21 research outputs found
Voting Power of Teams Working Together
Voting power determines the "power" of individuals who cast votes; their
power is based on their ability to influence the winning-ness of a coalition.
Usually each individual acts alone, casting either all or none of their votes
and is equally likely to do either. This paper extends this standard "random
voting" model to allow probabilistic voting, partial voting, and correlated
team voting. We extend the standard Banzhaf metric to account for these cases;
our generalization reduces to the standard metric under "random voting", This
new paradigm allows us to answer questions such as "In the 2013 US Senate, how
much more unified would the Republicans have to be in order to have the same
power as the Democrats in attaining cloture?
Long Distance Energy Correlations in Random Media
This thesis considers the long distance motion of waves in a random medium. Using the geometrical optics approximation and a stochastic limit theorem, we find evolution equations for rays and for energy correlations, in two and three dimensions.
Our equations are valid on a long distance scale, well after the focusing of rays has become significant. We construct asymptotic expansions of the two point energy correlation function in two and three dimensions.
In two dimensions we numerically solve the partial differential equation that determines the two point energy correlation function. We also perform Monte-Carlo simulations to calculate the same quantity. There is good agreement between the two solutions.
We present the solution for the two point energy correlation function obtained by regular perturbation techniques. This solution agrees with our solution until focusing becomes significant. Then our solution is valid (as shown by the Monte-Carlo simulations), while the regular perturbation solution becomes invalid.
Also presented are the equations that describe energy correlations after a wave has gone through a weakly stochastic plane layered medium.</p
Randomly Crosslinked Macromolecular Systems: Vulcanisation Transition to and Properties of the Amorphous Solid State
As Charles Goodyear discovered in 1839, when he first vulcanised rubber, a
macromolecular liquid is transformed into a solid when a sufficient density of
permanent crosslinks is introduced at random. At this continuous equi- librium
phase transition, the liquid state, in which all macromolecules are
delocalised, is transformed into a solid state, in which a nonzero fraction of
macromolecules have spontaneously become localised. This solid state is a most
unusual one: localisation occurs about mean positions that are distributed
homogeneously and randomly, and to an extent that varies randomly from monomer
to monomer. Thus, the solid state emerging at the vulcanisation transition is
an equilibrium amorphous solid state: it is properly viewed as a solid state
that bears the same relationship to the liquid and crystalline states as the
spin glass state of certain magnetic systems bears to the paramagnetic and
ferromagnetic states, in the sense that, like the spin glass state, it is
diagnosed by a subtle order parameter.
In this review we give a detailed exposition of a theoretical approach to the
physical properties of systems of randomly, permanently crosslinked
macromolecules. Our primary focus is on the equilibrium properties of such
systems, especially in the regime of Goodyear's vulcanisation transition.Comment: Review Article, REVTEX, 58 pages, 3 PostScript figure
A parametric model for the changes in the complex valued conductivity of a lung during tidal breathing
Classical homogenization theory based on the Hashin-Shtrikman coated ellipsoids is used to model the changes in the complex valued conductivity (or admittivity) of a lung during tidal breathing. Here, the lung is modeled as a two-phase composite material where the alveolar air-filling corresponds to the inclusion phase. The theory predicts a linear relationship between the real and the imaginary parts of the change in the complex valued conductivity of a lung during tidal breathing, and where the loss cotangent of the change is approximately the same as of the effective background conductivity and hence easy to estimate. The theory is illustrated with numerical examples, as well as by using reconstructed Electrical Impedance Tomography (EIT) images based on clinical data from an ongoing study within the EU-funded CRADL project. The theory may be potentially useful for improving the imaging algorithms and clinical evaluations in connection with lung EIT for respiratory management and monitoring in neonatal intensive care units
Handbook of differential equations
Handbook of Differential Equations is a handy reference to many popular techniques for solving and approximating differential equations, including exact analytical methods, approximate analytical methods, and numerical methods. Topics covered range from transformations and constant coefficient linear equations to finite and infinite intervals, along with conformal mappings and the perturbation method.Comprised of 180 chapters, this book begins with an introduction to transformations as well as general ideas about differential equations and how they are solved, together with the techniques nee