Physical Applications Research Articles

Weakly negative permittivity from three-dimensional printed polydimethylsiloxane/graphene films in the radio frequency band

Epsilon-negative materials (ENMs) has become a research hotspot due to their unique physical properties and practical applications in fields such as directional radiation and tunneling effects. In this work, weakly negative permittivity (from -50 at 10 kHz to -25 at 1 MHz) was realized from three-dimensional printed polydimethylsiloxane/graphene films. The dielectric properties including complex permittivity (ε', ε″), complex impedance (Z', Z″), alternating current conductivity (σac), and dielectric loss tangent (tanδ) were investigated. When graphene content reached 15 wt%, the interconnected graphene network was formed, resulting in negative permittivity. Theory calculations were further used to explore the mechanism. The electrons around carbon atoms showed significant delocalization. With the effect of the external electromagnetic field, the electrons on the surface of graphene could easily oscillate collectively, leading to negative permittivity. Differential charge density exhibited that interfacial electric fields were formed between polydimethylsiloxane and graphene, enhancing positive permittivity. Therefore, when the graphene content reached 15 wt%, the film exhibited weakly negative permittivity, which was the result of the mutual balance between the graphene conductive network and the interface electric fields.

Generalized bivariate Kummer-beta distribution with marginals defined on the unit interval.

In this paper, a generalized bivariate Kummer-beta distribution is proposed. The name derives from the fact that its particular cases include univariate Kummer-beta distributions. This distribution generalizes a number of existing bivariate beta distributions, including Nadarajah's bivariate distributions, Libby and Novick's bivariate beta distribution and a central bivariate Kummer-beta distribution. Various properties associated with this newly introduced distribution are derived. The derived properties include product moments, marginal densities, marginal moments, conditional densities, conditional moments, Rényi entropy and Shannon entropy. Motivated by possible applications in economics, genetics, hydrology, meteorology, nuclear physics, and reliability, we also derive distributions of the product and the ratio of the components following the proposed distribution. Parameter estimation by maximum likelihood method is discussed by deriving expressions for score functions. Inference based on maximum likelihood estimation supposes that the maximum likelihood estimators have zero bias and zero mean squared errors. A simulation study is performed to check this for finite samples.

Dynamic of bifurcation, chaotic structure and multi soliton of fractional nonlinear Schrödinger equation arise in plasma physics

In this study, we examine the third-order fractional nonlinear Schrödinger equation (FNLSE) in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(1+1)$$\\end{document}-dimensional, by employing the analytical methodology of the new extended direct algebraic method (NEDAM) alongside optical soliton solutions. In order to better understand high-order nonlinear wave behaviors in such systems, the researched model captures the physical and mathematical properties of nonlinear dispersive waves, with applications in plasma physics and optics. With the aid of above mentioned approach, we rigorously assess the novel optical soliton solutions in the form of dark, bright–dark, dark–bright, periodic, singular, rational, mixed trigonometric and hyperbolic forms. Additionally, stability assessments using conserved quantities, such as Hamiltonian property, and consistency checks were used to validate the solutions. The dynamic structure of the governing model is further examined using chaos, bifurcation, and sensitivity analysis. With the appropriate parameter values, 2D, 3D, and contour plots can all be utilized to graphically show the data. This work advances our knowledge of nonlinear wave propagation in Bose–Einstein condensates, ultrafast fibre optics, and plasma physics, among other areas with higher-order chromatic effects.

Differential and integral elastic cross sections for electrons and positrons collisions with carbon dioxide molecules

This study investigates the elastic scattering of electrons and positrons by carbon dioxide (CO2) molecules over a wide energy range from 1 eV to 1 KeV. We have computed differential and integral elastic cross-sections (DCS and ICS) using partial wave analysis and compared the theoretical results with available experimental data. Our findings show a strong correlation with experimental results, particularly at mid to high-energy ranges, validating the employed theoretical frameworks. Additionally, the Sherman function was examined to explore spin polarisation effects during scattering events. This research provides crucial insights for applications in atmospheric physics, materials science, and molecular scattering processes, demonstrating its direct relevance to real-world problems and paving the way for further investigation into particle-molecule interactions.

Spectral tau explicit form for approximating solutions to real-life IBVPs using Chebyshev derivatives

This paper established a functional design of the spectral Tau method (STM) upon the first derivatives of Chebyshev polynomials (FDCHPs). A new linearization relation has been developed. Hence, this relation and another investigated one for integration have been used via the Tau method to execute the Tau integration analytically. Moreover, explicit algebraic systems for solving the Lane–Emden and Riccati equations and the contamination of a system of three artificial lakes are introduced. The convergence and error analyses are explored in depth. Some enlightening boundary value problems (BVPs) for real-life and physical applications, as singularly perturbed equations, are provided to guarantee that this approach is authentic, reliable, and appropriate. Accurate results are obtained using only a few number of retained nodes. The different outcomes, patterns, and better results showed that the FDCHPs differ from Chebyshev polynomials of the second kind.

A new model describing improved bound-state and statistical properties in the framework of deformed Schrödinger equation for the improved Coshine Yukawa potential in 3D-NR(NCPS) symmetries

In this paper, within the three-dimensional non-relativistic non-commutative phase–space (3D-NR(NCPS)) symmetries, we examined the 3D deformed Schrödinger equation (3D-DSE) using the improved Coshine Yukawa potential (ICYP) model composed from Coshine Yukawa potential (CYP) ([Formula: see text]) and other terms produced from the effect of phase–space deformation ([Formula: see text] and [Formula: see text]). For this study, the 3D-DSE in the 3D-NR(NCPS) symmetry is solved and discussed with standard independent time perturbation theory and the generalized Bopp’s shifts method. For the homogeneous (H2 and N2) and heterogeneous (LiH, ScH, and HCL) diatomic molecules, it is obtained that the improved non-relativistic energy equation and eigenfunction for the ICYP in the presence of deformation phase–space are dependent on the discrete atomic quantum numbers ([Formula: see text],m), the dissociation energy [Formula: see text], the equilibrium bond length the screening parameter [Formula: see text], the deformation phase parameters ([Formula: see text]) and the deformation space parameters ([Formula: see text]). Additionally, the thermal properties of the CYP and ICYP with 3D Schrödinger equation (3D-SE) and 3D-DSE are thoroughly examined in the three-dimensional non-relativistic quantum mechanics (3D-NR(QM)) known in the literature symmetry and 3D-NR(NCPS) symmetries, including the partition function, mean energy, free energy, specific heat, and entropy. Furthermore, we discussed particular cases of thermodynamic characteristics for the ICYP model. In our study, we have shown that all the physical values related to energy and thermodynamic properties within the framework of the 3D(NR)NCPS symmetry are equal to the corresponding values within the framework of 3D-NR(QM) symmetry known in the literature, in addition to minor effects resulting from their interaction with the topological properties of the deformed phase–space. This study has multiple applications in various domains, including atomic and molecular physics.

Multiple Circular Polarizations Coexisting with Bound States in the Continuum Without Breaking Symmetry

AbstractBound states in the continuum (BICs) have been engineered in periodic photonic systems to achieve diverse polarization behavior in momentum space. By breaking C2z symmetry of photonic crystal slabs (PhCS), purely circular polarization, which hold significant potential for applications in topological physics and chiral optics, can be achieved near the BICs. In this study, the intriguing phenomenon of BICs on the degenerate band of PhCS with a triangular lattice featuring cylindrical holes are investigated. Unlike previous studies that mainly focused on BICs on non‐degenerate photonic bands, this research reveals a sophisticated interplay between BICs and Dirac points on the more intricate degenerate photonic band. This interaction gives birth to two pairs of purely circular polarizations with opposite chirality, even without breaking any symmetry of the PhCS. Additionally, It is find that by further breaking the σz mirror symmetry of the PhCS, these purely circular polarization states can be significantly amplified. This findings not only enrich the polarization responses of high‐Q photonic devices but also enables the modulation of chiral light, laying the groundwork for the creation of high‐quality optical devices with precisely engineered polarization properties.

Observation of quantum superposition of topological defects in a trapped-ion quantum simulator.

Topological defects are discontinuities of a system protected by global properties, with wide applications in mathematics and physics. While previous experimental studies mostly focused on their classical properties, it has been predicted that topological defects can exhibit quantum superposition. Despite the fundamental interest and potential applications in understanding symmetry-breaking dynamics of quantum phase transitions, its experimental realization still remains a challenge. Here, we report the observation of quantum superposition of topological defects in a trapped-ion quantum simulator. By engineering long-range spin-spin interactions, we observe a spin kink splitting into a superposition of kinks at different positions, creating a "Schrodinger kink" that manifests nonlocality and quantum interference. Furthermore, by preparing superposition states of neighboring kinks with different phases, we observe the propagation of the wave packet in different directions, thus unambiguously verifying the quantum coherence in the superposition states. Our work provides useful tools for nonequilibrium dynamics in quantum Kibble-Zurek physics.

Symmetries in particle physics: from nuclear isospin to the quark model

We present a concise pedagogic introduction to group representation theory motivated by the historical developments surrounding the advent of the Eightfold Way. definitions of groups and representations are avoided in favour of the physical intuition of symmetries of the nuclear interaction. The concept of nuclear isospin is used as a physical motivation to introduce SU(2) and discuss the main techniques of representation theory. The discovery of strange particles motivates extending the symmetry group to SU(3), at first in the context of the Sakata model. We highlight the successes in fitting mesons in the SU(3) octet, discuss the drawbacks of the Sakata model for baryonic classifications, and how the Eightfold Way finally led to the quark model. This approach has two major advantages: (i) the main concepts of the theory of Lie groups are introduced and discussed without ever losing touch with its applications in particle physics; (ii) it allows the beginner to study group theory while also becoming acquainted with the historical developments of particle physics that led to the concept of quarks. In particular, in this pedagogical path the quarks appear as yet another class of particles predicted from symmetry principles, rather than being introduced ad hoc for postulating an SU(3) symmetry, as usually done in the literature.

Neural-network approach to running high-precision atomic computations

Modern applications of atomic physics, including the determination of frequency standards and the analysis of astrophysical spectra, require prediction of atomic properties with exquisite accuracy. For complex atomic systems, high-precision calculations are a major challenge due to the exponential scaling of the involved electronic configuration sets. This exacerbates the problem of required computational resources for these computations and makes indispensable the development of approaches to select the most important configurations out of otherwise intractably huge sets. We have developed a neural-network (NN) tool for running high-precision atomic configuration interaction (CI) computations with iterative selection of the most important configurations. Integrated with the established atomic codes, our approach results in computations with significantly reduced computational requirements in comparison with those without NN support. We showcase a number of NN-supported computations for the energy levels of Fe16+ and Ni12+ and demonstrate that our approach can be reliably used and automated for solving specific computational problems for a wide variety of systems. Published by the American Physical Society 2024

Use of Differential Equations in Population Growth Analysis

In this assignment we discussed differential equation applications in real-world scenarios. Differential equations are a significant area of mathematics with applications in many fields, including engineering, astronomy, biology, chemistry, physics, economics, and finance. Differential equations are used in economics to explain many concepts such as restricted and infinite growth, equilibrium and stability, and the dynamics of supply and demand in an economy. Differential equations will be used to examine several facets of Nepal in this research assignment.

The number of spanning trees in K n -chain and ring graphs

The problem of counting spanning trees of graphs or networks is a fundamental and crucial area of research in combinatorics, while has numerous important applications in statistical physics, network theory and theoretical computer science. Very recently, Kosar, Zaman, Ali and Ullah obtained a nice formula on the number of spanning trees of a K 5-chain network K5ℓ constructed by connecting ℓcopys of complete graphs K 5. They made extensive use of matrix theory and spectral graph theory, especially the normalized Laplacian of graphs. In this paper, by using a rather simple and more physical treatment (the mesh-star transformation in electrical network) without any linear algebra, we generalize their result to K n -chain graphs and K n -ring graphs. The results show that there is a simple relation between the number of spanning trees of the K n -chain graph Lnℓ and the K n -ring graph Cnℓ . We also calculate the corresponding tree entropy (or so called ‘the asymptotic growth constant’) and find that the tree entropy of the corresponding K n -chain graphs and K n -ring graphs are totally the same.

Precision computation of one-dimensional quadratures

The calculation of quadratures arises in many physical and technical applications. In this paper, the best quadrature formulas are selected and their quantitative comparison is carried out on a number of representative examples.

3D alignment of distant patterns with deep-subwavelength precision using metasurfaces

Measurement of the relative positions of two objects in three dimensions with sub-nanometer precision is essential to fundamental physics experiments and applications such as aligning multi-layer patterns of semiconductor chips. Existing methods, which rely on microscopic imaging and registration of distant patterns, lack the required accuracy and precision for the next generation of three-dimensional (3D) chips. Here we show that 3D misalignment between two distant objects can be measured using metasurface alignment marks, a laser, and a camera with sub-nanometer precision. Through simulations, we demonstrate that the shot noise-limited precisions of the lateral and axial misalignments between the marks are λ0/50, 000 and λ0/6, 300 (λ0: laser’s wavelength), respectively. With its high precision and simplicity, the technique enables the next generation of 3D-integrated optical and electronic chips and paves the way for developing cost-effective and compact sensors relying on sub-nanometer displacement measurements.

Topological data analysis assisted machine learning for polar topological structures in oxide superlattices

Ferroelectric topological phases and phase transitions have been extensively investigated recently due to the rich physical insights and potential applications in next-generation electronic devices. However, precisely predicting the topological phase transitions under different internal and external conditions in polar oxide superlattice systems is challenging due to the complex energy competitions and highly nonlinear kinetics involved. Herein, we adopted a state-of-the-art mathematical concept called “persistent homology” from topological data analysis to extract the essential topological features for the polarization data in various topological structures. By implementing the persistent image as the descriptor, support vector regression (SVR) based convolutional neural network (CNN) models are developed for the automated and high precision classification and regression of topological states based on high-dimensional phase-field simulation data of the PTO/STO superlattice. Using this method, we can automatically construct the strain and electric field phase diagrams in seconds with high throughput phase-field data. We hope to spur further interest in the integration of state-of-the-art mathematical tools, machine learning algorithms, and condensed matter physics for predictions of topological phase transitions.

Historical Elite Differential Evolution Based on Particle Swarm Optimization Algorithm for Texture Optimization with Application in Particle Physics

Within the phenomenology of particle physics, the theoretical model of 4-zero textures is validated using a chi-square criterion that compares experimental data with the computational results of the model. Traditionally, analytical methods that often imply simplifications, combined with computational analysis, have been used to validate texture models. In this paper, we propose a new meta-heuristic variant of the differential evolution algorithm that incorporates aspects of the particle swarm optimization algorithm called “HE-DEPSO” to obtain chi-squared values that are less than a bound value, which exhaustive and traditional algorithms cannot obtain. The results show that the proposed algorithm can optimize the chi-square function according to the required criteria. We compare simulated data with experimental data in the allowed search region, thereby validating the 4-zero texture model.

Stripe Soliton in All‐Fiber Lasers

AbstractStripe solitons (SSs), the special localized wavepackets exhibiting periodic modulations, are identified in condensed matter physics and nonlinear science. Here, giant‐chirp and chirp‐free SSs in all‐fiber lasers are demonstrated composed of single‐mode fiber and polarization‐maintaining fiber. The chirp property of SSs depends on the cavity dispersion while the stripe period relies on the fiber birefringence. Theoretical and numerical results coincide with experimental findings, revealing that the filtering and frequency shift of two vector modes is governed by the mode coupling related to birefringence and the nonlinear coupling induced by the phase modulation, respectively, which disrupts their complementarity and ultimately leads to modulation of the overall spectrum. With the aid of the saturable absorption and cross‐phase modulation effects, the multi‐color pulses synergistically overlap, giving rise to the unique SSs. These results present a simple approach for generating chirp‐controllable SSs in all‐fiber lasers, which is crucial for applications in difference frequency generation and soliton physics.

Attenuation coefficients of soy-lignin bonded Rhizophora spp. particleboard as a potential phantom material using Monte Carlo GATE

This work aimed to determine the linear and mass attenuation coefficients of soy-lignin bonded Rhizophora spp. particleboard intended for use as a phantom material using Monte Carlo GATE simulation. At a desired density of 1.0 gcm-3, particleboard constructed of Rhizophora spp. wood trunk bonded with soy flour and lignin was created. The sample’s elemental composition was identified using energy dispersive X-ray spectroscopy. The GATE software was used to simulate the setup with the histories of 1 × 107, and comparison was made between the experimental and simulation data. The disparities between the linear and mass attenuation coefficients of the samples experimentally measured and calculated using GATE at low energy photons were quite small. The result revealed a good agreement between the experimental and simulation data, and the attenuation coefficients were in close proximity with XCOM of water. The outcome revealed GATE adequacy for validation of attenuation coefficient measurement in bioresources phantom material for medical physics application.

More quantum chemistry with fewer qubits

Quantum computation is one of the most promising new paradigms for the simulation of physical systems composed of electrons and atomic nuclei, with applications in chemistry, solid-state physics, materials science, and molecular biology. This requires a truncated representation of the electronic structure Hamiltonian using a finite number of orbitals. While it is, in principle, obvious how to improve on the representation by including more orbitals, this is usually unfeasible in practice (e.g., because of the limited number of qubits available) and severely compromises the accuracy of the obtained results. Here, we propose a quantum algorithm that improves on the representation of the physical problem by virtue of second-order perturbation theory. In particular, our quantum algorithm evaluates the second-order energy correction through a series of time-evolution steps under the unperturbed Hamiltonian. An important application is to go beyond the active-space approximation, allowing to include corrections of virtual orbitals, known as multireference perturbation theory. Here, we exploit the fact that the unperturbed Hamiltonian is diagonal for virtual orbitals and show that the number of qubits is independent of the number of virtual orbitals. This gives rise to more accurate energy estimates without increasing the number of qubits. Moreover, we demonstrate numerically for realistic chemical systems that the total runtime has highly favorable scaling in the number of virtual orbitals compared to previous studies. Numerical calculations confirm the necessity of the multireference perturbation theory energy corrections to reach accurate ground-state energy estimates. Our perturbation theory quantum algorithm can also be applied to symmetry-adapted perturbation theory. As such, we demonstrate that perturbation theory can help to reduce the quantum hardware requirements for quantum chemistry. Published by the American Physical Society 2024

Theoretical Design of Thorium Nitride MXenes.

Actinides with 5f6d7s valence orbitals feature special physicochemical properties different from those of the other elements. Actinide-based two-dimensional (2D) materials combine the distinctive physics of actinides with the quantum size effect of 2D materials, but relevant studies are scarce. Since Th has a valence electron configuration of 6d27s2 like Ti, and Ti-based MXenes show excellent stability and versatile applications, whether Th can form stable MXenes has become an intriguing question. Herein, we designed Th2N, Th3N2, and Th4N3 MXenes and investigated their physical properties, functionalization, and potential applications using density functional theory. Their stabilities are validated by global minimum search, phonon spectra, ab initio molecular dynamics, enthalpy of formation, and energy above the hull. All the Th-N MXenes exhibit metallic properties and are stabilized by the electrostatic interaction between Th and N ions, as well as the covalent bonding interaction between the Th 6d/5f and N 2p/2s orbitals. The H-, O-, and F-functionalization3N2 MXene improve its stability while preserving its metallicity, and the O-functionalized Th3N2 MXene shows promising catalytic activity for hydrogen evolution. The thorium nitride MXenes enrich the family of actinide-based 2D materials and extend our understanding of the structures and properties induced by actinide elements in low-dimensional materials.