相关论文: A Dichotomy between Discrete and Continuous Spectr…
Inspired by previous work on the constraints that duality imposes on beta functions of spin models, we propose a consistency condition between those functions and RG flows at different points in coupling constant space. We show that this…
Fluid dynamics corresponds to the dynamics of a substance in the long wavelength limit. Writing down all terms in a gradient (long wavelength) expansion up to second order for a relativistic system at vanishing charge density, one obtains…
Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics,…
We derive continuity equation and exact expression for flow probability density in a space with arbitrary deformed algebra leading to minimal length. In coordinate representation the flow probability density is presented as infinite series…
We consider here an elliptic coupled system describing the dynamics of liquid crystals flows. This system is posed on the whole n-dimensional space. We introduce first the notion of very weak solutions for this system. Then, within the…
Dense suspensions have previously been shown to produce a range of anomalous and gravity-defying behaviors when subjected to strong vibrations in the direction of gravity. These behaviors have previously been interpreted via analogies to…
We investigate the properties of the combinatorial Ricci flow for surfaces, both forward and backward -- existence, uniqueness and singularities formation. We show that the positive results that exist for the smooth Ricci flow also hold for…
Dense suspensions of particles are relevant to many applications and are a key platform for developing a fundamental physics of out-of-equilibrium systems. They present challenging flow properties, apparently turning from liquid to solid…
In this work, we show how the rheology of granular suspensions can be related to the properties of the fluctuations of the velocity field inside the medium. In particular, effective Navier-Stokes equations in the different flow regimes are…
This is a study of singular solutions of the problem of traveling gravity water waves on flows with vorticity. We show that, for a certain class of vorticity functions, a sequence of regular waves converges to an extreme wave with…
In this paper, we study the combinatorial Yamabe flow on infinite triangulated surfaces in Euclidean background geometry, aiming for solving discrete Yamabe problem on noncompact surfaces. Under suitable conditions, we establish the…
We study the convergence of complete non-compact conformally flat solutions to the Yamabe flow to Yamabe steady solitons. We also prove the existence of Type II singularities which develop at either a finite time $T$ or as $t \to +\infty$.
We prove that if $g\geq 2$ then the set of all Abelian differentials $(M,\omega)$ for which the vertical flow is mildly mixing is dense in every stratum of the moduli space $\mathcal{H}_g$. The proof is based on a sufficient condition for…
We study transport properties of isotropic Brownian flows. Under a transience condition for the two-point motion, we show asymptotic normality of the image of a finite measure under the flow and -- under slightly stronger assumptions --…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
We show that solutions to certain higher-order intrinsic geometric flows on a compact manifold, including some flows generated by the ambient obstruction tensor, are unique. With the goal of providing a complete self-contained proof,…
The spectra of parallel flows (that is, flows governed by first-order differential operators parallel to one direction) are investigated, on both $L^2$ spaces and weighted-$L^2$ spaces. As a consequence, an example of a flow admitting a…
In this survey, we address mixing from the point of view of partial differential equations, motivated by applications that arise in fluid dynamics. We give an account of optimal mixing, loss of regularity for transport equations, enhanced…
We consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular (co)adjoint orbits of compact Lie groups. We give the proof of the non-commutative integrability of flows and show, in addition, for…
Dynamists have been studying Hamiltonian systems for a long time. However, many physical systems are dissipative and do not preserve a symplectic form. This is the case, for example, with systems involving friction, which multiply the…