<i>Public and Private Government</i>. C. E. Merriam

Schneider, Herbert W.

doi:10.1086/290428

Cited by 3 publications

(3 citation statements)

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“…This proof also can be obtained in Mathematica using Carsten Schneider's 'Sigma' package available from RiscLinz, [33]. Both programs can certify the result, for example in Mathematica using 'CreativeTelescoping'.…”

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confidence: 96%

Hypergeometric Forms for Ising-Class Integrals

Bailey

Borwein

2007

Experimental Mathematics

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We apply experimental-mathematical principles to analyze integralsThese are generalizations of a previous integral C n := C n,1 relevant to the Ising theory of solid-state physics [8]. We find representations of the C n,k in terms of Meijer G-functions and nested-Barnes integrals. Our investigations began by computing 500-digit numerical values of C n,k for all integers n, k where n ∈ [2, 12] and k ∈ [0, 25]. We found that some C n,k enjoy exact evaluations involving Dirichlet L-functions or the Riemann zeta function. In the process of analyzing hypergeometric representations, we found-experimentally and strikingly-that the C n,k almost certainly satisfy certain inter-indicial relations including discrete k-recursions. Using generating functions, differential theory, complex analysis, and Wilf-Zeilberger algorithms we are able to prove some central cases of these relations.

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confidence: 96%

Hypergeometric Forms for Ising-Class Integrals

Bailey

Borwein

2007

Experimental Mathematics

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“…There is a clear difference in time-scales between simulation and experiment (left panel). This is suspected to be due to deviations in the prodcution process of the microfluidic device, which cause changes in the trapping potential [13]. To compare our results of the inter-particle CC functions, we renormalized the time scale to match the experimental relaxation time τ exp , which is given by the position of the minimum of z1 (0)x 2 (t) and which differs from the relaxation time used before in ref.…”

Section: Comparison With Experimentsmentioning

confidence: 99%

Hydrodynamic interactions of colloidal spheres under shear flow

Radu,

Schilling

2012

Preprint

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Particles that are immersed in a fluid exchange momentum via the fluid, hence their Brownian motion is correlated. By means of multiparticle-collision dynamics simulations we study the interactions between two colloidal beads in a sheared fluid suspension. Recently, this topic has been addressed in experiments on colloidal particles trapped by optical tweezers in a microfluidic device [PRL 103, 230602 (2009)] and theoretically by means of a Langevin model [Eur. Phys. J E 33, 313 (2010)]. Although we neglect the rotational degrees of freedom of the colloids, and employ a very simple coupling between the colloids and the flow field, we can reproduce the experimental data and partly explain why it differs from theory.

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“…From this relation we obtain with These crystals were grown by Gulton Industries from the intrinsic electronic equilibrium constant K.(= np), BDH zone-refined Optran Material. 8 and the equilibrium constants (3) and (4) for n 3. THEORY…”

Section: Single Crystals Was Presented (Temperature Region 300-mentioning

confidence: 99%