First-order Theory Research Articles

Quantum analysis of the recent cosmological bounce in the comoving Hubble length

We formulate the transition from decelerated to accelerated expansion as a bounce in connection space and study its quantum cosmology, knowing that reflections are notorious for bringing quantum effects to the fore. We use a formalism for obtaining a time variable via the demotion of the constants of nature to integration constants, and focus on a toy universe containing only radiation and a cosmological constant $\mathrm{\ensuremath{\Lambda}}$ for simplicity. We find that, beside the usual factor-ordering ambiguities, there is an ambiguity in the order of the quantum equation, leading to two distinct theories: one second order, and one first order. In both cases two time variables may be defined, conjugate to $\mathrm{\ensuremath{\Lambda}}$ and the radiation constant of motion. We make little headway with the second-order theory, but are able to produce solutions to the first-order theory. They exhibit the well-known ``ringing'' whereby incident and reflected waves interfere, leading to oscillations in the probability distribution even for well-peaked wave packets. We also examine in detail the probability measure within the semiclassical approximation. Close to the bounce, the probability distribution becomes double peaked, with one peak following a trajectory close to the classical limit but with a Hubble parameter slightly shifted downwards, and the other with a value of $b$ stuck at its minimum. An examination of the effects still closer to the bounce, and within a more realistic model involving matter and $\mathrm{\ensuremath{\Lambda}}$, is left to future work.

Photoelectron momentum distributions with twisted attosecond X waves carrying orbital angular momentum

We theoretically investigate the photoelectron momentum distributions of 1s and 2px,y states of hydrogen by twisted attosecond X waves carrying orbital angular momentum based on first-order perturbation theory. The photoionization spectra as a function of photoelectron energy and emission angle are analyzed respectively. The results indicate that there are interference fringes in the energy spectra and more nodes in the angular distributions. These angular nodes are attributed to both orbital structure and the temporal-spatial structure of X waves. We derive an equation that can quantitatively describe the angular nodes in the photoelectron angular distributions. Our results and analyses indicate that the angular distribution is an important observation for the investigation of the information of both orbitals and X waves.

State-resolved ionization dynamics of a neon atom induced by x-ray free-electron-laser pulses

We present a theoretical framework to describe state-resolved ionization dynamics of neon atoms driven by ultraintense x-ray free-electron-laser pulses. In general, x-ray multiphoton ionization dynamics of atoms have been described by time-dependent populations of the electronic configurations visited during the ionization dynamics, neglecting individual state-to-state transition rates and energies. Combining a state-resolved electronic-structure calculation, based on first-order many-body perturbation theory, with a Monte Carlo rate-equation method enables us to study state-resolved dynamics based on time-dependent state populations. Our results demonstrate that configuration-based and state-resolved calculations provide similar charge-state distributions, but the differences are visible when resonant excitations are involved, which are also reflected in calculated time-integrated electron and photon spectra. In addition, time-resolved spectra of ions, electrons, and photons are analyzed for different pulse durations to explore how frustrated absorption manifests itself during the ionization dynamics of neon atoms.

К построению релятивистских гидродинамических уравнений в искривленном пространстве-времени, записанных в абстрактных геометрических обозначениях

This paper presents a macroscopic derivation of the system of equations of relativistic dissipative hydrodynamics in an abstract geometrical form, which does not depend on the chosen space-time coordinates and reduces to equations valid in both flat and curved space-time. The above procedure, serving as a link between the non-gravitational laws of physics and gravitation, is based on Einstein's equivalence principle which guarantees that the laws of physics written in abstract geometrical representation have the same form both in flat and curved spacetime. A modern formulation of relativistic hydrodynamics based on both classical nonequilibrium thermodynamics (first-order theory) and expanded irreversible thermodynamics (second-order theory) is proposed. The theory presented has both purely conceptual and applied significance. In particular, this theory has applications in such important fields of knowledge as nuclear physics, astrophysics and cosmology. For example, in viscous cosmological models, bulk viscosity acts as a cause of dissipation, which has a significant impact on the processes in the Universe.

Оптические свойства ван-дер-ваальсовых гетероструктур на основе 2D-монослоев борофена, нитрида галлия и оксида цинка

In this paper, we consider two new atomic models of van der Waals vertical heterostructures of metal-semiconductor type based on a 2D buckled triangular borophene with metallic conductivity and graphene-like 2D monolayers of gallium nitride GaN and zinc oxide ZnO, which are semiconductors. Using the density functional theory, the equilibrium configurations of supercells of the borophene/GaN and borophene/ZnO heterostructures are found and their thermodynamic stability at room temperature is shown. Within the framework of the nonstationary first-order perturbation theory, the optical characteristics (complex permittivity and absorption coefficient) are calculated in the electromagnetic radiation wavelength range of 0.2–2 μm. The presence of anisotropy in the optical properties of the borophene/GaN and borophene/ZnO heterostructures is established when the direction of light polarization is chosen. This is due to different manifestations of the optical properties of the constituent monolayers of the heterostructure. When light is polarized in the direction of the zigzag edge of the GaN/ZnO (along the X axis), the optical properties of GaN and ZnO semiconductor monolayers are predominantly manifested. When light is polarized in the direction of the zigzag edge of the borophene monolayer (along the Y axis), the optical properties of borophene manifest themselves. A synergistic effect has been found from the combination of borophene and ZnO monolayers in the composition of the borophene/ZnO vertical heterostructure, which manifests itself in the form of a section of the increasing plot of the real and imaginary parts of the complex permittivity in the infrared region for both directions of light polarization. It is shown that the difference in the values of the absorption coefficient of the borophene/GaN heterostructure between the UV and visible ranges can reach ~ 7 times, between the UV and near IR ranges - ~ 14 times, and for the borophene/ZnO heterostructure this difference can be up to ~ 6 times and up to ~18 times, respectively. It is predicted that borophene/GaN and borophene/ZnO heterostructures can be used to create UV radiation detectors.

A cavity formation energy formula for hard spheres in simple electrolyte solutions.

A formula for cavity formation energy of a hard sphere in restricted primitive electrolyte solutions is derived based on the integral equation theory. Specifically, the contact values of radial distribution functions between the hard sphere and the ionic species, determined analytically from the first-order mean spherical approximation theory, are used to evaluate the cavity formation energy. In the large solute-size limit, the scaling relation of the cavity formation energy further leads to an analytical expression for the surface tension of the electrolyte solution near a curved interface. Our theory is applied to hard spheres immersed in restricted primitive electrolyte solutions, where the good agreement of the cavity formation energy with the hyper-netted chain theory demonstrates the accuracy of our theory.

Vibration analysis of a composite elastic metamaterial plate based on a semi-analytical method

A semi-analytical vibration analyzing process is presented for a kind of finite composite elastic metamaterial plate by combining the effective medium theory and the first-order shear deformation sandwich plate theory, and the natural and steady-state vibration characteristics of such complex composite structure are investigated by means of equivalent analysis. The effectiveness of the semi-analytical analyzing process is demonstrated and some extraordinary vibration behaviors of such composite structure are revealed, such as there is no natural frequency in the bandgap, the modal density consistently increases around the bandgap's starting frequency, and the modes of the appropriate orders before and after the bandgap are consistent at the macroscopic level. The semi-analytical analyzing process and the special vibration behaviors may provide useful reference for relevant investigation and design of composite elastic metamaterial plate structures in the field of vibration control and isolation.

Splitting of the atomic hydrogen 21-cm line induced by gravitational waves from a supermassive black hole binary

We investigate the characteristic of the hyperfine splitting of a ground-state hydrogen atom subjected to a field of a gravitational wave. In our consideration, hydrogen atoms are in the source’s local wave zone. The interaction between the atoms and the gravitational wave induces the shifts of some energy levels in the hyperfine structure, computed by the first-order perturbation theory. The splitting of energy levels leads to more than one hyperfine transition. Our analysis suggests that a gravitational wave emitted by supermassive black hole binaries could be strong enough to induce a significant effect on the hyperfine splitting. This radio-wave spectrum provides the gravitational-wave signature and thus offers a way of identifying the merger of supermassive black hole binaries.

Passive Multi-Channel Detection: A General First-Order Statistical Theory

Passive Multi-Channel Detection: A General First-Order Statistical Theory

NONLINEAR TRANSIENT RESPONSE OF A PERFORATED FGM PLATE UNDER THERMO-MECHANICAL CONDITIONS

The present study is aimed to investigate the nonlinear transient response of an aluminum-zirconia functionally graded material (FGM) plate with a central circular hole under thermo-mechanical loadings. The nonlinear formulation is based on the first-order shear deformation plate theory along with geometric nonlinearity incorporated in the von Karman sense. The finite element numerical technique is employed to solve approximately the governing equations of motion derived through Hamilton's principle. A MATLAB program, developed to carry out the investigation, is verified for accuracy by comparing the results with those reported in the literature-under mechanical and thermo-mechanical loadings. Numerical results are presented to show the effect of various parameters, viz. material gradation exponent, geometric variables, hole size, and boundary conditions, on the nonlinear transient response of the FGM plate. It is found that the material gradation exponent has a noticeable effect on the transverse deflection of vibration of the FGM plate with a hole, but the frequency of vibration is not affected much. Further, with the increase in the size of hole in the FGM plate, the amplitude of its vibration decreases while the frequency of vibration increases.

Aeroelastic Tailoring of Variable Stiffness Composite Laminated Quadrilateral and Circular Plates in Supersonic Flow Using Isogeometric Approach

In this study, a cubic NURBS-based isogeometric finite element method is developed to study the aeroelastic tailoring of variable stiffness composite laminated (VSCL) plates, including skew, skew-tapered, tapered, and circular shapes based on third-order shear deformation theory. Also, the first-order piston theory is employed to approximate aerodynamic loads with arbitrary yaw flow angles over the plate area to establish aeroelastic equations. The NURBS basis functions are then utilized to simulate exact geometries and estimate variable fields for discretizing governing equations by well-known isogeometric analysis. Finally, the free vibration and flutter analysis of a VSCL quadrilateral and circular plate will be presented via the obtained eigenvalue problem. The achieved results are compared with the available results in the literature to prove the accuracy and validity of the present method. The effect of different parameters such as the flow yaw angle, end and middle-length fiber orientation, longitudinal to transverse Young’s modulus ratio, geometric shape, boundary conditions, and turning symmetric layup to asymmetric layup is carried out on the critical flutter aerodynamic pressure and natural frequencies.

A variational derivation of the field equations of an action-dependent Einstein-Hilbert Lagrangian

<abstract><p>We derive the equations of motion of an action-dependent version of the Einstein-Hilbert Lagrangian as a specific instance of the Herglotz variational problem. Action-dependent Lagrangians lead to dissipative dynamics, which cannot be obtained with the standard method of Lagrangian field theory. First-order theories of this kind are relatively well understood, but examples of singular or higher-order action-dependent field theories are scarce. This work constitutes an example of such a theory. By casting the problem in clear geometric terms, we are able to obtain a Lorentz invariant set of equations, which contrasts with previous attempts.</p></abstract>

Teorija uma kod dece - preliminarno istraživanje o ulozi pamćenja i jezičkih sposobnosti kao razvojnih pokazatelja

Preschool age is a period of fundamental changes in child's ability to explicitly reason about the other people's mental states. The aim of the research was to determine the relationship between the development of theory of mind, working memory and language abilities in children with typical development, aged four to eight years. For the assessment of listed abilities several instruments were used: "Sanja and Ana" False belief task, Backward span task, Verbal memory test, Decision speed test, Toddler grammar and FONT test. The results of the research indicated statistically significant correlations between theory of mind, verbal memory, as well as some aspects of language abilities. However, as a statistically significant indicator of achievement on theory of mind tasks, only verbal memory stands out (p < .05) which together with verbal working memory predicts 26% of the variance of achievement in first-order theory of mind acquisition (F = 9.40, df = 2; p = .00) and 15% of the achievement variance in the total score on theory of mind tasks (F = 4.55, df = 2, p = .01). Research results suggest a close but intriguing relationship between theory of mind, executive functions, and language abilities.

Buckling of multilayered CNT/GPL/fibre/polymer hybrid composite plates resting on elastic support using modified nonlocal first-order plate theory

In the following research, the buckling of multilayered CNT/GPL/Fibre/Polymer hybrid composite Levy-type nanoplates resting on Winkler–Pasternak support is investigated using modified nonlocal first-order plate theory. The different layers of the plate are assumed to be reinforced with functionally graded carbon nanotube composite or functionally graded graphene platelets composite. Modified nonlocal first-order plate theory is used to capture the molecular effects at nanoscale and extract the buckling equations. The along-thickness variation of reinforcing nanocomposites may be uniform or functionally graded, and functionality can be linear or nonlinear based on specific functions presented by scientists. Using a closed-form analytical solution, these partial differential governing equations are changed to a set of coupled ordinary differential equations that may be solved for the Levy-type boundary conditions (i.e., two opposite edges with simply supported and two other with edges arbitrary). The obtained results may be used as a useful benchmark for validation of other works developed in the future.

Aeroelastic flutter behaviour of beam: effect of graded GPL and porosity

The present study investigates the aeroelastic flutter characteristics of the graphene platelets (GPL) reinforced metal foam beam. Closed-cell metal foam beams having graded distribution of pores and functionally graded reinforcement of GPLs are considered in this study. The closed-cell metal foam model has been used for deriving the mechanical properties of the foam matrix, which makes provision for determining the relation between the co-efficient of porosity and the co-efficient of density. Modified Halpin-Tsai micromechanics is used to obtain the effective Young’s modulus of the GPLs reinforced composite beam, Density and Poisson’s ratio are calculated with the help of the rule of mixture. The Hamilton’s principle together with the Ritz method, employing the first-order piston theory gives the governing equations of motion for aeroelastic flutter characteristics of the beam for different end conditions. Juxtaposition of dimensionless natural frequencies with the results previously published by others is executed for validating the correctness of the approach followed in the present model. A study of various parameters has been executed, and the results in tables and graphs present the influence of porosity as well as GPLs reinforcement, different boundary conditions and thermal loading on aeroelastic flutter characteristics of the FG-GPL reinforced metal foam beam.

NUMERICAL ANALYSIS OF GEOMETRIC AND MATERIAL NONLINEARITY OF BEAMS IN THE PLANE

The paper presents a simultaneous numerical analysis of the geometric and material nonlinearity of the beams. It describes a process of determining the bearing capacity of a stratified cross-section of a beam made of homogeneous and isotropic material in linear and nonlinear domains of material behaviour. Material nonlinearity is analysed by the variation of the cross-sectional stiffness of the beam on bending EI in the stiffness matrix of the system obtained according to the first-order theory. Geometric nonlinearity is introduced into the calculation using the geometric stiffness matrix of the system. Numerical examples present an application of the procedure for solving problems of nonlinear structure analysis. The calculation results obtained in accordance with the procedure described in the paper are compared with the results of the SCIA software package.

On One Normal Boundary Value Problem of the Field Theory

One normal problem of the field theory on a plane for a system of Poisson equations is studied. This problem is one of implementations of the general approach to formulation of boundary value problems of the field theory, which is based on studying the kernels of trace operators and kernels of trace functionals, which are taken as the main space of desired solutions. A peculiarity of this problem is that one of the boundary conditions imposed on the desired solution is nonlocal in nature. The considered boundary condition nonlocality is due to the fact that the base space in which the solution of the problem is sought is the kernel of the regular trace functional in the Sobolev space. The need to supplement the problem on the one-dimensional cokernel of the above-mentioned functional, which arises in this case, determines the second boundary condition, which is local (pointwise) in nature. That is why, in the framework of the duality of the Sobolev space and its conjugate space, the solution to the problem is the pair (u, с), where с is a constant that compensates for the one-dimensional “defect” of the problem. It should be noted that the theory of boundary value problems for vector fields on a plane differs essentially from the theory of boundary value problems for three-dimensional vector fields. One of the reasons for the difficulties in formulating three-dimensional boundary value problems is that a number of important surfaces cannot be made parallel to each other, which rules out the possibility to consider “tangential” boundary value problems, that is, problems with boundary tangential fields. In this respect, the theory of boundary value problems of plane vector fields differs from the three-dimensional theory for the better. On the other hand, the fact that a formula that would interrelating the Laplace operator with first-order field theory operations is not available on a plane is an obstacle to identifying new non-standard boundary value problems for plane fields. Revealing of this interrelation is a separate issue, the solution of which leads to the concept of the trace of first-order field theory operators as a singular functional above the space of traces of functions from the first-order Sobolev space. Thus, boundary value problems for plane fields are a separate section of the general theory of field boundary value problems. One of the non-standard problems in the theory of plane vector fields, which contains non-local boundary conditions, is considered. A theorem for existence and uniqueness of a weak solution of the problem posed is formulated and proved. The proof of the theorem includes a few steps: using the Galerkin method, the existence of a solution to the equation is established; the passage to the limit is made, and the vector function u(x) is found; the number α is determined, and the uniqueness of the function u and the number α is established. The main result of the work is that the problem posed is correct in nature.

Improving the electronic and optical properties of chalcogenide Cu2ZnSnS4 compound with transition metal dopants: A first-principles investigation

The influences of transition metal dopants including Ag, Au, and Pd at various atomic sites of Cu2ZnSnS4 compound are investigated by employing density functional theory. To find the most favorable doping sites, the formation energies are calculated revealing that the Sn site of Cu2ZnSnS4 compound has the lowest formation energy in contrast to Zn, Cu and S sites. In addition, the effect of Pd dopant at Sn site is more prominent than Ag and Au. Indeed, after introducing Pd dopant, the band gap of the compound is reduced and leads to higher electron conductivity and minority carrier lifetime, enabling the compound to be used in high efficiency and low loss energy harvesting solar cells. The first principles method based on first-order perturbation theory is employed for the calculation of optical properties. The Cu2ZnSnS4 compound shows a high dielectric constant of 9.23 at zero energy in the presence of Pd dopant, greater than 6.93 eV in pristine form. The good conductivity and high absorption coefficient, ⍺>104 cm−1 as well as a tunable wavelength from violet in the visible region to near infrared spectrum are also favorable for photovoltaic applications.

Bound-state formation in time-dependent potentials

We study the temporal formation of quantum-mechanical bound states within a one-dimensional attractive square-well potential by first solving the time-independent Schr\"odinger equation and then studying a time-dependent system with an external time-dependent potential. For this we introduce Gaussian potentials with different spatial and temporal extensions and generalize this description also for subsequent pulses and for random noisy potentials. Our main goal is to study the timescales in which the bound state is populated and depopulated. Particularly, we clarify a likely connection between the uncertainty relation for energy and time and the transition time between different energy eigenstates. We demonstrate that the formation of states is not delayed due to the uncertainty relation but follows the pulse shape of the perturbation. In addition we investigate the (non-)applicability of first-order perturbation theory on the considered quantum system.

Analysis of Smart Functionally Graded Beams combined with piezoelectric material using Finite Element Method

The present work devotes the static and vibration behaviour of Smart Functionally Graded (SFG) Beams combined with piezoelectric material. In this work, Lead Zirconate Titanate (PZT-4) is taken as the piezoelectric material which is commercially available. The efficiency of piezoelectric material integrated onto the functionally graded (FG) beams is evaluated. A finite element model is made for the FG beam combined with piezoelectric material considering first order theory (FSDT). The material properties of the FG beam is graded along the direction of its thickness following power law distribution method. Simulation models are also made employing finite element software (ANSYS) for the functionally graded beams. Different boundary conditions as well as and power law indexes are taken for analysis. Validation of results is presented with the results available in earlier research publications. Effects of gradation of material properties on static and dynamic behaviour of smart functionally graded beam are studied. Efforts are also made to examine the performance of piezoelectric patches towards control of deflections and vibrations.