The status of music education in the public junior high schools of Massachusetts as of the year 1945-1955

Thesis (Ed.M.)--Boston Universit

The Static Dielectric Constant of a Colloidal Suspension

We derive an expression for the static dielectric constant of the colloidal susp ensions based on the electrokinetic equations. The analysis assumes that the ions have the same diffusivity, and that the double layer is much thinner than the radius of curvature of the particles. It is shown that the dielectric increment of the double layer polarization mechanism is originated from the free energy stored in the salt concentration inhomogeniety. We also show that the dominant polarization charges in the theory are at the electrodes, rather than close to the particles.Comment: 15 pages, 1 figur

Mass of Clusters in Simulations

We show that dark matter haloes, in n--body simulations, have a boundary layer (BL) with precise features. In particular, it encloses all dynamically stable mass while, outside it, dynamical stability is lost soon. Particles can pass through such BL, which however acts as a confinement barrier for dynamical properties. BL is set by evaluating kinetic and potential energies (T(r) and W(r)) and calculating R=-2T/W. Then, on BL, R has a minimum which closely approaches a maximum of w= -dlog W/dlog r. Such $Rw$ ``requirement'' is consistent with virial equilibrium, but implies further regularities. We test the presence of a BL around haloes in spatially flat CDM simulations, with or without cosmological constant. We find that the mass M_c, enclosed within the radius r_c, where the $Rw$ requirement is fulfilled, closely approaches the mass M_{dyn}, evaluated from the velocities of all particles within r_c, according to the virial theorem. Using r_c we can then determine an individual density contrast Delta_c for each virialized halo, which can be compared with the "virial" density contrast $\Delta_v ~178 \Omega_m^{0.45}$ (Omega_m: matter density parameter) obtained assuming a spherically symmetric and unperturbed fluctuation growth. The spread in Delta_c is wide, and cannot be neglected when global physical quantities related to the clusters are calculated, while the average Delta_c is ~25 % smaller than the corresponding Delta_v; moreover if $M_{dyn}$ is defined from the radius linked to Delta_v, we have a much worse fit with particle mass then starting from {\it Rw} requirement.Comment: 4 pages, 5 figures, contribution to the XXXVIIth Rencontres de Moriond, The Cosmological Model, Les Arc March 16-23 2002, to appear in the proceeding