6,945 research outputs found
Criticality and convergence in Newtonian collapse
We study through numerical simulation the spherical collapse of isothermal
gas in Newtonian gravity. We observe a critical behavior which occurs at the
threshold of gravitational instability leading to core formation. For a given
initial density profile, we find a critical temperature, which is of the same
order as the virial temperature of the initial configuration. For the exact
critical temperature, the collapse converges to a self-similar form, the first
member in Hunter's family of self-similar solutions. For a temperature close to
the critical value, the collapse first approaches this critical solution. Later
on, in the supercritical case, the collapse converges to another self-similar
solution, which is called the Larson-Penston solution. In the subcritical case,
the gas bounces and disperses to infinity. We find two scaling laws: one for
the collapsed mass in the supercritical case and the other for the maximum
density reached before dispersal in the subcritical case. The value of the
critical exponent is measured to be in the supercritical case,
which agrees well with the predicted value . These critical
properties are quite similar to those observed in the collapse of a radiation
fluid in general relativity. We study the response of the system to temperature
fluctuation and discuss astrophysical implications for the insterstellar medium
structure and for the star formation process. Newtonian critical behavior is
important not only because it provides a simple model for general relativity
but also because it is relevant for astrophysical systems such as molecular
clouds.Comment: 15 pages, 8 figures, accepted for publication in PRD, figures 1 and 3
at lower resolution than in journal version, typos correcte
Spherical Vesicles Distorted by a Grafted Latex Bead: An Exact Solution
We present an exact solution to the problem of the global shape description
of a spherical vesicle distorted by a grafted latex bead. This solution is
derived by treating the nonlinearity in bending elasticity through the
(topological) Bogomol'nyi decomposition technique and elastic compatibility. We
recover the ``hat-model'' approximation in the limit of a small latex bead and
find that the region antipodal to the grafted latex bead flattens. We also
derive the appropriate shape equation using the variational principle and
relevant constraints.Comment: 12 pages, 2 figures, LaTeX2e+REVTeX+AmSLaTe
Raman scattering from fractals. Simulation on large structures by the method of moments
We have employed the method of spectral moments to study the density of
vibrational states and the Raman coupling coefficient of large 2- and 3-
dimensional percolators at threshold and at higher concentration. We first
discuss the over-and under-flow problems of the procedure which arise when
-like in the present case- it is necessary to calculate a few thousand moments.
Then we report on the numerical results; these show that different scattering
mechanisms, all {\it a priori} equally probable in real systems, produce
largely different coupling coefficients with different frequency dependence.
Our results are compared with existing scaling theories of Raman scattering.
The situation that emerges is complex; on the one hand, there is indication
that the existing theory is not satisfactory; on the other hand, the
simulations above threshold show that in this case the coupling coefficients
have very little resemblance, if any, with the same quantities at threshold.Comment: 26 pages, RevTex, 8 figures available on reques
Axially symmetric membranes with polar tethers
Axially symmetric equilibrium configurations of the conformally invariant
Willmore energy are shown to satisfy an equation that is two orders lower in
derivatives of the embedding functions than the equilibrium shape equation, not
one as would be expected on the basis of axial symmetry. Modulo a translation
along the axis, this equation involves a single free parameter c.If c\ne 0, a
geometry with spherical topology will possess curvature singularities at its
poles. The physical origin of the singularity is identified by examining the
Noether charge associated with the translational invariance of the energy; it
is consistent with an external axial force acting at the poles. A one-parameter
family of exact solutions displaying a discocyte to stomatocyte transition is
described.Comment: 13 pages, extended and revised version of Non-local sine-Gordon
equation for the shape of axi-symmetric membrane
Spatio-temporal ecology of sympatric felids on Borneo. Evidence for resource partitioning?
Niche differentiation, the partitioning of resources along one or more axes of a species’ niche hyper-volume, is widely recognised as an important mechanism for sympatric species to reduce interspecific competition and predation risk, and thus facilitate co-existence. Resource partitioning may be facilitated by behavioural differentiation along three main niche dimensions: habitat, food and time. In this study, we investigate the extent to which these mechanisms can explain the coexistence of an assemblage of five sympatric felids in Borneo. Using multi-scale logistic regression, we show that Bornean felids exhibit differences in both their broad and fine-scale habitat use. We calculate temporal activity patterns and overlap between these species, and present evidence for temporal separation within this felid guild. Lastly, we conducted an all-subsets logistic regression to predict the occurrence of each felid species as a function of the co-occurrence of a large number of other species and showed that Bornean felids co-occurred with a range of other species, some of which could be candidate prey. Our study reveals apparent resource partitioning within the Bornean felid assemblage, operating along all three niche dimension axes. These results provide new insights into the ecology of these species and the broader community in which they live and also provide important information for conservation planning for this guild of predators
Nesting Induced Precursor Effects: a Renormalization Group Approach
We develop a controlled weak coupling renormalization group (RG) approach to
itinerant electrons. Within this formalism we rederive the phase diagram for
two-dimensional (2D) non-nested systems. Then we study how nesting modifies
this phase diagram. We show that competition between p-p and p-h channels,
leads to the manifestation of unstable precursor fixed points in the RG flow.
This effect should be experimentally measurable, and may be relevant for an
explanation of pseudogaps in the high temperature superconductors (HTC), as a
crossover phenomenon.Comment: 4 pages, 4 figures, 1 tabl
Kondo engineering : from single Kondo impurity to the Kondo lattice
In the first step, experiments on a single cerium or ytterbium Kondo impurity
reveal the importance of the Kondo temperature by comparison to other type of
couplings like the hyperfine interaction, the crystal field and the intersite
coupling. The extension to a lattice is discussed. Emphasis is given on the
fact that the occupation number of the trivalent configuration may be the
implicit key variable even for the Kondo lattice. Three phase
diagrams are discussed: CeRuSi, CeRhIn and SmS
Self-Dual Bending Theory for Vesicles
We present a self-dual bending theory that may enable a better understanding
of highly nonlinear global behavior observed in biological vesicles. Adopting
this topological approach for spherical vesicles of revolution allows us to
describe them as frustrated sine-Gordon kinks. Finally, to illustrate an
application of our results, we consider a spherical vesicle globally distorted
by two polar latex beads.Comment: 10 pages, 3 figures, LaTeX2e+IOPar
Bogomol'nyi Decomposition for Vesicles of Arbitrary Genus
We apply the Bogomol'nyi technique, which is usually invoked in the study of
solitons or models with topological invariants, to the case of elastic energy
of vesicles. We show that spontaneous bending contribution caused by any
deformation from metastable bending shapes falls in two distinct topological
sets: shapes of spherical topology and shapes of non-spherical topology
experience respectively a deviatoric bending contribution a la Fischer and a
mean curvature bending contribution a la Helfrich. In other words, topology may
be considered to describe bending phenomena. Besides, we calculate the bending
energy per genus and the bending closure energy regardless of the shape of the
vesicle. As an illustration we briefly consider geometrical frustration
phenomena experienced by magnetically coated vesicles.Comment: 8 pages, 1 figure; LaTeX2e + IOPar
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