Pinned states in Josephson arrays: A general stability theorem

Using the lumped circuit equations, we derive a stability criterion for superconducting pinned states in two-dimensional arrays of Josephson junctions. The analysis neglects quantum, thermal, and inductive effects, but allows disordered junctions, arbitrary network connectivity, and arbitrary spatial patterns of applied magnetic flux and DC current injection. We prove that a pinned state is linearly stable if and only if its corresponding stiffness matrix is positive definite. This algebraic condition can be used to predict the critical current and frustration at which depinning occurs.Comment: To appear in Phys. Rev.

Effects of Volcanic Emissions on Clouds During Kilauea Degassing Events

Aerosols influence Earths radiative balance directly by scattering and absorbing solar radiation, and indirectly by modifying cloud properties. Current scientific consensus indicates that these effects may offset as much as 50% of the warming due to greenhouse gas emissions. Over the last two decades dramatic volcanic events in Hawaii have produced localized aerosol emissions in otherwise clean environments. These are natural experiments" where the aerosol effects on clouds and climate can be partitioned from other effects like meteorology and industrial emissions. Therefore, these events provide a unique opportunity to learn about possible effects of aerosol pollution on climate through cloud modification. In this work we use the version 5 of the NASA Goddard Earth Observing System (GEOS-5) and satellite retrievals to analyze and evaluate the strength of the aerosol indirect effect on liquid and ice clouds during the 2008 and 2018 Kilauea degassing events using different emissions scenarios (0, 1, and 5 actual emissions). Our results suggested that the 2018 event was stronger and more regionally significant with respect to cloud formation process for both liquid and ice clouds, while the 2008 affected local liquid clouds only. GEOS-5 predictions reproduced spatial patterns for all parameters, however better precision could be gained by using more accurate plume parameters for height and ash concentration

Great cities look small

Great cities connect people; failed cities isolate people. Despite the fundamental importance of physical, face-to-face social-ties in the functioning of cities, these connectivity networks are not explicitly observed in their entirety. Attempts at estimating them often rely on unrealistic over-simplifications such as the assumption of spatial homogeneity. Here we propose a mathematical model of human interactions in terms of a local strategy of maximising the number of beneficial connections attainable under the constraint of limited individual travelling-time budgets. By incorporating census and openly-available online multi-modal transport data, we are able to characterise the connectivity of geometrically and topologically complex cities. Beyond providing a candidate measure of greatness, this model allows one to quantify and assess the impact of transport developments, population growth, and other infrastructure and demographic changes on a city. Supported by validations of GDP and HIV infection rates across United States metropolitan areas, we illustrate the effect of changes in local and city-wide connectivities by considering the economic impact of two contemporary inter- and intra-city transport developments in the United Kingdom: High Speed Rail 2 and London Crossrail. This derivation of the model suggests that the scaling of different urban indicators with population size has an explicitly mechanistic origin.Comment: 19 pages, 8 figure

A new bound of the ℒ2[0, T]-induced norm and applications to model reduction

We present a simple bound on the finite horizon ℒ2/[0, T]-induced norm of a linear time-invariant (LTI), not necessarily stable system which can be efficiently computed by calculating the ℋ∞ norm of a shifted version of the original operator. As an application, we show how to use this bound to perform model reduction of unstable systems over a finite horizon. The technique is illustrated with a non-trivial physical example relevant to the appearance of time-irreversible phenomena in statistical physics

Switchable Genetic Oscillator Operating in Quasi-Stable Mode

Ring topologies of repressing genes have qualitatively different long-term dynamics if the number of genes is odd (they oscillate) or even (they exhibit bistability). However, these attractors may not fully explain the observed behavior in transient and stochastic environments such as the cell. We show here that even repressilators possess quasi-stable, travelling-wave periodic solutions that are reachable, long-lived and robust to parameter changes. These solutions underlie the sustained oscillations observed in even rings in the stochastic regime, even if these circuits are expected to behave as switches. The existence of such solutions can also be exploited for control purposes: operation of the system around the quasi-stable orbit allows us to turn on and off the oscillations reliably and on demand. We illustrate these ideas with a simple protocol based on optical interference that can induce oscillations robustly both in the stochastic and deterministic regimes.Comment: 24 pages, 5 main figure

Using network-flow techniques to solve an optimization problem from surface-physics

The solid-on-solid model provides a commonly used framework for the description of surfaces. In the last years it has been extended in order to investigate the effect of defects in the bulk on the roughness of the surface. The determination of the ground state of this model leads to a combinatorial problem, which is reduced to an uncapacitated, convex minimum-circulation problem. We will show that the successive shortest path algorithm solves the problem in polynomial time.Comment: 8 Pages LaTeX, using Elsevier preprint style (macros included

Evaluation of an entraining droplet activation parameterization using in situ cloud data

This study investigates the ability of a droplet activation parameterization (which considers the effects of entrainment and mixing) to reproduce observed cloud droplet number concentration (CDNC) in ambient clouds. Predictions of the parameterization are compared against cloud averages of CDNC from ambient cumulus and stratocumulus clouds sampled during CRYSTAL‐FACE (Key West, Florida, July 2002) and CSTRIPE (Monterey, California, July 2003), respectively. The entrainment parameters required by the parameterization are derived from the observed liquid water content profiles. For the cumulus clouds considered in the study, CDNC is overpredicted by 45% with the adiabatic parameterization. When entrainment is accounted for, the predicted CDNC agrees within 3.5%. Cloud‐averaged CDNC for stratocumulus clouds is well captured when entrainment is not considered. In all cases considered, the entraining parameterization compared favorably against a statistical correlation developed from observations to treat entrainment effects on droplet number. These results suggest that including entrainment effects in the calculation of CDNC, as presented here, could address important overprediction biases associated with using adiabatic CDNC to represent cloud‐scale average values

Low-Temperature Excitations of Dilute Lattice Spin Glasses

A new approach to exploring low-temperature excitations in finite-dimensional lattice spin glasses is proposed. By focusing on bond-diluted lattices just above the percolation threshold, large system sizes $L$ can be obtained which lead to enhanced scaling regimes and more accurate exponents. Furthermore, this method in principle remains practical for any dimension, yielding exponents that so far have been elusive. This approach is demonstrated by determining the stiffness exponent for dimensions $d=3$, $d=6$ (the upper critical dimension), and $d=7$. Key is the application of an exact reduction algorithm, which eliminates a large fraction of spins, so that the reduced lattices never exceed $\sim10^3$ variables for sizes as large as L=30 in $d=3$, L=9 in $d=6$, or L=8 in $d=7$. Finite size scaling analysis gives $y_3=0.24(1)$ for $d=3$, significantly improving on previous work. The results for $d=6$ and $d=7$, $y_6=1.1(1)$ and $y_7=1.24(5)$, are entirely new and are compared with mean-field predictions made for d>=6.Comment: 7 pages, LaTex, 7 ps-figures included, added result for stiffness in d=7, as to appear in Europhysics Letters (see http://www.physics.emory.edu/faculty/boettcher/ for related information

Finite Size Scaling Analysis of Exact Ground States for +/-J Spin Glass Models in Two Dimensions

With the help of EXACT ground states obtained by a polynomial algorithm we compute the domain wall energy at zero-temperature for the bond-random and the site-random Ising spin glass model in two dimensions. We find that in both models the stability of the ferromagnetic AND the spin glass order ceases to exist at a UNIQUE concentration p_c for the ferromagnetic bonds. In the vicinity of this critical point, the size and concentration dependency of the first AND second moment of the domain wall energy are, for both models, described by a COMMON finite size scaling form. Moreover, below this concentration the stiffness exponent turns out to be slightly negative \theta_S = -0.056(6) indicating the absence of any intermediate spin glass phase at non-zero temperature.Comment: 7 pages Latex, 5 postscript-figures include