Point-like Research Articles

Double copy, Kerr–Schild gauges and the effective-one-body formalism

Abstract We look for a classical double-copy-inspired relation between gravity and electrodynamics by connecting the descriptions of the scattering of two point masses, and of two point charges, in terms of perturbative (post-Minkowskian or post-Lorentzian) expansions. We do so by recasting available analytical information within the effective-one-body formalism using Kerr–Schild gauges in both cases. Working at the third perturbative level, we find that the usual linear relation (holding in the probe limit) between the adimensionalized electric potential, ϕ ~ = G M e 1 e 2 ϕ el , and the Schwarzschild-like gravitational one, Φ grav , is deformed, in the comparable-mass, comparable-charge, case, into a nonlinear relation which becomes universal in the high energy limit: Φ grav = 2 ϕ ~ − 5 ϕ ~ 2 + 18 ϕ ~ 3 .

Non-local quantum field theory from doubly special relativity

Abstract Doubly special relativity is usually regarded as a low-energy limit of a quantum gravity theory with testable predictions. On the other hand, non-local quantum field theories have been presented as a solution to the inconsistencies arising when quantizing gravity. Here, we present a new formulation of quantum field theories in doubly special relativity with non-local behavior. Our construction restricts the models to those showing linear Lorentz invariance. We derive the deformed Klein--Gordon, Dirac, and electromagnetic Lagrangians, as well as the deformed Maxwell equations. We also discuss the electric potential of a point charge. Finally, we analyze the connection between the nonlocality of field theories and doubly special relativity.

Spatial reorientation of a solid body using a moving mass in the presence of external forces specified as the functions of time

The spatial motion of a mechanical system consisting of a rigid body and a moving point mass, interacting with each other by means of unspecified internal forces, has been studied. The task is to construct such a trajectory for a point mass, when moving along which a rigid body, under the influence of the force of interaction with this mass, changes its orientation in space according to a known program. It is assumed that there are external forces acting on both objects, specified as functions of time. A system of three first-order ordinary differential equations, resolved with respect to derivatives, is obtained, which allows solving the problem. These relationships can be used to control spacecraft and robotic systems.

Newtonian restricted three-body gravitational problem with positive and negative point masses

The Newtonian restricted three-body problem involving a positive primary point mass, m+, and a negative secondary point mass, m−, in a circular orbit, and a positive or negative tertiary point mass, m3, with m+>|m−|≫|m3|, is solved. Five Lagrange points are found for m3, three of which are coplanar with m+ and m−, and two of which are not, a subtle consequence of the gravitational repulsion from m−. All Lagrange points are linearly unstable, except for one point in the regime m+≳8.4|m−|, which is linearly stable and collinear with m+ and m−. Published by the American Physical Society 2024

ETS-NOCV description of chemical bonding: from covalent bonds to non-covalent interactions

ContextThe interpretation of ETS-NOCV for typical covalent and dative-covalent chemical bonds is presented and compared with that for halogen bonds. Possible tuning of the strength of halogen bonding is considered, first by applying an electric field (modeled by the point charges or the electric field vector), and then by constructing a model transition-metal complex with enhanced strength of halogen bonding. For all the systems, the ETS-NOCV picture is supplemented by the analysis of the deformation in molecular electrostatic potential (ΔMEP). The results demonstrate important characteristic features of the analysis based on NOCV: (i) this approach is based on pairs of orbitals with antibonding and bonding character and, thus, allows us to “extract” the “diatomic-like” picture of chemical bonding; (ii) the NOCV-pair contributions to the deformation density often correspond to donation (AB) and back-donation (AB) of electron density between the fragments. The results for halogen bonding demonstrate that it is possible to tune their strength by an electric field in the molecular environment; the halogen-bond energy can reach the order of magnitude typical of dative-covalent bonds. However, the nature of halogen bonds still differs from that of dative-covalent interactions, as the accumulation of electron density between fragments is of significantly lower magnitude. The main effect of the electric field is an increase in the polarization of the fragments, which is clearly manifested by the deformation in the MEP.MethodsAll calculations were performed using the ADF/AMS package. The BLYP exchange–correlation functional was employed with Grimme’s dispersion correction (D3 version) and Becke-Johnson damping, using TZP basis sets. The deformation in the MEP was determined as ΔVr=VABr-VAr-VBr, with the same fragment definition as in the ETS-NOCV method.

Aspects of a novel nonlinear electrodynamics in flat spacetime and in a gravity-coupled scenario

A novel nonlinear electrodynamics (NLE) model with two dimensionful parameters is introduced and investigated. Our model obeys the Maxwellian limit and exhibits behaviour similar to the Born–Infeld Lagrangian in the weak field limit. It is shown that the electric field of a point charge in this model has a definite maximum value. Thus, the self-energy of the point charge is finite. The phenomenon of vacuum birefringence is found to occur in the presence of an external uniform electric field. Causality and unitarity conditions for all background electric fields hold, whereas, for magnetic fields, a restricted domain of validity is found. Moreover, a minimal coupling of Einstein’s General Relativity (GR) with this NLE results in solutions of regular black holes or naked singularities, depending on whether the source is a nonlinear magnetic monopole or an electric charge, respectively.

Thermo- and soluto-capillary convection and instability near the air–liquid interface

Steady thermo- and solute-capillary convection, instability, and pattern evolution near the air–liquid interface driven by point heat and mass sources are investigated. First, under the assumption of the conically similar viscous flow, an exact axi-symmetric solution of the steady thermo- and soluto-capillary convection near the air–liquid interface is determined due to the constant heat and mass fluxes. It is shown that the constant heat, mass fluxes, and the radial surface tension cause the divergent motion at the interface and the Marangoni convection beneath the interface. Then, the linear stability of the steady thermo- and soluto-capillary convection in response to the azimuthal disturbance is analyzed. At a given Peclet (or Schmidt), Marangoni (or Prandtl), and elasticity numbers, the steady basic flow loses its stability when Reynolds number is beyond the critical value. It is found that for small Schmidt numbers, a half-loop structure between the critical Reynolds number and the harmonic wave number of the azimuthal disturbance appears. For large Schmidt numbers, the critical Reynolds number monotonously increases as the harmonic wave number increases. The critical patterns of the velocity fields and the isothermal, iso-concentration lines in the three-dimensional flow system in response to the disturbance harmonic wave number are dominated by both the radial and azimuthal surface tensions. The results not only provide a valuable understanding of Marangoni convection and pattern information near the air–liquid interface but also inspire its potential practical applications in the material chemistry and biotechnology.

High-performance copper terephthalic acid metal-organic framework/gum Arabic/carrageenan composite beads for efficient lead(II) removal from aqueous solutions

Lead (Pb(II)) contamination poses a significant threat to human health and the environment. This study investigates a new approach for Pb(II) removal from polluted water using copper terephthalic acid metal-organic framework/gum Arabic/potassium carrageenan (MGC) composite beads. We synthesized copper terephthalic acid MOF, potassium carrageenan beads, and MGC composite beads to evaluate their adsorption potential. Characterization of the synthesized adsorbents was performed using TGA, nitrogen adsorption/desorption, ATR-FTIR, zeta potential, SEM, and TEM analyses, revealing that MOF > MGC > KG in thermal stability. The MGC composite exhibited a high specific surface area (398.03 m2/g) with mesopores and diverse functional groups, alongside a pH of zero point charge (pHpzc) of 6.8 and a small particle size (20 nm). The maximum Langmuir adsorption capacity for Pb(II) removal by MGC reached 374.7 mg/g under optimized conditions (20 °C, pH 5, 60 min shaking time, 3.0 g/L adsorbent dosage). The adsorption data fit well with the Pseudo-First-Order kinetic model and Langmuir and Dubinin-Radushkevich isotherm models. The adsorption process was physical, favorable, and endothermic. EDTA was used as a desorption agent, showing that the composite beads retained 97 % efficiency after ten cycles, highlighting MGC's potential as a sustainable strategy for Pb(II) remediation.

ONLINE MEASUREMENT OF FLOUR PARTICLE SIZE DISTRIBUTION USING PIEZOELECTRIC SENSOR

Obtaining the ideal particle size is a vital factor in dust processes, from turning wheat into flour to cement and calcite production. However, the technology to measure particle size instantaneously during the production phase is still an area under development. These measurements made with electro-optical methods have limited use in industry due to their difficulties and excessive costs. Studies conducted with innovative acoustic emission sensors offer new hopes in particle size detection. These sensors can successfully measure the dimensions of a wide range of materials, from coal dust to metal powders to grass particles. Our study shows that these sensors can also measure the size of light flour particles instantaneously. Using developed method, the dimensions of five types of flour mixtures in the size ranges of 0-80 µm, 80-118 µm, 118-150 µm, 150-180 µm and 180-212 µm could be measured and classified with 100% success. Considering its potential to increase the efficiency of the milling process, this technology could revolutionize the milling industry.

-Inflated Beta Regression Model for Estimating -Restricted Means and Event-Free Probabilities for Censored Time-to-Event Data.

In this research, we propose analysis of -restricted censored time-to-event data via a -inflated beta regression ( -IBR) model. The outcome of interest is , where and are the time-to-event and follow-up duration, respectively. Our analysis goals include estimation and inference related to -restricted mean survival time ( -RMST) values and event-free probabilities at that address the censored nature of the data. In this setting, it is common to observe many individuals with , a point mass that is typically overlooked in -restricted event-time analyses. Our proposed -IBR model is based on a decomposition of into . We model the mean of this latter expression using joint logistic and beta regression models that are fit using an expectation-maximization algorithm. An alternative multiple imputation (MI) algorithm for fitting the -IBR model has the additional advantage of producing uncensored datasets for analysis. Simulations indicate excellent performance of the -IBR model(s), and corresponding -RMST estimates, in independent and dependent censoring settings. We apply our method to the Azithromycin for Prevention of Chronic Obstructive Pulmonary Disease (COPD) Exacerbations Trial. In addition to -IBR model results providing a nuanced understanding of the treatment effect, visually appealing heatmaps of the -restricted event times based on our MI datasets are given, a visualization not typically available for censored time-to-eventdata.

Fluids with power-law repulsion: Hyperuniformity and energy fluctuations

We revisit the equilibrium statistical mechanics of a classical fluid of point-like particles with repulsive power-law pair interactions, focusing on density and energy fluctuations at finite temperature. Such long-range interactions, decaying with inter-particle distanceras1/rsinddimensions, are known to fall into two qualitatively different categories. Fors < d('strongly' long-range interactions) there are screening of correlations and suppression of large-wavelength density fluctuations (hyperuniformity). These effects eliminate density modes with arbitrarily large energy. Fors > d('weakly' long-range interactions) screening and hyperuniformity do not occur. Using scaling arguments, variational analysis, and Monte Carlo simulations, we find another qualitative distinction. Fors⩾d/2the strong repulsion at short distances leads to enhanced small-wavelength density fluctuations, decorrelating particle positions. This prevents indefinitely negative entropy and large energy fluctuations. The distinct behaviors fors⩾d/2ands<d/2give rise to qualitatively different dependencies of the entropy, heat capacity, and energy fluctuations on temperature and density. We investigate the effect of introducing an upper cutoff distance in the pair-potential. The effect of the cutoff on energy fluctuations is strong fors<d/2and negligible fors⩾d/2.

Low Computational Cost for Multiple Waypoints Trajectory Planning: A Time‐Optimal‐Based Approach

In the field of mobile robots, achieving minimum time in executing trajectories is crucial for applications like delivery, inspection, and search and rescue. In this article, a novel time‐optimal planner based on optimization methods is introduced. Despite the high computational cost associated with such methods, the solution calculates time‐optimal multi‐waypoint trajectories, achieving results in the order of milliseconds. The proposed method formulates a time‐optimal trajectory using the Pontryagin's maximum principle as a policy. By utilizing a point mass model, the planner generates trajectories that are adaptable to different robot models. The approach incorporates a definition of a search space to guarantee convergence while considering the system limits. Simulation and real‐world experiments are performed to validate the feasibility of our method with different configurations. Simulation results compared to a benchmark method demonstrate our approach's superior performance in terms of computational time, achieving near‐optimal solutions. In addition, in the real‐world experiments, the integration of the method into practical applications is validated.

Gravitational lensing in more realistic dark matter halo models

In this study, we explore gravitational lensing using more realistic dark matter halo models, moving beyond the limitations of spherical-collapse approximations. Through analytical calculations employing various mass functions, we address critical factors often neglected in the standard Press–Schechter formalism, such as ellipsoidal-collapse conditions, angular momentum, dynamical friction, and the cosmological constant. Our analysis incorporates two widely recognized halo density profiles, the Navarro-Frenk-White and Einasto profiles considering both spherical and ellipsoidal-collapse scenarios. We provide detailed calculations of key gravitational lensing observables, including Einstein radii, lensing optical depths, and time delays, across a broad range of redshifts and masses using two different lensing models: the point mass and singular isothermal sphere (SIS) models. The results demonstrate that employing more realistic dark matter halo models amplifies the lensing effects compared to those derived from spherical-collapse models. Additionally, our analyses of lensing optical depths and time delays reveal distinct differences between the point mass and SIS lens models. These findings highlight the importance of using more realistic halo descriptions rather than simplified approximations to accurately model the complex structures of dark matter in gravitational lensing.

Polarizable force field for TiO2 based on the Drude oscillator model

A polarizable force field has been developed for molecular dynamics simulations of titanium dioxide in an aqueous environment. The force field uses the standard functional form with an additional term accounting for polarizability, i.e., induction interaction, and has been derived exclusively from ab initio calculations by partitioning of electron density. Polarizability is described using the Drude oscillator model where each non-hydrogen atom is represented by two point charges connected by a harmonic potential. It is demonstrated that the force field provides a realistic description of the structure of anatase and rutile bulk materials from x-ray experiments. In addition, it is shown that, when combined with the popular SWM4-NDP polarizable water model, the force field describes the water structure at the titanium dioxide–water interface in agreement with results from ab initio molecular dynamics simulations. Importantly, our new model provides significant improvement of results for water differential adsorption enthalpy measured by calorimetry experiments compared to previous non-polarizable force field. The new force field allows for accurate simulations of titanium dioxide–aqueous interfaces for systems of a size of ∼105 atoms and simulation times up to the microsecond time scale.

Plasma-induced Fe-doped zeolitic imidazolate framework-8 derived P-Fe-N3C for enhanced phenol degradation

Plasma-synergistic catalysis is considered an effective method for degrading aromatic organic pollutants in water. However, the underlying synergistic catalytic mechanism between plasma and catalysts remains poorly understood. Here, we propose a plasma-metal organic frameworks (MOFs) synergistic strategy to investigate the mechanism of plasma-synergistic catalysts for phenol degradation. The results show that Fe-doped Zeolitic Imidazolate Framework-8 (Fex-ZIF8, x = 0, 0.1, 0.2, 0.4) undergoes the plasma-induced transformation into an Fe-N3C structure (P-Fe-N3C), leading to a 4.5-fold enhancement in the phenol degradation rate compared to only plasma discharge. Density functional theory (DFT) calculations indicate that the plasma-induced structural transformation of Fex-ZIF8 promotes the redistribution of point charges and space charges around the Fe center, thereby lowering the activation energy barrier in the rate-determining step (*C6H4(OH)2). These findings not only provide theoretical support for the degradation of water pollutants via plasma-synergistic catalysts but also offer a novel strategy for constructing MOFs-derived materials.

Transient longitudinal waves in 2D square lattices with Voigt elements under concentrated loading

The aim of this article is to study the attenuation of transient low-frequency waves in 2D lattices of point masses connected by Voigt elements, under an antiplane concentrated loading. The emphasis is on obtaining analytical estimates for solutions using methods of asymptotic inversion of the Laplace and Fourier transforms in the vicinity of the quasi-front of infinitely long waves. In addition, the problems under study are solved by a finite difference method. The main result of the article is the asymptotic estimates of low-frequency and high-frequency perturbations in the 2D lattice for long periods of time under a transient load. It is shown that the obtained asymptotic estimates qualitatively and quantitatively agree with the results of numerical calculations.

A new multiple-arc model of the resonant Kuiper belt objects – Plutinos

ABSTRACT To incorporate the gravitational influence of Kuiper belt objects (KBOs) in planetary ephemerides, uniform-ring models are commonly employed. In this paper, for representing the KBO population residing in Neptune’s 2:3 mean motion resonance (MMR), known as the Plutinos, we introduce a three-arc model by considering their resonant characteristics. Each ‘arc’ refers to a segment of the uniform ring and comprises an appropriate number of point masses. Then the total perturbation of Plutinos is numerically measured by the change in the Sun–Neptune distance ($\Delta d_{\mathrm {SN}}$). We conduct a comprehensive investigation to take into account various azimuthal and radial distributions associated with the resonant amplitudes (A) and eccentricities (e) of Plutinos, respectively. The results show that over a 100-yr period: (1) at the smallest $e=0.05$, the Sun–Neptune distance change $\Delta d_{\mathrm {SN}}$ caused by Plutinos decreases significantly as A reduces. It can deviate from the value of $\Delta d_{\mathrm {SN}}$ obtained in the ring model by approximately 100 km; (2) as e increases in the medium range of 0.1–0.2, the difference in $\Delta d_{\mathrm {SN}}$ between the arc and ring models becomes increasingly significant; (3) at the largest $e\gtrsim 0.25$, $\Delta d_{\mathrm {SN}}$ can approach zero regardless of A, and the arc and ring models exhibit a substantial difference in $\Delta d_{\mathrm {SN}}$, reaching up to 170 km. Then the applicability of our three-arc model is further verified by comparing it to the perturbations induced by observed Plutinos on the positions of both Neptune and Saturn. Moreover, the concept of the multiple-arc model, designed for Plutinos, can be easily extended to other MMRs densely populated by small bodies.

The Geometric Scale of an Urban Space—Neuro-perceptual Limitations for Face-to-Face Driver Behavior

For the last century, the roadway design paradigm has been grounded in the physics of point masses, adjusted for human limitations. However, this is inadequate to assure pedestrian safety in complete streets where vehicle kinematics no longer control. Instead, social and psychological factors manage behavior. Unfortunately, the appropriate design critical psychological principles have yet to be elucidated. We posit that interpersonal perception governs drivers’ behavior, attentiveness and speed in streets. This is bounded by previously delineated human neurological and perceptual propensities. Using these perceptual limitations as postulates in a geometric style proof, we derive the person perception panorama (PPP): a window of interactivity around the moving driver that is continuously monitored for human presence, roughly 60 to 90 feet wide. In this area interpersonal interaction is implicit, functional, and has an impact on driver behavior. Validating evidence, additional governing principles, and an initial speed prediction formula are also included.

Dissociation Energies via Embedding Techniques.

Due to the large number of interactions, evaluating interaction energies for large or periodic systems results in time-consuming calculations. Prime examples are liquids, adsorbates, and molecular crystals. Thus, there is a high demand for a cheap but still accurate method to determine interaction energies and gradients. One approach to counteract the computational cost is to fragment a large cluster into smaller subsystems, sometimes called many-body expansion, with the fragments being molecules or parts thereof. These subsystems can then be embedded into larger entities, representing the bigger system. In this work, we test several subsystem approaches and explore their limits and behaviors, determined by calculations of trimer interaction energies. The methods presented here encompass mechanical embedding, point charges, polarizable embedding, polarizable density embedding, and density embedding. We evaluate nonembedded fragmentation, QM/MM (quantum mechanics/molecular mechanics), and QM/QM (quantum mechanics/quantum mechanics) embedding theories. Finally, we make use of symmetry-adapted perturbation theory utilizing density functional theory for the monomers to interpret the results. Depending on the strength of the interaction, different embedding methods and schemes prove favorable to accurately describe a system. The embedding approaches presented here are able to decrease the interaction energy errors with respect to full system calculations by a factor of up to 20 in comparison to simple/unembedded approaches, leading to errors below 0.1 kJ/mol.

Probing massive gravitons in f(R) with lensed gravitational waves

We investigate the novel features of gravitational wave solutions in f(R) gravity under proper gauge considerations in the shifted Ricci scalar background curvature (R1+ϵ). The solution is further explored to study the modified dispersion relations for massive modes at local scales and to derive constraints on ϵ. Our analysis yields new insights as we scrutinize these dispersion effects on the polarization (modified Newman-Penrose content) and lensing properties of gravitational waves. It is discovered that the existing longitudinal scalar mode, and transverse breathing scalar mode are both independent of the mass parameter for ϵ<<1. Further, by analysing the lensing amplification factor for the point mass lens model, we show that lensing of gravitational wave is highly sensitive to these dispersion effects in the milli-Hertz frequency (wave optics regime). It is expected that ultra-light modes, having mass about O(10−15) eV for ϵ<<1(≈10−7) lensed by (103≤MLens≤106)M⊙ compact objects are likely to be detected by the advanced gravitational wave space-borne detectors, particularly within LISA's (The Laser Interferometer Space Antenna) sensitivity band.