Scale Free Cluster Distributions from Conserving Merging-Fragmentation Processes

We propose a dynamical scheme for the combined processes of fragmentation and merging as a model system for cluster dynamics in nature and society displaying scale invariant properties. The clusters merge and fragment with rates proportional to their sizes, conserving the total mass. The total number of clusters grows continuously but the full time-dependent distribution can be rescaled over at least 15 decades onto a universal curve which we derive analytically. This curve includes a scale free solution with a scaling exponent of -3/2 for the cluster sizes.Comment: 4 pages, 3 figure

Measurement Of Positron Annihilation Line Shapes With A Ge(Li) Detector

We observed that the annihilation radiation photopeak in a Ge(Li) detector is considerably broader than that of a γ ray of the same energy. It seems reasonable to assume that the increased width is the result of the Doppler broadening of the annihilation photopeak, i.e., the longitudinal Doppler shift of the radiations is measured, while the transverse shift is measured in the usual angular-correlation experiments. By using a computer stripping program to remove the distortion produced by the finite energy resolution of our detector, we obtain momentum distributions in agreement with those which have been published. Only one detector is necessary for these measurements, and all momentum channels are detected at once. However, the detector energy resolution severely limits the momentum resolution. Arguments are presented which indicate that no very large improvement in Ge(Li) detector resolution can be expected. © 1968 The American Physical Society

Four Measures of the Intracluster Medium Temperature and Their Relation to a Cluster's Dynamical State

We employ an ensemble of hydrodynamic cluster simulations to create spatially and spectrally resolved images of quality comparable to Chandra's expected performance. Emission from simulation mass elements is represented using the XSPEC mekal program assuming 0.3 solar metallicity, and the resulting spectra are fit with a single-temperature model. Despite significant departures from isothermality in the cluster gas, single-temperature models produce acceptable fits to 20,000 source photon spectra. The spectral fit temperature T_s is generally lower than the mass weighted average temperature T_m due to the influence of soft line emission from cooler gas being accreted as part of the hierarchical clustering process. In a Chandra-like bandpass of 0.5 to 9.5 keV we find a nearly uniform fractional bias of (T_m-T_s)/T_s = 20% with occasional large deviations in smaller clusters. In the more traditional 2.0 to 9.5 keV bandpass, the fractional deviation is scale-dependent and on average follows the relation (T_m-T_s)/T_s = 0.2 log(T_m). This bias results in a spectral mass-temperature relationship with slope about 1.6, intermediate between the virial relation M ~ T_m^{3/2} and the observed relation M_{ICM} ~ T^2. Imaging each cluster in the ensemble at 16 epochs in its evolutionary history, we catalogue merger events with mass ratios exceeding 10% in order to investigate the relationship between spectral temperature and proximity to a major merger event. Clusters that are very cool relative to the mean mass-temperature relationship lie preferentially close to a merger, suggesting a viable observational method to cull a subset of dynamically young clusters from the general population.Comment: 34 pages, including 2 tables and 14 figures (one in color). Compiled using LaTeX 2.09 with graphics package and aaspp4 style. The simulated spectral data files used in this paper are available for public consumption at http://redshift.stanford.edu/bfm

Persistent punishment : users views of short prison sentences

Semi-structured interviews were conducted of 22 prisoners to gather information about the characteristic features of short prison sentences. Themes raised in comments included: the frequency and quality of sentences, addiction, family, and penal legitimacy. Most of the participants had extensive experience of prison, and the effects of this played out across sentences and years, accumulating and amplifying impacts. And, despite expressions of guilt and remorse, most participants saw their sentence as unjust, and mainly a reaction to offending history. We conclude by suggesting the need for research to shift focus from evaluating individual penal interventions towards more holistic and narrative accounts that cut across sentences

The thermodynamics and roughening of solid-solid interfaces

The dynamics of sharp interfaces separating two non-hydrostatically stressed solids is analyzed using the idea that the rate of mass transport across the interface is proportional to the thermodynamic potential difference across the interface. The solids are allowed to exchange mass by transforming one solid into the other, thermodynamic relations for the transformation of a mass element are derived and a linear stability analysis of the interface is carried out. The stability is shown to depend on the order of the phase transition occurring at the interface. Numerical simulations are performed in the non-linear regime to investigate the evolution and roughening of the interface. It is shown that even small contrasts in the referential densities of the solids may lead to the formation of finger like structures aligned with the principal direction of the far field stress.Comment: (24 pages, 8 figures; V2: added figures, text revisions

A General Framework for Sound and Complete Floyd-Hoare Logics

This paper presents an abstraction of Hoare logic to traced symmetric monoidal categories, a very general framework for the theory of systems. Our abstraction is based on a traced monoidal functor from an arbitrary traced monoidal category into the category of pre-orders and monotone relations. We give several examples of how our theory generalises usual Hoare logics (partial correctness of while programs, partial correctness of pointer programs), and provide some case studies on how it can be used to develop new Hoare logics (run-time analysis of while programs and stream circuits).Comment: 27 page

Weak-Lensing Halo Numbers and Dark-Matter Profiles

Integral measures of weak gravitational lensing by dark-matter haloes, like the aperture mass, are sensitive to different physical halo properties dependent on the halo mass density profile. For isothermal profiles, the relation between aperture mass and virial mass is steeper than for haloes with the universal NFW profile. Consequently, the halo mass range probed by the aperture mass is much wider for NFW than for isothermal haloes. We use recent modifications to the Press-Schechter mass function in CDM models normalised to the local abundance of rich clusters, to predict the properties of the halo sample expected to be accessible with the aperture mass technique. While ~10 haloes should be detected per square degree if the haloes have NFW profiles, their number density is lower by approximately an order of magnitude if they have isothermal profiles. These results depend only very mildly on the cosmological background model. We conclude that counts of haloes with a significant weak-lensing signal are a powerful discriminator between different dark-matter profiles.Comment: submitted to A&

Nonsymbiotic hemoglobins in rice are synthesized during germination and in differentiating cell types

Nonsymbiotic hemoglobins (ns-Hbs) previously have been found in monocots and dicots; however, very little is known about the tissue and cell type localization as well as the physiological function(s) of these oxygen-binding proteins. We report the immunodetection and immunolocalization of ns-Hbs in rice (Oryza sativa L.) by Western blotting and in situ confocal laser scanning techniques. Ns-Hbs were detected in soluble extracts of different tissues from the developing rice seedling by immunoblotting. Levels of ns-Hbs increased in the germinating seed for the first six days following imbibition and remained relatively constant thereafter. In contrast, ns-Hb levels decreased during leaf maturation. Roots and mesocotyls contained detectable, but low levels of ns-Hbs. Split-seed experiments revealed that ns-Hbs are synthesized de novo during seed germination and are expressed in the absence of any signal originating from the embryo. Immunolocalization of ns-Hbs by con- focal microscopy indicated the presence of ns-Hbs primarily in differentiated and differentiating cell types of the developing seedling, such as the aleurone, scutellum, root cap cells, sclerenchyma, and tracheary elements. To our knowledge, this is the first report of the specific cellular localization of these proteins during seedling development