Related papers: Constrained maximization of conformal capacity
This paper investigates the optimal control problem for a class of parabolic equations where the diffusion coefficient is influenced by a control function acting nonlocally. Specifically, we consider the optimization of a cost functional…
Coagulation theory predicts that micron-sized dust grains grow into pebbles which drift inward towards the star, when they reach sizes of mm-cm. When they cross the orbit of a planet, a fraction of these drifting pebbles will be accreted.…
This paper is concerned with the distributed optimal control of a time-discrete Cahn--Hilliard/Navier--Stokes system with variable densities. It focuses on the double-obstacle potential which yields an optimal control problem for a family…
We prove that among all doubly connected domains of $\R^n$ bounded by two spheres of given radii, $Z(t)$, the trace of the heat kernel with Dirichlet boundary conditions, achieves its minimum when the spheres are concentric (i.e., for the…
This paper investigates the exact controllability problem for multi-dimensional stochastic first-order symmetric hyperbolic systems with control inputs acting in two distinct ways: an internal control applied to the diffusion term and a…
Most analytic work to date on protostellar disks has focused on those in isolation from their environments. However, observations are now beginning to probe the earliest, most embedded phases of star formation, during which disks are…
We introduce a notion of capacity for high dimensional critical percolation by showing that for any finite set $A$, the suitably rescaled probability that the cluster of $z$ intersects $A$ converges as $\|z\|\to\infty$. This can be viewed…
Disks of bodies orbiting a much more massive central object are extremely common in astrophysics. When the orbits comprising such disks are eccentric, we show they are susceptible to a new dynamical instability. Gravitational forces between…
Using resistive magnetohydrodynamics simulation, we investigate circumstellar disk formation in a strongly magnetized cloud. As the initial state, an isolated cloud core embedded in a low-density interstellar medium with a uniform magnetic…
We derive various sharp upper bounds for the $p$-capacity of a smooth compact set $K$ in the hyperbolic space $\mathbb{H}^n$ and the Euclidean space $\mathbb{R}^n$. Firstly, using the inverse mean curvature flow, for the mean convex and…
The minimal spherical cap dispersion ${\rm disp}_{\mathcal{C}}(n,d)$ is the largest number $\varepsilon\in (0,1]$ such that, for every $n$ points on the $d$-dimensional Euclidean unit sphere $\mathbb{S}^d$, there exists a spherical cap with…
Stochastic optimal control problems with constraints on the probability distribution of the final output are considered. Necessary conditions for optimality in the form of a coupled system of partial differential equations involving a…
The problem of the late accretion phase of the evolution of an axisymmetric, isothermal magnetic disk surrounding a forming star has been formulated in a companion paper. The "central sink approximation" is used to circumvent the problem of…
A region of two-dimensional space has been filled randomly with large number of growing circular discs allowing only a `slight' overlapping among them just before their growth stop. More specifically, each disc grows from a nucleation…
The development of percolation theory was historically shaped by its numerous applications in various branches of science, in particular in statistical physics, and was mainly constrained to the case of Euclidean spaces. One of its central…
We consider solutions of hyperbolic conservation laws regularized with vanishing diffusion and dispersion terms. Following a pioneering work by Schonbek, we establish the convergence of the regularized solutions toward discontinuous…
We study constrained percolation models on planar lattices including the $[m,4,n,4]$ lattice and the square tilings of the hyperbolic plane, satisfying certain local constraints on faces of degree 4, and investigate the existence of…
We derive a compatible discretization method that relies heavily on the underlying geometric structure, and obeys the topological sequences and commuting properties that are constructed. As a sample problem we consider the…
We consider the Gaussian channel with power constraint P. A gap exists between the channel capacity and the highest achievable rate of equiprobable uniformly spaced signal. Several approaches enable to overcome this limitation such as…
The circular restricted three body problem is investigated in the context of accretion and scattering processes. In our model a large number of identical non-interacting mass-less planetesimals are considered in planar case orbiting a…