Computational Design of Knit Templates

We present an interactive design system for knitting that allows users to create template patterns that can be fabricated using an industrial knitting machine. Our interactive design tool is novel in that it allows direct control of key knitting design axes we have identified in our formative study and does so consistently across the variations of an input parametric template geometry. This is achieved with two key technical advances. First, we present an interactive meshing tool that lets users build a coarse quadrilateral mesh that adheres to their knit design guidelines. This solution ensures consistency across the parameter space for further customization over shape variations and avoids helices, promoting knittability. Second, we lift and formalize low-level machine knitting constraints to the level of this coarse quad mesh. This enables us to not only guarantee hand- and machine-knittability, but also provides automatic design assistance through auto-completion and suggestions. We show the capabilities through a set of fabricated examples that illustrate the effectiveness of our approach in creating a wide variety of objects and interactively exploring the space of design variations.

Estimating the Cosmological Constant from Shadows of Kerr–de Sitter Black Holes

The Event Horizon Telescope collaboration has revealed the first direct image of a black hole, as per the shadow of a Kerr black hole of general relativity. However, other Kerr-like rotating black holes of modified gravity theories cannot be ignored, and they are essential as they offer an arena in which these theories can be tested through astrophysical observation. This motivates us to investigate asymptotically de Sitter rotating black holes wherein interpreting the cosmological constant Λ as the vacuum energy leads to a deformation in the vicinity of a black hole—new Kerr–de Sitter solution, which has a richer geometric structure than the original one. We derive an analytical formula necessary for the shadow of the new Kerr–de Sitter black holes and then visualize the shadow of black holes for various parameters for an observer at given coordinates (r0,θ0) in the domain (r0,rc) and estimate the cosmological constant Λ from its shadow observables. The shadow observables of the new Kerr–de Sitter black holes significantly deviate from the corresponding observables of the Kerr–de Sitter black hole over an appreciable range of the parameter space. Interestingly, we find a finite parameter space for (Λ, a) where the observables of the two black holes are indistinguishable.

Physics makes the difference: Bayesian optimization and active learning via augmented Gaussian process

Both experimental and computational methods for the exploration of structure, functionality, and properties of materials often necessitate the search across broad parameter spaces to discover optimal experimental conditions and regions of interest in the image space or parameter space of computational models. The direct grid search of the parameter space tends to be extremely time-consuming, leading to the development of strategies balancing exploration of unknown parameter spaces and exploitation towards required performance metrics. However, classical Bayesian optimization strategies based on the Gaussian process (GP) do not readily allow for the incorporation of the known physical behaviors or past knowledge. Here we explore a hybrid optimization/exploration algorithm created by augmenting the standard GP with a structured probabilistic model of the expected system’s behavior. This approach balances the flexibility of the non-parametric GP approach with a rigid structure of physical knowledge encoded into the parametric model. The fully Bayesian treatment of the latter allows additional control over the optimization via the selection of priors for the model parameters. The method is demonstrated for a noisy version of the classical objective function used to evaluate optimization algorithms and further extended to physical lattice models. This methodology is expected to be universally suitable for injecting prior knowledge in the form of physical models and past data in the Bayesian optimization framework.

The effect of inertia and vertical confinement on the flow past a circular cylinder in a Hele-Shaw configuration

The Poiseuille flow (centreline velocity $U_c$ ) of a fluid (kinematic viscosity $\nu$ ) past a circular cylinder (radius $R$ ) in a Hele-Shaw cell (height $2h$ ) is traditionally characterised by a Stokes flow ( $\varLambda =(U_cR/\nu )(h/R)^2 \ll 1$ ) through a thin gap ( $\epsilon =h/R \ll 1$ ). In this work we use asymptotic methods and direct numerical simulations to explore the parameter space $\varLambda$ – $\epsilon$ when these conditions are not met. Starting with the Navier–Stokes equations and increasing $\varLambda$ (which corresponds to increasing inertial effects), four successive regimes are identified, namely the linear regime, nonlinear regimes I and II in the boundary layer (the ‘ inner’ region) and a nonlinear regime III in both the inner and outer region. Flow phenomena are studied with extensive comparisons made between reduced calculations, direct numerical simulations and previous analytical work. For $\epsilon =0.01$ , the limiting condition for a steady flow as $\varLambda$ is increased is the instability of the Poiseuille flow. However, for larger $\epsilon$ , this limit is at a much higher $\varLambda$ , resulting in a laminar separation bubble, of size ${O}(h)$ , forming for a certain range of $\epsilon$ at the back of the cylinder, where the azimuthal location was dependent on $\epsilon$ . As $\epsilon$ is increased to approximately 0.5, the secondary flow becomes increasingly confined adjacent to the sidewalls. The results of the analysis and numerical simulations are summarised in a plot of the parameter space $\varLambda$ – $\epsilon$ .

Simulating of X-states and the two-qubit XYZ Heisenberg system on IBM quantum computer

Two qubit density matrices which are of X-shape, are a natural generalization of Bell Diagonal States (BDSs) recently simulated on the IBM quantum device. We generalize the previous results and propose a quantum circuit for simulation of a general two qubit X-state, implement it on the same quantum device, and study its entanglement for several values of the extended parameter space. We also show that their X-shape is approximately robust against noisy quantum gates. To further physically motivate this study, we invoke the two-spin Heisenberg XYZ system and show that for a wide class of initial states, it leads to dynamical density matrices which are X-states. Due to the symmetries of this Hamiltonian, we show that by only two qubits, one can simulate the dynamics of this system on the IBM quantum computer.

Preliminary modeling estimates of the relative transmissibility and immune escape of the Omicron SARS-CoV-2 variant of concern in South Africa

We develop a stochastic, multi-strain, compartmental epidemic model to estimate the relative transmissibility and immune escape of the Omicron variant of concern (VOC) in South Africa. The model integrates population, non-pharmaceutical interventions, vaccines, and epidemiological data and it is calibrated in the period May 1st, 2021 - November 23rd, 2021. We explore a parameter space of relative transmissibility with respect to the Delta variant and immune escape for Omicron by assuming an initial seeding, from unknown origin, in the first week of October 2021. We identify a region of the parameter space where combinations of relative transmissibility and immune escape are compatible with the growth of the epidemic wave. We also find that changes in the generation time associated with Omicron infections strongly affect the results concerning its relative transmissibility. The presented results are informed by current knowledge of Omicron and subject to changes.

Comparing Quantum Gravity Models: String Theory, Loop Quantum Gravity, and Entanglement Gravity versus SU(∞)-QGR

In a previous article we proposed a new model for quantum gravity (QGR) and cosmology, dubbed SU(∞)-QGR. One of the axioms of this model is that Hilbert spaces of the Universe and its subsystems represent the SU(∞) symmetry group. In this framework, the classical spacetime is interpreted as being the parameter space characterizing states of the SU(∞) representing Hilbert spaces. Using quantum uncertainty relations, it is shown that the parameter space—the spacetime—has a 3+1 dimensional Lorentzian geometry. Here, after a review of SU(∞)-QGR, including a demonstration that its classical limit is Einstein gravity, we compare it with several QGR proposals, including: string and M-theories, loop quantum gravity and related models, and QGR proposals inspired by the holographic principle and quantum entanglement. The purpose is to find their common and analogous features, even if they apparently seem to have different roles and interpretations. The hope is that this exercise provides a better understanding of gravity as a universal quantum force and clarifies the physical nature of the spacetime. We identify several common features among the studied models: the importance of 2D structures; the algebraic decomposition to tensor products; the special role of the SU(2) group in their formulation; the necessity of a quantum time as a relational observable. We discuss how these features can be considered as analogous in different models. We also show that they arise in SU(∞)-QGR without fine-tuning, additional assumptions, or restrictions.