相关论文: Confinement, Turbulence and Diffraction Catastroph…
Transitions between centre sectors are related to confinement in pure Yang-Mills theories. We study the impact of these transitions in QCD-like theories for which centre symmetry is explicitly broken by the presence of matter. For low…
Following our recent letter, we study in detail an entry-wise diffusion of non-hermitian complex matrices. We obtain an exact partial differential equation (valid for any matrix size $N$ and arbitrary initial conditions) for evolution of…
1-D scalar conservation laws with convex flux and Markov initial data are now known to yield a completely integrable Hamiltonian system. In this article, we rederive the analogue of Loitsiansky's invariant in hydrodynamic turbulence from…
We show that the large N partition functions and Wilson loop observables of two-dimensional Yang-Mills theories admit a universal functional form irrespective of the gauge group. We demonstrate that U(N) QCD_2 undergoes a large N,…
We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive…
In this thesis, several aspects of Yang-Mills theory are studied. It begins with the constrained quantization in the Coulomb gauge, using the Dirac bracket formalism. A nonperturbative analysis of the infrared asymptotics of propagators in…
We calculate one-loop scattering amplitudes in N=4 super Yang-Mills theory away from the origin of the moduli space and demonstrate that the results are extremely simple, in much the same way as in the conformally invariant theory.…
We present a mixing length-based algebraic turbulence model calibrated to pipe flow; the main purpose of the model is to capture the increasing turbulence production-to-dissipation ratio observed in connection with the high Reynolds number…
The probabilistic approach to turbulence is applied to investigate density fluctuations in supersonic turbulence. We derive kinetic equations for the probability distribution function (PDF) of the logarithm of the density field, $s$, in…
The tangled nodal lines (wave vortices) in random, three-dimensional wavefields are studied as an exemplar of a fractal loop soup. Their statistics are a three-dimensional counterpart to the characteristic random behaviour of nodal domains…
The macroscopic behavior of dense suspensions of neutrally-buoyant spheres in turbulent plane channel flow is examined. We show that particles larger than the smallest turbulence scales cause the suspension to deviate from the continuum…
We study the statistics of turbulent velocity fluctuations in the neighbourhood of a strong large scale vortex at very large Reynolds number. At each distance from the vortex core, we observe that the velocity spectrum has a power law…
In supersonic and hypersonic flows, the near-wall density variation due to wall cooling poses a challenge for accurately predicting the near-wall velocity and temperature profiles using classical eddy viscosity turbulence models.…
A random vortex world-surface model for the infrared sector of SU(4) Yang-Mills theory is constructed, focusing on the confinement properties and the behavior at the deconfinement phase transition. Although the corresponding data from…
Consider Ginibre's ensemble of $N \times N$ non-Hermitian random matrices in which all entries are independent complex Gaussians of mean zero and variance $\frac{1}{N}$. As $N \uparrow \infty$ the normalized counting measure of the…
We study stationary fluctuations of conserved slow modes in a two-lane model of hardcore particles which are expected to show universal behaviour. Specifically, we focus on the properties of fluctuations at a special umbilic point where the…
Anomalous dissipation is a dissipation mechanism of kinetic energy which is established by a sufficiently spatially rough velocity field. It implies that the rescaled mean kinetic energy dissipation rate becomes constant with respect to…
We introduce new variables in four dimensional SU(N) Yang-Mills theory. These variables emerge when we sum the path integral over classical solutions and represent the summation as an integral over appropriate degrees of freedom. In this…
We investigate the power spectra of outflow-driven turbulence through high-resolution three-dimensional isothermal numerical simulations where the turbulence is driven locally in real-space by a simple spherical outflow model. The resulting…
In Yang-Mills theory massless point sources lead naturally to shock-wave configurations. Their magnetic counterparts endow the vacuum of the four-dimensional compact abelian model with a Coulomb-gas behaviour whose physical implications are…