Phase transition in the collisionless regime for wave-particle interaction

Gibbs statistical mechanics is derived for the Hamiltonian system coupling self-consistently a wave to N particles. This identifies Landau damping with a regime where a second order phase transition occurs. For nonequilibrium initial data with warm particles, a critical initial wave intensity is found: above it, thermodynamics predicts a finite wave amplitude in the limit of infinite N; below it, the equilibrium amplitude vanishes. Simulations support these predictions providing new insight on the long-time nonlinear fate of the wave due to Landau damping in plasmas.Comment: 12 pages (RevTeX), 2 figures (PostScript

The Theory of the Interleaving Distance on Multidimensional Persistence Modules

In 2009, Chazal et al. introduced $\epsilon$-interleavings of persistence modules. $\epsilon$-interleavings induce a pseudometric $d_I$ on (isomorphism classes of) persistence modules, the interleaving distance. The definitions of $\epsilon$-interleavings and $d_I$ generalize readily to multidimensional persistence modules. In this paper, we develop the theory of multidimensional interleavings, with a view towards applications to topological data analysis. We present four main results. First, we show that on 1-D persistence modules, $d_I$ is equal to the bottleneck distance $d_B$. This result, which first appeared in an earlier preprint of this paper, has since appeared in several other places, and is now known as the isometry theorem. Second, we present a characterization of the $\epsilon$-interleaving relation on multidimensional persistence modules. This expresses transparently the sense in which two $\epsilon$-interleaved modules are algebraically similar. Third, using this characterization, we show that when we define our persistence modules over a prime field, $d_I$ satisfies a universality property. This universality result is the central result of the paper. It says that $d_I$ satisfies a stability property generalizing one which $d_B$ is known to satisfy, and that in addition, if $d$ is any other pseudometric on multidimensional persistence modules satisfying the same stability property, then $d\leq d_I$. We also show that a variant of this universality result holds for $d_B$, over arbitrary fields. Finally, we show that $d_I$ restricts to a metric on isomorphism classes of finitely presented multidimensional persistence modules.Comment: Major revision; exposition improved throughout. To appear in Foundations of Computational Mathematics. 36 page

Small denominators, frequency operators, and Lie transforms for nearly integrable quantum spin systems

Based on the previously proposed notions of action operators and of quantum integrability, frequency operators are introduced in a fully quantum-mechanical setting. They are conceptually useful because another formulation can be given to unitary perturbation theory. When worked out for quantum spin systems, this variant is found to be formally equivalent to canonical perturbation theory applied to nearly integrable systems consisting of classical spins. In particular, it becomes possible to locate the quantum-mechanical operator-valued equivalent of the frequency denominators that may cause divergence of the classical perturbation series. The results that are established here link the concept of quantum-mechanical integrability to a technical question, namely, the behavior of specific perturbation series

Field observations of soil temperature and water tension feedback effects on needle ice nights

Numerous laboratory studies have indicated that thermal gradients may produce appreciable soil water movement in the absence of a strong suction field. In addition the soil water flow and thermal properties are physically interrelated. This paper presents field data taken during needle ice events at Vancouver, Canada, and yields an indication of the magnitude of interaction between the thermal and water flow properties. This feedback determines the state of soil frost hazard in a location where damage to plant material is produced by ice frost hazard in a location where damage to plant material is produced by ice needle growth. Further apparently anomalous interruption in the normal parabolic temperature-time pattern during radiation events is interpreted as the product of water flow down a thermal gradient. Zahlreiche Laboratoriumsstudien deuteten darauf hin, daß thermische Gradienten selbst bei Abwesenheit starker Saugkräfte bedeutsame Wasserbewegungen im Boden hervorrufen können. Überdies stehen die Strömung des Bodenwassers und die thermischen Eigenschaften des Bodens damit in physikalischem Zusammenhang. Die vorliegende Arbeit enthält Meßdaten, die während der Bildung von Nadeleis in Vancouver, Kanada, gewonnen wurden und größenordnungsmäßige Beziehungen zwischen Wärme- und Wasserstrom im Boden angeben. Die Rückkopplung zwischen den beiden Strömen bestimmt die Bodenfrostgefahr an Orten, wo Pflanzenschäden durch Eisnadelbildung hervorgerufen werden. Eine offensichtlich abnormale Unterbrechung des normalen Temperatur-Zeit-Verhältnisses während des Ausstrahlungsvorganges wird als Effekt der Wasserströmung entsprechend einem einem thermischen Gradienten interpretiert.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41661/1/703_2005_Article_BF02247747.pd

Long-time discrete particle effects versus kinetic theory in the self-consistent single-wave model

The influence of the finite number N of particles coupled to a monochromatic wave in a collisionless plasma is investigated. For growth as well as damping of the wave, discrete particle numerical simulations show an N-dependent long time behavior resulting from the dynamics of individual particles. This behavior differs from the one due to the numerical errors incurred by Vlasov approaches. Trapping oscillations are crucial to long time dynamics, as the wave oscillations are controlled by the particle distribution inhomogeneities and the pulsating separatrix crossings drive the relaxation towards thermal equilibrium.Comment: 11 pages incl. 13 figs. Phys. Rev. E, in pres

ABA Criminal Justice Section Task Force on College Due Process Rights and Victim Protections: Recommendations for Colleges and Universities in Resolving Allegations of Campus Sexual Misconduct

The Executive Committee of the ABA Criminal Justice Section commissioned the Task Force on College Due Process Rights and Victim Protections in November 2016. Immediately after, extensive efforts were made to find members that represented all interested parties: victims, the accused, universities, other stakeholders, and national experts. The Task Force was fully constituted in the winter of 2017, and it ended up including two voting members who were originally liaisons from the ABA Commission on Domestic and Sexual Violence and the ABA Section of Civil Rights and Social Justice. This elevation was made in recognition of their significant contributions