Sensitivity analysis of 1-d steady forced scalar conservation laws

We analyze 1 - d forced steady state scalar conservation laws. We first show the existence and uniqueness of entropy solutions as limits as t→ ∞ of the corresponding solutions of the scalar evolutionary hyperbolic conservation law. We then linearize the steady state equation with respect to perturbations of the forcing term. This leads to a linear first order differential equation with, possibly, discontinuous coefficients. We show the existence and uniqueness of solutions in the context of duality solutions. We also show that this system corresponds to the steady state version of the linearized evolutionary hyperbolic conservation law. This analysis leads us to the study of the sensitivity of the shock location with respect to variations of the forcing term, an issue that is relevant in applications to optimal control and parameter identification problems

Least Squares Shadowing sensitivity analysis of chaotic limit cycle oscillations

The adjoint method, among other sensitivity analysis methods, can fail in chaotic dynamical systems. The result from these methods can be too large, often by orders of magnitude, when the result is the derivative of a long time averaged quantity. This failure is known to be caused by ill-conditioned initial value problems. This paper overcomes this failure by replacing the initial value problem with the well-conditioned "least squares shadowing (LSS) problem". The LSS problem is then linearized in our sensitivity analysis algorithm, which computes a derivative that converges to the derivative of the infinitely long time average. We demonstrate our algorithm in several dynamical systems exhibiting both periodic and chaotic oscillations.Comment: submitted to JCP in revised for

The implication of the hyperbolic discount model for annuitisation decisions

The low demand for immediate annuities at retirement has been a long-standing puzzle. We show that a hyperbolic discount model can explain this behaviour and results in the attractiveness of long-term deferred annuities. With a set of benchmark assumptions, we find that retirees would be willing to pay a much higher price than the actuarial fair price for annuities with longer deferred periods. Moreover, if governments were to introduce a pre-commitment device which requires pensioners to make annuitisation decisions around ten years before retirement, the take up rate of annuities could become higher

Robust Mission Design Through Evidence Theory and Multi-Agent Collaborative Search

In this paper, the preliminary design of a space mission is approached introducing uncertainties on the design parameters and formulating the resulting reliable design problem as a multiobjective optimization problem. Uncertainties are modelled through evidence theory and the belief, or credibility, in the successful achievement of mission goals is maximised along with the reliability of constraint satisfaction. The multiobjective optimisation problem is solved through a novel algorithm based on the collaboration of a population of agents in search for the set of highly reliable solutions. Two typical problems in mission analysis are used to illustrate the proposed methodology

Sacrifice, Discounting and Climate Policy: Five Questions

I offer a selective review of discounting and climate policy. Analytic and numerical models show that different assumptions greatly change the degree to which decisions about climate policy depend on the discount rate. I discuss a claim that standard models exaggerate the current generation’s sacrifices needed to internalize climate damages. This claim, if correct, affects the role of discounting. I argue that the assertion that the risk of catastrophic damage overwhelms discounting is unfounded. I show that the claim that we “view the world in perspective” implies hyperbolic rather than constant discounting.climate change, discounting, intergenerational conflict, catastrophic risk, hyperbolic discounting

Parameter identification in a semilinear hyperbolic system

We consider the identification of a nonlinear friction law in a one-dimensional damped wave equation from additional boundary measurements. Well-posedness of the governing semilinear hyperbolic system is established via semigroup theory and contraction arguments. We then investigte the inverse problem of recovering the unknown nonlinear damping law from additional boundary measurements of the pressure drop along the pipe. This coefficient inverse problem is shown to be ill-posed and a variational regularization method is considered for its stable solution. We prove existence of minimizers for the Tikhonov functional and discuss the convergence of the regularized solutions under an approximate source condition. The meaning of this condition and some arguments for its validity are discussed in detail and numerical results are presented for illustration of the theoretical findings