Live-timer method of automatic dead-time correction for precision counting

Automatic correction for dead time losses in nuclear counting experiments is implemented by a simple live timer arrangement in which each counting interval is extended for compensation for the dead time during that interval. this method eliminates repetitious manual calculations, source of error, and dependence upon paralysis shifts

Observed Faraday Effects in Damped Lyman-Alpha Absorbers and Lyman Limit Systems: The Magnetised Environment of Galactic Building Blocks at Redshift=2

Protogalactic environments are typically identified using quasar absorption lines, and these galactic building blocks can manifest as Damped Lyman-Alpha Absorbers (DLAs) and Lyman Limit Systems (LLSs). We use radio observations of Faraday effects to test whether DLAs and LLSs host a magnetised medium, by combining DLA and LLS detections throughout the literature with 1.4 GHz polarization data from the NRAO VLA Sky Survey (NVSS). We obtain a control, a DLA, and a LLS sample consisting of 114, 19, and 27 lines-of-sight respectively - all of which are polarized at $\ge8\sigma$ to ensure Rician bias is negligible. Using a Bayesian framework, we are unable to detect either coherent or random magnetic fields in DLAs: the regular coherent magnetic fields within the DLAs must be $\le2.8$ $\mu$G, and the lack of depolarization is consistent with the weakly magnetised gas in DLAs being non-turbulent and quiescent. However, we find mild suggestive evidence that LLSs have coherent magnetic fields: after controlling for the redshift-distribution of our data, we find a 71.5% probability that LLSs have a higher RM than a control sample. We also find strong evidence that LLSs host random magnetic fields, with a 95.5% probability that LLS lines-of-sight have lower polarized fractions than a control sample. The regular coherent magnetic fields within the LLSs must be $\le2.4$ $\mu$G, and the magnetised gas must be highly turbulent with a typical scale on the order of $\approx5$-20 pc, which is similar to that of the Milky Way. This is consistent with the standard dynamo pedagogy, whereby magnetic fields in protogalaxies increase in coherence and strength as a function of cosmic time. Our results are consistent with a hierarchical galaxy formation scenario, with the DLAs, LLSs, and strong magnesium II (MgII) systems exploring three different stages of magnetic field evolution in galaxies.Comment: Submitted to Ap

The effective potential, critical point scaling and the renormalization group

The desirability of evaluating the effective potential in field theories near a phase transition has been recognized in a number of different areas. We show that recent Monte Carlo simulations for the probability distribution for the order parameter in an equilibrium Ising system, when combined with low-order renormalization group results for an ordinary $\phi^4$ system, can be used to extract the effective potential. All scaling features are included in the process.Comment: REVTEX file, 22 pages, three figures, submitted to Phys. Rev.

Reaction-Diffusion Process Driven by a Localized Source: First Passage Properties

We study a reaction-diffusion process that involves two species of atoms, immobile and diffusing. We assume that initially only immobile atoms, uniformly distributed throughout the entire space, are present. Diffusing atoms are injected at the origin by a source which is turned on at time t=0. When a diffusing atom collides with an immobile atom, the two atoms form an immobile stable molecule. The region occupied by molecules is asymptotically spherical with radius growing as t^{1/d} in d>=2 dimensions. We investigate the survival probability that a diffusing atom has not become a part of a molecule during the time interval t after its injection and the probability density of such a particle. We show that asymptotically the survival probability (i) saturates in one dimension, (ii) vanishes algebraically with time in two dimensions (with exponent being a function of the dimensionless flux and determined as a zero of a confluent hypergeometric function), and (iii) exhibits a stretched exponential decay in three dimensions.Comment: 7 pages; version 2: section IV is re-written, references added, 8 pages (final version

High resolution Ge/Li/ spectrometer reduces rate-dependent distortions at high counting rates

Modified spectrometer system with a low-noise preamplifier reduces rate-dependent distortions at high counting rates, 25,000 counts per second. Pole-zero cancellation minimizes pulse undershoots due to multiple time constants, baseline restoration improves resolution and prevents spectral shifts

Polymer desorption under pulling: a novel dichotomic phase transition

We show that the structural properties and phase behavior of a self-avoiding polymer chain on adhesive substrate, subject to pulling at the chain end, can be obtained by means of a Grand Canonical Ensemble (GCE) approach. We derive analytical expressions for the mean length of the basic structural units of adsorbed polymer, such as loops and tails, in terms of the adhesive potential and detachment force, and determine values of the universal exponents which govern their probability distributions. Most notably, the hitherto controversial value of the critical adsorption exponent $\phi$ is found to depend essentially on the interaction between different loops. The chain detachment transition turns out to be of the first order, albeit dichotomic, i.e., no coexistence of different phase states exists. These novel theoretical predictions and the suggested phase diagram of the adsorption-desorption transformation under external pulling force are verified by means of extensive Monte Carlo simulations.Comment: 10 pages, 4 figure

Casimir versus Helmholtz forces: Exact results

Recently, attention has turned to the issue of the ensemble dependence of fluctuation induced forces. As a noteworthy example, in $O(n)$ systems the statistical mechanics underlying such forces can be shown to differ in the constant $\vec{M}$ magnetic canonical ensemble (CE) from those in the widely-studied constant $\vec{h}$ grand canonical ensemble (GCE). Here, the counterpart of the Casimir force in the GCE is the \textit{Helmholtz} force in the CE. Given the difference between the two ensembles for finite systems, it is reasonable to anticipate that these forces will have, in general, different behavior for the same geometry and boundary conditions. Here we present some exact results for both the Casimir and the Helmholtz force in the case of the one-dimensional Ising model subject to periodic and antiperiodic boundary conditions and compare their behavior. We note that the Ising model has recently being solved in Phys.Rev. E {\bf 106} L042103(2022), using a combinatorial approach, for the case of fixed value $M$ of its order parameter. Here we derive exact result for the partition function of the one-dimensional Ising model of $N$ spins and fixed value $M$ using the transfer matrix method (TMM); earlier results obtained via the TMM were limited to $M=0$ and $N$ even. As a byproduct, we derive several specific integral representations of the hypergeometric function of Gauss. Using those results, we rigorously derive that the free energies of the CE and grand GCE are related to each other via Legendre transformation in the thermodynamic limit, and establish the leading finite-size corrections for the canonical case, which turn out to be much more pronounced than the corresponding ones in the case of the GCE.Comment: 33 pages, 7 figures. The derivations in Appendix C are simplifie

Theory of monolayers with boundaries: Exact results and Perturbative analysis

Domains and bubbles in tilted phases of Langmuir monolayers contain a class of textures knows as boojums. The boundaries of such domains and bubbles may display either cusp-like features or indentations. We derive analytic expressions for the textures within domains and surrounding bubbles, and for the shapes of the boundaries of these regions. The derivation is perturbative in the deviation of the bounding curve from a circle. This method is not expected to be accurate when the boundary suffers large distortions, but it does provide important clues with regard to the influence of various energetic terms on the order-parameter texture and the shape of the domain or bubble bounding curve. We also look into the effects of thermal fluctuations, which include a sample-size-dependent effective line tension.Comment: replaced with published version, 21 pages, 16 figures include

Cassiopeia A: dust factory revealed via submillimetre polarimetry

If Type-II supernovae - the evolutionary end points of short-lived, massive stars - produce a significant quantity of dust (>0.1 M_sun) then they can explain the rest-frame far-infrared emission seen in galaxies and quasars in the first Gyr of the Universe. Submillimetre observations of the Galactic supernova remnant, Cas A, provided the first observational evidence for the formation of significant quantities of dust in Type-II supernovae. In this paper we present new data which show that the submm emission from Cas A is polarised at a level significantly higher than that of its synchrotron emission. The orientation is consistent with that of the magnetic field in Cas A, implying that the polarised submm emission is associated with the remnant. No known mechanism would vary the synchrotron polarisation in this way and so we attribute the excess polarised submm flux to cold dust within the remnant, providing fresh evidence that cosmic dust can form rapidly. This is supported by the presence of both polarised and unpolarised dust emission in the north of the remnant, where there is no contamination from foreground molecular clouds. The inferred dust polarisation fraction is unprecedented (f_pol ~ 30%) which, coupled with the brief timescale available for grain alignment (<300 yr), suggests that supernova dust differs from that seen in other Galactic sources (where f_pol=2-7%), or that a highly efficient grain alignment process must operate in the environment of a supernova remnant.Comment: In press at MNRAS, 10 pages, print in colou

The shape of invasion perclation clusters in random and correlated media

The shape of two-dimensional invasion percolation clusters are studied numerically for both non-trapping (NTIP) and trapping (TIP) invasion percolation processes. Two different anisotropy quantifiers, the anisotropy parameter and the asphericity are used for probing the degree of anisotropy of clusters. We observe that in spite of the difference in scaling properties of NTIP and TIP, there is no difference in the values of anisotropy quantifiers of these processes. Furthermore, we find that in completely random media, the invasion percolation clusters are on average slightly less isotropic than standard percolation clusters. Introducing isotropic long-range correlations into the media reduces the isotropy of the invasion percolation clusters. The effect is more pronounced for the case of persisting long-range correlations. The implication of boundary conditions on the shape of clusters is another subject of interest. Compared to the case of free boundary conditions, IP clusters of conventional rectangular geometry turn out to be more isotropic. Moreover, we see that in conventional rectangular geometry the NTIP clusters are more isotropic than TIP clusters