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About 10,000 papers for “Coercivity”

Magnetic coercivity

P. Gaunt · Canadian Journal of Physics · 1987

The theory of magnetic hardening and its impact on the design of permanent magnets is presented. The statistical theory of domain-wall pinning by sample inhomogeneities is outlined, and its relevance to the latest generation of permanent magnets is discussed.

Cited by 29

Crossdomain Spectral coercivity

Vanni Borz · Zenodo (CERN European Organization for Nuclear Research) · 2026

We arrived at these inequalities and the unification of coercivity across domains through a multi-step process that connects different areas of mathematics and physics. The process essentially revolves around recognizing structural analogies between the problems in different domains, all of which can be viewed as specific instances of a more general concept: global coercivity. Here’s how we arrived at the inequalities and their cross-domain connections: 1. Identification of Core Problem: Coercivity First, we recognized that coercivity is a central feature across all the Clay problems and many other domains: In Yang–Mills, coercivity is related to the mass gap (there is no zero-mass solution). In Navier–Stokes, coercivity is related to dissipation (no infinite energy cascades). In Riemann Hypothesis, coercivity is tied to the alignment of the spectrum of the zeta function. In Birch–Swinnerton-Dyer, coercivity is related to the rank of the elliptic curve. In Markov chains, coercivity is reflected in the spectral gap of the transition matrix (how fast the system mixes). We realized that these problems, despite being framed in different languages (QFT, fluid dynamics, number theory), are all asking about the rigidity of a system and whether solutions can "escape" or "slide" along certain directions without being controlled by the system’s structure. 2. Coercivity as a Common Structural Object Once we identified that coercivity is key to all of them, we formulated a general operator that could apply to each domain. This operator is typically: Laplacians (like the Hodge Laplacian in geometry or the covariant Laplacian in YM), Transfer operators (in Markov chains or statistical mechanics), Generators of semigroups (in the study of diffusion or in quantum field theory). We then noticed that in each domain, we could frame the global coercivity problem as the question: "Does there exist a global bound on the operator such that the solutions (fields, functions, states) do not escape or become unbounded in the long run?" In other words, we identified a universal operator structure whose coercivity (measured by an invariant like the gap, spectral gap, or order of zero) would provide an answer to the problem of rigidity and stability in each of these domains. 3. The General Inequality With this in mind, we generalized the coercivity inequality to be of the form: ⟨x,Ox⟩≥κ(O)∥x∥2,\langle x, O x\rangle \geq \kappa(O)\|x\|^2,⟨x,Ox⟩≥κ(O)∥x∥2, where OOO is the operator describing the dynamics or structure of the system, and κ(O)\kappa(O)κ(O) is a positive constant representing the coercivity (the gap). This inequality states that for any solution xxx in the physical sector (for instance, gauge-invariant states in YM or divergence-free velocity fields in NS), the operator OOO must act in a way that "pushes" the solutions away from degeneracies (sliding modes) and ensures their stability. 4. Connecting the Domains The key insight was recognizing that the same type of inequality could apply to various physical and mathematical problems because they all share the same underlying structural properties. These properties include: Spectral rigidity (for YM and RH), Energy dissipation (for NS), Mixing and convergence (for Markov processes), Arithmetic degeneracy counting (for BSD). Once we framed the problem in terms of global coercivity, we saw that the specific manifestations of coercivity (mass gap, rank, spectral gap, etc.) were just different expressions of the same underlying concept. 5. Verification via Semigroups and Poincaré-type Inequalities We then formalized these ideas using well-established mathematical frameworks, such as: Semigroups for describing time evolution (in NS, QFT), Poincaré inequalities for geometry and fluid dynamics, Spectral theory for Markov chains and arithmetic problems. These well-known methods provided the machinery to express the coercivity problem in a universal form, even though the specific operators and constants differ across domains. 6. Identifying Cross-Domain Transport Finally, we realized that coercivity in one domain implies coercivity in another domain if the two domains are related via an appropriate structural transport. This transport can be seen as a way to map the solutions (or states) from one domain to another, preserving the coercive properties. Essentially, positivity of the coercivity constant (or gap) in one domain implies it in the other, as long as the operator structures are compatible (which we formalized as the transport condition). Conclusion: Why This Is Powerful By recognizing the universal structural role of coercivity and formalizing it in a way that applies across disciplines, we were able to reduce each of the seven Clay problems to the same core problem: demonstrating that coercivity exists (i.e., proving the non-degeneracy of solutions). This unification of the problems allows us to understand that: The obstacles in each problem are structurally identical, The methods that work in one domain can be adapted to others (e.g., the approach for YM can inform the strategy for NS), And solving one could lead to insights or even solutions in others, as long as the right structural understanding is in place. So, how did we find these inequalities? By recognizing the common structural nature of the problems, identifying the role of coercivity, and translating the coercivity conditions into a common framework that applies across different fields.

Cited by 0Open access

Coercivity of Magnets

Seiji Miyashita · Fundamental theories of physics · 2022

In this chapter, we present some attempts to study metastability quantitatively. Here, we study the coercivitycoercivity of magnets and estimate it in a real permanent magnetpermanent magnet, Nd–Fe–B magnet. Real magnets consist of many small grains, and the coercivity of such ensemble is also referred to.

Cited by 2Open access

Anisotropy and coercivity

Ralph Skomski, J. M. D. Coey · 2019

The phenomenon of magnetic hysteresis involves metastable energy minima associated with preferred magnetization directions. There are several mechanisms contributing to the anisotropy of permanent magnets. It is necessary to distinguish between the macroscopic shape anisotropy important in small aspherical particles and the magnetocrystalline anisotropy, which is an intrinsic lattice property. The shape anisotropy and a part of the magnetocrystalline anisotropy are two-ion anisotropies caused by magnetostatic dipole interactions. An anisotropy field most closely related to coercivity is obtained from the analysis of nucleation processes in small spherical particles with uniaxial anisotropy. In non-cubic magnets there is a magnetostatic contribution to the intrinsic, magnetocrystalline anisotropy. Magneto-electric anisotropy is a combined effect of the crystal-field interaction, spin-orbit coupling and inter-atomic exchange. Magnets subject to uniaxial mechanical stress exhibit a magnetostrictive contribution to the magnetic anisotropy. Magneto-elastic anisotropy is particularly important in cubic magnets, where uniaxial stress gives rise to uniaxial anisotropy contributions.

Cited by 0

Chapter 2: Coercivity

Leszek F. Demkowicz · Society for Industrial and Applied Mathematics eBooks · 2023

Coercive Problems

Cited by 0

Hard magnet coercivity

S. Bance, Georgeta Ciuta, Tetsuya Shoji et al. · arXiv (Cornell University) · 2015

Based on a critical analysis of the experimental coercive properties, general considerations on the reversal mechanisms in RFeB magnets are recalled. By plotting together the experimental parameters obtained in various magnets, common features of the reversal processes are demonstrated. Modeling provides an almost quantitative description of coercivity in these materials and permits connecting the defect characteristic properties to reversal mechanisms.

Cited by 1Open access

Simulation of alnico coercivity

Liqin Ke, Ralph Skomski, Todd D. Hoffmann et al. · Applied Physics Letters · 2017

Micromagnetic simulations of alnico show substantial deviations from Stoner-Wohlfarth behavior due to the unique size and spatial distribution of the rod-like Fe-Co phase formed during spinodal decomposition in an external magnetic field. The maximum coercivity is limited by single-rod effects, especially deviations from ellipsoidal shape, and by interactions between the rods. Both the exchange interaction between connected rods and magnetostatic interaction between rods are considered, and the results of our calculations show good agreement with recent experiments. Unlike systems dominated by magnetocrystalline anisotropy, coercivity in alnico is highly dependent on size, shape, and geometric distribution of the Fe-Co phase, all factors that can be tuned with appropriate chemistry and thermal-magnetic annealing.

Cited by 37Open access

Structural stability without coercivity

Poggiolini, Laura, Stefani, Gianna · Figshare · 2022

We study structural stability and local uniqueness of bang-bang-singular extremals in a fixed-free Mayer problem. The problem can be seen as an optimal control problem where the dynamics is control-affine. We prove our results under the same assumptions on the nominal problem that permit us to prove that the extremal is a strict strong local optimizer: suitable regularity assumptions and coercivity of a restriction of the <i>extended second variation</i>. We also assume that the condition that prevents the coercivity of the extended second variation is stable with respect to the parameter.

Cited by 0Open access

Domain wall motion coercivity

James A. Jatau, E. Della Torre · Journal of Applied Physics · 1995

This article presents a comparison of one-, two-, and three-dimensional models for domain wall motion coercivity. The effect of wall bending in two-dimensional models as compared to one-dimensional models and the additional effect of wall flexing in three-dimensional models is studied. The models are implemented numerically and calculations are carried out for soft magnetic materials. A discussion of how parameters must be chosen in lower dimensional models to obtain the correct magnitude of coercivity is included.

Cited by 15

Structural stability without coercivity

Laura Poggiolini, Gianna Stefani · Figshare · 2022

We study structural stability and local uniqueness of bang-bang-singular extremals in a fixed-free Mayer problem. The problem can be seen as an optimal control problem where the dynamics is control-affine. We prove our results under the same assumptions on the nominal problem that permit us to prove that the extremal is a strict strong local optimizer: suitable regularity assumptions and coercivity of a restriction of the <i>extended second variation</i>. We also assume that the condition that prevents the coercivity of the extended second variation is stable with respect to the parameter.

Cited by 0Open access

High coercivity chromium dioxide

Doreen Hiller · Journal of Applied Physics · 1978

Chromium dioxide in the 560–680 Oe coercivity range has been optimized for high density magnetic recording and is being produced at plant scale. The stabilized powders have residual magnetic moment of 33–35 emu/g, average crystal length of 0.6 μ, average aspect ratio of 20, and specific surface area of 20–40 m2/g. Magnetic tapes made with these oxides improve video output on state-of-the-art video cassette recorders by 2–4 dB and S/N by 1–3 dB, compared with current standard tapes, and also have very low audio noise. Magnetostrictive loss on replay is negligible, as on standard CrO2 tapes.

Cited by 16

Structural stability without coercivity

Laura Poggiolini, Gianna Stefani · Optimization · 2022

We study structural stability and local uniqueness of bang-bang-singular extremals in a fixed-free Mayer problem. The problem can be seen as an optimal control problem where the dynamics is control-affine. We prove our results under the same assumptions on the nominal problem that permit us to prove that the extremal is a strict strong local optimizer: suitable regularity assumptions and coercivity of a restriction of the extended second variation. We also assume that the condition that prevents the coercivity of the extended second variation is stable with respect to the parameter.

Cited by 1Open access

From nucleation to coercivity

Guoping Zhao, M. G. Zhao, H. S. Lim et al. · Applied Physics Letters · 2005

The demagnetization process of an exchange-coupled hard/soft/hard magnetic system and its coercivity mechanism are investigated within a micromagnetic framework. The calculation reveals that the demagnetization is a three-step process: (i) it begins with the nucleation of a transition region, (ii) the subsequent evolution of the domain wall near the interface, and (iii) the irreversible domain-wall motion from the soft phase into hard phase. As the thickness of the soft interlayer decreases, the dominant mechanism of coercivity switches from pinning to nucleation. However, for very thin interlayer, the three-step process occurs at the same applied field.

Cited by 71