Consider binary and ternary mixtures of aromatic compounds composed of benzene/toluene and benzene/toluene/p-xylene, respectively. The present study shows how one can apply both mass and energy balance equations in order to understand the separation of such ideal mixtures by distillation. An adiabatic flash distillation problem is solved graphically for a mixture composed of benzene/toluene. Ri...

Knowledge of location and magnitude of charge density, together with the pore morphology allows one to calculate the Donnan potential, characterizing ion exclusion in charged porous materials. Use of the electro-chemical potential together with Gauss’ electrostatic theorem allows the computation of the ion and voltage distribution at the microscale. On the other hand, commonly used macroscopic ...

This paper treats a finite time horizon optimal control problem in which the controlled state dynamics is governed by a general system of stochastic functional differential equations with a bounded memory. An infinite-dimensional HJB equation is derived using a Bellman-type dynamic programming principle. It is shown that the value function is the unique viscosity solution of the HJB equation.

This paper derives the optimal debt ratio and dividend payment strategies for an insurance company. Taking into account the impact of reinsurance policies and claims from the credit derivatives, the surplus process is stochastic that is jointly determined by the reinsurance strategies, debt levels, and unanticipated shocks. The objective is to maximize the total expected discounted utility of d...

This paper presents a modular method for 3D dynamic simulation of wheeled mobile robots (WMRs). Our method extends efficient dynamics algorithms based on spatial vector algebra to accommodate any articulated WMR configuration. In contrast to some alternatives, our method also supports complex, nonlinear wheel-ground contact models. Instead of directly adding contact forces, we solve for them in...

We consider the problem of optimal investment and consumption when the investment opportunity is represented by a hedge-fund charging proportional fees on profit. The value of the fund evolves as a geometric Brownian motion and the performance of the investment and consumption strategy is measured using discounted power utility from consumption on infinite horizon. The resulting stochastic cont...

We prove a theorem of existence of time-optimal curves in the space of probability measures, a Dynamic Programming Principle, a controllability result and some comparisons between the classical and the generalized framework. A proper definition of viscosity solution, together with some approximation results, leaded us to prove that the generalization of the minimum time function solves a suitab...

The dynamic programming approach for the control of a 3D flow governed by the stochastic Navier-Stokes equations for incompressible fluid in a bounded domain is studied. By a compactness argument, existence of solutions for the associated Hamilton-Jacobi-Bellman equation is proved. Finally, existence of an optimal control through the feedback formula and of an optimal state is discussed.

We consider a class of optimal control problems of stochastic delay differential equations (SDDE) that arise in connection with optimal advertising under uncertainty for the introduction of a new product to the market, generalizing classical work of Nerlove and Arrow [30]. In particular, we deal with controlled SDDE where the delay enters both the state and the control. Following ideas of Vinte...

We report here new electrical laws, derived from nonlinear electro-diffusion theory, about the effect of the local geometrical structure, such as curvature, on the electrical properties of a cell. We adopt the Poisson-Nernst-Planck (PNP) equations for charge concentration and electric potential as a model of electro-diffusion. In the case at hand, the entire boundary is impermeable to ions and ...