557 research outputs found
Mixing by polymers: experimental test of decay regime of mixing
By using high molecular weight fluorescent passive tracers with different
diffusion coefficients and by changing the fluid velocity we study dependence
of a characteristic mixing length on the Peclet number, , which controls
the mixing efficiency. The mixing length is found to be related to by a
power law, , and increases faster than
expected for an unbounded chaotic flow. Role of the boundaries in the mixing
length abnormal growth is clarified. The experimental findings are in a good
quantitative agreement with the recent theoretical predictions.Comment: 4 pages,5 figures. accepted for publication in PR
Free-energy transition in a gas of non-interacting nonlinear wave-particles
We investigate the dynamics of a gas of non-interacting particle-like soliton
waves, demonstrating that phase transitions originate from their collective
behavior. This is predicted by solving exactly the nonlinear equations and by
employing methods of the statistical mechanics of chaos. In particular, we show
that a suitable free energy undergoes a metamorphosis as the input excitation
is increased, thereby developing a first order phase transition whose
measurable manifestation is the formation of shock waves. This demonstrates
that even the simplest phase-space dynamics, involving independent (uncoupled)
degrees of freedom, can sustain critical phenomena.Comment: 4 pages, 3 figure
Elastic turbulence in curvilinear flows of polymer solutions
Following our first report (A. Groisman and V. Steinberg, \sl Nature , 53 (2000)) we present an extended account of experimental observations of
elasticity induced turbulence in three different systems: a swirling flow
between two plates, a Couette-Taylor (CT) flow between two cylinders, and a
flow in a curvilinear channel (Dean flow). All three set-ups had high ratio of
width of the region available for flow to radius of curvature of the
streamlines. The experiments were carried out with dilute solutions of high
molecular weight polyacrylamide in concentrated sugar syrups. High polymer
relaxation time and solution viscosity ensured prevalence of non-linear elastic
effects over inertial non-linearity, and development of purely elastic
instabilities at low Reynolds number (Re) in all three flows. Above the elastic
instability threshold, flows in all three systems exhibit features of developed
turbulence. Those include: (i)randomly fluctuating fluid motion excited in a
broad range of spatial and temporal scales; (ii) significant increase in the
rates of momentum and mass transfer (compared to those expected for a steady
flow with a smooth velocity profile). Phenomenology, driving mechanisms, and
parameter dependence of the elastic turbulence are compared with those of the
conventional high Re hydrodynamic turbulence in Newtonian fluids.Comment: 23 pages, 26 figure
Propene Polymerization Promoted by C2-Symmetric Metallocene Catalysts: From Atactic to Isotactic Polypropene in Consequence of an Isotope Effect
We studied the polymerization of propene-2-d
promoted by the prototypical isotactic-specific catalyst system
rac-ethylenebis(4,5,6,7-tetrahydro-1-indenyl)ZrCl2/MAO. In
this communication, we report the results of our investigation,
documenting a large isotope effect on the balance between
polyinsertion and epimerization and, therefore, on the stereospecificity.
The mechanistic implications of such results are
also discusse
Relaxation Dynamics of Photoinduced Changes in the Superfluid Weight of High-Tc Superconductors
In the transient state of d-wave superconductors, we investigate the temporal
variation of photoinduced changes in the superfluid weight. We derive the
formula that relates the nonlinear response function to the nonequilibrium
distribution function. The latter qunatity is obtained by solving the kinetic
equation with the electron-electron and the electron-phonon interaction
included. By numerical calculations, a nonexponential decay is found at low
temperatures in contrast to the usual exponential decay at high temperatures.
The nonexponential decay originates from the nonmonotonous temporal variation
of the nonequilibrium distribution function at low energies. The main physical
process that causes this behavior is not the recombination of quasiparticles as
previous phenomenological studies suggested, but the absorption of phonons.Comment: 18 pages, 12 figures; to be published in J. Phys. Soc. Jpn. Vol. 80,
No.
Surfaces containing a family of plane curves not forming a fibration
We complete the classification of smooth surfaces swept out by a
1-dimensional family of plane curves that do not form a fibration. As a
consequence, we characterize manifolds swept out by a 1-dimensional family of
hypersurfaces that do not form a fibration.Comment: Author's post-print, final version published online in Collect. Mat
Chaotic flow and efficient mixing in a micro-channel with a polymer solution
Microscopic flows are almost universally linear, laminar and stationary
because Reynolds number, , is usually very small. That impedes mixing in
micro-fluidic devices, which sometimes limits their performance. Here we show
that truly chaotic flow can be generated in a smooth micro-channel of a uniform
width at arbitrarily low , if a small amount of flexible polymers is added
to the working liquid. The chaotic flow regime is characterized by randomly
fluctuating three-dimensional velocity field and significant growth of the flow
resistance. Although the size of the polymer molecules extended in the flow may
become comparable with the micro-channel width, the flow behavior is fully
compatible with that in a table-top channel in the regime of elastic
turbulence. The chaotic flow leads to quite efficient mixing, which is almost
diffusion independent. For macromolecules, mixing time in this microscopic flow
can be three to four orders of magnitude shorter than due to molecular
diffusion.Comment: 8 pages,7 figure
q-breathers in Discrete Nonlinear Schroedinger lattices
-breathers are exact time-periodic solutions of extended nonlinear systems
continued from the normal modes of the corresponding linearized system. They
are localized in the space of normal modes. The existence of these solutions in
a weakly anharmonic atomic chain explained essential features of the
Fermi-Pasta-Ulam (FPU) paradox. We study -breathers in one- two- and
three-dimensional discrete nonlinear Sch\"{o}dinger (DNLS) lattices --
theoretical playgrounds for light propagation in nonlinear optical waveguide
networks, and the dynamics of cold atoms in optical lattices. We prove the
existence of these solutions for weak nonlinearity. We find that the
localization of -breathers is controlled by a single parameter which depends
on the norm density, nonlinearity strength and seed wave vector. At a critical
value of that parameter -breathers delocalize via resonances, signaling a
breakdown of the normal mode picture and a transition into strong mode-mode
interaction regime. In particular this breakdown takes place at one of the
edges of the normal mode spectrum, and in a singular way also in the center of
that spectrum. A stability analysis of -breathers supplements these
findings. For three-dimensional lattices, we find -breather vortices, which
violate time reversal symmetry and generate a vortex ring flow of energy in
normal mode space.Comment: 19 pages, 9 figure
Nonlinear management of the angular momentum of soliton clusters
We demonstrate an original approach to acquire nonlinear control over the
angular momentum of a cluster of solitary waves. Our model, derived from a
general description of nonlinear energy propagation in dispersive media, shows
that the cluster angular momentum can be adjusted by acting on the global
energy input into the system. The phenomenon is experimentally verified in
liquid crystals by observing power-dependent rotation of a two-soliton cluster.Comment: 4 pages, 3 figure
Elastic turbulence in von Karman swirling flow between two disks
We discuss the role of elastic stress in the statistical properties of
elastic turbulence, realized by the flow of a polymer solution between two
disks. The dynamics of the elastic stress are analogous to those of a small
scale fast dynamo in magnetohydrodynamics, and to those of the turbulent
advection of a passive scalar in the Batchelor regime. Both systems are
theoretically studied in literature, and this analogy is exploited to explain
the statistical properties, the flow structure, and the scaling observed
experimentally. Several features of elastic turbulence are confirmed
experimentally and presented in this paper: (i) saturation of the rms of the
vorticity and of velocity gradients in the bulk, leading to the saturation of
the elastic stress; (ii) large rms of the velocity gradients in the boundary
layer, linearly growth with Wi; (iii) skewed PDFs of the injected power, with
exponential tails, which indicate intermittency; PDF of the acceleration
exhibit well-pronounced exponential tails too; (iv) a new length scale, i.e the
thickness of the boundary layer, as measured from the profile of the rms of the
velocity gradient, is found to be relevant and much smaller than the vessel
size; (v) the scaling of the structure functions of the vorticity, velocity
gradients, and injected power is found to be the same as that of a passive
scalar advected by an elastic turbulent velocity field.Comment: submitted to Physics of Fluids; 31 pages, 29 figures (resolution
reduced to screen quality
- …