A Cycle-Based Formulation and Valid Inequalities for DC Power Transmission Problems with Switching

It is well-known that optimizing network topology by switching on and off transmission lines improves the efficiency of power delivery in electrical networks. In fact, the USA Energy Policy Act of 2005 (Section 1223) states that the U.S. should "encourage, as appropriate, the deployment of advanced transmission technologies" including "optimized transmission line configurations". As such, many authors have studied the problem of determining an optimal set of transmission lines to switch off to minimize the cost of meeting a given power demand under the direct current (DC) model of power flow. This problem is known in the literature as the Direct-Current Optimal Transmission Switching Problem (DC-OTS). Most research on DC-OTS has focused on heuristic algorithms for generating quality solutions or on the application of DC-OTS to crucial operational and strategic problems such as contingency correction, real-time dispatch, and transmission expansion. The mathematical theory of the DC-OTS problem is less well-developed. In this work, we formally establish that DC-OTS is NP-Hard, even if the power network is a series-parallel graph with at most one load/demand pair. Inspired by Kirchoff's Voltage Law, we give a cycle-based formulation for DC-OTS, and we use the new formulation to build a cycle-induced relaxation. We characterize the convex hull of the cycle-induced relaxation, and the characterization provides strong valid inequalities that can be used in a cutting-plane approach to solve the DC-OTS. We give details of a practical implementation, and we show promising computational results on standard benchmark instances

Diffusion of a liquid nanoparticle on a disordered substrate

We perform molecular dynamic simulations of liquid nanoparticles deposited on a disordered substrate. The motion of the nanoparticle is characterised by a 'stick and roll' diffusive process. Long simulation times ($\simeq \mu s$), analysis of mean square displacements and stacking time distribution functions demonstrate that the nanoparticle undergoes a normal diffusion in spite of long sticking times. We propose a phenomenological model for the size and temperature dependence of the diffusion coefficient in which the activation energy scales as $N^{1/3}$.Comment: Accepted for publication in Phys. Rev.

Inverse estimation of the transfer velocity of money

Monitoring the money supply is an important prerequisite for conducting sound monetary policy, yet monetary indicators are conventionally estimated in aggregate. This paper proposes a new methodology that is able to leverage micro-level transaction data from real-world payment systems. We apply a novel computational technique to measure the durations for which money is held in individual accounts, and compute the transfer velocity of money from its inverse. Our new definition reduces to existing definitions under conventional assumptions. However, inverse estimation remains suitable for payment systems where the total balance fluctuates and spending patterns change in time. Our method is applied to study Sarafu, a small digital community currency in Kenya, where transaction data is available from 25 January 2020 to 15 June 2021. We find that the transfer velocity of Sarafu was higher than it would seem, in aggregate, because not all units of Sarafu remained in active circulation. Moreover, inverse estimation reveals strong heterogineities and enables comparisons across subgroups of spenders. Some units of Sarafu were held for minutes, others for months, and spending patterns differed across communities using Sarafu. The rate of circulation and the effective balance of Sarafu changed substantially over time, as these communities experienced economic disruptions related to the COVID-19 pandemic and seasonal food insecurity. These findings contribute to a growing body of literature documenting the heterogeneous patterns underlying headline macroeconomic indicators and their relevance for policy. Inverse estimation may be especially useful in studying the response of spenders to targeted monetary operations

Liquid-liquid phase transition in Stillinger-Weber silicon

It was recently demonstrated that the Stillinger-Weber silicon undergoes a liquid-liquid first-order phase transition deep into the supercooled region (Sastry and Angell, Nature Materials 2, 739 (2003)). Here we study the effects of perturbations on this phase transition. We show that the order of the liquid-liquid transition changes with negative pressure. We also find that the liquid-liquid transition disappears when the three-body term of the potential is strengthened by as little as 5 %. This implies that the details of the potential could affect strongly the nature and even the existence of the liquid-liquid phase.Comment: 13 page

Nonmonotonic dependence of the absolute entropy on temperature in supercooled Stillinger-Weber silicon

Using a recently developed thermodynamic integration method, we compute the precise values of the excess Gibbs free energy (G^e) of the high density liquid (HDL) phase with respect to the crystalline phase at different temperatures (T) in the supercooled region of the Stillinger-Weber (SW) silicon [F. H. Stillinger and T. A. Weber, Phys. Rev. B. 32, 5262 (1985)]. Based on the slope of G^e with respect to T, we find that the absolute entropy of the HDL phase increases as its enthalpy changes from the equilibrium value at T \ge 1065 K to the value corresponding to a non-equilibrium state at 1060 K. We find that the volume distribution in the equilibrium HDL phases become progressively broader as the temperature is reduced to 1060 K, exhibiting van-der-Waals (VDW) loop in the pressure-volume curves. Our results provides insight into the thermodynamic cause of the transition from the HDL phase to the low density phases in SW silicon, observed in earlier studies near 1060 K at zero pressure.Comment: This version is accepted for publication in Journal of Statistical Physics (11 figures, 1 table

Steering effect on the shape of islands for homoepitaxial growth of Cu on Cu(100)

The steering effect on the growth of islands is investigated by combining molecular dynamics (MD) and kinetic Monte Carlo (KMC) simulations. Dynamics of depositing atoms and kinetics of atoms on a substrate are realized by MD and KMC, respectively. The reported experimental results on the asymmetric island growth [van Dijken {\it et al.}, Phys. Rev. Lett. {\bf 82}, 4038 (1999).] is well reproduced. A salient phenomenon, the reversal of the asymmetry, is found as the island size increases, and attributed to the asymmetric flux on the lower terrace of island.Comment: 5 figur

Following Guidelines for Drug-Resistant Tuberculosis: “Yes, it’s a challenge”

BACKGROUND: Drug-resistant tuberculosis (DR-TB) is a major contributor to antimicrobial resistance (AMR) globally and is projected to be responsible for up to a quarter of AMR-associated deaths in the future. Management of DR-TB is increasingly decentralised to primary healthcare settings, and simultaneously becoming more complex due to a growing range of treatment options (e.g. novel agents, shorter regimens). This is reflected in the numerous recent updates to international guidelines and as such understanding the barriers and enablers to how healthcare workers access and use guidelines is vital. MATERIAL AND METHODS: We used an established psychological framework – the theoretical domains framework (TDF) – to construct and analyse an online survey and focus groups to explore healthcare workers current use of DR-TB guidelines in South Africa. We aimed to identify barriers and enablers with which to direct future attempts at improving guideline use. RESULTS: There were 19 responses to the online survey and 14 participants in two focus groups. 28% used the most up-to-date national guidelines, 79% accessed guidelines primarily on electronic devices. The TDF domains of ‘Social Influences’ (mean Likert score = 4.3) and ‘Beliefs about Consequences’ (4.2) were key enablers, with healthcare workers encouraged to use guidelines and also recognising the value in doing so. ‘Environmental Resources’ (3.7) and ‘Knowledge’ (3.3) were key barriers with limited, or variable access to guidelines and lack of confidence using them being notable issues. This was most noted for certain subgroups: children, HIV co-infected, pregnant women (2.7). DISCUSSION: Current use of DR-TB guidelines in South Africa is suboptimal. Planned interventions should focus on overcoming the identified key barriers and might include an increased use of digital tools

Application of collapsing methods for continuous traits to the Genetic Analysis Workshop 17 exome sequence data

Genetic Analysis Workshop 17 used real sequence data from the 1000 Genomes Project and simulated phenotypes influenced by a large number of rare variants. Our aim is to evaluate the performance of various collapsing methods that were developed for analysis of multiple rare variants. We apply collapsing methods to continuous phenotypes Q1 and Q2 for all 200 replicates of the unrelated individuals data. Within each gene, we collapse (1) all SNPs, (2) all SNPs with minor allele frequency (MAF) < 0.05, and (3) nonsynonymous SNPs with MAF < 0.05. We consider two tests when collapsing variants: using the proportion of variants and using the presence/absence of any variant. We also compare our results to a single-marker analysis using PLINK. For phenotype Q1, the proportion test for collapsing rare nonsynonymous SNPs often performed the best. Two genes (FLT1 and KDR) had statistically significant results. A single-marker analysis using PLINK also provided statistically significant results for some SNPs within these two genes. For phenotype Q2, collapsing rare nonsynonymous SNPs performed the best, with almost no difference between proportion and presence tests. However, neither collapsing methods nor a single-marker analysis provided statistically significant results at the true genes for Q2. We also found that a large number of noncausal genes had high correlations with causal genes for Q1 and Q2, which may account for inflated false positives

Diffusion of gold nanoclusters on graphite

We present a detailed molecular-dynamics study of the diffusion and coalescence of large (249-atom) gold clusters on graphite surfaces. The diffusivity of monoclusters is found to be comparable to that for single adatoms. Likewise, and even more important, cluster dimers are also found to diffuse at a rate which is comparable to that for adatoms and monoclusters. As a consequence, large islands formed by cluster aggregation are also expected to be mobile. Using kinetic Monte Carlo simulations, and assuming a proper scaling law for the dependence on size of the diffusivity of large clusters, we find that islands consisting of as many as 100 monoclusters should exhibit significant mobility. This result has profound implications for the morphology of cluster-assembled materials

Nanojets, Electrospray, and Ion Field Evaporation: Molecular Dynamics Simulations and Laboratory Experiments

The energetics, interfacial properties, instabilities, and fragmentation patterns of electrosprays made from formamide salt solutions are investigated in a mass spectrometric vacuum electrospray experiment and using molecular dynamics (MD) simulations. The electrospray source is operated in a Taylor cone-jet mode, with the nanojet that forms being characterized by high surface-normal electric field strengths in the vicinity of 1 V/nm. Mass-to-charge ratios were determined for both positive and negative currents sprayed from NaI−formamide solutions with solute−solvent mole ratios of 1:8.4 and 1:36.9, and from KI−formamide solutions with mole ratios of 1:41 and 1:83. The molecular dynamics simulations were conducted on isolated 10 nm NaI−formamide droplets at mole ratios of 1:8 and 1:16. The droplet was subjected to a uniform electric field with strengths ranging between 0.5 and 1.5 V/nm. Both the experiments and simulations demonstrate a mixed charge emission regime where field-induced desorption of solvated ions and charged droplets occurs. The macroscopic parameters, such as average mass-to-charge ratio and maximum surface-normal field strengths deduced from the simulations are found to be in good agreement with the experimental work and consistent with electrohydrodynamic theory of cone-jets. The observed mass spectrometric Na+ and I− solvated ion distributions are consistent with a thermal evaporation process, and are correctly reproduced by the simulation after incorporation of the different flight times and unimolecular ion dissociation rates in the analysis. Alignment of formamide dipoles and field-induced reorganization of the positive and negative ionic charges in the interfacial region are both found to contribute to the surface-normal field near the points of charge emission. In the simulations the majority of cluster ions are found to be emitted from the tip of the jet rather than from the neck region next to the Taylor cone. This finding is consistent with the experimental energy distributions of the solvated ions which demonstrate that indeed most ions are emitted closer to the jet region, that is, beyond the cone-neck region where ohmic losses occur. This observation is also consistent with continuum electrohydrodynamic predictions of cluster-ion evaporation at surface regions of high curvature and therefore maximum surface electric field strengths, which may be the cone-neck region, the breakup region of the jet (usually near the tip of the jet), or the emitted charged droplets. In the nanoscale jets observed in this study, the regions of highest spatial curvature are at the ends of the jets where nascent drops either are forming or have just detached