Search

Cavitation is a highly turbulent, multi-phase flow phenomenon that manifests in the form of vapor cavities as a result of a sudden drop in the liquid pressure. The phenomenon has been observed as widely detrimental in hydraulic and marine applications like propellers and pumps, while also accelerating the sub-processes involved for bio-diesel production. Modelling cavitating flows has been extremely challenging owing to the resulting flow unsteadiness, phase transition and the cavitation-turbulence interaction. Standard methods to model turbulence like Reynolds-Averaged Navier-Stokes equations (RANS) and hybrid RANS-Large Eddy Simulations (LES) models are unable to reproduce the local turbulence dynamics observed in cavitating flow experiments. In an effort to facilitate the development of accurate RANS modelling procedures for cavitating flows, a data-driven approach devised by integrating Gene-Expression Programming (GEP) into a traditional RANS approach, without continuous RANS model feedback is proposed. The GEP algorithm is employed to obtain an additional corrective term, composed of flow variables derived directly from a baseline URANS cavitating flow calculation to be fit directly in the Boussinesq approximation. In addition, an optimizer based on the BFGS algorithm is employed on top of the GEP algorithm to ensure the solution is independent of the uncertainties associated with GEP. To evaluate the complexity of the model, we compare the approach with a more elementary linear regression technique. The GEP-CFD method is then used to train two expressions, for the Reynolds shear stress and the Turbulent Kinetic Energy simultaneously. The GEP-CFD approach is able to produce the flow features not captured by baseline RANS simulations in several areas, outperforming the RANS simulations and thus projects as a promising approach to augment numerical simulations for cavitating flows.

Transition metal dichalcogenides (TMDCs) possess valley pseudospin, allowing photon spin to be coupled to electron spin and enabling initialization and readout of both classical and quantum information. Rapid valley-dephasing processes have impeded the development of scalable, high-performance valleytronic devices operating at room temperature. Here we demonstrate that a chiral resonant metasurface can enable room-temperature valley-selective emission, even with linearly polarized excitation. This platform provides circular eigen-polarization states with a high quality factor (Q-factor) and strong chiral near-field enhancement, resulting in unitary emission circular dichroism (i.e. single-handed circularly polarized emission). Our fabricated Si chiral metasurfaces exhibit chiral electromagnetic modes with Q-factors up to 450 at visible wavelengths, spectrally tuned to the exciton energy of MoSe2 monolayers. Using spatially- and spectrally-resolved mapping from temperatures of 100 K to 294 K, we demonstrate degrees of circular polarization (DOP) as high as 0.5 at room temperature. Reciprocal space mapping of the exciton emission reveals the chiral q-BIC localizes valley-selective emission in the vicinity of the photonic gamma-point. Photon-spin and time-resolved photoluminescence measurements show that the high DOP can be attributed to the significantly increased chiroptical local density of states provided by the metasurface, which enhances valley-specific radiative transition rates by a factor of approximately 13, with lifetimes as short as 189 ps. Our work could facilitate the development of compact chiral classical and quantum light sources and the creation of molecular chiral polaritons for quantum enantioselective synthesis.

Unsteady cloud cavitating flow is detrimental to the efficiency of hydraulic machinery like pumps and propellers due to the resulting side-effects of vibration, noise and erosion damage. Modelling such a unsteady and highly turbulent flow remains a challenging issue. In this paper, cloud cavitating flow in a venturi is calculated using the Detached Eddy Simulation (DES) model combined with the Merkle model. The Adaptive Mesh Refinement (AMR) method is employed to speed up the calculation and investigate the mechanisms for vortex development in the venturi. The results indicate the velocity gradients and the generalized fluid element strongly influence the formation of vortices throughout a cavitation cycle. In addition, the cavitation-turbulence coupling is investigated on the local scale by comparing with high-fidelity experimental data and using profile stations. While the AMR calculation is able to predict well the time-averaged velocities and turbulence-related aspects near the throat, it displays discrepancies further downstream owing to a coarser grid refinement downstream and under-performs compared to a traditional grid simulation . Additionally, the AMR calculations is unable to reproduce the cavity width as observed in the experiments. Therefore, while AMR promises to speed the process significantly by refining grid only in regions of interest, it is comparatively in line with a traditional calculation for cavitating flows. Thus, this study intends to provide a reference to employing AMR as a tool to speed up calculations and be able to simulate turbulence-cavitation interactions accurately.

In the rapidly evolving field of financial forecasting, the application of neural networks presents a compelling advancement over traditional statistical models. This research paper explores the effectiveness of two specific neural forecasting models, N-HiTS and N-BEATS, in predicting financial market trends. Through a systematic comparison with conventional models, this study demonstrates the superior predictive capabilities of neural approaches, particularly in handling the non-linear dynamics and complex patterns inherent in financial time series data. The results indicate that N-HiTS and N-BEATS not only enhance the accuracy of forecasts but also boost the robustness and adaptability of financial predictions, offering substantial advantages in environments that require real-time decision-making. The paper concludes with insights into the practical implications of neural forecasting in financial markets and recommendations for future research directions., Comment: This preprint has not undergone peer review or any post-submission improvements or corrections. The Version of Record of this contribution will be published in the Proceedings of the International Conference on Information Systems for Business Management (ISBM 2024), Springer Lecture Notes in Networks and Systems (LNNS), 2024

Monte Carlo methods have led to profound insights into the strong-coupling behaviour of lattice gauge theories and produced remarkable results such as first-principles computations of hadron masses. Despite tremendous progress over the last four decades, fundamental challenges such as the sign problem and the inability to simulate real-time dynamics remain. Neural network quantum states have emerged as an alternative method that seeks to overcome these challenges. In this work, we use gauge-invariant neural network quantum states to accurately compute the ground state of $\mathbb{Z}_N$ lattice gauge theories in $2+1$ dimensions. Using transfer learning, we study the distinct topological phases and the confinement phase transition of these theories. For $\mathbb{Z}_2$, we identify a continuous transition and compute critical exponents, finding excellent agreement with existing numerics for the expected Ising universality class. In the $\mathbb{Z}_3$ case, we observe a weakly first-order transition and identify the critical coupling. Our findings suggest that neural network quantum states are a promising method for precise studies of lattice gauge theory.

The Super-Kamiokande and T2K collaborations present a joint measurement of neutrino oscillation parameters from their atmospheric and beam neutrino data. It uses a common interaction model for events overlapping in neutrino energy and correlated detector systematic uncertainties between the two datasets, which are found to be compatible. Using 3244.4 days of atmospheric data and a beam exposure of $19.7(16.3) \times 10^{20}$ protons on target in (anti)neutrino mode, the analysis finds a 1.9$\sigma$ exclusion of CP-conservation (defined as $J_{CP}=0$) and a preference for the normal mass ordering., Comment: 12 pages, 4 figures

The concept of Hydrodynamic Cavitation (HC) has emerged as a promising method for wastewater treatment, bio-diesel production and multiple other environmental processes with Venturi-type cavitation reactors showing particular advantages. However, numerical simulations of a venturi-type reactor with an elucidated explanation of the underlying flow physics remain inadequate. The present study numerically investigates and analyzes the flow inside a venturi-type reactor from both global cavity dynamics and localized turbulence statistics perspectives. Some models in the Detached Eddy Simulation (DES) family are employed to model the turbulence with the study initially comparing 2D simulations before extending the analysis to 3D simulations. The results show that while URANS models show significantly different dynamics as a result of grid refinement, the DES models show standard flow dynamics associated with cavitating flows. Nevertheless, signifi- cant discrepancies continue to exist when comparing the turbulence statistics on the local scale. As the discussion extends to 3D calculations, the DES models are able to well predict the turbulence phenomena at the local scale and reveal some new insights regarding the role of baroclinic torque into the cavitation-vortex interaction.The findings of this study thus contribute to the fundamental understandings of the venturi-type reactor.

To create early warning capabilities for upcoming Space Weather disturbances, we have selected a dataset of 61 emerging active regions, which allows us to identify characteristic features in the evolution of acoustic power density to predict continuum intensity emergence. For our study, we have utilized Doppler shift and continuum intensity observations from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). The local tracking of 30.66 x 30.66-degree patches in the vicinity of active regions allowed us to trace the evolution of active regions starting from the pre-emergence state. We have developed a machine learning model to capture the acoustic power flux density variations associated with upcoming magnetic flux emergence. The trained Long Short-Term Memory (LSTM) model is able to predict 5 hours ahead whether, in a given area of the solar surface, continuum intensity values will decrease. The performed study allows us to investigate the potential of the machine learning approach to predict the emergence of active regions using acoustic power maps as input., Comment: 9 pages, 4 figures, IAU Symposium 365 Proceedings

First we show that physics-informed neural networks are not suitable for a large class of parabolic partial differential equations including the Fokker-Planck equation. Then we devise an algorithm to compute solutions of the Fokker-Planck equation using the zeros of Fokker-Planck operator and the Feynman-Kac formula. The resulting algorithm is mesh-free, highly parallelizable and able to compute solutions pointwise, thus mitigating the curse of dimensionality in a practical sense. We analyze various nuances of this algorithm that are determined by the drift term in the Fokker-Planck equation. We work with problems ranging in dimensions from 2 to 10. We demonstrate that this algorithm requires orders of magnitude fewer trajectories for each point in space when compared to Monte-Carlo. We also prove that under suitable conditions the error that is caused by letting some trajectories (associated with the Feynman-Kac expectation) escape our domain of knowledge is proportional to the fraction of trajectories that escape., Comment: 18 pages, 7 figures

We present four main contributions to enhance the performance of Large Language Models (LLMs) in generating domain-specific code: (i) utilizing LLM-based data splitting and data renovation techniques to improve the semantic representation of embeddings' space; (ii) introducing the Chain of Density for Renovation Credibility (CoDRC), driven by LLMs, and the Adaptive Text Renovation (ATR) algorithm for assessing data renovation reliability; (iii) developing the Implicit Knowledge Expansion and Contemplation (IKEC) Prompt technique; and (iv) effectively refactoring existing scripts to generate new and high-quality scripts with LLMs. By using engineering simulation software RedHawk-SC as a case study, we demonstrate the effectiveness of our data pre-processing method for expanding and categorizing scripts. When combined with IKEC, these techniques enhance the Retrieval-Augmented Generation (RAG) method in retrieving more relevant information, ultimately achieving a 73.33% "Percentage of Correct Lines" for code generation problems in MapReduce applications.

Computing Lyapunov vectors from partial and noisy observations is a challenging problem. We propose a method using data assimilation to approximate the Lyapunov vectors using the estimate of the underlying trajectory obtained from the filter mean. We then extensively study the sensitivity of these approximate Lyapunov vectors and the corresponding Oseledets' subspaces to the perturbations in the underlying true trajectory. We demonstrate that this sensitivity is consistent with and helps explain the errors in the approximate Lyapunov vectors from the estimated trajectory of the filter. Using the idea of principal angles, we demonstrate that the Oseledets' subspaces defined by the LVs computed from the approximate trajectory are less sensitive than the individual vectors., Comment: 20 pages, 9 figures and no tables

Pore-resolved direct numerical simulations (DNS) are performed to investigate the interactions between streamflow turbulence and groundwater flow through a randomly packed porous sediment bed for three permeability Reynolds numbers, $Re_K$, of 2.56, 5.17, and 8.94, representative of natural stream or river systems. Time-space averaging is used to quantify the Reynolds stress, form-induced stress, mean flow and shear penetration depths, and mixing length at the sediment-water interface (SWI). The mean flow and shear penetration depths increase with $Re_K$ and are found to be nonlinear functions of non-dimensional permeability. The peaks and significant values of the Reynolds stresses, form-induced stresses, and pressure variations are shown to occur in the top layer of the bed, which is also confirmed by conducting simulations of just the top layer as roughness elements over an impermeable wall. The probability distribution functions (PDFs) of normalized local bed stress are found to collapse for all Reynolds numbers and their root mean-squared fluctuations are assumed to follow logarithmic correlations. The fluctuations in local bed stress and resultant drag and lift forces on sediment grains are mainly a result of the top layer, their PDFs are symmetric with heavy tails, and can be well represented by a non-Gaussian model fit. The bed stress statistics and the pressure data at the SWI can potentially be used in providing better boundary conditions in modeling of incipient motion and reach-scale transport in the hyporheic zone., Comment: 34 pages, 15 figures, 9 tables. arXiv admin note: text overlap with arXiv:2204.13875

In a preliminary attempt to address the problem of data scarcity in physics-based machine learning, we introduce a novel methodology for data generation in physics-based simulations. Our motivation is to overcome the limitations posed by the limited availability of numerical data. To achieve this, we leverage a diffusion model that allows us to generate synthetic data samples and test them for two canonical cases: (a) the steady 2-D Poisson equation, and (b) the forced unsteady 2-D Navier-Stokes (NS) {vorticity-transport} equation in a confined box. By comparing the generated data samples against outputs from classical solvers, we assess their accuracy and examine their adherence to the underlying physics laws. In this way, we emphasize the importance of not only satisfying visual and statistical comparisons with solver data but also ensuring the generated data's conformity to physics laws, thus enabling their effective utilization in downstream tasks.

Study of dynamical systems using partial state observation is an important problem due to its applicability to many real-world systems. We address the problem by studying an echo state network (ESN) framework with partial state input with partial or full state output. Application to the Lorenz system and Chua's oscillator (both numerically simulated and experimental systems) demonstrate the effectiveness of our method. We show that the ESN, as an autonomous dynamical system, is capable of making short-term predictions up to a few Lyapunov times. However, the prediction horizon has high variability depending on the initial condition-an aspect that we explore in detail using the distribution of the prediction horizon. Further, using a variety of statistical metrics to compare the long-term dynamics of the ESN predictions with numerically simulated or experimental dynamics and observed similar results, we show that the ESN can effectively learn the system's dynamics even when trained with noisy numerical or experimental datasets. Thus, we demonstrate the potential of ESNs to serve as cheap surrogate models for simulating the dynamics of systems where complete observations are unavailable.

In this paper we devise a deep learning algorithm to find non-trivial zeros of Fokker-Planck operators when the drift is non-solenoidal. We demonstrate the efficacy of our algorithm for problem dimensions ranging from 2 to 10. This method scales linearly with dimension in memory usage. In the problems we studied, overall computational time seems to scale approximately quadratically with dimension. We present results that indicate the potential of this method to produce better approximations compared to Monte Carlo methods, for the same overall sample sizes, even in low dimensions. Unlike the Monte Carlo methods, the deep network method gives a functional form of the solution. We also demonstrate that the associated loss function is strongly correlated with the distance from the true solution, thus providing a strong numerical justification for the algorithm. Moreover, this relation seems to be linear asymptotically for small values of the loss function., Comment: 22 pages, 10 figures

The Quantum Approximate Optimization Algorithm and its generalization to Quantum Alternating Operator Ansatz (QAOA) is a promising approach for applying quantum computers to challenging problems such as combinatorial optimization and computational chemistry. In this paper, we study the underlying mechanisms governing the behavior of QAOA circuits beyond shallow depth in the practically relevant setting of gradually varying unitaries. We use the discrete adiabatic theorem, which complements and generalizes the insights obtained from the continuous-time adiabatic theorem primarily considered in prior work. Our analysis explains some general properties that are conspicuously depicted in the recently introduced QAOA performance diagrams. For parameter sequences derived from continuous schedules (e.g. linear ramps), these diagrams capture the algorithm's performance over different parameter sizes and circuit depths. Surprisingly, they have been observed to be qualitatively similar across different performance metrics and application domains. Our analysis explains this behavior as well as entails some unexpected results, such as connections between the eigenstates of the cost and mixer QAOA Hamiltonians changing based on parameter size and the possibility of reducing circuit depth without sacrificing performance.

We design, to the best of our knowledge, the first differentially private (DP) stream aggregation processing system at scale. Our system -- Differential Privacy SQL Pipelines (DP-SQLP) -- is built using a streaming framework similar to Spark streaming, and is built on top of the Spanner database and the F1 query engine from Google. Towards designing DP-SQLP we make both algorithmic and systemic advances, namely, we (i) design a novel (user-level) DP key selection algorithm that can operate on an unbounded set of possible keys, and can scale to one billion keys that users have contributed, (ii) design a preemptive execution scheme for DP key selection that avoids enumerating all the keys at each triggering time, and (iii) use algorithmic techniques from DP continual observation to release a continual DP histogram of user contributions to different keys over the stream length. We empirically demonstrate the efficacy by obtaining at least $16\times$ reduction in error over meaningful baselines we consider. We implemented a streaming differentially private user impressions for Google Shopping with DP-SQLP. The streaming DP algorithms are further applied to Google Trends.

The predictive capability of two way--coupled point-particle Euler-Lagrange model in accurately capturing particle-flow interactions under grid refinement, wherein the particle size can be comparable to the grid size, is systematically evaluated. Two situations are considered, (i) uniform flow over a stationary particle, and (ii) decaying isotropic turbulence laden with Kolmogorov-scale particles. Particle-fluid interactions are modeled using only the standard drag law, typical of large density-ratio systems. A zonal, advection-diffusion-reaction (Zonal-ADR) model is used to obtain the undisturbed fluid velocity needed in the drag closure. Two main types of interpolation kernels, grid-based and particle size--based, are employed. The effect of interpolation kernels on capturing the particle-fluid interactions, kinetic energy, dissipation rate, and particle acceleration statistics are evaluated in detail. It is shown that the interpolation kernels whose width scales with the particle size perform significantly better under grid refinement than kernels whose width scales with the grid size. Convergence with respect to spatial resolution is obtained with the particle size--based kernels with and without correcting for the self-disturbance effect. While the use of particle size--based interpolation kernels provide spatial convergence and perform better than kernels that scale based on grid size, small differences can still be seen in the converged results with and without correcting for the particle self-disturbance. Such differences indicate the need for self-disturbance correction to obtain the best results, especially when the particles are larger than the grid size., Comment: Submitted to International Journal of Multiphase Flow

Linear optical quantum circuits with photon number resolving (PNR) detectors are used for both Gaussian Boson Sampling (GBS) and for the preparation of non-Gaussian states such as Gottesman-Kitaev-Preskill (GKP), cat and NOON states. They are crucial in many schemes of quantum computing and quantum metrology. Classically optimizing circuits with PNR detectors is challenging due to their exponentially large Hilbert space, and quadratically more challenging in the presence of decoherence as state vectors are replaced by density matrices. To tackle this problem, we introduce a family of algorithms that calculate detection probabilities, conditional states (as well as their gradients with respect to circuit parametrizations) with a complexity that is comparable to the noiseless case. As a consequence we can simulate and optimize circuits with twice the number of modes as we could before, using the same resources. More precisely, for an $M$-mode noisy circuit with detected modes $D$ and undetected modes $U$, the complexity of our algorithm is $O(M^2 \prod_{i\in U} C_i^2 \prod_{i\in D} C_i)$, rather than $O(M^2 \prod_{i \in D\cup U} C_i^2)$, where $C_i$ is the Fock cutoff of mode $i$. As a particular case, our approach offers a full quadratic speedup for calculating detection probabilities, as in that case all modes are detected. Finally, these algorithms are implemented and ready to use in the open-source photonic optimization library MrMustard.

Cavitation is a complex multiphase phenomenon characterised by vapour bubbles forming due to a sudden pressure drop and is often accompanied by increased hull vibrations, increased radiated noise and decrease in propeller and impeller performance. Although the Reynolds-Averaged Navier-Stokes (RANS) method coupled with a cavitation model is still considered a practical tool to predict cavitating flows owing to its computational efficiency, it is unable to predict the unsteadiness of vapor shedding and over-predicts the eddy viscosity. To improve the prediction, an empirical eddy viscosity correction,[Reboud et al. 1998] was proposed to consider the compressibility effects produced by cavitation. Additionally, a new type of models termed as hybrid RANS-Large Eddy Simulation (LES) models have also been recently introduced in the community, having the ability to behave as a RANS or a LES model in different regions of the flow in order to combine the computational cost efficiency of RANS with the accuracy of LES modelling. However, there exists a lack of a comprehensive review of various such turbulence models like the k-{\omega} Shear Stress Transport Model (SST), k-{\omega} SST Scale-adaptive Simulation (SAS), k-{\omega} SST Detached Eddy Simulation (DES), k-{\omega} SST Delayed DES (DDES), Filter-Based Method (FBM) and Partially-Averaged Navier Stokes Method (PANS) to predict cavitating flows. In this work, we conduct such a review to compare their ability to predict cloud cavitating flows by comparing them with x-ray experimental data in a venturi. It is shown that with mesh refinement, standard models do show the vapor unsteadiness as seen in the experiment similar to that seen when using the Reboud correction. However, on local comparison of turbulence quantities, it is observed both forms of models have huge discrepancies with experimental data that does not improve downstream.