Classical Field Research Articles

Development of a ReaxFF reactive force field for ternary phosphate-based bioactive glasses.

Phosphate-based glasses (PBGs) in the CaO-Na2O-P2O5 system have diverse applications as biomaterials due to their unique dissolution properties. A reactive force field (ReaxFF) has been developed to simulate these materials at the atomic level. The ReaxFF parameters of PBGs, including the interaction between phosphorus and calcium atoms, have been developed using a published code based on genetic algorithms. The training data, including the atomic charges, atomic forces, bond and angle parameters, and different differential energies, are chosen and measured from static quantum-mechanical calculations and abinitio molecular dynamics of PBGs. We did different short- and medium-range structural analyses on the bulk simulated PBGs with different compositions to validate the developed potential. Radial and angular distribution functions and coordination numbers of network formers and modifiers, as well as the network connectivity of the glass, are in agreement with experimental and previous simulations using both shell-model classical force fields and abinitio simulated data; for example, the coordination number of phosphorus is 4.0. This successful development of ReaxFF parameters being able to describe the bulk PBGs enables us to work on the dissolution behavior of the glasses, including the interaction of water molecules with PBGs, in future works.

Quantum Phase Properties of a State Driven by a Classical Field

Quantum Phase Properties of a State Driven by a Classical Field

Quantum approach to bound states in field theory

It is well known that (possibly nonunique) suitable field dynamics can be prescribed in spacetimes with timelike boundaries by means of appropriate boundary conditions. In [R. M. Wald, ], Wald derived a conserved energy functional for each prescribed dynamics. This conserved energy is related to the positive self-adjoint extensions of the spatial part A of the wave equation ∂2Φ/∂t2=−AΦ (A may not be, in principle, essentially self-adjoint). This is quite surprising since the canonical energy is not conserved in these cases. In this paper, we rederive this energy functional from an action principle (with appropriate boundary terms) following [A. A. Saharian, ] and consider field dynamics arising from nonpositive self-adjoint extensions of A. The spectrum of the resulting theory fails to be positive and unstable mode solutions for classical fields come to light. By studying fields in half-Minkowski spacetime, we illustrate that these unstable classical solutions come as a consequence of an inverted parabolic potential governing their dynamics. From the quantum mechanical point of view, this leads to an effective inverted harmonic oscillator at the boundary. We then explore these unstable modes behavior, as well as their instabilities, at the quantum level. Published by the American Physical Society 2024

The classical double copy in curved spacetimes: perturbative Yang-Mills from the bi-adjoint scalar

We formulate a version of the double copy for classical fields in curved spacetimes. We provide a correspondence between perturbative solutions to the bi-adjoint scalar equations and those of the Yang-Mills equations in position space. At the linear level, we show that there exists a map between these solutions for maximally symmetric spacetime backgrounds, that provides every Yang-Mills solution by the action of an appropriate differential operator on a bi-adjoint scalar solution. Given the existence of a linearized map, we show that it is possible to cast the solutions of the Yang-Mills equations at arbitrary perturbation order in terms of the corresponding bi-adjoint scalar solutions. This all-order map is reminiscent of the flat space BCJ double copy, and works for any curved spacetime where the perturbative expansion holds. We show that these results have the right flat space limit, and that the correspondence is agnostic to the choice of gauge.

Assessment of Embedding Schemes in a Hybrid Machine Learning/Classical Potentials (ML/MM) Approach.

Machine learning (ML) methods have reached high accuracy levels for the prediction of in vacuo molecular properties. However, the simulation of large systems solely through ML methods (such as those based on neural network potentials) is still a challenge. In this context, one of the most promising frameworks for integrating ML schemes in the simulation of complex molecular systems are the so-called ML/MM methods. These multiscale approaches combine ML methods with classical force fields (MM), in the same spirit as the successful hybrid quantum mechanics-molecular mechanics methods (QM/MM). The key issue for such ML/MM methods is an adequate description of the coupling between the region of the system described by ML and the region described at the MM level. In the context of QM/MM schemes, the main ingredient of the interaction is electrostatic, and the state of the art is the so-called electrostatic-embedding. In this study, we analyze the quality of simpler mechanical embedding-based approaches, specifically focusing on their application within a ML/MM framework utilizing atomic partial charges derived in vacuo. Taking as reference electrostatic embedding calculations performed at a QM(DFT)/MM level, we explore different atomic charges schemes, as well as a polarization correction computed using atomic polarizabilites. Our benchmark data set comprises a set of about 80k small organic structures from the ANI-1x and ANI-2x databases, solvated in water. The results suggest that the minimal basis iterative stockholder (MBIS) atomic charges yield the best agreement with the reference coupling energy. Remarkable enhancements are achieved by including a simple polarization correction.

A new canonical affine bracket formulation of Hamiltonian classical field theories of first order

It has been a long standing question how to extend, in the finite-dimensional setting, the canonical Poisson bracket formulation from classical mechanics to classical field theories, in a completely general, intrinsic, and canonical way. In this paper, we provide an answer to this question by presenting a new completely canonical bracket formulation of Hamiltonian Classical Field Theories of first order on an arbitrary configuration bundle. It is obtained via the construction of the appropriate field-theoretic analogues of the Hamiltonian vector field and of the space of observables, via the introduction of a suitable canonical Lie algebra structure on the space of currents (the observables in field theories). This Lie algebra structure is shown to have a representation on the affine space of Hamiltonian sections, which yields an affine analogue to the Jacobi identity for our bracket. The construction is analogous to the canonical Poisson formulation of Hamiltonian systems although the nature of our formulation is linear-affine and not bilinear as the standard Poisson bracket. This is consistent with the fact that the space of currents and Hamiltonian sections are respectively, linear and affine. Our setting is illustrated with some examples including Continuum Mechanics and Yang–Mills theory.

Global ranking of the sensitivity of interaction potential contributions within classical molecular dynamics force fields

Uncertainty quantification (UQ) is rapidly becoming a sine qua non for all forms of computational science out of which actionable outcomes are anticipated. Much of the microscopic world of atoms and molecules has remained immune to these developments but due to the fundamental problems of reproducibility and reliability, it is essential that practitioners pay attention to the issues concerned. Here a UQ study is undertaken of classical molecular dynamics with a particular focus on uncertainties in the high-dimensional force-field parameters, which affect key quantities of interest, including material properties and binding free energy predictions in drug discovery and personalized medicine. Using scalable UQ methods based on active subspaces that invoke machine learning and Gaussian processes, the sensitivity of the input parameters is ranked. Our analyses reveal that the prediction uncertainty is dominated by a small number of the hundreds of interaction potential parameters within the force fields employed. This ranking highlights what forms of interaction control the prediction uncertainty and enables systematic improvements to be made in future optimizations of such parameters.

Personalized Path-Tracking Approach Based on Reference Vector Field for Four-Wheel Driving and Steering Wire-Controlled Chassis

It is essential and forward-thinking to investigate the personalized use of four-wheel driving and steering wire-controlled unmanned chassis. This paper introduces a personalized path-tracking approach designed to adapt the vehicle’s control system to human-like characteristics, enhancing the fit and maximizing the potential of the chassis’ multi-directional driving and steering capabilities. By modifying the classic vehicle motion controller design, this approach aligns with individual driving habits, significantly improving upon traditional path-tracking control methods that rely solely on reference vector fields. First, the classic reference vector field’s logic was expanded upon, and it is shown that a personalized upgrade is feasible. Then, driving behavior data from multiple drivers were collected using a driving simulator. The fuzzy c-means clustering method was used to categorize drivers based on typical states that match vehicle path-tracking performance. Additionally, the random forest algorithm was used as the method for recognizing driving style. Subsequently, a personalized path-tracking control strategy based on the reference vector field was developed and a distributed execution architecture for four-wheel driving and steering wire-controlled unmanned chassis was established. Finally, the proposed personalized path-tracking approach was validated using a driving simulator. The results of the experimental tests demonstrated that the personalized path-tracking control approach not only fits well with various driving styles but also delivers high accuracy in driving style identification, making it highly suitable for application in four-wheel driving and steering wire-controlled chassis.

Optical Nonreciprocity in a Multimode Cavity Optomechanical System Controlled by Dynamic Casimir Force

AbstractThe phenomenon of nonreciprocity arises from the disruption of time reversal symmetry, enabling the one‐way transfer of signals through specific channels. In the framework of cavity optomechanics, this symmetry breaking is attributed to a nonuniform radiation pressure force resulting from the interaction between light and matter. This study investigates a hybrid cavity optomechanical system (COMS) comprising two optical modes, directly coupled to each other via photon hopping interaction and indirectly via a common mechanical excitation in the form of a movable mirror, and an additional parallel metallic plate that induces a dynamical Casimir force (DCF) interaction between the plates. The two optical cavities are driven by two strong laser fields, accompanied by two weak probe classical fields from each port. The primary focus lies in exploring the nonreciprocal behavior of the light field across ports one and two, strongly manipulated by the DCF. The DCF plays a pivotal role in providing extra degrees of flexibility and manipulation in controlling the nonreciprocal signal transmission by modifying the resonance conditions of the fields within the hybrid COMS and is responsible for the amplification and swapping of information between the two ports.

Bogomol’nyi-like equations in gravity theories

Using the Bogomol’nyi–Prasad–Sommerfield Lagrangian method, we show that gravity theory coupled to matter in various dimensions may possess Bogomol’nyi-like equations, which are first-order differential equations, satisfying the Einstein equations and the Euler–Lagrange equations of classical fields (U(1) gauge and scalar fields). In particular we consider static and spherically symmetric solutions by taking proper ansatzes and then we find an effective Lagrangian density that can reproduce the Einstein equations and the Euler–Lagrange equations of the classical fields. We consider the BPS Lagrangian density to be linear function of first-order derivative of all the fields. From these two Lagrangian desities we are able to obtain the Bogomol’nyi-like equations whose some of solutions are well-known such as Schwarzschild, Reissner–Nordström, Tangherlini black holes, and the recent black holes with scalar hair in three dimensions (Phys. Rev. D 107, 124047). Using these Bogomol’nyi-like equations, we are also able to find new solutions for scalar hair black holes in three and four dimensional spacetime. Furthermore we show that the Bogomol’nyi–Prasad–Sommerfield Lagrangian method can provide a simple alternative proof of black holes uniqueness theorems in any dimension.

Regularized Loss With Hyperparameter Estimation for Weakly Supervised Single Class Segmentation.

We propose a new image level weakly supervised segmentation approach for datasets with a single object class of interest. Our approach is based on a regularized loss function inspired by the classical Conditional Random Field (CRF) modeling. Our loss models properties of generic objects, and we use it to guide CNN towards segments that are more likely to correspond to the object, thus avoiding the need for pixel precise annotations. Training CNN with regularized loss is a difficult task for gradient descent. We develop an annealing algorithm which is crucial for a successful training. Furthermore, we develop an approach for hyperparameter setting for the most important components of our regularized loss. This is far from trivial, since there is no pixel precise ground truth for guidance. The advantage of our method is that we use a standard CNN architecture and an easy to interpret loss function, derived from classical CRF models. Furthermore, we apply the same loss function for any task/dataset. We first evaluate our approach for salient object segmentation and co-segmentation. These tasks naturally involve one object class of interest. Then we adapt our approach to image level weakly supervised multi-class semantic segmentation. We obtain state-of-the-art results.

Molecular dynamics investigations on the thermophysical property of fatty acid ethyl esters

To develop innovative fuel additives or substitutes and design spray-assisted internal combustion engines, it is important to have a comprehensive understanding of the thermophysical characteristics of biodiesels. Rooted in statistical mechanics, the molecular simulation method can predict the thermophysical properties over a wide range of temperatures and pressures, which overcomes the challenges of experimental measurements and facility restrictions. This work focused on the evaluation of three classical force fields (FFs) in terms of their ability to predict the thermophysical properties of ethyl-caprylate (EtC8:0), ethyl-caprate (EtC10:0), ethyl-laurate (EtC12:0), ethyl-myristate (EtC14:0), ethyl-palmitate (EtC16:0), and ethyl-stearate (EtC18:0) within a temperature range of (303.15 to 403.15) K and pressures up to 100 MPa. The Optimized Potential for Liquid Simulations–All atom and its modification (OPLS and L–OPLS) and Transferable Potential for Phase Equilibria–United Atom (TraPPE–UA) FFs were evaluated. These findings demonstrated that the L–OPLS FF, when applied in the isobaric-isothermal (NPT) and canonical ensembles (NVT), effectively replicated the experimental data and semi-empirical models for density, viscosity, diffusivity coefficient, and interfacial behavior at elevated temperatures and pressures. Moreover, the utilization of the radial distribution function, radius of gyration, and end-to-end distance distribution in the analysis of liquid conformations allowed for a comprehensive investigation of the microscopic structure. This work provides the theoretical methodologies and empirical evidence for the advancement of biodiesel and other petrochemicals.

Covariantly constant Yang Mills vacuum fields and condensation of magnetic fluxes

Covariantly constant gauge fields are solutions of the sourceless Yang-Mills equation and represent classical vacuum fields. We found that the moduli space of covariantly constant gauge fields is infinite-dimensional and is much larger than the space of constant chromomagnetic fields. These solutions represent non-perturbative chromomagnetic flux tubes (vortices) and are the superposition of Nielsen-Olesen chromomagnetic vortices of opposite orientations. It is suggested that the solutions describe the condensate of superposed tubes (vortices) of opposite orientations and represent a dual analog of the Cooper pairs condensate in a superconductor.

Peripheral and bimanual reaching in a stroke survivor with left visual neglect and extinction

Whether attentional deficits are accompanied by visuomotor impairments following posterior parietal lesions has been debated for quite some time. This single-case study investigated reaching in a stroke survivor (E.B.) with left visual neglect and visual extinction following right temporo-parietal-frontal strokes. Unlike most neglect patients, E.B. did not present left hemiparesis, homonymous hemianopia nor showed evidence of motor neglect or extinction allowing us to examine, for the first time, if lateralised attentional deficits co-occur with deficits in peripheral and bimanual reaching. First, we found a classic optic ataxia field effect: E.B.’s accuracy was impaired when reaching to peripheral targets in her neglected left visual field (regardless of the hand used). Second, we found a larger bimanual cost for movement time in E.B. than controls when both hands reached to incongruent locations. E.B.’s visuomotor profile is similar the one of patients with optic ataxia showing that attentional deficits are accompanied by visuomotor deficits in the affected field.

How Large is the Space of Covariantly Constant Gauge Fields

The covariantly constant gauge fields are solutions of the sourceless Yang-Mills equation and represent classical vacuum fields. We found that the moduli space of the covariantly constant gauge fields is infinite-dimensional and is therefore much larger than the space of constant chromomagnetic fields. These solutions represent a space lattice of non-perturbative magnetic flux tubes/vertices oriented in the opposite directions, each of which has a Dirac quantum flux. The geometrical structure of the solutions is self-sustaining without presence of any Higgs field support. They are similar to a condensate of the Nielsen-Olesen magnetic flux tubes of opposite orientations. The solutions have a non-vanishing Hopf invariant density.

Feature Selection for High-Dimensional Neural Network Potentials with the Adaptive Group Lasso

Abstract Neural network potentials are a powerful tool for atomistic simulations, allowing to accurately reproduce ab initio potential energy surfaces with computational performance approaching classical force fields. A central component of such potentials is the transformation of atomic positions into a set of atomic features in a most efficient and informative way. In this work, a feature selection method is introduced for high dimensional neural network potentials, based on the Adaptive Group Lasso (AGL) approach. It is shown that the use of an embedded method, taking into account the interplay between features and their action in the estimator, is necessary to optimize the number of features. The method’s efficiency is tested on three different monoatomic systems, including Lennard-Jones as a simple test case, Aluminium as a system characterized by predominantly radial interactions, and Boron as representative of a system with strongly directional interactions. The AGL is compared with unsupervised filter methods and found to perform consistently better in reducing the number of features needed to reproduce the reference simulation data. In particular, our results show the importance of taking into account model predictions in feature selection for interatomic potentials.

Data-Driven Discovery of Gas-Selective Organic Linkers in Metal-Organic Frameworks for the Separation of Ethylene and Ethane.

Metal-organic frameworks (MOFs) are potential candidates for gas-selective adsorbents for the separation of an ethylene/ethane mixture. To accelerate material discovery, high-throughput computational screening is a viable solution. However, classical force fields, which were widely employed in recent studies of MOF adsorbents, have been criticized for their failure to cover complicated interactions such as those involving π electrons. Herein, we demonstrate that machine learning force fields (MLFFs) trained on quantum-chemical reference data can overcome this difficulty. We have constructed a MLFF to accurately predict the adsorption energies of ethylene and ethane on the organic linkers of MOFs and discovered that the π electrons from both the ethylene molecule and the aromatic rings in the linkers could substantially influence the selectivity for gas adsorption. Four kinds of MOF linkers are identified as having promise for the separation of ethylene and ethane, and our results could also offer a new perspective on the design of MOF building blocks for diverse applications.

Classical field approximation of ultralight dark matter: Quantum break times, corrections, and decoherence

Classical field approximation of ultralight dark matter: Quantum break times, corrections, and decoherence

Molecular dynamics simulations for the prediction of thermophysical properties of plutonium-based molten salts

Molten salt nuclear reactors are promising technologies for sustainable energy sources. In this context, understanding the physicochemical properties of molten salts is essential to the development, usage, and maintenance of reactors. Classical molecular simulations allow estimating the macroscopic properties of molten salts at a relatively low computational cost. In this work, we develop a new force field for plutonium-based molten salts. We validate our classical model by comparing molecular dynamics results with experimental measurements, obtaining a quantitative agreement. Our work demonstrates the reliability and transferability of classical force fields to represent the physicochemical properties of molten salts.

Hybrid geometrodynamics: a Hamiltonian description of classical gravity coupled to quantum matter

We generalize the Hamiltonian picture of general relativity coupled to classical matter, known as geometrodynamics, to the case where such matter is described by a quantum field theory in curved spacetime, but gravity is still described by a classical metric tensor field over a spatial hypersurface and its associated momentum. Thus, in our approach there is no non-dynamic background structure, apart from the manifold of events, and the gravitational and quantum degrees of freedom have their dynamics inextricably coupled. Given the Hamiltonian nature of the framework, we work with the generators of hypersurface deformations over the manifold of quantum states. The construction relies heavily on the differential geometry of a fibration of the set of quantum states over the set of gravitational variables. An important mathematical feature of this work is the use of Minlos’s theorem to characterize Gaussian measures over the space of matter fields and of Hida distributions to define a common superspace to all possible Hilbert spaces with different measures, to properly characterize the Schrödinger wave functional picture of QFT in curved spacetime. This allows us to relate states within different Hilbert spaces in the case of vacuum states or measures that depend on the gravitational degrees of freedom, as the ones associated to Ashtekar’s complex structure. This is achieved through the inclusion of a quantum Hermitian connection for the fibration, which will have profound physical implications. The most remarkable physical features of the construction are norm conservation of the quantum state (even if the total dynamics are non-unitary), the clear identification of the hybrid conserved quantities and the description of a dynamical backreaction of quantum matter on geometry and vice versa, which shall modify the physical properties the gravitational field would have in the absence of backreaction.