1,721,057 research outputs found
On the dynamics of structural phase transitions in shape memory alloys
No full textOn the dynamics of structural phase transitions in shape memory alloys / J. Sprekels ; M. Niezgódka. - In: Nonclassical continuum mechanics / ed. by R. J. Knops ... - Cambridge u. a. : Cambridge Univ. Press, 1986. - S. 284-302. - (London Mathematical Society lecture note series ; 122
Nonlocal phase-field models for non-isothermal phase transitions with non-constant specific heat
No full textPhase separation in a gravity field
No full textWe prove here well-posedness and convergence to equilibria for the solution trajectories associated with a model for solidification of the liquid content of a rigid container in a gravity field. We observe that the gravity effects, which can be neglected without considerable changes of the process on finite time intervals, have a substantial influence on the long time behavior of the evolution system. Without gravity, we find a temperature interval, in which all phase distributions with a prescribed total liquid content are admissible equilibria, while, under the influence of gravity, the only equilibrium distribution in a connected container consists in two pure phases separated by one plane interface perpendicular to the gravity force
A bottle in a freezer
No full textWe propose here a model for solidification of the liquid content of an elastic bottle
in a freezer. The main goal is to explain the occurrence of high stresses inside the bottle. As a byproduct,
we derive a formula for the undercooling coefficient in terms of the elasticity constants, latent
heat, and the phase expansion coefficient. We investigate the well-posedness of the three-dimensional
model: we prove the existence and uniqueness of a solution for the corresponding initial-boundary
value problem which couples a PDE with an integrodifferential equation and an ordinary differential
inclusion ruling the evolution of the phase parameter. Finally, we prove some results on the long
time behavior of solutions
On a Penrose-Fife model with zero interfacial energy leading to a phase-field system of relaxed Stefan type
Full text linkIn this paper we study an initial-boundary value Stefan-type problem with phase relaxation where the heat flux is proportional to the gradient of the inverse absolute temperature. This problem arises naturally as limiting case of the Penrose-Fife model for diffusive phase transitions with non-conserved order parameter if the coefficient of the interfacial energy is taken as zero. It is shown that the relaxed Stefan problem admits a weak solution which is obtained as limit of solutions to the Penrose-Fife phase-field equations. For a special boundary condition involving the heat exchange with the surrounding medium, also uniqueness of the solution is proved
Exact bounds for the radially symmetric shape of confined plasma in the unit circle
No full textExact bounds for the radially symmetric shape of confined plasma in the unit circle / K.-H. Hoffmann ; J. Sprekels. - In: Mathematical methods in the applied sciences. 6. 1984. S. 496-511
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