MRI edge enhancement as a diffusive discord of spin phase structure

The enhancement of magnetic resonance image intensity near impermeable boundaries can be nicely described by a new approach where the diffusional spin echo attenuation is linked to the correlation function of molecular motion. In this method the spin phase structure created by the applied gradient is considered to be a composition of plane waves with the wave vectors representing feasible momentum states of a particle in confinement. The enhancement of edges on the magnetic resonance images (MRI) comes out as a discord of plane waves due to particle motion. It results from the average of the wave phase by using the cumulant expansion in the Gaussian approximation. The acquired analytical expression describes the MRI signal space distribution where the enhancement of edges depends on the intensity and the duration of gradient sequence as well as on the length of the mean squared particle displacement in restricted geometry. This new method works well with gradients of general waveform and is, therefore, suitable for imaging sequences where finite or even modulated gradients are usually used.     

Functional MRI Using Spin Lock Editing Preparation Pulses

A novel approach for detecting blood oxygenation level-dependent (BOLD) signals in the brain is investigated using spin locking (SL) pulses to selectively edit the effects of extravascular diffusion in field gradients from different sized vascular structures. We show that BOLD effects from diffusion amongst susceptibility gradients will contribute significantly not only to transverse relaxation rates (R₂* and R₂) but also to R_1ρ, the rate of longitudinal relaxation in the rotating frame. Similar to the ability of 180-degree pulses to refocus static dephasing effects in a spin echo, moderately strong SL pulses can also reduce contributions of diffusion in large-scale gradients and the choice of SL amplitude can be used to selectively emphasize smaller scale inhomogeneities (such as microvasculature) and to drastically reduce the influence of larger structures (such as veins). Moreover, measurements over a range of locking fields can be used to derive estimates of the spatial scales of intrinsic gradients. The method was used to detect BOLD activation in human visual cortex. Eight healthy young adults were imaged at 3 T using a single-slice, SL-prepped turbo spin echo (TSE) sequence with spin-lock amplitudes ω₁ = 80 Hz and 400 Hz, along with conventional T₂*-weighted and T₂-prepped sequences. The BOLD signal varied from 1.1 ± 0.4 % (ω₁ = 80 Hz) to 0.7 ± 0.2 % (at 400 Hz), whereas the T₂-weighted sequence measured 1.3 ± 0.3 % and the T₂* sequence measured 1.9 ± 0.3 %. This new R_1ρ functional contrast can be made selectively sensitive to intrinsic gradients of different spatial scales, thereby increasing the spatial specificity of the evoked response.     

Spin injection-driven switching in a magnetic junction

We investigate a perpendicular electric current passing through a “ferromagnetic nanojunction”, that is through some layered nanosized structure of spin-valve type, containing two ferromagnetic metallic layers. Spacer may be used between the metallic layers to prevent the rotation of the moving spin phases. Such an arrangement is typical for spin valves: one of the metallic layers has strongly pinned magnetic lattice and the other one has free magnetic lattice and free mobile spins. Further the conditions are derived to provide a very high nonequilibrium spin injection level. It appears that the so-called spin resistances of the constitutive layers should be in definite relations to each other. These relations lead to the situation where the spin injection becomes dominant and significantly suppresses the “ordinary” spin-transfer torque. As a result, the threshold current becomes lowered down to 2-3 and even more orders of magnitude.     

Pulsed ENDOR Spectroscopy at Large Thermal Spin Polarizations and the Absolute Sign of the Hyperfine Interaction

It is shown that in pulsed Mims-type ENDOR experiments performed at 95 GHz and 1.2 K the sign of the ENDOR signal can be positive, corresponding to an increase of the stimulated echo intensity, as well as negative, corresponding to a decrease of the stimulated echo. The positive “anomalous” sign is not observed at conventional EPR frequencies. It is explained that the effect arises through spin–lattice relaxation in the situation of large thermal spin polarizations and that it allows the determination of the absolute sign of the hyperfine interaction.     

X- and Q-Band Electron Spin Echo Study of Stochastic Molecular Librations of Spin Labels in Lipid Bilayers

Electron spin echo (ESE) of nitroxide spin labels allows detecting fast nanosecond stochastic restricted rotations (stochastic molecular librations), which is a common property of molecules in disordered media including biological systems. Under the typical experimental conditions, the anisotropic electron paramagnetic resonance (EPR) spectrum of a nitroxide is only partly excited by microwave pulses, which allows selecting an anisotropic contribution to the transverse spin relaxation by comparing echo decays at different spectral positions. On the other hand, for low-amplitude orientational motion, the excitation bandwidth is large enough to cover the range of spectral diffusion occurring during the echo formation. To verify that the two-pulse echo decay is indeed related to fast motions, the stimulated electron spin echo can be used. In addition, theory predicts an increase of the relaxation rates at higher microwave resonance frequency. To check this prediction, in the present work we performed a comparative study of ESE decays at microwave X- and Q-bands, for spin-labeled lipids in the gel phase of a 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) bilayer. A good agreement found between experimental data and computer simulation provides additional justification for the model of fast stochastic molecular librations.     

Spin structure of the nucleon—status and recent results

After the initial discovery of the so-called “spin crisis in the parton model” in the 1980s, a large set of polarization data in deep inelastic lepton-nucleon scattering was collected at labs like SLAC, DESY and CERN. More recently, new high precision data at large x and in the resonance region have come from experiments at Jefferson Lab. These data, in combination with the earlier ones, allow us to study in detail the polarized parton densities, the Q² dependence of various moments of spin structure functions, the duality between deep inelastic and resonance data, and the nucleon structure in the valence quark region. Together with complementary data from HERMES, RHIC and COMPASS, we can put new limits on the flavor decomposition and the gluon contribution to the nucleon spin. In this report, we provide an overview of our present knowledge of the nucleon spin structure and give an outlook on future experiments. We focus in particular on the spin structure functions g₁ and g₂ of the nucleon and their moments.     

Viscosity and Diffusion Effects at the Boundary Surface of Viscous Fluid and Thermoelastic Diffusive Solid Medium

This paper concentrates on the wave motion at the interface of viscous compressible fluid half-space and homogeneous isotropic, generalized thermoelastic diffusive half-space. The wave solutions in both the fluid and thermoelastic diffusive half-spaces have been investigated; and the complex dispersion equation of leaky Rayleigh wave motion have been derived. The phase velocity and attenuation coefficient of leaky Rayleigh waves have been computed from the complex dispersion equation by using the Muller's method. The amplitudes of displacements, temperature change and concentration have been obtained. The effects of viscosity and diffusion on phase velocity and attenuation coefficient of leaky Rayleigh waves motion for different theories of thermoelastic diffusion have been depicted graphically. The magnitude of heat and mass diffusion flux vectors for different theories of thermoelastic diffusion have also been computed and represented graphically.     

Self-Diffusion Imaging by Spin Echo in Earth's Magnetic Field

The NMR of the Earth's magnetic field is used for diffusion-weighted imaging of phantoms. Due to a weak Larmor field, care needs to be taken regarding the use of the usual high field assumption in calculating the effect of the applied inhomogeneous magnetic field. The usual definition of the magnetic field gradient must be replaced by a generalized formula valid when the strength of a nonuniform magnetic field and a Larmor field are comparable (J. Stepišnik,Z. Phys. Chem.190, 51–62 (1995)). It turns out that the expression for spin echo attenuation is identical to the well-known Torrey formula only when the applied nonuniform field has a proper symmetry. This kind of problem may occur in a strong Larmor field as well as when the slow diffusion rate of particles needs an extremely strong gradient to be applied. The measurements of the geomagnetic field NMR demonstrate the usefulness of the method for diffusion and flow-weighted imaging.     

Uniqueness,reciprocity theorem,and plane waves in thermoelastic diffusion with a fractional order derivative

In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractional order generalized thermoelastic diffusive medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in the homogeneous transversely isotropic thermoelastic diffusive medium with fractional order derivative is studied. For the two-dimensional problem, there exist a quasi-longitudinal wave, a quasi-transverse wave, a quasi-mass diffusion wave, and a quasi-thermal wave. From the obtained results, the different characteristics of waves, like phase velocity, attenuation coefficient, specific loss, and penetration depth, are computed numerically and presented graphically. Some special cases are also discussed.     

Tricriticality in generalized Schloegl models for autocatalysis: Lattice-gas realization with particle diffusion

We analyze lattice-gas reaction-diffusion models which include spontaneous annihilation, autocatalytic creation, and diffusion of particles, and which incorporate the particle creation mechanisms of both Schloegl’s first and second models. For fixed particle diffusion or hop rate, adjusting the relative strength of these creation mechanisms induces a crossover between continuous and discontinuous transitions to a “poisoned” vacuum state. Kinetic Monte Carlo simulations are performed to map out the corresponding tricritical line as a function of hop rate. An analysis is also provided of the tricritical “epidemic exponent” for the case of no hopping. The phase diagram is also recovered qualitatively by applying mean-field and pair-approximations to the exact hierarchical form of the master equation for these models.     

Background gradient suppression in pulsed gradient stimulated echo measurements

Pulsed gradient spin echo (PGSE) experiments can be used to measure the probability distribution of molecular displacements. In homogeneous samples this reports on the molecular diffusion coefficient, and in heterogeneous samples, such as porous media and biological tissue, such measurements provide information about the sample's morphology. In heterogeneous samples however background gradients are also present and prevent an accurate measurement of molecular displacements. The interference of time independent background gradients with the applied magnetic field gradients can be removed through the use of bipolar gradient pulses. However, when the background gradients are spatially non-uniform molecular diffusion introduces a temporal modulation of the background gradients. This defeats simple bipolar gradient suppression of background gradients in diffusion related measurements. Here we introduce a new method that requires the background gradients to be constant over coding intervals only. Since the coding intervals are typically at least an order of magnitude shorter than the storage time, this new method succeeds in suppressing cross-terms for a much wider range of heterogeneous samples.     

Spin hall effect in the presence of spin diffusion

Hirsch [Phys. Rev. Lett. 83, 1834 (1999)] recently proposed a spin Hall effect based on the anomalous scattering mechanism in the absence of spin-flip scattering. Since the anomalous scattering causes both anomalous currents and a finite spin-diffusion length, we derive the spin Hall effect in the presence of spin diffusion from a semiclassical Boltzmann equation. When the formulation is applied to certain metals and semiconductors, the magnitude of the spin Hall voltage due to the spin accumulation is found to be much larger than that of magnetic multilayers. An experiment is proposed to measure this spin Hall effect.     

Diffusion measurements using the nonlinear stimulated echo

The nonlinear stimulated echo that is generated by a sequence of three radiofrequency pulses, 90 degrees-tau(1)-90 degrees-tau(2)-45 degrees, in high magnetic fields (or at low temperatures) in the presence of pulsed or steady field gradients can be applied for measurements of the diffusion coefficient. Corresponding test experiments are reported. Steady gradients can be used without knowledge of the relaxation times. Remarkably the attenuation of the nonlinear stimulated echo by diffusion is substantially stronger than in the case of the ordinary stimulated echo.     

A novel “magnetic” field and its dual non-commutative phase space

In this Letter we have studied a new form of non-commutative (NC) phase space with an operatorial form of noncommutativity. A point particle in this space feels the effect of an interaction with an “internal  ” magnetic field, that is singular at a specific position θ⁻¹${\theta }^{\mathrm{-1}}$. By “internal” we mean that the effective magnetic fields depends essentially on the particle properties and modifies the symplectic structure. Here θ is the NC parameter and induces the coupling between the particle and the “internal” magnetic field. The magnetic moment of the particle is computed. Interaction with an external physical magnetic field reveals interesting features induced by the inherent fuzziness of the NC phase space: introduction of non-trivial structures into the charge and mass of the particle and possibility of the particle dynamics collapsing to a Hall type of motion. The dynamics is studied both from Lagrangian and symplectic (Hamiltonian) points of view. The canonical (Darboux) variables are also identified. We briefly comment, that the model presented here, can play interesting role in the context of (recently observed) real space Berry curvature in material systems.     

Spin diffusion in anisotropic Heisenberg chains: S≥1/2

In this paper, we investigate spin diffusion in Heisenberg chains with uniaxial nearest-neighbor interactions. The approach followed is based on an analysis of the infinite-temperature longitudinal spin density and spin current correlation functions. For S=1/2, exact results are presented for the time-dependent correlation functions in the XY limit. Away from this limit, the second and fourth moments of the Fourier transform of the spin density correlation function provide information about spin dynamics for arbitrary values of the spin. The moments are used in an assessment of the accuracy of the Gaussian approximation for the spin diffusion constant for S=1/2. The general behavior of the Gaussian approximation when S>1/2 is discussed, and numerical results for the spin diffusion constant are presented for S=1/2, 1, 3/2, 2 and in the classical limit. A moment-based criterion for the boundary in reciprocal space between diffusive and non-diffusive dynamics that applies to arbitrary values of the spin is presented.     

Spin echo formation in the presence of stochastic dynamics

Spin echo formation in magnetic field gradients in the presence of fast stochastic motion is studied for hyperpolarized 3He gas at different diffusivities. The fast translational motion leads to frequency shifts already during echo formation, which can be described analytically for a linear gradient. Despite complete signal loss at the position of the spin echo itself, considerable intensity can be preserved at an earlier time (sqrt[2]tau rather than 2tau, where tau is the pulse delay). Hence, the phenomenon is designated as a pseudo spin echo.     

Relation of self-diffusion and the topological structure of flexible polymers as studied by NMR

A general approach to deriving formulas for calculating the diffusion attenuation of spin echo decay signal is developed and applied to obtaining data on random processes in linear and crosslinked polymers with different topological structures. The analysis explains the experimentally observed anomalous diffusion in polymer networks.     

Phase diagram of an Ising model with competitive interactions on a Husimi tree and its disordered counterpart

We consider an Ising competitive model defined over a triangular Husimi tree where loops, responsible for an explicit frustration, are even allowed. We first analyze the phase diagram of the model with fixed couplings in which a “gas of noninteracting dimers (or spin liquid) — ferro or antiferromagnetic ordered state” zero temperature transition is recognized in the frustrated regions. Then we introduce the disorder for studying the spin glass version of the model: the triangular ±J model. We find out that, for any finite value of the averaged couplings, the model exhibits always a finite temperature phase transition even in the frustrated regions, where the transition turns out to be a glassy transition. The analysis of the random model is done by applying a recently proposed method which allows us to derive the critical surface of a random model through a mapping with a corresponding nonrandom model.     

Spin — lattice relaxation in chlorofluorocarbon liquids

We have used the spin — echo method to measure spin — lattice relaxation times in liquid chlorofluorocarbons over a wide range of temperatures, frequencies, and molecular weights. Analysis of the experimental data shows that to determine the kinetic parameters of viscous liquids it is necessary to use the theory of nuclear magnetic relaxation by translational diffusion. We describe a method for the computer calculation of these parameters and discuss the results.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 46–51, March, 1976.     

Spin waves in cold gases with nondegenerate levels

The existence of spin waves of a new type is predicted for ultracold paramagnetic gases with nondegenerate energy levels. The waves are generated by creating a nonequilibrium population in the absence of external polarization and are damped not only by diffusion, but also by a previously ignored mechanism due to level splitting. Theoretical calculations are in fair agreement with experimental observations of spin waves in magnetically trapped clouds of rubidium atoms.