Viscosity solutions of Eikonal equations on topological networks

In this paper we introduce a notion of viscosity solutions for Eikonal equations defined on topological networks. Existence of a solution for the Dirichlet problem is obtained via representation formulas involving a distance function associated to the Hamiltonian. A comparison theorem based on Ishii's classical argument yields the uniqueness of the solution

Benefits and constraints associated to agroforestry systems: the case studies implemented in Italy within the AGFORWARD project

info:eu-repo/semantics/publishedVersio

Geologic considerations in underground coal mining system design

Geologic characteristics of coal resources which may impact new extraction technologies are identified and described to aid system designers and planners in their task of designing advanced coal extraction systems for the central Appalachian region. These geologic conditions are then organized into a matrix identified as the baseline mine concept. A sample region, eastern Kentucy is analyzed using both the developed baseline mine concept and the traditional geologic investigative approach

Existence and regularity results for viscous Hamilton–Jacobi equations with Caputo time-fractional derivative

We study existence, uniqueness and regularity properties of classical solutions to viscous Hamilton–Jacobi equations with Caputo time-fractional derivative. Our study relies on a combination of a gradient bound for the time-fractional Hamilton–Jacobi equation obtained via nonlinear adjoint method and sharp estimates in Sobolev and Hölder spaces for the corresponding linear problem

Homogenization of weakly coupled systems of Hamilton--Jacobi equations with fast switching rates

We consider homogenization for weakly coupled systems of Hamilton--Jacobi equations with fast switching rates. The fast switching rate terms force the solutions converge to the same limit, which is a solution of the effective equation. We discover the appearance of the initial layers, which appear naturally when we consider the systems with different initial data and analyze them rigorously. In particular, we obtain matched asymptotic solutions of the systems and rate of convergence. We also investigate properties of the effective Hamiltonian of weakly coupled systems and show some examples which do not appear in the context of single equations.Comment: final version, to appear in Arch. Ration. Mech. Ana

Stabilization of controlled diffusions via Zubov's method

We consider a controlled stochastic system which is exponentially stabilizable in probability near an attractor. Our aim is to characterize the set of points which can be driven by a suitable control to the attractor with either positive probability or with probability one. This will be done by associating to the stochastic system a suitable control problem and the corresponding Zubov equation. We then show that this approach can be used as a basis for numerical computations of these sets

The Solution of the Deep Boltzmann Machine on the Nishimori Line

The deep Boltzmann machine on the Nishimori line with a finite number of layers is exactly solved by a theorem that expresses its pressure through a finite dimensional variational problem of min–max type. In the absence of magnetic fields the order parameter is shown to exhibit a phase transition whose dependence on the geometry of the system is investigated

The value function of an asymptotic exit-time optimal control problem

We consider a class of exit--time control problems for nonlinear systems with a nonnegative vanishing Lagrangian. In general, the associated PDE may have multiple solutions, and known regularity and stability properties do not hold. In this paper we obtain such properties and a uniqueness result under some explicit sufficient conditions. We briefly investigate also the infinite horizon problem

Field emission from two-dimensional GeAs

GeAs is a layered material of the IV–V groups that is attracting growing attention for possible applications in electronic and optoelectronic devices. In this study, exfoliated multilayer GeAs nanoflakes are structurally characterized and used as the channel of back-gate field-effect transistors. It is shown that their gate-modulated p-type conduction is decreased by exposure to light or electron beam. Moreover, the observation of a field emission (FE) current demonstrates the suitability of GeAs nanoflakes as cold cathodes for electron emission and opens up new perspective applications of two-dimensional GeAs in vacuum electronics. FE occurs with a turn-on field of ~80 Vum-1 and attains a current density higher than 10 Acm-2, following the general Fowler–Nordheim model with high reproducibility

Convergence of a semi-discretization scheme for the Hamilton--Jacobi equation: a new approach with the adjoint method

We consider a numerical scheme for the one dimensional time dependent Hamilton--Jacobi equation in the periodic setting. This scheme consists in a semi-discretization using monotone approximations of the Hamiltonian in the spacial variable. From classical viscosity solution theory, these schemes are known to converge. In this paper we present a new approach to the study of the rate of convergence of the approximations based on the nonlinear adjoint method recently introduced by L. C. Evans. We estimate the rate of convergence for convex Hamiltonians and recover the O(sqrt{h}) convergence rate in terms of the L^infty norm and O(h) in terms of the L^1 norm, where h is the size of the spacial grid. We discuss also possible generalizations to higher dimensional problems and present several other additional estimates. The special case of quadratic Hamiltonians is considered in detail in the end of the paper