Related papers: Infinite-dimensional symplectic non-squeezing usin…
A Type-I model of a multicomponent system of fluids with non-constant temperature is derived as the high-friction limit of a Type-II model via a Chapman-Enskog expansion. The asymptotic model is shown to fit into the general theory of…
In the paper, we study the non-Hermitian system under dissipation and give the effective 2*2 Hamiltonian in the k-space by reducing the N*N Hamiltonian in the real space for them. It is discovered that the energy band shows an imaginary…
In this paper we find the first infinite family of hyperbolic 3-manifolds which admit tight contact structures but do not have any tight projectively Anosov flow. These manifolds are obtained as rational surgeries on the figure eight knot.
We present a comprehensive study of hydrodynamic theories for superfluids with dipole symmetry. Taking diffusion as an example, we systematically construct a hydrodynamic framework that incorporates an intrinsic dipole degree of freedom in…
We consider the elliptic-elliptic Davey-Stewartson system in the three-dimensional Euclidean space, and we give sufficient conditions for the existence of finite time blow-up solutions in non-isotropic spaces. The proof is based on some…
The goal of this paper is to discuss some of the results in [31] and [32] and expand upon the work there by proving a global weak existence result as well as a first bubbling analysis in finite time. In addition, an alternative local…
We study the evolution of a passive scalar subject to molecular diffusion and advected by an incompressible velocity field on a 2D bounded domain. The velocity field is $u = \nabla^\perp H$, where H is an autonomous Hamiltonian whose level…
We consider the volume preserving flow of smooth, closed and convex hypersurfaces in the hyperbolic space $\mathbb{H}^{n+1} (n\geq 2)$ with the speed given by arbitrary positive power $\alpha$ of the Gauss curvature. We prove that if the…
We show that there exist infinite-dimensional quasi-flats in the compactly supported Hamiltonian diffeomorphism group of the Liouville domain, with respect to the spectral norm, if and only if the symplectic cohomology of this Liouville…
We study the scaling limit of statistical mechanics models with non-convex Hamiltonians that are gradient perturbations of Gaussian measures. Characterising features of our gradient models are the imposed boundary tilt and the surface…
Non-Hermitian Hamiltonians are relevant to describe the features of a broad class of physical phenomena, ranging from photonics and atomic and molecular systems to nuclear physics and mesoscopic electronic systems. An important question…
We study the high-frequency limit of non-autonomous gradient flows in metric spaces of energy functionals comprising an explicitly time-dependent perturbation term which might oscillate in a rapid way, but fulfills a certain Lipschitz…
We revisit the existence of monotonic quantities along renormalization group flows using only the Null Energy Condition and the Ryu-Takayanagi formula for the entanglement entropy of field theories with anti-de Sitter gravity duals. In…
We show that any Hamiltonian system with one degree of freedom is invariant under a $w_\infty$ algebra of symmetries.
We prove that on certain closed symplectic manifolds a $C^1$-generic cyclic subgroup of the universal cover of the group of Hamiltonian diffeomorphisms is undistorted with respect to the Hofer metric.
This paper introduces equivariant hamiltonian flows, a method for learning expressive densities that are invariant with respect to a known Lie-algebra of local symmetry transformations while providing an equivariant representation of the…
We prove that an infinite family of virtually overtwisted tight contact structures discovered by Honda on certain circle bundles over surfaces admit no symplectic semi-fillings. The argument uses results of Mrowka, Ozsvath and Yu on the…
A well-developed method to induce mixing on microscopic scales is to exploit flows generated by steady streaming. Steady streaming is a classical fluid dynamics phenomenon whereby a time-periodic forcing in the bulk or along a boundary is…
We study the Hull-Strominger system and the Anomaly flow on a special class of 2-step solvmanifolds, namely the class of almost-abelian Lie groups. In this setting, we characterize the existence of invariant solutions to the Hull-Strominger…
For a mean curvature flow of complete graphical hypersurfaces $M_{t}=\operatorname{graph} u(\cdot,t)$ defined over domains $\Omega_{t}$, the enveloping cylinder is $\partial\Omega_{t}\times\mathbb{R}$. We prove the smooth convergence of…