982 research outputs found
The inflation bias under Calvo and Rotemberg pricing
New Keynesian analysis relies heavily on two workhorse models of nominal inertia – due to Calvo (1983) and Rotemberg (1982), respectively – to generate a meaningful role for monetary policy. These are often used interchangeably since they imply an isomorphic linearized Phillips curve and, if the steady-state is efficient, the same policy conclusions. In this paper we compute time-consistent optimal monetary policy in the benchmark New Keynesian model containing each form of price stickiness using global solution techniques. We find that, due to an offsetting endogenous impact on average markups, the inflation bias problem under Calvo contracts is often significantly greater than under Rotemberg pricing, despite the fact that the former typically exhibits far greater welfare costs of inflation. The nonlinearities inherent in the New Keynesian model are significant and the form of nominal inertia adopted is not innocuous
Spectral method for matching exterior and interior elliptic problems
A spectral method is described for solving coupled elliptic problems on an
interior and an exterior domain. The method is formulated and tested on the
two-dimensional interior Poisson and exterior Laplace problems, whose solutions
and their normal derivatives are required to be continuous across the
interface. A complete basis of homogeneous solutions for the interior and
exterior regions, corresponding to all possible Dirichlet boundary values at
the interface, are calculated in a preprocessing step. This basis is used to
construct the influence matrix which serves to transform the coupled boundary
conditions into conditions on the interior problem. Chebyshev approximations
are used to represent both the interior solutions and the boundary values. A
standard Chebyshev spectral method is used to calculate the interior solutions.
The exterior harmonic solutions are calculated as the convolution of the
free-space Green's function with a surface density; this surface density is
itself the solution to an integral equation which has an analytic solution when
the boundary values are given as a Chebyshev expansion. Properties of Chebyshev
approximations insure that the basis of exterior harmonic functions represents
the external near-boundary solutions uniformly. The method is tested by
calculating the electrostatic potential resulting from charge distributions in
a rectangle. The resulting influence matrix is well-conditioned and solutions
converge exponentially as the resolution is increased. The generalization of
this approach to three-dimensional problems is discussed, in particular the
magnetohydrodynamic equations in a finite cylindrical domain surrounded by a
vacuum
Efficient Implementation of Elastohydrodynamics via Integral Operators
The dynamics of geometrically non-linear flexible filaments play an important
role in a host of biological processes, from flagella-driven cell transport to
the polymeric structure of complex fluids. Such problems have historically been
computationally expensive due to numerical stiffness associated with the
inextensibility constraint, as well as the often non-trivial boundary
conditions on the governing high-order PDEs. Formulating the problem for the
evolving shape of a filament via an integral equation in the tangent angle has
recently been found to greatly alleviate this numerical stiffness. The
contribution of the present manuscript is to enable the simulation of non-local
interactions of multiple filaments in a computationally efficient manner using
the method of regularized stokeslets within this framework. The proposed method
is benchmarked against a non-local bead and link model, and recent code
utilizing a local drag velocity law. Systems of multiple filaments (1) in a
background fluid flow, (2) under a constant body force, and (3) undergoing
active self-motility are modeled efficiently. Buckling instabilities are
analyzed by examining the evolving filament curvature, as well as by
coarse-graining the body frame tangent angles using a Chebyshev approximation
for various choices of the relevant non-dimensional parameters. From these
experiments, insight is gained into how filament-filament interactions can
promote buckling, and further reveal the complex fluid dynamics resulting from
arrays of these interacting fibers. By examining active moment-driven
filaments, we investigate the speed of worm- and sperm-like swimmers for
different governing parameters. The MATLAB(R) implementation is made available
as an open-source library, enabling flexible extension for alternate
discretizations and different surrounding flows.Comment: 37 pages, 17 figure
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