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Since the seminal work of Schoen-Uhlenbeck, many authors have studied properties of harmonic maps satisfying Dirichlet boundary conditions. In this article, we instead investigate regularity and symmetry of $\mathbb{S}^2-$valued minimizing harmonic maps subject to a tangency constraint in the model case of the unit ball in $\mathbb{R}^{3}$. In particular, we obtain a monotonicity formula respecting tangentiality on a curved boundary in order to show optimal regularity up to the boundary. We introduce novel sufficient conditions under which the minimizer must exhibit symmetries. Under a symmetry assumption, we present a delineation of the singularities of minimizers, namely that a mimimizer has exactly two point singularities, located on the boundary at opposite points., Comment: 47 pages, 5 figures

Friction is a phenomenon that manifests across all spatial and temporal scales, from the molecular to the macroscopic scale. It describes the dissipation of energy from the motion of particles or abstract reaction coordinates and arises in the transition from a detailed molecular-level description to a simplified, coarse-grained model. It has long been understood that time-dependent (non-Markovian) friction effects are critical for describing the dynamics of many systems, but that they are notoriously difficult to evaluate for complex physical, chemical, and biological systems. In recent years, the development of advanced numerical friction extraction techniques and methods to simulate the generalized Langevin equation have enabled exploration of the role of time-dependent friction across all scales. We discuss recent applications of these friction extraction techniques and the growing understanding of the role of friction in complex equilibrium and non-equilibrium dynamic many-body systems., Comment: 26 pages, 6 figures

An isolated Leidenfrost droplet levitating over its own vapor above a superheated flat substrate is considered theoretically, the superheating for water being up to several hundred degrees above the boiling temperature. The focus is on the limit of small, practically spherical droplets of several tens of micrometers or less. This may occur when the liquid is sprayed over a hot substrate, or just be a late life stage of an initially large Leidenfrost droplet. A rigorous numerically-assisted analysis is carried out within verifiable assumptions such as quasi-stationarities and small Reynolds/P\'{e}clet numbers. It is considered that the droplet is surrounded by its pure vapor. Simple fitting formulas of our numerical data for the forces and evaporation rates are preliminarily obtained, all respecting the asymptotic behaviors (also investigated) in the limits of small and large levitation heights. They are subsequently used within a system of ODEs to study the droplet dynamics and take-off (drastic height increase as the droplet vaporizes). A previously known quasi-stationary inverse-square root law for the droplet height as a function of its radius (at the root of the take-off) is recovered, although we point out different prefactors in the two limits. Deviations of a dynamic nature therefrom are uncovered as the droplet radius further decreases due to evaporation, improving the agreement with experiment. Furthermore, we reveal that, if initially large enough, the droplets vanish at a universal finite height (just dependent on the superheat and fluid properties). Scalings in various distinguished cases are obtained in the way.

We consider minimizers $u_\varepsilon$ of the Ginzburg-Landau energy with quadratic divergence penalization on a simply-connected two-dimensional domain $\Omega$. On the boundary, strong tangential anchoring is imposed. We prove that minimizers satisfy a $L^\infty$-bound uniform in $\varepsilon$ when $\Omega$ has $C^{2,1}-$boundary and that the Lipschitz constant blows up like $\varepsilon^{-1}$ when $\Omega$ has $C^{3,1}-$boundary. Our theorem extends to $W^{2,p}-$regularity result for our elliptic system with mixed Dirichlet-Neumann boundary condition., Comment: 32 pages, 3 figures

A classical result in the study of Ginzburg-Landau equations is that, for Dirichlet or Neumann boundary conditions, if a sequence of functions has energy uniformly bounded on a logarithmic scale then we can find a subsequence whose Jacobians are convergent in suitable dual spaces and whose renormalized energy is at least the sum of absolute degrees of vortices. However, the corresponding question for the case of tangential or normal boundary conditions has not been considered. In addition, the question of convergence of up to the boundary is not very well understood. Here, we consider these questions for a bounded, connected, open set of $\mathbb{R}^{2}$ with $C^{2,1}$ boundary., Comment: 48 pages, 3 figures

In the setting of a compact Riemannian manifold of dimension $N\ge3$ we provide a structural description of the limiting behaviour of the energy measures of solutions to the parabolic Ginzburg-Landau equation. In particular, we provide a decomposition of the limiting energy measure into a diffuse part, which is absolutely continuous with respect to the volume measure, and a concentrated part supported on a codimension $2$ rectifiable subset. We also demonstrate that the time evolution of the diffuse part is determined by the heat equation while the concentrated part evolves according to a Brakke flow. This paper extends the work of Bethuel, Orlandi, and Smets., Comment: 63 pages

The Open Databases Integration for Materials Design (OPTIMADE) consortium has designed a universal application programming interface (API) to make materials databases accessible and interoperable. We outline the first stable release of the specification, v1.0, which is already supported by many leading databases and several software packages. We illustrate the advantages of the OPTIMADE API through worked examples on each of the public materials databases that support the full API specification., Comment: 11 pages, 1 table

It is well-known that under suitable hypotheses, for a sequence of solutions of the (simplified) Ginzburg-Landau equations $-\Delta u_\varepsilon +\varepsilon^{-2}(|u_\varepsilon|^2-1)u_\varepsilon = 0$, the energy and vorticity concentrate as $\varepsilon\to 0$ around a codimension $2$ stationary varifold -- a (measure theoretic) minimal surface. Much less is known about the question of whether, given a codimension $2$ minimal surface, there exists a sequence of solutions for which the given minimal surface is the limiting concentration set. The corresponding question is very well-understood for minimal hypersurfaces and the scalar Allen-Cahn equation, and for the Ginzburg-Landau equations when the minimal surface is locally area-minimizing, but otherwise quite open. We consider this question on a $3$-dimensional closed Riemannian manifold $(M,g)$, and we prove that any embedded nondegenerate closed geodesic can be realized as the asymptotic energy/vorticity concentration set of a sequence of solutions of the Ginzburg-Landau equations., Comment: 35 pages

The celebrated Lott-Sturm-Villani theory of metric measure spaces furnishes synthetic notions of a Ricci curvature lower bound $K$ joint with an upper bound $N$ on the dimension. Their condition, called the Curvature-Dimension condition and denoted by $\mathrm{CD}(K,N)$, is formulated in terms of a modified displacement convexity of an entropy functional along $W_{2}$-Wasserstein geodesics. We show that the choice of the squared-distance function as transport cost does not influence the theory. By denoting with $\mathrm{CD}_{p}(K,N)$ the analogous condition but with the cost as the $p^{th}$ power of the distance, we show that $\mathrm{CD}_{p}(K,N)$ are all equivalent conditions for any $p>1$ -- at least in spaces whose geodesics do not branch. We show that the trait d'union between all the seemingly unrelated $\mathrm{CD}_{p}(K,N)$ conditions is the needle decomposition or localization technique associated to the $L^{1}$-optimal transport problem. We also establish the local-to-global property of $\mathrm{CD}_{p}(K,N)$ spaces.

We study the effect of bulk perturbations of N=(2,2) superconformal minimal models on topological defects. In particular, symmetries and more general topological defects which survive the flow to the IR are identified. Our method is to consider the topological subsector and make use of the Landau-Ginzburg formulation to describe RG flows and topological defects in terms of matrix factorizations., Comment: 39 pages, 6 figures

Proceedings of the workshop "Boundary and Defect Conformal Field Theory: Open Problems and Applications," Chicheley Hall, Buckinghamshire, UK, 7-8 Sept. 2017., Comment: Conference proceedings of "Boundary and Defect Conformal Field Theory: Open Problems and Applications." Invited submission to Proceedings of the Royal Society A. Section 17 is a more condensed version of arXiv:1711.05049

Droplets can be levitated by their own vapour when placed onto a superheated plate (the Leidenfrost effect). It is less known that the Leidenfrost effect can likewise be observed over a liquid pool (superheated with respect to the drop), which is the study case here. Emphasis is placed on an asymptotic analysis in the limit of small evaporation numbers, which proves to be a realistic one indeed for not so small drops. The global shapes are found to resemble "superhydrophobic drops" that follow from the equilibrium between capillarity and gravity. However, the morphology of the thin vapour layer between the drop and the pool is very different from that of classical Leidenfrost drops over a flat rigid substrate, and exhibits different scaling laws. We determine analytical expressions for the vapour thickness as a function of temperature and material properties, which are confirmed by numerical solutions. Surprisingly, we show that deformability of the pool suppresses the chimney instability of Leidenfrost drops.

One of the main challenges to overcome to perform nanomechanical Mass Spectrometry (NEMS-MS) analysis in a practical time frame stems from the size mismatch between the analyte beam and the extremely small nanomechanical detector area. We report here the demonstration of NEMS-MS with arrays of 20 individually addressed nanomechanical resonators where the number of inputs-outputs for the whole array is the same as that of a single resonator. While all resonators within an array are interconnected via two metal levels, each resonator is designed with a distinct resonance frequency which becomes its individual address. In order to perform single-particle Mass Spectrometry, the resonance frequencies of the two first modes of each NEMS within an array are monitored simultaneously. Using such an array, mass spectra of metallic aggregates in the MDa range are acquired with more than one order of magnitude improvement in analysis time due to the increase in capture cross section compared to individual resonators. A 20 NEMS array is probed in 150ms with the same mass limit of detection as a single resonator. Spectra acquired with a conventional Time- of-Flight (TOF) mass spectrometer in the same system show excellent agreement. As individual information for each resonator within the array is retained, the array becomes a particle imager, each resonator acting as a pixel. With this technique, we demonstrate how Mass Spectrometry Imaging (MSI) at the single particle level becomes possible by mapping a 4cm-particle beam in the MDa range and above.

We introduce and study renormalization group interfaces between two holographic conformal theories which are related by deformation by a scalar double trace operator. At leading order in the 1/N expansion, we derive expressions for the two point correlation functions of the scalar, as well as the spectrum of operators living on the interface. We also compute the interface contribution to the sphere partition function, which in two dimensions gives the boundary g factor. Checks of our proposal include reproducing the g factor and some defect overlap coefficients of Gaiotto's RG interfaces at large N, and the two-point correlation function whenever conformal perturbation theory is valid., Comment: 59 pages, 2 figures

We show that a volatile liquid drop placed at the surface of a non-volatile liquid pool warmer than the boiling point of the drop can experience a Leidenfrost effect even for vanishingly small superheats. Such an observation points to the importance of the substrate roughness, negligible in the case considered here, in determining the threshold Leidenfrost temperature. A theoretical model based on the one proposed by Sobac et al. [Phys. Rev. E 90, 053011 (2014)] is developed in order to rationalize the experimental data. The shapes of the drop and of the substrate are analyzed. The model notably provides scalings for the vapor film thickness. For small drops, these scalings appear to be identical to the case of a Leidenfrost drop on a solid substrate. For large drops, in contrast, they are different and no evidence of chimney formation has been observed either experimentally or theoretically in the range of drop sizes considered in this study. Concerning the evaporation dynamics, the radius is shown to decrease linearly with time whatever the drop size, which differs from the case of a Leidenfrost drop on a solid substrate. For high superheats, the characteristic lifetime of the drops versus the superheat follows a scaling law that is derived from the model but, at low superheats, it deviates from this scaling by rather saturating.

In this paper we consider entanglement entropies in two-dimensional conformal field theories in the presence of topological interfaces. Tracing over one side of the interface, the leading term of the entropy remains unchanged. The interface however adds a subleading contribution, which can be interpreted as a relative (Kullback-Leibler) entropy with respect to the situation with no defect inserted. Reinterpreting boundaries as topological interfaces of a chiral half of the full theory, we rederive the left/right entanglement entropy in analogy with the interface case. We discuss WZW models and toroidal bosonic theories as examples., Comment: 30 pages, 2 figures. References added, typos corrected

We consider reflection and transmission of interfaces which implement renormalisation group flows between conformal fixed points in two dimensions. Such an RG interface is constructed from the identity defect in the ultraviolet CFT by perturbing the theory on one side of the defect line. We compute reflection and transmission coefficients in perturbation theory to third order in the coupling constant and check our calculations against exact constructions of RG interfaces between coset models., Comment: 24 pages, 1 figure. Minor explanations and some references added, typos corrected

Frequency stability is key to performance of nanoresonators. This stability is thought to reach a limit with the resonator's ability to resolve thermally-induced vibrations. Although measurements and predictions of resonator stability usually disregard fluctuations in the mechanical frequency response, these fluctuations have recently attracted considerable theoretical interest. However, their existence is very difficult to demonstrate experimentally. Here, through a literature review, we show that all studies of frequency stability report values several orders of magnitude larger than the limit imposed by thermomechanical noise. We studied a monocrystalline silicon nanoresonator at room temperature, and found a similar discrepancy. We propose a new method to show this was due to the presence of frequency fluctuations, of unexpected level. The fluctuations were not due to the instrumentation system, or to any other of the known sources investigated. These results challenge our current understanding of frequency fluctuations and call for a change in practices.

During the spreading of a liquid over a solid substrate, the contact line can stay pinned at sharp edges until the contact angle exceeds a critical value. At (or sufficiently near) equilibrium, this is known as Gibbs' criterion. Here, we show both experimentally and theoretically that for completely wetting volatile liquids there also exists a dynamically-produced critical angle for depinning, which increases with the evaporation rate. This suggests that one may introduce a simple modification of the Gibbs' criterion for (de)pinning, that accounts for the non-equilibrium effect of evaporation.

We consider perturbation defects obtained by perturbing a 2D conformal field theory (CFT) by a relevant operator on a half-plane. If the perturbed bulk theory flows to an infrared fixed point described by another CFT, the defect flows to a conformal defect between the ultraviolet and infrared fixed point CFTs. For short bulk renormalization group flows connecting two fixed points which are close in theory space we find a universal perturbative formula for the boundary entropy of the corresponding conformal perturbation defect. We compare the value of the boundary entropy that our formula gives for the flows between nearby Virasoro minimal models Mm with the boundary entropy of the defect constructed by Gaiotto in [1] and find a match at the first two orders in the 1/m expansion., Comment: 24 pages, 2 figures

A drop of water deposited on a cold plate freezes into an ice drop with a pointy tip. While this phenomenon clearly finds its origin in the expansion of water upon freezing, a quantitative description of the tip singularity has remained elusive. Here we demonstrate how the geometry of the freezing front, determined by heat transfer considerations, is crucial for the tip formation. We perform systematic measurements of the angles of the conical tip, and reveal the dynamics of the solidification front in a Hele-Shaw geometry. It is found that the cone angle is independent of substrate temperature and wetting angle, suggesting a universal, self-similar mechanism that does not depend on the rate of solidification. We propose a model for the freezing front and derive resulting tip angles analytically, in good agreement with observations., Comment: Letter format, 5 pages, 3 figures. Note: authors AGM and ORE contributed equally to the paper

We report an ab initio study of the semiconducting Mg2X (with X = Si, Ge) compounds and in particular we analyze the formation energy of the different point defects with the aim to understand the intrinsic doping mechanisms. We find that the formation energy of Mg2Ge is 50 % larger than the one of Mg2Si, in agreement with the experimental tendency. From the study of the stability and the electronic properties of the most stable defects taking into account the growth conditions, we show that the main reason for the n-doping in these materials comes from interstitial magnesium defects. Conversely, since other defects acting like acceptors such as Mg vacancies or multivacancies are more stable in Mg2Ge than in Mg2Si, this explains why Mg2Ge can be of n or p type, contrary to Mg2Si. The finding that the most stable defects are different in Mg2Si and Mg2Ge and depend on the growth conditions is important and must be taken into account in the search of the optimal doping to improve the thermoelectric properties of these materials., Comment: 25 pages, 6 Tables

In this paper we develop further the linear functional method of deriving lower bounds on the boundary entropy of conformal boundary conditions in 1+1 dimensional conformal field theories (CFTs). We show here how to use detailed knowledge of the bulk CFT spectrum. Applying the method to the Monster CFT with c=\bar c=24 we derive a lower bound s > - 3.02 x 10^{-19} on the boundary entropy s=ln g, and find compelling evidence that the optimal bound is s>= 0. We show that all g=1 branes must have the same low-lying boundary spectrum, which matches the spectrum of the known g=1 branes, suggesting that the known examples comprise all possible g=1 branes, and also suggesting that the bound s>= 0 holds not just for critical boundary conditions but for all boundary conditions in the Monster CFT. The same analysis applied to a second bulk CFT -- a certain c=2 Gaussian model -- yields a less strict bound, suggesting that the precise linear functional bound on s for the Monster CFT is exceptional., Comment: 1+18 pages

We present a fluid dynamics video showing the behavior of Leidenfrost droplets composed by a mixture of water and surfactant (SDS, Sodium Dodecyl sulfate). When a droplet is released on a plate heated above a given temperature a thin layer of vapor isolates the droplet from the plate. The droplet levitates over the plate. This is called the Leidenfrost effect. In this work we study the influence of the addition of a surfactant on the Leidenfrost phenomenon. As the droplet evaporates the concentration of SDS rises up to two orders of magnitude over the Critical Micelle Concentration (CMC). An unexpected and violent explosive behavior is observed. The video presents several explosions taken with a high speed camera (IDT-N4 at 30000 fps). All the presented experiments were performed on a plate heated at 300{\deg}C. On the other hand, the initial quantity of SDS was tuned in two ways: (i) by varying the initial concentration of SDS and (ii) by varying the initial size of the droplet. By measuring the volume of the droplet just before the explosion, we were able to estimate the final concentration of SDS. We found that the explosion always occurs around a critical concentration, about 100 times the CMC. The droplets have also been studied just before the explosion. By isolating the droplet on a cold plate just before the explosion, we evidenced the presence of a shell surrounding a liquid core. We conclude that above a critical concentration a solid shell is formed. This leads to an increase of pressure into the droplet until the shell breaks. The release of the pressure is accompanied by a violent explosion, and in some cases foaming., Comment: 1 page, 2 videos included, submission to Gallery of Fluid Motion 2012

This work presents fluid dynamics videos obtained via numerical (CFD) calculations using ComSol (finite elements method) software, showing the evaporation of HFE7100 (3M company refrigerant) into a nitrogen gas flow along the liquid interface. The overall temperature evolution and liquid motion, which is caused by surface-tension (Marangoni) and buoyancy (Rayleigh) instability mechanisms, are shown as well. Flow behavior in the liquid caused by the aforementioned instability mechanisms can be nicely seen. Finally, these observations are made for three liquid thicknesses in order to appreciate the qualitative influence of confinement., Comment: Videos are included

A lower bound is derived for the boundary entropy s = ln g of a 1+1d quantum critical system with boundary, under the conditions that the bulk conformal central charge c is >=1 and the most relevant bulk scaling dimension is >(c-1)/12. This is the first general restriction on the possible values of g for bulk critical systems with c >= 1., Comment: 7 pages, 1 figure, pdflatex

This paper shows the effect of scaling silicon accelerometers down from MEMS to NEMS. It models both electronics and Brownian noise sources for both capacitive and resonant devices, and computes the minimum detectable signal attainable. Computed results are remarkably close to published experimental results. It shows the relatively low influence of the quality factor and of the beam width in the resonant case. Different scaling rules are investigated, and it appears that resonant sensing may satisfy some new application requirements, in particular for critical dimensions below a few hundreds of nm, when it is better resolved than capacitive sensing.

We derive a universal formula for the one-loop renormalization of the effective K\"ahler potential that applies to general supersymmetric effective field theories of chiral multiplets, with arbitrary interactions respecting N=1 supersymmetry in four dimensions. The resulting expression depends only on the tree-level mass spectrum and the form of the regulator. This formula simplifies and generalizes existing results in the literature. We include two examples to illustrate its use., Comment: 16+5 pages