Dynamics of a particle confined in a two-dimensional dilating and deforming domain

Some recent results concerning a particle confined in a one-dimensional box with moving walls are briefly reviewed. By exploiting the same techniques used for the 1D problem, we investigate the behavior of a quantum particle confined in a two-dimensional box (a 2D billiard) whose walls are moving, by recasting the relevant mathematical problem with moving boundaries in the form of a problem with fixed boundaries and time-dependent Hamiltonian. Changes of the shape of the box are shown to be important, as it clearly emerges from the comparison between the "pantographic", case (same shape of the box through all the process) and the case with deformation.Comment: 13 pages, 2 figure

Introducing Variable Cell Shape Methods in Field Theory Simulations of Polymers

We propose a new method for carrying out field-theoretic simulations of polymer systems under conditions of prescribed external stress, allowing for shape changes in the simulation box. A compact expression for the deviatoric stress tensor is derived in terms of the chain propagator, and is used to monitor changes in the box shape according to a simple relaxation scheme. The method allows fully relaxed, stress free configurations to be obtained even in non trivial morphologies, and enables the study of morphology transitions induced by external stresses

Point of view: Te Ruru light festival 2019

Point of View is a perception based installation presented as part of Te Ruru Light Festival 2019. The work consists of a 3 sided box suspended above the viewer. The box is painted white and is projected onto from above the primary viewing point (this prevents the viewer from noticing the projector, but also from blocking the projection). The light-based projection onto the surface of the box creates the illusion that the 3 sided box is actually a 6 sided cube. The viewer is invited to move around the space, observing the cube. Once the viewer walks under or past the suspended cube, they enter the secondary viewpoint in which they see the actual form of the box – a 3 sided/open box. The work talks about how our individual experiences shape the way we see. It raises questions about the difference between reality and perception

Physically-Based Modeling

Physically based modeling is a growing trend in computer animation. There are many implementations available for this topic. The most basic of these involves the movement of single particles (without a shape) moving through space. This implementation involves the movement of particles that have a rigid structure, such as a box or ball, known as rigid bodies. It features a simple box comprised of 8 points moving through space according to the laws of physics as it makes contact with a surface

Heat-treatment of metal parts facilitated by sand embedment

Embedding metal parts of complex shape in sand contained in a steel box prevents strains and warping during heat treatment. The sand not only provides a simple, inexpensive support for the parts but also ensures more uniform distribution of heat to the parts

Tableaux and plane partitions of truncated shapes

We consider a new kind of straight and shifted plane partitions/Young tableaux --- ones whose diagrams are no longer of partition shape, but rather Young diagrams with boxes erased from their upper right ends. We find formulas for the number of standard tableaux in certain cases, namely a shifted staircase without the box in its upper right corner, i.e. truncated by a box, a rectangle truncated by a staircase and a rectangle truncated by a square minus a box. The proofs involve finding the generating function of the corresponding plane partitions using interpretations and formulas for sums of restricted Schur functions and their specializations. The number of standard tableaux is then found as a certain limit of this function.Comment: Accepted to Advances in Applied Mathematics. Final versio