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  1. Proceedings of the Steklov Institute of Mathematics
  2. Proceedings of the Steklov Institute of Mathematics : Volume 281
  3. Proceedings of the Steklov Institute of Mathematics : Volume 281, Issue 1, Supplement,June 2013
  4. Analysis of the bloch equations for the nuclear magnetization model
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Proceedings of the Steklov Institute of Mathematics : Volume 296
Proceedings of the Steklov Institute of Mathematics : Volume 295
Proceedings of the Steklov Institute of Mathematics : Volume 294
Proceedings of the Steklov Institute of Mathematics : Volume 293
Proceedings of the Steklov Institute of Mathematics : Volume 292
Proceedings of the Steklov Institute of Mathematics : Volume 291
Proceedings of the Steklov Institute of Mathematics : Volume 290
Proceedings of the Steklov Institute of Mathematics : Volume 289
Proceedings of the Steklov Institute of Mathematics : Volume 288
Proceedings of the Steklov Institute of Mathematics : Volume 287
Proceedings of the Steklov Institute of Mathematics : Volume 286
Proceedings of the Steklov Institute of Mathematics : Volume 285
Proceedings of the Steklov Institute of Mathematics : Volume 284
Proceedings of the Steklov Institute of Mathematics : Volume 283
Proceedings of the Steklov Institute of Mathematics : Volume 282
Proceedings of the Steklov Institute of Mathematics : Volume 281
Proceedings of the Steklov Institute of Mathematics : Volume 281, Issue 1, July 2013
Proceedings of the Steklov Institute of Mathematics : Volume 281, Issue 1, Supplement,June 2013
On the 80th birthday of Arlen Mikhailovich Il’in
On a PT-symmetric waveguide with a pair of small holes
Asymptotic representation of a solution to a singular perturbation linear time-optimal problem
Asymptotic analysis of the diffusion-absorption equation with fast and strongly oscillating absorbtion coefficient in the two-dimensional case
On Friedrichs inequalities for a disk
Autoresonance excitation of a soliton of the nonlinear Schrödinger equation
Analysis of the bloch equations for the nuclear magnetization model
Oscillations near a separatrix in the duffing equation
On the asymptotics of a solution to an equation with a small parameter at some of the highest derivatives
Special solutions of the first and second Painlevé equations and singularities of the monodromy data manifold
Partial asymptotic decomposition of the domain for the diffusion-discrete absorption equation
Numerical methods for solving a hereditary equation of hyperbolic type
Asymptotics of the Gurevich-Pitaevskii universal special solution of the Korteweg-de Vries equation as |x| → ∞
Regular asymptotics of a generalized solution of the stationary Navier-Stokes system
Proceedings of the Steklov Institute of Mathematics : Volume 280
Proceedings of the Steklov Institute of Mathematics : Volume 279
Proceedings of the Steklov Institute of Mathematics : Volume 278
Proceedings of the Steklov Institute of Mathematics : Volume 277
Proceedings of the Steklov Institute of Mathematics : Volume 276
Proceedings of the Steklov Institute of Mathematics : Volume 275
Proceedings of the Steklov Institute of Mathematics : Volume 274
Proceedings of the Steklov Institute of Mathematics : Volume 273
Proceedings of the Steklov Institute of Mathematics : Volume 272
Proceedings of the Steklov Institute of Mathematics : Volume 271
Proceedings of the Steklov Institute of Mathematics : Volume 270
Proceedings of the Steklov Institute of Mathematics : Volume 269
Proceedings of the Steklov Institute of Mathematics : Volume 268
Proceedings of the Steklov Institute of Mathematics : Volume 267
Proceedings of the Steklov Institute of Mathematics : Volume 266
Proceedings of the Steklov Institute of Mathematics : Volume 265
Proceedings of the Steklov Institute of Mathematics : Volume 264
Proceedings of the Steklov Institute of Mathematics : Volume 263
Proceedings of the Steklov Institute of Mathematics : Volume 262
Proceedings of the Steklov Institute of Mathematics : Volume 261
Proceedings of the Steklov Institute of Mathematics : Volume 260
Proceedings of the Steklov Institute of Mathematics : Volume 259
Proceedings of the Steklov Institute of Mathematics : Volume 258
Proceedings of the Steklov Institute of Mathematics : Volume 257
Proceedings of the Steklov Institute of Mathematics : Volume 256
Proceedings of the Steklov Institute of Mathematics : Volume 255
Proceedings of the Steklov Institute of Mathematics : Volume 254
Proceedings of the Steklov Institute of Mathematics : Volume 253
Proceedings of the Steklov Institute of Mathematics : Volume 252

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Analysis of the bloch equations for the nuclear magnetization model

Content Provider Springer Nature Link
Author Kalyakin, L. A.
Copyright Year 2013
Abstract We consider a system of three ordinary first-order differential equations known in the theory of nuclear magnetism as the Bloch equations. The system contains four dimensionless parameters as coefficients. Equilibrium states and the dependence of their stability on these parameters are investigated. The possibility of the appearance of two stable equilibrium states is discovered. The equations are integrable in the absence of dissipation. For the problem with small dissipation far from equilibrium, approximate solutions are constructed by the method of averaging.
Starting Page 64
Ending Page 81
Page Count 18
File Format PDF
ISSN 00815438
Journal Proceedings of the Steklov Institute of Mathematics
Volume Number 281
Issue Number 1
e-ISSN 15318605
Language English
Publisher SP MAIK Nauka/Interperiodica
Publisher Date 2013-06-17
Publisher Place Dordrecht
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword nonlinear equations equilibrium dissipation stability asymptotics averaging Mathematics
Content Type Text
Resource Type Article
Subject Mathematics
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