Unjamming in models with analytic pairwise potentials

The canonical models for studying the unjamming scenario in systems of soft repulsive particles assume pairwise potentials with a sharp cut-off in the interaction range. The sharp cut-off renders the potential non-analytic, but makes it possible to describe many properties of the solid in terms of the coordination number $z$, which has an unambiguous definition in these cases. Pairwise potentials without a sharp cut-off in the interaction range have not been considered in this context, but are of interest for understanding the relevance of the unjamming phenomenology to systems in which such a cut-off cannot be assumed. In this work we explore two systems with such interactions: an inverse power law and an exponentially decaying pairwise potential, with the control parameters being the exponent (of the inverse power-law) for the former and the number density for the latter. Both systems are shown to exhibit the characteristic features of the unjamming transition, among which are the vanishing of the shear to bulk modulus ratio and the emergence of an excess of low-frequency vibrational modes. We establish a relation between the hydrostatic pressure to bulk modulus ratio and the distance to unjamming in each of our model systems. This allows us to predict the dependence of other key observables on the distance to unjamming. Our results provide the means for a quantitative estimation of the proximity of generic glass forming models to the unjamming transition in the absence of a clear-cut definition of the coordination number, and highlight the general irrelevance of nonaffine contributions to the bulk modulus.Comment: 8 pages, 7 figure

Droplet size from Venturi air induction spray nozzles

Sprays are of great importance for many applications, with drop size being a crucial parameter. Especially in agriculture applications, simple flat fan spray nozzles are often supplemented by a Venturi component to achieve larger drop sizes and hence, prevent unwanted spray drift of the smallest droplets. The general believe is that these larger drops are usually attributed to the fact that the liquid sheet produced by the nozzle breaks up more easily due to the pre-existing ’holes’ formed by the induced air bubbles. Here, we extend descriptions of how nozzle and fluid parameters determine droplet size distributions from Venturi nozzles. We show that the mean droplet size is determined by the nozzle’s orifice area as is the case for ordinary flat fan nozzles, but that the additional pressure drop over the Venturi chamber needs to be taken into account. Using this parameter, relations that were derived for flat fan nozzles can be re-used. This allows to show that the increase in droplet size compared to conventional nozzles is due to the additional pressure drop in the Venturi chamber, and not to a change in breakup mechanism due to the presence of air bubbles in the liquid sheet.</p

lassopack: Model selection and prediction with regularized regression in Stata

This article introduces lassopack, a suite of programs for regularized regression in Stata. lassopack implements lasso, square-root lasso, elastic net, ridge regression, adaptive lasso and post-estimation OLS. The methods are suitable for the high-dimensional setting where the number of predictors $p$ may be large and possibly greater than the number of observations, $n$. We offer three different approaches for selecting the penalization (`tuning') parameters: information criteria (implemented in lasso2), $K$-fold cross-validation and $h$-step ahead rolling cross-validation for cross-section, panel and time-series data (cvlasso), and theory-driven (`rigorous') penalization for the lasso and square-root lasso for cross-section and panel data (rlasso). We discuss the theoretical framework and practical considerations for each approach. We also present Monte Carlo results to compare the performance of the penalization approaches.Comment: 52 pages, 6 figures, 6 tables; submitted to Stata Journal; for more information see https://statalasso.github.io

Further remarks on rational albime triangles

In this note we present further number theoretic properties of the rational albime triangles, in particular, the distribution of acute vs. obtuse rational albime triangles. The notion of albime triangle is extended to include the case of external angle bisector. The proportion of internal vs. external rational albime triangles is also computed<br/

Electric field assisted nanocolloidal gold deposition

The deposition of nanocolloidal gold particles under the influence of an externally applied electric field is studied in situ by means of spectroscopic ellipsometry. The variation of the relative coverage with time, as a function of applied potential, is determined using a principal component analysis. Calibration of the absolute coverage is done by means of ex situ electron microscopy. The results reveal that the deposition rate is directly related to the electrochemical current. A threshold potential exists for current and therewith also deposition to occur. The spatial distribution of nanoparticles deposited in an applied field exhibits a higher degree of order as compared to the random, irreversibly deposited nanocolloids at chemically functionalized surfaces. The experimental findings are discussed in terms of a simple electrochemical model

Field induced phase segregation in ferrofluids

We study the phase segregation in magnetite ferrofluids under the influence of an external magnetic field. A phase with lower nanoparticle density and corresponding higher optical transmission is formed in the bottom of a glass cell in the presence of only a very modest magnetic field gradient (smaller than 25 T/m). The flux density in our magnetic configuration is simulated using finite element methods. Upon switching off the external magnetic field, the low-density phase develops into a ‘bubble’-like feature. The kinetics of this ‘bubble’ in the absence and presence of a magnetic field are described and analyzed in terms of a simple model, which takes into account buoyancy and drag force