相关论文: Algebraic entropy of sign-stable mutation loops
We study the topological entropy of a two-parameter family of maps related to (a,b)-continued fraction algorithms and prove that it is constant on a square within the parameter space (two vertices of this square correspond to well-studied…
Associated to any acyclic cluster algebra is a corresponding triangulated category known as the cluster category. It is known that there is a one-to-one correspondence between cluster variables in the cluster algebra and exceptional…
The log-periodic equation for the entropy $S = - (k/a) \sum_{i=1}^{N} p_{i} \sin(a \ln p_{i})$, based on the forgotten Sharma-Taneja entropy measure, is studied for the first time with $N$ the total number of system states and $p_{i}$ the…
We show that the vibrational entropy can play a crucial role in determining the equilibrium structure of clusters by constructing structural phase diagrams showing how the structure depends upon both size and temperature. These phase…
We study entropies caused by the unstable part of partially hyperbolic systems. We define unstable metric entropy and unstable topological entropy, and establish a variational principle for partially hyperbolic diffeomorphsims, which states…
We consider reshaping of closed Janus filaments acquiring intrinsic curvature upon actuation of an active component -- a nematic elastomer elongating upon phase transition. Linear stability analysis establishes instability thresholds of…
A general link between geometry and intermittency in passive scalar turbulence is established. Intermittency is qualitatively traced back to events where tracer particles stay for anomalousy long times in degenerate geometries characterized…
The cluster distributions of different systems are examined to search for signatures of a continuous phase transition. In a system known to possess such a phase transition, both sensitive and insensitive signatures are present; while in…
We present a spherically-symmetric, steady-state model of galaxy clusters in which radiative cooling from the hot gas is balanced by heat transport through turbulent mixing. We assume that the gas is in hydrostatic equilibrium, and describe…
We revisit Pollard's classical result on consistency for $k$-means clustering in Euclidean space, with a focus on extensions in two directions: first, to problems where the data may come from interesting geometric settings (e.g., Riemannian…
The clustering of small heavy inertial particles subjected to Stokes drag in turbulence is known to be minimal at small and large Stokes number and substantial at $\rm St = \mathcal O(1)$. This non-monotonic trend, which has been shown…
We give upper bounds on limit multiplicities of certain non-tempered representations of unitary groups $U(a,b)$. These include some cohomological representations, and we give applications to the growth of cohomology of cocompact arithmetic…
Influence of surrounding matter on the properties of clusters is considered by an approach combining the methods of statistical and quantum mechanics. A cluster is treated as a bound N-particle system and surrounding matter as thermostat.…
Consistency and stability are two essential ingredients in the design of numerical algorithms for partial differential equations. Robust algorithms can be developed by incorporating nonlinear physical stability principles in their design,…
The exponential sensitivity of cluster number counts to the properties of the dark energy implies a comparable sensitivity to not only the mean but also the actual_distribution_ of an observable mass proxy given the true cluster mass. For…
We apply a common measure of randomness, the entropy, in the context of iterated functions on a finite set with n elements. For a permutation, it turns out that this entropy is asymptotically (for a growing number of iterations) close to…
We present a high-resolution set of adiabatic binary galaxy cluster merger simulations using FLASH. These are the highest-resolution simulations to date of such mergers using an AMR grid-based code with Eulerian hydrodynamics. In this first…
Inspired by work of Colding-Minicozzi on mean curvature flow, Zhang introduced a notion of entropy stability for harmonic map flow. We build further upon this work in several directions. First we prove the equivalence of entropy stability…
An analytic framework based on partial differential equations is derived for certain dynamic clustering methods. The proposed mathematical framework is based on the application of the conservation law in physics to characterize successive…
The formation, movement and gluing of clusters can be described through a system of non local balance laws. Here, the well posedness of this system is obtained, as well as various stability estimates. Remarkably, qualitative properties of…