相关论文: RG stability of integrable fishnet models

We consider instability of the Friedmann world model to the second-order in perturbations. We present the perturbed set of equations up to the second-order in the Friedmann background world model with general spatial curvature and the…

Serre-Green-Naghdi equations (SGN equations) is the most simple dispersive model of long water waves having "good" mathematical and physical properties. First, the model is a mathematically justified approximation of the exact water wave…

We study strong instability of standing waves $e^{i\omega t} \phi_{\omega}(x)$ for nonlinear Schr\"odinger equations with $L^2$-supercritical nonlinearity and a harmonic potential, where $\phi_{\omega}$ is a ground state of the…

Despite being under intense scrutiny for 50 years, the Kuramoto oscillator model has remained a quintessential representative of non-equilibrium phase transitions. One of the reasons for its enduring relevance is the apparent lack of an…

Nonlinear stripe patterns occur in many different systems, from the small scales of biological cells to geological scales as cloud patterns. They all share the universal property of being stable at different wavenumbers $q$, i.e., they are…

We consider a multidimensional model of the universe given as a $D$-dimensional geometry, represented by a Riemannian manifold $(M,g)$ with arbitrary signature of $g$, $M= \R\times M_1\times \cdots \times M_n$, where the $M_i$ of dimension…

Let (M,g) be a three-dimensional steady gradient Ricci soliton which is non-flat and \kappa-noncollapsed. We prove that (M,g) is isometric to the Bryant soliton up to scaling. This solves a problem mentioned in Perelman's first paper.

The universality of intermittency in hydrodynamic turbulence is considered based on a recent model for the velocity gradient tensor evolution. Three possible versions of the model are investigated differing in the assumed correlation…

Stability is a key property of both forward models and inverse problems, and depends on the norms considered in the relevant function spaces. For instance, stability estimates for hyperbolic partial differential equations are often based on…

In this paper, we study the stability and bifurcations of spontaneous stochasticity using an approach reminiscent of the Feigenbaum renormalization group (RG). We consider dynamical models on a self-similar space-time lattice as toy models…

In this work analyze the physical consistency of a nonbirefringent Lorentz-violating planar model via the analysis of the pole structure of its Feynman propagators. The nonbirefringent planar model, obtained from the dimensional reduction…

We prove two general results concerning spectral sequences of $\mathbf{FI}$-modules. These results can be used to significantly improve stable ranges in a large portion of the stability theorems for $\mathbf{FI}$-modules currently in the…

We discuss examples of (1+1)-dimensional models where the perturbative renormalization group (RG) indicates a tendency to restore the symmetry in the strong coupling limit. We show that such restoration does occur sometimes, but the…

In this paper we develop hydrodynamic models using spectral differential operators to investigate the spatial stability of swirling fluid systems. Including viscosity as a valid parameter of the fluid, the hydrodynamic model is derived…

We consider a model, which we named the Kakinuma model, for interfacial gravity waves. As is well-known, the full model for interfacial gravity waves has a variational structure whose Lagrangian is an extension of Luke's Lagrangian for…

The intent of this short note is to provide context for and an independent proof of the discovery of Klaus Kroencke that complex projective space with its canonical Fubini--Study metric is dynamically unstable under Ricci flow in all…

We develop a new approach and employ it to establish the global existence and nonlinear structural stability of attached weak transonic shocks in steady potential flow past three-dimensional wedges; in particular, the restriction that the…

We study the duality cascade of softly broken supersymmetric theories. We investigate the renormalization group (RG) flow of SUSY breaking terms as well as supersymmetric couplings. It is found that the magnitudes of SUSY breaking terms are…

Statistical features of homogeneous, isotropic, two-dimensional turbulence is discussed on the basis of a set of direct numerical simulations up to the unprecedented resolution $32768^2$. By forcing the system at intermediate scales, narrow…

In the unitary gauge the unphysical degrees of freedom of spontaneously broken gauge theories are eliminated. The Feynman rules are simpler than in other gauges, but it is non-renormalizable by the rules of power counting. On the other…