46,291 research outputs found
A two-dimensional non-equilibrium dynamic model
This paper develops a non-equilibrium dynamic model (NEDyM) with Keynesian features (it allows for a disequilibrium between output and demand and it considers a constant marginal propensity to consume), but where production is undertaken under plain neoclassical conditions (a constant returns to scale production function, with the stocks of capital and labor fully employed, is assumed). The model involves only two endogenous / prognostic variables: the stock of physical capital per unit of labor and a goods inventory measure. The two-dimensional system allows for a careful analysis of local and global dynamics. Points of bifurcation and long-term cyclical motion are identified. The main conclusion is that the disequilibrium hypothesis leads to persistent fluctuations generated by intrinsic deterministic factors
On the Nonlinear Stability of Asymptotically Anti-de Sitter Solutions
Despite the recent evidence that anti-de Sitter spacetime is nonlinearly
unstable, we argue that many asymptotically anti-de Sitter solutions are
nonlinearly stable. This includes geons, boson stars, and black holes. As part
of our argument, we calculate the frequencies of long-lived gravitational
quasinormal modes of AdS black holes in various dimensions. We also discuss a
new class of asymptotically anti-de Sitter solutions describing noncoalescing
black hole binaries.Comment: 26 pages. 5 figure
Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts
Fronts that start from a local perturbation and propagate into a linearly
unstable state come in two classes: pulled and pushed. ``Pulled'' fronts are
``pulled along'' by the spreading of linear perturbations about the unstable
state, so their asymptotic speed equals the spreading speed of linear
perturbations of the unstable state. The central result of this paper is that
the velocity of pulled fronts converges universally for time like
. The parameters ,
, and are determined through a saddle point analysis from the
equation of motion linearized about the unstable invaded state. The interior of
the front is essentially slaved to the leading edge, and we derive a simple,
explicit and universal expression for its relaxation towards
. Our result, which can be viewed as a general center
manifold result for pulled front propagation, is derived in detail for the well
known nonlinear F-KPP diffusion equation, and extended to much more general
(sets of) equations (p.d.e.'s, difference equations, integro-differential
equations etc.). Our universal result for pulled fronts thus implies
independence (i) of the level curve which is used to track the front position,
(ii) of the precise nonlinearities, (iii) of the precise form of the linear
operators, and (iv) of the precise initial conditions. Our simulations confirm
all our analytical predictions in every detail. A consequence of the slow
algebraic relaxation is the breakdown of various perturbative schemes due to
the absence of adiabatic decoupling.Comment: 76 pages Latex, 15 figures, submitted to Physica D on March 31, 1999
-- revised version from February 25, 200
Null cone evolution of axisymmetric vacuum spacetimes
We present the details of an algorithm for the global evolution of
asymptotically flat, axisymmetric spacetimes, based upon a characteristic
initial value formulation using null cones as evolution hypersurfaces. We
identify a new static solution of the vacuum field equations which provides an
important test bed for characteristic evolution codes. We also show how
linearized solutions of the Bondi equations can be generated by solutions of
the scalar wave equation, thus providing a complete set of test beds in the
weak field regime. These tools are used to establish that the algorithm is
second order accurate and stable, subject to a Courant-Friedrichs-Lewy
condition. In addition, the numerical versions of the Bondi mass and news
function, calculated at scri on a compactified grid, are shown to satisfy the
Bondi mass loss equation to second order accuracy. This verifies that numerical
evolution preserves the Bianchi identities. Results of numerical evolution
confirm the theorem of Christodoulou and Klainerman that in vacuum, weak
initial data evolve to a flat spacetime. For the class of asymptotically flat,
axisymmetric vacuum spacetimes, for which no nonsingular analytic solutions are
known, the algorithm provides highly accurate solutions throughout the regime
in which neither caustics nor horizons form.Comment: 25 pages, 6 figure
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