Related papers: Interleaving Mayer-Vietoris spectral sequences
We introduce a two-dimensional Keller-Segel type free boundary model for motility of eukaryotic cells on substrates. The key ingredients of this model are the Darcy law for overdamped motion of the cytoskeleton (active) gel and Hele-Shaw…
We investigate the appearance of spontaneous coherence in the parametric emission from planar semiconductor microcavities in the strong coupling regime. Calculations are performed by means of a Quantum Monte Carlo technique based on the…
Stability, bifurcation properties, and the spatiotemporal behavior of different nonlinear combination structures of spiral vortices in the counter rotating Taylor-Couette system are investigated by full numerical simulations and by coupled…
We study a prototypical model of two coupled two-level systems, where the competition between coherent and dissipative coupling gives rise to a rich phenomenology. In particular, we analyze the case of asymmetric coupling, as well as the…
This paper mainly concerns the KAM persistence of the mapping $\mathscr{F}:\mathbb{T}^{n}\times E\rightarrow \mathbb{T}^{n}\times \mathbb{R}^{n}$ with intersection property, where $E\subset \mathbb{R}^{n}$ is a connected closed bounded…
This paper is a review containing new original results on the finite order variational sequence and its different representations with emphasis on applications in the theory of variational symmetries and conservation laws in physics.
In this work, we build a spectral sequence in motivic homotopy that is analogous to both the Serre spectral sequence in algebraic topology and the Leray spectral sequence in algebraic geometry. Here, we focus on laying the foundations…
We establish asymptotic properties of $M$-estimators, defined in terms of a contrast function and observations from a continuous-time locally stationary process. Using the stationary approximation of the sequence, $\theta$-weak dependence,…
We derive analytical expressions for the coherence in the onset of modulation instability, in excellent agreement with thorough numerical simulations. As usual, we start by a linear perturbation analysis, where broadband noise is added to a…
We construct a spectral sequence associated to a stratified space, which computes the compactly supported cohomology groups of an open stratum in terms of the compactly supported cohomology groups of closed strata and the reduced cohomology…
A classical problem in electromagnetics concerns the representation of the electric and magnetic fields in the low-frequency or static regime, where topology plays a fundamental role. For multiply connected conductors, at zero frequency the…
We investigate the optomechanical properties of a periodic array of identical scatterers placed inside an optical cavity and extend the results of [A. Xuereb, C. Genes, and A. Dantan, Phys. Rev. Lett. 109, 223601 (2012)]. We show that…
We discuss spectral properties of a charged quantum particle confined to a chain graph consisting of an infinite array of rings under influence of a magnetic field assuming a $\delta$-coupling at the points where the rings touch. We start…
We study linear cocycles generated by nonautonomous delay equations in a suitable Hilbert space and their extensions, called compound cocycles, to exterior powers. Using a recent version of the frequency theorem, we develop analytical…
We discuss complementarity relations in a bipartite continuous variable system. Building up from the work done on discrete d-dimensional systems, we prove that for symmetric two-mode states, quantum complementarity relations can be put in a…
In this paper, we generalize the embedded homology groups of hypergraphs initially given in [S. Bressan, J. Li, S. Ren, and J. Wu, The embedded homology of hypergraphs and applications, Asian J. Math. 23(3)(2019) 479-500] and study the…
Dense distributions of string-like objects in material media are considered in terms of continuum field theory. The strings are assumed to carry a quantized abelian topological charge, such as the Burgers vector of dislocations in solids or…
We are concerned with supersonic vortex sheets for the Euler equations of compressible inviscid fluids in two space dimensions. For the problem with constant coefficients, in [10] the authors have derived a pseudo-differential equation…
The higher derivative field theories are notorious for the stability problems both at classical and quantum level. Classical instability is connected with unboundedness of the canonical energy, while the unbounded energy spectrum leads to…
We discover that some unstable vacua have long memory. By that we mean that even in the theories containing only massive particles, there are correllators and expectation values which grow with time. We examine the cases of instabilities…