First-order Correction Research Articles

Cavity-modified local and non-local electronic interactions in molecular ensembles under vibrational strong coupling.

Resonant vibrational strong coupling (VSC) between molecular vibrations and quantized field modes of low-frequency optical cavities constitutes the conceptual cornerstone of vibro-polaritonic chemistry. In this work, we theoretically investigate the role of complementary nonresonant electron-photon interactions in the cavity Born-Oppenheimer (CBO) approximation. In particular, we study cavity-induced modifications of local and non-local electronic interactions in dipole-coupled molecular ensembles under VSC. Methodologically, we combine CBO perturbation theory (CBO-PT) [E. W. Fischer and P. Saalfrank, J. Chem. Theory Comput. 19, 7215 (2023)] with non-perturbative CBO Hartree-Fock (HF) and coupled cluster (CC) theories. In a first step, we derive up to second-order CBO-PT cavity potential energy surfaces, which reveal non-trivial intra- and inter-molecular corrections induced by the cavity. We then introduce the concept of a cavity reaction potential (CRP), minimizing the electronic energy in the cavity subspace to discuss vibro-polaritonic reaction mechanisms. We present reformulations of CBO-HF and CBO-CC approaches for CRPs and derive second-order approximate CRPs from CBO-PT for unimolecular and bimolecular scenarios. In the unimolecular case, we find small local modifications of molecular potential energy surfaces for selected isomerization reactions dominantly captured by the first-order dipole fluctuation correction. Excellent agreement between CBO-PT and non-perturbative wave function results indicates minor VSC-induced state relaxation effects in the single-molecule limit. In the bimolecular scenario, CBO-PT reveals an explicit coupling of interacting dimers to cavity modes besides cavity-polarization dependent dipole-induced dipole and van der Waals interactions with enhanced long-range character. An illustrative CBO-coupled cluster theory with singles and doubles-based numerical analysis of selected molecular dimer models provides a complementary non-perturbative perspective on cavity-modified intermolecular interactions under VSC.

All-electron first-principles GWΓ simulations for accurately predicting core-electron binding energies considering first-order three-point vertex corrections.

In the conventional GW method, the three-point vertex function (Γ) is approximated to unity (Γ ∼ 1). Here, we developed an all-electron first-principles GWΓ method beyond a conventional GW method by considering a first-order three-point vertex function (Γ(1) = 1 + iGGW) in a one-electron self-energy operator. We applied the GWΓ method to simulate the binding energies (BEs) of B1s, C1s, N1s, O1s, and F1s for 19 small-sized molecules. Contrary to the one-shot GW method [or G0W0(LDA)], which underestimates the experimentally determined absolute BEs by about 3.7eV for B1s, 5.1eV for C1s, 6.9eV for N1s, 7.8eV for O1s, and 5.8eV for F1s, the GWΓ method successfully reduces these errors by approximately 1-2eV for all the elements studied here. Notably, the first-order three-point vertex corrections are more significant for heavier elements, following the order of F > O > N > C > B1s. Finally, the computational cost analysis revealed that one term in the GWΓ one-electron self-energy operator, despite being computationally intensive, contributes negligibly (<0.1eV) to the C1s, N1s, O1s, and F1s.

Study of first-order quantum corrections of thermodynamics to a Dyonic black hole solution surrounded by a perfect fluid

In this work, we review the metric for a dyonic global monopole with a perfect fluid. To calculate the standard temperature of a Dyonic black hole surrounded by a perfect fluid, we analyze the graphical interpretation of the Hawking temperature concerning the horizon under the effects of the black hole's surrounding field and electric-magnetic charges. For this purpose, we follow the semi-classical method, the Wentzel-Kramers-Brillouin (WKB) approximation, and the Lagrangian equation in the presence of quantum gravity as seen in the generalized uncertainty principle (GUP). We calculate the improved temperature of a Dyonic black hole using a bosonic tunneling strategy based on the Hamilton-Jacobi technique. We observe that the physical state of the Dyonic black hole is surrounded by a perfect fluid under the effects of the black hole solution and the gravity parameter. Further, we examine the improved entropy to study the influences of quantum gravity and black hole geometry on entropy. We explore the graphical behavior of entropy based on the black hole's horizon structure and analyze the influence of perfect fluid parameters, electric charge, magnetic charge, and quantum gravity on entropy. Finally, we investigate the unstable and stable conditions of a black hole via graphical results.

Short-time self-diffusion in binary colloidal suspensions

The Brownian dynamics of a colloidal particle is consistently modified by the presence in the solvent of other particles of comparable size, whose effects on the particle diffusion coefficient cannot be attributed to a change of the effective solvent viscosity. So far, despite their impact on subjects ranging from microrheology to phoretic transport in crowded environments, a detailed experimental survey of these effects is still lacking. By exploiting the peculiar properties of fluorinated colloidal particle, we have performed an extensive dynamic light scattering (DLS) investigation of short-time self-diffusion in binary colloidal mixtures, focusing on systems where one of the two species (the “tracer” particles) is very diluted compared to the other one (the “host” particles). From the dependence on the host concentration of the DLS correlation function, we have obtained the first-order correction hs1s to the tracer single-particle diffusion coefficient, varying the tracer-to-host size ratio q in the range 0.2 ≤ q ≤ 2. Our results support the functional relation of hs1s on q proposed to account for the theoretical and numerical results for hard-sphere mixtures. However, hs1s seems to have a weaker dependence on the size ratio than theoretically predicted, possibly because of an imperfect matching of the suspensions we used for an ideal hard-sphere mixture. This may be due to the presence of a stabilizing surfactant layer on the particle surface that, although very thin, has significant effects on hydrodynamic lubrication forces.

Extreme eigenvalues of random matrices from Jacobi ensembles

Two-term asymptotic formulæ for the probability distribution functions for the smallest eigenvalue of the Jacobi β-Ensembles are derived for matrices of large size in the régime where β &amp;gt; 0 is arbitrary and one of the model parameters α1 is an integer. By a straightforward transformation this leads to corresponding results for the distribution of the largest eigenvalue. The explicit expressions are given in terms of multi-variable hypergeometric functions, and it is found that the first-order corrections are proportional to the derivative of the leading order limiting distribution function. In some special cases β = 2 and/or small values of α1, explicit formulæ involving more familiar functions, such as the modified Bessel function of the first kind, are presented.

Wave-Current Interaction Effects on the OC4 DeepCwind Semi-Submersible Floating Offshore Wind Turbine

In order to investigate the hydrodynamic performances of semi-submersible type floating offshore wind turbines (FOWTs), particularly the effect of body-wave-current interaction, the OC4 FOWT is considered in the presence of co-existing regular wave and uniform current fields. The wind loads are not considered at this stage. The problem is treated in the framework of potential-flow theory in the frequency domain, assuming waves of small steepness, and the solution is obtained by using a perturbation expansion method for the diffraction potential with respect to the normalized current speed. Analytical and numerical formulations have been used to treat the inhomogeneous free-surface boundary condition involved in the hydrodynamic problem formulation for the derivation of the associated perturbation potential. The hydrodynamic loads were obtained after evaluating the pressure field around the multi-body configuration using three different computer codes. The results from the three computer codes compare very well with each other and with the numerical predictions of other investigators. Finally, the mean second-order drift forces are calculated by superposing their zero-current values with the corresponding current-dependent first-order corrections, with the latter being evaluated using a ‘heuristic’ approach.

A new local and explicit kinetic method for linear and non-linear convection-diffusion problems with finite kinetic speeds: II. Multi-dimensional case

We extend to multi-dimensions the work of [1], where new fully explicit kinetic methods were built for the approximation of linear and non-linear convection-diffusion problems. The fundamental principles from the earlier work are retained: (1) rather than aiming for the desired equations in the strict limit of a vanishing relaxation parameter, as is commonly done in the diffusion limit of kinetic methods, diffusion terms are sought as a first-order correction of this limit in a Chapman-Enskog expansion, (2) introducing a coupling between the conserved variables within the relaxation process by a specifically designed collision matrix makes it possible to systematically match a desired diffusion. Extending this strategy to multi-dimensions cannot, however, be achieved through simple directional splitting, as diffusion is likely to couple space directions with each other, such as with shear viscosity in the Navier-Stokes equations. In this work, we show how rewriting the collision matrix in terms of moments can address this issue, regardless of the number of kinetic waves, while ensuring conservation systematically. This rewriting allows for introducing a new class of kinetic models called regularized models, simplifying the numerical methods and establishing connections with Jin-Xin models. Subsequently, new explicit arbitrary high-order kinetic schemes are formulated and validated on standard two-dimensional cases from the literature. Excellent results are obtained in the simulation of a shock-boundary layer interaction, validating their ability to approximate the Navier-Stokes equations with kinetic speeds obeying nothing but a subcharacteristic condition along with a hyperbolic constraint on the time step.

Run-time motion and first-order shim control by expanded servo navigation.

To provide a navigator-based run-time motion and first-order field correction for three-dimensional human brain imaging with high precision, minimal calibration and acquisition, and fast processing. A complex-valued linear perturbation model with feedback control is extended to estimate and correct for gradient shim fields using orbital navigators (2.3 ms). Two approaches for sensitizing the model to gradient fields are presented, one based on finite differences with three additional navigators, and another projection-based approximation requiring no additional navigators. A mechanism for noise decorrelation of the matrix and the data is proposed and evaluated to reduce unwanted parameter biases. The rigid motion and first-order field control achieves robust motion and gradient shim corrections improving image quality in a series of phantom and in vivo experiments with varying field conditions. In phantom scans, magnet drifts, forced gradient field perturbations and field distortions from shifts of a second bottle phantom are successfully corrected. Field estimates of the magnet drifts are in good agreement with concurrent field probe measurements. For in vivo scans, the proposed method mitigates field variations from torso motions while being robust to head motion. In vivo gradient field precisions were along with single-digit micrometer and millidegree rigid precisions. The navigator-based method achieves accurate, high-precision run-time motion and field corrections with low sequence impact and calibration requirements.

Spurious self-feedback of mean-field predictions inflates infection curves.

The susceptible-infected-recovered (SIR) model and its variants form the foundation of our understanding of the spread of diseases. Here, each agent can be in one of three states (susceptible, infected, or recovered), and transitions between these states follow a stochastic process. The probability of an agent becoming infected depends on the number of its infected neighbors, hence all agents are correlated. The simplest mean-field theory of the same stochastic process, however, assumes that the agents are statistically independent. This leads to a self-feedback effect in the approximation: when an agent infects its neighbors, this infection may subsequently travel back to the original agent at a later time, leading to a self-infection of the agent which is not present in the underlying stochastic process. We here compute the first-order correction to the mean-field assumption from a systematic expansion, called dynamical TAP theory. This correction, which takes fluctuations up to second order in the interaction strength into account, cancels the self-feedback effect, leading to smaller infection rates. The correction significantly improves predictions compared to mean-field theory. In particular, it captures how sparsity dampens the spread of the disease: this indicates that reducing the number of contacts is more effective than predicted by mean-field models. We further apply the expansion to variants of the SIR model, such as the SIRS model, in which the immunity of an individual to the disease wanes over time. We find that up to the second order, the correction terms in the SIR and SIRS model are equivalent, meaning that fluctuations partially cancel the self-feedback effect even when self-feedback is in principle allowed.

Æther coupling effects on casimir energy for self-interacting scalar field within extra dimension

This paper presents comprehensive calculations for thermal and first-order radiative corrections to the Casimir energy in systems involving self-interacting massive and massless scalar fields coupled with æther in a fifth compact dimension. The method used to compute the radiative correction to the Casimir energy differs from conventional approaches by applying a unique renormalization scheme that is consistent with specific boundary conditions or backgrounds. Despite this divergence from conventional methodologies, our results demonstrate consistency within established physical limits. Furthermore, employing a toy model, we calculated the total Casimir energy density in the bulk, taking into account both thermal and radiative corrections. We also provide a thorough characterization of the total Casimir energy density in the compact dimension, detailing its magnitude and sign using graphical representations and quantitative data.

Bottomonia in quark-antiquark confining potential

This paper comprehensively explores bottomonia mass spectra and their decay properties by solving the non-relativistic Schrodinger wave equation numerically with an approximate quark-antiquark potential form. We also incorporate spin-dependent terms—spin-spin, spin-orbit, and tensor terms to remove mass degeneracy and to obtain excited states (nS, nP, nD, nF, n = 1, 2, 3, 4, 5) mass spectra. Using the Van Royen—Weisskopf formula, we investigate leptonic decay constants, di-leptonic, di-gamma, tri-gamma, di-gluon decay widths and incorporate first-order radiative corrections. We also computed radiative transition widths, which provide better insight into the non-perturbative aspects of QCD. The states ϒ(10750), ϒ(10860), ϒ(11020) are analyzed as pure states 33 D 1, 53 S 1 and 43 D 1, respectively. The present mass spectroscopy and decay properties results align with available experimental values and other theoretical predictions. Our results may provide better insight into upcoming experimental information in the near future.

An optimal midcourse guidance method for dual pulse air-to-air missiles using linear Gauss pseudospectral model predictive control method

This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles, which is based on the framework of the linear Gauss pseudospectral model predictive control method. Firstly, a multistage optimal control problem with unspecified terminal time is formulated. Secondly, the control and terminal time update formulas are derived analytically. In contrast to previous work, the derivation process fully considers the Hamiltonian function corresponding to the unspecified terminal time, which is coupled with control, state, and costate. On the assumption of small perturbation, a special algebraic equation is provided to represent the equivalent optimal condition for the terminal time. Also, using Gauss pseudospectral collocation, error propagation dynamical equations involving the first-order correction term of the terminal time are transformed into a set of algebraic equations. Furthermore, analytical modification formulas can be derived by associating those equations and optimal conditions to eliminate terminal error and approach nonlinear optimal control. Even with their mathematical complexity, these formulas produce more accurate control and terminal time corrections and remove reliance on task-related parameters. Finally, several numerical simulations, comparisons with typical methods, and Monte Carlo simulations have been done to verify its optimality, high convergence rate, great stability and robustness.

Stable envelopes for slices of the affine Grassmannian

The affine Grassmannian associated to a reductive group G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extbf{G}}$$\\end{document} is an affine analogue of the usual flag varieties. It is a rich source of Poisson varieties and their symplectic resolutions. These spaces are examples of conical symplectic resolutions dual to the Nakajima quiver varieties. We study the cohomological stable envelopes of Maulik and Okounkov (Astérisque 408:ix+209, 2019) in this family. We construct an explicit recursive relation for the stable envelopes in the G=PSL2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extbf{G}}= \ extbf{PSL}_{2}$$\\end{document} case and compute the first-order correction in the general case. This allows us to write an exact formula for multiplication by a divisor.

Life and death of a thin liquid film

Thin films, bubbles and membranes are central to numerous natural and engineering processes, i.e., in solar cells, coatings, biosensors, foams, and emulsions. Yet, the characterization and understanding of their rupture is limited by the scarcity of atomic detail. We present here the complete life-cycle of freely suspended films using non-equilibrium molecular dynamics simulations of a simple atomic fluid free of surfactants and surface impurities, thus isolating the fundamental rupture mechanisms. We identified a short-term ‘memory’ by rewinding in time from a rupture event, extracting deterministic behaviors from apparent stochasticity. A comprehensive investigation of the key rupture-stages including both unrestrained and frustrated propagation is made—characterization of the latter leads to a first-order correction to the classical film-retraction theory. The highly resolved time window reveals that the different modes of the morphological development, typically characterized as nucleation and spinodal rupture, continuously evolve seamlessly with time from one into the other.

Isochronous bifurcations of magnetic islands in tokamaks

On a rational magnetic surface, an isochronous bifurcation transforms one island chain into another chain with the same winding number. This transformation has been the subject of recent studies in tokamak plasmas. Namely, visco-resistive magnetohydrodynamic simulations of NSTX-U and DIII-D plasmas showed the onset of bifurcations with new magnetic isochronous islands for two competing helical perturbations on the same rational magnetic surface. To investigate these bifurcations, we use a cylindrical plasma model, with first-order correction for toroidicity, subject to externally applied magnetic perturbations, generated by a pair of resonant helical windings (RHWs) on the external wall and superposed to a helical current sheet (HCS) located on a rational plasma surface. We numerically integrate the magnetic field line equation and show that isochronous islands emerge when the perturbation created by the HCS increases. We present examples of such bifurcations on primary and secondary magnetic surfaces for different RHW configurations.

Generalized covariant entropy bound in Einstein gravity with quadratic curvature corrections

We explore the generalized covariant entropy bound in the theory where Einstein gravity is perturbed by quadratic curvature terms, which can be viewed as the first-order quantum correction to Einstein gravity. By replacing the Bekenstein-Hawking entropy with the holographic entanglement entropy of this theory and introducing two reasonable physical assumptions, we demonstrate that the corresponding Generalized Covariant Entropy Bound is satisfied under a first-order approximation of the perturbation from the quadratic curvature terms. Our findings suggest that the entropy bound and the Generalized Second Law of black holes are satisfied in the Einstein gravity under the first-order perturbation from the quadratic curvature corrections, and they also imply that the generalized covariant entropy bound may still hold even after considering the quantum correction of gravity, but in this case, we may need to use holographic entanglement entropy as the formula for gravitational entropy.

A qualitative examination of weapon violence against teachers: A theoretical framework and analysis.

Weapon violence in schools is a pressing concern with serious consequences. In this study, we propose and evaluate a theoretical framework of school-based weapon violence comprised of contributors, triggers, and motivation leading to weapon behaviors, taking into account weapon type, origin, and availability. This framework provides a foundation to investigate the multifaceted nature of weapon violence in schools. Specifically, we examine the weapon violence experiences of 417 U.S. teachers based on their reports of their most upsetting experiences with violence in their schools from various aggressors (i.e., students, parents, colleagues). Qualitative open-ended survey data were coded in NVivo after achieving strong interrater reliability (Gwet's agreement coefficient with first-order chance correction, AC₁ = .97; κ = .80), and analyses were guided by the proposed theoretical framework. Results indicated that individual, school, peer, family, and community conditions contributed to situational triggers (teacher or other school-stakeholder actions), and aggressor motivation was typically instrumental or expressive. The type and origin of weapons also played a role in weapon behaviors of carrying, threats, and usage. Aggressors often used readily available objects (e.g., chair, pencil) as weapons against teachers in addition to traditional weapons (e.g., knives, guns). Findings suggest that weapon violence in schools requires a broader conceptualization beyond traditional weapons and violence between students. This study advances our understanding of pathways to weapon behaviors for prevention and intervention. Implications of findings for school-stakeholder training and policies are discussed. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Free Electron-Plasmon Coupling Strength and Near-Field Retrieval through Electron Energy-Dependent Cathodoluminescence Spectroscopy.

Tightly confined optical near fields in plasmonic nanostructures play a pivotal role in important applications ranging from optical sensing to light harvesting. Energetic electrons are ideally suited to probing optical near fields by collecting the resulting cathodoluminescence (CL) light emission. Intriguingly, the CL intensity is determined by the near-field profile along the electron propagation direction, but the retrieval of such field from measurements has remained elusive. Furthermore, the conditions for optimum electron near-field coupling in plasmonic systems are critically dependent on such field and remain experimentally unexplored. In this work, we use electron energy-dependent CL spectroscopy to study the tightly confined dipolar mode in plasmonic gold nanoparticles. By systematically studying gold nanoparticles with diameters in the range of 20-100 nm and electron energies from 4 to 30 keV, we determine how the coupling between swift electrons and the optical near fields depends on the energy of the incoming electron. The strongest coupling is achieved when the electron speed equals the mode phase velocity, meeting the so-called phase-matching condition. In aloof experiments, the measured data are well reproduced by electromagnetic simulations, which explain that larger particles and faster electrons favor a stronger electron near-field coupling. For penetrating electron trajectories, scattering at the particle produces severe corrections of the trajectory that defy existing theories based on the assumption of nonrecoil condition. Therefore, we develop a first-order recoil correction model that allows us to account for inelastic electron scattering, rendering better agreement with measured data. Finally, we consider the albedo of the particles and find that, to approach unity coupling, a highly confined electric field and very slow electrons are needed, both representing experimental challenges. Our findings explain how to reach unity-order coupling between free electrons and confined excitations, helping us understand fundamental aspects of light-matter interaction at the nanoscale.

Mathematical Model for a Lithium-Ion Battery with a SiO/Graphite Blended Electrode Based on a Reduced Order Model Derived Using Perturbation Theory

Silicon oxide (SiO) is a promising anode material for high-energy lithium-ion batteries, as it is made from low-cost precursors, has a potential close to that of Li, and has high theoretical specific capacity. However, the applications of SiO are limited by the intrinsic low electrical conductivity, large volume change, and low coulombic efficiency, which often lead to poor cycling performance. A common strategy to address these shortcomings is to blend SiO with graphite active materials to form a composite anode for better capacity retention. In this work, we derive a reduced order model (ROM1) using perturbation theory. We employ the multi-site, multi-reaction (MSMR) framework of a composite porous electrode blend consisting of two lithium-host materials, SiO and graphite. The ROM1 model employs a single-particle model (SPM) approach as the leading-order solution and involves the numerical analysis of a single, nonlinear partial differential equation for each host material that describes diffusion by means of irreversible thermodynamics, wherein chemical-potential gradients are the driving forces for the diffusion. The first-order correction treats losses other than that of the SPM.

FUNCTIONAL INTEGRAL APPROACH AND THE EIKONAL APPROXIMATION TO THE POLARON ENERGY AND MASS

This article uses the functional integral method and eikonal approximation to calculate the first-order correction for the energy and (effective) mass of the Polaron. The obtained results have demonstrated the effectiveness of the functional integral method compared to conventional perturbation theory when considering the Polaron problem in solid crystal.