We study the quasilinear evolution of the one-point probability density functions (PDFs) of the smoothed density and velocity fields in a cosmological gravitating system beginning with Gaussian initial fluctuations. Our analytic results are based on the Zel'dovich approximation and laminar flow. A numerical analysis extends the results into the multistreaming regime using the smoothed fields of a CDM N-body simulation. We find that the PDF of velocity, both Lagrangian and Eulerian, remains Gaussian under the laminar Zel'dovich approximation, and it is almost indistinguishable from Gaussian in the simulations. The PDF of mass density deviates from a normal distribution early in the quasilinear regime and it develops a shape remarkably similar to a lognormal distribution with one parameter, the rms density fluctuation σ. Applying these results to currently available data we find that the PDFs of the velocity and density fields, as recovered by the P OT ENT procedure from observed velocities assuming Ω = 1, or as deduced from a redshift survey of IRAS galaxies assuming that galaxies trace mass, are consistent with Gaussian initial fluctuations.

We calculate the influence of resonant neutrino scattering [the Mikheyev-Smirnov-Wolfenstein (MSW) effect] in the Sun and in the Earth on measurable quantities in solar-neutrino-electron scattering experiments. The MSW effect reduces the expected rate for X~-neutrino-electron scattering by a factor that ranges from -0.8 to -0.2 if resonant scattering is the correct explanation for the discrepancy between observation and calculation in the ' '~1 experiment. The Earth can produce a significant diurnal effect for certain values of the neutrino mixing angle and mass difference. I. I N T R O D U C T I O NHow do neutrino oscillations that are amplified by interactions with matter, the Mikheyev-SmirnovWolfenstein (MSW) effect,"' influence the observable quantities in v-e solar-neutrino scattering experiments? The general effect of oscillations is to reduce the cross section for solar-neutrino-electron scattering: electron neutrinos have a larger cross section (by a factor3 that is e 6 to 7 for the most likely experimental conditions) than do neutrinos of other flavors by virtue of the same charged-current diagram as is responsible for the MSW effect itself. Thus the total cross section decreases whenever electron neutrinos are converted to other types of neutrinos. For the experimentally most accessible neutrinos that are produced by the decay of 'B and by the 3~e + p reaction, we calculate the different observable quantities that are implied by a wide range of possible MSW parameters. The results will be useful in planning and interpreting a number of experiments which are presently underway or being d e v e~o~e d .~-'~ Many have contributed recently to the basic understanding of the MSW effect and have determined the range of parameters appropriate to an explanation of the solar-neutrino problem by means of resonantly amplified neutrino oscillations. We adopt here the parameters determined in previous studies and apply the results to neutrino-electron scattering experiments. For the commonly discussed case in which two neutrino flavors are related to the mass eigenstates by a mixing angle 0, solutions compatible with both standard solar models and the 3 7~1 experiment25 requirewhere Am '=rnz2-rn ' and 1,2 are the two mass eigenstates. I n uacuo, the mass eigenstates are related to the flavor eigenstates by the transformation vl=cosOv, -sinOvp, v2=sin0v, +cosOvp. The MSW effect can explain the solar-neutrino problem provided that Am ' lies in the above range. For each value of Am 2, specific values of sin220 are reauired in order to match the observed counting rate in the "CI experiment. For mass differences larger than the range shown in Eq. (la), there is no resonance conversion in the Sun and for smaller mass differences the conversion effect is insufficient to exwlain the difference between calculation and observation (conventional assumptions) in the 3 7~1 experiment.We have purposely refrained from showing explicitly the coupled nature of the constraints in Eqs. ( l a ) and (lb), since the numerical expression of...

In this review we discuss Cosmological N-Body codes with a special emphasis on Particle Mesh codes. We present the mathematical model for each component of N-Body codes. We compare alternative methods for computing each quantity by calculating errors for each of the components. We suggest an optimum set of components that can be combined reduce overall errors in N-Body codes.

We use numerical simulations of critically-closed cold dark matter (CDM) models to study the effects of numerical resolution on observable quantities. We study simulations with up to 256 3 particles using the particle-mesh (PM) method and with up to 144 3 particles using the adaptive particle-particle-particle-mesh (P 3 M) method. Comparisons of galaxy halo distributions are made among the various simulations. We also compare distributions with observations and we explore methods for identifying halos, including a new algorithm that finds all particles within closed contours of the smoothed density field surrounding a peak. The simulated halos show more substructure than predicted by the Press-Schechter theory. We are able to rule out all Ω = 1 CDM models for linear amplitude σ 8 > ∼ 0.5 because the simulations produce too many massive halos compared with the observations. The simulations also produce too many low mass halos. The distribution of halos characterized by their circular velocities for the P 3 M simulations is in reasonable agreement with the observations for 150 km s −1 < ∼ V circ < ∼ 350 km s −1 .

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