A. Kondorskiy - Academia.edu (original) (raw)

Papers by A. Kondorskiy

Research paper thumbnail of A Hybrid Mid-IR Photodetector Based on Semiconductor Quantum Wells

Technical Physics Letters, 2021

Research paper thumbnail of 12pTE-3 Semiclassical Formulation of Optimal Control Theory

Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2004

Research paper thumbnail of 13pTA-7 Selective bond breaking with use of the periodically chirped pulses

Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2004

Research paper thumbnail of Near-Field Electromagnetic Coupling Effects in Optical Spectra of One-Dimensional and Two-Dimensional Arrays of Metal Nanoparticles

Bulletin of the Lebedev Physics Institute, 2021

Research paper thumbnail of Effects of Plasmon–Exciton Interaction in the Spectra of Light Absorption by Hybrid Systems Consisting of Two- and Three-Layer Organometallic Nanoparticles

Bulletin of the Russian Academy of Sciences: Physics, 2018

The effects of plasmon-exciton interaction on the spectra of light absorption by hybrid systems o... more The effects of plasmon-exciton interaction on the spectra of light absorption by hybrid systems of two-and three-layer nanoparticles that consist of a metallic nucleus, the outer shells of ordered molecular dye J-aggregates, and an intermediate passive organic spacer between them is analyzed theoretically. It is established that the type of the absorption spectra and the efficiency of a near-field electromagnetic coupling between the particles in the system depends largely on the distance between the centers of concentric spheres and the direction of light polarization.

Research paper thumbnail of Threshold Effect in the Photoemission of Composite Nanoantennas Irradiated by Intense Femtosecond Laser Pulses

Jetp Letters, 2020

A new mechanism has been proposed for the formation of energy spectra of photoelectrons by above-... more A new mechanism has been proposed for the formation of energy spectra of photoelectrons by above-threshold photoemission of composite nanoantennas with small gaps between elements irradiated by femtosecond laser pulses. According to this mechanism, a photoelectron can be rescattered under certain conditions not only by a “parent” element of the composite nanoantenna but also by a neighboring element. As a result, the upper edge of the plateau region in the energy spectra of photoelectrons increases strongly. Relations between the parameters determining the efficiency of the process have been found. The mechanism proposed is promising for the development of efficient compact sources of high-energy attosecond electron beams and ultrashort X-ray pulses.

Research paper thumbnail of Resonance effects at interactions of short laser pulses with atoms

Laser Physics, 2002

The influence of transitions through intermediate discrete states on the formation of the electro... more The influence of transitions through intermediate discrete states on the formation of the electron energy spectra, ionization probabilities and excited levels populations is studied. The processes of ionization and excitation of the hydrogen-like atoms by short laser pulses are studied using the close coupling (CC) analysis, without discretization of the continuum. The resonance structures in ionization probabilities are given at different values of the laser field parameters. Electron energy spectra are calculated for the pulses with linear and circular polarization. The scaling laws are discussed.

Research paper thumbnail of Particle Shape Effects in the Extinction Spectra of Gold and Silver Nanoparticles

Bulletin of the Russian Academy of Sciences: Physics, 2018

Particle shape effects in the absorption and scattering spectra of gold and silver nanoparticles ... more Particle shape effects in the absorption and scattering spectra of gold and silver nanoparticles are studied for optical-range radiation. Numerical calculations of extinction cross section are performed using the FDTD approach for particles of three shapes: disks, triangular prisms, and triradial-base prisms. It is established that the spectra of nanoparticles of different shapes differ qualitatively even if they are of the same characteristic dimensions. The obtained results can be used to develop a spectroscopic procedure for determining the shape of metallic nanoparticles and producing quantitative estimates of their characteristic dimensions.

Research paper thumbnail of Extinction Spectra of Bilayer Organometallic Nanoplatelets

Bulletin of the Lebedev Physics Institute, 2019

Spectra of light extinction by metal nanoprisms and nanostars coated with molecular aggregates of... more Spectra of light extinction by metal nanoprisms and nanostars coated with molecular aggregates of organic dyes are calculated and theoretically analyzed. Qualitatively different nature of the spectra of organometallic nanoparticles under study is established when using J-aggregates of various cyanine dyes as their capping layer, as well as silver and gold as the cores. This results from the implementation of various plasmon-exciton coupling modes in the systems under consideration.

Research paper thumbnail of Spectral-band replication phenomenon in a single pair of hybrid metal-organic nanospheres and nanodisks caused by plexcitonic coupling

Optics Express, 2019

We study an unusual effect of spectral-band replication in the optical spectra of dimers, consist... more We study an unusual effect of spectral-band replication in the optical spectra of dimers, consisting of spherical nanoparticles or nanodisks with a silver core and a J-aggregate shell of TDBC-dye. It consists in the emergence of a doubled number of plexcitonic spectral bands compared to the case of a plasmonic dimer and in narrow peaks associated with the resonances of the J-aggregate shell. The plexcitonic bands can be divided into two groups: the "original" bands, accurately reproducing plasmonic peaks, and their "replicas," with a specific mutual arrangement and intensity distributions. The effect is interpreted using the multi-state effective Hamiltonian model describing a strong coupling between the quasi-degenerate Frenkel excitonic modes in the organic shells and multiple plasmonic modes in the pair of Ag-cores. We quantitatively explain some available experimental data on the optical properties of nanodisks and suggest a way for the observation of the replication effect. Our results extend the understanding of the nature of plexcitonic coupling to more complex systems compared to individual metal/J-aggregate nanoparticles.

Research paper thumbnail of Effects of near-field electromagnetic coupling in dimers of nanoparticles with a silver core and a J-aggregate dye shell

Quantum Electronics, 2018

We report a theoretical study of the plasmon-exciton coupling effect on the absorption spectra of... more We report a theoretical study of the plasmon-exciton coupling effect on the absorption spectra of pairs of closely spaced double-layer hybrid nanoparticles consisting of a metallic core and a J-aggregate dye shell. The effect of frequency conversion of plasmonic lines due to the near-field interaction between plasmons and Frenkel excitons of the organic shell is demonstrated. The effect leads to the appearance of additional spectral lines in the longwavelength part of the spectrum of the system of hybrid particles. The shapes and the relative intensities of the additional lines exactly reproduce the specific features of the original spectrum of plasmonic absorption bands in uncoated metallic nanoparticles. The discovered phenomenon can be used to design new types of highsensitivity nanosensors, based on plasmon-exciton effects and principles of near-field optics.

Research paper thumbnail of Electronically nonadiabatic wave packet propagation using frozen Gaussian scattering

The Journal of Chemical Physics, 2015

We present an approach, which allows to employ the adiabatic wave packet propagation technique an... more We present an approach, which allows to employ the adiabatic wave packet propagation technique and semiclassical theory to treat the nonadiabatic processes by using trajectory hopping. The approach developed generates a bunch of hopping trajectories and gives all additional information to incorporate the effect of nonadiabatic coupling into the wave packet dynamics. This provides an interface between a general adiabatic frozen Gaussian wave packet propagation method and the trajectory surface hopping technique. The basic idea suggested in [A. D. Kondorskiy and H. Nakamura, J. Chem. Phys. 120, 8937 (2004)] is revisited and complemented in the present work by the elaboration of efficient numerical algorithms. We combine our approach with the adiabatic Herman-Kluk frozen Gaussian approximation. The efficiency and accuracy of the resulting method is demonstrated by applying it to popular benchmark model systems including three Tully's models and 24D model of pyrazine. It is shown that photoabsorption spectrum is successfully reproduced by using a few hundreds of trajectories. We employ the compact finite difference Hessian update scheme to consider feasibility of the ab initio "on-the-fly" simulations. It is found that this technique allows us to obtain the reliable final results using several Hessian matrix calculations per trajectory.

Research paper thumbnail of Controlling the angular distribution of atomic photoelectrons in the region of laser-induced continuum structure in the femtosecond time domain

Journal of Physics B: Atomic, Molecular and Optical Physics, 2006

ABSTRACT

Research paper thumbnail of Manifestation of the anisotropic properties of the molecular J-aggregate shell in the optical spectra of plexcitonic nanoparticles

Optics Express, 2022

The theoretical studies of light absorption and scattering spectra of the plexcitonic two-layer t... more The theoretical studies of light absorption and scattering spectra of the plexcitonic two-layer triangular nanoprisms and three-layer nanospheres are reported. The optical properties of such metal-organic core–shell and core–double-shell nanostructures were previously explained within the framework of pure isotropic models for describing their outer excitonic shell. In this work, we show that the anisotropy of the excitonic shell permittivity can drastically affect the optical spectra of such hybrid nanostructures. This fact is confirmed by directly comparing our theory with some available experimental data, which cannot be treated using conventional isotropic shell models. We have analyzed the influence of the shell anisotropy on the optical spectra and proposed a type of hybrid nanostructure that seems the most convenient for experimental observation of the effects associated with the anisotropy of the excitonic shell. A strong dependence of the anisotropic properties of the J-agg...

Research paper thumbnail of Electronically nonadiabatic wave packet propagation using frozen Gaussian scattering

We present an approach, which allows to employ the adiabatic wave packet propagation technique an... more We present an approach, which allows to employ the adiabatic wave packet propagation technique and semiclassical theory to treat the nonadiabatic processes by using trajectory hopping. The approach developed generates a bunch of hopping trajectories and gives all additional information to incorporate the effect of nonadiabatic coupling into the wave packet dynamics. This provides an interface between a general adiabatic frozen Gaussian wave packet propagation method and the trajectory surface hopping technique. The basic idea suggested in [A. D. Kondorskiy and H. Nakamura, J. Chem. Phys. 120, 8937 (2004)] is revisited and complemented in the present work by the elaboration of efficient numerical algorithms. We combine our approach with the adiabatic Herman-Kluk frozen
Gaussian approximation. The efficiency and accuracy of the resulting method is demonstrated by applying it to popular benchmark model systems including three Tully’s models and 24D model of pyrazine. It is shown that photoabsorption spectrum is successfully reproduced by using a few hundreds of trajectories.We employ the compact finite difference Hessian update scheme to consider feasibility of the ab initio “on-the-fly” simulations. It is found that this technique allows us to obtain the reliable final results using several Hessian matrix calculations per trajectory.

Research paper thumbnail of Light absorption and plasmon – exciton interaction in three-layer nanorods with a gold core and outer shell composed of molecular J- and H-aggregates of dyes

Quantum Electronics, 2015

Research paper thumbnail of Absorption of Light by Hybrid Metalorganic Nanostructures of Elongated Shape

Journal of Russian Laser Research, 2015

ABSTRACT

Research paper thumbnail of Laser Control of Chemical Dynamics. I. Control of Electronic Transitions by Quadratic Chirping

Springer Series in Chemical Physics, 2000

An effective scheme of laser control of wave packet dynamics applicable to the systems of many de... more An effective scheme of laser control of wave packet dynamics applicable to the systems of many degrees of freedom is discussed. It is demonstrated that by using specially designed quadratically chirped pulses fast and nearly complete excitation of wave packet can be achieved without significant distortion of its shape. The parameters of laser pulse can be estimated analytically from the Zhu-Nakamura (ZN) theory of nonadiabatic transition. The scheme is applicable to various processes such as simple electronic excitation, pump-dump, and selective bond breaking, and it is actually numerically demonstrated to work well by taking diatomic and triatomic molecules as examples.

Research paper thumbnail of Laser Control of Chemical Dynamics. II. Control of Wavepacket Motion

Springer Series in Chemical Physics, 2000

An efficient semiclassical optimal control theory for controlling wave packet dynamics on a singl... more An efficient semiclassical optimal control theory for controlling wave packet dynamics on a single adiabatic potential energy surface applicable to the systems of many degrees of freedom is discussed with all the details. The approach combines advantages of different formulations of optimal control theory: quantum and classical on one hand, and global and local on the other. The efficiency and reliability of the method is demonstrated by taking the systems of two and four dimensions as examples.

Research paper thumbnail of Semiclassical Frozen Gaussian Propagation Approach for Molecular Dynamics with Nonadiabatic Transitions

The modern tends in physics of molecular interactions in chemical and biological systems, polyato... more The modern tends in physics of molecular interactions in chemical and biological systems, polyatomic molecule -laser interactions and further development of optimal control theory (OCT) needs development of effective semiclassical approaches for wave packet propagation with nonadiabatic transition. Natural treatment of various quantum effects becomes an important requirement for such theories.

Research paper thumbnail of A Hybrid Mid-IR Photodetector Based on Semiconductor Quantum Wells

Technical Physics Letters, 2021

Research paper thumbnail of 12pTE-3 Semiclassical Formulation of Optimal Control Theory

Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2004

Research paper thumbnail of 13pTA-7 Selective bond breaking with use of the periodically chirped pulses

Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2004

Research paper thumbnail of Near-Field Electromagnetic Coupling Effects in Optical Spectra of One-Dimensional and Two-Dimensional Arrays of Metal Nanoparticles

Bulletin of the Lebedev Physics Institute, 2021

Research paper thumbnail of Effects of Plasmon–Exciton Interaction in the Spectra of Light Absorption by Hybrid Systems Consisting of Two- and Three-Layer Organometallic Nanoparticles

Bulletin of the Russian Academy of Sciences: Physics, 2018

The effects of plasmon-exciton interaction on the spectra of light absorption by hybrid systems o... more The effects of plasmon-exciton interaction on the spectra of light absorption by hybrid systems of two-and three-layer nanoparticles that consist of a metallic nucleus, the outer shells of ordered molecular dye J-aggregates, and an intermediate passive organic spacer between them is analyzed theoretically. It is established that the type of the absorption spectra and the efficiency of a near-field electromagnetic coupling between the particles in the system depends largely on the distance between the centers of concentric spheres and the direction of light polarization.

Research paper thumbnail of Threshold Effect in the Photoemission of Composite Nanoantennas Irradiated by Intense Femtosecond Laser Pulses

Jetp Letters, 2020

A new mechanism has been proposed for the formation of energy spectra of photoelectrons by above-... more A new mechanism has been proposed for the formation of energy spectra of photoelectrons by above-threshold photoemission of composite nanoantennas with small gaps between elements irradiated by femtosecond laser pulses. According to this mechanism, a photoelectron can be rescattered under certain conditions not only by a “parent” element of the composite nanoantenna but also by a neighboring element. As a result, the upper edge of the plateau region in the energy spectra of photoelectrons increases strongly. Relations between the parameters determining the efficiency of the process have been found. The mechanism proposed is promising for the development of efficient compact sources of high-energy attosecond electron beams and ultrashort X-ray pulses.

Research paper thumbnail of Resonance effects at interactions of short laser pulses with atoms

Laser Physics, 2002

The influence of transitions through intermediate discrete states on the formation of the electro... more The influence of transitions through intermediate discrete states on the formation of the electron energy spectra, ionization probabilities and excited levels populations is studied. The processes of ionization and excitation of the hydrogen-like atoms by short laser pulses are studied using the close coupling (CC) analysis, without discretization of the continuum. The resonance structures in ionization probabilities are given at different values of the laser field parameters. Electron energy spectra are calculated for the pulses with linear and circular polarization. The scaling laws are discussed.

Research paper thumbnail of Particle Shape Effects in the Extinction Spectra of Gold and Silver Nanoparticles

Bulletin of the Russian Academy of Sciences: Physics, 2018

Particle shape effects in the absorption and scattering spectra of gold and silver nanoparticles ... more Particle shape effects in the absorption and scattering spectra of gold and silver nanoparticles are studied for optical-range radiation. Numerical calculations of extinction cross section are performed using the FDTD approach for particles of three shapes: disks, triangular prisms, and triradial-base prisms. It is established that the spectra of nanoparticles of different shapes differ qualitatively even if they are of the same characteristic dimensions. The obtained results can be used to develop a spectroscopic procedure for determining the shape of metallic nanoparticles and producing quantitative estimates of their characteristic dimensions.

Research paper thumbnail of Extinction Spectra of Bilayer Organometallic Nanoplatelets

Bulletin of the Lebedev Physics Institute, 2019

Spectra of light extinction by metal nanoprisms and nanostars coated with molecular aggregates of... more Spectra of light extinction by metal nanoprisms and nanostars coated with molecular aggregates of organic dyes are calculated and theoretically analyzed. Qualitatively different nature of the spectra of organometallic nanoparticles under study is established when using J-aggregates of various cyanine dyes as their capping layer, as well as silver and gold as the cores. This results from the implementation of various plasmon-exciton coupling modes in the systems under consideration.

Research paper thumbnail of Spectral-band replication phenomenon in a single pair of hybrid metal-organic nanospheres and nanodisks caused by plexcitonic coupling

Optics Express, 2019

We study an unusual effect of spectral-band replication in the optical spectra of dimers, consist... more We study an unusual effect of spectral-band replication in the optical spectra of dimers, consisting of spherical nanoparticles or nanodisks with a silver core and a J-aggregate shell of TDBC-dye. It consists in the emergence of a doubled number of plexcitonic spectral bands compared to the case of a plasmonic dimer and in narrow peaks associated with the resonances of the J-aggregate shell. The plexcitonic bands can be divided into two groups: the "original" bands, accurately reproducing plasmonic peaks, and their "replicas," with a specific mutual arrangement and intensity distributions. The effect is interpreted using the multi-state effective Hamiltonian model describing a strong coupling between the quasi-degenerate Frenkel excitonic modes in the organic shells and multiple plasmonic modes in the pair of Ag-cores. We quantitatively explain some available experimental data on the optical properties of nanodisks and suggest a way for the observation of the replication effect. Our results extend the understanding of the nature of plexcitonic coupling to more complex systems compared to individual metal/J-aggregate nanoparticles.

Research paper thumbnail of Effects of near-field electromagnetic coupling in dimers of nanoparticles with a silver core and a J-aggregate dye shell

Quantum Electronics, 2018

We report a theoretical study of the plasmon-exciton coupling effect on the absorption spectra of... more We report a theoretical study of the plasmon-exciton coupling effect on the absorption spectra of pairs of closely spaced double-layer hybrid nanoparticles consisting of a metallic core and a J-aggregate dye shell. The effect of frequency conversion of plasmonic lines due to the near-field interaction between plasmons and Frenkel excitons of the organic shell is demonstrated. The effect leads to the appearance of additional spectral lines in the longwavelength part of the spectrum of the system of hybrid particles. The shapes and the relative intensities of the additional lines exactly reproduce the specific features of the original spectrum of plasmonic absorption bands in uncoated metallic nanoparticles. The discovered phenomenon can be used to design new types of highsensitivity nanosensors, based on plasmon-exciton effects and principles of near-field optics.

Research paper thumbnail of Electronically nonadiabatic wave packet propagation using frozen Gaussian scattering

The Journal of Chemical Physics, 2015

We present an approach, which allows to employ the adiabatic wave packet propagation technique an... more We present an approach, which allows to employ the adiabatic wave packet propagation technique and semiclassical theory to treat the nonadiabatic processes by using trajectory hopping. The approach developed generates a bunch of hopping trajectories and gives all additional information to incorporate the effect of nonadiabatic coupling into the wave packet dynamics. This provides an interface between a general adiabatic frozen Gaussian wave packet propagation method and the trajectory surface hopping technique. The basic idea suggested in [A. D. Kondorskiy and H. Nakamura, J. Chem. Phys. 120, 8937 (2004)] is revisited and complemented in the present work by the elaboration of efficient numerical algorithms. We combine our approach with the adiabatic Herman-Kluk frozen Gaussian approximation. The efficiency and accuracy of the resulting method is demonstrated by applying it to popular benchmark model systems including three Tully's models and 24D model of pyrazine. It is shown that photoabsorption spectrum is successfully reproduced by using a few hundreds of trajectories. We employ the compact finite difference Hessian update scheme to consider feasibility of the ab initio "on-the-fly" simulations. It is found that this technique allows us to obtain the reliable final results using several Hessian matrix calculations per trajectory.

Research paper thumbnail of Controlling the angular distribution of atomic photoelectrons in the region of laser-induced continuum structure in the femtosecond time domain

Journal of Physics B: Atomic, Molecular and Optical Physics, 2006

ABSTRACT

Research paper thumbnail of Manifestation of the anisotropic properties of the molecular J-aggregate shell in the optical spectra of plexcitonic nanoparticles

Optics Express, 2022

The theoretical studies of light absorption and scattering spectra of the plexcitonic two-layer t... more The theoretical studies of light absorption and scattering spectra of the plexcitonic two-layer triangular nanoprisms and three-layer nanospheres are reported. The optical properties of such metal-organic core–shell and core–double-shell nanostructures were previously explained within the framework of pure isotropic models for describing their outer excitonic shell. In this work, we show that the anisotropy of the excitonic shell permittivity can drastically affect the optical spectra of such hybrid nanostructures. This fact is confirmed by directly comparing our theory with some available experimental data, which cannot be treated using conventional isotropic shell models. We have analyzed the influence of the shell anisotropy on the optical spectra and proposed a type of hybrid nanostructure that seems the most convenient for experimental observation of the effects associated with the anisotropy of the excitonic shell. A strong dependence of the anisotropic properties of the J-agg...

Research paper thumbnail of Electronically nonadiabatic wave packet propagation using frozen Gaussian scattering

We present an approach, which allows to employ the adiabatic wave packet propagation technique an... more We present an approach, which allows to employ the adiabatic wave packet propagation technique and semiclassical theory to treat the nonadiabatic processes by using trajectory hopping. The approach developed generates a bunch of hopping trajectories and gives all additional information to incorporate the effect of nonadiabatic coupling into the wave packet dynamics. This provides an interface between a general adiabatic frozen Gaussian wave packet propagation method and the trajectory surface hopping technique. The basic idea suggested in [A. D. Kondorskiy and H. Nakamura, J. Chem. Phys. 120, 8937 (2004)] is revisited and complemented in the present work by the elaboration of efficient numerical algorithms. We combine our approach with the adiabatic Herman-Kluk frozen
Gaussian approximation. The efficiency and accuracy of the resulting method is demonstrated by applying it to popular benchmark model systems including three Tully’s models and 24D model of pyrazine. It is shown that photoabsorption spectrum is successfully reproduced by using a few hundreds of trajectories.We employ the compact finite difference Hessian update scheme to consider feasibility of the ab initio “on-the-fly” simulations. It is found that this technique allows us to obtain the reliable final results using several Hessian matrix calculations per trajectory.

Research paper thumbnail of Light absorption and plasmon – exciton interaction in three-layer nanorods with a gold core and outer shell composed of molecular J- and H-aggregates of dyes

Quantum Electronics, 2015

Research paper thumbnail of Absorption of Light by Hybrid Metalorganic Nanostructures of Elongated Shape

Journal of Russian Laser Research, 2015

ABSTRACT

Research paper thumbnail of Laser Control of Chemical Dynamics. I. Control of Electronic Transitions by Quadratic Chirping

Springer Series in Chemical Physics, 2000

An effective scheme of laser control of wave packet dynamics applicable to the systems of many de... more An effective scheme of laser control of wave packet dynamics applicable to the systems of many degrees of freedom is discussed. It is demonstrated that by using specially designed quadratically chirped pulses fast and nearly complete excitation of wave packet can be achieved without significant distortion of its shape. The parameters of laser pulse can be estimated analytically from the Zhu-Nakamura (ZN) theory of nonadiabatic transition. The scheme is applicable to various processes such as simple electronic excitation, pump-dump, and selective bond breaking, and it is actually numerically demonstrated to work well by taking diatomic and triatomic molecules as examples.

Research paper thumbnail of Laser Control of Chemical Dynamics. II. Control of Wavepacket Motion

Springer Series in Chemical Physics, 2000

An efficient semiclassical optimal control theory for controlling wave packet dynamics on a singl... more An efficient semiclassical optimal control theory for controlling wave packet dynamics on a single adiabatic potential energy surface applicable to the systems of many degrees of freedom is discussed with all the details. The approach combines advantages of different formulations of optimal control theory: quantum and classical on one hand, and global and local on the other. The efficiency and reliability of the method is demonstrated by taking the systems of two and four dimensions as examples.

Research paper thumbnail of Semiclassical Frozen Gaussian Propagation Approach for Molecular Dynamics with Nonadiabatic Transitions

The modern tends in physics of molecular interactions in chemical and biological systems, polyato... more The modern tends in physics of molecular interactions in chemical and biological systems, polyatomic molecule -laser interactions and further development of optimal control theory (OCT) needs development of effective semiclassical approaches for wave packet propagation with nonadiabatic transition. Natural treatment of various quantum effects becomes an important requirement for such theories.