相关论文: Stability of gas measures under perturbations and …
This thesis consists of two separate parts: in each we study the stability under small perturbations of certain probability models in different contexts. In the first, we study small random perturbations of a deterministic dynamical system…
Numerical simulations of compressible real-fluid flows are notoriously plagued by spurious pressure oscillations arising in regions of abrupt flow variations. As a possible remedy, several numerical formulations enforce the pressure…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
The generalized entropic measure, which is optimized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity, is considered and its…
We continue our study of the problem of mixing for a class of PDEs with very degenerate noise. As we established earlier, the uniqueness of stationary measure and its exponential stability in the dual-Lipschitz metric holds under the…
We study the gravitational stability of gaseous streams in the complex environment of a galaxy merger, because mergers are known to be places of ongoing massive cluster formation and bursts of star formation. We find an analytic stability…
We use ideal hydrodynamics to investigate clustering in a gas of inelastically colliding spheres. The hydrodynamic equations exhibit a new type of finite-time density blowup, where the gas pressure remains finite. The density blowups signal…
This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a…
Mathematical models in equilibrium statistical mechanics describe physical systems with many particles interacting with an external force and with one another. Gibbs measure is a fundamental concept in this theory. In existing literature…
Numerical analysis is conducted for a generalized particle method for a Poisson equation. Unique solvability is derived for the discretized Poisson equation by introducing a connectivity condition for particle distributions. Moreover, by…
We performed molecular dynamics simulations to investigate the clustering instability of a freely cooling dilute gas of inelastically colliding disks in a quasi-one-dimensional setting. We observe that, as the gas cools, the shear stress…
In this paper, we define and study a new notion of stability for the $k$-means clustering scheme building upon the notion of quantization of a probability measure. We connect this notion of stability to a geometric feature of the underlying…
We study the notion of stochastic stability with respect to diffusive perturbations for flows with smooth invariant measures. We investigate the question fully for non-singular flows on the circle. We also show that volume-preserving flows…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…
We develop and analyse finite volume methods for the Poisson problem with boundary conditions involving oblique derivatives. We design a generic framework, for finite volume discretisations of such models, in which internal fluxes are not…
Particle models with finitely many types of particles are considered, both on $\mathbb{Z}^d$ and on discrete point sets of finite local complexity. Such sets include many standard examples of aperiodic order such as model sets or certain…
We find conditions for stationary measures of random dynamical systems on surfaces having dissipative diffeomorphisms to be absolutely continuous. These conditions involve a uniformly expanding on average property in the future (UEF) and…
In this work we study the stability, convergence, and pressure-robustness of discretization methods for incompressible flows with hybrid velocity and pressure. Specifically, focusing on the Stokes problem, we identify a set of assumptions…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
We study the properties of modulational instability and discrete breathers arising in a quasi-one-dimensional discrete Gross-Pitaevskii equation with Lee-Huang-Yang corrections. Conditions for modulation instability and instability regions…