Landau-Lifshitz Equations

Guo, Boling; Ding, Shijin

doi:10.1142/9789812778765

Cited by 46 publications

(39 citation statements)

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“…Total concentrations of PCNs in north Bohai Sea coastline were in the range of 0.03–0.28 ng/g dw, which were comparable to Laizhou Bay located in south Bohai Sea coastline [27]. Compared with other areas in China, sediment PCNs concentrations in Bohai Sea were similar to that in Yangtze River Estuary (0.03–0.30 ng/g dw), Qingdao coast (0.21–1.21 ng/g dw), and Yellow River Estuary (0.006–0.41 ng/g dw [29, 30]. Globally, PCNs in sediments were relatively low compared to North America [31], and the possible reason might be that commercial PCNs have never been historically produced in China.…”

Section: Distributions Of Emerging Pops In Water Body and Sedimentssupporting

confidence: 54%

Emerging Persistent Organic Pollutants in Chinese Bohai Sea and Its Coastal Regions

Gao

Wang

et al. 2014

The Scientific World Journal

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Emerging persistent organic pollutants (POPs) have widely aroused public concern in recent years. Polybrominated diphenyl ethers (PBDEs) and perfluorooctane sulfonyl fluoride/perfluorooctane sulfonic acid (POSF/PFOS) had been newly listed in Stockholm Convention in 2009, and short chain chlorinated paraffins (SCCPs) and hexabromocyclododecanes (HBCDs) were listed as candidate POPs. Bohai Sea is located in the arms of numbers of industrial cities, the semienclosed location of which makes it an ideal sink of emerging pollutants. In the present paper, latest contamination status of emerging POPs in Bohai Sea was reviewed. According to the literature data, Bohai Sea areas are not heavily contaminated by emerging POPs (PBDE: 0.01–720 ng/g; perfluorinated compounds: 0.1–304 ng/g; SCCPs: 64.9–5510 ng/g; HBCDs: nd-634 ng/g). Therefore, humans are not likely to be under serious risk of emerging POPs exposure through consuming seafood from Bohai Sea. However, the ubiquitous occurrence of emerging POPs in Bohai Sea region might indicate that more work should be done to expand the knowledge about potential risk of emerging POPs pollution.

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Section: Distributions Of Emerging Pops In Water Body and Sedimentssupporting

confidence: 54%

Emerging Persistent Organic Pollutants in Chinese Bohai Sea and Its Coastal Regions

Gao

Wang

et al. 2014

The Scientific World Journal

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“…In order to carry out physically relevant experiments, the initial conditions of the mllg equations should be chosen to satisfy the divergence-free constraint [7] div(…”

Section: A Basis For Y Hmentioning

confidence: 99%

A finite element approximation for the quasi-static Maxwell--Landau--Lifshitz--Gilbert equations

Tran

2013

ANZIAMJ

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The quasi-static Maxwell-Landau-Lifshitz-Gilbert equations which describe the electromagnetic behaviour of a ferromagnetic material are highly nonlinear. Sophisticated numerical schemes are required to solve the equations, given their nonlinearity and the constraint that the solution stays on a sphere. We propose an implicit finite element solution to the problem. The resulting system of algebraic equations is linear which facilitates the solution process compared to nonlinear methods. We present numerical results to show the efficacy of the proposed method.

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“…As we all know, the Landau‐Lifshitz equation for isotropic ferromagnetic chains (also known as the Heisenberg model, and, in geometry, as the Schrödinger flow or Schrödinger map), say

{\overset{u}{true}}_{t} = \overset{u}{true} \times normalΔ \overset{u}{true}

with

false| \overset{u}{true} false| = 1

, has been widely researched and developed in recent decades (see, eg, Guo and Ding). In 1976, Lakshmanan et al constructed a class of explicit solutions of one‐dimensional isotropic ferromagnetic chains.…”

Section: Introductionmentioning

confidence: 99%

Some explicit solutions of the Landau‐Lifshitz equation for anisotropic ferromagnets

Han

Yang

2018

Math Methods in App Sciences

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The aim of this paper is to construct explicit solutions of the Landau‐Lifshitz equation for anisotropic ferromagnets. Firstly, we present some explicit solutions for n‐dimensional Landau‐Lifshitz equation with a generalized uniaxial anisotropy field (depending only on time) under a suitable transformation, where the generalized uniaxial anisotropy field contains the classical easy‐axis case and the important higher‐order approximations. Some relevant examples are indicated that contains the cubic system proposed by Landau and Lifshitz in 1960. Secondly, an explicit plane‐wave solution of Landau‐Lifshitz equation for the completely anisotropic case is obtained. Finally, some properties of magnetization for ferromagnets are provided by analysis of the solutions.

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Landau-Lifshitz Equations

Cited by 46 publications

References 0 publications

Emerging Persistent Organic Pollutants in Chinese Bohai Sea and Its Coastal Regions

Emerging Persistent Organic Pollutants in Chinese Bohai Sea and Its Coastal Regions

A finite element approximation for the quasi-static Maxwell--Landau--Lifshitz--Gilbert equations

Some explicit solutions of the Landau‐Lifshitz equation for anisotropic ferromagnets

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