Fragmentation of Random Trees

We study fragmentation of a random recursive tree into a forest by repeated removal of nodes. The initial tree consists of N nodes and it is generated by sequential addition of nodes with each new node attaching to a randomly-selected existing node. As nodes are removed from the tree, one at a time, the tree dissolves into an ensemble of separate trees, namely, a forest. We study statistical properties of trees and nodes in this heterogeneous forest, and find that the fraction of remaining nodes m characterizes the system in the limit N --> infty. We obtain analytically the size density phi_s of trees of size s. The size density has power-law tail phi_s ~ s^(-alpha) with exponent alpha=1+1/m. Therefore, the tail becomes steeper as further nodes are removed, and the fragmentation process is unusual in that exponent alpha increases continuously with time. We also extend our analysis to the case where nodes are added as well as removed, and obtain the asymptotic size density for growing trees.Comment: 9 pages, 5 figure

Extensions of Effective Medium Theory of Transport in Disordered Systems

Effective medium theory of transport in disordered systems, whose basis is the replacement of spatial disorder by temporal memory, is extended in several practical directions. Restricting attention to a 1-dimensional system with bond disorder for specificity, a transformation procedure is developed to deduce, from given distribution functions characterizing the system disorder, explicit expressions for the memory functions. It is shown how to use the memory functions in the Lapace domain forms in which they first appear, and in the time domain forms which are obtained via numerical inversion algorithms, to address time evolution of the system beyond the asymptotic domain of large times normally treated. An analytic but approximate procedure is provided to obtain the memories, in addition to the inversion algorithm. Good agreement of effective medium theory predictions with numerically computed exact results is found for all time ranges for the distributions used except near the percolation limit as expected. The use of ensemble averages is studied for normal as well as correlation observables. The effect of size on effective mediumtheory is explored and it is shown that, even in the asymptotic limit, finite size corrections develop to the well known harmonic mean prescription for finding the effective rate. A percolation threshold is shown to arise even in 1-d for finite (but not infinite) systems at a concentration of broken bonds related to the system size. Spatially long range transfer rates are shown to emerge naturally as a consequence of the replacement of spatial disorder by temporal memories, in spite of the fact that the original rates possess nearest neighbor character. Pausing time distributions in continuous time random walks corresponding to the effective medium memories are calculated.Comment: 15 pages, 11 figure

Variabilitas Suhu Dan Salinitas Di Laut Halmahera

Suhu dan salinitas memiliki peranan penting dalam mencerminkan kondisi massa air dan secara langsung berpengaruh terhadap kondisi biologi dan kimia perairan. Tujuan penelitian ini adalah menganalisis dinamika angin di perairan Laut Halmahera dan mendiskripsikan kondisi suhu dan salinitas permukaan laut (SPL) di Laut Halmahera. Data yang digunakan yaitu data penginderaan jauh Marine Copernicus untuk data Suhu dan salinitas sedangkan data angin dari ECMWF. Pengolahan data menggunakan software ODV untuk mengolah data SPL dan salinitas dari tahun 2016-2020, selanjutnya data angin diolah menggunakan software surfer 16. Laut Halmahera memiliki suhu permukaan laut berkisar antara 26.20 - 31.6°C dimana kondisi maksimum terjadi bulan Mei dan November. Sedangkan salinitas berkisar antara 29.38 - 34.9 psu, dimana kondisi maksimum pada bulan Desember sampai Maret. Dinamika angin di Laut Halmahera mempengaruhi pola sebaran suhu permukaan laut dan salinitas yang ada pada perairan tersebut, dimana kecepatan angin berkisar antara 6.5 - 2.5 m/s

Effects of disorder in location and size of fence barriers on molecular motion in cell membranes

The effect of disorder in the energetic heights and in the physical locations of fence barriers encountered by transmembrane molecules such as proteins and lipids in their motion in cell membranes is studied theoretically. The investigation takes as its starting point a recent analysis of a periodic system with constant distances between barriers and constant values of barrier heights, and employs effective medium theory to treat the disorder. The calculations make possible, in principle, the extraction of confinement parameters such as mean compartment sizes and mean intercompartmental transition rates from experimentally reported published observations. The analysis should be helpful both as an unusual application of effective medium theory and as an investigation of observed molecular movements in cell membranes.Comment: 9 pages, 5 figure

Molecular motion in cell membranes: analytic study of fence-hindered random walks

A theoretical calculation is presented to describe the confined motion of transmembrane molecules in cell membranes. The study is analytic, based on Master equations for the probability of the molecules moving as random walkers, and leads to explicit usable solutions including expressions for the molecular mean square displacement and effective diffusion constants. One outcome is a detailed understanding of the dependence of the time variation of the mean square displacement on the initial placement of the molecule within the confined region. How to use the calculations is illustrated by extracting (confinement) compartment sizes from experimentally reported published observations from single particle tracking experiments on the diffusion of gold-tagged G-protein coupled mu-opioid receptors in the normal rat kidney cell membrane, and by further comparing the analytical results to observations on the diffusion of phospholipids, also in normal rat kidney cells.Comment: 10 pages, 5 figure

High-Accuracy X-Ray Diffraction Analysis of Phase Evolution Sequence During Devitrification of Cu50Zr50 Metallic Glass

Real-time high-energy X-ray diffraction (HEXRD) was used to investigate the crystallization kinetics and phase selection sequence for constant-heating-rate devitrification of fully amorphous Cu50Zr50, using heating rates from 10 K/min to 60 K/min (10 °C/min to 60 °C/min). In situ HEXRD patterns were obtained by the constant-rate heating of melt-spun ribbons under synchrotron radiation. High-accuracy phase identification and quantitative assessment of phase fraction evolution though the duration of the observed transformations were performed using a Rietveld refinement method. Results for 10 K/min (10 °C/min) heating show the apparent simultaneous formation of three phases, orthorhombic Cu10Zr7, tetragonal CuZr2 (C11b), and cubic CuZr (B2), at 706 K (433 °C), followed immediately by the dissolution of the CuZr (B2) phase upon continued heating to 789 K (516 °C). Continued heating results in reprecipitation of the CuZr (B2) phase at 1002 K (729 °C), with the material transforming completely to CuZr (B2) by 1045 K (772 °C). The Cu5Zr8 phase, previously reported to be a devitrification product in C50Zr50, was not observed in the present study

Confining Domains Lead to Reaction Bursts: Reaction Kinetics in the Plasma Membrane

Confinement of molecules in specific small volumes and areas within a cell is likely to be a general strategy that is developed during evolution for regulating the interactions and functions of biomolecules. The cellular plasma membrane, which is the outermost membrane that surrounds the entire cell, was considered to be a continuous two-dimensional liquid, but it is becoming clear that it consists of numerous nano-meso-scale domains with various lifetimes, such as raft domains and cytoskeleton-induced compartments, and membrane molecules are dynamically trapped in these domains. In this article, we give a theoretical account on the effects of molecular confinement on reversible bimolecular reactions in a partitioned surface such as the plasma membrane. By performing simulations based on a lattice-based model of diffusion and reaction, we found that in the presence of membrane partitioning, bimolecular reactions that occur in each compartment proceed in bursts during which the reaction rate is sharply and briefly increased even though the asymptotic reaction rate remains the same. We characterized the time between reaction bursts and the burst amplitude as a function of the model parameters, and discussed the biological significance of the reaction bursts in the presence of strong inhibitor activity

Running With the Ball? Making a Play for Sport Heritage Archives in Higher Education Contexts

For considerable time, academia (in particular, the Humanities) has been in an intellectual, economic and pragmatic par des deux with the culture and arts sector (in this case, heritage, museums and archives). In many ways, given their respective pursuits of scientific enquiry and learning, valuable contribution to a knowledge economy, commitment to public enlightenment, and exploration of critical and creative endeavour, a relationship between the sectors makes sense. Unity notwithstanding, the relationships have become increasingly now influenced by (en)forced contextual constraints (e.g., government policy development and intervention, neoliberal market forces, structural and ideological shifts in funding acquisition and allocation, patronage changes and demands, and/or individual political priorities) (Dubuc 2011; McCall and Gray 2014; Watson 2002). Drawing on education and heritage scholarship, and theoretical frameworks of sport culture spaces (Hardy, Loy and Booth 2009; Phillips 2012; Pinson 2017), this paper examines efforts undertaken at one specific Higher Education establishment in the United Kingdom in which institutional agendas (vis-à-vis historical and cultural foci, encouraging ‘impactful’ academic activity, brand exposure, economic efficiency, and community engagement) have contoured, and become entwined with, an embryonic sport heritage and archive project. Recalling similar arrangements elsewhere (Krüger 2014; Reilly, Clayton and Hughson 2014; Reilly 2015), the aim of this case study is to explore how the wider education and cultural policy context have precipitated an increasingly symbiotic and dependent relationship between university and cultural/arts initiatives. The paper considers how the impetus to develop a sports-based (basketball) heritage archive and study centre reflects the current fragilities of the two sectors, yet, concomitantly, reveals the potentials that might be developed from fostering greater intellectual and pragmatic alliances. The paper concludes by advocating the practical, political and ideological usefulness of network formation, sustainability measures and continued cross-sector dialogue

DIY John Curtin: Uncertain futures for heritage and citizenship in the era of digital friends and foes

This article introduces some of the problems confronting the popularization of national, civic and cultural heritage in the era of complex digital systems and social networks. Taking contemporary knowledge of John Curtin (Australia’s wartime PM) as its point of departure, the discussion explores some of the broader transformations of the conditions of citizenship, communication, heritage and knowledge production, and considers their implications for civic education and the uses of archives. In a novel thought experiment, the article explores some ways in which the figure of ‘John Curtin’ may be repurposed and reinvented for a new kind of DIY civic education based on user-led innovation