#### 636 Citations

Blow-up profile of rotating 2D focusing Bose gases

- Physics, Mathematics
- 2018

We consider the Gross-Pitaevskii equation describing an attractive Bose gas trapped to a quasi 2D layer by means of a purely harmonic potential, and which rotates at a fixed speed of rotation… Expand

Onsager’s Ensemble for Point Vortices with Random Circulations on the Sphere

- Mathematics
- 2012

Onsager’s ergodic point vortex (sub-)ensemble is studied for N vortices which move on the 2-sphere $\mathbb{S}^{2}$ with randomly assigned circulations, picked from an a-priori distribution. It is… Expand

Rise of Correlations of Transformation Strains in Random Polycrystals

- Mathematics, Computer Science
- SIAM J. Math. Anal.
- 2008

Under the scaling limits (i), (ii), and (iii) the arrays of transformation strains arising from given boundary conditions exhibit no correlations, long-range correlations, and exponentially decaying short-range correlation, respectively. Expand

Propagation of chaos for the 2D viscous vortex model

- Mathematics
- 2014

We consider a stochastic system of $N$ particles, usually called vortices in that setting, approximating the 2D Navier-Stokes equation written in vorticity. Assuming that the initial distribution of… Expand

Phase Diagram of the ABC Model on an Interval

- Mathematics, Physics
- 2009

The three species asymmetric ABC model was initially defined on a ring by Evans, Kafri, Koduvely, and Mukamel, and the weakly asymmetric version was later studied by Clincy, Derrida, and Evans. Here… Expand

Surfaces with prescribed Gauss curvature

- Mathematics
- 2000

where dx denotes Lebesgue measure on R2, is called the integral curvature of the surface (sometimes called total curvature). We say that Sg is a classical surface over R2 if u ∈ C2(R2). Clearly, K ∈… Expand

Statistical mechanics of classical particles with logarithmic interactions

- Mathematics
- 1993

The inhomogeneous mean-field thermodynamic limit is constructed and evaluated for both the canonical thermodynamic functions and the states of systems of classical point particles with logarithmic… Expand

Negative-temperature states and large-scale, long-lived vortices in two-dimensional turbulence

- Mathematics
- 1993

We study Onsager's theory of large, coherent vortices in turbulent flows in the approximation of the point-vortex model for two-dimensional Euler hydrodynamics. In the limit of a large number of… Expand

Surfaces with radially symmetric prescribed Gauss curvature

- Mathematics, Physics
- 1999

We study conformally flat surfaces with prescribed Gaussian curvature, described by solutions $u$ of the PDE: $\Delta u(x)+K(x)\exp(2u(x))=0$, with $K(x)$ the Gauss curvature function at $x\in\RR^2$.… Expand

#### References

SHOWING 1-10 OF 35 REFERENCES

On integration in vector spaces

- Mathematics
- 1938

Introduction. Several authors ([3]-[10], inclusive; [15])t have already given generalized Lebesgue integrals for functions x(s) whose values lie in a Banach space (B-space) X.: In the following pages… Expand

Grundzüge der Mengenlehre

- Philosophy
- 1914

Mengen und ihre Verknupfungen: Summe, Durchschnitt, Differenz Mengen und ihre Verknupfungen: Funktion, Produkt, Potenz Kardinalzahlen oder Machtigkeiten Geordnete Mengen. Ordnungstypen Wohlgeordnete… Expand

Finitely additive measures

- Mathematics
- 1952

0. Introduction. The present paper is concerned with real-valued measures which enjoy the property of finite additivity but not necessarily the property of countable additivity. Our interest in such… Expand

On the representation of $\sigma$-complete Boolean algebras

- Mathematics
- 1947

A <r-complete Boolean algebra is a Boolean algebra in which for every sequence of elements a$-, i = l, • • • , there is an element U?an, the countable union of the a», such that aiQU?an for every i,… Expand

The theory of representations for Boolean algebras

- Mathematics
- 1936

Boolean algebras are those mathematical systems first developed by George Boole in the treatment of logic by symbolic methodsf and since extensively investigated by other students of logic, including… Expand

Espaces vectoriels topologiques

- Philosophy
- 1955

Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements. Ce livre est le cinquieme du… Expand

Applications of the theory of Boolean rings to general topology

- Mathematics
- 1937

In an earlier paperf we have developed an abstract theory of Boolean algebras and their representations by algebras of classes. We now relate this theory to the study of general topology. The first… Expand

Hincin, O klassah ekvivalentnyh sobytii

- Doklady Akad. Nauk SSSR vol
- 1952

Dynkin, Klassy ekvivalentnyh Sluiainyh veliiin

- Uspehi Matematiceskih Nauk 8 vol
- 1953