5,933 research outputs found
Weakly nonlinear subcritical instability of visco-elastic Poiseuille flow
It is well known that the Poiseuille flow of a visco-elastic polymer fluid
between plates or through a tube is linearly stable in the zero Reynolds number
limit, although the stability is weak for large Weissenberg numbers. In this
paper we argue that recent experimental and theoretical work on the instability
of visco-elastic fluids in Taylor-Couette cells and numerical work on channel
flows suggest a scenario in which Poiseuille flow of visco-elastic polymer
fluids exhibits a nonlinear "subcritical" instability due to normal stress
effects, with a threshold which decreases for increasing Weissenberg number.
This proposal is confirmed by an explicit weakly nonlinear stability analysis
for Poiseuille flow of an UCM fluid. Our analysis yields explicit predictions
for the critical amplitude of velocity perturbations beyond which the flow is
nonlinearly unstable, and for the wavelength of the mode whose critical
amplitude is smallest. The nonlinear instability sets in quite abruptly at
Weissenberg numbers around 4 in the planar case and about 5.2 in the
cylindrical case, so that for Weissenberg numbers somewhat larger than these
values perturbations of the order of a few percent in the wall shear stress
suffice to make the flow unstable. We have suggested elsewhere that this
nonlinear instability could be an important intrinsic route to melt fracture
and that preliminary experiments are both qualitatively and quantitatively in
good agreement with these predictions.Comment: 20 pages, 16 figures. Accepted for publication in J. of Non-Newtonian
Fluid Mechanic
Molecular Motors Interacting with Their Own Tracks
Dynamics of molecular motors that move along linear lattices and interact
with them via reversible destruction of specific lattice bonds is investigated
theoretically by analyzing exactly solvable discrete-state ``burnt-bridge''
models. Molecular motors are viewed as diffusing particles that can
asymmetrically break or rebuild periodically distributed weak links when
passing over them. Our explicit calculations of dynamic properties show that
coupling the transport of the unbiased molecular motor with the bridge-burning
mechanism leads to a directed motion that lowers fluctuations and produces a
dynamic transition in the limit of low concentration of weak links. Interaction
between the backward biased molecular motor and the bridge-burning mechanism
yields a complex dynamic behavior. For the reversible dissociation the backward
motion of the molecular motor is slowed down. There is a change in the
direction of the molecular motor's motion for some range of parameters. The
molecular motor also experiences non-monotonic fluctuations due to the action
of two opposing mechanisms: the reduced activity after the burned sites and
locking of large fluctuations. Large spatial fluctuations are observed when two
mechanisms are comparable. The properties of the molecular motor are different
for the irreversible burning of bridges where the velocity and fluctuations are
suppressed for some concentration range, and the dynamic transition is also
observed. Dynamics of the system is discussed in terms of the effective driving
forces and transitions between different diffusional regimes
New and Old Results in Resultant Theory
Resultants are getting increasingly important in modern theoretical physics:
they appear whenever one deals with non-linear (polynomial) equations, with
non-quadratic forms or with non-Gaussian integrals. Being a subject of more
than three-hundred-year research, resultants are of course rather well studied:
a lot of explicit formulas, beautiful properties and intriguing relationships
are known in this field. We present a brief overview of these results,
including both recent and already classical. Emphasis is made on explicit
formulas for resultants, which could be practically useful in a future physics
research.Comment: 50 pages, 15 figure
Phase behaviour of block copolymer melts with arbitrary architecture
The Leibler theory [L. Leibler, Macromolecules, v.13, 1602 (1980)] for
microphase separation in AB block copolymer melts is generalized for systems
with arbitrary topology of molecules. A diagrammatic technique for calculation
of the monomeric correlation functions is developed. The free energies of
various mesophases are calculated within the second-harmonic approximation.
Model highly-branched tree-like structures are considered as an example and
their phase diagrams are obtained. The topology of molecules is found to
influence the spinodal temperature and asymmetry of the phase diagrams, but not
the types of phases and their order. We suggest that all model AB
block-copolymer systems will exhibit the typical phase behaviour.Comment: Submitted to J. Chem. Phys., see also
http://rugmd4.chem.rug.nl/~morozov/research.htm
Dualities in persistent (co)homology
We consider sequences of absolute and relative homology and cohomology groups
that arise naturally for a filtered cell complex. We establish algebraic
relationships between their persistence modules, and show that they contain
equivalent information. We explain how one can use the existing algorithm for
persistent homology to process any of the four modules, and relate it to a
recently introduced persistent cohomology algorithm. We present experimental
evidence for the practical efficiency of the latter algorithm.Comment: 16 pages, 3 figures, submitted to the Inverse Problems special issue
on Topological Data Analysi
Some remarks on one-dimensional force-free Vlasov-Maxwell equilibria
The conditions for the existence of force-free non-relativistic
translationally invariant one-dimensional (1D) Vlasov-Maxwell (VM) equilibria
are investigated using general properties of the 1D VM equilibrium problem. As
has been shown before, the 1D VM equilibrium equations are equivalent to the
motion of a pseudo-particle in a conservative pseudo-potential, with the
pseudo-potential being proportional to one of the diagonal components of the
plasma pressure tensor. The basic equations are here derived in a different way
to previous work. Based on this theoretical framework, a necessary condition on
the pseudo-potential (plasma pressure) to allow for force-free 1D VM equilibria
is formulated. It is shown that linear force-free 1D VM solutions, which so far
are the only force-free 1D VM solutions known, correspond to the case where the
pseudo-potential is an attractive central potential. A general class of
distribution functions leading to central pseudo-potentials is discussed.Comment: Physics of Plasmas, accepte
Continuum Limits of ``Induced QCD": Lessons of the Gaussian Model at d=1 and Beyond
We analyze the scalar field sector of the Kazakov--Migdal model of induced
QCD. We present a detailed description of the simplest one dimensional
{()} model which supports the hypothesis of wide applicability of the
mean--field approximation for the scalar fields and the existence of critical
behaviour in the model when the scalar action is Gaussian. Despite the
ocurrence of various non--trivial types of critical behaviour in the
model as , only the conventional large- limit is
relevant for its {\it continuum} limit. We also give a mean--field analysis of
the model in {\it any} and show that a saddle point always exists in
the region . In it exhibits critical behaviour as
. However when there is no critical
behaviour unless non--Gaussian terms are added to the scalar field action. We
argue that similar behaviour should occur for any finite thus providing a
simple explanation of a recent result of D. Gross. We show that critical
behaviour at and can be obtained by adding a
term to the scalar potential. This is equivalent to a local
modification of the integration measure in the original Kazakov--Migdal model.
Experience from previous studies of the Generalized Kontsevich Model implies
that, unlike the inclusion of higher powers in the potential, this minor
modification should not substantially alter the behaviour of the Gaussian
model.Comment: 31 page
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