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At least 451 records · Page 25

Emulators for Scarce and Noisy Data: Application to Auxiliary-Field Diffusion Monte Carlo for Neutron Matter

Understanding the equation of state (EOS) of pure neutron matter is necessary for interpreting multimessenger observations of neutron stars. Reliable data analyses of these observations require well-quantified uncertainties for the EOS input, ideally propagating uncertainties from nuclear interactions directly to the EOS. This, however, requires calculations of the EOS for a prohibitively larger number of nuclear Hamiltonians, solving the nuclear many-body problem for each one. Quantum Monte Carlo methods, such as auxiliary-field diffusion Monte Carlo (AFDMC), provide precise and accurate results for the neutron matter EOS, but they are very computationally expensive, making them unsuitable for the fast evaluations necessary for uncertainty propagation. Here, we employ parametric matrix models to develop fast emulators for AFDMC calculations of neutron matter and use them to directly propagate uncertainties of coupling constants in the Hamiltonian to the EOS. As these uncertainties include estimates of the effective field theory truncation uncertainty, this approach provides robust uncertainty estimates for use in astrophysical data analyses. In conclusion, this Letter will enable novel applications such as using astrophysical observations to put constraints on coupling constants for nuclear interactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Quantum-Inspired Bayesian Sampling for Uncertainty Quantification and Machine Learning (Final Technical Report)

With increasing simulation and measurement data, machine learning and artificial intelligence have been widely used in computational decision-making of complex engineering systems. The resulting tools, such as uncertainty quantification solvers, reinforcement learning, and physics-informed machine learning, have achieved great success in critical DOE tasks such as material discovery and design, energy system modeling and control, and numerical weather and climate prediction. A core topic in scientific machine learning and artificial intelligence is Bayesian inference: given an observed data set, people want to estimate the posterior distribution of a (possibly large) number of hidden parameters. Due to the flexibility and weak assumptions, Bayesian sampling has been the mainstream Bayesian inference solvers despite the rapid progress of approximate Bayesian inference. Classical Bayesian sampling methods such as Markov-chain Monte Carlo suffer from a low-acceptance rate due to the random walk nature, therefore state-of-the-art techniques use Hamiltonian Monte Carlo and its variants to efficiently draw posterior samples in a high dimension. The key idea of Hamiltonian Monte Carlo and its variants is to simulate the Hamiltonian dynamics of a classical particle with a fixed mass, and their performance significantly degrades when the posterior distribution is highly spiky or has multiple modes. Leveraging the idea of quantum physics, this project has investigated new theory, algorithms and applications of Bayesian inference (especially Bayesian sampling). The main results include: (1) novel quantum-inspired Bayesian sampling methods that can lead to better accuracy for challenging multi-modal or spiky distributions, (2) more scalable machine learning framework leveraging tensor-compressed Bayesian inference, and (3) Bayesian and sampling approaches for verifying the robustness of continuous and binary neural networks.

97 MATHEMATICS AND COMPUTING↗

QM Investigation of Rare Earth Ion Interactions with First Hydration Shell Waters and Protein-Based Coordination Models

Here, conventional methods for extracting rare earth metals (REMs) from mined mineral ores are inefficient, expensive, and environmentally damaging. Recent discovery of lanmodulin (LanM), a protein that coordinates REMs with high-affinity and selectivity over competing ions, provides inspiration for new REM refinement methods. Here, we used quantum mechanical (QM) methods to investigate trivalent lanthanide cation (Ln 3+ ) interactions with coordination systems representing bulk solvent water and protein binding sites. Energy decomposition analysis (EDA) showed differences in the energetic components of Ln 3+ interaction with representatives of solvent (water, H 2 O) and protein binding sites (acetate, CH 3 COO – ), highlighting the importance of accurate description of electrostatics and polarization in computational modeling of REM interactions with biological and bioinspired molecules. Relative binding free energies were obtained for Ln 3+ with coordination complexes originating from binding sites in PDB structures of a lanthanum binding peptide (PDB entry 7CCO) and LanM, with explicit consideration of the first hydration shell waters, according to quasi-chemical theory (QCT). Beyond the first shell, the bulk solvent environment was represented with an implicit continuum model. Ln 3+ interactions with (H 2 O) 9 and both binding site models became more favorable, moving down the periodic series. This trend was more pronounced with the protein binding site models than with water, resulting in affinity increasing with periodic number, except for the last REM, Lu 3+ , which bound less favorably than the preceding element, Yb 3+ . Using the truncated 7CCO binding site model, the magnitude and trend of the experimental Ln 3+ relative binding free energies for the whole 7CCO peptide were reproduced. Conversely, the previously reported experimental data for LanM show a preference for the earlier lanthanides; this is likely due to longer-range interactions and cooperative effects, which are not represented by the reduced models. Using the truncated 7CCO binding site model, the magnitude and trend of the experimental Ln 3+ relative binding free energies for the whole 7CCO peptide were reproduced. In contrast to the previously reported experimental data for LanM, the peptide preferentially binds the earlier lanthanides. This difference likely arises due to longer-range interactions and cooperative effects not represented by the peptide. Further investigation of Ln 3+ interactions with whole proteins using polarizable molecular mechanics models with explicit solvent is warranted to understand the influence of longer-ranged interactions, cooperativity, and bulk solvent. Nevertheless, the present work provides new insights into Ln 3+ interactions with biomolecules and presents an effective computational platform for designing specific single-site REM binding peptides more efficiently.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Vidyut3d: A GPU accelerated fluid solver for non-equilibrium plasmas on adaptive grids

We present the numerical methods, programming methodology, verification, and performance assessment of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures, in this work. Our plasma fluid model solves the coupled conservation equations for species transport, electrostatic Poisson and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive-grid/particle management library, AMReX, and is portable over widely available vendor specific GPU architectures. We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth-order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on capacitive discharges and atmospheric pressure streamer propagation. We demonstrate the use of our solver on two 3D simulation cases: an atmospheric streamer propagation in Ar-H2 mixtures and a low pressure three-electrode radio frequency reactor. Our performance studies on three different CPU+GPU architectures indicate ~ 150-400X speed-up using AMD and NVIDIA GPUs per time step compared to a single CPU core for a 4 million cell simulation with 15 species.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Improved Charge Sensing on a SiMOS Double Quantum Dot using a Cryogenic Skipper Readout ASIC (Quandarum)

Major outstanding questions in high-energy physics such as the nature of dark matter and the existence of interactions beyond the standard model require new measurement techniques which are extremely sensitive to minute electromagnetic fields. An array of entangled spin qubits is a promising system for building novel detectors due to its combination of sensitivity and controllability. CMOS-based electron spin qubits, which have demonstrated the operational requirements for fault-tolerant quantum computing [1], offer a particular opportunity due to their compatibility with classical electronics, which allows the leveraging of decades of development of low-noise cryogenic detectors for physics. In this work, we combine a SiMOS double-quantum dot device architecture with a state-of-the-art cryoelectronic readout circuit [2-3] aimed to demonstrate improved charge readout using a single-electron transistor (SET). We identify the design characteristics for an SET that facilitate the use of on-chip classical electronics as a low-power, high-bandwidth first amplification stage and explore opportunities for sensor-readout co-design to minimize noise. This is the first of a series of steps to demonstrate high-fidelity readout of a large array of spin qubit with enough sensitivity to probe processes of interest for the investigation of beyond-standard-model physics.

Quinn, Adam [Fermilab]↗

Improving the efficiency of learning-based error mitigation

Error mitigation will play an important role in practical applications of near-term noisy quantum computers. Current error mitigation methods typically concentrate on correction quality at the expense of frugality (as measured by the number of additional calls to quantum hardware). To fill the need for highly accurate, yet inexpensive techniques, we introduce an error mitigation scheme that builds on Clifford data regression (CDR). The scheme improves the frugality by carefully choosing the training data and exploiting the symmetries of the problem. We test our approach by correcting long range correlators of the ground state of XY Hamiltonian on IBM Toronto quantum computer. We find that our method is an order of magnitude cheaper while maintaining the same accuracy as the original CDR approach. The efficiency gain enables us to obtain a factor of 10 improvement on the unmitigated results with the total budget as small as 2 ⋅ 10 5 shots. Furthermore, we demonstrate orders of magnitude improvements in frugality for mitigation of energy of the LiH ground state simulated with IBM's Ourense-derived noise model.

97 MATHEMATICS AND COMPUTING↗

A Tensor Network-Based Quantum Algorithm for the Nonlinear 1D Burgers' Equation

In this work, we implement a tensor network-based quantum algorithm to solve unsteady, nonlinear partial differential equations (PDEs). The challenge lies in how to effectively represent, encode, process, and evolve the nonlinear system of PDEs on quantum computers. We will discuss the new techniques using the compressible 1-dimensional (1D) Burgers' equation as an example, because it represents the fundamental nonlinear feature and yet removes certain complexity in physics, allowing us to focus on the design of quantum algorithms. Previous attempts to solve nonlinear PDEs in quantum computation have often involved storing multiple copies of solutions or employing linearizations. Neither is practical due to exponential scaling with evolution time or insufficient solution accuracy. Our framework is based on matrix product states (MPSs) and matrix product operators (MPOs). For example, the velocity field is represented by MPS, whereas the linear and nonlinear spatial differential terms of the velocity field are processed by MPOs. Our primary focus herein is to verify and validate the various tensor network components of the algorithm using solutions obtained by the classical algorithms on high performance computing (HPC) architectures. We use a classical time marching method to demonstrate the functionality of the tensor network operations to model the PDE and their robustness with the time evolution of the system. Our classical simulation results demonstrate the utility of tensor network-based operations in modeling nonlinear PDEs and highlight the necessity as well as potential advantages of using quantum simulations for these techniques.

Gopalakrishnan Meena, Murali [ORNL] (ORCID:0000000↗

A new rotational relaxation model for use in hypersonic computational fluid dynamics

The theoretical basis for the Landau-Teller equation commonly used to model rotational nonequilibrium is reviewed. Several assumptions underlying this model are indicated to be unrealistic for rarefied hypersonic flow. A new rotational nonequilibrium model based on recent measurements up to 2000K of quantum state transition rates is presented. The new model is applied to the continuum study of normal shock wave structure using both the Burnett equations and a simplified nonlinear constitutive relation. Comparisons are made between shock wave temperature profiles generated from the new model and those generated using the Landau-Teller model. Comparisons of shock reciprocal thicknesses between experimental data for nitrogen and continuum solutions using both rotational models are made. The new rotational model agrees well with experiment up to Mach 6, and under predicts shock thickness at higher Mach numbers. The Landau-Teller model agrees well with experimental shock thickness up to Mach 3, and over predicts the thickness at higher Mach numbers. A modification to the rotational collision number in the Landau-Teller model is found to give results which agree with experimental shock thicknesses at all Mach numbers up to 11.

Chapman, Dean E.↗

Diabatization with Electrostatic Embedding for Studying Photophysics in Organic Molecular Crystals

Highly emissive organic molecular crystals find applications in several areas, such as organic electronics, solar cells, and sensors. Understanding the excited-state mechanisms underlying these applications is essential for optimizing and controlling them effectively. Exciton models coupled with nonadiabatic dynamics, particularly quantum dynamics, provide crucial insights into photochemical and photophysical processes in molecular crystals. Nevertheless, there remains a lack of general tools and automated workflows to facilitate such simulations. In this paper, we present a computational strategy to investigate the photoactivated dynamics of organic molecular crystals, bridging methodologies traditionally used for molecular systems and materials science, with a particular focus on the interplay between local excitations and charge transfer (CT) processes. We have implemented an interface between the fromage and Overdia programs, enabling the construction of vibronic Hamiltonians for molecular crystals within an excited-state ONIOM(QM:QM′) framework, incorporating long-range electrostatics through a RESP-based Ewald summation. Fragment-based diabatization provides a route to quantum dynamics simulations in weak-to-intermediate coupling regimes. The method was applied to the photophysics of dibenzo[g,p]chrysene (DBC) crystals using time-dependent DFT. The fromage/ Overdia interface was employed to compute the couplings of local excitations and CT states for 18 unique DBC dimers in the crystal and to quantify the influence of electrostatic embedding, which was found to be modest (10−20%). Simulations on π-stacked dimers reproduced the small red shift observed experimentally from solution to crystal, attributed to electronic interactions among fixed monomers rather than crystal electrostatics. Quantum dynamics simulations revealed ultrafast population transfer from bright local excitations to CT states. This approach establishes a robust framework linking molecular and solid-state excited-state dynamics, with potential applications for studying excitations, defects, and impurities in molecular crystals.

Crystals↗

Sparsity-Independent Lyapunov Exponent in the Sachdev-Ye-Kitaev Model

The saturation of a recently proposed universal bound on the Lyapunov exponent has been conjectured to signal the existence of a gravity dual. This saturation occurs in the low-temperature limit of the dense Sachdev-Ye-Kitaev (SYK) model, N Majorana fermions with q body ( q > 2 ) infinite-range interactions. We calculate certain out-of-time-order correlators (OTOCs) for N ≤ 64 fermions for a highly sparse SYK model and find no significant dependence of the Lyapunov exponent on sparsity up to near the percolation limit where the Hamiltonian breaks up into blocks. This provides strong support to the saturation of the Lyapunov exponent in the low-temperature limit of the sparse SYK. A key ingredient to reaching N = 64 is the development of a novel quantum spin model simulation library that implements highly optimized matrix-free Krylov subspace methods on graphical processing units. This leads to a significantly lower simulation time as well as vastly reduced memory usage over previous approaches, while using modest computational resources. Strong sparsity-driven statistical fluctuations require both the use of a much larger number of disorder realizations with respect to the dense limit and a careful finite size scaling analysis. The saturation of the bound in the sparse SYK points to the existence of a gravity analog that would enlarge substantially the number of field theories with this feature. Published by the American Physical Society 2024

Physics↗

Thermodynamic Modeling of Intrinsic Defects in MnBi₂Te₄

This repository contains the computational data supporting the manuscript titled “The critical role of intrinsic defects and many-body interactions on the stability of MnBi₂Te₄.” It includes: 1. DFT data generated using VASP, used for training and benchmarking electronic structure models. 2. Quantum Monte Carlo (QMC) data produced with QMCPACK, used to apply many-body corrections and validate the electronic and magnetic properties of MnBi₂Te₄. 3. Relevant scripts used to run, analyze, and process the calculations, enabling reproducibility and transparency of the workflows.

36 MATERIALS SCIENCE↗

Theoretical Study of the Transverse Dielectric Constant of Superlattices and Their Alloys

The optical properties of III to V binary and ternary compounds and GaAs-Al(x)Ga(1-x)As superlattices are determined by calculating the real and imaginary parts of the transverse dielectric constant. Emphasis is given to determining the influence of different material and superlattice parameters on the values of the index of refraction and absorption coefficient. In order to calculate the optical properties of a material, it is necessary to compute its electronic band structure. This was accomplished by introducing a partition band structure approach based on a combination of the vector k x vector p and nonlocal pseudopotential techniques. The advantages of this approach are that it is accurate, computationally fast, analytical, and flexible. These last two properties enable incorporation of additional effects into the model, such as disorder scattering, which occurs for alloy materials and excitons. Furthermore, the model is easily extended to more complex structures, for example multiple quantum wells and superlattices. The results for the transverse dielectric constant and absorption coefficient of bulk III to V compounds compare well with other one-electron band structure models and the calculations show that for small frequencies, the index of refraction is determined mainly by the contibution of the outer regions of the Brillouin zone.

Kahen, K. B.↗

Joint Acceptance Attenuation Factor of Integrated Pressure with Unsteady Pressure-Sensitive Paint Measurements

The Unsteady Pressure-Sensitive Paint (uPSP) is widely used to measure the surface pressure of the scaled model in the wind tunnel tests. Compared to the conventional pressure transducers, uPSP has the advantage of high spatial resolution. With multiple high-speed cameras, the uPSP data collected with the camera pixels are mapped to the surface grid of the scaled model and converted to pressure. The shot noise, which is associated with the quantum processes both in the generation of the photons by the luminescent uPSP and in the conversion of the photons into electrons within the camera, is the dominant component of the noise in the uPSP measurement. The integrated pressure is usually computed as an area-weighted average of the uPSP measured pressures on the grid nodes of a user-defined patch. The effect of the shot noise is reduced in the integrated pressure; however, the measurement of the aerodynamic pressure is also attenuated. This paper discusses the Joint Acceptance Attenuation Factor (JAAF) of the integrated pressure with uPSP measurements. The JAAF is defined as the ratio of the auto or cross Power Spectral Density (PSD) of the integrated aerodynamic pressure on the patch to the average auto PSD of the aerodynamic pressure on the grid nodes of the patch. Under the assumption that the cross spectrum of the aerodynamic pressure can be described with the Corcos model, the closed-form formula of the JAAF is derived for the integrated pressure on rectangular patches via the summation of uPSP measurements on discrete grid nodes. The closed-form formula is verified via the integration of the pressure field of Corcos model over continuous areas. The properties of the JAAF with different parameters are presented and the applications in the comparison of the spectrum of the pressure transducers and uPSP measurements, which were collected in the NASA Space Launch System (SLS) tests with the 11-by-11-foot transonic wind tunnel at NASA Ames Research Center in December 2017 and September 2019 respectively, are also discussed. The work described in this paper is a part of NASA’s development of a new state-of-the-art uPSP capability in production wind tunnels. Funding was provided by the NASA Aerosciences Evaluation and Test Capabilities(AETC) Portfolio Office.

Unsteady Pressure-Sensitive Paint↗

Convergent Protocols for Computing Protein–Ligand Interaction Energies Using Fragment-Based Quantum Chemistry

Fragment-based quantum chemistry methods offer a way to sidestep the steep nonlinear scaling of electronic structure calculations so that large molecular systems can be investigated using high-level methods. Here, we use fragmentation to compute protein–ligand interaction energies in systems with several thousand atoms, using a new software platform for managing fragment-based calculations that implements a screened many-body expansion. Convergence tests using a minimal-basis semiempirical method (HF-3c) indicate that two-body calculations, with single-residue fragments and simple hydrogen caps, are sufficient to reproduce interaction energies obtained using conventional supramolecular electronic structure calculations, to within 1 kcal/mol at about 1% of the computational cost. We also demonstrate that the HF-3c results are illustrative of trends obtained with density functional theory in basis sets up to augmented quadruple-ζ quality. Strategic deployment of fragmentation facilitates the use of converged biomolecular model systems alongside high-quality electronic structure methods and basis sets, bringing ab initio quantum chemistry to systems of hitherto unimaginable size. This will be useful for generation of high-quality training data for machine learning applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Steady-state properties of multi-orbital systems using quantum Monte Carlo

A precise dynamical characterization of quantum impurity models with multiple interacting orbitals is challenging. In quantum Monte Carlo methods, this is embodied by sign problems. A dynamical sign problem makes it exponentially difficult to simulate long times. A multi-orbital sign problem generally results in a prohibitive computational cost for systems with multiple impurity degrees of freedom even in static equilibrium calculations. Here, we present a numerically exact inchworm method that simultaneously alleviates both sign problems, enabling simulation of multi-orbital systems directly in the equilibrium or nonequilibrium steady-state. The method combines ideas from the recently developed steady-state inchworm Monte Carlo framework [Erpenbeck et al., Phys. Rev. Lett. 130, 186301 (2023)] with other ideas from the equilibrium multi-orbital inchworm algorithm [Eidelstein et al., Phys. Rev. Lett. 124, 206405 (2020)]. We verify our method by comparison with analytical limits and numerical results from previous methods.

Chemistry↗

Applicability of PM3 to transphosphorylation reaction path: Toward designing a minimal ribozyme

A growing body of evidence shows that RNA can catalyze many of the reactions necessary both for replication of genetic material and the possible transition into the modern protein-based world. However, contemporary ribozymes are too large to have self-assembled from a prebiotic oligonucleotide pool. Still, it is likely that the major features of the earliest ribozymes have been preserved as molecular fossils in the catalytic RNA of today. Therefore, the search for a minimal ribozyme has been aimed at finding the necessary structural features of a modern ribozyme (Beaudry and Joyce, 1990). Both a three-dimensional model and quantum chemical calculations are required to quantitatively determine the effects of structural features of the ribozyme on the reaction it catalyzes. Using this model, quantum chemical calculations must be performed to determine quantitatively the effects of structural features on catalysis. Previous studies of the reaction path have been conducted at the ab initio level, but these methods are limited to small models due to enormous computational requirements. Semiempirical methods have been applied to large systems in the past; however, the accuracy of these methods depends largely on a simple model of the ribozyme-catalyzed reaction, or hydrolysis of phosphoric acid. We find that the results are qualitatively similar to ab initio results using large basis sets. Therefore, PM3 is suitable for studying the reaction path of the ribozyme-catalyzed reaction.

Manchester, John I.↗

Thermodynamics and its prediction and CALPHAD modeling: Review, state of the art, and perspectives

Thermodynamics is a science concerning the state of a system, whether it is stable, metastable, or unstable, when interacting with its surroundings. The combined law of thermodynamics derived by Gibbs about 150 years ago laid the foundation of thermodynamics. In Gibbs combined law, the entropy production due to internal processes was not included, and the 2nd law was thus practically removed from the Gibbs combined law, so it is only applicable to systems under equilibrium, thus commonly termed as equilibrium or Gibbs thermodynamics. Gibbs further derived the classical statistical thermodynamics in terms of the probability of configurations in a system in the later 1800's and early 1900's. With the quantum mechanics (QM) developed in 1920's, the QM-based statistical thermodynamics was established and connected to classical statistical thermodynamics at the classical limit as shown by Landau in the 1940's. In 1960's the development of density functional theory (DFT) by Kohn and co-workers enabled the QM prediction of properties of the ground state of a system. On the other hand, the entropy production due to internal processes in non-equilibrium systems was studied separately by Onsager in 1930's and Prigogine and co-workers in the 1950's. In 1960's to 1970's the digitization of thermodynamics was developed by Kaufman in the framework of the CALculation of PHAse Diagrams (CALPHAD) modeling of individual phases with internal degrees of freedom. CALPHAD modeling of thermodynamics and atomic transport properties has enabled computational design of complex materials in the last 50 years. Our recently termed zentropy theory integrates DFT and statistical mechanics through the replacement of the internal energy of each individual configuration by its DFT-predicted free energy. The zentropy theory is capable of accurately predicting the free energy of individual phases, transition temperatures and properties of magnetic and ferroelectric materials with free energies of individual configurations solely from DFT-based calculations and without fitting parameters, and is being tested for other phenomena including superconductivity, quantum criticality, and black holes. Those predictions include the singularity at critical points with divergence of physical properties, negative thermal expansion, and the strongly correlated physics. Furthermore, those individual configurations may thus be considered as the genomic building blocks of individual phases in the spirit of the materials genome®. This has the potential to shift the paradigm of CALPHAD modeling from being heavily dependent on experimental inputs to becoming fully predictive with inputs solely from DFT-based calculations and machine learning models built on those calculations and existing experimental data through newly developed and future open-source tools. Furthermore, through the combined law of thermodynamics including the internal entropy production, it is shown that the kinetic coefficient matrix of independent internal processes is diagonal with respect to the conjugate potentials in the combined law, and the cross phenomena that the phenomenological Onsager flux and reciprocal relationships are due to the dependence of the conjugate potential of a molar quantity on nonconjugate molar quantities and other potentials, which can be predicted by the zentropy theory and CALPHAD modeling.

42 ENGINEERING↗

Applications of flow models to the generation of correlated lattice QCD ensembles

Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these correlations can be exploited for variance reduction in the computation of observables. Three different proof-of-concept applications are demonstrated using a novel residual flow architecture: continuum limits of gauge theories, the mass dependence of QCD observables, and hadronic matrix elements based on the Feynman–Hellmann approach. In all three cases, it is shown that statistical uncertainties are significantly reduced when machine-learned flows are incorporated as compared with the same calculations performed with uncorrelated ensembles or direct reweighting. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗