66,065 research outputs found
From Network Structure to Dynamics and Back Again: Relating dynamical stability and connection topology in biological complex systems
The recent discovery of universal principles underlying many complex networks
occurring across a wide range of length scales in the biological world has
spurred physicists in trying to understand such features using techniques from
statistical physics and non-linear dynamics. In this paper, we look at a few
examples of biological networks to see how similar questions can come up in
very different contexts. We review some of our recent work that looks at how
network structure (e.g., its connection topology) can dictate the nature of its
dynamics, and conversely, how dynamical considerations constrain the network
structure. We also see how networks occurring in nature can evolve to modular
configurations as a result of simultaneously trying to satisfy multiple
structural and dynamical constraints. The resulting optimal networks possess
hubs and have heterogeneous degree distribution similar to those seen in
biological systems.Comment: 15 pages, 6 figures, to appear in Proceedings of "Dynamics On and Of
Complex Networks", ECSS'07 Satellite Workshop, Dresden, Oct 1-5, 200
Hydrodynamics of Binary Coalescence.I. Polytropes with Stiff Equations of State
We have performed a series of three-dimensional hydrodynamic calculations of
binary coalescence using the smoothed particle hydrodynamics (SPH) method. The
initial conditions are exact polytropic equilibrium configurations with \gam >
5/3, on the verge of dynamical instability. We calculate the emission of
gravitational radiation in the quadrupole approximation. The fully nonlinear
development of the instability is followed until a new equilibrium
configuration is reached. We find that the properties of this final
configuration depend sensitively on both the compressibility and mass ratio. An
{\em axisymmetric} merged configuration is always produced when \gam\lo2.3.
As a consequence, the emission of gravitational radiation shuts off abruptly
right after the onset of dynamical instability. In contrast, {\em triaxial\/}
merged configurations are obtained when \gam\go2.3, and the system continues
to emit gravitational waves after the final coalescence. Systems with mass
ratios typically become dynamically unstable before the onset of mass
transfer. Stable mass transfer from one neutron star to another in a close
binary is therefore probably ruled out. The maximum amplitude and
peak luminosity of the gravitational waves emitted during the final
coalescence are nearly independent of \gam, but depend very sensitively on
the mass ratio .Comment: 27 pages, uuencoded compressed postscript, 16 figures upon request
from [email protected], IAS-AST-94-
On the Hamiltonian structure and three-dimensional instabilities of rotating liquid bridges
We consider a rotating inviscid liquid drop trapped between two parallel plates. The liquid–air interface is a free surface and the boundaries of the wetted regions in the plates are also free. We assume that the two contact angles at the plates are equal. We present drop shapes that generalize the catenoids, nodoids and unduloids in the presence of rotation. We describe profile curves of these drops and investigate their stability to three-dimensional perturbations. The instabilities are associated with degeneracies of eigenvalues of the corresponding Hamiltonian linear stability problem. We observe that these instabilities are present even in the case when the analogue of the Rayleigh criterion for two-dimensional stability is satisfie
Twin Binaries: Studies of Stability, Mass Transfer, and Coalescence
Motivated by suggestions that binaries with almost equal-mass components
("twins") play an important role in the formation of double neutron stars and
may be rather abundant among binaries, we study the stability of synchronized
close and contact binaries with identical components in circular orbits. In
particular, we investigate the dependency of the innermost stable circular
orbit on the core mass, and we study the coalescence of the binary that occurs
at smaller separations. For twin binaries composed of convective main-sequence
stars, subgiants, or giants with low mass cores (M_c <~0.15M, where M is the
mass of a component), a secular instability is reached during the contact
phase, accompanied by a dynamical mass transfer instability at the same or at a
slightly smaller orbital separation. Binaries that come inside this instability
limit transfer mass gradually from one component to the other and then coalesce
quickly as mass is lost through the outer Lagrangian points. For twin giant
binaries with moderate to massive cores (M_c >~0.15M), we find that stable
contact configurations exist at all separations down to the Roche limit, when
mass shedding through the outer Lagrangian points triggers a coalescence of the
envelopes and leaves the cores orbiting in a central tight binary. In addition
to the formation of binary neutron stars, we also discuss the implications of
our results for the production of planetary nebulae with double degenerate
central binaries.Comment: 17 pages, accepted to ApJ, final version includes discussion of
planetary nebulae with central binaries and a new figure about shock heating,
visualizations at http://webpub.allegheny.edu/employee/j/jalombar/movies
Fractal free energy landscapes in structural glasses
Glasses are amorphous solids whose constituent particles are caged by their
neighbors and thus cannot flow. This sluggishness is often ascribed to the free
energy landscape containing multiple minima (basins) separated by high
barriers. Here we show, using theory and numerical simulation, that the
landscape is much rougher than is classically assumed. Deep in the glass, it
undergoes a "roughness transition" to fractal basins. This brings about
isostaticity at jamming and marginality of glassy states near jamming. Critical
exponents for the basin width, the weak force distribution, and the spatial
spread of quasi-contacts at jamming can be analytically determined. Their value
is found to be compatible with numerical observations. This advance therefore
incorporates the jamming transition of granular materials into the framework of
glass theory. Because temperature and pressure control which features of the
landscape are experienced, glass mechanics and transport are expected to
reflect the features of the topology we discuss here. Hitherto mysterious
properties of low-temperature glasses could be explained by this approach.Comment: 13 pages, 4 figures. This version was initially submitted to Nature
Communications in December 2013. The (much improved) final version is
available on the Nature Communications website (see DOI below). A detailed
version of this work is available on arXiv:1310.254
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