Talks

We develop a Machine-Learning Renormalization Group (MLRG) algorithm to explore and analyze many-body lattice models in statistical physics. Using the representation learning capability of generative modeling, MLRG automatically learns the optimal renormalization group (RG) transformations from self-generated spin configurations and formulates RG equations without human supervision. The algorithm does not focus on simulating any particular lattice model but broadly explores all possible models compatible with the internal and lattice symmetries given the on-site symmetry representation. It can uncover the RG monotone that governs the RG flow, assuming a strong form of the $c$-theorem. This enables several downstream tasks, including unsupervised classification of phases, automatic location of phase transitions or critical points, controlled estimation of critical exponents, and operator scaling dimensions. We demonstrate the MLRG method in two-dimensional lattice models with Ising symmetry and show that the algorithm correctly identifies and characterizes the Ising criticality.

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A fundamental model for large-scale ocean flow is two-dimensional (2D) turbulence above topography and has been studied since the 1970s. Ocean observations show that long-lived vortices sit astride prominent topographic features. Using a suite of numerical experiments, we illustrate the phenomenology of random topographic turbulence. As in two-dimensional turbulence, the energy of the flow is transferred towards larger scales of motion; after some rotation periods, however, the process is halted as the flow pattern becomes aligned along the topographic contours. It is found that global energy decays faster as the roughness of topography increases due to more effective viscous dissipation. The quasi-steady state reached by the flow is characterized by the relationship between potential vorticity and stream function which is found using minimum enstrophy arguments.

Internal gravity waves pervade the oceans, profoundly shaping their dynamics. Their interactions with eddies and other waves govern energy transfers and can lead to wave breaking, and density mixing, thus influencing large-scale mean flows. Despite their significance, the relative importance of wave-mean flow interactions vis-à-vis wave-wave interactions remains elusive. We investigate internal gravity wave-mean flow interactions with the novel numerical Internal Wave Energy Model (IWEM) based on the six-dimensional radiative transfer equation. We simulate wave interactions with local coherent mesoscale eddies, to find a wave energy loss at the eddy rim akin to critical layer behavior. We investigate internal gravity wave-wave interactions by numerically evaluating the kinetic equation derived from weak interaction assumptions. Our findings unveil a predominantly forward energy cascade from wave-wave interactions

We focus on plane Poiseuille flow where an incompressible fluid is pushed between two parallel plates by maintaining a constant bulk velocity. Plane Poiseuille flow is a canonical wall-bounded shear flow where a subcritical transition to turbulence is observed. Assuming periodic boundary conditions in streamwise and spanwise directions, we classify invariant subspaces of the plane Poiseuille flow up to half-box shifts. Exploiting the interplay between symmetries and dynamics, we find new finite amplitude traveling wave solutions in some invariant subspaces, far below the linear stability threshold.

Planning and adapting to future coastal ocean conditions requires accurate coastal ocean predictions of the nutrient, pollutant, heat and sediment transport. As coastal ocean turbulence is often driven by relatively small scale processes such as high-frequency internal waves and submesocale eddies that are not captured in most regional ocean models turbulence parameterisation is challenging Using a combination of process-based field campaigns and long-term monitoring data we have characterised the relationship between diapycnal mixing and diverse external forcings and differing flow regimes on the Australian northwest shelf. We show that the overall diapycnal mixing is dominated by relatively rare but energetic mixing events. We observe that the semi-diurnal barotropic tide, the spring-neap tidal variability, and the seasonal variability in stratification all affect the magnitude of diapycnal mixing and its vertical distribution.

Advanced subjects and complicated applications. Applications to the interacting theories. Appelquist and Carazzone theorem in QED. Decupling of massive degrees of freedom in polynomial higher derivative quantum gravity: mixed diagrams. Non-local theories of quantum gravity. On the possibility of the universal IR limit in quantum gravity

Asymptotically safe quantum gravity might provide a unified description of the fundamental dynamics of quantum gravity and matter. The realization of asymptotic safety, i.e., of scale symmetry at high energies, constraints the possible interactions and dynamics of a system. In this talk, I will first introduce the scenario of asymptotic safety for gravity with matter, and explain how it can be explored using functional methods. I will then emphasize, how the constraints on the microscopic dynamics of matter arising from quantum scale symmetry can turn into constraints on the gravitational dynamics, both by exploring the asymptotically safe fixed-point structure, and by exploring resulting infrared physics.

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