44,219 research outputs found
Necrotic tumor growth: an analytic approach
The present paper deals with a free boundary problem modeling the growth
process of necrotic multi-layer tumors. We prove the existence of flat
stationary solutions and determine the linearization of our model at such an
equilibrium. Finally, we compute the solutions of the stationary linearized
problem and comment on bifurcation.Comment: 14 pages, 3 figure
Large-Scale Synchrony in Weakly Interacting Automata
We study the behavior of two spatially distributed (sandpile) models which
are weakly linked with one another. Using a Monte-Carlo implementation of the
renormalization group and algebraic methods, we describe how large-scale
correlations emerge between the two systems, leading to synchronized behavior.Comment: 6 pages, 3 figures; to appear PR
Covariant Uniform Acceleration
We show that standard Relativistic Dynamics Equation F=dp/d\tau is only
partially covariant. To achieve full Lorentz covariance, we replace the
four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By
taking this tensor to be constant, we obtain a covariant definition of
uniformly accelerated motion. We compute explicit solutions for uniformly
accelerated motion which are divided into four types: null, linear, rotational,
and general. For null acceleration, the worldline is cubic in the time. Linear
acceleration covariantly extends 1D hyperbolic motion, while rotational
acceleration covariantly extends pure rotational motion.
We use Generalized Fermi-Walker transport to construct a uniformly
accelerated family of inertial frames which are instantaneously comoving to a
uniformly accelerated observer. We explain the connection between our approach
and that of Mashhoon. We show that our solutions of uniformly accelerated
motion have constant acceleration in the comoving frame. Assuming the Weak
Hypothesis of Locality, we obtain local spacetime transformations from a
uniformly accelerated frame K' to an inertial frame K. The spacetime
transformations between two uniformly accelerated frames with the same
acceleration are Lorentz. We compute the metric at an arbitrary point of a
uniformly accelerated frame.
We obtain velocity and acceleration transformations from a uniformly
accelerated system K' to an inertial frame K. We derive the general formula for
the time dilation between accelerated clocks. We obtain a formula for the
angular velocity of a uniformly accelerated object. Every rest point of K' is
uniformly accelerated, and its acceleration is a function of the observer's
acceleration and its position. We obtain an interpretation of the
Lorentz-Abraham-Dirac equation as an acceleration transformation from K' to K.Comment: 36 page
Thirring Solitons in the presence of dispersion
The effect of dispersion or diffraction on zero-velocity solitons is studied
for the generalized massive Thirring model describing a nonlinear optical fiber
with grating or parallel-coupled planar waveguides with misaligned axes. The
Thirring solitons existing at zero dispersion/diffraction are shown numerically
to be separated by a finite gap from three isolated soliton branches. Inside
the gap, there is an infinity of multi-soliton branches. Thus, the Thirring
solitons are structurally unstable. In another parameter region (far from the
Thirring limit), solitons exist everywhere.Comment: 12 pages, Latex. To appear in Phys. Rev. Let
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