1,223 research outputs found
Analytical solution of Stokes flow inside an evaporating sessile drop: Spherical and cylindrical cap shapes
Exact analytical solutions are derived for the Stokes flows within
evaporating sessile drops of spherical and cylindrical cap shapes. The results
are valid for arbitrary contact angle. Solutions are obtained for arbitrary
evaporative flux distributions along the free surface as long as the flux is
bounded at the contact line. The field equations, E^4(Psi)=0 and Del^4(Phi)=0,
are solved for the spherical and cylindrical cap cases, respectively. Specific
results and computations are presented for evaporation corresponding to uniform
flux and to purely diffusive gas phase transport into an infinite ambient.
Wetting and non-wetting contact angles are considered with the flow patterns in
each case being illustrated. For the spherical cap with evaporation controlled
by vapor phase diffusion, when the contact angle lies in the range
0<theta_c<pi, the mass flux of vapor becomes singular at the contact line. This
condition required modification when solving for the liquid phase transport.
Droplets in all of the above categories are considered for the following two
cases: the contact lines are either pinned or free to move during evaporation.
The present viscous flow behavior is compared to the inviscid flow behavior
previously reported. It is seen that the streamlines for viscous flow lie
farther from the substrate than the corresponding inviscid ones.Comment: Revised version; in review in Physics of Fluid
Which canonical algebras are derived equivalent to incidence algebras of posets?
We give a full description of all the canonical algebras over an
algebraically closed field that are derived equivalent to incidence algebras of
finite posets. These are the canonical algebras whose number of weights is
either 2 or 3.Comment: 8 pages; slight revision; to appear in Comm. Algebr
No many-scallop theorem: Collective locomotion of reciprocal swimmers
To achieve propulsion at low Reynolds number, a swimmer must deform in a way
that is not invariant under time-reversal symmetry; this result is known as the
scallop theorem. We show here that there is no many-scallop theorem. We
demonstrate that two active particles undergoing reciprocal deformations can
swim collectively; moreover, polar particles also experience effective
long-range interactions. These results are derived for a minimal dimers model,
and generalized to more complex geometries on the basis of symmetry and scaling
arguments. We explain how such cooperative locomotion can be realized
experimentally by shaking a collection of soft particles with a homogeneous
external field
Galois coverings of weakly shod algebras
We investigate the Galois coverings of weakly shod algebras. For a weakly
shod algebra not quasi-tilted of canonical type, we establish a correspondence
between its Galois coverings and the Galois coverings of its connecting
component. As a consequence, we show that a weakly shod algebra is simply
connected if and only if its first Hochschild cohomology group vanishes.Comment: Some references were added. The proof of Lemma 6.5 was modifie
Tilted algebras and short chains of modules
We provide an affirmative answer for the question raised almost twenty years
ago concerning the characterization of tilted artin algebras by the existence
of a sincere finitely generated module which is not the middle of a short
chain
Symmetric three-particle motion in Stokes flow: equilibrium for heavy spheres in contrast to "end-of-world" for point forces
A stationary stable solution of the Stokes equations for three identical
heavy solid spheres falling in a vertical plane is found. It has no analog in
the point-particle approximation. Three spheres aligned horizontally at equal
distances evolve towards the equilibrium relative configuration while the point
particles collapse onto a single point in a finite time.Comment: 4 pages, 7 figure
Non-equilibrium hydrodynamics of a rotating filament
The nonlinear dynamics of an elastic filament that is forced to rotate at its
base is studied by hydrodynamic simulation techniques; coupling between
stretch, bend, twist elasticity and thermal fluctuations is included. The
twirling-overwhirling transition is located and found to be strongly
discontinuous. For finite bend and twist persistence length, thermal
fluctuations lower the threshold rotational frequency, for infinite persistence
length the threshold agrees with previous analytical predictions
Microscale swimming: The molecular dynamics approach
The self-propelled motion of microscopic bodies immersed in a fluid medium is
studied using molecular dynamics simulation. The advantage of the atomistic
approach is that the detailed level of description allows complete freedom in
specifying the swimmer design and its coupling with the surrounding fluid. A
series of two-dimensional swimming bodies employing a variety of propulsion
mechanisms -- motivated by biological and microrobotic designs -- is
investigated, including the use of moving limbs, changing body shapes and fluid
jets. The swimming efficiency and the nature of the induced, time-dependent
flow fields are found to differ widely among body designs and propulsion
mechanisms.Comment: 5 pages, 3 figures (minor changes to text
Hydrodynamics of flagellated microswimmers near free-slip interfaces
The hydrodynamics of a flagellated microorganism is investigated when
swimming close to a planar free-slip surface by means of numerical solu- tions
of the Stokes equations obtained via a Boundary Element Method. Depending on
the initial condition, the swimmer can either escape from the free-slip surface
or collide with the boundary. Interestingly, the mi- croorganism does not
exhibit a stable orbit. Independently of escape or attraction to the interface,
close to a free-slip surface, the swimmer fol- lows a counter-clockwise
trajectory, in agreement with experimental find- ings, [15]. The hydrodynamics
is indeed modified by the free-surface. In fact, when the same swimmer moves
close to a no-slip wall, a set of initial conditions exists which result in
stable orbits. Moreover when moving close to a free-slip or a no-slip boundary
the swimmer assumes a different orientation with respect to its trajectory.
Taken together, these results contribute to shed light on the hydrodynamical
behaviour of microorgan- isms close to liquid-air interfaces which are relevant
for the formation of interfacial biofilms of aerobic bacteria
On Berenstein-Douglas-Seiberg Duality
I review the proposal of Berenstein-Douglas for a completely general
definition of Seiberg duality. To give evidence for their conjecture I present
the first example of a physical dual pair and explicitly check that it
satisfies the requirements. Then I explicitly show that a pair of toric dual
quivers is also dual according to their proposal. All these computations go
beyond tilting modules, and really work in the derived category. I introduce
all necessary mathematics where needed.Comment: 22 pages, LaTe
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