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Viscoelasticity and shear flow of concentrated, non-crystallizing colloidal suspensions: Comparison with Mode-Coupling Theory
We present a comprehensive rheological study of a suspension of
thermosensitive particles dispersed in water. The volume fraction of these
particles can be adjusted by the temperature of the system in a continuous
fashion. Due to the finite polydispersity of the particles (standard deviation:
17%), crystallization is suppressed and no fluid-crystal transition intervenes.
Hence, the moduli and in the linear viscoelastic regime as well as
the flow curves (shear stress as the function of the
shear rate ) could be measured in the fluid region up to the
vicinity of the glass transition. Moreover, flow curves could be obtained over
a range of shear rates of 8 orders of magnitude while and could be
measured spanning over 9 orders of magnitude. Special emphasis has been laid on
precise measurements down to the smallest shear rates/frequencies. It is
demonstrated that mode-coupling theory generalized in the integration through
transients framework provides a full description of the flow curves as well as
the viscoelastic behavior of concentrated suspensions with a single set of
well-defined parameters
Two-Qubit Separability Probabilities and Beta Functions
Due to recent important work of Zyczkowski and Sommers (quant-ph/0302197 and
quant-ph/0304041), exact formulas are available (both in terms of the
Hilbert-Schmidt and Bures metrics) for the (n^2-1)-dimensional and
(n(n-1)/2-1)-dimensional volumes of the complex and real n x n density
matrices. However, no comparable formulas are available for the volumes (and,
hence, probabilities) of various separable subsets of them. We seek to clarify
this situation for the Hilbert-Schmidt metric for the simplest possible case of
n=4, that is, the two-qubit systems. Making use of the density matrix (rho)
parameterization of Bloore (J. Phys. A 9, 2059 [1976]), we are able to reduce
each of the real and complex volume problems to the calculation of a
one-dimensional integral, the single relevant variable being a certain ratio of
diagonal entries, nu = (rho_{11} rho_{44})/{rho_{22} rho_{33})$. The associated
integrand in each case is the product of a known (highly oscillatory near nu=1)
jacobian and a certain unknown univariate function, which our extensive
numerical (quasi-Monte Carlo) computations indicate is very closely
proportional to an (incomplete) beta function B_{nu}(a,b), with a=1/2,
b=sqrt{3}in the real case, and a=2 sqrt{6}/5, b =3/sqrt{2} in the complex case.
Assuming the full applicability of these specific incomplete beta functions, we
undertake separable volume calculations.Comment: 17 pages, 4 figures, paper is substantially rewritten and
reorganized, with the quasi-Monte Carlo integration sample size being greatly
increase
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