642,961 research outputs found
Interacting Two-Country Business Fluctuations
In this paper we investigate the closed-economy Keynes-Wicksell-Goodwin model of Chiarella and Flaschel (2000) for the case of two interacting open economies. We introduce these coupled two-country KWG dynamics on the extensive form level by means of a subdivision into nine modules describing the behavioral equations, the laws of motion and the identities or budget equations of the model. We then derive their intensive form representation and the 10 laws of motion of the model on the basis of certain simplifying assumptions. Thereafter we present the uniquely determined steady state solution of the dynamics and discuss in a mathematically informal way its stability properties, concerning asymptotic stability and loss of stability by way of super- or subcritical Hopf-bifurcations. In a final section we explore numerically a variety of situations of interacting real and financial cycles, where the steady state is locally repelling, but where the overall dynamics are bounded in an economically meaningful domain by means of a kinked money wage Phillips curve, exhibiting downward rigidity of the money-wage, coupled with upward flexibility of the usual type.Interacting KWG economies, stability, persistent cycles, coupled oscillators.
Foundations of Dissipative Particle Dynamics
We derive a mesoscopic modeling and simulation technique that is very close
to the technique known as dissipative particle dynamics. The model is derived
from molecular dynamics by means of a systematic coarse-graining procedure.
Thus the rules governing our new form of dissipative particle dynamics reflect
the underlying molecular dynamics; in particular all the underlying
conservation laws carry over from the microscopic to the mesoscopic
descriptions. Whereas previously the dissipative particles were spheres of
fixed size and mass, now they are defined as cells on a Voronoi lattice with
variable masses and sizes. This Voronoi lattice arises naturally from the
coarse-graining procedure which may be applied iteratively and thus represents
a form of renormalisation-group mapping. It enables us to select any desired
local scale for the mesoscopic description of a given problem. Indeed, the
method may be used to deal with situations in which several different length
scales are simultaneously present. Simulations carried out with the present
scheme show good agreement with theoretical predictions for the equilibrium
behavior.Comment: 18 pages, 7 figure
PI output feedback control of differential linear repetitive processes
Repetitive processes are characterized by a series of sweeps, termed passes, through a set of dynamics defined over a finite duration known as the pass length. On each pass an output, termed the pass profile, is produced which acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile. This can lead to oscillations which increase in amplitude in the pass-to-pass direction and cannot be controlled by standard control laws. Here we give new results on the design of physically based control laws. These are for the sub-class of so-called differential linear repetitive processes which arise in applications areas such as iterative learning control. They show how a form of proportional-integral (PI) control based only on process outputs can be designed to give stability plus performance and disturbance rejection
Multisymplectic formulation of fluid dynamics using the inverse map
We construct multisymplectic formulations of fluid dynamics using the inverse of the Lagrangian path map. This inverse map, the ‘back-to-labels’ map, gives the initial Lagrangian label of the fluid particle that currently occupies each Eulerian position. Explicitly enforcing the condition that the fluid particles carry their labels with the flow in Hamilton's principle leads to our multisymplectic formulation. We use the multisymplectic one-form to obtain conservation laws for energy, momentum and an infinite set of conservation laws arising from the particle relabelling symmetry and leading to Kelvin's circulation theorem. We discuss how multisymplectic numerical integrators naturally arise in this approach.</p
Scaling of Local Slopes, Conservation Laws and Anomalous Roughening in Surface Growth
We argue that symmetries and conservation laws greatly restrict the form of
the terms entering the long wavelength description of growth models exhibiting
anomalous roughening. This is exploited to show by dynamic renormalization
group arguments that intrinsic anomalous roughening cannot occur in local
growth models. However some conserved dynamics may display super-roughening if
a given type of terms are present.Comment: To appear in Phys. Rev. Lett., 4 pages in RevTeX style, no fig
Conservation Laws and Hamilton's Equations for Systems with Long-Range Interaction and Memory
Using the fact that extremum of variation of generalized action can lead to
the fractional dynamics in the case of systems with long-range interaction and
long-term memory function, we consider two different applications of the action
principle: generalized Noether's theorem and Hamiltonian type equations. In the
first case, we derive conservation laws in the form of continuity equations
that consist of fractional time-space derivatives. Among applications of these
results, we consider a chain of coupled oscillators with a power-wise memory
function and power-wise interaction between oscillators. In the second case, we
consider an example of fractional differential action 1-form and find the
corresponding Hamiltonian type equations from the closed condition of the form.Comment: 30 pages, LaTe
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