Related papers: Feigenbaum universality in subcritical Taylor-Coue…
A linear flow on the torus $\mathbb{R}^d / \mathbb{Z}^d$ is uniformly distributed in the Weyl sense if the direction of the flow has linearly independent coordinates over $\mathbb{Q}$. In this paper we combine Fourier analysis and the…
The transition route and bifurcations of the buoyant flow developing on a heated circular horizontal surface are elaborated using direct numerical simulations and direct stability analysis. A series of bifurcations, as a function of…
A large number of flows with distinctive patterns have been observed in experiments and simulations of Rayleigh-Benard convection in a water-filled cylinder whose radius is twice the height. We have adapted a time-dependent pseudospectral…
We investigate the non-linear dynamics of a two-dimensional film flowing down a finite heater, for a non-volatile and a volatile liquid. An oscillatory instability is predicted beyond a critical value of Marangoni number using linear…
The main objective of this article is to derive a mathematical theory associated with the nonlinear stability and dynamic transitions of the basic shear flows associated with baroclinic instability, which plays a fundamental role in the…
We show that in the neighborhood of the tripling bifurcation of a periodic orbit of a Hamiltonian flow or of a fixed point of an area preserving map, there is generically a bifurcation that creates a ``twistless'' torus. At this…
The main goal of this work is to provide a description of transitions from uniform to non-uniform snychronization in diffusions based on large deviation estimates for finite time Lyapunov exponents. These can be characterized in terms of…
Systematic microcanonical inflection-point analysis of precise numerical results obtained in extensive generalized-ensemble Monte Carlo simulations reveals a bifurcation of the coil-globule transition line for polymers with a bending…
We present the detailed bifurcation structure and associated flow patterns near the onset of zero Prandtl number Rayleigh B\'enard convection. We employ both direct numerical simulation and a low-dimensional model ensuring qualitative…
Bifurcation analysis is used to study an effective model of QCD$_4$ with four-fermi interactions. Our analysis supports the scenario of a fixed point merger at the lower edge of the conformal window. This indicates square root scaling of…
In recent years, experimental data were published which point to the possibility of the existence of superfluidity in solid helium. To investigate this phenomenon theoretically we employ a hierarchy of equations for reduced density matrices…
We prove regularity, global existence, and convergence of Lagrangian mean curvature flows in the two-convex case. Such results were previously only known in the convex case, of which the current work represents a significant improvement.…
In this paper, by combining techniques from Ricci flow and algebraic geometry, we prove the following generalization of the classical uniformization theorem of Riemann surfaces. Given a complete noncompact complex two dimensional K\"ahler…
We confront exact analytical predictions for the finite-volume scaling of the chiral condensate with data from quenched lattice gauge theory simulations. Using staggered fermions in both the fundamental and adjoint representations, and…
We investigate the critical behavior of the two-dimensional spin-$1$ Baxter-Wu model in the presence of a crystal-field coupling $\Delta$ with the goal of determining the universality class of transitions along the second-order part of the…
In [5], S\'aez and Schn\"urer studied the graphical mean curvature flow of complete hypersurfaces defined on subsets of Euclidean space. They obtained long time existence. Moreover, they provided a new interpretation of weak mean curvature…
We present a systematic approach to deriving normal forms and related amplitude equations for flows and discrete dynamics on the center manifold of a dynamical system at local bifurcations and unfoldings of these. We derive a general,…
We consider fluid wetting on a corrugated substrate using effective interfacial Hamiltonian theory and show that breaking the translational invariance along the wall can induce an 'unbending' phase transition in addition to unbinding. Both…
Stationary bifurcations in several nonlinear models of fluid conveying pipes fixed at both ends are analyzed with the use of Lyapunov-Schmidt reduction and singularity theory. Influence of gravitational force, curvature and vertical elastic…
A new universal {\it empirical} function that depends on a single critical exponent (acceleration exponent) is proposed to describe the scaling behavior in a dissipative kicked rotator. The scaling formalism is used to describe two regimes…