Marcus Aguiar (UNICAMP): Generalized frustration in multi-dimensional Kuramoto models

Synchronization is a phenomenon found in many natural and artificial systems, from fireflies and pacemaker cells in the heart to metronomes and power grids. The model developed by Kuramoto became a paradigm in the field and has been studied and modified in many ways. One recent extension has generalized the model to more dimensions, where particles are allowed to move on the surface of spheres and are represented by unit vectors. In this talk I will argue that, in this setup, the coupling constant can be naturally extended to a coupling matrix acting on the vectors. The matrix breaks the rotational symmetry and results in a kind of generalized frustration that includes the Kuramoto-Sakaguchi model. I will show analytical results for identical oscillators in arbitrary dimensions and for Lorentz distributed oscillators in D=2.

Hilda Cerdeira (ICTP-SAIFR/IFT-UNESP): Phase Transitions in Swarmalators

Systems of oscillators called Swarmalators, whose phase and spatial dynamics are coupled, have been used to describe the dynamics of some living systems. Their collective behavior presents simultaneous aggregation in space and synchronization in phase which in turn leads in some cases to explosive synchronization in a finite population as a function of the coupling parameter between the phases of the internal dynamics. This phenomenon is described using the order parameter and the Hamiltonian formalism. Near the synchronization transition the internal phases of the particles are represented by the XY model, and their transition to synchronization, which will be discussed, can be of the first or second order. We shall also discuss a multilayer system of swarmalators, which presents some interesting phases on their way to synchronization.

Pablo de Castro (ICTP-SAIFR/IFT-UNESP): Random searches with chemotaxis: Optimal strategy transitions induced by target scent

We investigate the optimal movement strategy in random searches, such as animal foraging, assisted by chemotaxis. To do that, we introduce a minimalist one-dimensional model of Lévy walkers in the presence of both a near and a far target. Each target produces a stationary concentration of scent molecules, exponentially decaying with distance. The decay or spread length of the scent depends on the diffusivity of its molecules. In the model, the scent concentration gradient is used by the searcher to increase its probability of choosing the near-target direction. Without scent, by employing very long steps in the far-target direction, finding a target is guaranteed, but at the cost of a long walk. Conversely, by employing very small steps, the searcher may get stuck in between targets for a long time. The optimal strategy corresponds to a certain superdiffusive balance between short and long steps. At intermediate scent spread length, however, the scent becomes so important that a discontinuous strategy transition occurs, over which the optimal step-length strategy becomes completely Brownian since longer steps would risk placing the searcher too far from where the scent is useful. At an even higher scent spread length, a second discontinuous transition occurs, now “backwards”: the scent profile becomes so flat that, despite far reaching, it cannot be useful. Our results shine a light on how the degree and spatial arrangement of external information sampling changes optimal foraging strategies for searchers in scarce environments, which leads to ecological implications.

Silvio Salinas (USP): Modulated structures in a nematic model with chiral interactions

We have been using elementary Maier-Saupe statistical lattice models, with a choice of discrete microscopic nematic directors, to account for the sequences of uniaxial and biaxial structures in the phase diagrams of nematic liquid crystals. In some more recent works, we have included chiral interactions to explain the onset of cholesteric structures. If the nematic directors are restricted to point along p planar directions, which is a nematic version of the p-state chiral clock model, calculations on a Bethe lattice led to a phase diagram with uniform and modulated structures, depending on temperature and a parameter of chirality (1). We then consider analogous model systems, with directors of three-dimensional symmetry, and resort to real-space renormalization-group calculations.

(1) Modulated structures in a Lebwohl–Lasher model with chiral interactions, E.S. Nascimento, A. Petri, S.R. Salinas, Physica A531, 121592 (2019).

Alexandre Souto Martinez (USP, Ribeirão Preto): Solutions of simple systems of the deformed quantum mechanics based on a new extended uncertainty principle

Integral transforms serve as potent mathematical tools for converting functions between different domains, offering a versatile way to analyze systems from varied perspectives due to their linearity and invertibility. Here, we introduce a novel kernel for an integral transform, which plays a pivotal role in defining an extended uncertainty principle. Our proposed integral transform kernel significantly expands the applicability of generalized exponential functions within non-additive statistical mechanics, enabling these functions to encompass negative or complex values. Furthermore, it demonstrates analyticity by being mappable to the standard Fourier transform within the complex plane. The functions derived from this novel kernel, termed "deformed functions," exhibit properties reminiscent of hyperbolic and trigonometric functions. These deformed functions stand as solutions to straightforward systems within the framework of deformed quantum algebra, aligning with the extended uncertainty principle we introduced. Our work focuses on extending the formalism of quantum mechanics through an innovative uncertainty principle, leveraging integral transforms and specialized kernels to generate deformed functions that adhere to this extended principle and display characteristics akin to well-known mathematical functions.

Maurice de Koning (UNICAMP): Phase transitions involving superionic ice XVIII

Following the experimental verification in 2019 of the existence of a face-centered-cubic superionic form of water in extreme settings of pressure and temperature, known as ice XVIII, there has been an increased interest in understanding the phase behavior of water under such extraordinary circumstances, in particular due to their potential role in the anomalous magnetic fields of Neptune and Uranus. Given the  experimental challenges associated with the creation and maintenance of such conditions, atomic-level modeling techniques have played a central role in making progress towards this goal. In this talk, we will describe a recent application of such methods to investigate the thermodynamics and kinetics of phase transitions between superionic ice XVIII and the insulating ice X phase as described by a machine-learned interaction model derived from density-functional-theory calculations. The results highlight the dual displacive/martensitic nature of the transition and provide insight into its kinetics.