Related papers: Asymptotic shape of small cells
We consider a scheme of equiprobable allocation of particles into cells by sets. The Edgeworth type asymptotic expansion in the local central limit theorem for a number of empty cells left after allocation of all sets of particles is…
An asymptotic analysis is performed for thin anisotropic elastic plate clamped along its lateral side and also supported at a small area $\theta_{h}$ of one base with diameter of the same order as the plate thickness $h\ll1.$ A…
Half-cycle laser pulse is applied on an absorbed molecule to investigate its alignment and orientation behavior. Crossover from field-free to hindered rotation motion is observed by varying the angel of hindrance of potential well. At small…
Differential growth processes play a prominent role in shaping leaves and biological tissues. Using both analytical and numerical calculations, we consider the shapes of closed, elastic strips which have been subjected to an inhomogeneous…
An asymptotic theory is developed for a moving drop driven by a wettability gradient. We distinguish the mesoscale where an exact solution is known for the properly simplified problem. This solution is matched at both -- the advancing and…
Let $X$ be the mosaic generated by a stationary Poisson hyperplane process $\hat X$ in ${\mathbb R}^d$. Under some mild conditions on the spherical directional distribution of $\hat X$ (which are satisfied, for example, if the process is…
We study the variance of the number of zeroes of a stationary Gaussian process on a long interval. We give a simple asymptotic description under mild mixing conditions. This allows us to characterise minimal and maximal growth. We show that…
Since the seminal work of Mecke, Nagel and Weiss, the iteration stable (STIT) tessellations have attracted considerable interest in stochastic geometry as a natural and flexible yet analytically tractable model for hierarchical spatial…
A 2D nonlinear model for the electrical potential in the edge plasma in a tokamak generates a stiff problem due to the low resistivity in the direction parallel to the magnetic field lines. An asymptotic-preserving method based on a…
We consider random rooted maps without regard to their genus, with fixed large number of edges, and address the problem of limiting distributions for six different parameters: vertices, leaves, loops, root edges, root isthmus, and root…
The present work deals with the resolution of the Poisson equation in a bounded domain made of a thin and periodic layer of finite length placed into a homogeneous medium. We provide and justify a high order asymptotic expansion which takes…
An asymptotic expansion for inverse moments of positive binomial and Poisson distributions is derived. The expansion coefficients of the asymptotic series are given by the positive central moments of the distribution. Compared to previous…
The dynamics of entanglement between two - level atoms interacting with a common squeezed reservoir is investigated. It is shown that for spatially separated atoms there is a unique asymptotic state depending on the distance between the…
Main characteristics of stationary anisotropic Poisson processes of cylinders (dilated k-dimensional flats) in d-dimensional Euclidean space are studied. Explicit formulae for the capacity functional, the covariance function, the contact…
We derive an asymptotic equation for quasi-static, nonlinear surface plasmons propagating on a planar interface between isotropic media. The plasmons are nondispersive with a constant linearized frequency that is independent of their…
Understanding how growth induces form is a longstanding biological question. Many studies concentrated on the shapes of plant cells, fungi or bacteria. Some others have shown the importance of the mechanical properties of bacterial walls…
An asymptotic theory is developed to generate equations that model the global behaviour of electromagnetic waves in periodic photonic structures when the wavelength is not necessarily long relative to the periodic cell dimensions;…
The distribution of the deformations of elementary cells is studied in an abstract lattice constructed from the existence of the empty set. One combination rule determining oriented sequences with continuity of set-distance function in such…
One of the molecular properties most intuitive to the human perception is the geometrical shape. However, when exploring a large chemical space the determination of shape needs to be automated. We present a fast and simple approach to…
A nonuniform Neumann boundary-value problem is considered for the Poisson equation in a thin $3D$ aneurysm-type domain that consists of thin curvilinear cylinders that are joined through an aneurysm of diameter $\mathcal{O}(\varepsilon).$ A…