相关论文: Approximation in an optimal design problem governe…
In this paper we consider non-local (in time) heat equations on time-increasing parabolic sets whose boundary is determined by a suitable curve. We provide a notion of solution for these equations and we study well-posedness under Dirichlet…
Recent studies have advocated using the total dissipation rate under topology optimization to realize material designs involving the flow of fluids through porous media. However, these studies decided how to pose the design problem, such as…
In this paper, we investigate the asymptotic behavior of optimal designs for the shape optimization of 2D heat equations in long time horizons. The control is the shape of the domain on which heat diffuses. The class of 2D admissible shapes…
In this paper we discuss the numerical solution of elliptic distributed optimal control problems with state or control constraints when the control is considered in the energy norm. As in the unconstrained case we can relate the…
We prove sharp estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations on a bounded domain subject to a homogeneous Dirichlet boundary condition. Important special cases are the…
We consider the following geometric optics problem: Construct a system of two reflectors which transforms a spherical wavefront generated by a point source into a beam of parallel rays. This beam has a prescribed intensity distribution. We…
This article presents a theoretical analysis of a one-dimensional heat transfer problem in two layers involving diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, and heat generation due…
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…
Topology optimization has matured to become a powerful engineering design tool that is capable of designing extraordinary structures and materials taking into account various physical phenomena. Despite the method's great advancements in…
In this paper we study an optimal shape design problem for the first eigenvalue of the fractional $p-$laplacian with mixed boundary conditions. The optimization variable is the set where the Dirichlet condition is imposed (that is…
We present a framework leveraging a novel variant of the model-based diffusion algorithm to minimize the time required for a redundant dual-arm robot configuration to follow a desired relative Cartesian path. Our prior work proposed a…
A heat exchanger can be modeled as a closed domain containing an incompressible fluid. The moving fluid has a temperature distribution obeying the advection-diffusion equation, with zero temperature boundary conditions at the walls.…
We prove that among all doubly connected domains of R^n (n>=2) bounded by two spheres of given radii, the Dirichlet heat content at any fixed time achieves its minimum when the spheres are concentric. This is shown to be a special case of a…
We consider the steady heat transfer between a collection of impermeable obstacles immersed in an incompressible 2D potential flow, when each obstacle has a prescribed boundary temperature distribution. Inside the fluid, the temperature…
We consider the dunking problem: a solid body at uniform temperature $T_\text{i}$ is placed in a environment characterized by farfield temperature $T_\infty$ and time-independent spatially uniform heat transfer coefficient; we permit…
This paper presents new existence, dual representation, and approximation results for the information projection in the infinite-dimensional setting for moment inequality models. These results are established under a general specification…
Continuous data assimilation addresses time-dependent problems with unknown initial conditions by incorporating observations of the solution into a nudging term. For the prototypical heat equation with variable conductivity and the Neumann…
In this work, we consider the problem of optimal design of an acoustic cloak under uncertainty and develop scalable approximation and optimization methods to solve this problem. The design variable is taken as an infinite-dimensional…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
The design of numerical tools to model the behavior of building materials is a challenging task. The crucial point is to save computational cost and maintain high accuracy of predictions. There are two main limitations on the time scale…