On the other hand, the black solid curves fitting the long time intervals in the Fig. 4 may be representative of the Abrikosov dynamics. The Abrikosov dynamics can be characterized by the penetration of vortices into the superconducting platelets in the form of intragrain vortices (Abrikosov vortices), with the subsequent pinning by the Y211 particles dispersed into the grains. This mechanism practically dominates the **relaxation** process, as can be seen in the three measurements shown in the Fig.4. The two **magnetic** flux dynamics are indicated in the Fig. 4a. More results are presented in the Fig. 5 for different experimental conditions, corroborating the results presented in the Figs. 3 and 4. The splitting of the **magnetic** **relaxation** in two components can be clearly observed for both samples, independent on the cooling rate and the **magnetic** field employed, configuring the different **magnetic** flux dynamics proposed, as indicated in the Fig. 5b.

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The samples were also investigated in a SQUID magnetometer in the conventional ZFC/FC manner, in which a sample is cooled under zero applied field, heated again in an applied field, cooled again with this field still applied and reheated again. This method highlights any irreversibility in the system at lower temperatures. For a bulk ferromagnet, a ZFC/FC plot shows only a little splitting and a slightly decreasing FC component described by the Brillouin law. In a superparamagnet, a significant splitting will be seen and also a peak in the ZFC component at Tg, followed at higher temperature by coincidence of the ZFC and FC components and a steady reduction in the magnetisation, as moments fluctuate faster than the measurement time of the equipment. Below 7h, there is a gradual realignment o f moments until they are all aligned with the applied field. Above 7b the **magnetic** moments start fluctuating and are lost to the sensors, since they appear paramagnetic. This means that the magnetisation rises up to a peak due to moments aligning themselves more readily with the applied field (due to thermal effects), but then starting to fluctuate in spite o f the field. M will never go to zero, since the applied field is high enough to cause a significant non-relaxing component M^r (see chapter 2).

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The goal of this study was to measure T1 and T2 **relaxation** times, as well as PD values, of normal structures included in nor- mal spine MR imaging (CSF, spinal cord, healthy-versus-desic- cated intervertebral disc, and vertebral body) using Synthetic MRI (SyMRI) 8.0 software (SyntheticMR) (this method has already been used for quantifying **relaxation** times in the brain, but, as far as we know, it has not been used in the spinal region). Further- more, we aimed to compare our values with those found in the literature from studies using relaxometry.

spin-lattice **relaxation** times are much longer than those found experimentally. The interaction of the **magnetic** dipoles in suoh a lattice due to the thermal vibrations in the lattice le ds to spin- lattice **relaxation** times T^ of the order of 10^ seconds at room temperature. This is the prediction from the theory of Waller 1932 for paramagnetic **relaxation*** adapted to the nuclear problem. As the values of T^ found for suoh crystals are of the order of 1 second the discrepancy la too large to hope for agreement by modiflaationa of the Waller theory. Instead two theories depending on different spin - lattice **relaxation** mechanisms have been proposed. The first of these* due principally to Bloemborgen 1 9L&» applies to all nuclei of spin j ~ £ while the second* due to Fount 1950 and Van Xranendonk 1954 applies to

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it is possible to reformulate the quantum-mechanical stochastic spin dynamics as an essentially classical prob- lem. We have derived the phase space Langevin equa- tion for a spin of arbitrary size S placed in a uniform **magnetic** ﬁeld in the weak spin-bath coupling limit. The form of the Langevin equation is, however, quiet general, hence it also holds for phase space master equations of the form of eq. (6) with drift and diﬀusion coeﬃcients depend- ing explicitly on time [8,9,14,15]. We emphasize, however, that the Langevin equation is written down from a priori knowledge of the master equation whereas in the classical case the Langevin equations are written down indepen- dently of the Fokker-Planck equation and the results of the two methods coincide entirely due to the Gaussian white noise properties of the random ﬁeld. We reiterate that the density matrix, phase space master equation and Langevin equation treatments are completely equivalent and yield the same results [10]. However, the Langevin equation has, in our opinion, the advantage that it both provides a basis for numerical simulation of the quan- tum **relaxation** processes and also allows one to evalu- ate the observables in the familiar classical manner. We remark that the present problem constitutes the simplest example of the phase space method for spins because the evolution equation is merely the Fokker-Planck equation with time independent drift and diﬀusion coeﬃcients. This would not be true in general, e.g., for **relaxation** in mixed magnetocrystalline anisotropy and external ﬁeld poten- tials, e.g., for a uniaxial paramagnet subjected to a dc **magnetic** ﬁeld. Here, the phase spase evolution equation can also be presented in the form of a generalized Fokker- Planck equation, however, it has a much more complicated form, where the drift and diﬀusion coeﬃcients are diﬀer- ential operators [34,35]. Nevertheless, the corresponding Langevin equation can also be derived in this case just in quantum optics, where the drift and diﬀusion coeﬃcients of the generalized Fokker-Planck equation of the laser are also diﬀerential operators [36]. Furthermore, the Langevin method may also be extended to non-axially symmetric spin systems in order to include spin size eﬀects in impor- tant **magnetic** **relaxation** problems such as the reversal time of the magnetization, switching and hysteresis curves, etc. Thus, it will be possible to evaluate the tempera- ture dependence of the switching ﬁelds and corresponding hysteresis loops via obvious spin size corrected generaliza- tions of the known classical methods used in the analysis of the classical spin dynamics.

The **magnetic** **relaxation** of single-domain ferromagnetic particles with cubic **magnetic** anisotropy is treated by averaging the Gilbert-Langevin equation for an individual particle, so that the system of linear differential- recurrence relations for the appropriate equilibrium correlation functions is derived without recourse to the Fokker-Planck equation. The solution of this system ~ in terms of matrix continued fractions ! is determined and the longitudinal **relaxation** time and spectrum of the complex **magnetic** susceptibility are evaluated. It is shown that in contrast to particles with uniaxial anisotropy, there is an inherent geometric dependence of the complex susceptibility and the **relaxation** time on the damping parameter arising from coupling of longitudinal and transverse **relaxation** modes. @ S0163-1829 ~ 98 ! 06829-5 #

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The applications of the research described in this report can be found in in vitro sens- ing and immunoassays, which cannot be accomplished with radioactive materials. The focus of this research is on **magnetic** **relaxation** behaviour of superparamagnetic nanopar- ticles. **Relaxation** is defined as the return or adjustment to equilibrium after a change of the environment, in this case an external **magnetic** field. The **relaxation** behaviour is determined by the characteristics of the particles and their environment, for example the material, size, shape, temperature and medium. Measurement of the **relaxation** behaviour reveals changes in one of these parameters. **Relaxation** measurements can therefore be used to identify the viscosity of body fluids or to monitor **magnetic** particles as they travel through areas with different fluids viscosities. Another application of **relaxation** measure- ment involves biomarkers, attached to the particles, that bind with specific substances. The particle size increases when the substance is bonded to the biomarker, which leads to a change of the **relaxation** behaviour. This indicates the presence of the specific substance. In this research a model is developed that describes the **relaxation** behaviour of various particles, so optimum particle dimensions can be found. Special attention is paid to the shape of the particles. Cylindrical superparamagnetic particles are expected to be bene- ficial over spherical particles due to their shape anisotropy [4]. Therefore, these particles are described in separate models.

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Sensitive and quantitative measurements of clinically relevant protein biomarkers, pathogens and cells in biological samples would be invaluable for disease diagnosis, monitoring of ma- lignancy, and for evaluating therapy efficacy. Biosensing strategies using **magnetic** nanoparticles (MNPs) have recently received considerable attention, since they offer unique advantages over traditional detection methods. Specifically, because biological samples have negligible **magnetic** background, MNPs can be used to obtain highly sensitive measurements in minimally processed samples. This review focuses on the use of MNPs for in vitro detection of cellular biomarkers based on nuclear **magnetic** resonance (NMR) effects. This detection platform, termed diagnostic **magnetic** resonance (DMR), exploits MNPs as proximity sensors to modulate the spin-spin **relaxation** time of water molecules surrounding the molecular- ly-targeted nanoparticles. With new developments such as more effective MNP biosensors, advanced conjugational strategies, and highly sensitive miniaturized NMR systems, the DMR detection capabilities have been considerably improved. These developments have also ena- bled parallel and rapid measurements from small sample volumes and on a wide range of targets, including whole cells, proteins, DNA/mRNA, metabolites, drugs, viruses and bacteria. The DMR platform thus makes a robust and easy-to-use sensor system with broad applica- tions in biomedicine, as well as clinical utility in point-of-care settings.

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The stability of the fluid against sedimentation is deci- ded collectively by competing interactions [1, 3, 17, 18] such as van der waals interactions, dipolar interactions, viscous force of the carrier liquid, and the electrostatic and steric repulsion of the surfactant. Surfacted ferrofluid have a long chain of organic molecule around the surface and mainly, steric repulsion provides stabilization. In ionic fluids, the electrostatic repulsion provides stabilization. Hence, the pH of such fluids may vary considerably (from 3 to 9) from basic to acidic depending on the treatment of the nanoparticles after precipitation. Citric acid, a bio- compatible surfactant, presents both electrostatic and steric effects and could easily get conjugated to iron oxide par- ticles. Iron oxide is most recommended because of its higher magnetization values, lesser toxicity [19] and the ease of metabolism by the liver. In the present study, we report the synthesis of highly stable water-based iron oxide fluid with narrow particle size distribution at neutral pH, and the evaluation of **magnetic** properties for hyperthermia application. The cell viability test conducted with these fluids on He La cells was promising (not included). To study the **relaxation** of the fluid in an external **magnetic** field, the magneto-optic linear dichroism measurement is presented. The power loss spectrum of these nanoparticles in an external alternating **magnetic** field is simulated to investigate the possibility of applying in AC **magnetic** heating.

It can be found from Fig. 8(a) that the two curves coincide when the frequency of driving signal is low, which proves that there is no change of **magnetic** ﬁeld or phase shift. From the comparison with Figs. 8(b), (c) and (d), it can be seen that with the increase of driving signal frequency, the **magnetic** ﬁeld amplitude decreases, and the phase shift increases, indicating that high frequency driving signal causes the change of **magnetic** ﬁeld. The higher the frequency is, the more signiﬁcant the change will be.

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Parnell et al. (1997) proved that the **magnetic** field locally about a non-potential 3D null point, i.e. the linear field about a non-potential null, produces a Lorentz force that cannot be bal- anced by a plasma pressure force. So there are no static equi- librium models of linear non-potential or force-free nulls. This means that in 3D, the **relaxation** towards an equilibrium mag- netic field very close to a **magnetic** null point has the same choices that a 2D linear null has, i.e., i) to evolve towards a potential null or ii) to develop a current singularity (current accumulation) at the null. Klapper (1997) proves analytically that in 2D, in the absence of plasma, the collapse of an X-type null results in the current building up at the null forming an infinite-time singularity. Numerical experiments of null collapse in non-zero beta plasmas show that an infinite-time singularity is still found (Craig & Litvinenko 2005; Pontin & Craig 2005; Fuentes-Fern´andez et al. 2011).

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and Laws [4]. Green and Lindsay [5] obtained another version of the constitutive equations. These equations were also obtained independently and more explicitly by Suhubi [6]. This theory contains two constants that act as **relaxation** times and modify all the equations of the coupled theory, not only the heat equation. The classical Fourier’s law of heat conduction is not violated if the medium under consideration has a center of symmetry.

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In this work we set a theoretical model for the calcula- tion of electronic **relaxation** rates in the QCL active region in a strong **magnetic** field, due to optical- and acoustic-phonon- induced transitions between Landau levels, which enables one to find the electron distribution over the states of the system by solving the full set of rate equations describing the transitions between levels, and eventually determine the op- tical gain. Calculations are performed for a GaAs/ Al x Ga 1−x As QCL structure designed to emit in the mid-IR

The values β=0=λ correspond to the flow of viscous fluid. Influence of **magnetic** parameter M on temperature field is analyzed in Fig.9. From this figure we examine that the temperature of hydromagnetic flow (M>0) is higher in comparison to hydrodynamic case (M=0). The Lorentz force appeared in hydromagnetic flow due to presence of **magnetic** parameter. The Lorentz force is stronger corresponding to larger **magnetic** parameter due to which higher temperature and thicker thermal boundary layer thickness are noticed in Fig. 7. Fig. 8 elucidates that the larger values of thermal radiation parameter correspond to higher temperature and thicker thermal boundary layer thickness. Physically, the fluid absorbs more heat when we give rise to thermal radiation parameter due to which both temperature and its associated boundary layer thickness are enhanced. From Fig. 9, we investigated that the temperature and thermal boundary layer thickness are lower for smaller values of thermal radiation parameter and corresponds to the case when thermal radiation is not present. When thermal heat radiation parameter is increased, more heat is produced due to which temperature and boundary layer thickness is higher. It is found that an increase in constant of fractional second grade fluid results in the decrease of velocity profile for the case of fractional second grade fluid. But we noticed that velocity remains unchanged for the case of second grade fluid. The variation of heat transfer coefficient has been presented in Fig. 6. It is interesting to note that the absolute value of heat transfer coefficient increases with an increase in β and φ. It is noticed that the nature of heat transfer is oscillatory. This is accordance with the physical expectation due to oscillatory nature of the tube wall. Fig. 7presents the change in temperature field

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T2 also includes the loss of phase coherence due to field inhomogeneities and susceptibility effects. The degree to which these time constants determine signal intensity in an MR image depend on the technical parameters that are used for image acquisition [1,2]. In clinical MR imaging, all three time constants represent characteristic **magnetic** properties of a given tissue [3], and changes from their normal values can be used to identify pathological states of that tissue. Examples for recent research efforts include investigations into the **relaxation** behavior of human brain in patients with multiple sclerosis [4,5], studies of T1 and T2* changes

The integral **relaxation** time, because it is the area under the curve of the decay of the magnetization, is a **relaxation** time which provides a measure of the relative contributions of all the decay modes of the system ~ both long and short lived ! . In measurements of the reversal of the magnetization, however, we are concerned only with the longest lived ~ Ne´el ! mode. In high frequency measurements such as those of the complex susceptibility, the integral **relaxation** time rather than the Ne´el time should be used, 3 since at high frequencies, the contribution of the fast modes is significant. In order to cal- culate the smallest nonvanishing eigenvalue ~ which is essen- tially the reciprocal of the mean first passage time ! , it is first necessary ~ as in Ref. 12 ! to represent the Fokker-Planck equation in Eq. ~ 6 ! as a differential recurrence relation which is then converted to a first order matrix differential equation with constant coefficients. The smallest nonvanishing eigen-

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Co is incorporated within the superconducting Fe arsenide planes, and therefore one would naively expect it to act as a quite effective point pinning center for vortices. This result is particularly difﬁcult to understand if one considers that F − is incorporated within the nearly electronically inert rare-earth oxide layer having an ionic radius in the order of ∼1 ˚ A, thus being just about 15% larger than the ionic radius of Co + 2 which in addition is expected to be nearly **magnetic**. Another surprising result is the large anisotropy (nearly one order of magnitude) between the values of U 0 for ﬁelds applied

Relativistic ab initio calculations were performed using the CASPT2/RASSI-SO 35 method as implemented in the MOLCAS 7.8 package. 36 This relativistic quantum-chemistry approach has proven suitable to analyse the **magnetic** anisotropy and direction of the easy axis of magnetization (EAM) of lantha- nide ions. 37 The atomic positions were extracted from the X-ray crystal structure. The cluster model for complex (1) includes the studied Nd ion, its ligands, 5 furoate molecules and two waters, and the closest C 3 H 7 NO moiety. The model

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We study the electron spin resonance (ESR) line width for localized moments within the frame- work of the Kondo lattice model. An ESR signal for an impurity can only be observed if the Kondo temperature is sufficiently small. On the other hand, for the Kondo lattice, short-range ferromag- netic correlations (FM) between the localized spins are necessary to obtain an observable signal. The spin **relaxation** rate (line width) is inversely proportional to the static **magnetic** susceptibility. The FM enhance the susceptibility and hence reduce the line width. For most of the heavy fermion systems displaying an ESR signal the FM arise in the ab-plane from the strong lattice anisotropy. An ESR signal was observed in the cubic heavy fermion compound CeB 6 which has a Γ 8 ground-

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O. Abou et al (1982) succeeded in simplifying the rate equations due to Richards' (1978). These equations have a simple form and can be used without the need for substantial numerical work, hence simply allow appreciation of the effect of paramagnetic ions on the **relaxation** rates. This model although simple does not have the versatility of that of Richards', since it deals with the general c a s e of the transferred hyperfine interaction. The model assumes that the diffusing ions need not feel a continuous range of local fields but o n l y a few should be sufficient, especially when dealing with fast ion conductors. Assuming three types of local fields; zero and + 5/Y referred to as [11, [2J and [31. When the diffusing ion is far from the impurity, local field [11 is assumed, [21 and [31 refer to spin up and down respectively. 6 is the interaction strength which is taken as the transferred hyperfine constant and Y is the nuclear gyromagnetic ratio.

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