Gilbert Theory Research Articles

Symmetry and Nonlinearity of Spin Wave Resonance Excited by Focused Surface Acoustic Waves

AbstractThe use of a complex ferromagnetic system to manipulate GHz surface acoustic waves (SAWs) is a rich current topic under investigation, but the high‐power nonlinear regime is under‐explored. Focused SAWs are introduced, which provide a way to access this regime with modest equipment. The symmetry of the magneto‐acoustic interaction can be tuned by interdigitated transducer design which can introduce additional strain components. Here, the impact of focused acoustic waves versus standard unidirectional acoustic waves in significantly enhancing the magnon‐phonon coupling behavior is compared. Analytical simulation results based on the modified Landau–Lifshitz–Gilbert theory show good agreement with experimental findings. Nonlinear input power dependence of the transmission through the device is also reported. This experimental observation is supported by the micromagnetic simulation using mumax3 to model the nonlinear dependence. These results pave the way for extending the understanding and design of acoustic wave devices for the exploration of acoustically driven spin wave resonance physics.

Simulation of Gilbert theory for self-association in sedimentation velocity experiments: a guide to evaluate best fitting models.

There is a long tradition in the Biophysics community of using simulations as a means to understand macromolecular behavior in various physicochemical methods. This allows a rigorous means to interpret observations in terms of fundamental principles, including chemical equilibrium, reaction kinetics, transport processes and thermodynamics. Here we simulate data for the Gilbert Theory for self-association, a fundamental analytical ultracentrifuge (AUC) technique to understand the shape of sedimentation velocity reaction boundaries that involve reversible monomer-Nmer interactions. Simulating monomer-dimer through monomer-hexamer systems as a function of concentration about the equilibrium constant allows a visual means to differentiate reaction stoichiometry by determining end points and inflection positions. Including intermediates (eg A1-A2-A3-A4-A5-A6) in the simulations reveals the smoothing of the reaction boundary and the removal of sharp inflections between monomers and polymers. The addition of cooperativity restores sharp boundaries or peaks to the observation and allows more discrimination in the selection of possible fitting models. Thermodynamic nonideality adds additional features when applied across wide ranges of concentration that might be appropriate for high-concentration therapeutic monoclonal antibody (mAb) solutions. This presentation serves as a tutorial for using modern AUC analysis software like SEDANAL for selecting potential fitting models.

The Role of Social Safeness and Self-compassion in Mental Health Problems: A Model Based on Gilbert Theory of Emotion Regulation Systems

Objective: This study aimed to investigate the role of social safeness and self-compassion, as two essential components of Gilbert’s theory, in mental health. In this regard and based on theoretical foundations, the mediation model of the relationship between social safeness and mental health problems was examined through self-compassion as a mediator. Methods: A total of 344 students from the University of Bojnord, Bojnord City, Iran, in the 2019-2020 academic year were recruited using the cluster sampling method. They were responded to the social safeness and pleasure scale, self-compassion scale (short form), and depression, anxiety, and stress scale. The obtained data were analyzed using Structural Equation Modeling (SEM). Results: The mediation model showed a good fit (χ2⁄df: 1.77; RMSEA: 0.043; CFI: 0.99; GFI: 0.98; AGFI: 0.96; NFI: 0.98; TLI: 0.98). Beta coefficients indicate significant direct effect of social safeness on self-compassion (Beta=0.57; P≤0.001), significant direct effect of self-compassion on mental health problems (Beta=-0.75; P≤0.001), as well as a significant indirect effect of social safeness on mental health problems (Beta=-0.42; P≤0.001). Conclusion: Social safeness affects mental health problems (depression, anxiety, and stress) through self-compassion as a mediator. A high sense of social safeness protects against depression, anxiety, and stress through increasing self-compassion. However, low social safeness increases vulnerability to depression, anxiety, and stress by reducing self-compassion.

Gaussian process models—I. A framework for probabilistic continuous inverse theory

SUMMARYWe develop a theoretical framework for framing and solving probabilistic linear(ized) inverse problems in function spaces. This is built on the statistical theory of Gaussian Processes, and allows results to be obtained independent of any basis, avoiding any difficulties associated with the fidelity of representation that can be achieved. We show that the results of Backus–Gilbert theory can be fully understood within our framework, although there is not an exact equivalence due to fundamental differences of philosophy between the two approaches. Nevertheless, our work can be seen to unify several strands of linear inverse theory, and connects it to a large body of work in machine learning. We illustrate the application of our theory using a simple example, involving determination of Earth’s radial density structure.

Interplay of spin and mass superfluidity in antiferromagnetic spin-1 Bose-Einstein condensates and bicirculation vortices

The paper investigates the coexistence and interplay of spin and mass superfluidity in the antiferromagnetic spin-1 BEC. The hydrodynamical theory describes the spin degree of freedom by the equations similar to the Landau--Lifshitz--Gilbert theory for bipartite antiferromagnetic insulator. The variables in the spin space are two subspins with absolute value $\hbar/2$, which play the role of two sublattice spins in the antiferromagnetic insulators. As well as in bipartite antiferromagnetic insulators, in the antiferromagnetic spin-1 BEC there are two spin-wave modes, one is a gapless Goldstone mode, another is gapped. The Landau criterion shows that in limit of small total spin (two subspins are nearly antiparallel) instability of supercurrents starts from the gapped mode. In the opposite limit of large total spin (two subspins are nearly parallel) the gapless modes become unstable earlier than the gapped one. Mass and spin supercurrents decay via phase slips, when vortices cross streamlines of supercurrent. The vortices participating in phase slips are nonsingular bicirculation vortices. They are characterized by two topological charges, which are winding numbers describing circulations of two angles around the vortex axis. The winding numbers can be half-integer. A particular example of a half-integer vortex is a half-quantum vortex with the superfluid velocity circulation $h/2m$. But the superfluid velocity circulation is not a topological charge, and in general the quantum of this circulation can be continuously tuned from 0 to $h/2m$.

Alternating current electrohydrodynamics in microsystems: Pushing biomolecules and cells around on surfaces.

Electrohydrodynamics (EHD) deals with the fluid motion induced by an electric field. This phenomenon originally developed in physical science, and engineering is currently experiencing a renaissance in microfluidics. Investigations by Taylor on Gilbert's theory proposed in 1600 have evolved to include multiple contributions including the promising effects arising from electric field interactions with cells and particles to influence their behaviour on electrode surfaces. Theoretical modelling of electric fields in microsystems and the ability to determine shear forces have certainly reached an advanced state. The ability to deftly manipulate microscopic fluid flow in bulk fluid and at solid/liquid interfaces has enabled the controlled assembly, coagulation, or removal of microstructures, nanostructures, cells, and molecules on surfaces. Furthermore, the ability of electrohydrodynamics to generate fluid flow using surface shear forces generated within nanometers from the surface and their application in bioassays has led to recent advancements in biomolecule, vesicle and cellular detection across different length scales. With the integration of Alternating Current Electrohydrodynamics (AC-EHD) in cellular and molecular assays proving to be highly fruitful, challenges still remain with respect to understanding the discrepancies between each of the associated ac-induced fluid flow phenomena, extending their utility towards clinical diagnostic development, and utilising them in tandem as a standard tool for disease monitoring. In this regard, this article will review the history of electrohydrodynamics, followed by some of the recent developments in the field including a new dimension of electrohydrodynamics that deals with the utilization of surface shear forces for the manipulation of biological cells or molecules on electrode surfaces. Recent advances and challenges in the use of electrohydrodynamic forces such as dielectrophoresis and ac electrosmosis for the detection of biological analytes are also reviewed. Additionally, the fundamental mechanisms of fluid flow using electrohydrodynamics forces, which are still evolving, are reviewed. Challenges and future directions are discussed from the perspective of both fundamental understanding and potential applications of these nanoscaled shear forces in diagnostics.

Model for temperature-dependent magnetization of nanocrystalline materials

A magnetization model of nanocrystalline materials incorporating intragrain anisotropies, intergrain interactions, and texture effects has been extended to include the thermal fluctuations. The method relies on the stochastic Landau–Lifshitz–Gilbert theory of magnetization dynamics and permits to study the magnetic properties of nanocrystalline materials at arbitrary temperature below the Currie temperature. The model has been used to determine the intergrain exchange constant and grain boundary anisotropy constant of nanocrystalline Ni at 100 K and 298 K. It is found that the thermal fluctuations suppress the strength of the intergrain exchange coupling and also reduce the grain boundary anisotropy. In comparison with its value at 2 K, the interparticle exchange constant decreases by 16% and 42% and the grain boundary anisotropy constant decreases by 28% and 40% at 100 K and 298 K, respectively. An application of the model to study the grain size-dependent magnetization indicates that when the thermal activation energy is comparable to the free energy of grains, the decrease in the grain size leads to the decrease in the magnetic permeability and saturation magnetization. The mechanism by which the grain size influences the magnetic properties of nc–Ni is discussed.

Model design on calculations of microwave permeability and permittivity of Fe/SiO2 particles with core/shell structure

Fe/SiO2 particles with core/shell structure were prepared by coating silica on the surface of a commercial spherical carbonyl iron via the hydrolysis process of tetraethyl orthosilicate (TEOS). The electromagnetic performance of commercial carbonyl iron and as-prepared Fe/SiO2 particles was studied theoretically and experimentally. As predicted by the theoretical calculation based on the Bruggeman formula and the Landau–Lifshitz–Gilbert (LLG) theory, the insulating surface layer of silica was effective to reduce the permittivity parameters of pure carbonyl iron. The measured results showed good agreement with the theoretical prediction. Although there was a little decrease in the permeability of the Fe/SiO2 core/shell particles, a better impedance match especially at higher frequency range was obtained when used as a microwave absorber. The reflection loss (RL) curves show that the lowest reflection loss of Fe/Epoxy composite (−20.5GHz) was obtained corresponding to the frequency of 8.5GHz when the thickness of the absorber was 3mm. A different trend was observed in Fe/SiO2/Epoxy composite. The reflection loss value got lower by decreasing the thickness of absorbers. At the thickness of 2.2mm, a relative low reflection loss (−17GHz) corresponding to the frequency of 13.6GHz was obtained. Compared with the Fe/Epoxy composite, the improvement on shifting the reflection loss peak to higher frequency and on reducing the optimal thickness of absorbers was made by Fe/SiO2/Epoxy composite.

Joint Commitments and Individual Participation: Critical Reflections on Margaret Gilbert's Theory of Political Obligations

The widely accepted liberal paradigm that people are born free and the empirical fact that sometimes we feel or do have obligations to various groups we are members of rest quite uneasily together. The joint commitment that we may have in the latter case is the basis on which Margaret Gilbert develops quite plausible theory for legitimation of political obligations. However in her account the individual freedom seems forgone. In this paper I show this and several related problems of the actual contract theory and discuss a possible way to avoid them. I suggest that obligations to the group may be understood to arise not from mere belonging but from the actual participation in certain collective activities coupled with the ordinary meaning of that participation within the group. This solves the problem but only at the expense of considerably atenuation of the meaning of freedom. That is why I find my solution not entirely satisfactory and maintain that the actual contract theory remains at odds with freedom.

An algorithm to extract effective magnetic parameters of thin film with in-plane uniaxial magnetic anisotropy

The calculation of high frequency complex permeability of thin ferromagnetic film requires the measured values of its saturation magnetization, anisotropic magnetic field intensity, resistivity, and thickness. It is often observed that the calculated permeability using the Landau–Lifshitz–Gilbert (LLG) theory does not agree well with the measured permeability of thin film with in-plane uniaxial magnetic anisotropy, owing to the measured anisotropic magnetic field intensity, saturation magnetization, etc., are not effective values at high frequency. In this work, the Landau–Lifshitz ferromagnetic resonance model is modified to take the skin depth effect into consideration. In the comparison study, its calculated magnetic permeability curves (real and imaginary) agrees very well with those calculated from the LLG model. In addition, an algorithm process to extract effective magnetic parameters (saturation magnetization Ms, magnetic anisotropy field Ha, and damping factor α) has been developed. The algorithm process has been tested for the reported magnetic permeability curves of two magnetic films (Si/NiFe/FeCoB and CoZrRe). The extracted parameters are well agreed with those reported. It is also reported that the consideration of skin depth effect is necessary for samples with lower electrical resistivity.

A new perturbation method for determining the broadband complex permeability of magnetic thin films

In this paper, a new one-port microstrip line permeameter using the perturbation method is presented. A short-ended circuited microstrip line fixture was designed and implemented. Completely new analytical calculation formulas and a two-step measurement procedure were applied to deduce the complex permeability of the material in the frequency range from 100 MHz to 5 GHz. The measured results showed good agreement with the Landau–Lifchitz–Gilbert theory.

Broadband complex permeability characterization of magnetic thin films using shorted microstrip transmission-line perturbation

A brief review of the methods used for broadband complex permeability measurement of magnetic thin films up to microwave frequencies is given. In particular, the working principles of the transmission-line perturbation methods for the characterization of magnetic thin films are discussed, with emphasis on short-circuited planar transmission-line perturbation methods. The algorithms for calculating the complex permeability of magnetic thin films for short-circuited planar transmission-line perturbation methods are analyzed. A shorted microstrip line is designed and fabricated as a prototype measurement fixture. The structure of the microstrip fixture and the corresponding measurement procedure are discussed in detail. A piece of 340 nm thick FeTaN thin film deposited on Si substrate using sputtering method is characterized using the microstrip fixture. An improved technique for obtaining permeability by using a saturation magnetization field is demonstrated here, and the results fit well with the Landau–Lifchitz–Gilbert theory. Approaches to extending this method to other aspects in the investigation of magnetic thin film are also discussed.

Highly sensitive permeability measurements obtained by electrical impedance

We propose a highly sensitive method of obtaining permeability. Permeability was obtained from electrical impedance of strips by using wafer probe. The permeability of a CoNbZr strip was evaluated as a function of magnetic field intensity. Measured values approached those of the Landai–Lifshitz–Gilbert (LLG) theory with decreasing field intensity. The proposed method is better than the conventional shielded loop coil method when measuring permeability in a small area.

A note on digital filtering with the second moment norm

The linear inverse method developed by Backus and Gilbert (1968) relates model estimates to actual earth models by use of a resolving kernel. Seismic source wavelet deconvolution can be treated within the framework of the Backus and Gilbert (1968) inverse theory as presented in Oldenburg (1981) and Treitel and Lines (1982). The model of the Backus and Gilbert theory is the ground impulse response, the mapping kernel is the source wavelet, and the resolving kernel is the convolution between the source wavelet and the shaping filter. Backus and Gilbert formalism introduces several measures for the resolving kernel.

Generalized Huzinaga building-block equations for nonorthogonal electronic groups: Relation to the Adams–Gilbert theory

We show in this article that the Huzinaga building-block equations for many-electron systems, derived under the hypothesis of strong orthogonality among the system groups, can be also deduced as a particular case of the Adams–Gilbert formalism, in which intergroup overlapping is recognized from the outset. This viewpoint is more realistic because the strong orthogonality cannot be fully achieved in most practical cases due to basis-set truncation. Incomplete orthogonality leads to nonzero expectation values of the projection operators appearing in the Fock Hamiltonian (projection energy). This fact raises some conceptual problems since the projection energy has been used to interpret several important physical effects in recent investigations. The present work clarifies several practical aspects relative to the incomplete fulfillment of the strong-orthogonality hypothesis, in particular (a) the analytical relationship between the projection energy and the intergroup overlap energy involving weakly overlapping groups; (b) the required values for the projection constants in cases of incomplete orthogonality; and (c) how the effects of basis-set truncation can be analyzed unambiguously.

Rotation of magnetization in unison and langevin equations for a large spin

A single-domain ferromagnetic particle is represented as a large spin (model of rotation in unison) whose stochastic dynamics is derived from a spin-boson Hamiltonian. It is shown in the Markovian limit that thermal equilibrium exists provided that the fluctuation-dissipation theorem is supplemented by a symmetry constraint which for bilinear anisotropic and nonlinear (magnetoelastic) spin-bath coupling can only be satisfied in the underdamped limit. Only for bilinear isotropic coupling (Gilbert's theory) is it satisfied identically for arbitrary damping strength. Uniaxial and cubic symmetries are considered. For a model uniaxial crystal the thermal decay rate of M and the thermal enhancement of the macroscopic quantum tunneling rate are calculated for Gilbert and magnetoelastic dissipative couplings and compared. The effects of memory are discussed.

Chromatographic behaviour of reversibly associating macromolecules. Part 1.—Theoretical model

Block copolymers in selective precipitants form multimolecular micelles via closed association, which is characterized by an equilibrium between a unimer (molecularly dissolved copolymer) and micelles. A theoretical model is developed which accounts for: (i) relatively fast equilibration of the unimer between mobile and stationary phases, (ii) continuous perturbation and re-establishment of unimer ⇌ micelles equilibrium, and (iii) axial dispersion in the mobile phase during the passage of a solute through a column. This model describes quantitatively the behaviour of micellizing systems in size-exclusion chromatography. Chromatograms have been calculated for a wide range of association numbers and rates of association and dissociation. The results are compared with qualitative predictions of Coll's theory and Gilbert's theory of associating systems.

Size Exclusion Chromatography of Associating Systems. I. The Theoretical Model

Abstract Block copolymers in dilute solutions in selective solvents form micelles via closed association which is characterized by equilibrium between unimer and n-mer. A simple theoretical model has been proposed describing the behavior of such a system in the size exclusion chromatography (SEC). Chromatograms have been calculated varying association number and relative rates of association and dissociation. The results are compared with those of Coll's theory for SEC of surfactants and Gilbert's theory of associating systems.

Construction of non-negative resolving kernels in Backus--Gilbert theory

In linear Backus—Gilbert theory, resolving kernel approximations to delta distributions are linear combinations of data kernels which sometimes exhibit undesirable negative side lobes. For some problems, optimum delta-like data kernel combinations can be constructed which are everywhere non-negative. The square root of the resolving kernel is expanded in terms of a complete set of basis functions. Then, a standard measure of delta-ness (here the quadratic criterion) is minimized to find real expansion coefficients, subject to constraints of unimodularity and approximate equality of the square of the expansion to a linear combination of data kernels. The resulting non-linear Lagrange multipier problem is solved by a multidimensional Newton iteration. As an example, the method is applied to the gravitational edge-effect problem.

Reversible association of half-molecules of ovotransferrin in solution. Basis of co-operative binding to reticulocytes.

In the present paper, gel-filtration studies of diferric-ovotransferrin (Fe2OTf), the individual half-molecules of ovotransferrin (OTf) and equimolar mixtures of half-molecules have been interpreted according to the Gilbert theory as developed by Ackers & Thompson [(1965) Proc. Natl. Acad. Sci. U.S.A. 53, 342-349]. The data indicate that the half-molecules associate reversibly in solution and allow determination of a dissociation constant, Kd' = 8.0 (+/- 2.7) microM. Equilibrium binding studies have been performed using NH4Cl to block removal of iron from equimolar differentially iodine-labelled half-molecules (125I and 131I), in order to evaluate the binding of each to chick-embryo red blood cells under identical conditions. The amount of associated half-molecules over a range of concentrations has been calculated using the constant derived from the gel-filtration experiments described above. A computerized non-linear least-squares regression analysis of the data leads to determination of Kd* (the apparent dissociation constant for the interaction between OTf or half-molecules and the transferrin (Tf) receptors of chick-embryo red blood cells) and Bmax (binding at infinite free-ligand concentration) for the half-molecules similar to those found for Fe2OTf. Recent reports confirm that the two iron-binding domains of both OTf and human lactotransferrin associate non-covalently in solution. Our work shows that the isolated half-molecules of OTf are able to reassociate in solution and that this reassociation has functional significance by allowing the complex to be recognized by the Tf receptor.