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Forced motion of an initially stressed rectangular plate - An elasticity solution
An initially stressed rectangular plate is subjected to a transverse, time dependent load. The initial stress field is constant and parallel to two of the plate edges. The transverse load is uniformly distributed over a rectangular area, the sides of which are parallel to the sides of the plate. The problem is formulated within the framework of classical, three-dimensional elasticity theory, and an exact solution is obtained in series form. The case of static stability under pre-stress is also considered.
A classical model for three-body interactions in aqueous ionic systems
We present a classical induction model to evaluate the three-body ion–water–water (I–W–W) and water–water–water (W–W–W) interactions in aqueous ionic systems. The classical description of the induction energy is based on electrostatic distributed multipoles up to hexadecapole and distributed polarizabilities up to quadrupole–quadrupole on the O and H atoms of water. The monatomic ions were described by a point charge and a dipole–dipole polarizability, while for the polyatomic ions, distributed multipoles up to hexadecapole and distributed polarizabilities up to quadrupole–quadrupole were used. The accuracy of the classical model is benchmarked against an accurate dataset of 936 (I–W–W) and 2184 (W–W–W) three-body terms for 13 different monatomic and polyatomic cation and anion systems. The classical model shows excellent agreement with the reference second order Moller–Plesset and coupled-cluster single double and perturbative triple [CCSD(T)] three-body energies. The Root-Mean-Square-Errors (RMSEs) for monatomic cations, monatomic anions, and polyatomic ions were 0.29, 0.25, and 0.12 kcal/mol, respectively. The corresponding RMSE for 1744 CCSD(T)/aVTZ three-body (W–W–W) energies, used to train MB-pol, was 0.12 kcal/mol. The accuracy of the proposed classical model demonstrates that the three-body term for aqueous ionic systems can be accurately modeled classically. This approach provides a fast, efficient, and as-accurate path toward modeling the three-body term in aqueous ionic systems that is fully transferable across systems with different ions without the need to fit to tens of thousands of ab initio calculations for each ion to extend existing many-body force fields to interactions between water and ions.
Bond order predictions using deep neural networks
Machine learning is an extremely powerful tool for the modern theoretical chemist since it provides a method for bypassing costly algorithms for solving the Schrödinger equation. Already, it has proven able to infer molecular and atomic properties such as charges, enthalpies, dipoles, excited state energies, and others. Most of these machine learning algorithms proceed by inferring properties of individual atoms, even breaking down total molecular energy into individual atomic contributions. In this paper, we introduce a modified version of the Hierarchically Interacting Particle Neural Network (HIP-NN) capable of making predictions on the bonds between atoms rather than on the atoms themselves. We train the modified HIP-NN to infer bond orders for a large number of small organic molecules as computed via the Natural Bond Orbital package. We demonstrate that the trained model is extensible to molecules much larger than those in the training set by studying its performance on the COMP6 dataset. This method has applications in cheminformatics and force field parameterization and opens a promising future for machine learning models to predict other quantities that are defined between atoms such as density matrix elements, Hamiltonian parameters, and molecular reactivities.
Quasilinear theory: the lost ponderomotive effects and why they matter
Quasilinear theory (QLT) has been used for modeling wave–plasma interactions for decades but remains largely heuristic. Plasma inhomogeneity, ponderomotive effects, microscopic fluctuations, and collisions are not easily accommodated from first principles in QLT, and typically are ignored entirely, due to the limitations of the standard Fourier–Laplace global-mode approach. This results in inconsistencies, for example, violation of the action conservation for nonresonant waves. However, these issues can be avoided, and the theory can be substantially generalized and corrected, if QLT is formulated using more suitable analytical tools, particularly, the Weyl symbol calculus. Here, an attempt is made to deliver an accessible review of this modern formulation, provide intuitive calculations for special cases, and elaborate on the connection with the ‘oscillation-center QLT’ originally proposed by Dewar (Phys Fluids 16:1102, 1973). A Fokker–Planck equation for a ‘dressed’ distribution is derived from the Klimontovich equation and captures quasilinear diffusion, ponderomotive forces, and interactions with background fields for a generic Hamiltonian, so many known formulations of QLT for specific plasma models become corollaries of a single unifying theory. Also, waves are allowed to be off-shell (not constrained by a dispersion relation), which allows them to accommodate microscopic fluctuations. This leads to a collision integral of the Balescu–Lenard type that has all the usual properties but is not restricted to any specific plasma model. For on-shell waves, a generalized version of the classic oscillation-center QLT is obtained. Finally, combined with the wave-kinetic equation, this formulation not only conserves particles, momentum, and energy, like the classic QLT but also reinstates the action conservation for nonresonant waves.
Quantum electrodynamics mediated by a photon with continuous spin
In recent work with Zhou, we studied classical interactions of matter with a “continuous spin” field, whose excitations have zero mass but nonzero spin Casimir (spin scale) ρ . We reported evidence that such theories are a calculable infrared deformation of familiar massless theories including electromagnetism. Building on the aforementioned work, this paper presents rules for computing scattering amplitudes involving charged scalar matter and continuous spin photons with nonzero spin scale. As a concrete example, we compute the pair annihilation and Compton scattering amplitudes in this theory and comment on their physical properties, including unitarity and scaling behavior at small and large ρ . Like the classical physics and soft factors studied in prior work, these amplitudes exhibit “helicity correspondence,” recovering familiar amplitudes at energy scales ≫ ρ , but with calculable deviations that could be experimentally tested. These results bolster the conjecture that continuous spin particles with a very small ρ could mediate long-range forces in nature (e.g., the photon could be a continuous spin particle), and extend the range of physical effects that could be used to test this hypothesis. Published by the American Physical Society 2024
Insight into SEI Growth in Li-Ion Batteries using Molecular Dynamics and Accelerated Chemical Reactions
The performance of lithium-ion batteries (LIB) using organic electrolytes strongly depends on the formation of a stable solid electrolyte interphase (SEI) film. Elucidating the dynamic evolution and spatial composition of the SEI can be very useful to study the stability of SEI components and help optimize the formation cycles of LIB. We propose a classical molecular dynamics simulation protocol for predicting the first stages of SEI formation using a reaction method involving the decomposition of EC and LiPF 6 molecules in the electrolyte. We accelerate the formation of SEI components near the anode surface by increasing the probability of reactions, implemented through a geometry matching scheme, followed by a force-field reconfiguration. We observe the formation of gases (C 2 H 4 ), inorganic (Li 2 CO 3 and LiF) and organic (LEDC) components. Finally, this protocol shows promise to be able to evaluate the effects of varying electrolyte compositions and additives on SEI layer structure and composition.
Collective coordinate fix in the path integral
Collective coordinates are frequently employed in path integrals to manage divergences caused by fluctuations around saddle points that align with classical symmetries. These coordinates parametrize a manifold of zero modes and more broadly provide judicious coordinates on the space of fields. However, changing from local coordinates around a saddle point to more global collective coordinates is remarkably subtle. The main complication is that the mapping from local coordinates to collective coordinates is generically multivalued. Consequently one is forced to either restrict the domain of path integral in a delicate way, or otherwise correct for the multivaluedness by dividing the path integral by certain intersection numbers. We provide a careful treatment of how to fix collective coordinates while accounting for these intersection numbers, and then demonstrate the importance of the fix for free theories. We also provide a detailed study of the fix for interacting theories and show that the contributions of higher intersections to the path integral can be nonperturbatively suppressed. Using a variety of examples ranging from single-particle quantum mechanics to quantum field theory, we explain and resolve various pitfalls in the implementation of collective coordinates. Published by the American Physical Society 2024
Half-magnetization plateau and the origin of threefold symmetry breaking in an electrically switchable triangular antiferromagnet
Not Available
On the molecular correlations that result in field-dependent conductivities in electrolyte solutions
Employing recent advances in response theory and nonequilibrium ensemble reweighting, we study the dynamic and static correlations that give rise to an electric field-dependent ionic conductivity in electrolyte solutions. We consider solutions modeled with both implicit and explicit solvents, with different dielectric properties, and at multiple concentrations. Implicit solvent models at low concentrations and small dielectric constants exhibit strongly field-dependent conductivities. We compare these results to Onsager-Wilson theory of the Wien effect, which provides a qualitatively consistent prediction at low concentrations and high static dielectric constants but is inconsistent away from these regimes. The origin of the discrepancy is found to be increased ion correlations under these conditions. Explicit solvent effects act to suppress nonlinear responses, yielding a weakly field-dependent conductivity over the range of physically realizable field strengths. By decomposing the relevant time correlation functions, we find that the insensitivity of the conductivity to the field results from the persistent frictional forces on the ions from the solvent. Our findings illustrate the utility of nonequilibrium response theory in rationalizing nonlinear transport behavior.
Magnetic Imaging of Domain Walls in the Antiferromagnetic Topological Insulator MnBi 2 Te 4
The control of domain walls or spin textures is crucial for spintronic applications of antiferromagnets. Despite many efforts, it has been challenging to directly visualize antiferromagnetic domains or domain walls with nanoscale resolution, especially in magnetic field. Here, we report magnetic imaging of domain walls in several uniaxial antiferromagnets, the topological insulator MnBi 2 Te 4 family, using cryogenic magnetic force microscopy (MFM). Our MFM results reveal higher magnetic susceptibility inside the domain walls than in domains. Domain walls in these antiferromagnets form randomly with strong thermal and magnetic field dependence. Here, the direct visualization of these domain walls and domain structures in the magnetic field will not only facilitate the exploration of intrinsic topological phenomena in antiferromagnetic topological insulators but will also open a new path toward control and manipulation of domain walls or spin textures in functional antiferromagnets.
Extended Lagrangian Born–Oppenheimer molecular dynamics using a Krylov subspace approximation
It is shown how the electronic equations of motion in extended Lagrangian Born–Oppenheimer molecular dynamics simulations can be integrated using low-rank approximations of the inverse Jacobian kernel. This kernel determines the metric tensor in the harmonic oscillator extension of the Lagrangian that drives the evolution of the electronic degrees of freedom. The proposed kernel approximation is derived from a pseudoinverse of a low-rank estimate of the Jacobian, which is expressed in terms of a generalized set of directional derivatives with directions that are given from a Krylov subspace approximation. The approach allows a tunable and adaptive approximation that can take advantage of efficient preconditioning techniques. The proposed kernel approximation for the integration of the electronic equations of motion makes it possible to apply extended Lagrangian first-principles molecular dynamics simulations to a broader range of problems, including reactive chemical systems with numerically sensitive and unsteady charge solutions. This can be achieved without requiring exact full calculations of the inverse Jacobian kernel in each time step or relying on iterative non-linear self-consistent field optimization of the electronic ground state prior to the force evaluations as in regular direct Born–Oppenheimer molecular dynamics. We note the low-rank approximation of the Jacobian is directly related to Broyden’s class of quasi-Newton algorithms and Jacobian-free Newton–Krylov methods and provides a complementary formulation for the solution of nonlinear systems of equations.
Emergent Inductance from Chiral Orbital Currents in a Bulk Ferrimagnet
Here, we report the discovery of a new form of inductance in the bulk ferrimagnet Mn 3 Si 2 Te 6 , which features strong spin-orbit coupling, large magnetic anisotropy, and pronounced magnetoelastic interactions. Below its Curie temperature (𝑇 𝐶 ≈ 78 K), Mn 3 Si 2 Te 6 hosts chiral orbital currents (COC) that circulate within the crystal lattice and give rise to collective electronic behavior [Control of chiral orbital currents in a colossal magnetoresistance material, Nature (London) 611, 467 (2022).]. By applying a magnetic field along the hard 𝑐 axis and driving the system with low-frequency currents, we uncover a giant inductive response up to millhenry scale, originating from first-order reconfigurations of COC domains. These domains act as coherent mesoscopic inductive elements that resist reversal upon current reduction, producing a large electromotive force and sharply increasing voltage. This emergent inductance defies classical models, occurs without superconductivity or engineered nanostructures, and opens a new frontier in orbital-based quantum functionality and device concepts.
Predicted vibration responses of Apollo structure and effects of pressure correlation lengths on response
Progressive wove and reverberant acoustic fields ore often used in the laboratory for qualification testing of aerospace structures that are subjected to unsteady aerodynamic environments which occur during flight through the atmosphere. Acoustic simulation of these in-flight environments i s achieved i f the structural vibration response to acoustic excitation is equivalent, over the frequency range of interest, to the response caused by aerodynamic turbulence. To determine the degree of response simulation that could be expected for such qualification testing of the Apollo Spacecraft, responses of a segment of the Apollo structure were estimated theoretically for both acoustic and flight environments. The vibration analysis presented in this report was performed for the Spacecraft Lunar Module Adaptor; and the three environments treated are turbulence at Mach 1 and Mach 2, a reverberant acoustic field, and a modified acoustic progressive wave field. The progressive wave field is assumed to be generated within a specially designed shroud of sixteen axially oriented ducts which is constructed around and contoured to the external skin of the vehicle. Each duct is open on the side adjacent to the skin and is driven acoustically at one end by an independent noise source, thus allowing for different pressure correlation patterns around the circumference of the vehicle. The purpose of the analysis was to determine the effects of surface pressure correlation lengths on the response characteristics of representative Apollo structure, and to select on this basis, the optimum acoustic environment for structural vibration qualification tests of the Apollo in the Spacecraft Acoustic Laboratory at MSC. The method of analysis employed consists of determining, independently, the space average, mean-square acceleration spectral density for each of the significant modes of vibration of an equivalent cylindrical shell, and then expressing the total structural response as a linear summation of these modal responses. Approximately 570 classical modes of a pinned-end cylinder were used in order to find the spectral response characteristics of the structure throughout the frequency range of 10 - 1,000 Hz. The effective forcing functions or joint acceptances of the various modes of vibration were computed and are presented graphically for each of the pressure excitation environments. A brief development of the response equations used is presented in the report. Space average acceleration response spectra were computed for twelve different cases including aerodynamic turbulence at Mach 1 and Mach 2, reverberant acoustic field, five duct correlation patterns, two cases of an axially damped progressive wave field, and two cases in which the structural damping constant was varied from the expected value. The response spectra were computed and plotted by a high speed digital computer far a flat excitation pressure spectrum; and the response spectra were numerically integrated to give one-third octave bond average responses. A complete set of digital computer programs has been developed for both flat plate and cylindrical shell structures for the above environments, and each requires run times of three minutes or less. Thus, the work presented herein, along with the results, constitutes a practical advancement to the existing state-of-the-art of vibration prediction.
Optical matter machines: angular momentum conversion by collective modes in optically bound nanoparticle arrays
The creation of optically powered self-assembling nano-to-meso-scale machines that do work is a long-standing goal in photonics. We demonstrate an optical matter (OM) machine that converts the spin angular momentum (SAM) of light into orbital angular momentum (OAM) to do mechanical work. The specific OM machine we study is based on a sixfold symmetric hexagonally ordered nanoparticle array that operates as an OM “gear” that is assembled and made to rotate in a circularly polarized Gaussian beam. The rotational symmetry of the OM gear leads to a selection rule for the allowed scattering modes based on their angular momentum. Electrodynamics calculations show that the collective scattering modes with the largest angular momentum scatter strongly in the transverse direction. Simulations and experiments show that the angular momentum that accompanies the scattered light causes a “negative torque” response on the OM gear and drives a “probe” particle placed outside the OM gear around the gear in an asymmetric force field analogously to Brownian ratchets. The gear–probe OM machine concept can be expanded to applications in nanofluidics and particle sorting.
Computing Gravitational Fields of Finite-Sized Bodies
A computer program utilizes the classical theory of gravitation, implemented by means of the finite-element method, to calculate the near gravitational fields of bodies of arbitrary size, shape, and mass distribution. The program was developed for application to a spacecraft and to floating proof masses and associated equipment carried by the spacecraft for detecting gravitational waves. The program can calculate steady or time-dependent gravitational forces, moments, and gradients thereof. Bodies external to a proof mass can be moving around the proof mass and/or deformed under thermoelastic loads. An arbitrarily shaped proof mass is represented by a collection of parallelepiped elements. The gravitational force and moment acting on each parallelepiped element of a proof mass, including those attributable to the self-gravitational field of the proof mass, are computed exactly from the closed-form equation for the gravitational potential of a parallelepiped. The gravitational field of an arbitrary distribution of mass external to a proof mass can be calculated either by summing the fields of suitably many point masses or by higher-order Gauss-Legendre integration over all elements surrounding the proof mass that are part of a finite-element mesh. This computer program is compatible with more general finite-element codes, such as NASTRAN, because it is configured to read a generic input data file, containing the detailed description of the finiteelement mesh.
Modeling the Influences of Aerosols on Pre-Monsoon Circulation and Rainfall over Southeast Asia
We conduct several sets of simulations with a version of NASA's Goddard Earth Observing System, version 5, (GEOS-5) Atmospheric Global Climate Model (AGCM) equipped with a two-moment cloud microphysical scheme to understand the role of biomass burning aerosol (BBA) emissions in Southeast Asia (SEA) in the pre-monsoon period of February-May. Our experiments are designed so that both direct and indirect aerosol effects can be evaluated. For climatologically prescribed monthly sea surface temperatures, we conduct sets of model integrations with and without biomass burning emissions in the area of peak burning activity, and with direct aerosol radiative effects either active or inactive. Taking appropriate differences between AGCM experiment sets, we find that BBA affects liquid clouds in statistically significantly ways, increasing cloud droplet number concentrations, decreasing droplet effective radii (i.e., a classic aerosol indirect effect), and locally suppressing precipitation due to a deceleration of the autoconversion process, with the latter effect apparently also leading to cloud condensate increases. Geographical re-arrangements of precipitation patterns, with precipitation increases downwind of aerosol sources are also seen, most likely because of advection of weakly precipitating cloud fields. Somewhat unexpectedly, the change in cloud radiative effect (cloud forcing) at surface is in the direction of lesser cooling because of decreases in cloud fraction. Overall, however, because of direct radiative effect contributions, aerosols exert a net negative forcing at both the top of the atmosphere and, perhaps most importantly, the surface, where decreased evaporation triggers feedbacks that further reduce precipitation. Invoking the approximation that direct and indirect aerosol effects are additive, we estimate that the overall precipitation reduction is about 40% due to the direct effects of absorbing aerosols, which stabilize the atmosphere and reduce surface latent heat fluxes via cooler land surface temperatures. Further refinements of our two-moment cloud microphysics scheme are needed for a more complete examination of the role of aerosol-convection interactions in the seasonal development of the SEA monsoon.
Hydrodynamic instabilities and heat transfer characteristics in the duct flow of a fluid in the supercritical thermodynamic regime
The behavior of fluids at supercritical thermodynamic conditions is inherently complex due to large variations in thermodynamic and transport properties. Recent numerical and experimental investigations illustrate ongoing interest for these fluids, especially supercritical CO 2 and supercritical water, for a variety of applications. For example, supercritical water reactors (SCWR) operate in this extreme condition of high-pressure and temperature, resulting in highly dynamic flow fields and unexpected heat transfer regimes. The potential heat transfer benefits in this regime are directly associated with the extreme variations in thermodynamic and transport properties, which occur at, and above, the critical point. This work characterizes the hydrodynamic instabilities that arise for fluids at supercritical thermodynamic conditions when buoyancy forces are significant. Two specific configurations are considered, a natural convection cavity flow, and a mixed convection, heated, horizontal channel flow. Natural convection flow in a cavity is a classical configuration with expected behavior below the critical point. This configuration aids in characterizing the effect of the variable properties in the supercritical thermodynamic regime. Further, limited studies in the existing literature have been conducted for low-Reynolds and intermediate-Rayleigh numbers, mixed-convection channel flows for supercritical water, which is the focus of the channel flow configuration. To investigate the thermally driven hydrodynamic instabilities in this regime, a high-order fully-implicit numerical method is used. Such strong variations in thermophysical properties (in particular, density) are difficult to simulate and an altogether compressible framework is needed. Therefore, the compressible Navier-Stokes equations are solved without any additional assumptions. The fully implicit, high-order in space and time, reconstructed discontinuous Galerkin method as implemented within the multi-physics code called ALE3D (Arbitrary Lagrangian and Eulerian in 2D and 3D), developed at Lawrence Livermore National Laboratory (LLNL), is used. This fully implicit, L-stable method accurately captures the compressible nature of the ow in the limit of very low Mach number. It has been widely accepted that above the critical point, only one phase is observed. However, recent research has indicated the existence of the distinct gas-like and liquid-like regions separated by the Widom line, the locus of the maxima of the specific heat. Along the Widom line, density decreases 6-fold, viscosity drops by a factor of 2, while specific heat spikes by an order of magnitude. These variations, specifically in density and viscosity, produce a thick pseudo-interface and flow dynamics behavior akin to film boiling. A pseudo-film at the heated wall of the cavity and the horizontal channel is observed where buoyancy forces induce mixing through the specific configurations. Further the local Rayleigh and Richardson numbers provide maps of the flow field and the buoyancy forces driving the microscopic mixing. In the first chapter, I describe a background of supercritical fluid and the various applications. The second chapter focuses on the mathematical model and numerical method used for simulations, where a description of the equation of state for supercritical water is described. The third chapter focuses on the natural convection cavity with a heated bottom wall. In this cavity a gas-like and a liquid-like flow within the supercritical thermodynamic regime are observed. The fourth chapter focuses on a forced convection, horizontal channel, distinguishing between the gas-like, liquid-like, and mixed flow regimes. Mixed convection flow, with the addition of gravitational forces in the horizontal channel show the influence of variable properties on the hydrodynamic development, heat transfer, and rising instabilities. The last chapter of this research focuses on characterizing the unstable hydrodynamics through time-averaging processes and analysis of the movement of energy through the developing plumes.