Related papers: Airy process at a thin rough region between frozen…
A new series expansion for the the Airy function is presented here that stems from the method of steepest descents and can be related to the Hadamard expansions as presented in prevous works cited in the manuscript, and which is convergent…
We consider the asymptotics of the Plancherel measures on partitions of $n$ as $n$ goes to infinity. We prove that the local structure of a Plancherel typical partition (which we identify with a Young diagram) in the middle of the limit…
A fully discrete finite element method, based on a new weak formulation and a new time-stepping scheme, is proposed for the surface diffusion flow of closed curves in the two-dimensional plane. It is proved that the proposed method can…
We prove a fluid limit for the coarsening phase of the condensing zero-range process on a finite number of sites. When time and occupation per site are linearly rescaled by the total number of particles, the evolution of the process is…
The Airy line ensemble is a positive-integer indexed system of random continuous curves whose finite dimensional distributions are given by the multi-line Airy process. It is a natural object in the KPZ universality class: for example, its…
We study two geometric properties of reproducing kernels in model spaces $K\_\theta$where $\theta$ is an inner function in the disc: overcompleteness and existence of uniformly minimalsystems of reproducing kernels which do not contain…
Recent studies have indicated that the coarse grained dynamics of a large class of traffic models and driven-diffusive systems may be described by urn models. We consider a class of one-dimensional urn models whereby particles hop from an…
We study the effects of disorder on semi-infinite Weyl and Dirac semimetals where the presence of a boundary leads to the formation of either Fermi arcs/rays or Dirac surface states. Using a local version of the self-consistent Born…
We consider the rheology of soft-core frictionless disks in two dimensions in the neighborhood of the athermal jamming transition. From numerical simulations of bidisperse, overdamped, particles, we argue that the divergence of the…
The amorphous-to-crystalline transition in Al(1.0%wtSi)/Zr and Al(Pure)/Zr multilayers grown by direct-current magnetron sputtering system has been characterized over a range of Al layer thicknesses (1.0-5.0 nm) by using a series of…
We study theoretically the yielding of sheared amorphous materials as a function of increasing levels of initial sample annealing prior to shear, in three widely used constitutive models and three widely studied annealing protocols. In…
We consider an incompressible Bingham flow in a thin domain with rough boundary, under the action of given external forces and with no-slip boundary condition on the whole boundary of the domain. In mathematical terms, this problem is…
We report extensive simulation studies of phase behaviour in single component systems of particles interacting via a core-softened interparticle potential. Two recently proposed examples of such potentials are considered; one in which the…
In the present paper, we study the asymptotics of the Fredholm determinant $D(x,s)$ of the finite-temperature deformation of the sine kernel, which represents the probability that there is no particles on the interval $(-x/\pi,x/\pi)$ in…
We present a class of diffraction-free partially coherent beams each member of which is comprised of a finite power, non-accelerating Airy bump residing on a statistically homogeneous, Gaussian-correlated background. We examine free-space…
We show that under the 1:2:3 scaling, critically probing large space and time, the height function of finite range asymmetric exclusion processes and the KPZ equation converge to the KPZ fixed point, constructed earlier as a limit of the…
We demonstrate the fabrication of sub-micron layers of single-crystal diamond suitable for subsequent processing as demonstrated by this test ring structure. This method is a significant enabling technology for nanomechanical and photonic…
We consider the dimer model in cylindrical domains $\Omega_\delta$ on square grids of mesh size $\delta$ with two Temperleyan boundary components of different colors. Assuming that the $\Omega_\delta$ approximate a cylindrical domain…
The existence of \emph{weak conical K\"ahler-Einstein} metrics along smooth hypersurfaces with angle between $0$ and $2\pi$ is obtained by studying a smooth continuity method and a \emph{local Moser's iteration} technique. In the case of…
Under the assumption that data lie on a compact (unknown) manifold without boundary, we derive finite sample bounds for kernel smoothing and its (first and second) derivatives, and we establish asymptotic normality through Berry-Esseen type…