Scaling of the turbulence transition threshold in a pipe

We report the results of an experimental investigation of the transition to turbulence in a pipe over approximately an order of magnitude range in $Re$. A novel scaling law is uncovered using a systematic experimental procedure which permits contact to be made with modern theoretical thinking. The principal result we uncover is a scaling law which indicates that the amplitude of perturbation required to cause transition scales as $O(Re^{-1})$.Comment: 4 pages, RevTex (submitted to Phys. Rev. Lett.

Beyond spontaneously broken symmetry in Bose-Einstein condensates

Spontaneous symmetry breaking (SSB) for Bose-Einstein condensates cannot treat phase off-diagonal effects, and thus not explain Bell inequality violations. We describe another situation that is beyond a SSB treatment: an experiment where particles from two (possibly macroscopic) condensate sources are used for conjugate measurements of the relative phase and populations. Off-diagonal phase effects are characterized by a "quantum angle" and observed via "population oscillations", signaling quantum interference of macroscopically distinct states (QIMDS).Comment: 10 pages 4 figure

Ursell Operators in Statistical Physics III: thermodynamic properties of degenerate gases

We study in more detail the properties of the generalized Beth Uhlenbeck formula obtained in a preceding article. This formula leads to a simple integral expression of the grand potential of the system, where the interaction potential appears only through the matrix elements of the second order Ursell operator $U_{2}$. Our results remain valid for significant degree of degeneracy of the gas, but not when Bose Einstein (or BCS) condensation is reached, or even too close from this transition point. We apply them to the study of the thermodynamic properties of degenerate quantum gases: equation of state, magnetic susceptibility, effects of exchange between bound states and free particles, etc. We compare our predictions to those obtained within other approaches, especially the ``pseudo potential'' approximation, where the real potential is replaced by a potential with zero range (Dirac delta function). This comparison is conveniently made in terms of a temperature dependent quantity, the ``Ursell length'', which we define in the text. This length plays a role which is analogous to the scattering length for pseudopotentials, but it is temperature dependent and may include more physical effects than just binary collision effects; for instance at very low temperatures it may change sign or increase almost exponentially, an effect which is reminiscent of a precursor of the BCS pairing transition. As an illustration, numerical results for quantum hard spheres are given.Comment: 26 pages, 4 figures, LaTeX (amssymb), slight changes to first versio

Absence of Fragmentation in Two-Dimensional Bose-Einstein Condensation

We investigate the possibility that the BEC-like phenomena recently detected on two-dimensional finite trapped systems consist of fragmented condensates. We derive and diagonalize the one-body density matrix of a two-dimensional isotropically trapped Bose gas at finite temperature. For the ideal gas, the procedure reproduces the exact harmonic-oscillator eigenfunctions and the Bose distribution. We use a new collocation-minimization method to study the interacting gas in the Hartree-Fock approximation and obtain a ground-state wavefunction and condensate fraction consistent with those obtained by other methods. The populations of the next few eigenstates increase at the expense of the ground state but continue to be negligible; this supports the conclusion that two-dimensional BEC is into a single state.Comment: 6 pages, 1 figur

Some fundamental fracture mechanisms applicable to advanced filament reinforced composites

Stress analysis and fracture mechanisms of advanced fiber reinforced composite

Investigation of the reinforcement of ductule metals with strong, high modulus discontinuous, brittle fibers Quarterly report, 1 May - 1 Aug. 1968

Factors affecting tensile strength of ductile metals reinforced with short, brittle fiber

Eighteen Is Not a Magic Number: Why the Eighth Amendment Requires Protection for Youth Aged Eighteen to Twenty-Five

The Eighth Amendment protects a criminal defendant’s right to be free from cruel and unusual punishment. This Note argues that any punishment of eighteen- to twenty-five-year-olds is cruel and unusual without considering their youthfulness at every stage of the criminal process, and that it is unconstitutional under the Eighth Amendment for these youths to be automatically treated as fully-developed adults. This Note will explore in depth how juveniles differ from adults, both socially and scientifically, and how the criminal justice system fails every youth aged eighteen- to twenty-five by subjecting them to criminal, rather than juvenile, court without considering their youthfulness and diminished capacity. This Note proposes three reforms that, implemented together, aim to remedy this Eighth Amendment violation. First, the Supreme Court should apply the seminal cases of Miller, Roper, and Graham to eighteen- to twenty-five-year-olds. Second, all states should extend the age of juvenile jurisdiction to twenty-five, processing offenders twenty-five and younger through the juvenile system accordingly. Finally, every actor in the system—including courts, lawyers, and legislatures—should label eighteen- to twenty-five-year-olds as “youth” and consider their age at every stage of the criminal system