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Search results for: PERTURBATION THEORY
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Canonical perturbation theory for inhomogeneous systems of interacting fermions
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Multi-state multi-reference Møller-Plesset second-order perturbation theory for molecular calculations
PublicationThis work presents multi‐state multi‐reference Møller–Plesset second‐order perturbation theory as a variant of multi‐reference perturbation theory to treat electron correlation in molecules. An effective Hamiltonian is constructed from the first‐order wave operator to treat several strongly interacting electronic states simultaneously. The wave operator is obtained by solving the generalized Bloch equation within the first‐order...
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Theoretical study of the photoelectron spectrum of ethyl formate: Ab initio and density functional theory investigation
PublicationThe first ionization energy and associated photoelectron spectrum of ethyl formate are investigated with quantum chemistry calculations. The geometries, harmonic vibrational frequencies and first ionization energy are computed at the Hartree-Fock (HF) and at the second order Moller-Plesset perturbation theory (MP2). Moreover, accurate ionization energies are obtained with the Coupled-Cluster theory including singles and doubles...
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Two-dimensional hydrogen-like atom in a weak magnetic field
PublicationWe consider a non-relativistic two-dimensional (2D) hydrogen-like atom in a weak, static, uniform magnetic field perpendicular to the atomic plane. Within the framework of the Rayleigh-Schr¨odinger perturbation theory, using the Sturmian expansion of the generalized radial Coulomb Green function, we derive explicit analytical expressions for corrections to an arbitrary planar hydrogenic bound-state energy level, up to the fourth...
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Production of singlet oxygen atoms by photodissociation of oxywater
PublicationQuantum chemical calculations are reported for the energies of the few lowest electronic singlet states of oxywater along dissociation of the oxygen-oxygen bond into water and singlet oxygen using multistate multireference second-order Møller–Plesset perturbation theory. We compute an energy of 21 kcal/mol to remove one oxygen atom in the lowest singlet state. The two lowest excited singlet states have vertical excitation energies...
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The 41Σ+ electronic state of LiCs molecule
PublicationThe 41Σ+ state of LiCs molecule is observed experimentally for the first time. The inverted perturbation approach (IPA) method is used to derive the potential energy curve of the state from the measured spectra. The experiment is accompanied by theoretical calculations of adiabatic potentials for excited states in LiCs including 41Σ+, performed with the MOLPRO program package. The irregular shape of the 41Σ+ state potential predicted...
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Refined theoretical study of radiative association: Cross sections and rate constants for the formation of SiN
PublicationRadiative association of silicon mononitride (SiN) in its two lowest molecular electronic states is studied through quantum and classical dynamics. Special attention is paid to the behavior of the cross section at high collision energies. A modified expression for the semiclassical cross section is presented which excludes transitions to continuum states. This gives improved agreement with quantum mechanical perturbation theory...
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Ab Initio Study of the Electronic Spectrum of 7-Hydroxyquinoline
PublicationThe electronic spectrum of 7-hydroxyquinoline has been studied by using ab initio Multi-State Multi-Reference Møller-Plesset Second-Order Perturbation Theory (MSMRMP2). The energy range up to 6.5 eV is taken into consideration. The lowest π–π* transition is calculated to have an energy of 3.65 eV in good agreement with experimental data. Several other π–π* transitions are predicted to have excitation energies of 4.93, 5.20, 5.47,...
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Periodic Solutions of Generalized Lagrangian Systems with Small Perturbations
PublicationIn this paper we study the generalized Lagrangian system with a small perturbation. We assume the main term in the system to have a maximum, but do not suppose any condition for perturbation term. Then we prove the existence of a periodic solution via Ekeland’s principle. Moreover, we prove a convergence theorem for periodic solutions of perturbed systems.
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DFT study of low-energy electron interaction with pyridine, pyrazine and their halo derivatives
PublicationIn this work, the density functional theory with B3LYP hybrid functional was employed to calculate quantities useful for estimating the behavior of pyridine, pyrazine and their derivatives monosubstituted with Cl or Br atom, when exposed to low-energy electron impact. Vertical electron affinities obtained in several Pople basis sets and in aug-cc-pVTZ basis set are reported. Although some of the investigated molecules do not form...
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Flexural buckling and post-buckling of columns made of aluminium alloy
PublicationThe paper concerns flexural buckling and initial post-buckling of axially compressed columns made of aluminium alloy described by the Ramberg-Osgood relationship. The non-linear differential equation of the problem is derived using the stationary total energy principle and the assumptions of classical beam theory within a finite range. The approximate analytical solution of the equation leading to the buckling loads and initial...
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Second-order Stark effect and polarizability of a relativistic two-dimensional hydrogenlike atom in the ground state
PublicationThe second-order Stark effect for a planar Dirac one-electron atom in the ground state is analyzed within the framework of the Rayleigh-Schrödinger perturbation theory, with the use of the Sturmian series expansion of the generalized Dirac-Coulomb Green's function. A closed-form analytical expression for the static dipole polarizability of that system is found. The formula involves the generalized hypergeometric function ${}_{3}F_{2}$...
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Simulating coherent light propagation in a random scattering materials using the perturbation expansion
PublicationMultiple scattering of a coherent light plays important role in the optical metrology. Probably the most important phenomenon caused by multiple scattering are the speckle patterns present in every optical imaging method based on coherent or partially coherent light illumination. In many cases the speckle patterns are considered as an undesired noise. However, they were found useful in various subsurface imaging methods such as...
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Relations between magnetosonic perturbations as an indicator of a magnetosonic exciter and equilibrium parameters of a plasma
PublicationThe thermodynamic relations between perturbation of pressure and pertur- bation of mass density and between components of velocity which specify a magnetosonic wave are theoretically studied. A planar flow with the wave vec- tor forming a constant angle with the equilibrium magnetic field is investigated. The theory considers deviation from the adiabaticity of a flow due to some kind of heating–cooling function and thermal conduction...
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Relativistic two-dimensional hydrogen-like atom in a weak magnetic field
PublicationA two-dimensional (2D) hydrogen-like atom with a relativistic Dirac electron, placed in a weak, static, uniform magnetic field perpendicular to the atomic plane, is considered. Closed forms of the first- and second-order Zeeman corrections to energy levels are calculated analytically, within the framework of the Rayleigh–Schrödinger perturbation theory, for an arbitrary electronic bound state. The second-order calculations are...
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Hysteresis curves for some periodic and aperiodic perturbations in magnetosonic flow
PublicationA thermodynamic relation between perturbations of pressure and mass density in the magnetohydrodynamic flow is theoretically studied. Planar magnetohydrodynamic perturbations with the wave vector, which forms a constant angle with the equilibrium magnetic field, are under study. The theory considers thermal conduction of a plasma and the deviation from adiabaticity of a flow due to some kind of heating–cooling function. It also...
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Critical Review on Robust Speed Control Techniques for Permanent Magnet Synchronous Motor (PMSM) Speed Regulation
PublicationThe permanent magnet synchronous motor (PMSM) is a highly efficient energy saving machine. Due to its simple structural characteristics, good heat radiation capability, and high efficiency, PMSMs are gradually replacing AC induction motors in many industrial applications. The PMSM has a nonlinear system and lies on parameters that differ over time with complex high-class dynamics. To achieve the excessive performance operation...
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Two-photon double ionization of atoms in attosecond x-ray radiation fields
PublicationWe consider two-photon double ionization of helium with 100, 200, and 400 eV excess energy for the two ejected electrons, corresponding to photon energies of 89.5, 139.5, and 239.5 eV, respectively. We focus on the case of ultrashort pulses (two oscillations of the field) and develop an approach to calculate the two-photon transition matrix elements within the lowest order of the time-dependent perturbation theory. One of the...
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Static magnetic multipole susceptibilities of the relativistic hydrogenlike atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationWe study far- and near-field magnetic and electric multipole moments induced in the ground state of the Dirac one-electron atom placed in a weak 2L-pole magnetostatic field. The analysis is carried out within the framework of the first-order Rayleigh-Schrödinger perturbation theory, with the use of the Sturmian expansion of the generalized Dirac-Coulomb Green function [Szmytkowski, J. Phys. B 30, 825 (1997);J. Phys. B 30, 2747(E)...
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Jednoelektronowy atom Diraca w słabym polu magnetycznym
PublicationW rozprawie przedstawiono opis wpływu zewnętrznego stałego, słabego, jednorodnego pola magnetycznego na jednoelektronowy atom Diraca. Wykorzystując funkcje gęstości ładunku elektrycznego oraz gęstości prądu elektrycznego, rozważono procesy indukowania się w atomie dodatkowych elektromagnetycznych momentów multipolowych. Dokonano analizy indukowanego momentu dipolowego, w wyniku której uzyskano wyrażenie dla magnetyzowalności atomu....
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On time-dependent nonlinear dynamic response of micro-elastic solids
PublicationA new approach to the mechanical response of micro-mechanic problems is presented using the modified couple stress theory. This model captured micro-turns due to micro-particles' rotations which could be essential for microstructural materials and/or at small scales. In a micro media based on the small rotations, sub-particles can also turn except the whole domain rotation. However, this framework is competent for a static medium....
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New Method of Non-Linear Electrochemical Impedance Spectroscopy with an Amplitude-Modulated Perturbation Signal
PublicationThe paper presents a new method of non-linear electrochemical impedance spectroscopy (NLEIS), which allows fast and nondestructive evaluation of the corrosion rate and determination of the Tafel coefficients values for a corrosion system under investigation. This method employs amplitude modulation of the ac perturbation signal. The study demonstrated that it was possible to obtain impedance characteristic as a function of the...
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Static electric multipole susceptibilities of the relativistic hydrogenlike atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationThe ground state of the Dirac one-electron atom, placed in a weak, static electric field of definite $2^{L}$ polarity, is studied within the framework of the first-order perturbation theory. The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 825 (1997); erratum R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 2747 (1997)] is used to derive closed-form analytical...
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Perturbation analysis of electric field around objects in sea water
PublicationThe paper presents an analytical approach to the perturbation analysis of electric field distribution caused by a sphere and an ellipsoid placed in a uniform electric field.
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A convergence result for mountain pass periodic solutions of perturbed Hamiltonian systems
PublicationIn this work, we study second-order Hamiltonian systems under small perturbations. We assume that the main term of the system has a mountain pass structure, but do not suppose any condition on the perturbation. We prove the existence of a periodic solution. Moreover, we show that periodic solutions of perturbed systems converge to periodic solutions of the unperturbed systems if the perturbation tends to zero. The assumption on...
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Otopy Classification of Gradient Compact Perturbations of Identity in Hilbert Space
PublicationWe prove that the inclusion of the space of gradient local maps into the space of all local maps from Hilbert space to itself induces a bijection between the sets of the respective otopy classes of these maps, where by a local map we mean a compact perturbation of identity with a compact preimage of zero.
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Periodic solutions of Lagrangian systems under small perturbations
PublicationIn this paper we prove the existence of mountain pass periodic solutions of a certain class of generalized Lagrangian systems under small perturbations. We show that the found periodic solutions converge to a periodic solution of the unperturbed system if the perturbation tends to 0. The proof requires to work in a rather unusual (mixed) Orlicz–Sobolev space setting, which bears several challenges.
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Implementation and Validation of Multisinusoidal, Fast Impedance Measurements in Atomic Force Microscope Contact Mode.
PublicationThis study presents a novel approach to impedance measurements. The methodology discussed is limited to contact in the sample-probe system under ambient conditions without the presence of electrolyte. Comparison with results of direct and alternating current measurements for well-defined metallic surfaces are made. In spite of idealization related to the type of contact examined, the proposed technique provides an improvement of...
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Conducted EMI Propagation Paths in DC-AC Hard Switching Converter
PublicationIn order to limit the electromagnetic interference (EMI) in power electronics devices, knowledge about the phenomena connected with EMI generation and propagation is necessary. This papers describes the propagation paths in the 3 phase voltage source inverter using wide-band simulation and laboratory test with the signal processing method Wiener filtering, where the transfer functions between voltage across switches and the perturbation...
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Local buckling and initial post-buckling behaviour of channel member flange - analytical approach
PublicationThe local buckling and initial post-buckling behaviour of the cold-formed channel member flange is investigated. The governing nonlinear differential equation for axially compressed columns and beams undergoing pure bending is derived using the stationary total potential energy principle. The critical stress and initial post-buckling equilibrium path is determined by means of a perturbation approach. The results obtained allow...
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Induction of chirality in 4,4'-azopyridine by halogen-bonding interaction with optically active ditopic donors
PublicationOptically active ditopic halogen bond donors bearing two 4-iodotetrafluorophenyl groups were obtained by reaction of chiral diols with iodopentafluorobenzene. Co-crystallization of these donors with anti-4,4′-azopyridine afforded binary complexes containing infinite chains of the alternating component molecules connected by halogen bonds. The solid state CD measurements confirmed that complexation induces optical activity of the...
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SPECTRAL RESPONSE OF STATIONARY JACK-UP PLATFORMS LOADED BY SEA WAVES AND WIND USING PERTURBATION METHOD
PublicationThe paper addresses non-linear vibrations of offshore jack-up drilling platforms loaded by sea waves and wind in their stationary condition using the perturbation method. Non-linearity of dynamic equations of motion for fixed offshore platforms yields from two factors. The first is load excitation generating non-linear velocity coupling in a dynamic system. This coupling is inherent in the modified Morison equation, involving the...
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Development Of Dynamic Method For Evaluation Of Corrosion Rate On The Example Of Organic Corrosion İnhibitor
PublicationMeasurements of the corrosion rate belong to the most important aspects of materials science. In order to reduce material loss corrosion inhibitors are used. However selection of proper inhibitor should be based on evaluation of its mechanism and effective concentrations. Mechanism of inhibition usually has dynamic character so physicochemical parameters are changing in time. Most of actually used methods...
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Impedance monitoring of corrosion degradation of plasma electrolytic oxidation coatings (PEO) on magnesium alloy
PublicationImpedance technique based on continuous multisinusoidal current perturbation was used to explain degradation process of plasma electrolytic oxidation coatings (PEO) on magnesium alloy. An obtained impedance spectrum was fitted by electrical equivalent circuit to describe properties of conversion layer on magnesium alloy. Additionally, galvanostatic mode maintained during experiment, with DC current equal to zero, allowed to achieve...
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Assessment of copper surface coverage with corrosion inhibitor using AFM-based local electrical measurements
PublicationThe paper presents a new method of assessment of metal surface coverage with corrosion inhibitor and thus of inhibitor protective performance. It is based on the atomic force microscopy measurement performed in a contact mode. Apart from topography images the proposed approach allows acquisition of local DC maps and local electrical impedance spectra via application of DC bias voltage or AC perturbation signal between the conductive...
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Magnetosonic Excitation of the Entropy Perturbations in a Plasma with Thermal Conduction Depending on Temperature
PublicationNonlinear excitation of the entropy perturbations by magnetosonic waves in a uniform and infinite plasma model is considered. The wave vector of slow or fast mode forms an arbitrary angle (0 B B ) with the equilibrium straight magnetic field, and all perturbations are functions of the time and longitudinal coordinate. Thermal conduction is the only factor which destroys isentropicity of wave perturbations and causes the nonlinear...
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Weak Stability of Centred Quadratic Stochastic Operators
PublicationWe consider the weak convergence of iterates of so-called centred quadratic stochastic operators. These iterations allow us to study the discrete time evolution of probability distributions of vector-valued traits in populations of inbreeding or hermaphroditic species, whenever the offspring’s trait is equal to an additively perturbed arithmetic mean of the parents’ traits. It is shown that for the existence of a weak limit, it...
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Running characteristics of aerodynamic bearing with self-lifting capability at low rotational speed
PublicationAn aerodynamic journal bearing that is capable of self-generating squeeze-film pressure is presented and its dynamic characteristics investigated numerically and experimentally. A numerical method based on a time marching static model was applied to assess the orbit trajectory path of the rotor upon a perturbation. Experimental results were obtained to validate the effect of the self- generated squeeze-film pressure on the stability...
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Quantum-state transfer in spin chains via isolated resonance of terminal spins
PublicationWe propose a quantum-state transfer protocol in a spin chain that requires only the control of the spins at the ends of the quantum wire. The protocol is to a large extent insensitive to inhomogeneity caused by local magnetic fields and perturbation of exchange couplings. Moreover, apart from the free evolution regime, it allows one to induce an adiabatic spin transfer, which provides the possibility of performing the transfer...
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Magnetic-field-induced electric quadrupole moments for relativistic hydrogenlike atoms: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationWe consider a Dirac one-electron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength of the external field, the only electric multipole moments, which are induced by the perturbation in the atom, are those of an even order. Using the Sturmian expansion of the generalized Dirac-Coulomb Green function we derive a closed-form expression for the electric quadrupole moment induced...
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Torsional buckling and post-buckling of columns made of aluminium alloy
PublicationThe paper concerns torsional buckling and the initial post-buckling of axially compressed thin-walled aluminium alloy columns with bisymmetrical cross-section. It is assumed that the column material behaviour is described by the Ramberg–Osgood constitutive equation in non-linear elastic range. The stationary total energy principle is used to derive the governing non-linear differential equation. An approximate solution of the equation...
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Application of Galvanostatic Non-Linear Impedance Spectroscopy to the Analysis of Metallic Material Degradation
PublicationThis study presents a novel application of Non-Linear Electrochemical Impedance Spectroscopy (NLEIS) in galvanostatic mode for the rapid, non-destructive assessment of metal degradation. By using galvanostatic mode instead of traditional potentiostatic methods, polarization-related challenges are mitigated, enabling more accurate and reliable analysis. The technique allows for the determination of corrosion rates (corrosion current)...
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Application of galvanodynamic impedance spectroscopy for studying passive film cracking under mechanical strain
PublicationThe paper reports the results of simultaneous mechanical and electrochemical investigations on austenitic (18/8) stainless steel in a 2 % solution of sulphuric acid. The measurements were performed using Galvanodynamic Electrochemical Impedance Spectroscopy (GDEIS). Electrochemical analysis of mechanical passive layer cracking and repassivation conditions during a tensile test was carried out. Application of this methodology allowed...
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Buckling and initial post-local buckling behaviour of cold-formed channel member flange
PublicationThe initial post-buckling behaviour of a cold-formed channel member flange after its local buckling is investigated. An axially compressed column or beam subjected to pure bending is considered. The member material is assumed to follow a linear stress-strain relationship. The governing non-linear differential equation of the problem is derived using the minimum total potential energy principle. An approximate solution for the equation...
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Determination of pitting corrosion stage of stainless steel by galvanodynamic impedance spectroscopy
PublicationThis paper investigates the methodology for differentiation of multistep process of pitting corrosion of AISI 304 stainless steel in the environment of iron (III) chloride. Measurements were performed using Galvanodynamic Electrochemical Impedance Spectroscopy (GDEIS). Application of this methodology allowed monitoring of natural corrosion process without external current (IDC = 0A) nor potential perturbation of the system. Applied...
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Development of dynamic method for evaluation of inhibition efficiency on the example of 8-hydroxyquinolin
PublicationSelection of a proper inhibitor should be based on the evaluation of its mechanism and effective concentrations. Mechanism of inhibition usually has dynamic character due to changing physicochemical conditions of the environment and corroding metal surface. Most of actually used methods are stationary or contain assumptions which highly influences obtained values. Development of new dynamic method, based on modified EIS, allows...
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Signal propagation in electromagnetic media described by fractional-order models
PublicationIn this paper, signal propagation is analysed in electromagnetic media described by fractional-order (FO) models (FOMs). Maxwell’s equations with FO constitutive relations are introduced in the time domain. Then, their phasor representation is derived for one-dimensional case of the plane wave propagation. With the use of the Fourier transformation, the algorithm for simulation of the non-monochromatic wave propagation is introduced....
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Computational methods for calculation of binding free energy for ligand-receptor complexes
PublicationAccurate description of the molecular complexes energetic influence is required for understanding of many biological functions carried out by proteins. Therefore, estimation of binding free energy for ligand-receptor complexes is of highest importance for structure-based ligand design and drug discovery approaches.Experimental methods of determination of difference in Gibbs'es free energy have many limitations. Thus, computational...
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Design and optimization of a novel miniaturized low-profile circularly polarized wide-slot antenna
PublicationThis paper presents a novel structure of a compact circularly polarized (CP) antenna. CP is obtained using a parasitic quasi-rectangular strip placed coplanar to the feedline. A ground plane perturbation combined with the asymmetric geometry of the coplanar waveguide ground planes is utilized to excite additional CP modes. All antenna dimensions are rigorously optimized to achieve the best possible performance in terms of the impedance...
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Peptide dendrimers as antifungal agents and carriers for potential antifungal agent—N3‐(4‐methoxyfumaroyl)‐(S)‐2,3‐ diaminopropanoic acid—synthesis and antimicrobial activity
PublicationA series of peptide dendrimers and their conjugates with antimicrobial agent FMDP (N3‐(4‐methoxyfumaroyl)‐(S)‐2,3‐diamino‐propanoic acid) were synthesized. The obtained compounds were tested for the antibacterial and antifungal activity. All novel dendrimers displayed much better activity against the tested strains than FMDP itself. Moreover, their conjugates with FMDP also exhibited antimicrobial activity. The most promising molecules...