Numerical solution of Fokker-Planck equation for single domain particles
The Fokker-Planck equation proposed by Brown to describe the evolution of the probability distribution density of the orientation of the magnetic moment of a single-domain particle is usually solved by expanding the unknown function in a series of spherical harmonics. In this paper, we use a differe...
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| Veröffentlicht in: | Physica. B, Condensed matter Condensed matter, 2019-10, Vol.571, p.142-148 |
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| creator | Peskov, N.V. Semendyaeva, N.L. |
| description | The Fokker-Planck equation proposed by Brown to describe the evolution of the probability distribution density of the orientation of the magnetic moment of a single-domain particle is usually solved by expanding the unknown function in a series of spherical harmonics. In this paper, we use a different method to solve the Fokker-Planck equation, namely, the finite element method. We describe the procedure for constructing a triangular grid on the surface of a sphere and give formulas for calculating the coefficients of the equations for the probability density values at the grid nodes. As an example, the results of calculating the dynamic magnetic hysteresis for particles with cubic anisotropy are demonstrated.
•The numerical solution of Brown's Fokker-Planck equation is obtained by the finite element method.•FEM implementation details are described.•The dynamic magnetic hysteresis of particles with cubic anisotropy is calculated by solving the Fokker-Planck equation. |
| doi_str_mv | 10.1016/j.physb.2019.07.004 |
| format | Article |
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•The numerical solution of Brown's Fokker-Planck equation is obtained by the finite element method.•FEM implementation details are described.•The dynamic magnetic hysteresis of particles with cubic anisotropy is calculated by solving the Fokker-Planck equation.</description><subject>Anisotropy</subject><subject>Density</subject><subject>Dynamic hysteresis</subject><subject>Finite element method</subject><subject>Finite element solution</subject><subject>Fokker-Planck equation</subject><subject>Harmonic analysis</subject><subject>Hysteresis</subject><subject>Magnetic moments</subject><subject>Magnetism</subject><subject>Numerical analysis</subject><subject>Probability distribution</subject><subject>Single domain particles</subject><subject>Spherical harmonics</subject><issn>0921-4526</issn><issn>1873-2135</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9kDFPwzAQhS0EEqXwC1giMSf47MSxBwZUUYpUAQPMluNcwG0at3aC1H9P2jJzyw3vvTu9j5BboBlQEPerbPu9j1XGKKiMlhml-RmZgCx5yoAX52RCFYM0L5i4JFcxrug4UMKELF6HDQZnTZtE3w69813im2Tu12sM6XtrOrtOcDeYo9L4kETXfbWY1H5jXJdsTeidbTFek4vGtBFv_vaUfM6fPmaLdPn2_DJ7XKaWc-jTStGqKgBQcos5VRWgaAwVUiopTSOpBclUUdZcMGBCSGYwV6MiStEoiXxK7k53t8HvBoy9XvkhdONLzTiovGS5UqOLn1w2-BgDNnob3MaEvQaqD8j0Sh-R6QMyTUs9IhtTD6cUjgV-HAYdrcPOYu0C2l7X3v2b_wUFanU_</recordid><startdate>20191015</startdate><enddate>20191015</enddate><creator>Peskov, N.V.</creator><creator>Semendyaeva, N.L.</creator><general>Elsevier B.V</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>L7M</scope></search><sort><creationdate>20191015</creationdate><title>Numerical solution of Fokker-Planck equation for single domain particles</title><author>Peskov, N.V. ; Semendyaeva, N.L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c331t-b90bb511e83ce409b1e6fa0688988af80c182957d362126682ae498af676f98e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Anisotropy</topic><topic>Density</topic><topic>Dynamic hysteresis</topic><topic>Finite element method</topic><topic>Finite element solution</topic><topic>Fokker-Planck equation</topic><topic>Harmonic analysis</topic><topic>Hysteresis</topic><topic>Magnetic moments</topic><topic>Magnetism</topic><topic>Numerical analysis</topic><topic>Probability distribution</topic><topic>Single domain particles</topic><topic>Spherical harmonics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Peskov, N.V.</creatorcontrib><creatorcontrib>Semendyaeva, N.L.</creatorcontrib><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Physica. B, Condensed matter</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Peskov, N.V.</au><au>Semendyaeva, N.L.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Numerical solution of Fokker-Planck equation for single domain particles</atitle><jtitle>Physica. B, Condensed matter</jtitle><date>2019-10-15</date><risdate>2019</risdate><volume>571</volume><spage>142</spage><epage>148</epage><pages>142-148</pages><issn>0921-4526</issn><eissn>1873-2135</eissn><abstract>The Fokker-Planck equation proposed by Brown to describe the evolution of the probability distribution density of the orientation of the magnetic moment of a single-domain particle is usually solved by expanding the unknown function in a series of spherical harmonics. In this paper, we use a different method to solve the Fokker-Planck equation, namely, the finite element method. We describe the procedure for constructing a triangular grid on the surface of a sphere and give formulas for calculating the coefficients of the equations for the probability density values at the grid nodes. As an example, the results of calculating the dynamic magnetic hysteresis for particles with cubic anisotropy are demonstrated.
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| subjects | Anisotropy Density Dynamic hysteresis Finite element method Finite element solution Fokker-Planck equation Harmonic analysis Hysteresis Magnetic moments Magnetism Numerical analysis Probability distribution Single domain particles Spherical harmonics |
| title | Numerical solution of Fokker-Planck equation for single domain particles |
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