8,814 research outputs found
Subdynamic asymptotic behavior of microfluidic valves
Decreasing the Reynolds number of microfluidic
no-moving-part flow control valves considerably below the usual operating range leads to a distinct “subdynamic” regime of viscosity- dominated flow, usually entered through a clearly defined transition. In this regime, the dynamic effects on which the operation of large-scale no-moving-part fluidic valves is based, cease to be useful, but fluid may be driven through the valve (and any
connected load) by an applied pressure difference, maintained by an external pressure regulator. Reynolds number ceases to characterize the valve operation, but the driving pressure effect is usefully characterized by a newly introduced dimensionless number and it is this parameter which determines the valve behavior. This summary paper presents information about the subdynamic regime using data (otherwise difficult to access) obtained for several recently developed flow control valves. The purely subdynamic regime is an extreme. Most present-day microfluidic valves are operated at higher Re, but the paper shows that the laws governing subdynamic flows provide relations useful as an asymptotic reference
Reciprocal relativity of noninertial frames: quantum mechanics
Noninertial transformations on time-position-momentum-energy space {t,q,p,e}
with invariant Born-Green metric ds^2=-dt^2+dq^2/c^2+(1/b^2)(dp^2-de^2/c^2) and
the symplectic metric -de/\dt+dp/\dq are studied. This U(1,3) group of
transformations contains the Lorentz group as the inertial special case. In the
limit of small forces and velocities, it reduces to the expected Hamilton
transformations leaving invariant the symplectic metric and the nonrelativistic
line element ds^2=dt^2. The U(1,3) transformations bound relative velocities by
c and relative forces by b. Spacetime is no longer an invariant subspace but is
relative to noninertial observer frames. Born was lead to the metric by a
concept of reciprocity between position and momentum degrees of freedom and for
this reason we call this reciprocal relativity.
For large b, such effects will almost certainly only manifest in a quantum
regime. Wigner showed that special relativistic quantum mechanics follows from
the projective representations of the inhomogeneous Lorentz group. Projective
representations of a Lie group are equivalent to the unitary reprentations of
its central extension. The same method of projective representations of the
inhomogeneous U(1,3) group is used to define the quantum theory in the
noninertial case. The central extension of the inhomogeneous U(1,3) group is
the cover of the quaplectic group Q(1,3)=U(1,3)*s H(4). H(4) is the
Weyl-Heisenberg group. A set of second order wave equations results from the
representations of the Casimir operators
The Riemann Surface of a Static Dispersion Model and Regge Trajectories
The S-matrix in the static limit of a dispersion relation is a matrix of a
finite order N of meromorphic functions of energy in the plane with
cuts . In the elastic case it reduces to N functions
connected by the crossing symmetry matrix A. The scattering of
a neutral pseodoscalar meson with an arbitrary angular momentum l at a source
with spin 1/2 is considered (N=2). The Regge trajectories of this model are
explicitly found.Comment: 5 pages, LaTe
Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift
This paper establishes the global asymptotic equivalence between a Poisson
process with variable intensity and white noise with drift under sharp
smoothness conditions on the unknown function. This equivalence is also
extended to density estimation models by Poissonization. The asymptotic
equivalences are established by constructing explicit equivalence mappings. The
impact of such asymptotic equivalence results is that an investigation in one
of these nonparametric models automatically yields asymptotically analogous
results in the other models.Comment: Published at http://dx.doi.org/10.1214/009053604000000012 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Toward a general theory of linking invariants
Let N_1, N_2, M be smooth manifolds with dim N_1 + dim N_2 +1 = dim M$ and
let phi_i, for i=1,2, be smooth mappings of N_i to M with Im phi_1 and Im phi_2
disjoint. The classical linking number lk(phi_1,phi_2) is defined only when
phi_1*[N_1] = phi_2*[N_2] = 0 in H_*(M).
The affine linking invariant alk is a generalization of lk to the case where
phi_1*[N_1] or phi_2*[N_2] are not zero-homologous. In arXiv:math.GT/0207219 we
constructed the first examples of affine linking invariants of
nonzero-homologous spheres in the spherical tangent bundle of a manifold, and
showed that alk is intimately related to the causality relation of wave fronts
on manifolds.
In this paper we develop the general theory. The invariant alk appears to be
a universal Vassiliev-Goussarov invariant of order < 2. In the case where
phi_1*[N_1] and phi_2*[N_2] are 0 in homology it is a splitting of the
classical linking number into a collection of independent invariants.
To construct alk we introduce a new pairing mu on the bordism groups of
spaces of mappings of N_1 and N_2 into M, not necessarily under the restriction
dim N_1 + dim N_2 +1 = dim M. For the zero-dimensional bordism groups, mu can
be related to the Hatcher-Quinn invariant. In the case N_1=N_2=S^1, it is
related to the Chas-Sullivan string homology super Lie bracket, and to the
Goldman Lie bracket of free loops on surfaces.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol9/paper42.abs.htm
Mapped Null Hypersurfaces and Legendrian Maps
For an -dimensional space-time define a mapped null
hypersurface to be a smooth map (that is not necessarily
an immersion) such that there exists a smooth field of null lines along
that are both tangent and -orthogonal to We study relations between
mapped null hypersurfaces and Legendrian maps to the spherical cotangent bundle
of an immersed spacelike hypersurface We show
that a Legendrian map \wt \lambda: L^{m-1}\to (ST^*M)^{2m-1} defines a mapped
null hypersurface in On the other hand, the intersection of a mapped null
hypersurface with an immersed spacelike hypersurface
defines a Legendrian map to the spherical cotangent
bundle This map is a Legendrian immersion if came from a
Legendrian immersion to for some immersed spacelike hypersurface
Comment: 13 pages, 1 figur
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