The Tulip in the Swan

We present a detailed study of the local atomic and magnetic structure of the type-I multiferroic perovskite system (Sr,Ba) (Mn,Ti) O₃ using x-ray and neutron pair distribution function (PDF) analysis, polarized neutron scattering, and muon spin relaxation (μSR) techniques. The atomic PDF analysis reveals widespread nanoscale tetragonal distortions of the crystal structure even in the paraelectric phase with average cubic symmetry, corresponding to incipient ferroelectricity in the local structure. Magnetic PDF analysis, polarized neutron scattering, and μSR likewise confirm the presence of short-range antiferromagnetic correlations in the paramagnetic state, which grow in magnitude as the temperature approaches the magnetic transition. We show that these short-range magnetic correlations coincide with a reduction of the tetragonal (i.e., ferroelectric) distortion in the average structure, suggesting that short-range magnetism can play an important role in magnetoelectric and/or magnetostructural phenomena even without genuine long-range magnetic order. The reduction of the tetragonal distortion scales linearly with the local magnetic order parameter, pointing to spontaneous linear magnetoelectric coupling in this system. These findings provide greater insight into the multiferroic properties of (Sr,Ba) (Mn,Ti) O₃ and demonstrate the importance of investigating the local atomic and magnetic structure to gain a deeper understanding of the intertwined degrees of freedom in multiferroics.

Bifurcation phenomena are common in multidimensional multiparameter dynamical systems. Normal form theory suggests that bifurcations are driven by relatively few combinations of parameters. Models of complex systems, however, rarely appear in normal form, and bifurcations are controlled by nonlinear combinations of the bare parameters of differential equations. Discovering reparameterizations to transform complex equations into a normal form is often very difficult, and the reparameterization may not even exist in a closed form. Here we show that information geometry and sloppy model analysis using the Fisher information matrix can be used to identify the combination of parameters that control bifurcations. By considering observations on increasingly long timescales, we find those parameters that rapidly characterize the system's topological inhomogeneities, whether the system is in normal form or not. We anticipate that this novel analytical method, which we call time-widening information geometry (TWIG), will be useful in applied network analysis.

Bifurcation phenomena are common in multidimensional multiparameter dynamical systems. Normal form theory suggests that bifurcations are driven by relatively few combinations of parameters. Models of complex systems, however, rarely appear in normal form, and bifurcations are controlled by nonlinear combinations of the bare parameters of differential equations. Discovering reparameterizations to transform complex equations into a normal form is often very difficult, and the reparameterization may not even exist in a closed form. Here we show that information geometry and sloppy model analysis using the Fisher information matrix can be used to identify the combination of parameters that control bifurcations. By considering observations on increasingly long timescales, we find those parameters that rapidly characterize the system's topological inhomogeneities, whether the system is in normal form or not. We anticipate that this novel analytical method, which we call time-widening information geometry (TWIG), will be useful in applied network analysis.

Accurate interatomic energies and forces enable high-quality molecular dynamics simulations, torsion scans, potential energy surface mappings, and geometry optimizations. Machine learning algorithms have enabled rapid estimates of the energies and forces with high accuracy. Further development of machine learning algorithms holds promise for producing universal potentials that support many different atomic species. We present the Transformer Interatomic Potential (TrIP): a chemically sound potential based on the SE(3)-Transformer. TrIP’s species-agnostic architecture, which uses continuous atomic representation and homogeneous graph convolutions, encourages parameter sharing between atomic species for more general representations of chemical environments, maintains a reasonable number of parameters, serves as a form of regularization, and is a step toward accurate universal interatomic potentials. TrIP achieves state-of-the-art accuracies on the COMP6 benchmark with an energy prediction of just 1.02 kcal/mol MAE. We introduce physical bias in the form of Ziegler–Biersack–Littmark-screened nuclear repulsion and constrained atomization energies. An energy scan of a water molecule demonstrates that these changes improve long- and near-range interactions compared to other neural network potentials. TrIP also demonstrates stability in molecular dynamics simulations, demonstrating reasonable exploration of Ramachandran space.

Theoretical models based on spherical geometries have long provided essential insights into the directional behavior of sound sources such as loudspeakers and human speech. Because commonly applied models predict omnidirectional radiation at low frequencies and increasing directionality at higher frequencies, they fail to predict the directional characteristics of certain sources with different source geometries. These sources include violins and open-back guitar amplifiers that have openings or ports connecting a cavity or enclosure to the exterior domain. This work presents the low-frequency radiation from a vibrating cap on a rigid spherical shell with a circular aperture to study the directional characteristics of such sources. The proposed model predicts dipolar radiation at very low frequencies, monopolar radiation near the Helmholtz resonance, and increasing directionality at higher frequencies. Experimental results based on measuring the sound field of an open-back spherical loudspeaker validate the theoretical model and highlight its utility in predicting directional behavior.

Aims. The origin and maintenance of spiral structure in galaxies, the correlation between different types of spiral structure and several proposed mechanisms for their generation, and the evolution of spiral arms of galaxies with time are questions that are still controversial. In this note we study the spiral structure in a sample of distant galaxies in order to infer the evolution of spiral arm characteristics with redshift.

Methods. We considered a sample of 171 face-on spiral galaxies in the Hubble Space Telescope COSMOS (The Cosmic Evolution Survey) field. The galaxies are distributed up to z approximate to 1 with a mean value of 0.44. For all galaxies, we determined the pitch angles of the spiral arms and analysed their dependence on redshift; a total of 359 arms were measured.

Results. Analyses of our measurements combined with the literature data suggest a possible evolution of the pitch angles of spiral galaxies: by the modern epoch the spiral pattern, on average, becomes more tightly wound. This may be a consequence of the general evolution of the structure of galaxies as galaxies become more massive over time and their bulges grow. In addition, the distribution of the cotangent of pitch angle of galaxies indicates the possibility that the dominant mechanism of spiral pattern generation changes over time.