Shape in an Atom of Space: Exploring quantum geometry phenomenology

A phenomenology for the deep spatial geometry of loop quantum gravity is introduced. In the context of a simple model, an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used to develop a model of angular corrections to local, continuum flat-space 3-geometries. The physical effects involve neither breaking of local Lorentz invariance nor Planck scale suppression, but rather reply on only the combinatorics of SU(2) recoupling. Bhabha scattering is discussed as an example of how the effects might be observationally accessible.Comment: 14 pages, 7 figures; v2 references adde

Simplicial minisuperspace models in the presence of a massive scalar field with arbitrary scalar coupling

We extend previous simplicial minisuperspace models to account for arbitrary scalar coupling \eta R\phi^2.Comment: 24 pages and 9 figures. Accepted for publication by Classical and Quantum Gravit

Linearization of generalized interval exchange maps

A standard interval exchange map is a one-to-one map of the interval which is locally a translation except at finitely many singularities. We define for such maps, in terms of the Rauzy-Veech continuous fraction algorithm, a diophantine arithmetical condition called restricted Roth type which is almost surely satisfied in parameter space. Let $T_0$ be a standard interval exchange map of restricted Roth type, and let $r$ be an integer $\geq 2$. We prove that, amongst $C^{r+3}$ deformations of $T_0$ which are $C^{r+3}$ tangent to $T_0$ at the singularities, those which are conjugated to $T_0$ by a $C^r$ diffeomorphism close to the identity form a $C^1$ submanifold of codimension $(g-1)(2r+1) +s$. Here, $g$ is the genus and $s$ is the number of marked points of the translation surface obtained by suspension of $T_0$. Both $g$ and $s$ can be computed from the combinatorics of $T_0$.Comment: 52 pages. This version includes a new section where we explain how to adapt our result to the setting of perturbations of linear flows on translation surface

A Monolithically Fabricated Combinatorial Mixer for Microchip-Based High-Throughput Cell Culturing Assays

We present an integrated method to fabricate 3- D microfluidic networks and fabricated the first on-chip cell culture device with an integrated combinatorial mixer. The combinatorial mixer is designed for screening the combinatorial effects of different compounds on cells. The monolithic fabrication method with parylene C as the basic structural material allows us to avoid wafer bonding and achieves precise alignment between microfluidic channels. As a proof-of-concept, we fabricated a device with a three-input combinatorial mixer and demonstrated that the mixer can produce all the possible combinations. Also, we demonstrated the ability to culture cells on-chip and performed a simple cell assay on-chip using trypan blue to stain dead cells