Firm Dynamics and Institutional Participation: A Case Study on Informality of Micro-Enterprises in Peru

Using panel data on micro-enterprises from Peru, we find evidence suggesting that firm dynamics explain 'formality', i.e. the decision to participate in societal institutions. In particular, we find that participation increases with firm size and age, implying transition of firms to formality as they grow. The distinct characteristics of sub-groups, segmented according to life-cycle criteria, further support the role of firm dynamics and life-cycle considerations for the analysis of participation.

Spiral model, jamming percolation and glass-jamming transitions

The Spiral Model (SM) corresponds to a new class of kinetically constrained models introduced in joint works with D.S. Fisher [8,9]. They provide the first example of finite dimensional models with an ideal glass-jamming transition. This is due to an underlying jamming percolation transition which has unconventional features: it is discontinuous (i.e. the percolating cluster is compact at the transition) and the typical size of the clusters diverges faster than any power law, leading to a Vogel-Fulcher-like divergence of the relaxation time. Here we present a detailed physical analysis of SM, see [5] for rigorous proofs. We also show that our arguments for SM does not need any modification contrary to recent claims of Jeng and Schwarz [10].Comment: 9 pages, 7 figures, proceedings for StatPhys2

Fast Simulation of Facilitated Spin Models

We show how to apply the absorbing Markov chain Monte Carlo algorithm of Novotny to simulate kinetically constrained models of glasses. We consider in detail one-spin facilitated models, such as the East model and its generalizations to arbitrary dimensions. We investigate how to maximise the efficiency of the algorithms, and show that simulation times can be improved on standard continuous time Monte Carlo by several orders of magnitude. We illustrate the method with equilibrium and aging results. These include a study of relaxation times in the East model for dimensions d=1 to d=13, which provides further evidence that the hierarchical relaxation in this model is present in all dimensions. We discuss how the method can be applied to other kinetically constrained models.Comment: 8 pages, 4 figure

A Mini-PET beamline for optimized proton delivery to the ISOTRACE™ target system

Introduction The ISOTRACE™ Super-Conducting Cyclotron is PMB-Alcen’s redeveloped and modernized version of Oxford Instrument’s OSCAR superconducting cyclotron [1]. Its extracted 80+ mi-croamperes of 12 MeV protons are used for the production of PET radioisotopes. Following the philosophy of Dickie, Stevenson, Szlavik [2] for minimizing dose to personnel, and as developed by Dehnel et al [3,4], and Stokely et al [5], the ISOTRACE™ shall utilize an innovative, light-weight, integrated and self-supporting Mini-Beamline. This permits the relatively high residual radiation fields around PET targets to be moved ~1 metre away from the cyclotron, and facilitates the use of local shielding (around the targets) that limits prompt gammas and neutrons, but more importantly attenuates the residual target radiation, so that maintenance/research staff can work on the cyclotron in a relatively low activity environment. In addition, the mini-beamline for PET utilizes a compound quadrupole/steerer doublet that permits active and dynamic focusing/steering of the extracted proton beam for optimized production and minimized losses [3], so it improves on the successful work of Theroux et al [6]. The integrated beamline unit is extremely small, so that it is very unlike bulky traditional PET and SPECT beamlines that require substantial support structures, such as described by Dehnel in [7,8]. Material and Methods The ISOTRACE™ cyclotron is pictured in FIG. 1. The exit port flange and gate valve to which the integrated mini-beamline for PET shall be mounted is shown. Immediately upstream of the exit port, hidden from view, is a 4 jaw collimator (called BPI for Beam Position Indicator) with spilled beam current readbacks to the control system. TABLE 1 shows the nominal beam emittance and Twiss parameter values at the exit port flange location. This ion-optical information is necessary to simulate ion beam transport, develop the mini-beamline, and determine a nominal tune (i.e. magnet settings). Results and Conclusion TABLE 2 shows the ion-optical system parameters. FIGS. 2 and 3 show the horizontal and vertical beam profiles. The Horizontally focusing Quadrupole magnet (HQ), and Vertically focusing Quadrupole magnet (VQ) aperture diameter, 33 mm, was chosen to give sufficient beam acceptance. The focusing strength is a function of BL, so the effective length, L = 150 mm, was chosen to ensure Bmax less than 0.3 Tesla, while keeping overall magnet mass down. The quad-rupole magnets are fitted with water-cooled compound coils in which the copper/mylar strip wound portion of each coil is a winding for the quadrupole focusing function, and the wire wound portion is for the steering function. To increase beam acceptance and provide additional section strength for the pipe support function, the internal aperture of the low-activation aluminium beam pipe and the external shape are in the shape of a cross. FIG. 4 shows the beam crosssection at the mid-point of the downstream quadrupole magnet, and illustrates the additional acceptance as compared to a round beampipe. In order to machine the interior profile, the pipe is comprised of two premachined pieces that are friction stirwelded together. FIG. 5 is an isometric of the mini-beamline for PET. The four upstream HQ compound coils are excited with a 75A power supply for the horizontally focusing quadrupole magnet function, and a ± 10A power supply for a vertical steering function. The same power supplies are used for the four downstream VQ compound coils for the purpose of a vertically focusing quadrupole magnet function and horizontal steering function

Facilitated spin models: recent and new results

Facilitated or kinetically constrained spin models (KCSM) are a class of interacting particle systems reversible w.r.t. to a simple product measure. Each dynamical variable (spin) is re-sampled from its equilibrium distribution only if the surrounding configuration fulfills a simple local constraint which \emph{does not involve} the chosen variable itself. Such simple models are quite popular in the glass community since they display some of the peculiar features of glassy dynamics, in particular they can undergo a dynamical arrest reminiscent of the liquid/glass transitiom. Due to the fact that the jumps rates of the Markov process can be zero, the whole analysis of the long time behavior becomes quite delicate and, until recently, KCSM have escaped a rigorous analysis with the notable exception of the East model. In these notes we will mainly review several recent mathematical results which, besides being applicable to a wide class of KCSM, have contributed to settle some debated questions arising in numerical simulations made by physicists. We will also provide some interesting new extensions. In particular we will show how to deal with interacting models reversible w.r.t. to a high temperature Gibbs measure and we will provide a detailed analysis of the so called one spin facilitated model on a general connected graph.Comment: 30 pages, 3 figure

Relaxation times of kinetically constrained spin models with glassy dynamics

We analyze the density and size dependence of the relaxation time $\tau$ for kinetically constrained spin systems. These have been proposed as models for strong or fragile glasses and for systems undergoing jamming transitions. For the one (FA1f) or two (FA2f) spin facilitated Fredrickson-Andersen model at any density $\rho<1$ and for the Knight model below the critical density at which the glass transition occurs, we show that the persistence and the spin-spin time auto-correlation functions decay exponentially. This excludes the stretched exponential relaxation which was derived by numerical simulations. For FA2f in $d\geq 2$, we also prove a super-Arrhenius scaling of the form $\exp(1/(1-\rho))\leq \tau\leq\exp(1/(1-\rho)^2)$. For FA1f in $d$=$1,2$ we rigorously prove the power law scalings recently derived in \cite{JMS} while in $d\geq 3$ we obtain upper and lower bounds consistent with findings therein. Our results are based on a novel multi-scale approach which allows to analyze $\tau$ in presence of kinetic constraints and to connect time-scales and dynamical heterogeneities. The techniques are flexible enough to allow a variety of constraints and can also be applied to conservative stochastic lattice gases in presence of kinetic constraints.Comment: 4 page

Nonlinear acoustic and microwave absorption in glasses

A theory of weakly-nonlinear low-temperature relaxational absorption of acoustic and electromagnetic waves in dielectric and metallic glasses is developed. Basing upon the model of two-level tunneling systems we show that the nonlinear contribution to the absorption can be anomalously large. This is the case at low enough frequencies, where freqeuency times the minimal relaxation time for the two-level system are much less than one. In dielectric glasses, the lowest-order nonlinear contribution is proportional to the wave's intensity. It is negative and exhibits anomalous frequency and temperature dependencies. In metallic glasses, the nonlinear contribution is also negative, and it is proportional to the square root of the wave's intensity and to the frequency. Numerical estimates show that the predicted nonlinear contribution can be measured experimentally

Jamming percolation and glassy dynamics

We present a detailed physical analysis of the dynamical glass-jamming transition which occurs for the so called Knight models recently introduced and analyzed in a joint work with D.S.Fisher \cite{letterTBF}. Furthermore, we review some of our previous works on Kinetically Constrained Models. The Knights models correspond to a new class of kinetically constrained models which provide the first example of finite dimensional models with an ideal glass-jamming transition. This is due to the underlying percolation transition of particles which are mutually blocked by the constraints. This jamming percolation has unconventional features: it is discontinuous (i.e. the percolating cluster is compact at the transition) and the typical size of the clusters diverges faster than any power law when $\rho\nearrow\rho_c$. These properties give rise for Knight models to an ergodicity breaking transition at $\rho_c$: at and above $\rho_{c}$ a finite fraction of the system is frozen. In turn, this finite jump in the density of frozen sites leads to a two step relaxation for dynamic correlations in the unjammed phase, analogous to that of glass forming liquids. Also, due to the faster than power law divergence of the dynamical correlation length, relaxation times diverge in a way similar to the Vogel-Fulcher law.Comment: Submitted to the special issue of Journal of Statistical Physics on Spin glasses and related topic

High frequency online data collection in an annual household panel study: some evidence on bias prevention and bias adjustment.

Understanding Society is the UK’s largest household panel survey. From April 2020, Understanding Society participants were invited to partake in a series of web surveys (the Understanding Society COVID-19 Study) designed to capture higher frequency information during the pandemic. To prevent bias, the COVID-19 Study invites the full range of Understanding Society participants – both those who regularly use the internet and those who do not – to take part and, furthermore, periodically invites a subset of non-respondents to a telephone follow-up. To adjust for bias, a weighting strategy is implemented that takes advantage of the rich background information available from past annual interviews. We examine the efficacy of these bias reduction and bias adjustment measures. We find that both the telephone follow-ups and weighting help to reduce bias, but that inviting those who do not regularly use the internet to the web survey appears to be of little benefit

Slow Relaxation in a Constrained Ising Spin Chain: a Toy Model for Granular Compaction

We present detailed analytical studies on the zero temperature coarsening dynamics in an Ising spin chain in presence of a dynamically induced field that favors locally the `-' phase compared to the `+' phase. We show that the presence of such a local kinetic bias drives the system into a late time state with average magnetization m=-1. However the magnetization relaxes into this final value extremely slowly in an inverse logarithmic fashion. We further map this spin model exactly onto a simple lattice model of granular compaction that includes the minimal microscopic moves needed for compaction. This toy model then predicts analytically an inverse logarithmic law for the growth of density of granular particles, as seen in recent experiments and thereby provides a new mechanism for the inverse logarithmic relaxation. Our analysis utilizes an independent interval approximation for the particle and the hole clusters and is argued to be exact at late times (supported also by numerical simulations).Comment: 9 pages RevTeX, 1 figures (.eps