Choice Of Potential Research Articles

Determination of the Ion—Solid Interaction Potential from the Experiment and Its Influence on the Profiles of Implanted Particles

Based on the analysis of the angular distributions of particles passing through thin gold films, the parameters of the potential that best describes the experiment are obtained. The resulting potential differs from the potential describing collisions in the gaseous phase by a noticeable change in the screening constant. The influence of the collision energy, the choice of potential, and the model of electron bremsstrahlung on the depth distribution of implanted particles is analyzed.

Two particles in one-dimensional confinement: the role of mass imbalance and Pauli's exclusion principle within short and long range interactions

Abstract We consider the problem of two interacting particles in one-dimensional harmonic confinement. By considering both particles are subject to the same harmonic curvature, we obtain exact numerical solutions in a straightforward way for any choice of interaction potential. The formulation is then applied in the situations of ({\it i}) non-identical particles with different masses $m_1$ and $m_2$; ({\it ii}) bosons and fermions; ({\it iii}) short and long range interactions; and ({\it iv}) combining all these ingredients within a time-dependent applied electric field. We analyze the role of the mass imbalance and Pauli's exclusion principle by investigating the formation of bound pairs, the expected value of the separation between the particles and the effects of interaction and exclusion principle on the density distributions.

Crossover in densities of confined particles with finite range of interaction

We study a one-dimensional classical system of N particles confined within a harmonic trap. Interactions among these particles are dictated by a pairwise potential V(x), where x is the separation between two particles. Each particle can interact with a maximum of d neighbouring particles on either side (left or right), if available. By adjusting the parameter d, the system can be made nearest neighbour (d=1) to all-to-all (d=N−1) interacting. As suggested by prior studies, the equilibrium density profile of these particles is expected to undergo shape variations as d is changed. In this paper, we investigate this crossover by tuning the parameter f(=d/N) from 1 to 0 in the large N limit for two distinct choices of interaction potentials, V(x)=−|x| and V(x)=−log⁡(|x|) which correspond to 1d one-component plasma and the log-gas model, respectively. For both models, the system size scaling of the density profile for fixed f turns out to be the same as in their respective all-to-all case. However, the scaling function exhibits diverse shapes as f varies. We explicitly compute the average density profile for any f∈(0,1] in the 1d plasma model, while for the log-gas model, we provide approximate calculations for large (close to 1) and small (close to 0) f. Additionally, we present simulation results to numerically demonstrate the crossover and compare these findings with our theoretical results.

Further investigation on the fusion of 6Li with 209Bi target at near-barrier energies

Abstract The complete and incomplete fusion cross sections for 6Li+209Bi were measured via the in-beam γ-ray method around the Coulomb barrier. The cross sections of (deuteron captured) incomplete fusion (ICF) products were re-quantified experimentally for this reaction system. The results reveal that the ICF cross section is equivalent to that of complete fusion (CF) above the Coulomb barrier and dominant near or below the barrier. A theoretical calculation based on the Continuum Discretized Coupled Channel (CDCC) method is performed for the aforementioned CF and ICF cross sections, and the result is consistent with the experimental ones. The universal fusion function (UFF) is also compared with the measured CF cross section with different barrier parameters, demonstrating that the CF suppression factor is quite sensitive to the choice of potential, which can reflect both dynamic and static effects of breakup on the fusion process.

Short review of the main achievements of the scalar field, fuzzy, ultralight, wave, BEC dark matter model

The Scalar Field Dark Matter model has been known in various ways throughout its history; Fuzzy, BEC, Wave, Ultralight, Axion-like Dark Matter, etc. All of them consist in proposing that dark matter of the universe is a spinless field Φ that follows the Klein-Gordon (KG) equation of motion □Φ −dV/dΦ = 0, for a given scalar field potentialV. The difference between different models is sometimes the choice of the scalar field potentialV. In the literature we find that people usually work in the non-relativistic, weak-field limit of the Klein-Gordon equation, where it transforms into the Schrödinger equation and the Einstein equations into the Poisson equation, reducing the KG-Einstein system, to the Schrödinger-Poisson system. In this paper, we review some of the most interesting achievements of this model from the historical point of view and its comparison with observations, showing that this model could be the last answer to the question about the nature of dark matter in the universe.

Reconstructing Modified and Alternative Theories of Gravity

A viable radiation-dominated era in the early universe is best described by the standard (FLRW) model of cosmology. In this short review, we demonstrate reconstruction of the forms of F(R) in the modified theory of gravity and the metric compatible F(T) together with the symmetric F(Q) in alternative teleparallel theories of gravity, from different perspectives, primarily rendering emphasis on a viable FLRW radiation era. Inflation has also been studied for a particular choice of the scalar potential. The inflationary parameters are found to agree appreciably with the recently released observational data.

Interactions between adsorbed hydrogen and water molecules on a polycrystalline Pt electrode studied by in-situ ATR-FTIR spectroscopy

In order to gain further insight into the interactions between hydrogen adsorbed on platinum and water in an acid electrolyte, in situ infrared spectra were examined in detail. A polycrystalline Pt electrode/sulfuric acid solution interphase was observed by in-situ attenuated total reflectance (ATR) FTIR spectroscopy in the potential region between the double layer and hydrogen evolution by use of the potential difference method. The background potential in the measurements was chosen first at 0.7 V vs. RHE to examine the effect of underpotentially deposited hydrogen (HUPD) adsorption on the interfacial water spectra. Analysis of the spectra revealed two well-defined HOH bending bands, a sharp one at 1620 cm−1 and a broad one at 1700 cm−1. The intensity of the 1620 cm−1 band was found to increase linearly with increasing coverage of HUPD determined by the cyclic voltammogram (CV) corrected for the HER current. This led to an assignment to water molecules co-adsorbed with HUPD with only weak interactions with the latter and between each other. The broad band at 1700 cm−1 was assigned to the HOH bending mode of water associated with hydronium ions. Its intensity was found to increase at lower potentials due to its electrostatic attraction to the increasingly negative surface charge. An intense, broad, negative-going band around 2970 cm−1 was found to develop below 0.4 V, which is assigned to water dimers adsorbed at on-top Pt sites in the double layer potential region and desorbed upon adsorption of HUPD. A new choice of the reference potential at 0.2 V was successful in detecting a distinct OH stretching band around 3580 cm−1, which developed in close correlation with the band assigned to overpotentially deposited hydrogen (HOPD) at ca. 2080 cm−1. The band was assigned to the asymmetric OH stretching mode of water molecules hydrogen-bonded with HOPD. Its band intensity was found to increase linearly with that of HOPD with a slope close to 1.0, which suggests a highly polar nature of the Pt-HOPD bond.

Systematic First-Principles Calculations of Ce3+-Dopant in Garnet-Type Oxide Phosphors

A study of Ce3+-doped oxide phosphors was performed using first-principles calculations based on the relativistic DV-Xα method. In particular, we focused on the Ce3+-doped garnet-type oxides, which have potential applications in solid-state lighting and display devices. The electronic structure and optical properties of the phosphors were analyzed. The energy levels of the Ce3+ ions were affected by the coordination number and the crystal field strength of the surrounding oxygen ions. In addition, the crystal structure of the material had a significant impact on the energy levels of the Ce3+ ions, with different crystal structures leading to different energy levels.The Ce3+ ion is substitutionally incorporated in the garnet lattice, and the 4f electron of Ce3+ plays an important role in the luminescence of the material. The emission wavelengths of the 5d-4f transition energy of Ce3+ can be tailored by varying the crystal structure and the composition. The 5d orbitals of Ce3+ are substantially affected by the crystal field splitting while the amplitude of crystal field splitting (εcfs) is caused by many parameters: coordination number, symmetry of Ce3+ site, and bond lengths between the Ce3+ ion and the oxygen ions (O2-). This study incorporated the following computational conditions: i) lattice relaxation, ii) the choice of the exchange-correlation potential, and iii) Slater’s transition state method. The effects of these conditions were analyzed. In addition, the correlations among physical properties and electronic structure parameters were also investigated in detail.The first-principles calculation results were compared to the experimental data to validate the accuracy of the theoretical models, which showed a good agreement between the experimental and predicted values.

(Invited) Why and How Should the PEMFCs be Recycled? – Focus on the MEA Case

Proton-Exchange Membrane Fuel Cells (PEMFCs) are electrochemical devices with potential applications in mobility and stationary energy storage. Last decades have seen a growing interest in the research, the development and the small-scale industrialization of PEMFC. However, PEMFC requires Pt as catalyst for both electrochemical reactions.From the geological point of view, Pt is a scarce element, while between 7 to 12 t of mineral must be extracted to obtain 31.1 g of Pt. Moreover, Pt is considered as a critical raw material by the E.U. with a high supply shortage/breakdown risk.1 The recycling might be a feasible way how to face the current and future supply issues and to secure the access to resources.Although there are currently no legal obligation regarding the PEMFCs recycling, it is highly probable that regulations close to those already existing for batteries will be soon applied, implementing mandatory collection and recycling targets for spent PEMFCs. Finally, this might also be a way to decrease the costs and the environmental impacts of the PEMFCs’ sector as the use of Pt affects both its cost and is considered as a burden from the environmental point of view.2,3 Recycling it might be a feasible option to counteract these issues in a comparable manner to (i) an increase of the Pt catalyst durability, (ii) a decrease of its loading and (iii) its substitution by less noble metals. While the three latter pathways are already widely studied by different research teams, the recycling option has not attracted, up to now, significant attention and will be the scope of this presentation.Two different recycling approaches might be used to recover Pt. Pyrometallurgy is based on thermal treatment of metals, namely their reduction and smelting, while hydrometallurgy is a chemical approach consisting in metals dissolution and further purification. Each of them has its own pros and cons, whereas both approaches can be combined. Both have also been exploited for MEA recycling.Within our research group hydrometallurgical approach has been applied to MEA recycling. This approach is traditionally composed of several successive steps: pretreatment (including shredding and grinding), leaching, separation and purification followed by the final recovery. We have progressively exploited several manners to dissolve platinum. The Pt/C catalyst might be dissolved at room temperature by combining appropriate concentrations of oxidizing and complexing agents. We have namely achieved very high leaching yield when using either H2O2 (3%) and HNO3 (5%) as oxidizer diluted in concentrated HCl playing the role of the complexing agent.4 We have further demonstrated that electro-assisted leaching of Pt might also be feasible if an appropriate electrolyte is combined to the appropriate choice of oxidation and reduction potential that are applied alternatively.Once the Pt is dissolved its purification might be carried out via ion exchange or solvent extraction.4 These operations might also be feasible for its separation from Co in case of Pt3Co alloys presence in the spent MEAs.5,6 Finally, the recovery of Pt might be carried out by precipitation or Pt/C catalyst might be synthetized in a closed-loop manner.5 Two different approaches have been attempted within our research team and both of them have provided a catalyst which exhibited similar performance to a reference Pt/C catalyst in a single-cell PEMFC.5 Moreover, the environmental benefits of the recycling process have been assessed using the LCA methodology.5,7 The results show that primary platinum production remains the most impacting stage, even when MEA recycling is considered. Moreover, the assessment reveals that the MEA life-cycle impacts can be reduced significantly if electrodes recycling is carried out, while the main impact categories decrease is proportional to the platinum recycling rate.References1 European Commission, Study on the Critical Raw Materials for the EU 2023 - Final Report, 2023.2 M. Miotti, J. Hofer and C. Bauer, Int. J. Life Cycle Assess., 2017, 22, 94–110.3 A. Simons and C. Bauer, Appl. Energy, 2015, 157, 884–896.4 L. Duclos, L. Svecova, V. Laforest, G. Mandil and P.-X. Thivel, Hydrometallurgy, 2016, 160, 79–89.5 L. Duclos, R. Chattot, L. Dubau, P. X. Thivel, G. Mandil, V. Laforest, M. Bolloli, R. Vincent and L. Svecova, Green Chem., 2020, 22, 1919–1933.6 M. Gras, L. Duclos, N. Schaeffer, V. Mogilireddy, L. Svecova, Eric Chaînet, I. Billard and N. Papaiconomou, ACS Sustain. Chem. Eng., 2020, 8, 15865–15874.7 L. Duclos, M. Lupsea, G. Mandil, L. Svecova, P.-X. Thivel and V. Laforest, J. Clean. Prod., 2017, 142, 2618–2628.

Corrosion Behavior of Binary Ni-Cr Alloys in Molten FLiNaK Salts at Different Electrochemical Potentials

The development of molten salt reactors (MSRs) is a collaborative effort among academia, government laboratories, and industry, with the aim of realizing the potential of clean nuclear energy. However, the corrosion of structural alloys presents a significant engineering challenge in this application. Addressing this issue requires investment not only in testing and characterizing candidate alloys, but also in developing a scientific framework to understand the fundamental mechanisms governing the corrosion of metallic materials in molten fluorides which can then guide alloy design [1].In this work, the corrosion behavior of binary Ni-Cr alloys (5-20 wt.% Cr) in molten LiF-NaF-KF (or FLiNaK) salts between 550oC and 750oC was interrogated using electrochemical methods coupled with thermo-kinetic analysis. Electrochemical techniques, including linear sweep voltammetry, electrochemical impedance spectroscopy (EIS) and chronoamperometry, were utilized to elucidate the rate-limiting kinetic factors and to identify the dependence of corrosion morphology on applied potential. Additionally, Ni-Cr alloys were also immersed 99.9% pure FLiNaK salts with a known oxidizer concentration (e.g., 0.1-5 wt.% EuF3) coupled with open-circuit potential measurement to provide a time-based description of morphological evolution in the case of a dynamically changing electrode potential. These results are corroborated by examination of the post-corrosion morphology using scanning electron microscopy (SEM), transmission electron microscopy (TEM), and electron backscatter diffraction (EBSD) techniques as well as salt composition analysis using inductively coupled plasma mass spectrometry (ICP-MS), X-ray diffraction (XRD) and in situ cyclic voltammetry.The systematic choice of potential revealed multiple potential regimes in which Ni-Cr alloys exhibit distinctly different corrosion morphologies. At intermediate potentials, a porous bicontinuous structure is formed by dealloying of the less noble element (Cr) and percolation into the Ni-rich alloy within grains and along grain boundaries. At other potentials, charge transfer control dissolution of both Cr and Ni leads to the formation of a crystallographic faceted structure. The morphological differences suggest the presence of multiple corrosion processes in Ni-Cr in FLiNaK controlled by either transport or interfacial reaction. These findings can be explained through electrochemical processes at the alloy-salt interface, as well as the roles of surface, grain boundary and bulk diffusion kinetics involving the alloying constituents. Furthermore, the effect of radiation damage on Ni20Cr alloys on these rate-limiting corrosion regimes will be investigated. Acknowledgment Research is primarily supported as part of the fundamental understanding of transport under reactor extremes (FUTURE), an Energy Frontier Research Center (EFRC) funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES).[1] Chan, H.L., et al. Npj Materials Degradation 6(1), 46 (2022).

Effective field theory analysis of the Coulomb breakup of the one-neutron halo nucleus 19\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{19}$$\\end{document}C

We analyse the Coulomb breakup of 19\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{19}$$\\end{document}C measured at 67A MeV at RIKEN. We use the Coulomb-Corrected Eikonal (CCE) approximation to model the reaction and describe the one-neutron halo nucleus 19\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{19}$$\\end{document}C within Halo Effective Field Theory (Halo EFT). At leading order we obtain a fair reproduction of the measured cross section as a function of energy and angle. The description is insensitive to the choice of optical potential, as long as it accurately represents the size of 18\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{18}$$\\end{document}C. It is also insensitive to the interior of the 19\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{19}$$\\end{document}C wave function. Comparison between theory and experiment thus enables us to infer asymptotic properties of the ground state of 19\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{19}$$\\end{document}C: these data put constraints on the one-neutron separation energy of this nucleus and, for a given binding energy, can be used to extract an asymptotic normalisation coefficient (ANC). These results are confirmed by CCE calculations employing next-to-leading order Halo EFT descriptions of 19\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{19}$$\\end{document}C: at this order the results for the Coulomb breakup cross section are completely insensitive to the choice of the regulator. Accordingly, this reaction can be used to constrain the one-neutron separation energy and ANC of 19\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{19}$$\\end{document}C.

Effect of electric potential on the structure and yield of graphene oxide using electrochemical exfoliation method

Optimization of the electrochemical exfoliation of graphene oxide synthesis was investigated in this report using varying potentials. Graphite from waste lithium-ion batteries was used as the electrodes for the DC (direct current) electrochemical set-up. Electric potentials of 7.5 V, 12 V, and 15 V were applied for 225 minutes using 0.2M H2SO4 as the electrolyte. The characterization of the produced graphene oxide was done using Raman spectroscopy, high-resolution scanning electron microscopy (HRSEM), and energy dispersive x-ray spectroscopy (EDS) attached to the scanning electron microscope (SEM). The results obtained showed that both the rate of graphene oxide yield and the C/O ratio increased correspondingly with the increase in electric potential. However, the structure of graphene oxide produced at 7.5 V was of superior quality compared to others produced at higher potentials with regards to the crystallite lattice characteristics such as defects, lateral dimensions, thickness, and the number of graphene layers. Consequently, tailor-made graphene oxide properties (and yield) for target applications may be achieved using the electrochemical exfoliation method via the choice of the electric potential.

Quantized Berry winding from an emergent $\mathcal{PT}$ symmetry

Linear crossings of energy bands occur in a wide variety of materials. In this paper we address the question of the quantization of the Berry winding characterizing the topology of these crossings in dimension D=2D=2. Based on the historical example of 22-bands crossing occuring in graphene, we propose to relate these Berry windings to the topological Chern number within a D=3D=3 dimensional extension of these crossings. This dimensional embedding is obtained through a choice of a gap-opening potential. We show that the presence of an (emergent) \mathcal{PT}𝒫𝒯 symmetry, local in momentum and antiunitary, allows the quantization of the Berry windings as multiples of \piπ. We illustrate this quantization mechanism on a variety of three-band crossings.

Theoretical and observational prescription of warm-inflation in FLRW universe with torsion

The paper deals with Warm Inflationary scenario in FLRW with torsion both from theoretical and observational point of view. In the background of flat FLRW model the Hubble parameter is found to be proportional to the torsion function and warm inflation is examined both in weak and strong dissipation regimes for the power law choice of potential using slow-roll approximation with quasi-stable criteria for radiation. The slow-roll parameters, no.of e-folds, scalar spectral index, and tensor-to-scalar ratio are determined in the present model for mainly three choices of the dissipation coefficient Gamma using the Planck data set. Finally, we focus on single-field chaotic quartic potential with the above choices of the dissipation coefficient to confront the warm inflation observational predictions directly with the latest observational data set.

Anisotropic diffusion of radiation-induced self-interstitial clusters in HCP zirconium: A molecular dynamics and rate-theory assessment

Under irradiation, Zr and Zr alloys undergo growth in the absence of applied stress. This phenomenon is thought to be associated with the anisotropy of diffusion of either or both radiation-induced point defects and defect clusters. In this work, molecular dynamic simulations are used to study the anisotropy of diffusion of self-interstitial atom clusters. Both near-equilibrium clusters generated by aggregation of self-interstitial atoms and cascade-induced clusters were considered. The cascade-induced clusters display more anisotropy than their counterparts produced by aggregation. In addition to 1-dimensional diffusing clusters, 2-dimensional diffusing clusters were observed. Using our molecular dynamic simulations, the input parameters for the “self-interstitial atom cluster bias” rate-theory model were estimated. The radiation-induced growth strains predicted using this model are largely consistent with experiments, but are highly sensitive to the choice of interatomic interaction potential.

Stream Fanning and Bifurcations: Observable Signatures of Resonances in Stellar Stream Morphology

Recent observations have revealed a trove of unexpected morphological features in many of the Milky Way’s stellar streams. Explanations for such features include time-dependent deformations of the Galactic gravitational potential, local disruptions induced by dark matter substructure, and special configurations of the streams’ progenitors. In this paper, we study how these morphologies can also arise in certain static, nonspherical gravitational potentials that host a subset of resonantly trapped orbit families. The transitions, or separatrices, between these orbit families mark abrupt discontinuities in the orbital structure of the potential. We develop a novel numerical approach for measuring the libration frequencies of resonant and near-resonant orbits and apply it to study the evolution of stellar streams on these orbits. We reveal two distinct morphological features that arise in streams on near-resonant orbits: fans, which come about due to a large spread in the libration frequencies near a separatrix, and bifurcations, which arise when a separatrix splits the orbital distribution of the stellar stream between two (or more) distinct orbit families. We demonstrate that these effects can arise in some Milky Way streams for certain choices of the dark matter halo potential and discuss how this might be used to probe and constrain the global shape of the Milky Way’s gravitational potential.

Role of preferential hydration on diffusiophoresis of globular proteins

Diffusiophoresis is the migration of a colloidal particle through a fluid, caused by a cosolute concentration gradient. Preferential hydration is a thermodynamic phenomenon responsible for particle diffusiophoresis from high to low cosolute concentration in water. Here, steady-state Navier-Stokes equation for incompressible fluids, with particle modeled as an inpenetrable rigid sphere, is employed for deriving a mathematical expression of the diffusiophoresis coefficient. Mean-force potentials with arbitrary interaction range but with interaction energies small or comparable with thermal energy are employed to describe water-mediated particle-cosolute interactions. This choice of potential is movitated by previous work showing that only fluid particles weakly interacting with the colloildal particle can cause diffusiophoresis. Preferential hydration has been extensively investigated for proteins. Thus, the proposed model is applied to available experimental diffusiophoresis coefficients of lysozyme in aqueous NaCl and KCl at pH 4.5 and 25 °C. This analysis also includes data on salt osmotic diffusion, describing salt diffusion caused by protein concentration gradients. The preferential-hydration contribution of experimental lysozyme diffusiophoresis is obtained after removing electrophoretic diffusiophoresis. Examination of these experimental data shows that the mean-force potential describing preferential hydration is indeed weak, with an interaction range that is an appreciable fraction of particle size.

Integrability in the Chiral Model of Magic Angles

Magic angles in the chiral model of twisted bilayer graphene are parameters for which the chiral version of the Bistritzer–MacDonald Hamiltonian exhibits a flat band at energy zero. We compute the sums over powers of (complex) magic angles and use that to show that the set of magic angles is infinite. We also provide a new proof of the existence of the first real magic angle, showing also that the corresponding flat band has minimal multiplicity for the simplest possible choice of potentials satisfying all symmetries. These results indicate (though do not prove) a hidden integrability of the chiral model.

Geometrothermodynamic Cosmology.

We review the main aspects of geometrothermodynamics, a formalism that uses contact geometry and Riemannian geometry to describe the properties of thermodynamic systems. We show how to handle in a geometric way the invariance of classical thermodynamics with respect to Legendre transformations, which means that the properties of the systems do not depend on the choice of the thermodynamic potential. Moreover, we show that, in geometrothermodynamics, it is possible to apply a variational principle to generate thermodynamic fundamental equations, which can be used in the context of relativistic cosmology to generate cosmological models. As a particular example, we consider a fundamental equation that relates the entropy with the internal energy and the volume of the Universe, and construct cosmological models with arbitrary parameters, which can be fixed to reproduce the main aspects of the inflationary era and the standard cosmological paradigm.

Dynamical Compactification with Matter

In this work, we study cosmological solutions of the 8-dimensional Einstein Yang-Mills theory coupled to a perfect-fluid matter. A Yang-Mills instanton of extra dimensions causes a 4-dimensional expanding universe with dynamical compactification of the extra dimensions. To construct physically reliable situations, we impose the null energy condition on the matter. This energy condition is affected by the extra dimensions. Then, we consider cosmological constant to grasp the structure of the solution space. Even in this simple case, we find several interesting solutions, such as bouncing universes and oscillatory solutions, eventually arriving at a de Sitter universe with stabilized compact dimensions. In addition, we consider a class of matters whose energy density depends on the volume of the extra dimensions. This case shows another set of bouncing universes. Also, a real scalar with potential is taken into account. The scalar field model admits de Sitter solutions due to the choice of potential, and we demonstrate how potentials can be constructed using flow equations. Thus, what we discuss in this work is based on the 8-dimensional Einstein frame, which corresponds to the 4-dimensional Jordan frame by dimensional reduction. Consequently, the results are derived in the 4-dimensional Jordan frame, not in the 4-dimensional Einstein frame.