A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation

The fractional Fokker-Planck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the non-local property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations. In this paper, a space-time spectral method is presented for the numerical solution of the time fractional Fokker-Planck initial-boundary value problem. The proposed method employs the Jacobi polynomials for the temporal discretization and Fourier-like basis functions for the spatial discretization. Due to the diagonalizable trait of the Fourier-like basis functions, this leads to a reduced representation of the inner product in the Galerkin analysis. We prove that the time fractional Fokker-Planck equation attains the same approximation order as the time fractional diffusion equation developed in [23] by using the present method. That indicates an exponential decay may be achieved if the exact solution is sufficiently smooth. Finally, some numerical results are given to demonstrate the high order accuracy and efficiency of the new numerical scheme. The results show that the errors of the numerical solutions obtained by the space-time spectral method decay exponentially.

Reflexive and automatic violence: A function of aberrant perceptual inhibition

It’s commonly assumed that psychiatric violence is motivated by delusions, but here the concept of a reversed impetus is explored, to understand whether delusions are formed as ad-hoc or post-hoc rationalizations of behaviour or in advance of the actus reus. The reflexive violence model proposes that perceptual stimuli has motivational power and this may trigger unwanted actions and hallucinations. The model is based on the theory of ecological perception, where opportunities enabled by an object are cues to act. As an apple triggers a desire to eat, a gun triggers a desire to shoot. These affordances (as they are called) are part of the perceptual apparatus, they allow the direct recognition of objects – and in emergencies they enable the fastest possible reactions. Even under normal circumstances, the presence of a weapon will trigger inhibited violent impulses. The presence of a victim will also, but under normal circumstances, these affordances don’t become violent because negative action impulses are totally inhibited, whereas in psychotic illness, negative action impulses are treated as emergencies and bypass frontal inhibitory circuits. What would have been object recognition becomes a blind automatic action. A range of mental illnesses can cause inhibition to be bypassed. At its most innocuous, this causes both simple hallucinations (where the motivational power of an object is misattributed). But ecological perception may have the power to trigger serious violence also –a kind that’s devoid of motives or planning and is often shrouded in amnesia or post-rational delusions.

Permanent shift: the topology of Didier Vermeiren's Cariatide à la Pierre

Photographic documentation of sculpture produces significant consequences for the way in which sculptural space is conceived. When viewed as discrete mediums the interaction of the photograph and its sculptural subject is always framed by notions of loss. However, when taken as a composite system, the sculpture-photograph proposes a new ontology of space. In place of the fixity of medium, we can observe a topology at play: a theory drawn from mathematics in which space is understood not as a static field but in terms of properties of connectedness, movement and differentiation. Refracted through the photographic medium, sculpture becomes not a field of fixed points in space, but rather as a fluid set of relations - a continuous sequence of multiple ‘surfaces’, a network of shifting views. This paper will develop a topological account of studio practice through an examination of the work of the contemporary Belgian sculptor Didier Vermeiren (b. 1951). Since the 1980s, Vermeiren has made extensive use of photography in his sculptural practice. By analysing a series of iterations of his work Cariatide à la Pierre (1997-1998), this paper proposes that Vermeiren’s use of photography reveals patterns of connection that expand and complicate the language of sculpture, while also emphasising the broader topology of the artist’s practice as a network of ‘backward glances’ to previous works from the artist’s oeuvre and the art-historical canon. In this context, photography is not simply a method of documentation, but rather a means of revealing the intrinsic condition of sculpture as medium shaped by dynamic patterns of connection and change. In Vermeiren’s work the sculpture-photograph, has a composite identity that exceeds straightforward categories of medium. In their place, we can observe a practice based upon the complex interactions of objects whose ontology is always underpinned by a certain contingency. It is in this fundamental mobility, that the topology of Vermeiren’s practice can be said to rest.

The future passenger experience: A shift from physical to virtual design

The importance of passenger experience in aviation has become well understood in the last several years. It is now generally accepted that the provision of good passenger experience is not an option, but a necessity, from an aviation profitability perspective. In this paper, we paint a picture of the future passenger experience by consolidating a number of industry and research perspectives. Using the future passenger experience as a starting point, we explore the components needed to enable this future vision. From this bottom-up approach, we identify the need to resolve data formatting and data ownership issues. The resolution of these data integration issues is necessary to enable the seamless future travel experience that is envisioned by the aviation industry. By looking at the passenger experience from this bottom-up, data centric perspective, we identify a potential shift in the way that future passenger terminals will be designed. Whereas currently the design of terminals is largely an architectural practice, in the near future, the design of the terminal building may become more of a virtual technology practice. This of course will pose a new set of challenges to designers of airport terminal environments.