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This paper employs physics-informed neural networks (PINNs) to solve Fisher's equation, a fundamental reaction-diffusion system with both simplicity and significance. The focus is on investigating Fisher's equation under conditions of large reaction rate coefficients, where solutions exhibit steep traveling waves that often present challenges for traditional numerical methods. To address these challenges, a residual weighting scheme is introduced in the network training to mitigate the difficulties associated with standard PINN approaches. Additionally, a specialized network architecture designed to capture traveling wave solutions is explored. The paper also assesses the ability of PINNs to approximate a family of solutions by generalizing across multiple reaction rate coefficients. The proposed method demonstrates high effectiveness in solving Fisher's equation with large reaction rate coefficients and shows promise for meshfree solutions of generalized reaction-diffusion systems., Comment: 15 pages, 6 figures

Flamelet models are widely used in computational fluid dynamics to simulate thermochemical processes in turbulent combustion. These models typically employ memory-expensive lookup tables that are predetermined and represent the combustion process to be simulated. Artificial neural networks (ANNs) offer a deep learning approach that can store this tabular data using a small number of network weights, potentially reducing the memory demands of complex simulations by orders of magnitude. However, ANNs with standard training losses often struggle with underrepresented targets in multivariate regression tasks, e.g., when learning minor species mass fractions as part of lookup tables. This paper seeks to improve the accuracy of an ANN when learning multiple species mass fractions of a hydrogen (\ce{H2}) combustion lookup table. We assess a simple, yet effective loss weight adjustment that outperforms the standard mean-squared error optimization and enables accurate learning of all species mass fractions, even of minor species where the standard optimization completely fails. Furthermore, we find that the loss weight adjustment leads to more balanced gradients in the network training, which explains its effectiveness., Comment: 8 pages. Part of Scientific Computing 2023 Conference Proceedings (ISBN e-Book: 978-3-903318-20-5)

We embarked on a high-resolution optical spectroscopic survey of bright Transiting Exoplanet Survey Satellite (TESS) stars around the Northern Ecliptic Pole (NEP), dubbed the Vatican-Potsdam-NEP (VPNEP) survey. Our NEP coverage comprises 1067 stars, of which 352 are bona fide dwarf stars and 715 are giant stars, all cooler than spectral type F0 and brighter than V=8. m 5. Our aim is to characterize these stars for the benefit of future studies in the community. We analyzed the spectra via comparisons with synthetic spectra. Particular line profiles were analyzed by means of eigen-profiles, equivalent widths, and relative emission-line fluxes (when applicable). Two R=200 000 spectra were obtained for each of the dwarf stars with the Vatican Advanced Technology Telescope (VATT) and the Potsdam Echelle Polarimetric and Spectroscopic Instrument (PEPSI), with typically three R=55 000 spectra obtained for the giant stars with STELLA and the STELLA Echelle Spectrograph (SES). Combined with V-band magnitudes, Gaia eDR3 parallaxes, and isochrones from the Padova and Trieste Stellar Evolutionary Code, the spectra can be used to obtain radial velocities, effective temperatures, gravities, rotational and turbulence broadenings, stellar masses and ages, and abundances for 27 chemical elements, as well as isotope ratios for lithium and carbon, line bisector spans, convective blue-shifts (when feasible), and levels of magnetic activity from H{\alpha}, H{\beta}, and the Ca ii infrared triplet. In this initial paper, we discuss our analysis tools and biases, presenting our first results from a pilot sub-sample of 54 stars (27 bona-fide dwarf stars observed with VATT+PEPSI and 27 bona-fide giant stars observed with STELLA+SES) and making all reduced spectra available to the community.

This paper empirically studies commonly observed training difficulties of Physics-Informed Neural Networks (PINNs) on dynamical systems. Our results indicate that fixed points which are inherent to these systems play a key role in the optimization of the in PINNs embedded physics loss function. We observe that the loss landscape exhibits local optima that are shaped by the presence of fixed points. We find that these local optima contribute to the complexity of the physics loss optimization which can explain common training difficulties and resulting nonphysical predictions. Under certain settings, e.g., initial conditions close to fixed points or long simulations times, we show that those optima can even become better than that of the desired solution., Comment: 22 pages

We employ general arguments and numerical simulations to show that unpaired Majorana zero modes can occur in cores of Abrikosov vortices at the interface between a three-dimensional topological insulator, such as Bi$_2$Se$_3$, and a twisted bilayer of high-$T_c$ cuprate superconductor, such as Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. When the twist angle is close to $45^{\rm o}$ the latter forms a fully gapped topological superconductor up to temperatures approaching its native $T_c\simeq 90$K. Majorana zero modes in these structures will persist up to unprecedented high temperatures and, depending on the quality of the interface, may be protected by gaps with larger magnitudes than other candidate systems., Comment: 4+2 pages, 5 figures. Version 2 (to appear in Phys. Rev. Letters) contains a significant change: edge mode argument replaced by a direct analytical calculation of the vortex core zero mode

Second harmonic generation amplitude and phase measurements are acquired in real time from fused silica:water interfaces that are subjected to ionic strength transitions conducted at pH 5.8. In conjunction with atomistic modeling, we identify correlations between structure in the Stern layer, encoded in the total second-order nonlinear susceptibility, chi(2)tot, and in the diffuse layer, encoded in the product of chi(2)tot and the total interfacial potential, phi(0)tot. chi(2)tot:phi(0)tot correlation plots indicate that the dynamics in the Stern and diffuse layers are decoupled from one another under some conditions (large change in ionic strength), while they change in lockstep under others (smaller change in ionic strength) as the ionic strength in the aqueous bulk solution varies. The quantitative structural and electrostatic information obtained also informs on the molecular origin of hysteresis in ionic strength cycling over fused silica. Atomistic simulations suggest a prominent role of contact ion pairs (as opposed to solvent-separated ion pairs) in the Stern layer. Those simulations also indicate that net water alignment is limited to the first 2 nm from the interface, even at 0 M ionic strength, highlighting water's polarization as an important contributor to nonlinear optical signal generation., Comment: Pe-edited version, 21 pages main text, 6 Figures, Supporting Information available upon request

Physics-informed neural networks (PINNs) have emerged as a promising deep learning method, capable of solving forward and inverse problems governed by differential equations. Despite their recent advance, it is widely acknowledged that PINNs are difficult to train and often require a careful tuning of loss weights when data and physics loss functions are combined by scalarization of a multi-objective (MO) problem. In this paper, we aim to understand how parameters of the physical system, such as characteristic length and time scales, the computational domain, and coefficients of differential equations affect MO optimization and the optimal choice of loss weights. Through a theoretical examination of where these system parameters appear in PINN training, we find that they effectively and individually scale the loss residuals, causing imbalances in MO optimization with certain choices of system parameters. The immediate effects of this are reflected in the apparent Pareto front, which we define as the set of loss values achievable with gradient-based training and visualize accordingly. We empirically verify that loss weights can be used successfully to compensate for the scaling of system parameters, and enable the selection of an optimal solution on the apparent Pareto front that aligns well with the physically valid solution. We further demonstrate that by altering the system parameterization, the apparent Pareto front can shift and exhibit locally convex parts, resulting in a wider range of loss weights for which gradient-based training becomes successful. This work explains the effects of system parameters on MO optimization in PINNs, and highlights the utility of proposed loss weighting schemes., Comment: 11 pages

Non-resonant second harmonic generation phase and amplitude measurements obtained from the silica:water interface at varying pH and 0.5 M ionic strength point to the existence of a nonlinear susceptibility term, which we call chi(3)X, that is associated with a 90 deg phase shift. Including this contribution in a model for the total effective second-order nonlinear susceptibility produces reasonable point estimates for interfacial potentials and second-order nonlinear susceptibilities when chi(3)Xis about 1.5 times chi(3)water. A model without this term and containing only traditional chi(2) and chi(3) terms cannot recapitulate the experimental data. The new model also provides a demonstrated utility for distinguishing apparent differences in the second-order nonlinear susceptibility when the electrolyte is NaCl vs MgSO4, pointing to the possibility of using HD-SHG to investigate ion-specificity in interfacial processes., Comment: Pre-edited version, 16 Pages main text, 4 Figures, Supporting Information

Drive towards improved performance of machine learning models has led to the creation of complex features representing a database of condensed matter systems. The complex features, however, do not offer an intuitive explanation on which physical attributes do improve the performance. The effect of the database on the performance of the trained model is often neglected. In this work we seek to understand in depth the effect that the choice of features and the properties of the database have on a machine learning application. In our experiments, we consider the complex phase space of carbon as a test case, for which we use a set of simple, human understandable and cheaply computable features for the aim of predicting the total energy of the crystal structure. Our study shows that (i) the performance of the machine learning model varies depending on the set of features and the database, (ii) is not transferable to every structure in the phase space and (iii) depends on how well structures are represented in the database., Comment: 18 pages, 11 figures

Parkinson's disease (PD) is the second most common neurodegenerative disease worldwide and affects around 1% of the (60+ years old) elderly population in industrial nations. More than 80% of PD patients suffer from motor symptoms, which could be well addressed if a personalized medication schedule and dosage could be administered to them. However, such personalized medication schedule requires a continuous, objective and precise measurement of motor symptoms experienced by the patients during their regular daily activities. In this work, we propose the use of a wrist-worn smart-watch, which is equipped with 3D motion sensors, for estimating the motor fluctuation severity of PD patients in a free-living environment. We introduce a novel network architecture, a post-training scheme and a custom loss function that accounts for label noise to improve the results of our previous work in this domain and to establish a novel benchmark for nine-level PD motor state estimation., Comment: Machine Learning for Health (ML4H) at NeurIPS 2019 -- Extended Abstract

Majorana zero modes (MZMs), fundamental building blocks for realizing topological quantum computers, can appear at the interface between a superconductor and a topological material. One of the experimental signatures that has been widely pursued to confirm the existence of MZMs is the observation of a large, quantized zero-bias conductance peak (ZBCP) in the differential conductance measurements. In this Letter, we report observation of such a large ZBCP in junction structures of normal metal (titanium/gold Ti/Au) + Dirac semimetal (cadmium arsenide Cd3As2) + conventional superconductor (aluminum Al), with a value close to four times that of the normal state conductance. Our detailed analyses suggest that this large ZBCP is most likely not caused by MZMs. We attribute the ZBCP, instead, to the existence of a supercurrent between two far-separated superconducting Al electrodes, which shows up as a zero-bias peak because of the circuitry and thermal fluctuations of the supercurrent phase, a mechanism conceived by Ivanchenko and Zil'berman more than 50 years ago [JETP 28, 1272 (1969)]. Our results thus call for extreme caution when assigning the origin of a large ZBCP to MZMs in a multiterminal semiconductor or topological insulator/semimetal setup. We thus provide criteria for identifying when the ZBCP is definitely not caused by an MZM. Furthermore, we present several remarkable experimental results of a supercurrent effect occurring over unusually long distances and clean perfect Andreev reflection features., Comment: with Supplemental Material, which includes theoretical modeling, experimental raw data sets used in Figure 3, and data fitting code

Current approaches for electric power generation from nanoscale conducting or semi-conducting layers in contact with moving aqueous droplets are promising as they show efficiencies of around 30 percent, yet, even the most successful ones pose challenges regarding fabrication and scaling. Here, we report stable, all-inorganic single-element structures synthesized in a single step that generate electrical current when alternating salinity gradients flow along its surface in a liquid flow cell. 10 nm to 30 nm thin nanolayers of iron, vanadium, or nickel produce several tens of mV and several microA cm^-2 at aqueous flow velocities of just a few cm s^-1. The principle of operation is strongly sensitive to charge-carrier motion in the thermal oxide nano-overlayer that forms spontaneously in air and then self terminates. Indeed, experiments suggest a role for intra-oxide electron transfer for Fe, V, and Ni nanolayers, as their thermal oxides contain several metal oxidation states, whereas controls using Al or Cr nanolayers, which self-terminate with oxides that are redox inactive under the experimental conditions, exhibit dramatically diminished performance. The nanolayers are shown to generate electrical current in various modes of application with moving liquids, including sliding liquid droplets, salinity gradients in a flowing liquid, and in the oscillatory motion of a liquid without a salinity gradient., Comment: Pre-edited final version, 16 pages main text, 5 figures

Ion specific outcomes at aqueous interfaces remain among the most enigmatic phenomena in interfacial chemistry. Here, charged fused silica/water interfaces have been probed by homodyne- and heterodyne-detected (HD) second harmonic generation (SHG) spectroscopy at pH 7 and pH 5.8 and for concentrations of LiCl, NaCl, NaBr, NaI, KCl, RbCl, and CsCl ranging from 10 mc microM to several 100 mM. For ionic strengths around 0.1 mM to 1 mM, SHG intensities increase reversibly by up to 15% compared to the condition of zero added salt because of optical phase matching and electrical double layer. For ionic strengths above 1 mM, use of any combination of cations and anions produces decreases in SHG response by as much as 50%, trending with ion softness when compared to the condition of zero added salt. Gouy- Chapman model fits to homodyned SHG intensities for the alkali halides studied here show charge densities increase significantly with decreasing cation size. HD-SHG measurements indicate diffuse layer properties probed by the SHG process are invariant with ion identity, while Stern layer properties, as reported by chi(2), are subject to ion specificity for the ions surveyed in this work in the order of chi(2)RbCl = 1/2 chi(2)NaCl = 1/4 chi(2)NaI ., Comment: Pre-edited version, 15 manuscript pages, 2 tables, 5 figures. Supporting Information available up request to the corresponding author

We report ionic strength-dependent phase shifts in second harmonic generation (SHG) signals from charged interfaces that verify a recent model in which dispersion between the fundamental and second harmonic beams modulates observed signal intensities. We show how phase information can be used to unambiguously separate the chi(2) and interfacial potential-dependent chi(3) terms that contribute to the total signal and provide a path to test primitive ion models and mean field theories for the electrical double layer with experiments to which theory must conform. Finally, we demonstrate the new method on supported lipid bilayers and comment on the ability of our new instrument to identify hyper-Rayleigh scattering contributions to common homodyne SHG measurements in reflection geometries., Comment: 21 manuscript pages, four figures, 10 pages supporting information included, pre-edited version

Graphene is a powerful playground for studying a plethora of quantum phenomena. One of the remarkable properties of graphene arises when it is strained in particular geometries and the electrons behave as if they were under the influence of a magnetic field. Previously, these strain-induced pseudomagnetic fields have been explored on the nano- and micrometer-scale using scanning probe and transport measurements. Heteroepitaxial strain, in contrast, is a wafer-scale engineering method. Here, we show that pseudomagnetic fields can be generated in graphene through wafer-scale epitaxial growth. Shallow triangular nanoprisms in the SiC substrate generate strain-induced uniform fields of 41 T. This enables the observation of strain-induced Landau levels at room temperature, as detected by angle-resolved photoemission spectroscopy, and confirmed by model calculations and scanning tunneling microscopy measurements. Our work demonstrates the feasibility of exploiting strain-induced quantum phases in two-dimensional Dirac materials on a wafer-scale platform, opening the field to new applications., Comment: Revised version as published in Science Advances

Atom probe tomography (APT) analysis of chemically pure nanofilms of zero-valent iron (Fe(0), or ZVI) and their thermal oxide nano-overlayers reveals the presence of dendritic iron oxide features that extend from the oxide nano-overlayer surface into the ZVI bulk. The dendrites are observed by APT to be in the 5 nm x 10 nm size range and form quickly under natural atmospheric conditions. Their growth into the ZVI lalyer is, within the limit of our three-month long study, self-limiting (i.e. their initial growth appears to quickly discontinue). The atomistic views presented here shed first light on the atmospheric corrosion process of Fe(0)-bearing engineered nanostructures and their surfaces in the limit of low bulk impurities. Possible roles of the newly identified oxidized iron dendrites are also discussed in the context of passivation processes limiting technological applications of Fe(0)., Comment: Pre-edited version, 14 pages main manuscript text, 7 figures, supporting information

The assessment of Parkinson's disease (PD) poses a significant challenge as it is influenced by various factors which lead to a complex and fluctuating symptom manifestation. Thus, a frequent and objective PD assessment is highly valuable for effective health management of people with Parkinson's disease (PwP). Here, we propose a method for monitoring PwP by stochastically modeling the relationships between their wrist movements during unscripted daily activities and corresponding annotations about clinical displays of movement abnormalities. We approach the estimation of PD motor signs by independently modeling and hierarchically stacking Gaussian process models for three classes of commonly observed movement abnormalities in PwP including tremor, (non-tremulous) bradykinesia, and (non-tremulous) dyskinesia. We use clinically adopted severity measures as annotations for training the models, thus allowing our multi-layer Gaussian process prediction models to estimate not only their presence but also their severities. The experimental validation of our approach demonstrates strong agreement of the model predictions with these PD annotations. Our results show the proposed method produces promising results in objective monitoring of movement abnormalities of PD in the presence of arbitrary and unknown voluntary motions, and makes an important step towards continuous monitoring of PD in the home environment.

Holographic quantum matter exhibits an intriguing connection between quantum black holes and more conventional (albeit strongly interacting) quantum many-body systems. This connection is manifested in the study of their thermodynamics,statistical mechanics and many-body quantum chaos. After explaining some of those connections and their significance, we focus on the most promising example to date of holographic quantum matter, the family of Sachdev-Ye-Kitaev (SYK) models. Those are simple quantum mechanical models that are thought to realize, holographically, quantum black holes. We review and assess various proposals for experimental realizations of the SYK models. Such experimental realization offers the exciting prospect of accessing black hole physics, and thus addressing many mysterious questions in quantum gravity, in tabletop experiments., Comment: 13 pages with 8 figures. Review article solicited by Nature Review Materials

We present high-precision spectro-polarimetric data with high spatial resolution (0.4$''$) of the very quiet Sun at 1.56$\mu$m obtained with the GREGOR telescope to shed some light on this complex magnetism. Half of our observed quiet-Sun region is better explained by magnetic substructure within the resolution element. However, we cannot distinguish whether this substructure comes from gradients of the physical parameters along the line of sight or from horizontal gradients (across the surface). In these pixels, a model with two magnetic components is preferred, and we find two distinct magnetic field populations. The population with the larger filling factor has very weak ($\sim$150 G) horizontal fields similar to those obtained in previous works. We demonstrate that the field vector of this population is not constrained by the observations, given the spatial resolution and polarimetric accuracy of our data. The topology of the other component with the smaller filling factor is constrained by the observations for field strengths above 250 G: we infer hG fields with inclinations and azimuth values compatible with an isotropic distribution. The filling factors are typically below 30\%. We also find that the flux of the two polarities is not balanced. From the other half of the observed quiet-Sun area $\sim$50\% are two-lobed Stokes $V$ profiles, meaning that 23\% of the field of view can be adequately explained with a single constant magnetic field embedded in a non-magnetic atmosphere. The magnetic field vector and filling factor are reliable inferred in only 50\% based on the regular profiles. Therefore, 12\% of the field of view harbour hG fields with filling factors typically below 30\%. At our present spatial resolution, 70\% of the pixels apparently are non-magnetised., Comment: published in A&A

We report vibrational sum frequency generation spectra from supported lipid bilayers in which the OH and the CH stretching signals are probed at different salt concentrations. Atomistic simulations show a negligible impact of salt on the OH stretching spectra, indicating the observed SFG intensity changes are due to chi(3) and potential dependent contributions. These are further analyzed in the contact of exact-zero reference states. Further experiments and simulations identify specific hydrogen bonding interactions between interfacial water molecules at the PC head group of the zwitterionic DMPC lipids at 3200 wavenumbers., Comment: Pre-edited version, 14 Manuscript pages, 5 Figures, 1 Table, 29 pages Supporting Information available upon request

Electrons in clean macroscopic samples of graphene exhibit an astonishing variety of quantum phases when strong perpendicular magnetic field is applied. These include integer and fractional quantum Hall states as well as symmetry broken phases and quantum Hall ferromagnetism. Here we show that mesoscopic graphene flakes in the regime of strong disorder and magnetic field can exhibit another remarkable quantum phase described by holographic duality to an extremal black hole in two dimensional anti-de Sitter space. This phase of matter can be characterized as a maximally chaotic non-Fermi liquid since it is described by a complex fermion version of the Sachdev-Ye-Kitaev model known to possess these remarkable properties., Comment: 5 pages main text plus 4 pages supplement; V2 published version

We explore by means of modeling how absorptive-dispersive mixing between the second- and third-order terms modify the imaginary chi(2)total responses from air/water interfaces under conditions of varying charge densities and ionic strength. To do so, we use published Im(chi(2)) and chi(3) spectra of the neat air/water interface that were obtained either from computations or experiments. We find that the chi(2)total spectral lineshapes corresponding to experimentally measured spectra contain significant contributions from both interfacial chi(2) and bulk chi(3) terms at interfacial charge densities equivalent to less than 0.005% of a monolayer of water molecules, especially in the 3100 wavenumber to 3300 wavenumber frequency region. Additionally, the role of short-range static dipole potentials is examined under conditions mimicking brine. Our results indicate that surface potentials, if indeed present at the air/water interface, manifest themselves spectroscopically in the tightly bonded H-bond network observable in the 3200 wavenumber frequency range., Comment: Pre-edited version, 21 pages, 3 figures, supporting information available upon request

When magnetic field is applied to metals and semimetals quantum oscillations appear as individual Landau levels cross the Fermi level. Quantum oscillations generally do not occur in superconductors (SC) because magnetic field is either expelled from the sample interior or, if strong enough, drives the material into the normal state. In addition, elementary excitations of a superconductor -- Bogoliubov quasiparticles -- do not carry a well defined electric charge and therefore do not couple in a simple way to the applied magnetic field. We predict here that in Weyl superconductors certain types of elastic strain have the ability to induce chiral pseudo-magnetic field which can reorganize the electronic states into Dirac-Landau levels with linear band crossings at low energy. The resulting quantum oscillations in the quasiparticle density of states and thermal conductivity can be experimentally observed under a bending deformation of a thin film Weyl SC and provide new insights into this fascinating family of materials., Comment: Version accepted by PRB, minor changes, references added

Topological phases of fermions in two-dimensions are often characterized by chiral edge states. By definition these propagate in the opposite directions at the two parallel edges when the sample geometry is that of a rectangular strip. We introduce here a model which exhibits what we call "antichiral" edge modes. These propagate in the same direction at both parallel edges of the strip and are compensated by counter-propagating modes that reside in the bulk. General arguments and numerical simulations show that backscattering is suppressed even when strong disorder is present in the system. We propose a feasible experimental realization of a system showing such antichiral edge modes in transition metal dichalcogenide monolayers., Comment: Version to be published in PRL. 7 pages, 5 figures

We investigate the properties of a sunspot light-bridge, focusing on the changes produced by the impact of a plasma blob ejected from a C-class flare. We observed a sunspot in active region NOAA 12544 using spectropolarimetric raster maps of the four Fe I lines around 15655 \AA\ with the GREGOR Infrared Spectrograph (GRIS), narrow-band intensity images sampling the Fe I 6173 \AA\ line with the GREGOR Fabry-P\'erot Interferometer (GFPI), and intensity broad band images in G-band and Ca II H band with the High-resolution Fast Imager (HiFI). All these instruments are located at the GREGOR telescope at the Observatorio del Teide, Tenerife, Spain. The data cover the time before, during, and after the flare event. The analysis is complemented with Atmospheric Imaging Assembly (AIA) and Helioseismic and Magnetic Imager (HMI) data from the Solar Dynamics Observatory (SDO). The physical parameters of the atmosphere at differents heights were inferred using spectral-line inversion techniques. We identify photospheric and chromospheric brightenings, heating events, and changes in the Stokes profiles associated to the flare eruption and the subsequent arrival of the plasma blob to the light bridge, after traveling along an active region loop. The measurements suggest that these phenomena are the result of reconnection events driven by the interaction of the plasma blob with the magnetic field topology of the light bridge., Comment: Accepted for publication in A&A

$Context$. The thermal structure of the penumbra below its visible surface (i.e., $\tau_5 \ge 1$) has important implications for our present understanding of sunspots and their penumbrae: their brightness and energy transport, mode conversion of magneto-acoustic waves, sunspot seismology, and so forth. $Aims$. We aim at determining the thermal stratification in the layers immediately beneath the visible surface of the penumbra: $\tau_5 \in [1,3]$ ($\approx 70-80$ km below the visible continuum-forming layer). $Methods$. We analyzed spectropolarimetric data (i.e., Stokes profiles) in three Fe \textsc{i} lines located at 1565 nm observed with the GRIS instrument attached to the 1.5-meter solar telescope GREGOR. The data are corrected for the smearing effects of wide-angle scattered light and then subjected to an inversion code for the radiative transfer equation in order to retrieve, among others, the temperature as a function of optical depth $T(\tau_5)$. $Results$. We find that the temperature gradient below the visible surface of the penumbra is smaller than in the quiet Sun. This implies that in the region $\tau_5 \ge 1$ the penumbral temperature diverges from that of the quiet Sun. The same result is obtained when focusing only on the thermal structure below the surface of bright penumbral filaments. We interpret these results as evidence of a thick penumbra, whereby the magnetopause is not located near its visible surface. In addition, we find that the temperature gradient in bright penumbral filaments is lower than in granules. This can be explained in terms of the limited expansion of a hot upflow inside a penumbral filament relative to a granular upflow, as magnetic pressure and tension forces from the surrounding penumbral magnetic field hinder an expansion like this., Comment: 5 pages; 2 figures; accepted for publication in Astronomy and Astrophysics Letters

Second-order nonlinear spectroscopy has proven to be a powerful tool in elucidating key chemical and structural characteristics at a variety of interfaces. However, the presence of interfacial potentials may lead to complications regarding the interpretation of second harmonic and vibrational sum frequency generation responses from charged interfaces due to mixing of absorptive and dispersive contributions. Here, we examine by means of mathematical modeling how this interaction influences second-order spectral lineshapes. We discuss our findings in the context of reported nonlinear optical spectra obtained from charged water/air and solid/liquid interfaces and demonstrate the importance of accounting for the interfacial potential-dependent \c{hi}(3) term in interpreting lineshapes when seeking molecular information from charged interfaces using second-order spectroscopy., Comment: Pre-edited final accepted version, 24 Pages, 6 Figures, Supplementary Data 1-7 available upon request to geigerf@chem.northwestern.edu