External Potential Research Articles

Supermassive black hole formation via collisions in black hole clusters

More than 300 supermassive black holes have been detected at redshifts larger than six, and they are abundant in the centers of local galaxies. Their formation mechanisms, however, are still rather unconstrained. A possible origin of these supermassive black holes could be mergers in dense black hole clusters, forming as a result of mass segregation within nuclear star clusters at the center of galaxies. In this study, we present the first systematic investigation of the evolution of such black hole clusters in which the effect of an external potential is taken into account. Such a potential could be the result of gas inflows into the central region; for example, as a result of galaxy mergers. We show here that the efficiency of the formation of a massive central object is mostly regulated by the ratio of cluster velocity dispersion divided by the speed of light, potentially reaching efficiencies of 0.05–0.08 in realistic systems. Our results show that this scenario is potentially feasible and may provide black hole seeds of at least 103 M⊙. We conclude that the formation of seed black holes via this channel should be taken into account in statistical assessments of the black hole population.

Tunnelling amplitudes through localised external potentials from Feynman diagram summation

AbstractCurrently there is no general theory of quantum tunnelling of a particle through a potential barrier which is compatible with QFT. We present a complete calculation of tunnelling amplitudes for a scalar field for some simple potentials using quantum field-theoretic methods. Using the perturbative S-matrix formalism, starting with the Klein–Gordon Lagrangian, we show that an infinite summation of Feynman diagrams can recover tunnelling amplitudes consistent with relativistic quantum mechanics. While this work does not include many-particle effects arising from a fully quantised QFT, it is necessary to investigate QFT corrections to tunnelling amplitudes.

On a New Point of View Toward the Mechanism of Those Electrochemical Reactions Driven by the External Potential

In the search of electrochemical reaction, uncovering the reaction mechanism plays a decisive role in analyzing the production of diverse products. We believe that all types of electrochemical reaction driven by external potential should follow a general process. In this paper, we propose that in those electrochemical reactions driven by the external potential, the formation of radicals via electron transfer between electrode and the species carrying electric charge serves as the first step, triggering subsequent reactions. This suggestion might be considerable electrochemical interest.

Quantum corrections to tunnelling amplitudes of neutral scalar fields

Though theoretical treatments of quantum tunnelling within single-particle quantum mechanics are well-established, at present, there is no quantum field-theoretic description (QFT) of tunnelling. Due to the single-particle nature of quantum mechanics, many-particle effects arising from quantum field theory are not accounted for. Such many-particle effects, including pair-production, have proved to be essential in resolving the Klein-paradox. This work seeks to determine how quantum corrections affect the tunnelling probability through an external field. We investigate a massive neutral scalar field, which interacts with an external field in accordance with relativistic quantum mechanics. To consider QFT corrections, we include another massive quantised neutral scalar field coupling to the original via a cubic interaction. This study formulates an all-order recursive expression for the loop-corrected scalar propagator, which contains only the class of vertex-corrected Feynman diagrams. This equation applies for general external potentials. Though there is no closed-form analytic solution, we also demonstrate how to approximate the QFT corrections if a perturbative coupling to the quantised field is assumed.

Effects of fluorine atom numbers on electrochromic properties of the benzothiadiazole-based D-A polymers

In this work, two fluorinated D-π-A-π-D type monomers, F-EDOT and FF-EDOT, were facilely synthesized by donor-acceptor-donor method via Stille coupling reaction, with monofluorinated benzothiadiazole and difluorinated benzothiadiazole as the acceptor units and 3,4-ethylenedioxythiophene (EDOT) as the donor units. The electrochemical polymerization behavior of the fluorinated monomers, electrochemical and electrochromic properties of the corresponding fluorinated D-A polymers were compared to study the effects of different fluorine atom numbers on the optoelectronic properties of the monomers and their resultant D-A polymers. The results show that the introduction of more F atoms into the conjugated backbone increases the oxidation potential of monomers, both of them have low initial oxidation potential (0.65 V/0.70 V). As in the case of monomers, the substitution of more F atoms also leads to the decreased HOMO energy level of the polymers, thus leading to the increased band gap energy of P(FF-EDOT) (1.39 eV). This result can be attributed to the deviation of planarity and the reduced effective conjugate length. As prepared fluorinated D-A polymers also have good adhesion on the electrode surface, favorable redox activity, and outstanding redox stability (the redox activity of P(F-EDOT) remains 99 % after 1000 cycles). At the same time, the fluorinated D-A polymers also show distinguish electrochromic properties under various external potentials; both the optical contrast and coloration efficiency decreased with the increase of F atom numbers, and the corresponding response time increased. As a result, both the fluorinated D-A polymers show light green in the neutral state, P(F-EDOT) shows more obvious electrochromic performance in the near infrared region (optical contrast: 35.02 %, coloration efficiency: 159.94 cm2 C−1, and quick response time: 0.2 s), accompanied with excellent discoloration stability and optical memory effect. The study of novel fluorinated-based electrochromic materials further expands the selection of acceptor units and the application prospect of electrochromic materials.

Extended transfer matrix method for electron transmission in anisotropic 2D materials: Interplay of strain and (a)periodicity of potentials

We extend the conventional transfer matrix method to include anisotropic features for electron transmission in two-dimensional materials, such as breaking reflection law in pseudo-spin phases and wave vectors, which are not usually considered appropriately in the literature. This method allows us to study transmission properties of anisotropic and stratified electrostatic potential media from a wide range of tunable parameters, which include strain tensor and gating. We apply the extended matrix method to obtain the electron transmission, conductance, and Fano factor for the interplay of a uniaxially strained graphene sheet with external one-dimensional aperiodic potentials. Our results suggest the possibility of visualizing this interplay from conductance measurements.

Hyperhardness and hypersoftness of atoms and their ions

ContextThe theory of reactivity based on cDFT has been supplemented with the new method of calculating the atomic and local indices. With the use of previously derived relationship of the electron density gradient to the softness kernel and to the linear response function, we deliver theoretical analysis to obtain significant reactivity indices—the electron density derivatives: local softness and local hypersoftness together with the global hyperhardness index and the derivative of the global softness with respect to the number of electrons. The local derivatives have been applied in the calculation of responses of atoms to perturbation by an external potential by the alchemical approach. The vital role of the local softness has been confirmed; the potential role of the hypersoftness has been indicated.MethodOur original theoretical scheme has been numerically illustrated with the results obtained with electron density calculations with B3LYP method implemented in Gaussian 16 package. The aug-cc-pvqz basis set has been routinely applied, except for the Ca atom (cc-pvqz). Using the pVTZ basis set recommended by Sadlej was necessary for the potassium atom.Graphical

Study on the elimination characteristics of smoke particles with different materials using electric agglomeration technology

ABSTRACT Fire smoke, consisting of solid particles and liquid droplets, poses risks of asphyxiation, poisoning, making it a significant contributor to fire-related fatalities and environmental pollution. The exploration of effective smoke control methods represents a vital approach to reducing the threat of fire smoke to public health and safety. This study aims to determine the characteristics of elimination for the fire smoke generated from burning four typical materials, thereby validating the universality of electric agglomeration smoke elimination technology. The results indicate that the elimination efficiency of electric agglomeration varies with the material type of the smoke. The rate of change in smoke transmittance from fast to slow is: polyvinyl chloride (PVC), polystyrene (PS), wood, and styrene butadiene rubber (SBR), respectively. With an external potential of 4 kV, PVC smoke reaches the safe threshold after 12.1 s, while SBR smoke achieves it in just 4.9 s. Analysis of the microscopic morphology of agglomerates with scanning electron microscopy (SEM) reveals that particle size distribution is an important factor affecting electric agglomeration elimination. This is because larger initial particles carry a greater charge, enabling the formation of larger agglomerates for more efficient removal. This study provides theoretical guidance for the practical application of electric agglomeration in eliminating smoke particles.

Combined extension and torsion of hydrogels with chemo-mechanical coupling: Revealing positive poynting effect

In this paper, combined extension and torsion of hydrogel subject to a chemo-mechanical coupled loading is described in the framework of continuum mechanics, where the free energy density consists of the elastic, mixing and chemical contributions. A simplified, closed-form and exactly analytical solution to the mechanical response is obtained, which accounts for the coupling effect of external loading, chemical potential and microstructural parameters, such as crosslinking degree, Flory-Huggins parameter, etc. In particular, the effect of free swelling and microscopic diffusion on deformation of the hydrogel at equilibrium state is discussed, reaching some fundamental conclusions. Negative axial forces are captured, revealing the typical positive Poynting effect where the cylinder tends to elongate on twisting, and an inhomogeneous deformation, induced by torsion, along the radial direction is demonstrated. Furthermore, the dynamic competition between external loading and solvent environment is revealed and investigated, where the direct connection between internal micro-physical parameters and macroscopic deformation is demonstrated. The theoretical results presented in this paper may provide predictions and guidance for the mechanical analysis and design of hydrogel cylinder subject to extension and torsion in a solvent.

Dunkl algebra and vacuum pair creation: Exact analytical results via Bogoliubov method

This paper examines the generation of scalar particle pairs resulting from the application of an external electric field's Coulomb potential in both three- and two-dimensional scenarios, employing Dunkl's formalism. In doing this, we present two distinct sets of exact solutions to the Dunkl-Klein-Gordon equation. Subsequently, we employ the canonical approach based on the Bogoliubov transformation to link the “in” and “out” states in order to compute both the probability of pair creation and the density of particle creation. It is shown that the conditions necessary for the creation of pairs of spinless particles depend on several factors: nucleus charge Z, quantum numbers, and Dunkl parameter. It is also shown that the Dunkl formalism enhances particle pair production.

The localized excitation on the Weierstrass elliptic function periodic background for the (3+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili equation

In this paper, the linear spectral problem associated with the (3+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili (gvcKP) equation with the Weierstrass function as the external potential is investigated based on the Lamé function, from which some new localized nonlinear wave solutions on the Weierstrass elliptic ℘-function periodic background are obtained by the Darboux transformation. The degenerate solutions on the ℘-function periodic background for the gvcKP equation can be derived by taking the limits of the half-periods ω 1, ω 2 of ℘(x), whose evolution and corresponding dynamics are also discussed. The findings show that nonlinear waves on the ℘-function periodic background behave as different types of nonlinear waves in different spaces, including periodic waves, vortex solitons and interaction solutions, aiding in elucidating some physical phenomena in the related fields, such as the physical ocean and nonlinear optics.

Nonequilibrium relaxation of soft responsive colloids.

Stimuli-responsive macromolecules display large conformational changes during their dynamics, sometimes switching between states. Such a multi-stability is useful for the development of soft functional materials. Here, we introduce a mean-field dynamical density functional theory for a model of responsive colloids to study the nonequilibrium dynamics of a colloidal dispersion in time-dependent external fields, with a focus on the coupling of translational and conformational dynamics during their relaxation. Specifically, we consider soft Gaussian particles with a bimodal size distribution between two confining walls with time-dependent (switching-on and off) external gravitational and osmotic fields. We find a rich relaxation behavior of the systems in excellent agreement with particle-based Brownian dynamics computer simulations. In particular, we find time-asymmetric relaxations of integrated observables (wall pressures, mean size, and liquid center-of-mass) for activation/deactivation of external potentials, respectively, which are tunable by the ratio of translational and conformational diffusion time scales. Our work thus paves the way for studying the nonequilibrium relaxation dynamics of complex soft matter with multiple degrees of freedom and hierarchical relaxations.

Two-dimensional Diffusion with a Transverse Gravitational Force: Analytical, Numerical and Simulations Results

Abstract Using the Kalinay and Percus projection method a new effective diffusion coefficient is found. This diffusivity generalizes the well-known results previously reported in the literature. Specifically, it is a coefficient that can be applied to two-dimensional asymmetrical channels under an external gravitational-like potential. Furthermore, Brownian Dynamics simulations are performed, and their agreement with the theoretical results is shown. Also, the Mean First-Passage Time is studied for two-dimensional straight conical channels, where the analytical results are analyzed to understand its applicability range using numerical methods, which are compared with Brownian Dynamics simulations. A remarkable result is also presented: the Mean First-Passage Time assumes a minimum at finite values of the external potential amplitude.

Free Vibration of the Magneto-Electro-Elastic Plates Resting on Elastic Foundation Using the Refined Plate Theory with Two Variables

The objective of this article is to investigate the free vibration analyses of the functionally graded magneto-electro-elastic (FG MEE) plates supported by an elastic foundation using the refined plate theory (RPT) with two variables. The elastic foundation is modeled utilizing the Winkler-Pasternak theory. The power-law model is employed to characterize the graded material properties of the FG MEE plates. According to the RPT and Hamilton's principle, the governing equations of the FG MEE plate are derived. The displacement fields and electric and magnetic potentials are approximated using the Non-Uniform Rational B-Splines (NURBS) basic functions of the isogeometric approach (IGA). The proposed model’s advantages and accuracy are demonstrated by comparing the obtained results with those reported in the existing literature. The study comprehensively examines and discusses the impact of several parameters, including the power index, initial external magnetic potential and electric voltage, and the geometry, on the vibration frequency of the FG MEE plates. The numerical findings indicate that an increase in the power index leads to a decrease in the frequency of the FG MEE plates. Besides, the stiffness of FG MEE plates decreases with an increase in the initial external electric voltage, whereas it increases with an increase in the initial external magnetic potential. This article presents valuable perspectives on examining vibration analysis of the FG MEE plates, which can inform the design of innovative materials and structures with customized properties.

Polarization textures in crystal supercells with topological bands

Two-dimensional materials are a highly tunable platform for studying the momentum space topology of the electronic wavefunctions and real space topology in terms of skyrmions, merons, and vortices of an order parameter. Such textures for electronic polarization can exist in moiré heterostructures. A quantum-mechanical definition of local polarization textures in insulating supercells was recently proposed. Here, we propose a definition for local polarization that is also valid for systems with topologically nontrivial bands. We introduce semilocal hybrid polarizations, which are valid even when the Wannier functions in a system cannot be made exponentially localized in all dimensions. We use this definition to explicitly show that nontrivial real-space polarization textures can exist in topologically nontrivial systems with nonzero Chern number under (1) an external superlattice potential, and (2) under a stacking-induced moiré potential. In the latter, we find that while the magnitude of the local polarization decreases discontinuously across a topological phase transition from trivial to topologically nontrivial, the polarization does not completely vanish. Our findings suggest that band topology and real-space polar topology may coexist in real materials. Published by the American Physical Society 2024

Similarity transformations and exact solutions of the (3+1)-dimensional nonlinear Schrödinger equation with spatiotemporally varying coefficients

In this paper, an extended (3+1)-dimensional nonlinear Schrödinger equation is studied. By using similarity transformation, some exact solutions of this equation are obtained, which include soliton solutions and periodic function solutions, its nonlinear spatial modulation and external potential are affected by time and space. Based on the solution obtained previously, some figures are displayed.

Oxidation of Ammonia in Water Microdroplets Produces Nitrate and Molecular Hydrogen.

Water microdroplets containing dissolved ammonia (30-300 μM) are sprayed through a copper oxide mesh with a 200 μm average pore size, resulting in the formation of nitrate (NO3-) and the release of molecular hydrogen (H2). The products result from a redox process that takes place at the liquid-solid interface through contact electrification, where no external potential is applied. Oxidation is initiated by superoxide radical anions (O2-) that originate from the oxygen in the air surrounding the microdroplets and from the hydroxyl radicals (OH•) originating from the water-air interface. Two spin traps (TEMPO and DMPO) capture these radicals as well as NH2OH+•, HNO, NO•, NO2•, and NOOH, which are detected by mass spectrometry. We also directly observed N2O2-• by the same means. We found that the hydrogen atom from the ammonia molecule can be set free not only in the form of H• but also as H2, which is detected using a residue gas analyzer. The oxidation process can be significantly enhanced by a factor of 3 when the sprayed microdroplets are irradiated with ultraviolet light (265 nm, 5 W). 35% of 300 μM ammonia can be degraded within 20 μs, and the nitrate conversion rate is estimated to be 15 nmol·mg-1·h-1.

Exfoliated g-C3N4-CdS-MXene an efficient all-solid-state Z-type heterojunction serving as efficient photo/electro/photoeletro catalyst for oxygen evolution reaction and dye degradation under visible light at low bias voltage

The rational design of highly active catalysts for the photo/electro/photoelectro catalytic O2 evolution reaction (OER) and water treatment plays a crucial role in the development of sustainable energy generation and environment remediation technologies. Catalysts which are effective in solar light at a low external bias potential are in great demand. Herein, a novel catalyst consisting of all-solid-state Z-scheme g-C3N4-CdS-MXene heterojunction has been designed for photo/electro/photoelectro catalytic reactions. g-C3N4-CdS-MXene exhibited excellent photocatalytic efficiency towards Methylene Blue degradation under simulated solar light irradiation and superb electrocatalytic and photoelectron catalytic efficiency for OER. This catalyst showed high OER performance with an early onset potential of 1.58 V, a low overpotential of 350 mV (at 10 mA cm−2), and low value of Tafel slope (98 mV dec−1). When OER was combined with the photoelectro catalytic reaction for Methylene Blue degradation, g-C3N4-CdS-MXene demonstrated an exceptional photoelectro catalytic performance by degrading 100 % Methylene Blue within 4 min under solar light irradiation at a very low bias of 350 mV. This catalyst also exhibited its capability to degrade various dyes used in textile industries. This work provides an interesting strategy for simultaneous O2 production and efficient dye degradation for environmental and energy engineering.

Approximation of a two‐dimensional Gross–Pitaevskii equation with a periodic potential in the tight‐binding limit

AbstractThe Gross–Pitaevskii (GP) equation is a model for the description of the dynamics of Bose–Einstein condensates. Here, we consider the GP equation in a two‐dimensional setting with an external periodic potential in the ‐direction and a harmonic oscillator potential in the ‐direction in the so‐called tight‐binding limit. We prove error estimates which show that in this limit the original system can be approximated by a discrete nonlinear Schrödinger equation. The paper is a first attempt to generalize the results from [19] obtained in the one‐dimensional setting to higher space dimensions and more general interaction potentials. Such a generalization is a non‐trivial task due to the oscillations in the external periodic potential which become singular in the tight‐binding limit and cause some irregularity of the solutions which are harder to handle in higher space dimensions. To overcome these difficulties, we work in anisotropic Sobolev spaces. Moreover, additional non‐resonance conditions have to be satisfied in the two‐dimensional case.

Dirac fermions in a spinning conical Gödel-type spacetime

Abstract In this paper, we determine the relativistic and nonrelativistic energy levels for Dirac fermions in a spinning conical Gödel-type spacetime in (2+1)-dimensions, where we work with the Dirac equation in polar coordinates and we use the tetrads formalism. Solving a second-order differential equation for the two components of the Dirac spinor, we obtain a generalized Laguerre equation, and the relativistic energy levels, where such levels are quantized in terms of the quantum numbers n and m j, and explicitly depends on the spin parameter s, spinorial parameter u, curvature and rotation parameters α and β, and on the vorticity parameter Ω. In particular, the quantization is a direct result of the existence of Ω (i.e., Ω acts as a kind of ``external field or potential''). We see that for m j>0, the energy levels do not depend on s and u; however, depend on n, m j, α, and β. In this case, α breaks the degeneracy of the energy levels and such levels can increase infinitely in the limit 4Ωβ/α→1. Already for m j<0, we see that the energy levels depend on s, u and n; however, it no longer depends on m j, α and β. In this case, it is as if the fermion ``lives only in a flat Gödel-type spacetime''. Besides, we also study the low-energy or nonrelativistic limit of the system. In both cases (relativistic and nonrelativistic), we graphically analyze the behavior of energy levels as a function of Ω, α, and β for three different values of n.