Stability Boundary and Design Criteria for Haptic Rendering of Virtual Walls

This paper is about haptic simulations of virtual walls, which are represented by a discrete PD-control. A normalized discrete-time transfer function is used to derive the fundamental stability boundaries for this problem. Hereby, the case of direct action and the more often case of an one sampling step delayed action are addressed. Inside the stable region the set of all parameters was determined that result in real system poles. Furthermore, three dierent design criteria are compared to nd optimum control parameters for the virtual wall. Finally, important conclusions for haptic simulations are derived

Toroidal mirrors provide virtual walls for breaks in light pipes

Section of light pipe consists of separated segments having opposed toroidal mirrors that intercept meridional rays to present virtual wall in space between mirrors, thus insuring uninterrupted light transmission down the pipe. Design affords internal access to pipe section. Segments are electrically or thermally insulated from one another

Stress tensor for a scalar field in a spatially varying background potential: Divergences, "renormalization," anomalies, and Casimir forces

Motivated by a desire to understand quantum fluctuation energy densities and stress within a spatially varying dielectric medium, we examine the vacuum expectation value for the stress tensor of a scalar field with arbitrary conformal parameter, in the background of a given potential that depends on only one spatial coordinate. We regulate the expressions by incorporating a temporal-spatial cutoff in the (imaginary) time and transverse-spatial directions. The divergences are captured by the zeroth- and second-order WKB approximations. Then the stress tensor is "renormalized" by omitting the terms that depend on the cutoff. The ambiguities that inevitably arise in this procedure are both duly noted and restricted by imposing certain physical conditions; one result is that the renormalized stress tensor exhibits the expected trace anomaly. The renormalized stress tensor exhibits no pressure anomaly, in that the principle of virtual work is satisfied for motions in a transverse direction. We then consider a potential that defines a wall, a one-dimensional potential that vanishes for $z<0$ and rises like $z^\alpha$, $\alpha>0$, for $z>0$. The full finite stress tensor is computed numerically for the two cases where explicit solutions to the differential equation are available, $\alpha=1$ and 2. The energy density exhibits an inverse linear divergence as the boundary is approached from the inside for a linear potential, and a logarithmic divergence for a quadratic potential. Finally, the interaction between two such walls is computed, and it is shown that the attractive Casimir pressure between the two walls also satisfies the principle of virtual work (i.e., the pressure equals the negative derivative of the energy with respect to the distance between the walls).Comment: 20 pages, 6 figure

MetaSpace II: Object and full-body tracking for interaction and navigation in social VR

MetaSpace II (MS2) is a social Virtual Reality (VR) system where multiple users can not only see and hear but also interact with each other, grasp and manipulate objects, walk around in space, and get tactile feedback. MS2 allows walking in physical space by tracking each user's skeleton in real-time and allows users to feel by employing passive haptics i.e., when users touch or manipulate an object in the virtual world, they simultaneously also touch or manipulate a corresponding object in the physical world. To enable these elements in VR, MS2 creates a correspondence in spatial layout and object placement by building the virtual world on top of a 3D scan of the real world. Through the association between the real and virtual world, users are able to walk freely while wearing a head-mounted device, avoid obstacles like walls and furniture, and interact with people and objects. Most current virtual reality (VR) environments are designed for a single user experience where interactions with virtual objects are mediated by hand-held input devices or hand gestures. Additionally, users are only shown a representation of their hands in VR floating in front of the camera as seen from a first person perspective. We believe, representing each user as a full-body avatar that is controlled by natural movements of the person in the real world (see Figure 1d), can greatly enhance believability and a user's sense immersion in VR.Comment: 10 pages, 9 figures. Video: http://living.media.mit.edu/projects/metaspace-ii

Tensor Networks with a Twist: Anyon-permuting domain walls and defects in PEPS

We study the realization of anyon-permuting symmetries of topological phases on the lattice using tensor networks. Working on the virtual level of a projected entangled pair state, we find matrix product operators (MPOs) that realize all unitary topological symmetries for the toric and color codes. These operators act as domain walls that enact the symmetry transformation on anyons as they cross. By considering open boundary conditions for these domain wall MPOs, we show how to introduce symmetry twists and defect lines into the state.Comment: 11 pages, 6 figures, 2 appendices, v2 published versio

Illusion optics: The optical transformation of an object into another object

We propose to use transformation optics to generate a general illusion such that an arbitrary object appears to be like some other object of our choice. This is achieved by using a remote device that transforms the scattered light outside a virtual boundary into that of the object chosen for the illusion, regardless of the profile of the incident wave. This type of illusion device also enables people to see through walls. Our work extends the concept of cloaking as a special form of illusion to the wider realm of illusion optics.Comment: Including a paper and its auxiliary materia

Field Fluctuations in a One-Dimensional Cavity with a Mobile Wall

We consider a scalar field in a one-dimensional cavity with a mobile wall. The wall is assumed bounded by a harmonic potential and its mechanical degrees of freedom are treated quantum mechanically. The possible motion of the wall makes the cavity length variable, and yields a wall-field interaction and an effective interaction among the modes of the cavity. We consider the ground state of the coupled system and calculate the average number of virtual excitations of the cavity modes induced by the wall-field interaction, as well as the average value of the field energy density. We compare our results with analogous quantities for a cavity with fixed walls, and show a correction to the Casimir potential energy between the cavity walls. We also find a change of the field energy density in the cavity, particularly relevant in the proximity of the mobile wall, yielding a correction to the Casimir-Polder interaction with a polarizable body placed inside the cavity. Similarities and differences of our results with the dynamical Casimir effect are also discussed.Comment: 5 pages, 2 figure