19,098 research outputs found
Channel flows of granular materials and their rheological implications
While the flow of a dry granular material down an inclined channel may seem at first sight to be a relatively simple flow, the experiments which have been conducted up to now suggest sufficient complexity which may be present in all but the very simplest granular material flows; consequently it is important to our general understanding of granular material rheology that these experimental observations be fully understood. This review of the current knowledge of channel flows will focus on the basic mechanics of these flows and the contributions the observations have made to an understanding of the rheology. In order to make progress in this objective, it is necessary to avoid some of the complications which can occur in practice. Thus we shall focus only on those flows in which the interstitial fluid plays very little role in determining the rheology. In his classic paper, Bagnold (1954) was able to show that the regime in which the rheology was dominated by particle/particle or particle/wall interactions and in which the viscous stresses in the interstitial fluid played a negligible role could be defined by a single, Reynolds-number-like parameter. It transpires that the important component in this parameter is a number which we shall call the Bagnold number, Ba, defined by Ba = p₈d²δ/µF where p₈,µF are the particle density and interstitial fluid viscosity, d is the particle diameter and δ is the principal velocity gradient in the flow. In the shear flows explored by Bagnold δ is the shear rate. Bagnold (1954) found that when Ba was greater than about 450 the rheology was dominated by particle/particle and particle/wall collisions. On the other hand, for Ba < 40, the viscosity of the interstitial fluid played the dominant role. More recently Zeininger and Brennen (1985) showed that the same criteria were applicable to the extensional flows in hoppers provided the extensional velocity gradient was used for δ. This review will focus on the simpler flows at large Ba where the interstitial fluid effects are small.
Other important ancillary effects can be caused by electrical charge separation between the particles or between the particles and the boundary walls. Such effects can be essential in some flows such as those in electrostatic copying machines. Most experimenters have observed electrical effects in granular material flows, particularly when metal components of the structure are not properly grounded. The effect of such electrical forces on the rheology of the flow is a largely unexplored area of research. The lack of discussion of these effects in
this review should not be interpreted as a dismissal of their importance.
Apart from electrical and interstitial fluid effects, this review will also neglect the effects caused by non-uniformities in the size and shape of the particles. Thus, for the most part, we focus on flows of particles of spherical shape and uniform size. It is clear that while an understanding of all of these effects will be necessary in the long term, there remain some important issues which need to be resolved for even the simplest granular material flows
The Operator Product Expansion of the Lowest Higher Spin Current at Finite N
For the N=2 Kazama-Suzuki(KS) model on CP^3, the lowest higher spin current
with spins (2, 5/2, 5/2,3) is obtained from the generalized GKO coset
construction. By computing the operator product expansion of this current and
itself, the next higher spin current with spins (3, 7/2, 7/2, 4) is also
derived. This is a realization of the N=2 W_{N+1} algebra with N=3 in the
supersymmetric WZW model. By incorporating the self-coupling constant of lowest
higher spin current which is known for the general (N,k), we present the
complete nonlinear operator product expansion of the lowest higher spin current
with spins (2, 5/2, 5/2, 3) in the N=2 KS model on CP^N space. This should
coincide with the asymptotic symmetry of the higher spin AdS_3 supergravity at
the quantum level. The large (N,k) 't Hooft limit and the corresponding
classical nonlinear algebra are also discussed.Comment: 62 pages; the footnotes added, some redundant appendices removed, the
presentations in the whole paper improved and to appear in JHE
Meta-Stable Brane Configurations by Adding an Orientifold-Plane to Giveon-Kutasov
In hep-th/0703135, they have found the type IIA intersecting brane
configuration where there exist three NS5-branes, D4-branes and anti-D4-branes.
By analyzing the gravitational interaction for the D4-branes in the background
of the NS5-branes, the phase structures in different regions of the parameter
space were studied in the context of classical string theory. In this paper, by
adding the orientifold 4-plane and 6-plane to the above brane configuration, we
describe the intersecting brane configurations of type IIA string theory
corresponding to the meta-stable nonsupersymmetric vacua of these gauge
theories.Comment: 21 pp, 6 figures; reduced bytes of figures, DBI action analysis added
and to appear in JHE
More on N=1 Matrix Model Curve for Arbitrary N
Using both the matrix model prescription and the strong-coupling approach, we
describe the intersections of n=0 and n=1 non-degenerated branches for quartic
(polynomial of adjoint matter) tree-level superpotential in N=1 supersymmetric
SO(N)/USp(2N) gauge theories with massless flavors. We also apply the method to
the degenerated branch. The general matrix model curve on the two cases we
obtain is valid for arbitrary N and extends the previous work from
strong-coupling approach. For SO(N) gauge theory with equal massive flavors, we
also obtain the matrix model curve on the degenerated branch for arbitrary N.
Finally we discuss on the intersections of n=0 and n=1 non-degenerated branches
for equal massive flavors.Comment: 36pp; to appear in JHE
Geometrically Induced Phase Transitions at Large N
Utilizing the large N dual description of a metastable system of branes and
anti-branes wrapping rigid homologous S^2's in a non-compact Calabi-Yau
threefold, we study phase transitions induced by changing the positions of the
S^2's. At leading order in 1/N the effective potential for this system is
computed by the planar limit of an auxiliary matrix model. Beginning at the two
loop correction, the degenerate vacuum energy density of the discrete confining
vacua split, and a potential is generated for the axion. Changing the relative
positions of the S^2's causes discrete jumps in the energetically preferred
confining vacuum and can also obstruct direct brane/anti-brane annihilation
processes. The branes must hop to nearby S^2's before annihilating, thus
significantly increasing the lifetime of the corresponding non-supersymmetric
vacua. We also speculate that misaligned metastable glueball phases may
generate a repulsive inter-brane force which stabilizes the radial mode present
in compact Calabi-Yau threefolds.Comment: 47 pages, 7 figure
Modulation Doping near Mott-Insulator Heterojunctions
We argue that interesting strongly correlated two-dimensional electron
systems can be created by modulation doping near a heterojunction between Mott
insulators. Because the dopant atoms are remote from the carrier system, the
electronic system will be weakly disordered. We argue that the competition
between different ordered states can be engineered by choosing appropriate
values for the dopant density and the setback distance of the doping layer. In
particular larger setback distances favor two-dimensional antiferromagnetism
over ferromagnetism. We estimate some key properties of modulation-doped Mott
insulator heterojunctions by combining insights from Hartree-Fock-Theory and
Dynamical-Mean-Field-Theory descriptions and discuss potentially attractive
material combinations.Comment: 9 pages, 9 figures, submitte
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