408 research outputs found
Stability of parallel/perpendicular domain boundaries in lamellar block copolymers under oscillatory shear
We introduce a model constitutive law for the dissipative stress tensor of
lamellar phases to account for low frequency and long wavelength flows. Given
the uniaxial symmetry of these phases, we argue that the stress tensor must be
the same as that of a nematic but with the local order parameter being the
slowly varying lamellar wavevector. This assumption leads to a dependence of
the effective dynamic viscosity on orientation of the lamellar phase. We then
consider a model configuration comprising a domain boundary separating
laterally unbounded domains of so called parallel and perpendicularly oriented
lamellae in a uniform, oscillatory, shear flow, and show that the configuration
can be hydrodynamically unstable for the constitutive law chosen. It is argued
that this instability and the secondary flows it creates can be used to infer a
possible mechanism for orientation selection in shear experiments.Comment: 26 pages, 10 figure
Orientation selection in lamellar phases by oscillatory shears
In order to address the selection mechanism that is responsible for the
unique lamellar orientation observed in block copolymers under oscillatory
shears, we use a constitutive law for the dissipative part of the stress tensor
that respects the uniaxial symmetry of a lamellar phase. An interface
separating two domains oriented parallel and perpendicular to the shear is
shown to be hydrodynamically unstable, a situation analogous to the thin layer
instability of stratified fluids under shear. The resulting secondary flows
break the degeneracy between parallel and perpendicular lamellar orientation,
leading to a preferred perpendicular orientation in certain ranges of
parameters of the polymer and of the shear.Comment: 4 pages, 3 figure
Lattice-Ordered Algebras That are Subdirect Products of Valuation Domains
An f-ring (i.e., a lattice-ordered ring that is a subdirect product of totally ordered rings) A is called an SV-ring if A/P is a valuation domain for every prime ideal P of A. If M is a maximal ℓ-ideal of A , then the rank of A at M is the number of minimal prime ideals of A contained in M, rank of A is the sup of the ranks of A at each of its maximal ℓ-ideals. If the latter is a positive integer, then A is said to have finite rank, and if A = C(X) is the ring of all real-valued continuous functions on a Tychonoff space, the rank of X is defined to be the rank of the f-ring C(X), and X is called an SV-space if C(X) is an SV-ring. X has finite rank k iff k is the maximal number of pairwise disjoint cozero sets with a point common to all of their closures. In general f-rings these two concepts are unrelated, but if A is uniformly complete (in particular, if A = C(X)) then if A is an SV-ring then it has finite rank. Showing that ihis latter holds makes use of the theory of finite-valued lattice-ordered (abelian) groups. These two kinds of rings are investigated with an emphasis on the uniformly complete case. Fairly powerful machinery seems to have to be used, and even then, we do not know if there is a compact space X of finite rank that fails to be an SV-space
Shear-thickening and entropy-driven reentrance
We discuss a generic mechanism for shear-thickening analogous to
entropy-driven phase reentrance. We implement it in the context of
non-relaxational mean-field glassy systems: although very simple, the
microscopic models we study present a dynamical phase diagram with second and
first order stirring-induced jamming transitions leading to intermittency,
metastability and phase coexistence as seen in some experiments. The jammed
state is fragile with respect to change in the stirring direction. Our approach
provides a direct derivation of a Mode-Coupling theory of shear-thickening.Comment: 4 pages, 4 figures, minor changes, references adde
The scale-free character of the cluster mass function and the universality of the stellar IMF
Our recent determination of a Salpeter slope for the IMF in the field of 30
Doradus (Selman and Melnick 2005) appears to be in conflict with simple
probabilistic counting arguments advanced in the past to support observational
claims of a steeper IMF in the LMC field. In this paper we re-examine these
arguments and show by explicit construction that, contrary to these claims, the
field IMF is expected to be exactly the same as the stellar IMF of the clusters
out of which the field was presumably formed. We show that the current data on
the mass distribution of clusters themselves is in excellent agreement with our
model, and is consistent with a single spectrum {\it by number of stars} of the
type with beta between -1.8 and -2.2 down to the smallest clusters
without any preferred mass scale for cluster formation. We also use the random
sampling model to estimate the statistics of the maximal mass star in clusters,
and confirm the discrepancy with observations found by Weidner and Kroupa
(2006). We argue that rather than signaling the violation of the random
sampling model these observations reflect the gravitationally unstable nature
of systems with one very large mass star. We stress the importance of the
random sampling model as a \emph{null hypothesis} whose violation would signal
the presence of interesting physics.Comment: 9 pages emulateap
Shear induced grain boundary motion for lamellar phases in the weakly nonlinear regime
We study the effect of an externally imposed oscillatory shear on the motion
of a grain boundary that separates differently oriented domains of the lamellar
phase of a diblock copolymer. A direct numerical solution of the
Swift-Hohenberg equation in shear flow is used for the case of a
transverse/parallel grain boundary in the limits of weak nonlinearity and low
shear frequency. We focus on the region of parameters in which both transverse
and parallel lamellae are linearly stable. Shearing leads to excess free energy
in the transverse region relative to the parallel region, which is in turn
dissipated by net motion of the boundary toward the transverse region. The
observed boundary motion is a combination of rigid advection by the flow and
order parameter diffusion. The latter includes break up and reconnection of
lamellae, as well as a weak Eckhaus instability in the boundary region for
sufficiently large strain amplitude that leads to slow wavenumber readjustment.
The net average velocity is seen to increase with frequency and strain
amplitude, and can be obtained by a multiple scale expansion of the governing
equations
Does Turbulent Pressure Behave as a Logatrope?
We present numerical simulations of an isothermal turbulent gas undergoing
gravitational collapse, aimed at testing for ``logatropic'' behavior of the
form , where is the ``turbulent pressure'' and
is the density. To this end, we monitor the evolution of the turbulent velocity
dispersion as the density increases during the collapse. A logatropic
behavior would require that , a result which,
however, is not verified in the simulations. Instead, the velocity dispersion
increases with density, implying a polytropic behavior of . This behavior
is found both in purely hydrodynamic as well as hydromagnetic runs. For purely
hydrodynamic and rapidly-collapsing magnetic cases, the velocity dispersion
increases roughly as , implying ,
where is the turbulent pressure. For slowly-collapsing magnetic cases the
behavior is close to , which implies . We thus suggest that the logatropic ``equation of state'' may
represent only the statistically most probable state of an ensemble of clouds
in equilibrium between self-gravity and kinetic support, but does not
adequately represent the behavior of the ``turbulent pressure'' within a cloud
undergoing a dynamic compression due to gravitational collapse. Finally, we
discuss the importance of the underlying physical model for the clouds (in
equilibrium vs. dynamic) on the results obtained.Comment: Accepted in ApJ. 10 pages, 3 postscript figure
The Life and Death of Dense Molecular Clumps in the Large Magellanic Cloud
We report the results of a high spatial (parsec) resolution HCO+ (J = 1-0)
and HCN (J = 1-0) emission survey toward the giant molecular clouds of the star
formation regions N105, N113, N159, and N44 in the Large Magellanic Cloud. The
HCO+ and HCN observations at 89.2 and 88.6 GHz, respectively, were conducted in
the compact configuration of the Australia Telescope Compact Array. The
emission is imaged into individual clumps with masses between 10^2 and 10^4
solar masses and radii of <1 pc to ~2 pc. Many of the clumps are coincident
with indicators of current massive star formation, indicating that many of the
clumps are associated with deeply-embedded forming stars and star clusters. We
find that massive YSO-bearing clumps tend to be larger (>1 pc), more massive (M
> 10^3 solar masses), and have higher surface densities (~1 g cm^-2), while
clumps without signs of star formation are smaller (<1 pc), less massive (M <
10^3 solar masses), and have lower surface densities (~0.1 g cm^-2). The dearth
of massive (M >10^3 solar masses) clumps not bearing massive YSOs suggests the
onset of star formation occurs rapidly once the clump has attained physical
properties favorable to massive star formation. Using a large sample of LMC
massive YSO mid-IR spectra, we estimate that ~2/3 of the massive YSOs for which
there are Spitzer mid-IR spectra are no longer located in molecular clumps; we
estimate that these young stars/clusters have destroyed their natal clumps on a
time scale of at least 3 x 10^{5}$ yrs.Comment: Accepted to ApJ 3-19-201
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