Related papers: Business Cycle and Conserved Quantity in Economics
We consider an unpinned chain of harmonic oscillators with periodic boundary conditions, whose dynamics is perturbed by a random flip of the sign of the velocities. The dynamics conserves the total volume (or elongation) and the total…
The study of the response of amorphous materials to oscillatory strain is traditionally performed with many repeated cycles. We argue that it pays to consider carefully just one cycle (and may be a second), to reveal the rich physics that…
Modeling processes are the activities of capturing and representing processes and control of their dynamic behavior. Desired features of the model include capture of relevant aspects of a real phenomenon, understandability, and completeness…
Conservation principles like conservation of charge or energy provide a natural way to couple and constrain different physical variables. In this letter, we propose a dynamical system model that exploits these constraints for solving…
This paper aims to improve existing results about using averaging method for analysis of dynamic systems on time scales. We obtain a more accurate estimate for proximity between solutions of original and averaged systems regarding…
In this work, we study the optimization problem of a renewable resource in finite time. The resource is assumed to evolve according to a logistic stochastic differential equation. The manager may harvest partially the resource at any time…
Energy storage shifts energy from off-peak periods to on-peak periods. Unlike conventional generation, storage is duration-limited: the stored energy capacity constrains the duration over which it can supply power. To understand how these…
This paper deals with optimal prediction in a regime-switching model driven by a continuous-time Markov chain. We extend existing results for geometric Brownian motion by deriving optimal stopping strategies that depend on the current…
We consider the problem of optimizing the steady state of a dynamical system in closed loop. Conventionally, the design of feedback optimization control laws assumes that the system is stationary. However, in reality, the dynamics of the…
To reduce computational complexity, macro-energy system models commonly implement reduced time-series data. For renewable energy systems dependent on seasonal storage and characterized by intermittent renewables, like wind and solar,…
A new microeconomic model is presented that aims at a description of the long-term unit sales and price evolution of homogeneous non-durable goods in polypoly markets. It merges the product lifecycle approach with the price dispersion…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
A re-entrant manufacturing system producing a large number of items and involving many steps can be approximately modeled by a hyperbolic partial differential equation (PDE) according to mass conservation law with respect to a continuous…
The computation of multiphase flows presents a subtle energetic equilibrium between potential (i.e., surface) and kinetic energies. The use of traditional interface-capturing schemes provides no control over such a dynamic balance. In the…
We propose a set of conservative models in which agents exchange wealth with a preference in the choice of interacting agents in different ways. The common feature in all the models is that the temporary values of financial status of agents…
In this work, we suggest a system of differential equations that quantitatively models the formulation and evolution of a trend cycle through the consideration of underlying dynamics between the trend participants. Our model captures the…
We build a state-of-the-art dynamic model of private asset allocation that considers five key features of private asset markets: (1) the illiquid nature of private assets, (2) timing lags between capital commitments, capital calls, and…
The inter-temporal consumption flexibility of commercial buildings can be harnessed to improve the energy efficiency of buildings, or to provide ancillary service to the power grid. To do so, a predictive model of the building's thermal…
We consider in this work a model conservative system subject to dissipation and Gaussian-type stochastic perturbations. The original conservative system possesses a continuous set of steady states, and is thus degenerate. We characterize…
In this paper we prove the existence of solutions for a class of viscoelastic dynamic systems on time--dependent cracked domains, with possibly degenerate viscosity coefficients. Under stronger regularity assumptions we also show a…