R-matrix-Floquet formulation can be implemented for coherent atomic radiative processes, we discuss applications to electromagnetically induced transparency, as well as to related pump–probe optical phenomena, and also to the unified description of radiative and dielectronic recombination in electron–ion beam interactions and high-temperature plasmas.

Valence and L-shell photoionization of Cl-like argon using R-matrix techniques

Photoionization cross-sections are obtained using the relativistic DiracAtomic R-matrix Codes (DARC) for all valence and L-shell energy ranges between 27 and 270 eV. A total of 557 levels arising from the dominant configurations 3s²3p⁴, 3s³p5, 3p⁶, 3s²3p³[3d, 4s, 4p], 3p⁵3d, 3s²3p²3d², 3s³p4³d, 3s³p3³d2 and 2s²2p⁵3s²3p⁵ have been included in the targetwavefunction representation of the Ar III ion, including up to 4p in the orbital basis. We also performed a smaller Breit-Pauli (BP) calculation containing the lowest 124 levels. Direct comparisons are made with previous theoretical and experimental work for both valence shell and L-shell photoionization. Excellent agreement was found for transitions involving the ²P^o initial state to all allowed final states for both calculations across a range of photon energies. A number of resonant states have been identified to help analyse and explain the nature of the spectra at photon energies between 250 and 270 eV.

Photoionization of Co+ and electron-impact excitation of Co2 + using the Dirac R-matrix method

Modelling of massive stars and supernovae (SNe) plays a crucial role in understanding galaxies. From this modelling we can derive fundamental constraints on stellar evolution, mass-loss processes, mixing, and the products of nucleosynthesis. Proper account must be taken of all important processes that populate and depopulate the levels (collisional excitation, de-excitation, ionization, recombination, photoionization, bound–bound processes). For the analysis of Type Ia SNe and core collapse SNe (Types Ib, Ic and II) Fe group elements are particularly important. Unfortunately little data is currently available and most noticeably absent are the photoionization cross-sections for the Fe-peaks which have high abundances in SNe. Important interactions for both photoionization and electron-impact excitation are calculated using the relativistic Dirac atomic R-matrix codes (DARC) for low-ionization stages of Cobalt. All results are calculated up to photon energies of 45 eV and electron energies up to 20 eV. The wavefunction representation of Co III has been generated using GRASP0 by including the dominant 3d⁷, 3d⁶[4s, 4p], 3p⁴3d⁹ and 3p⁶3d⁹ configurations, resulting in 292 fine structure levels. Electron-impact collision strengths and Maxwellian averaged effective collision strengths across a wide range of astrophysically relevant temperatures are computed for Co III. In addition, statistically weighted level-resolved ground and metastable photoionization cross-sections are presented for Co II and compared directly with existing work.