Modified Perturbation Theory Research Articles

ENSURING ECOLOGICAL AND FIRE SAFETY DURING THE OPERATION OF MOTOR VEHICLES WITH PISTON PNEUMATIC AND CRYO ENGINES WHICH USING THE NITROGEN AS WORKING BODY

In the study, the purpose of which is to improve the mathematical apparatus based on the modified thermodynamic theory of disturbances for describing the thermophysical characteristics of nitrogen in the gaseous and liquid states as the working fluid of fire-safe and environmentally safe motor vehicles with piston pneumatic or cryoengines, a mathematical model was suggested to describe for describing the thermodynamic properties of gaseous and liquid of nitrogen, which is intended for the development of a new type of fire-safe and environmentally efficient vehicle with a piston pneumo- or cryoengine and its application is illustrated. The object of the study is the thermophysical characteristics of nitrogen in a liquid or gaseous aggregate state, as a working fluid of fire-safe and eco-safe motor vehicles with a piston pneumatic or cryoengine. The subject of the research is a mathematical apparatus based on the modified perturbation theory for describing the thermophysical characteristics of nitrogen in gaseous and liquid states. The scientific novelty of the research results is that a mathematical apparatus based on a modified thermodynamic theory of disturbances has been improved for a comprehensive description of all thermophysical characteristics of nitrogen, which is in both liquid and gaseous aggregate state, in terms of reducing calculation time and reducing the error of obtaining thermophysical characteristics compared to reference and experimental data. The practical significance of the research results is that the improved mathematical apparatus is marketable for providing accurate information to the composition of the initial data set in studies on the use of nitrogen in various aggregate states as the working fluid of fire-safe and eco-safe motor vehicles with a piston pneumatic or cryoengine.

IMPROVEMENT OF THE MATHEMATICAL DESCRIPTION OF THERMOPHYSICAL PROPERTIES OF ALTERNATIVE MOTOR FUELS BASED ON THE MODIFIED THERMODYNAMIC THEORY OF DISTURBANCE. PART 2

In the study, the purpose of which was to improve the mathematical apparatus based on the modified thermodynamic perturbation theory for describing the thermophysical characteristics of alternative motor fuels with a spherical configuration of interacting structural elements and an arbitrary aggregate state, the formal scheme of the modified perturbation theory was consistently constructed, the main characteristics of the model system were described, the parameters of the interaction potentials of the alternative fuel components were described, the thermophysical properties of the alternative fuel components were obtained by calculation, the thermodynamic properties of the alternative fuel components were calculated, the results of the calculation of the thermodynamic characteristics of the alternative fuel were analyzed and illustrated in the form of isotherm of phase equilibrium diagrams and data tables. The object of the study is the thermophysical characteristics of traditional, alternative and mixed motor fuels in a liquid or gaseous aggregate state. The subject of the study is a mathematical apparatus based on the modified thermodynamic perturbation theory for describing the thermophysical characteristics of motor fuels. The scientific novelty of the study results lies in the fact that a mathematical apparatus based on a modified perturbation theory has been improved for a comprehensive description of all thermophysical characteristics of motor fuels of any genesis, i.e. traditional, alternative and mixed, which are in both liquid and gaseous aggregate states in terms of reducing the calculation time and reducing the error of obtaining thermophysical characteristics in comparison with reference and experimental data. The practical significance of the research results is that the improved mathematical apparatus is marketable for providing accurate information to the composition of the initial data set in research on the production, storage, transportation, distribution, use of motor fuels of any genesis, which are in different states, as well as forecasting the course and results of processes of atmospheric pollution by gaseous products of complete and incomplete combustion of fuel components in combustion chambers of various types of heat engines.

IMPROVEMENT OF THE MATHEMATICAL DESCRIPTION OF THERMOPHYSICAL PROPERTIES OF ALTERNATIVE MOTOR FUELS BASED ON THE MODIFIED THERMODYNAMIC THEORY OF DISTURBANCE

In the study, the purpose of which was to improve the mathematical apparatus based on the modified thermodynamic perturbation theory for describing the thermophysical characteristics of alternative motor fuels with a spherical configuration of interacting structural elements and an arbitrary aggregate state, the formal scheme of the modified perturbation theory was consistently constructed, the main characteristics of the model system were described, the parameters of the interaction potentials of the alternative fuel components were described, the thermophysical properties of the alternative fuel components were obtained by calculation, the thermodynamic properties of the alternative fuel components were calculated, the results of the calculation of the thermodynamic characteristics of the alternative fuel were analyzed and illustrated in the form of isotherm of phase equilibrium diagrams and data tables. The object of the study is the thermophysical characteristics of traditional, alternative and mixed motor fuels in a liquid or gaseous aggregate state. The subject of the study is a mathematical apparatus based on the modified thermodynamic perturbation theory for describing the thermophysical characteristics of motor fuels. The scientific novelty of the study results lies in the fact that a mathematical apparatus based on a modified perturbation theory has been improved for a comprehensive description of all thermophysical characteristics of motor fuels of any genesis, i.e. traditional, alternative and mixed, which are in both liquid and gaseous aggregate states in terms of reducing the calculation time and reducing the error of obtaining thermophysical characteristics in comparison with reference and experimental data. The practical significance of the research results is that the improved mathematical apparatus is marketable for providing accurate information to the composition of the initial data set in research on the production, storage, transportation, distribution, use of motor fuels of any genesis, which are in different states, as well as forecasting the course and results of processes of atmospheric pollution by gaseous products of complete and incomplete combustion of fuel components in combustion chambers of various types of heat engines.

Terahertz biosensor integrated with Au nanoparticles to improve the sensing performance.

A terahertz (THz) sensor is presented based on a metasurface integrated with Au nanoparticles (AuNPs). It was used to improve the sensitivity of the detection of whey protein and to enhance the sensing index of group delay. This demonstrates that AuNPs can improve the sensing performance of the biosensor. The internal mechanism can be explained by the modified perturbation theory and the coupled harmonic oscillator model. This study provides a means of enhancing the sensitivity of the THz biosensor.

THEORETICAL COMPLEX ENERGIES OF STARK RESONANCES IN LITHIUM BY OPERATOR PERTURBATION THEORY APPROACH

The theoretical complex energies of the Stark resonances in the lithium atom (non-hydrogenic atomic system) in a DC electric are calculated within the operator form of the modified perturbation theory for the non-H atomic systems. The method includes the physically reasonable distorted-waves approximation in the frame of the formally exact quantum-mechanical procedure. The calculated Stark resonances energies and widths in the lithium atom are calculated and compared with results of calculations on the basis of the method of complex eigenvalue Schrödinger equation by Themelis-Nicolaides, the complex absorbing potential method by Sahoo-Ho and the B-spline-based coordinate rotation method approach by Hui-Yan Meng et al.

Solution of coupled nonlinear Schrödinger equations in focusing-defocusing medium by modified perturbation theory

The interaction of bright solitons of different orders and two different wavelengths propagating in the medium focusing for one wavelength and defocusing for the other is considered. The system of nonlinear Schrödinger equations is solved by means of perturbation theory. Application of an additional postulate to adjust both widths of the solitons and to modify the amplitude by a factor determined by the overlap integral greatly improves the accuracy of the description. The good accuracy of description is confirmed by numerical calculations. Full Text: PDF ReferencesY. Kivshar, G. P. Agrawal, Optical Solitons. From Fibers to Photonic Crystals, (Amsterdam, Academic Press 2003). CrossRef F. Abdullaev, S. Darmanyan, P. Khabibullaev, Optical Solitons, (Springer-Verlag, Berlin, 1993) CrossRef G.I.A Stegema, D.N. Christodoulides, M. Segev, IEEE J. Selected Topics Quantum Electron. 6, (2000), 1419 CrossRef J. Yang, "Nonlinear Waves in Integrable and Nonintegrable Systems", (SIAM, Philadelphia 2010). CrossRef Y. Kivshar, B. Malomed, "Dynamics of solitons in nearly integrable systems", Rev. Mod. Phys. 61, 763 (1989). CrossRef P.G. Kevrekidis, D.J. Frantzeskakis, "Solitons in coupled nonlinear Schrödinger models: A survey of recent developments", Reviews in Physics 1 (2016), 140 CrossRef R. de la Fuente, A. Barthelemy, "Spatial soliton-induced guiding by cross-phase modulation", IEEE J. Quantum Electron. 28, 547 (1992). CrossRef H. T. Tran, R. A. Sammut, "Families of multiwavelength spatial solitons in nonlinear Kerr media", Phys. Rev. A 52, 3170 (1995). CrossRef S. Leble, B. Reichel, "Coupled nonlinear Schrödinger equations in optic fibers theory", Eur. Phys. J. Special Topics 173, 5 (2009). CrossRef M. Vijayajayanthi, T.Kanna, M. Lakshmanan, "Multisoliton solutions and energy sharing collisions in coupled nonlinear Schrödinger equations with focusing, defocusing and mixed type nonlinearities", Eur. Phys. J. Special Topics 173, 57 (2009). CrossRef S. V. Manakov, "On the theory of two-dimensional stationary self-focusing of electromagnetic waves ", Sov. Phys. JETP 38 (1973), 248 DirectLink J. Yang, Phys. Rev. E 65, 036606 (2002). CrossRef T.Kanna, M. Lakshmanan, "Exact Soliton Solutions, Shape Changing Collisions, and Partially Coherent Solitons in Coupled Nonlinear Schrödinger Equations", Phys. Rev. Lett. 86, 5043 (2001). CrossRef M. Jakubowski, K. Steiglitz, R. Squier, "State transformations of colliding optical solitons and possible application to computation in bulk media", Phys. Rev. E 58, 6752 (1998). CrossRef P. S. Jung, W. Krolikowski, U. A. Laudyn, M. Trippenbach, and M. A. Karpierz, "Supermode spatial optical solitons in liquid crystals with competing nonlinearities", Phys. Rev. A 95 (2017). CrossRef P. S. Jung, M. A. Karpierz, M. Trippenbach, D. N. Christodoulides, and W. Krolikowski, "Supermode spatial solitons via competing nonlocal nonlinearities", Photonics Lett. Pol. 10 (2018). CrossRef A. Ramaniuk, M. Trippenbach, P.S. Jung, D.N. Christodoulides, W.Krolikowski, G. Assanto, "Scalar and vector supermode solitons owing to competing nonlocal nonlinearities", Opt. Express 29, 8015 (2021) CrossRef

Linear and Weakly Nonlinear Double-Diffusive Magnetoconvection in a Non-Newtonian Fluid Layer

The linear and weakly nonlinear stability of a doubly diffusive electrically conducting non-Newtonian couple stress fluid layer in the presence of a uniform vertical magnetic field is investigated. The system behaves like a triply diffusive one with the magnetic field as a third diffusing component. Several remarkable departures from those of doubly diffusive couple stress fluid systems are recognized and the implications of couple stresses on the same are explored. By performing the linear stability analysis, it has been recognized that (i) oscillatory convection occurs even if the diffusivity ratios are greater than unity, (ii) the bottom-heavy solute gradient in the presence of magnetic field, as well as magnetic field in the presence of bottom-heavy solute gradient, destabilize the system under certain conditions, (iii) disconnected closed oscillatory neutral curves occur for certain choices of physical parameters indicating the necessity of three critical values of thermal Rayleigh number to specify the linear stability criteria instead of the usual single value. A weakly nonlinear stability analysis has been performed using modified perturbation theory and the steady bifurcating equilibrium solution is found to be subcritical in some parameter space. Heat and mass transports are calculated in terms of Nusselt numbers and the influence of physical parameters on the same is discussed in detail.

The contribution of effective quantum gravity to the high energy scattering in the framework of modified perturbation theory and one loop approximation

The asymptotic behavior of the scattering amplitude for two scalar particles at high energies with fixed momentum transfers is studied. The study is done within the effective theory of quantum gravity based on quasi-potential equation. By using the modified perturbation theory, a systematic method is developed to find the leading eikonal scattering amplitudes together with corrections to them in the one-loop gravitational approximation. The relation is established and discussed between the solutions obtained by means of the operator and functional approaches applied to quasi-potential equation. The first non-leading corrections to the leading eikonal amplitude are found.

An Analysis of Thermodynamic Characteristics of Metal-Hydride Systems for Hydrogen Storage, Using a Modified Scheme of the Perturbation Theory

The use of hydrides of intermetallic compounds (IMC) to implement the working processes of thermo sorption compressors, heat pumps, storage systems, cleaning, and programmable supply of hydrogen is due to a number of unique properties of these hydrogen sorbents. These include, first of all, the fact that the saturation of IMCs with a large sorption capacity occurs under relatively mild thermodynamic conditions, as well as the selectivity of sorption processes and the presence of the effect of thermodesorptional activation of atoms and molecules of hydrogen isotopes. The work is devoted to the description of phase equilibria in IMC hydrides. The proposed approach to the problem of calculating phase equilibria in metal hydrides consists in determining the properties of the lattice gas of H atoms and the H2 molecular phase (which is in equilibrium with it) within the framework of a single method, the modified perturbation theory. The thermodynamic description of the hydrogen subsystem in the region of disordered α-, β-phases is carried out on the basis of the model of the non-ideal (interacting) lattice gas of hydrogen atoms. In this case, both the direct interaction between hydrogen atoms and the indirect deformation contributions to the potential energy due to the expansion of the lattice during hydrogen dissolution are taken into account. Simulation of phase transitions in IMC-hydrogen systems based on the modified perturbation theory scheme gives a correct description of the main features of phase diagrams in a wide range of hydrogen pressures. From the condition of the equality of the chemical potentials of the H-subsystem of the hydride and H2-phase (calculated on the H atom), equations are obtained, relating the pressure of the gaseous H2 phase to the hydride parameters c and T (phase diagrams). The proposed computational procedure does not use adjustable parameters or empirical correlations. It relies on the atomic characteristics of the hydrogen subsystem and metal matrix, which have an unambiguous physical meaning. The object of this research is the LaNi5 intermetallic hydride. Of particular interest is the position of the critical point of the β→α-transition in the LaNi5-hydrogen system, for which there are no experimentally obtained parameter values. The paper presents the calculated values of the β→α-transition critical parameters Tc=445 K, pc=87 atm. The calculated data on the thermodynamic parameters of the α→β-transition (enthalpy, entropy, and pressure on the isotherm plateau) make it possible to describe the solubility of hydrogen in LaNi5 at pressures up to 500 atm and are in good agreement with the available experimental data in the literature.

On the globularization of the shapes associated with alpha-precipitate of two phase titanium alloys: Insights from phase-field simulations

In two-phase titanium alloys, α-precipitate exhibits plate morphology which spheroidizes during static globularization. The stability of the 3-dimensional plates to withstand perturbation is well-established. However, based on Rayleigh instabilities, the current understanding rendered by ‘the modified perturbation theory’ holds that the spheroidization of the plates is governed by the stable growth of the ridges. To address this counterintuitive view, a multiphase-field model, which recovers the sharp interface solutions, is employed to investigate the morphological transformation accompanying globularization of shapes that resemble α-precipitate. The present investigation unravels an alternate mechanism, wherein the plates globularize by the successive formation and decay, by lateral expansion, of multiple terminal perturbations. This unique mode of spheroidization, distinctly, characterizes the temporal evolution of the driving force which contradicts the hitherto assumed conventional monotonic-decrease in the curvature-difference. Particularly, it is identified that the ellipsoidal plates exhibit a step-wise change in the curvature-difference while non-monotonic series of peaks are observed during the evolution of the pancake structures. To aid the optimization of the thermal cycle involved in the globularization treatment, a simplified relation between the aspect ratio and spheroidization time, which encompasses the influence of the transformation mechanism, is derived.

Asymmetry in attosecond streaking from a degenerate state

By the numerical solution to the time-dependent Schr\"odinger equation, we observe a remarkable asymmetry in the photoelectron streaking spectra when the ${\mathrm{He}}^{+}$ ion is ionized by an attosecond pulse from the $2s$ state in the presence of a weak infrared pulse. An analytical theory based on the modified perturbation theory is developed to quantitatively account for the underlying mechanism. We find that a transition occurs between the degenerate $2s$ and $2p$ states under the influence of the infrared electric field before the arrival of the attosecond pulse. The observed asymmetry in the attosecond streaking is formed by the interference of photoelectrons ionized from the $2s$ and $2p$ states. Using the sensitivity of the asymmetry to the infrared (IR) electric field at the moment of attosecond photoionization, we show that the present finding provides a highly reliable way to fully characterize the IR waveform in the streaking experiment.

Applying the Modified Perturbation Theory to High Energy Scattering in the Quasi-Potential Approach

Applying the Modified Perturbation Theory to High Energy Scattering in the Quasi-Potential Approach

The WKB method for the quantum mechanical two-Coulomb-center problem

Using a modified perturbation theory, we obtain asymptotic expressions for the two-center quasiradial and quasiangular wave functions for large internuclear distances R. We show that in each order of 1/R, corrections to the wave functions are expressed in terms of a finite number of Coulomb functions with a modified charge. We derive simple analytic expressions for the first, second, and third corrections. We develop a consistent scheme for obtaining WKB expansions for solutions of the quasiangular equation in the quantum mechanical two-Coulomb-center problem. In the framework of this scheme, we construct semiclassical two-center wave functions for large distances between fixed positively charged particles (nuclei) for the entire space of motion of a negatively charged particle (electron). The method ensures simple uniform estimates for eigenfunctions at arbitrary large internuclear distances R, including R ≥ 1. In contrast to perturbation theory, the semiclassical approximation is not related to the smallness of the interaction and hence has a wider applicability domain, which permits investigating qualitative laws for the behavior and properties of quantum mechanical systems.

Modified equation of motion approach for metallic ferromagnetic systems with the correlated hopping interaction

We consider the extended Hubbard model with included nearest neighbors off‐diagonal correlated hopping interaction. This model is analyzed using the modified equation of motion (EOM) approach with double‐time Green's functions. In modified EOM method we calculate the retarded Green's function of the impurity by differentiating Green's functions over both time variables. The proposed model is used to investigate possibility of ferromagnetism in the itinerant system. We calculate the Curie temperature for different carrier concentrations, state densities with different asymmetry, different values of the Coulomb interaction and correlated hopping interaction. Results of our relatively simple method are compared and agree with the results of previous Quantum Monte Carlo and Modified Perturbation Theory calculations. This legitimates further use of this model in different physical applications, e.g., quantum dots.

Two Anderson impurities in a two-dimensional host with Rashba spin-orbit interaction

We have studied the two-dimensional two-impurity Anderson model with additional Rashba spin-orbit interaction by means of the modified perturbation theory. The impurity Green's functions we have constructed exactly reproduce the first four spectral moments. We discuss the height and the width of the even/odd Kondo peaks as functions of the inter-impurity distance and the Rashba energy $E_R$ (the strength of the Rashba spin-orbit interaction). For small impurity separations the Kondo temperature shows a non-monotonic dependence on $E_R$ being different in the even and the odd channel. We predict that the Kondo temperature has only almost linear dependence on $E_R$ and not an exponential increase with $E_R$

MODIFIED PERTURBATION THEORY FOR ANGULAR DISTRIBUTION IN W-PAIR PRODUCTION

We examine the capabilities of the modified perturbation theory (MPT) for description of W-pair production and decay in e+ e- annihilation. In a model with Dyson-resummed propagators of unstable particles, we calculate even and odd contributions to the distribution in the cosine of the W- production angle relative to the e- beam. On comparing the results of calculations in the NNLO approximation of MPT with the exact results in the model, a coincidence of outcomes at the ILC energies is detected at the per-mille level.

Ferromagnetism and nonlocal correlations in the Hubbard model

We study the possibility and stability of band ferromagnetism in the single-band Hubbard model for the simple cubic (sc) lattice. A nonlocal self-energy is derived within a modified perturbation theory. Results for the spectral density and quasiparticle density of states are shown with special attention to the effects of $\mathbf{k}$ dependence. The importance of nonlocal correlations for the fulfillment of the Mermin-Wagner theorem is our main result. A phase diagram showing regions of ferromagnetic order is calculated for the three-dimensional lattice. Besides, we show results for the optical conductivity and prove that the renormalized one-loop contribution to the conductivity already cancels the Drude peak exactly in case of a local self-energy which is not true anymore for a nonlocal self-energy.

HIGH ENERGY SCATTERING IN THE QUASIPOTENTIAL APPROACH

Asymptotic behavior of the scattering amplitude for two scalar particles by scalar, vector and tensor exchanges at high energy and fixed momentum transfers is reconsidered in quantum field theory. In the framework of the quasipotential approach and the modified perturbation theory a systematic scheme of finding the leading eikonal scattering amplitudes and its corrections are developed and constructed. The connection between the solutions obtained by quasipotential and functional approaches is also discussed. The first correction to leading eikonal amplitude is found.

Interplay of Kondo and superconducting correlations in the nonequilibrium Andreev transport through a quantum dot

Using the modified perturbation theory, we theoretically study the nonequilibrium Andreev transport through a quantum dot coupled to normal and superconducting leads (N-QD-S), which is strongly influenced by the Kondo and superconducting correlations. From the numerical calculation, we find that the renormalized couplings between the leads and the dot in the equilibrium states characterize the peak formation in the nonequilibrium differential conductance. In particular, in the Kondo regime, the enhancement of the Andreev transport via a Kondo resonance occurs in the differential conductance at a finite bias voltage, leading to an anomalous peak whose position is given by the renormalized parameters. In addition to the peak, we show that the energy levels of the Andreev bound states give rise to other peaks in the differential conductance in the strongly correlated N-QD-S system. All these features of the nonequilibrium transport are consistent with those in the recent experimental results [R. S. Deacon {\it et al.}, Phys. Rev. Lett. {\bf 104}, 076805 (2010); Phys. Rev. B {\bf 81}, 12308 (2010)]. We also find that the interplay of the Kondo and superconducting correlations induces an intriguing pinning effect of the Andreev resonances to the Fermi level and its counter position.

W-PAIR PRODUCTION IN MODIFIED PERTURBATION THEORY

We examine capabilities of the modified perturbation theory (MPT) for description of the processes with productions and decays of fundamental unstable particles. We calculate total cross-section for e+e- → γ, Z → W+W- → 4f in a model with the Dyson-resummed and with the MPT-expanded up to the NNLO Breit–Wigner factors, and compare the outcomes. At the ILC energies a coincidence of the outcomes is detected with precision better than one per-mille.