Related papers: Critical and flow-critical snarks coincide

A significant mathematical error is identified and corrected in a recent highly-cited paper on oscillatory flows of second-grade fluids [Fetecau & Fetecau (2005). Int. J. Eng. Sci., 43, 781--789]. The corrected solutions are shown to agree…

As a promising computational paradigm, occurrence of critical states in artificial and biological neural networks has attracted wide-spread attention. An often-made explicit or implicit assumption is that one single critical state is…

We present microscopic models of spin ladders which exhibit continuous critical surfaces whose properties and existence, unusually, cannot be inferred from those of the flanking phases. These models exhibit either `multiversality' -- the…

Scale-free behavior as well as oscillations are frequently observed in the activity of many natural systems. One important example is the cortical tissues of mammalian brain where both phenomena are simultaneously observed. Rhythmic…

In this work we study the problem of positiveness of topological entropy for flows using pointwise dynamics. We show that the existence of a non-periodic nonwandering point of an expansive and non-singular flow with shadowing is a…

We prove that, in several settings, a graph has exponentially many nowhere-zero flows. These results may be seen as a counting alternative to the well-known proofs of existence of $Z_3$-, $Z_4$-, and $Z_6$-flows. In the dual setting,…

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 define two conformal structures on $S^1$ which give rise to a different view of the affine curvature flow and a new curvature flow, the ``$Q$-curvature flow". The steady state of these flows are studied. More specifically, we prove four…

This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html). The logical vocabulary of the system consists of…

We consider the critical behavior at an interface which separates two semi-infinite subsystems belonging to different universality classes, thus having different set of critical exponents, but having a common transition temperature. We…

Comments are special types of publications whose aim is to correct or criticize previously published papers. For this reason, comments are believed to make commented papers less worthy or trusty to the eyes of the scientific community, and…

A simple model of the driven motion of interacting particles in a two dimensional random medium is analyzed, focusing on the critical behavior near to the threshold that separates a static phase from a flowing phase with a steady-state…

A vertex coloring of a graph is said to be pseudocomplete if, for any two distinct colors, there exists at least one edge with those two colors as its end vertices. The pseudoachromatic number of a graph is the greatest number of colors…

We show some results for the $L^2$ curvature flow linked by the theme of addressing collapsing phenomena. First we show long time existence and convergence of the flow for $SO(3)$-invariant initial data on $S^3$, as well as a long time…

The relation between the trace and R-current anomalies in 4D supersymmetric theories implies that the U(1)$_R$F$^2$, U(1)$_R$ and U(1)$^3_R$ anomalies which matched in studies of N=1 Seiberg duality satisfy positivity constraints. These…

In this survey we present the state of the art about the asymptotic behavior and stability of the modified Mullins--Sekerka flow and the surface diffusion flow of smooth sets, mainly due to E.~Acerbi, N.~Fusco, V.Julin and M.Morini. First…

Are solids intrinsically different from liquids? Must a finite stress be applied in order to induce flow? Or, instead, do all solids only look rigid on some finite timescales and eventually flow if an infinitesimal shear stress is applied?…

It has been claimed [1-6] that fractal analysis can be applied to unambiguously characterize works of art such as the drip paintings of Jackson Pollock. This academic issue has become of more general interest following the recent discovery…

For the water waves equations, the existence of splat singularities has been shown in [3], i.e., the interface self-intersects along an arc in finite time. The aim of this paper is to show the absence of splat singularities for the…

In his lecture notes on mean curvature flow, Ilmanen conjectured the existence of noncompact self-shrinkers with arbitrary genus. Here, we employ min-max techniques to give a rigorous existence proof for these surfaces. Conjecturally, the…