Glasses are mechanically rigid, but still undergo structural relaxation that changes their properties and affects potential technological applications. Understanding the underlying physical processes is a problem of broad theoretical and practical interest. We investigate intermittent structural relaxation events or “avalanches” occurring inside a glassy regime. Contrary to the more well-known avalanches due to shear, here they are induced by thermal fluctuations in undeformed glass. By analyzing changes in the structural, mechanical, dynamical, topological, and vibrational properties of the system, we provide a multifaceted characterization of avalanches. Overall we find that the system softens due to avalanches. Further, we extend a formalism to extract local measures of nonaffine displacement and tensorial strain for thermal amorphous solids in the absence of any external deformation. Our analysis highlights a key difference between two types of driving: while the shear deformation response is dominated by volume preserving deviatoric strain, changes in local density must be considered to model the response of undeformed glass under thermal noise. The observations suggest the idea of Generalized Strain Transformation Zones, where coupled shear and volume‐changing deformations govern thermally mediated plasticity. Our work paves the way for a unified description of the elastoplastic response of (athermal) mechanically deformed and thermally driven undeformed glasses.

An antlike observer confined to a two-dimensional surface traversed by stripes would wonder whether such a striped landscape could be devised in such a way as to appear to be the same wherever they go. Differently stated, this is the problem studied in this paper. In a more technical jargon, we determine all possible uniform nematic fields on a smooth surface. It was already known that for such a field to exist, the surface must have constant negative Gaussian curvature. Here we show that all uniform nematic fields on such a surface are parallel transported (in Levi-Civita's sense) by special systems of geodesics, which are termed uniform. We prove that, for every geodesic on the surface, there are two systems of uniform geodesics that include it; they are conventionally called right and left, to evoke handedness. We found explicitly all uniform fields for Beltrami's pseudosphere. Since both geodesics and uniformity are preserved under isometries, by a classical theorem of Minding, the solution for the pseudosphere carries over all other admissible surfaces, thus providing a general solution to the problem (at least in principle). The proved existence of surface nematic uniform fields suggests the definition of a generalized intrinsic elastic energy for fluid membranes with nematic order, which is but one of the many possible applications of our geometric result.

We study the dynamical behavior of an anisotropic active Brownian particle subjected to various stochastic resetting protocols in two dimensions. The motion of shape-asymmetric active Brownian particles in two dimensions leads to anisotropic diffusion at short times, whereas rotational diffusion causes the transport to become isotropic at longer times. We have considered three different resetting protocols: (1) complete resetting, when both position and orientation are reset to their initial states, (2) only the position is reset to its initial state, and (3) only orientation is reset to its initial state. We reveal that orientational resetting sustains anisotropy even at late times. When both the spatial position and orientation are subject to resetting, a complex position probability distribution forms in the steady state. This distribution is shaped by factors such as the initial orientation angle, the anisotropy of the particle, and the resetting rate. We have calculated the exact expressions for mean-square displacements using a renewal approach for different resetting protocols and numerically verified the analytical results. When only the translational degrees of freedom are reset, while the particle's orientation evolves naturally, the steady state no longer depends on particle asymmetry. In contrast, if only the orientation is reset, the long-term probability distribution becomes Gaussian, using an effective diffusion tensor—containing nondiagonal elements—defined by the resetting rate. More broadly, the interaction between translational and rotational dynamics, in combination with stochastic resetting, produces distinct behaviors at late times that are absent in symmetric particles. Given recent progress in experimental resetting techniques, these results could be highly useful for controlling asymmetric active colloids, such as in self-assembly applications.

We study harmonic chains with i.i.d. random spring constants $K_n$ and i.i.d. random masses $m_n$. We introduce a combinatorial approach which allows us to derive a compact and general approximate formula for the complex Lyapunov exponent, in terms of the solutions of two transcendental equations involving the distributions of the spring constants and the masses. Our result makes easy the asymptotic analysis of the low-frequency properties of the eigenmodes (spectral density and localization) for arbitrary disorder distribution, as well as their high-frequency properties. We apply the method to the case of power-law distributions $p\left(K\right)=\mu K^{-1+\mu }$ with $0<K<1$ and $q\left(m\right)=\nu m^{-1-\nu }$ with $m>1$ (with $\mu ,\nu >0$). At low frequency, the spectral density presents the power law $\varrho (\omega \to 0)\sim {\omega }^{2\eta -1}$, where the exponent $\eta$ exhibits first-order phase transitions on the line $\mu =1$ and on the line $\nu =1$. The exponent of the nondisordered chain ($\eta =1/2$) is recovered when $\langle K_n^{-1}\rangle$ and $\langle m_n\rangle$ are both finite, i.e., $\mu >1$ and $\nu >1$. The Lyapunov exponent (inverse localization length) shows also a power-law behavior $\gamma ({\omega }^2\to 0)\sim {\omega }^{2\zeta }$, where the exponent $\zeta$ exhibits several phase transitions: the exponent is $\zeta =\eta$ for $\mu <1$ or $\nu <1$ ($\langle K_n^{-1}\rangle$ or $\langle m_n\rangle$ infinite) and $\zeta =1$ when $\mu >2$ and $\nu >2$ ($\langle K_n^{-2}\rangle$ and $\langle m_n^2\rangle$ both finite). In the intermediate region it is given by $\zeta =\min (\mu ,\nu )/2$. On the transition lines, $\varrho \left(\omega \right)$ and $\gamma \left({\omega }^2\right)$ receive logarithmic corrections. Finally, we illustrate the versatility of our combinatorial approach by considering the case of the Anderson model with random couplings (a model known to be mapped onto the random spring chain for “Dyson type I” disorder).

This work investigates the dynamics of dual-drop impact on a solid surface, encompassing both simultaneous and nonsimultaneous side-by-side impact of equal-sized drops, as well as successive impact of unequal-sized drops. Numerical simulations are performed using smoothed particle hydrodynamics method to capture the associated complex fluid dynamics. For side-by-side impact, the influences of the Weber number, horizontal spacing, and vertical spacing on liquid film merging are examined. The impact dynamics are characterized using three dimensionless parameters: the spread factor of the merged liquid film, the dimensionless central liquid sheet height, and dimensionless time. The results indicate that both the maximum spread factor and the dimensionless central sheet height increase with the Weber number. The spacings significantly affect the impact outcomes: horizontal spacing primarily influences the spread factor, whereas vertical spacing governs the morphology, inclination angle, and height of the central liquid sheet. For successive impact, simulations are conducted to analyze the effects of leading and trailing drop diameters, vertical spacing, Weber number, wall temperature, and ambient pressure. The conditions influencing the spread factor, apex height, crown height, and rebound height are investigated. The results demonstrate that an increase in the trailing drop's diameter enhances the spread factor, while the crown height diminishes with reduced vertical spacing. Furthermore, increasing the vertical spacing elevates the crown height but reduces the spread factor for different Weber numbers of the trailing drop. A higher trailing drop Weber number increases the spread factor. An increase in wall temperature reduces the spread factor and elevates the apex height, while elevated ambient pressure suppresses rebound and prolongs residence time. Based on these results, predictive models for dual-drop impact dynamics are proposed.

Elastic interfaces in quenched random media driven by external forces exhibit a continuous depinning phase transition between pinned and moving phases at a critical external force. Recent work [Phys. Rev. Lett. 129, 175701 (2022)] has shown that the distribution of local interface heights at depinning displays negative skewness. Here, by considering local, long-range, and fully coupled (mean-field) elasticity, we expand on this result by demonstrating the robustness of the negative skewness at depinning when approaching the thermodynamic limit and considering different values of the spring stiffness controlling the avalanche cutoff. Additionally, we investigate the evolution of the height distribution as the external force is ramped up from zero, approaching the critical force from below. Starting from a symmetric height distribution at zero force, the distribution initially develops positive skewness increasing with the external force, followed by a steep drop to the negative value characteristic of the critical point as the depinning transition is reached.

Synchronization phenomena in higher-order coupled systems have been widely studied, but the synergistic effect of microstructure and phase lag on synchronization has not been revealed. In this paper, we introduce the hyperedge overlap to quantify the degree of overlap between 2-hyperedges and analyze the hypergraph structures with the phase lag. The results show that increasing the phase lag and the hyperedge overlap drives the synchronization phase transition from first order to second order. Meanwhile, these changes decrease the global synchronization level, and this effect is independent of the network size. Under weak global synchronization, the smaller hyperedge overlap is associated with improved local synchronization performance. Furthermore, the phase lag changes the effective frequency distribution of the system, and the larger the coupling strength deviates more from the initial average frequency.

Spatiotemporal chaos in systems such as turbulent flows often resides on finite-dimensional attractors, enabling the construction of reduced-order models. Unfortunately, as the dimension of these attractors increases it becomes more difficult to train reduced-order models because more data are needed to sample states of the system. For example, the attractor dimension often scales linearly with the domain size in a single direction for large-scale spatially extended systems, thus we need methods for decomposing these systems to overcome the burden of increasing dimensionality. Here, we develop a framework that constructs local reduced-order models by decomposing spatially extended systems into patches. Each patch uses autoencoders for dimension reduction and neural ordinary differential equations for learning the temporal dynamics locally. We apply this framework to the Kuramoto-Sivashinsky equation and two-dimensional Kolmogorov flow. Our approach reduces the dimension by up to two orders of magnitude while accurately capturing both short-term dynamics and long-term statistics. This framework is applicable to any dissipative partial differential equations, thereby offering broad implications for a wide range of physical and engineering systems.

Designing stable cluster synchronization patterns is a fundamental challenge in nonlinear dynamics of networks with great relevance to understanding neuronal and brain dynamics. So far, cluster synchronization has been studied exclusively in a node-based dynamical approach, according to which oscillators are associated only with the nodes of the network. Here we propose a topological synchronization dynamics model based on the use of the topological Dirac operator, which allows us to design cluster synchronization patterns for topological oscillators associated with both nodes and edges of a network. In particular, by modulating the ground state of the free energy associated with the dynamical model, we construct topological cluster synchronization patterns. These are aligned with the eigenstates of the topological Dirac equation that provide a very useful decomposition of the dynamical state of node and edge signals associated with the network. We use linear stability analysis to predict the stability of the topological cluster synchronization patterns and provide numerical evidence of the ability to design several stable topological cluster synchronization states on real connectome data, random graphs, and on stochastic block models.

We study the mean-square displacement (MSD) of a tracer particle diffusing in a granular gas of inelastic hard spheres under homogeneous cooling state. Tracer and granular gas particles are in general mechanically different. Our approach uses a series representation of the MSD where the $k\mathrm{th}$ term is given in terms of the mean scalar product $\langle {\mathbf{r}}_1·{\mathbf{r}}_k\rangle$, with ${\mathbf{r}}_i$ denoting the displacements of the tracer between successive collisions. We find that this series approximates a geometric series with the ratio $\mathrm{\Omega }$. We derive an explicit analytical expression of $\mathrm{\Omega }$ for granular gases in three dimensions and validate it through a comparison with the numerical results obtained from the direct simulation Monte Carlo (DSMC) method. Our comparison covers a wide range of masses, sizes, and inelasticities. From the geometric series, we find that the MSD per collision is simply given by the mean-square free path of the particle divided by $1-\mathrm{\Omega }$. The analytical expression for the MSD derived here is compared with DSMC data and with the first- and second-Sonine approximations to the MSD obtained from the Chapman-Enskog solution of the Boltzmann equation. Surprisingly, despite their simplicity, our results outperform the predictions of the first-Sonine approximation to the MSD, achieving accuracy comparable to the second-Sonine approximation.

The Sachdev-Ye-Kitaev (SYK) model may provide us with a good starting point for the experimental study of quantum chaos and holography in the laboratory. Still, the four-local interaction of fermions makes quantum simulation challenging, and it would be good to search for simpler models that keep the essence. In this paper, we argue that the four-local interaction may not be important by introducing a few models that have two-local interactions. The first model is a generalization of the spin-SYK model, which is obtained by replacing the spin variables with $\mathrm{SU}\left(d\right)$ generators. Simulations of this class of models might be straightforward on qudit-based quantum devices. We study the case of $d=3,4,5,6$ numerically and observe quantum chaos already for two-local interactions in a wide energy range. We also introduce modifications of spin-SYK and SYK models that have similar structures as the $\mathrm{SU}\left(d\right)$ model (e.g., $H={\sum }_{p,q}{J}_{pq}{\chi }_p{\chi }_{p+1}{\chi }_q{\chi }_{q+1}$ instead of the original SYK Hamiltonian $H={\sum }_{p,q,r,s}{J}_{pqrs}{\chi }_p{\chi }_q{\chi }_r{\chi }_s$), which shows strongly chaotic features although the interaction is essentially two-local. These models may be a good starting point for the quantum simulation of the original SYK model.

We present an exact diagonalization study of the spectral properties of bosons harmonically confined in a quasi-2D plane and interacting via repulsive Gaussian potential. We consider the lowest 100 energy levels for systems of $N=12,16$, and 20 bosons in two distinct regimes: (a) when the interaction energy is small compared to the trap energy (moderate interaction) and (b) when the interaction energy is comparable to the trap energy (strong interaction), for the nonrotating $(L_z=0)$ as well as the rotating single-vortex state $(L_z=N)$. For higher angular momenta, $L_z=2N$ and $L_z=3N$, only the strong interaction regime is considered. While the nearest-neighbor spacing distribution (NNSD) $P\left(s\right)$ and the ratios of consecutive level spacings distribution $P\left(r\right)$ are used to study the short-range correlations, the Dyson-Mehta ${\mathrm{\Delta }}_3$ statistic and the level number variance ${\mathrm{\Sigma }}^2\left(L\right)$ are used to examine the long-range correlations. In the moderate interaction regime, the nonrotating system exhibits Poisson distribution, a characteristic of the regular energy spectra. In the strong interaction regime, the nonrotating system exhibits chaotic behavior signified by GOE distribution. Furthermore, in the rotating case for the single-vortex state $(L_z=N)$ in the moderate interaction regime, the system exhibits signatures of weak chaos with some degree of regularity in the energy-level spectra. However, in the strong interaction regime for the rotating case with $L_z=N$, $2N$ and $3N$, the system exhibits strong chaotic behavior. The rotation is found to contribute to enhancement of chaotic behavior in the system for both the moderate and the strong interaction regimes. Our results of NNSD analysis are supported by the analysis of the ratios of consecutive level spacings distribution $P\left(r\right)$, which does not involve unfolding.

Gap solitons (GSs) bifurcating from flat bands, which may be represented in terms of Wannier functions, have garnered significant interest due to their strong localization with extremely small norms. Moiré lattices (MLs), with multiple flat bands, offer an appropriate platform for creating such solitons. We explore the formation mechanism and stability of GSs in spin-1 Bose-Einstein condensates under the combined action of the Rashba spin-orbit coupling (SOC) and an ML potential. We identify five Wannier-type GS families bifurcating from the lowest five energy bands in the spectrum induced by the ML with sufficiently large period and depth. These fundamental GSs serve as basic elements for constructing more complex Wannier-type GS states. Reducing the lattice period and depth triggers a transition from the Wannier-type GSs to those of the Bloch type, the latter exhibiting higher norm thresholds and pronounced spatial broadening near edges of the energy bands. In addition to tuning the lattice-potential parameters, adjusting the SOC strength can also modulate the flatness of energy bands and enhance the localization of gap solitons, enabling reversible transitions between the GSs of the Wannier and Bloch types. Distinctive properties of GSs in the quasiperiodic ML are uncovered too. Thus, we propose the theoretical foundation for the creation of and manipulations with strongly localized GSs.

Synchronization in systems with higher-order interactions remains a frontier in understanding collective behavior beyond pairwise coupling. This study investigates a minimal model of three nonidentical phase oscillators governed by pure three-body interactions, isolating the effects of three-body coupling from traditional pairwise terms. Key findings include the emergence of a complete devil's staircase in rotation numbers, structured by an anomalous Farey sequence, which arises from mutual coupling rather than external driving. The system exhibits robust multistability, where synchronous states coexist with phase-locked or quasi-periodic regimes, and basin stability of attractors is uncorrelated with their linear stability. Arnold tongues governing frequency-locking transitions display nonmonotonic broadening and bending, contrasting classical circle map predictions, and preventing chaotic dynamics. Notably, synchronous states revive at weak coupling strengths due to parameter-dependent reorganization of nullcline structures in the reduced phase-difference subsystem. These results highlight the intrinsic complexity of pure multibody interactions and provide insights into synchronization control in neural, social, and engineered systems. Our work establishes a foundational framework for studying minimal higher-order motifs and their role in collective dynamics.

The segmentation clock is an emergent embryonic oscillator that controls the periodic formation of vertebrae precursors (or somites). It relies on the self-organization at the presomitic mesoderm (PSM) level of multiple coupled cellular oscillators. Dissociation-reaggregation experiments have further revealed that ensembles made of such cellular oscillators self-organize into an oscillatory bidimensional system, showing concentric waves around multiple foci. Here, we systematically study the dynamics of a two-dimensional lattice of phase oscillators locally coupled to their nearest neighbors through a biharmonic coupling function of the form $sin\theta +\mathrm{\Lambda }{sin}^2\theta$. This coupling was inferred from the phase response curve of entrainment experiments on cell cultures, leading to the formulation of a minimal Elliptic Radial Isochron Cycle (ERIC) phase model. We show that such ERIC-based coupling parsimoniously explains the emergence of self-organized concentric phase wave patterns around multiple foci for a range of weak couplings and wide distributions of initial random phases, closely mimicking experimental conditions. We further study extended modalities of this problem to derive an atlas of possible behaviors. In particular, we predict the dominant observation of spirals over target wave patterns for initial phase distributions wider than approximately $\pi$. Since PSM cells further display properties of an excitable system, we also introduce excitability into our simple model and show that it also supports the observation of concentric phase waves for the conditions of the experiment. Our work suggests important modifications that can be made to the simple phase model with Kuramoto coupling, which can provide further layers of complexity and aid in the explanation of the spatial aspects of self-organization in the segmentation clock.

Neural processing in animals facilitates sensory adaptation by eliciting appropriate responses to changing environmental stimuli. Although sensory adaptation is well recognized, the specific role of individual neurons in these adaptive mechanisms remains poorly understood from a theoretical standpoint. Specifically, it is unclear how single neurons influence the processing of sensory information and modulate their responses to environmental changes. In Caenorhabditis elegans, the primary AFD thermosensory neurons respond to external thermal stimuli incorporating experience-dependent temperature response thresholds. While extensive experimental studies have highlighted the functional features of the AFD neurons, mathematical understanding of their responses is still not well established. In this study, we develop a theoretical framework that captures how a single pair of AFD neurons encodes sensory information and regulates their responses to thermal warming signals, with a focus on how prior environmental experiences influence these responses. Through this framework we find that the interaction between two key entities, i.e., cGMP and calcium, plays a crucial role in processing sensory information and fine-tuning neuronal responses to thermal changes. In addition to reproducing experimentally known trends, our results show that growth conditions such as cultivation temperature of the worms significantly shape the neurons' functional properties, including their operating range, activation thresholds and response start time and duration. The findings in this work, therefore, enhance the overall understanding of how environmental experiences by single neuron shape sensory systems and provide a deeper connection between experimental data and quantitative models.

A single droplet can be effectively isolated from a capillary liquid jet by applying a short-duration velocity oscillatory pulse at its exit from the nozzle outlet. The previous temporal analysis of F. J. García et al. [Phys. Rev. E 100, 053111 (2019)], which modeled the jet as an infinite liquid column subjected to a local axisymmetric spatial perturbation, revealed that Gaussian wave packets are the optimal choice for this purpose. Here, a more realistic semi-infinite jet model was selected to confirm the validity of the simpler infinite-jet model and identify new phenomena. To this end, a semi-infinite jet subjected to a symmetrical Gaussian oscillatory pulse of velocity at the outlet was investigated through both a linear spatial analysis and nonlinear numerical simulations. The spatiotemporal evolution of the Gaussian wave packets thus generated was described by fitting their relevant parameters and compared with the prediction of the temporal analysis of an infinite jet. Nonlinear simulations confirmed the results of the linear spatial analysis whenever the amplitude remained sufficiently small. A Gaussian wave packet forms during the stimulation stage, which then moves advectively and disperses as if it were on a perturbed infinite jet, even for small velocities. This explains the parametric agreement between the spatial and temporal analyses, especially for brief stimulation pulses. The most relevant discrepancy was a phase shift in the carrier wave, whose magnitude can be explained in terms of the stimulation and initial-transient characteristic times. It could be reverted through an appropriate initial phase of the stimulation pulse. An example with symmetrical breakup pattern was achieved in this way, which could be useful for further isolation of single droplets.