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The high-temperature superconducting cuprates are governed by intertwined spin, charge, and superconducting orders. While various state-of-the-art numerical methods have demonstrated that these phases also manifest themselves in doped Hubbard models, they differ on which is the actual ground state. Finite-cluster methods typically indicate that stripe order dominates, while embedded quantum-cluster methods, which access the thermodynamic limit by treating long-range correlations with a dynamical mean field, conclude that superconductivity does. Here, we report the observation of fluctuating spin and charge stripes in the doped single-band Hubbard model using a quantum Monte Carlo dynamical cluster approximation (DCA) method. By resolving both the fluctuating spin and charge orders using DCA, we demonstrate that they survive in the doped Hubbard model in the thermodynamic limit. This discovery also provides an opportunity to study the influence of fluctuating stripe correlations on the model’s pairing correlations within a unified numerical framework. Using this approach, we also find evidence for pair-density-wave correlations whose strength is correlated with that of the stripes.

We develop a real space cluster extension of the typical medium theory (cluster-TMT) to study Anderson localization. By construction, the cluster-TMT approach is formally equivalent to the real space cluster extension of the dynamical mean field theory. Applying the developed method to the 3D Anderson model with a box disorder distribution, we demonstrate that cluster-TMT successfully captures the localization phenomena in all disorder regimes. As a function of the cluster size, our method obtains the correct critical disorder strength for the Anderson localization in 3D, and systematically recovers the re-entrance behavior of the mobility edge. From a general perspective, our developed methodology offers the potential to study Anderson localization at surfaces within quantum embedding theory. This opens the door to studying the interplay between topology and Anderson localization from first principles.

We present a numerical study on the non-Fermi liquid behavior of a three-dimensional strongly correlated system. The Hubbard model in a simple cubic lattice is simulated by the dynamical cluster approximation; in particular, the quasi-particle weight is calculated at finite dopings for a range of temperatures. By fitting the quasi-particle weight to the marginal Fermi liquid form at finite doping near the putative quantum critical point, we find evidence of a separatrix between Fermi liquid and non-Fermi liquid regions. Our results suggest that a marginal Fermi liquid and possibly a quantum critical point exist in the non-symmetry broken solution of the three-dimensional interacting electron systems. We also calculate the spectral function, close to the half-filling, and we obtain evidence of pseudogap.

Transport measurements on the cuprates suggest the presence of a quantum critical point (QCP) hiding underneath the superconducting dome near optimal hole doping. We provide numerical evidence in support of this scenario via a dynamical cluster quantum Monte Carlo study of the extended two-dimensional Hubbard model. Single-particle quantities, such as the spectral function, the quasi-particle weight and the entropy, display a crossover between two distinct ground states: a Fermi liquid at low filling and a non-Fermi liquid with a pseudo-gap at high filling. Both states are found to cross over to a marginal Fermi-liquid state at higher temperatures. For finite next-nearest-neighbour hopping t′, we find a classical critical point at temperature Tc. This classical critical point is found to be associated with a phase-separation transition between a compressible Mott gas and an incompressible Mott liquid corresponding to the Fermi liquid and the pseudo-gap state, respectively. Since the critical temperature Tc extrapolates to zero as t′ vanishes, we conclude that a QCP connects the Fermi liquid to the pseudo-gap region, and that the marginal Fermi-liquid behaviour in its vicinity is the analogue of the supercritical region in the liquid-gas transition.

We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the graph Laplacian matrix. The transition comes out to be made of a well defined sequence of events, each of which corresponds to a specific clustered state. The network’s nodes involved in each of the clusters can be identified, and the value of the coupling strength at which the events are taking place can be approximately ascertained. Finally, we present large-scale simulations which show the accuracy of the approximation made, and of our predictions in describing the synchronization transition of both synthetic and real-world large size networks, and we even report that the observed sequence of clusters is preserved in heterogeneous networks made of slightly non-identical systems. Natural and synthetic networked systems can be characterized by synchrony or asynchrony of groups of their nodes (clusters) and undergo different scenarios of synchronization transitions. The authors propose an approach to predict the entire sequence of events that are taking place during the synchronization transition in networks of identical elements with any preferrable architecture.

Background The dynamics of many gene regulatory networks (GRNs) is characterized by the occurrence of metastable phenotypes and stochastic phenotype switches. The chemical master equation (CME) is the most accurate description to model such stochastic dynamics, whereby the long-time dynamics of the system is encoded in the spectral properties of the CME operator. Markov State Models (MSMs) provide a general framework for analyzing and visualizing stochastic multistability and state transitions based on these spectral properties. Until now, however, this approach is either limited to low-dimensional systems or requires the use of high-performance computing facilities, thus limiting its usability. Results We present a domain decomposition approach (DDA) that approximates the CME by a stochastic rate matrix on a discretized state space and projects the multistable dynamics to a lower dimensional MSM. To approximate the CME, we decompose the state space via a Voronoi tessellation and estimate transition probabilities by using adaptive sampling strategies. We apply the robust Perron cluster analysis (PCCA+) to construct the final MSM. Measures for uncertainty quantification are incorporated. As a proof of concept, we run the algorithm on a single PC and apply it to two GRN models, one for the genetic toggle switch and one describing macrophage polarization. By comparing the results with reference solutions, we demonstrate that our approach correctly identifies the number and location of metastable phenotypes with adequate accuracy and uncertainty bounds. We show that accuracy mainly depends on the total number of Voronoi cells, whereas uncertainty is determined by the number of sampling points. Conclusions A DDA enables the efficient computation of MSMs with quantified uncertainty. Since the algorithm is trivially parallelizable, it can be applied to larger systems, which will inevitably lead to new insights into cell-regulatory dynamics.

The application of the electronic control unit (ECU) motivates dynamic models with high precision to simulate mechatronic systems for various analysis and design tasks like hardware-in-the-loop (HiL) simulation. Unlike traditional physical models which are established based on the research experience or the mechanics mechanism, in this study, a novel data-driven modeling approach is presented based on the piecewise affine (PWA) identification method. In this work, the highly nonlinear dynamic of automotive actuators is well approximated by the PWA model. To obtain experimental data that can accurately reflect the characteristics of actuators, a test bench was first built. On this basis, the PWA identification of automotive is composed of the data clustering, the model structure selection, and the model parameter estimation. The proposed clustering method improves the widely used balanced iterative reducing and clustering using hierarchies (BIRCH) by introducing a refinement phase for handling clusters with arbitrary shapes. The model structure selection and the parameter estimation are jointly solved by using the optimization method. The presented method is demonstrated with an academic example and an automotive throttle, and the results show that the proposed method can achieve a high model quality, which means that the normalized root mean squared error (NRMSE) is 0.03 and the absolute maximal prediction error can reach 2.43°. Compared to other models like a physical model or a fuzzy model, the improvement using the proposed model can be up to 50%. Thus, the quality of the proposed PWA model is sufficient for HiL simulation.

A synchronised multi-axis digital holographic interferometry set-up is presented for the study of 3-D flow fields with large density gradients. This optical configuration provides instantaneous interferograms with fine spatial resolution in six directions of projection. A regularised tomographic approach taking into account the presence of possible shock waves is furthermore considered to reconstruct 3-D density fields. Applied to a screeching under-expanded supersonic jet with helical dynamics, this set-up is used to provide dense optical phase measurements in the initial region of the jet. The jet mean density field is shown to be satisfactorily estimated with sharply resolved density gradients. In addition, an approach based on azimuthal Fourier transform and snapshot proper orthogonal decomposition (POD) applied to the instantaneous flow observations is proposed to study the main coherent dynamics of the jet. Relying on a cluster analysis of the azimuthal POD mode coefficients, a reduced dynamical model in the POD mode phase space is used as an approximation of the two observed limit cycles. A clear 3-D representation of the density field of a helical instability associated with screech mode C is then evidenced, with two equally probable directions of rotation. Switching between the two directions is reported, highlighting intermittency in the feedback loop. This helical structure is particularly seen to extend to the jet core, driving its internal dynamics and inducing out-of-phase density fluctuations between the outer and inner shear layers. These out-of-phase motions are related to the non-uniform radial distribution of fluctuation phase associated with the outer-layer Kelvin–Helmholtz instability wave.

In hydrology, a fundamental task involves enhancing the predictive power of a model in ungagged basins by transferring information on physical attributes and hydroclimate dynamics from gauged basins. Introducing an integrated nonlinear clustering framework, this study aims to develop a comprehensive framework that augments predictive performance in basins where direct measurements are sparse or absent. In this framework, uniform manifold approximation and projection (UMAP) is used as a nonlinear method to extract the essential features embedded in hydro‐climatological attributes and physical properties. Then, the Growing Neural Gas (GNG) clustering model is used to find the basins that potentially share similar hydro‐climatological behaviors. Besides UMAP‐GNG, the integration of Principal Component Analysis (PCA) as a linear method to reduce dimensionality with common clustering methods are also assessed to serve as benchmarks. The results reveal that the combination of clustering algorithms with the PCA method may lead to loss of information while the nonlinear method (UMAP) can extract more informative features. The efficacy of the proposed framework is assessed across the Contiguous United States (CONUS) by training a single Base Model using long short‐term memory (LSTM) for the centroids of all clusters and then, fine‐tuning the model on the centroids of each cluster separately to create a regional model. The results indicate that using the information extracted by the UMAP‐GNG method to guide a Base Model can significantly improve the accuracy in most of the clusters and enhance the median prediction accuracy within different clusters from 0.04 to 0.37 of KGE in ungauged basins. Key Points The developed framework can stand as a fundamental guide for transferring the extracted knowledge from gauged basins to ungauged basins The attributes of western Contiguous United States (CONUS) direct the growing neurons to create more sparsely distributed patterns compared to the eastern parts The proposed framework could significantly improve the performance of the LSTM model for predicting streamflow in ungauged basins

Kinetics of collision-sticking processes between vapor molecules and clusters of low-volatility compounds govern the initial steps of atmospheric new particle formation. Conventional non-interacting hard-sphere models underestimate the collision rate by neglecting long-range attractive forces, and the commonly adopted assumption that every collision leads to the formation of a stable cluster (unit mass accommodation coefficient) is questionable for small clusters, especially at elevated temperatures. Here, we present a generally applicable analytical interacting hard-sphere model for evaluating collision rates between molecules and clusters, accounting for long-range attractive forces. In the model, the collision cross section is calculated based on an effective molecule–cluster potential, derived using Hamaker's approach. Applied to collisions of sulfuric acid or dimethylamine with neutral bisulfate–dimethylammonium clusters composed of 1–32 dimers, our new model predicts collision rates 2–3 times higher than the non-interacting model for small clusters, while decaying asymptotically to the non-interacting limit as cluster size increases, in excellent agreement with a collision-rate-theory atomistic molecular dynamics simulation approach. Additionally, we calculated sticking rates and mass accommodation coefficients (MACs) using atomistic molecular dynamics collision simulations. For sulfuric acid, a MAC ≈1 is observed for collisions with all cluster sizes at temperatures between 200 and 400 K. For dimethylamine, we find that MACs decrease with increasing temperature and decreasing cluster size. At low temperatures, the MAC ≈1 assumption is generally valid, but at elevated temperatures MACs can drop below 0.2 for small clusters.