String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group $G$ and a 4-cocycle twist $\omega_4$ of $G$'s cohomology group $\mathcal{H}^4(G,\mathbb{R}/\mathbb{Z})$ in 3 dimensional space and 1 dimensional time (3+1D). We establish the topological spin and the spin-statistics relation for the closed strings, and their multi-string braiding statistics. The 3+1D twisted gauge theory can be characterized by a representation of a modular transformation group SL$(3,\mathbb{Z})$. We express the SL$(3,\mathbb{Z})$ generators $\mathsf{S}^{xyz}$ and $\mathsf{T}^{xy}$ in terms of the gauge group $G$ and the 4-cocycle $\omega_4$. As we compactify one of the spatial %3D's directions $z$ into a compact circle with a gauge flux $b$ inserted, we can use the generators $\mathsf{S}^{xy}$ and $\mathsf{T}^{xy}$ of an SL$(2,\mathbb{Z})$ subgroup to study the dimensional reduction of the 3D topological order $\mathcal{C}^{3\text{D}}$ to a direct sum of degenerate states of 2D topological orders $\mathcal{C}_b^{2\text{D}}$ in different flux $b$ sectors: $\mathcal{C}^{3\text{D}} = \oplus_b \mathcal{C}_b^{2\text{D}}$. The 2D topological orders $\mathcal{C}_b^{2\text{D}}$ are described by 2D gauge theories of the group $G$ twisted by the 3-cocycles $\omega_{3(b)}$, dimensionally reduced from the 4-cocycle $\omega_4$. We show that the SL$(2,\mathbb{Z})$ generators, $\mathsf{S}^{xy}$ and $\mathsf{T}^{xy}$, fully encode a particular type of three-string braiding statistics with a pattern that is the connected sum of two Hopf links. With certain 4-cocycle twists, we discover that, by threading a third string through two-string unlink into three-string Hopf-link configuration, Abelian two-string braiding statistics is promoted to non-Abelian three-string braiding statistics.

Gapped domain walls, as topological line defects between 2+1D topologically ordered states, are examined. We provide simple criteria to determine the existence of gapped domain walls, which apply to both Abelian and non-Abelian topological orders. Our criteria also determine which 2+1D topological orders must have gapless edge modes, namely which 1+1D global gravitational anomalies ensure gaplessness. Furthermore, we introduce a new mathematical object, the tunneling matrix $W$, whose entries are the fusion-space dimensions $W_{ia}$, to label different types of gapped domain walls. Mathematically, we propose a classification of bimodule categories between modular tensor categories. By studying many examples, we find evidence that the tunneling matrices are powerful quantities to classify different types of gapped domain walls. Since a gapped boundary is a gapped domain wall between a bulk topological order and the vacuum, regarded as the trivial topological order, our theory of gapped domain walls inclusively contains the theory of gapped boundaries. In addition, we derive a topological ground state degeneracy formula, applied to arbitrary orientable spatial 2-manifolds with gapped domain walls, including closed 2-manifolds and open 2-manifolds with gapped boundaries.

For spacetimes that are not asymptotic to anti-de Sitter Space (non AAdS), we adapt the Lewkowycz-Maldacena procedure to find the holographic entanglement entropy. The key observation, which to our knowledge is not very well appreciated, is that asymptotic boundary conditions play an essential role on extending the replica trick to the bulk. For non AAdS, we expect the following three main modifications: (1) the expansion near the special surface has to be compatible with the asymptotic expansion; (2) periodic conditions are imposed to coordinates on the phase space with diagonalized symplectic structure, not to all fields appearing in the action; (3) evaluating the entanglement functional using the boundary term method amounts to evaluating the presymplectic structure at the special surface, where some additional exact form may contribute. An explicit calculation is carried out for three-dimensional warped anti-de Sitter spacetime (WAdS3) in a consistent truncation of string theory, the so-called S-dual dipole theory. It turns out that the generalized gravitational entropy in WAdS3 is captured by the least action of a charged particle in WAdS3 space, or equivalently, by the geodesic length in an auxiliary AdS3. Consequently, the bulk calculation agrees with the CFT results, providing another piece of evidence for the WAdS3/CFT2 correspondence.

We present a network flow model to compute transport, through a pore network, of a compositional fluid consisting of water with a dissolved hydrocarbon gas. The model captures single-phase flow (below local bubble point conditions) as well as the genesis and migration of the gas phase when bubble point conditions are achieved locally. Constant temperature computational tests were run on simulated 2D and 3D micro-networks near bubble point pressure conditions. In the 2D simulations which employed a homogeneous network, negligible capillary pressure, and linear relative permeability relations, the observed concentration of CO2 dissolved in the liquid phase throughout the medium was linearly related to the liquid pressure. In the case of no gravity, the saturation of the gas phase throughout the medium was also linearly related to the liquid pressure; under gravity, the relationship became nonlinear in regions where buoyancy forces were significant. The 3Dheterogeneous network model had non-negligible capillary pressure and nonlinear relative permeability functions. While 100 % of the CO2 entered the 3D network dissolved in the liquid phase, 25 % of the void space was occupied by gas phase and 47 % of the CO2 exiting the outlet face did so via the gaseous phase after 500 s of simulation time.

We apply our model of quantum gravity to an AdS black hole resulting in a wave equation in a quantum spacetime which has a sequence of solutions that can be expressed as a product of stationary and temporal eigenfunctions. The stationary eigenfunctions can be interpreted as radiation and the temporal as gravitational waves. The event horizon corresponds in the quantum model to a Cauchy hypersurface that can be crossed by causal curves in both directions such that the information paradox does not occur.