Computing Markov-Perfect Optimal Policies in Business-Cycle Models

Time-inconsistency is an essential feature of many policy problems (Kydland and Prescott, 1977). This paper presents and compares three methods for computing Markov-perfect optimal policies in stochastic nonlinear business cycle models. The methods considered include value function iteration, generalized Euler-equations, and parameterized shadow prices. In the context of a business cycle model in which a scal authority chooses government spending and income taxation optimally, while lacking the ability to commit, we show that the solutions obtained using value function iteration and generalized Euler equations are somewhat more accurate than that obtained using parameterized shadow prices. Among these three methods, we show that value function iteration can be applied easily, even to environments that include a risk-sensitive scal authority and/or inequality constraints on government spending. We show that the risk-sensitive scal authority lowers government spending and income-taxation, reducing the disincentive households face to accumulate wealth.

Apparent competition through facilitation between Melanoides tuberculata and Biomphalaria glabrata and the control of schistosomiasis

Interactions between two species that result in reduced growth rates for both and extinction of one of the species are generally considered cases of asymmetric interspecific competition. Exploitative or interference competition is the usual mechanism invoked. Here we describe another mechanism producing the same result, named apparent competition through facilitation (ACF), observed between Melanoides tuberculata and Biomphalaria glabrata populations. The superior competitor actually gives some benefit to the other species, whose population becomes unstable with progressively increasing oscillations, leading to extinction. A model of ACF using difference equations suggests initial dynamics distinct from traditional interspecific competition. The dynamics of two freshwater snails in the field and in laboratory experiments suggest ACF, and these relations should be considered in studies of schistosomiasis control. ACF could occur in natural populations, but might have gone undetected because the final result is similar to traditional interspecific competition.

Analysis and Monte Carlo simulations of a model for the spread of infectious diseases in heterogeneous metapopulations

We present a study of the continuous-time equations governing the dynamics of a susceptible infected-susceptible model on heterogeneous metapopulations. These equations have been recently proposed as an alternative formulation for the spread of infectious diseases in metapopulations in a continuous-time framework. Individual-based Monte Carlo simulations of epidemic spread in uncorrelated networks are also performed revealing a good agreement with analytical predictions under the assumption of simultaneous transmission or recovery and migration processes

Driven fragmentation of granular gases

The dynamics of homogeneously heated granular gases which fragment due to particle collisions is analyzed. We introduce a kinetic model which accounts for correlations induced at the grain collisions and analyze both the kinetics and relevant distribution functions these systems develop. The work combines analytical and numerical studies based on direct simulation Monte Carlo calculations. A broad family of fragmentation probabilities is considered, and its implications for the system kinetics are discussed. We show that generically these driven materials evolve asymptotically into a dynamical scaling regime. If the fragmentation probability tends to a constant, the grain number diverges at a finite time, leading to a shattering singularity. If the fragmentation probability vanishes, then the number of grains grows monotonously as a power law. We consider different homogeneous thermostats and show that the kinetics of these systems depends weakly on both the grain inelasticity and driving. We observe that fragmentation plays a relevant role in the shape of the velocity distribution of the particles. When the fragmentation is driven by local stochastic events, the longvelocity tail is essentially exponential independently of the heating frequency and the breaking rule. However, for a Lowe-Andersen thermostat, numerical evidence strongly supports the conjecture that the scaled velocity distribution follows a generalized exponential behavior f (c)~exp (−cⁿ), with n ≈1.2, regarding less the fragmentation mechanisms

Policy and the Evolution of the US Economy: 1948-2002

This paper investigates the relationship between monetary policy and the changes experienced by the US economy using a small scale New-Keynesian model. The model is estimated with Bayesian techniques and the stability of policy parameter estimates and of the transmission of policy shocks examined. The model fits well the data and produces forecasts comparable or superior to those of alternative specifications. The parameters of the policy rule, the variance and the transmission of policy shocks have been remarkably stable. The parameters of the Phillips curve and of the Euler equations are varying.

Solving non-linear stochastic models by parameterizing expectations: An application to asset pricing with production

A new algorithm called the parameterized expectations approach(PEA) for solving dynamic stochastic models under rational expectationsis developed and its advantages and disadvantages are discussed. Thisalgorithm can, in principle, approximate the true equilibrium arbitrarilywell. Also, this algorithm works from the Euler equations, so that theequilibrium does not have to be cast in the form of a planner's problem.Monte--Carlo integration and the absence of grids on the state variables,cause the computation costs not to go up exponentially when the numberof state variables or the exogenous shocks in the economy increase. \\As an application we analyze an asset pricing model with endogenousproduction. We analyze its implications for time dependence of volatilityof stock returns and the term structure of interest rates. We argue thatthis model can generate hump--shaped term structures.

Boson-boson mixtures and triplet correlations

The hypernetted-chain formalism for boson-boson mixtures described by an extended Jastrow correlated wave function is derived, taking into account elementary diagrams and triplet correlations. The energy of an ideal boson 3He-4He mixture is computed for low values of the 3He concentration. The zero-3He-concentration limit provides a 3He chemical potential in good agreement with the experimental value, when a McMillan two-body correlation factor and the Lennard-Jones potential are adopted. If the Euler equations for the two-body correlation factors are solved in presence of triplet correlations, the agreement is again improved. At the experimental 4He equilibrium density, the 3He chemical potential turns out to be -2.58 K, to be compared with the experimental value, -2.79 K.

A reduction of order two for infinite-order Lagrangians

Given a Lagrangian system depending on the position derivatives of any order, and assuming that certain conditions are satisfied, a second-order differential system is obtained such that its solutions also satisfy the Euler equations derived from the original Lagrangian. A generalization of the singular Lagrangian formalism permits a reduction of order keeping the canonical formalism in sight. Finally, the general results obtained in the first part of the paper are applied to Wheeler-Feynman electrodynamics for two charged point particles up to order 1/c4.

Cardan Gear Mechanism versus Slider-Crank Mechanism in Pumps and Engines

In machine design we always want to save space, save energy and produce as much power as possible. We can often reduce accelerations, inertial loads and energy consumption by changing construction. In this study the old cardan gear mechanism (hypocycloid mechanism) has been compared with the conventional slider-crank mechanism in air pumps and four-stroke engines. Comprehensive Newtonian dynamics has been derived for the both mechanisms. First the slidercrank and the cardan gear machines have been studied as lossless systems. Then the friction losses have been added to the calculations. The calculation results show that the cardan gear machines can be more efficient than the slider-crank machines. The smooth running, low mass inertia, high pressures and small frictional power losses make the cardan gear machines clearly better than the slider-crank machines. The dynamic tooth loads of the original cardan gear construction do not rise very high when the tooth clearances are kept tight. On the other hand the half-size crank length causes high bearing forces in the cardan gear machines. The friction losses of the cardan gear machines are generally quite small. The mechanical efficiencies are much higher in the cardan gear machines than in the slider-crank machines in normal use. Crankshaft torques and power needs are smaller in the cardan gear air pumps than in the equal slider-crank air pumps. The mean crankshaft torque and the mean output power are higher in the cardan gear four-stroke engines than in the slider-crank four-stroke engines in normal use. The cardan gear mechanism is at its best, when we want to build a pump or an engine with a long connecting rod (≈ 5⋅crank length) and a thin piston (≈ 1.5⋅crank length) rotating at high angular velocity and intermittently high angular acceleration. The cardan gear machines can be designed also as slide constructions without gears. Suitable applications of the cardan gear machines are three-cylinder half-radial engines for motorcycles, sixcylinder radial engines for airplanes and six-cylinder double half-radial engines for sport cars. The applied equations of Newtonian dynamics, comparative calculations, calculation results (tables, curves and surface plots) and recommendations presented in this study hold novelty value and are unpublished before. They have been made and written by the author first time in this study.

Accounting for adsorption and desorption in Lattice Boltzmann simulations

We report a Lattice-Boltzmann scheme that accounts for adsorption and desorption in the calculation of mesoscale dynamical properties of tracers in media of arbitrary complexity. Lattice Boltzmann simulations made it possible to solve numerically the coupled Navier-Stokes equations of fluid dynamics and Nernst-Planck equations of electrokinetics in complex, heterogeneous media. With the moment propagation scheme, it became possible to extract the effective diffusion and dispersion coefficients of tracers, or solutes, of any charge, e.g., in porous media. Nevertheless, the dynamical properties of tracers depend on the tracer-surface affinity, which is not purely electrostatic and also includes a species-specific contribution. In order to capture this important feature, we introduce specific adsorption and desorption processes in a lattice Boltzmann scheme through a modified moment propagation algorithm, in which tracers may adsorb and desorb from surfaces through kinetic reaction rates. The method is validated on exact results for pure diffusion and diffusion-advection in Poiseuille flows in a simple geometry. We finally illustrate the importance of taking such processes into account in the time-dependent diffusion coefficient in a more complex porous medium.

Sarasuon hiilikaasudynamiikka muuttuvissa kosteusolosuhteissa

Seloste väitöskirjasta: Fen ecosystem carbon gas dynamics in changing hydrological conditions. Dissertationes Forestales 67.

Modeling of the Fluid-Structure Interaction in Inelastic Piping Systems

In many engineering applications, compliant piping systems conveying liquids are subjected to inelastic deformations due to severe pressure surges such as plastic tubes in modern water supply transmission lines and metallic pipings in nuclear power plants. In these cases the design of such systems may require an adequate modeling of the interactions between the fluid dynamics and the inelastic structural pipe motions. The reliability of the prediction of fluid-pipe behavior depends mainly on the adequacy of the constitutive equations employed in the analysis. In this paper it is proposed a systematic and general approach to consistently incorporate different kinds of inelastic behaviors of the pipe material in a fluid-structure interaction analysis. The main feature of the constitutive equations considered in this work is that a very simple numerical technique can be used for solving the coupled equations describing the dynamics of the fluid and pipe wall. Numerical examples concerning the analysis of polyethylene and stainless steel pipe networks are presented to illustrate the versatility of the proposed approach.

Preconditioner updates applied to CFD model problems

In the present paper we concentrate on solving sequences of nonsymmetric linear systems with block structure arising from compressible flow problems. We attempt to improve the solution process by sharing part of the computational effort throughout the sequence. This is achieved by application of a cheap updating technique for preconditioners which we adapted in order to be used for our applications. Tested on three benchmark compressible flow problems, the strategy speeds up the entire computation with an acceleration being particularly pronounced in phases of instationary behavior.

Trajectory and Force Control of a Direct Drive Arm

Using the MIT Serial Link Direct Drive Arm as the main experimental device, various issues in trajectory and force control of manipulators were studied in this thesis. Since accurate modeling is important for any controller, issues of estimating the dynamic model of a manipulator and its load were addressed first. Practical and effective algorithms were developed fro the Newton-Euler equations to estimate the inertial parameters of manipulator rigid-body loads and links. Load estimation was implemented both on PUMA 600 robot and on the MIT Serial Link Direct Drive Arm. With the link estimation algorithm, the inertial parameters of the direct drive arm were obtained. For both load and link estimation results, the estimated parameters are good models of the actual system for control purposes since torques and forces can be predicted accurately from these estimated parameters. The estimated model of the direct drive arm was them used to evaluate trajectory following performance by feedforward and computed torque control algorithms. The experimental evaluations showed that the dynamic compensation can greatly improve trajectory following accuracy. Various stability issues of force control were studied next. It was determined that there are two types of instability in force control. Dynamic instability, present in all of the previous force control algorithms discussed in this thesis, is caused by the interaction of a manipulator with a stiff environment. Kinematics instability is present only in the hybrid control algorithm of Raibert and Craig, and is caused by the interaction of the inertia matrix with the Jacobian inverse coordinate transformation in the feedback path. Several methods were suggested and demonstrated experimentally to solve these stability problems. The result of the stability analyses were then incorporated in implementing a stable force/position controller on the direct drive arm by the modified resolved acceleration method using both joint torque and wrist force sensor feedbacks.

A cell by cell anisotropic adaptive mesh ALE method

A cell by cell anisotropic adaptive mesh Arbitrary Lagrangian Eulerian (ALE) method for the solution of the Euler equations is described. An efficient approach to equipotential mesh relaxation on anisotropically refined meshes is developed. Results for two test problems are presented.