Grisha Furman - Academia.edu (original) (raw)

Papers by Grisha Furman

Research paper thumbnail of Nuclear spin-lattice relaxation in nanofluids with paramagnetic impurities

Journal of magnetic resonance (San Diego, Calif. : 1997), 2015

We study the spin-lattice relaxation of the nuclear spins in a liquid or a gas entrapped in nanos... more We study the spin-lattice relaxation of the nuclear spins in a liquid or a gas entrapped in nanosized ellipsoidal cavities with paramagnetic impurities. Two cases are considered where the major axes of cavities are in orientational order and isotropically disordered. The evolution equation and analytical expression for spin lattice relaxation time are obtained which give the dependence of the relaxation time on the structural parameters of a nanocavity and the characteristics of a gas or a liquid confined in nanocavities. For the case of orientationally ordered cavities, the relaxation process is exponential. When the nanocavities are isotropically disordered, the time dependence of the magnetization is significantly non-exponential. As shown for this case, the relaxation process is characterized by two time constants. The measurements of the relaxation time, along with the information about the cavity size, allow determining the shape and orientation of the nanocavity and concentra...

Research paper thumbnail of Multicomponents of Spin–Spin Relaxation, Anisotropy of the Echo Decay, and Nanoporous Sample Structure

Applied Magnetic Resonance

Research paper thumbnail of Nuclear spin-lattice relaxation in nanofluids with paramagnetic impurities

We study the spin-lattice relaxation of the nuclear spins in a liquid or a gas entrapped in nanos... more We study the spin-lattice relaxation of the nuclear spins in a liquid or a gas entrapped in nanosized ellipsoidal cavities with paramagnetic impurities. Two cases are considered where the major axes of cavities are in orientational order and isotropically disordered. The evolution equation and analytical expression for spin lattice relaxation time are obtained which give the dependence of the relaxation time on the structural parameters of a nanocavity and the characteristics of a gas or a liquid confined in nanocavities. For the case of orientationally ordered cavities, the relaxation process is exponential. When the nanocavities are isotropically disordered, the time dependence of the magnetization is significantly non-exponential. As shown for this case, the relaxation process is characterized by two time constants. The measurements of the relaxation time, along with the information about the cavity size, allow determining the shape and orientation of the nanocavity and concentration of the paramagnetic impurities.

Research paper thumbnail of Spin locking in liquid entrapped in nanocavities: Application to study connective tissues

Study of the spin-lattice relaxation in the spin-locking state offers important information about... more Study of the spin-lattice relaxation in the spin-locking state offers important information about atomic and molecular motions, which cannot be obtained by spin lattice relaxation in strong external magnetic fields. The application of this technique for the investigation of the spin-lattice relaxation in biological samples with fibril structures reveals an anisotropy effect for the relaxation time under spin locking, T 1q. To explain the anisotropy of the spin-lattice relaxation under spin-locking in connective tissue a model which represents a tissue by a set of nanocavities containing water is used. The developed model allows us to estimate the correlation time for water molecular motion in articular cartilage, s c ¼ 30 ls and the averaged nanocavity volume, V h i ' 5400 nm 3. Based on the developed model which represents a connective tissue by a set of nanocavities containing water, a good agreement with the experimental data from an articular cartilage and a tendon was demonstrated. The fitting parameters were obtained for each layer in each region of the articular cartilage. These parameters vary with the known anatomic microstructures of the tissue. Through Gaussian distributions to nanocavity directions, we have calculated the anisotropy of the relaxation time under spin locking T 1q for a human Achilles tendon specimen and an articular cartilage. The value of the fitting parameters obtained at matching of calculation to experimental results can be used in future investigations for characterizing the fine fibril structure of biological samples.

Research paper thumbnail of Spin-lattice relaxation in liquid entrapped in a nanocavity

We consider the spin lattice relaxation in bulk liquid and liquid entrapped in a nanocavity. The ... more We consider the spin lattice relaxation in bulk liquid and liquid entrapped in a nanocavity. The kinetic equation which describes the spin lattice relaxation is obtained by using the theory of the nonequilibrium state operator. A solution of the kinetic equation gives the quadrature expression for the relaxation time, T 1. The calculated relaxation time agrees well with the experimental data. The spin-lattice relaxation time is calculated for nanocavities with a characteristic size much less than 700 nm, with the assumption that the spin-lattice relaxation mechanism is determined by nanocavity fluctuations. The resulting expression shows an explicit dependence of the relaxation time T 1 on the volume, density of nuclear spins, and parameters of the cavity (shape and orientation relatively to the applied field). To compare with the experiment on the detection of the anisotropy of the relaxation time, we average the expression that describes the relaxation time over the orientation of the nanocavities relative to the applied magnetic field. The good agreement with the experimental data for fibril tissues was achieved by adjustment of few fitting parameters-the standard deviation, averaged fiber direction, and weight factors-which characterize the ordering of fibrils.

Research paper thumbnail of The spin-diffusion effect in the dipolar ordering state

Journal of Physics: Condensed Matter, 1999

ABSTRACT The theory of spin diffusion is extended to the case of nuclear dipolar order in solids ... more ABSTRACT The theory of spin diffusion is extended to the case of nuclear dipolar order in solids containing paramagnetic impurities. We show that at the beginning of the relaxation process the relaxation function of the dipolar order is non-exponential, due to the direct interaction with paramagnetic impurities, and proceeds to become an exponential function of time, when spin diffusion of the dipolar order takes place. Using experimental data on these two relaxation regimes in CaF2 doped with Mn2+, the diffusion coefficient and the radius of the diffusion barrier were estimated.

Research paper thumbnail of Spatio-temporal modeling of COVID-19 epidemic

Health Risk Analysis, 2021

In autumn and winter 2020–2021 there was a growth in morbidity with COVID-19. Since there are no ... more In autumn and winter 2020–2021 there was a growth in morbidity with COVID-19. Since there are no efficient medications and mass vaccination has only just begun, quarantine, limitations on travels and contacts between people as well as use of personal protection equipment (masks) still remain priority measures aimed at preventing the disease from spreading. In this work we have analyzed how the epidemic developed and what impacts quarantine measures exerted on the disease spread; to do that we applied various mathematical models. It was shown that simple models belonging to SIR-type (S means susceptible; I, infected; and R, recovered or removed from the infected group) allowed estimating certain model parameters such as morbidity and recovery coefficients that could be used in more complicated models. We examined spatio-temporal epidemiologic models based on finding solutions to non-stationary two-dimensional reaction-diffusion equations. Such models allow taking into account uneven ...

Research paper thumbnail of NMR method for amplification of single-spin state

Solid state nuclear magnetic resonance, 2007

Amplification of a single-spin state using nuclear magnetic resonance (NMR) techniques in a rotat... more Amplification of a single-spin state using nuclear magnetic resonance (NMR) techniques in a rotating frame is considered. The main aim is to investigate the efficiency of various schemes for quantum detection. Results of numerical simulation of the time dependence of individual and total nuclear polarizations for 1D, 2D, and 3D configurations of the spin systems are presented.

Research paper thumbnail of Zeroth order quantum coherences and preparation of pseudopure state in homonuclear dipolar coupling spin systems

Dynamics of zeroth order quantum coherences and preparation of the pseudopure states in homonucle... more Dynamics of zeroth order quantum coherences and preparation of the pseudopure states in homonuclear systems of dipolar coupling spins is closely examined. It has been shown an extreme important role of the non-diagonal part of zeroth order coherence in construction of the pseudopure state. Simulations of the preparation process of pseudopure states with the real molecular structures (a rectangular (1-chloro-4nitrobenzene molecule), a chain (hydroxyapatite molecule), a ring (benzene molecule), and a double ring (cyclopentane molecule)) open the way to experimental testing of the obtained results. multiple-quantum dynamics, pseudopure state

Research paper thumbnail of Anisotropy of transverse spin relaxation in H2O-D2O liquid entrapped in Nanocavities: application to studies of connective tissues

Hyperfine Interactions, 2021

The spin-spin relaxation in connective tissues is simulated using a model in which the tissue is ... more The spin-spin relaxation in connective tissues is simulated using a model in which the tissue is represented by a set of nanocavities containing H 2 O-D 2 O liquid. Collagen fibrils in connective tissues form ordered hierarchical long structures of hydrated nano-cavities with characteristic diameter from 1 nm to several tens of nanometers and length of about 100 nm. We consider influence of the restricted Brownian motion of molecules inside a nano-cavity on spin-spin relaxation. The analytical expression for the transverse time T 2 for H 2 O-D 2 O the liquid in contained a nanocavity was obtained. We show that the angular dependence of the transverse relaxation rate does not depend on the concentration of D 2 O. The theoretical results could explain the experimentally observed dependence of the degree of deuteration on the relaxation time T 2 . Accounting the orientation distribution of the nanocavities well agreement with the experimental dependence of the relaxation for articular cartilage on the deuteration degree was obtained.

Research paper thumbnail of Anisotropy of transverse and longitudinal relaxations in liquids entrapped in nano- and micro-cavities of a plant stem

Journal of Magnetic Resonance, 2021

We studied the anisotropy of 1H NMR spin-lattice and spin-spin relaxations in a fresh celery stem... more We studied the anisotropy of 1H NMR spin-lattice and spin-spin relaxations in a fresh celery stem experimentally and modeled the sample theoretically as the water-containing nano- and micro-cavities. The angular dependence of the spin-lattice and the spin-spin relaxation times was obtained, which clearly shows the presence of water-filled nano- and micro-cavities in the celery stem, which have elongated shapes and are related to non-spherical vascular cells in the stem. To explain the experimental data, we applied the relaxation theory developed by us and used previously to interpret similar effects in liquids in nanocavities located in biological tissues such as cartilages and tendons. Good agreement between the experimental data and theoretical results was obtained by adjusting the fitting parameters. The obtained values of standard deviations (0.33 for the mean polar angle and 0.1 for the mean azimuthal angle) indicate a noticeable ordering of the water-filled nano- and micro-cavities in the celery stem. Our approach allows the use of the NMR technique to experimentally determine the order parameters of the microscopic vascular structures in plants.

Research paper thumbnail of Determining the internal orientation, degree of ordering, and volume of elongated nanocavities by NMR: Application to studies of plant stem

Journal of Magnetic Resonance

Research paper thumbnail of Dynamics of Zeeman and dipolar states in the spin locking in a liquid entrapped in nano-cavities: Application to study of biological systems

Journal of Magnetic Resonance, 2021

We analyze the application of the spin locking method to study the spin dynamics and spin-lattice... more We analyze the application of the spin locking method to study the spin dynamics and spin-lattice relaxation of nuclear spins-1/2 in liquids or gases enclosed in a nano-cavity. Two cases are considered: when the amplitude of the radio-frequency field is much greater than the local field acting the nucleus and when the amplitude of the radio-frequency field is comparable or even less than the local field. In these cases, temperatures of two spin reservoirs, the Zeeman and dipole ones, change in different ways: in the first case, temperatures of the Zeeman and dipolar reservoirs reach the common value relatively quickly, and then turn to the lattice temperature; in the second case, at the beginning of the process, these temperatures are equal, and then turn to the lattice temperature with different relaxation times. Good agreement between the obtained theoretical results and the experimental data is achieved by fitting the parameters of the distribution of the orientation of nanocavities. The parameters of this distribution can be used to characterize the fine structure of biological samples, potentially enabling the detection of degradative changes in connective tissues.

Research paper thumbnail of Losses in Superconductors Under Non-Sinusoidal Currents and Magnetic Fields

IEEE Transactions on Applied Superconductivity, 2009

Study of AC losses in superconducting wires and tapes is usually restricted by consideration of a... more Study of AC losses in superconducting wires and tapes is usually restricted by consideration of applied sinusoidal currents and/or magnetic fields. However, currents in electric power systems contain a wide variety of harmonics. The currents become strongly non-sinusoidal at the operation of converters, non-linear reactors, and during transient and overload conditions. We report the results of the analysis of the influence of higher harmonics of the current and magnetic field on AC losses in superconducting slabs, strips and coated conductors. Analytical expressions are obtained in the framework of Bean's critical state model; the power law voltage-current characteristics are treated numerically. It is shown that the contribution of higher harmonics to AC losses in superconducting elements can be tens times larger than in normal metals and the 5% harmonic can increases the losses by up to 20%.

Research paper thumbnail of Spin-lattice relaxation in liquid entrapped in a nanocavity

Journal of Magnetic Resonance

We consider the spin lattice relaxation in bulk liquid and liquid entrapped in a nanocavity. The ... more We consider the spin lattice relaxation in bulk liquid and liquid entrapped in a nanocavity. The kinetic equation which describes the spin lattice relaxation is obtained by using the theory of the nonequilibrium state operator. A solution of the kinetic equation gives the quadrature expression for the relaxation time, T1. The calculated relaxation time agrees well with the experimental data. The spin-lattice relaxation time is calculated for nanocavities with a characteristic size much less than 700 nm, with the assumption that the spin-lattice relaxation mechanism is determined by nanocavity fluctuations. The resulting expression shows an explicit dependence of the relaxation time T1 on the volume, density of nuclear spins, and parameters of the cavity (shape and orientation relatively to the applied field). To compare with the experiment on the detection of the anisotropy of the relaxation time, we average the expression that describes the relaxation time over the orientation of the nanocavities relative to the applied magnetic field. The good agreement with the experimental data for fibril tissues was achieved by adjustment of few fitting parameters - the standard deviation, averaged fiber direction, and weight factors - which characterize the ordering of fibrils.

Research paper thumbnail of Berry's phase in the Floquet representation

Journal of Physics A: Mathematical and General, 1994

ABSTRACT By means of the Floquet theory the investigation of Berry's phase for the quantu... more ABSTRACT By means of the Floquet theory the investigation of Berry's phase for the quantum system with time-dependent periodic Hamiltonian is transformed into the study of a time-independent eigenvalue equation. An expression for the infinite-dimensional matrix is obtained describing the Berry's phase in terms of the Floquet state.

Research paper thumbnail of Nuclear spin-lattice relaxation via thermal vortex motion in superconductors

Physica C: Superconductivity, 1996

The theory of the growth of the nuclear magnetization in the presence of paramagnetic impurities ... more The theory of the growth of the nuclear magnetization in the presence of paramagnetic impurities and the absence of spin diffusion is extended to the nuclear spin-lattice relaxation in type-II superconductors in the mixed state. The results obtained can be used to determine the magnetic-field distribution and/or the dimensionality of the vortex lattice in conventional and high-temperature superconductors.

Research paper thumbnail of Multiple quantum NMR dynamics in pseudopure states

Journal of Physics: Condensed Matter, 2009

We investigate numerically the Multiple Quantum (MQ) NMR dynamics in systems of nuclear spins 1/2... more We investigate numerically the Multiple Quantum (MQ) NMR dynamics in systems of nuclear spins 1/2 coupled by the dipole-dipole interactions in the case of the pseudopure initial state. Simulations of the MQ NMR with the real molecular structures such as six dipolar-coupled proton spins of a benzene, hydroxyl proton chains in calcium hydroxyapatite and fluorine chains in calcium fluorapatite open the way to experimental NMR testing of the obtained results. It was found that multiple-spin correlations are created faster in such experiments than in the usual MQ NMR experiments and can be used for the investigation of many-spin dynamics of nuclear spins in solids

Research paper thumbnail of Stimulated wave of polarization in spin chains

Physical Review B, 2006

Stimulated wave of polarization, triggered by a flip of a single spin, presents a simple model of... more Stimulated wave of polarization, triggered by a flip of a single spin, presents a simple model of quantum amplification. Previously, it has been found that such wave can be excited in a 1D Ising chain with nearest-neighbor interactions, irradiated by a weak resonant transverse field. Here we explore models with more realistic Hamiltonians, in particular, with natural dipole-dipole interactions. Results of simulations for 1D spin chains and rings with up to nine spins are presented.

Research paper thumbnail of The pseudopure state in homonuclear dipolar coupling spin systems

Journal of Physics A: Mathematical and General, 2006

ABSTRACT Preparation of the pseudopure states in homonuclear systems of dipolar coupling spins is... more ABSTRACT Preparation of the pseudopure states in homonuclear systems of dipolar coupling spins is closely examined. An extremely important role of the non-diagonal part of zeroth-order coherence in the construction of the pseudopure state has been shown. Simulations of the preparation process of pseudopure states with the real molecular structures (a rectangular (1-chloro-4-nitrobenzene molecule), a chain (hydroxyapatite molecule), a ring (benzene molecule) and a double ring (cyclopentane molecule)) open the way to experimental NMR testing of the obtained results. The proposed method could be considered as a fruitful technology for quantum computation.

Research paper thumbnail of Nuclear spin-lattice relaxation in nanofluids with paramagnetic impurities

Journal of magnetic resonance (San Diego, Calif. : 1997), 2015

We study the spin-lattice relaxation of the nuclear spins in a liquid or a gas entrapped in nanos... more We study the spin-lattice relaxation of the nuclear spins in a liquid or a gas entrapped in nanosized ellipsoidal cavities with paramagnetic impurities. Two cases are considered where the major axes of cavities are in orientational order and isotropically disordered. The evolution equation and analytical expression for spin lattice relaxation time are obtained which give the dependence of the relaxation time on the structural parameters of a nanocavity and the characteristics of a gas or a liquid confined in nanocavities. For the case of orientationally ordered cavities, the relaxation process is exponential. When the nanocavities are isotropically disordered, the time dependence of the magnetization is significantly non-exponential. As shown for this case, the relaxation process is characterized by two time constants. The measurements of the relaxation time, along with the information about the cavity size, allow determining the shape and orientation of the nanocavity and concentra...

Research paper thumbnail of Multicomponents of Spin–Spin Relaxation, Anisotropy of the Echo Decay, and Nanoporous Sample Structure

Applied Magnetic Resonance

Research paper thumbnail of Nuclear spin-lattice relaxation in nanofluids with paramagnetic impurities

We study the spin-lattice relaxation of the nuclear spins in a liquid or a gas entrapped in nanos... more We study the spin-lattice relaxation of the nuclear spins in a liquid or a gas entrapped in nanosized ellipsoidal cavities with paramagnetic impurities. Two cases are considered where the major axes of cavities are in orientational order and isotropically disordered. The evolution equation and analytical expression for spin lattice relaxation time are obtained which give the dependence of the relaxation time on the structural parameters of a nanocavity and the characteristics of a gas or a liquid confined in nanocavities. For the case of orientationally ordered cavities, the relaxation process is exponential. When the nanocavities are isotropically disordered, the time dependence of the magnetization is significantly non-exponential. As shown for this case, the relaxation process is characterized by two time constants. The measurements of the relaxation time, along with the information about the cavity size, allow determining the shape and orientation of the nanocavity and concentration of the paramagnetic impurities.

Research paper thumbnail of Spin locking in liquid entrapped in nanocavities: Application to study connective tissues

Study of the spin-lattice relaxation in the spin-locking state offers important information about... more Study of the spin-lattice relaxation in the spin-locking state offers important information about atomic and molecular motions, which cannot be obtained by spin lattice relaxation in strong external magnetic fields. The application of this technique for the investigation of the spin-lattice relaxation in biological samples with fibril structures reveals an anisotropy effect for the relaxation time under spin locking, T 1q. To explain the anisotropy of the spin-lattice relaxation under spin-locking in connective tissue a model which represents a tissue by a set of nanocavities containing water is used. The developed model allows us to estimate the correlation time for water molecular motion in articular cartilage, s c ¼ 30 ls and the averaged nanocavity volume, V h i ' 5400 nm 3. Based on the developed model which represents a connective tissue by a set of nanocavities containing water, a good agreement with the experimental data from an articular cartilage and a tendon was demonstrated. The fitting parameters were obtained for each layer in each region of the articular cartilage. These parameters vary with the known anatomic microstructures of the tissue. Through Gaussian distributions to nanocavity directions, we have calculated the anisotropy of the relaxation time under spin locking T 1q for a human Achilles tendon specimen and an articular cartilage. The value of the fitting parameters obtained at matching of calculation to experimental results can be used in future investigations for characterizing the fine fibril structure of biological samples.

Research paper thumbnail of Spin-lattice relaxation in liquid entrapped in a nanocavity

We consider the spin lattice relaxation in bulk liquid and liquid entrapped in a nanocavity. The ... more We consider the spin lattice relaxation in bulk liquid and liquid entrapped in a nanocavity. The kinetic equation which describes the spin lattice relaxation is obtained by using the theory of the nonequilibrium state operator. A solution of the kinetic equation gives the quadrature expression for the relaxation time, T 1. The calculated relaxation time agrees well with the experimental data. The spin-lattice relaxation time is calculated for nanocavities with a characteristic size much less than 700 nm, with the assumption that the spin-lattice relaxation mechanism is determined by nanocavity fluctuations. The resulting expression shows an explicit dependence of the relaxation time T 1 on the volume, density of nuclear spins, and parameters of the cavity (shape and orientation relatively to the applied field). To compare with the experiment on the detection of the anisotropy of the relaxation time, we average the expression that describes the relaxation time over the orientation of the nanocavities relative to the applied magnetic field. The good agreement with the experimental data for fibril tissues was achieved by adjustment of few fitting parameters-the standard deviation, averaged fiber direction, and weight factors-which characterize the ordering of fibrils.

Research paper thumbnail of The spin-diffusion effect in the dipolar ordering state

Journal of Physics: Condensed Matter, 1999

ABSTRACT The theory of spin diffusion is extended to the case of nuclear dipolar order in solids ... more ABSTRACT The theory of spin diffusion is extended to the case of nuclear dipolar order in solids containing paramagnetic impurities. We show that at the beginning of the relaxation process the relaxation function of the dipolar order is non-exponential, due to the direct interaction with paramagnetic impurities, and proceeds to become an exponential function of time, when spin diffusion of the dipolar order takes place. Using experimental data on these two relaxation regimes in CaF2 doped with Mn2+, the diffusion coefficient and the radius of the diffusion barrier were estimated.

Research paper thumbnail of Spatio-temporal modeling of COVID-19 epidemic

Health Risk Analysis, 2021

In autumn and winter 2020–2021 there was a growth in morbidity with COVID-19. Since there are no ... more In autumn and winter 2020–2021 there was a growth in morbidity with COVID-19. Since there are no efficient medications and mass vaccination has only just begun, quarantine, limitations on travels and contacts between people as well as use of personal protection equipment (masks) still remain priority measures aimed at preventing the disease from spreading. In this work we have analyzed how the epidemic developed and what impacts quarantine measures exerted on the disease spread; to do that we applied various mathematical models. It was shown that simple models belonging to SIR-type (S means susceptible; I, infected; and R, recovered or removed from the infected group) allowed estimating certain model parameters such as morbidity and recovery coefficients that could be used in more complicated models. We examined spatio-temporal epidemiologic models based on finding solutions to non-stationary two-dimensional reaction-diffusion equations. Such models allow taking into account uneven ...

Research paper thumbnail of NMR method for amplification of single-spin state

Solid state nuclear magnetic resonance, 2007

Amplification of a single-spin state using nuclear magnetic resonance (NMR) techniques in a rotat... more Amplification of a single-spin state using nuclear magnetic resonance (NMR) techniques in a rotating frame is considered. The main aim is to investigate the efficiency of various schemes for quantum detection. Results of numerical simulation of the time dependence of individual and total nuclear polarizations for 1D, 2D, and 3D configurations of the spin systems are presented.

Research paper thumbnail of Zeroth order quantum coherences and preparation of pseudopure state in homonuclear dipolar coupling spin systems

Dynamics of zeroth order quantum coherences and preparation of the pseudopure states in homonucle... more Dynamics of zeroth order quantum coherences and preparation of the pseudopure states in homonuclear systems of dipolar coupling spins is closely examined. It has been shown an extreme important role of the non-diagonal part of zeroth order coherence in construction of the pseudopure state. Simulations of the preparation process of pseudopure states with the real molecular structures (a rectangular (1-chloro-4nitrobenzene molecule), a chain (hydroxyapatite molecule), a ring (benzene molecule), and a double ring (cyclopentane molecule)) open the way to experimental testing of the obtained results. multiple-quantum dynamics, pseudopure state

Research paper thumbnail of Anisotropy of transverse spin relaxation in H2O-D2O liquid entrapped in Nanocavities: application to studies of connective tissues

Hyperfine Interactions, 2021

The spin-spin relaxation in connective tissues is simulated using a model in which the tissue is ... more The spin-spin relaxation in connective tissues is simulated using a model in which the tissue is represented by a set of nanocavities containing H 2 O-D 2 O liquid. Collagen fibrils in connective tissues form ordered hierarchical long structures of hydrated nano-cavities with characteristic diameter from 1 nm to several tens of nanometers and length of about 100 nm. We consider influence of the restricted Brownian motion of molecules inside a nano-cavity on spin-spin relaxation. The analytical expression for the transverse time T 2 for H 2 O-D 2 O the liquid in contained a nanocavity was obtained. We show that the angular dependence of the transverse relaxation rate does not depend on the concentration of D 2 O. The theoretical results could explain the experimentally observed dependence of the degree of deuteration on the relaxation time T 2 . Accounting the orientation distribution of the nanocavities well agreement with the experimental dependence of the relaxation for articular cartilage on the deuteration degree was obtained.

Research paper thumbnail of Anisotropy of transverse and longitudinal relaxations in liquids entrapped in nano- and micro-cavities of a plant stem

Journal of Magnetic Resonance, 2021

We studied the anisotropy of 1H NMR spin-lattice and spin-spin relaxations in a fresh celery stem... more We studied the anisotropy of 1H NMR spin-lattice and spin-spin relaxations in a fresh celery stem experimentally and modeled the sample theoretically as the water-containing nano- and micro-cavities. The angular dependence of the spin-lattice and the spin-spin relaxation times was obtained, which clearly shows the presence of water-filled nano- and micro-cavities in the celery stem, which have elongated shapes and are related to non-spherical vascular cells in the stem. To explain the experimental data, we applied the relaxation theory developed by us and used previously to interpret similar effects in liquids in nanocavities located in biological tissues such as cartilages and tendons. Good agreement between the experimental data and theoretical results was obtained by adjusting the fitting parameters. The obtained values of standard deviations (0.33 for the mean polar angle and 0.1 for the mean azimuthal angle) indicate a noticeable ordering of the water-filled nano- and micro-cavities in the celery stem. Our approach allows the use of the NMR technique to experimentally determine the order parameters of the microscopic vascular structures in plants.

Research paper thumbnail of Determining the internal orientation, degree of ordering, and volume of elongated nanocavities by NMR: Application to studies of plant stem

Journal of Magnetic Resonance

Research paper thumbnail of Dynamics of Zeeman and dipolar states in the spin locking in a liquid entrapped in nano-cavities: Application to study of biological systems

Journal of Magnetic Resonance, 2021

We analyze the application of the spin locking method to study the spin dynamics and spin-lattice... more We analyze the application of the spin locking method to study the spin dynamics and spin-lattice relaxation of nuclear spins-1/2 in liquids or gases enclosed in a nano-cavity. Two cases are considered: when the amplitude of the radio-frequency field is much greater than the local field acting the nucleus and when the amplitude of the radio-frequency field is comparable or even less than the local field. In these cases, temperatures of two spin reservoirs, the Zeeman and dipole ones, change in different ways: in the first case, temperatures of the Zeeman and dipolar reservoirs reach the common value relatively quickly, and then turn to the lattice temperature; in the second case, at the beginning of the process, these temperatures are equal, and then turn to the lattice temperature with different relaxation times. Good agreement between the obtained theoretical results and the experimental data is achieved by fitting the parameters of the distribution of the orientation of nanocavities. The parameters of this distribution can be used to characterize the fine structure of biological samples, potentially enabling the detection of degradative changes in connective tissues.

Research paper thumbnail of Losses in Superconductors Under Non-Sinusoidal Currents and Magnetic Fields

IEEE Transactions on Applied Superconductivity, 2009

Study of AC losses in superconducting wires and tapes is usually restricted by consideration of a... more Study of AC losses in superconducting wires and tapes is usually restricted by consideration of applied sinusoidal currents and/or magnetic fields. However, currents in electric power systems contain a wide variety of harmonics. The currents become strongly non-sinusoidal at the operation of converters, non-linear reactors, and during transient and overload conditions. We report the results of the analysis of the influence of higher harmonics of the current and magnetic field on AC losses in superconducting slabs, strips and coated conductors. Analytical expressions are obtained in the framework of Bean's critical state model; the power law voltage-current characteristics are treated numerically. It is shown that the contribution of higher harmonics to AC losses in superconducting elements can be tens times larger than in normal metals and the 5% harmonic can increases the losses by up to 20%.

Research paper thumbnail of Spin-lattice relaxation in liquid entrapped in a nanocavity

Journal of Magnetic Resonance

We consider the spin lattice relaxation in bulk liquid and liquid entrapped in a nanocavity. The ... more We consider the spin lattice relaxation in bulk liquid and liquid entrapped in a nanocavity. The kinetic equation which describes the spin lattice relaxation is obtained by using the theory of the nonequilibrium state operator. A solution of the kinetic equation gives the quadrature expression for the relaxation time, T1. The calculated relaxation time agrees well with the experimental data. The spin-lattice relaxation time is calculated for nanocavities with a characteristic size much less than 700 nm, with the assumption that the spin-lattice relaxation mechanism is determined by nanocavity fluctuations. The resulting expression shows an explicit dependence of the relaxation time T1 on the volume, density of nuclear spins, and parameters of the cavity (shape and orientation relatively to the applied field). To compare with the experiment on the detection of the anisotropy of the relaxation time, we average the expression that describes the relaxation time over the orientation of the nanocavities relative to the applied magnetic field. The good agreement with the experimental data for fibril tissues was achieved by adjustment of few fitting parameters - the standard deviation, averaged fiber direction, and weight factors - which characterize the ordering of fibrils.

Research paper thumbnail of Berry's phase in the Floquet representation

Journal of Physics A: Mathematical and General, 1994

ABSTRACT By means of the Floquet theory the investigation of Berry's phase for the quantu... more ABSTRACT By means of the Floquet theory the investigation of Berry's phase for the quantum system with time-dependent periodic Hamiltonian is transformed into the study of a time-independent eigenvalue equation. An expression for the infinite-dimensional matrix is obtained describing the Berry's phase in terms of the Floquet state.

Research paper thumbnail of Nuclear spin-lattice relaxation via thermal vortex motion in superconductors

Physica C: Superconductivity, 1996

The theory of the growth of the nuclear magnetization in the presence of paramagnetic impurities ... more The theory of the growth of the nuclear magnetization in the presence of paramagnetic impurities and the absence of spin diffusion is extended to the nuclear spin-lattice relaxation in type-II superconductors in the mixed state. The results obtained can be used to determine the magnetic-field distribution and/or the dimensionality of the vortex lattice in conventional and high-temperature superconductors.

Research paper thumbnail of Multiple quantum NMR dynamics in pseudopure states

Journal of Physics: Condensed Matter, 2009

We investigate numerically the Multiple Quantum (MQ) NMR dynamics in systems of nuclear spins 1/2... more We investigate numerically the Multiple Quantum (MQ) NMR dynamics in systems of nuclear spins 1/2 coupled by the dipole-dipole interactions in the case of the pseudopure initial state. Simulations of the MQ NMR with the real molecular structures such as six dipolar-coupled proton spins of a benzene, hydroxyl proton chains in calcium hydroxyapatite and fluorine chains in calcium fluorapatite open the way to experimental NMR testing of the obtained results. It was found that multiple-spin correlations are created faster in such experiments than in the usual MQ NMR experiments and can be used for the investigation of many-spin dynamics of nuclear spins in solids

Research paper thumbnail of Stimulated wave of polarization in spin chains

Physical Review B, 2006

Stimulated wave of polarization, triggered by a flip of a single spin, presents a simple model of... more Stimulated wave of polarization, triggered by a flip of a single spin, presents a simple model of quantum amplification. Previously, it has been found that such wave can be excited in a 1D Ising chain with nearest-neighbor interactions, irradiated by a weak resonant transverse field. Here we explore models with more realistic Hamiltonians, in particular, with natural dipole-dipole interactions. Results of simulations for 1D spin chains and rings with up to nine spins are presented.

Research paper thumbnail of The pseudopure state in homonuclear dipolar coupling spin systems

Journal of Physics A: Mathematical and General, 2006

ABSTRACT Preparation of the pseudopure states in homonuclear systems of dipolar coupling spins is... more ABSTRACT Preparation of the pseudopure states in homonuclear systems of dipolar coupling spins is closely examined. An extremely important role of the non-diagonal part of zeroth-order coherence in the construction of the pseudopure state has been shown. Simulations of the preparation process of pseudopure states with the real molecular structures (a rectangular (1-chloro-4-nitrobenzene molecule), a chain (hydroxyapatite molecule), a ring (benzene molecule) and a double ring (cyclopentane molecule)) open the way to experimental NMR testing of the obtained results. The proposed method could be considered as a fruitful technology for quantum computation.