Phase transitions and hysteresis in nonlocal and order-parameter models

DOI10.1007/BF01557084zbMath0835.73005OpenAlexW2015082568MaRDI QIDQ1905577

Robert C. Rogers, Deborah Brandon, Tao Lin

Publication date: 16 April 1996

Published in: Meccanica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01557084

zbMATH Keywords

regularityexistencespatially nonlocal termquasistatic double-well potential problem

Mathematics Subject Classification ID

Thermodynamics in solid mechanics (74A15) Optimization of other properties in solid mechanics (74P10) Phase transitions (general) in equilibrium statistical mechanics (82B26)

Related Items

Stick-Slip Interface Motion as a Singular Limit of the Viscosity-Capillarity Model ⋮ Relative entropy method for the relaxation limit of hydrodynamic models ⋮ A nonlocal species concentration theory for diffusion and phase changes in electrode particles of lithium ion batteries ⋮ Convergence of a low order non-local Navier–Stokes–Korteweg system: The order-parameter model ⋮ Singular limits for a parabolic-elliptic regularization of scalar conservation laws ⋮ Local in time results for local and non-local capillary Navier-Stokes systems with large data ⋮ Young measures in a nonlocal phase transition problem ⋮ The role of the spinodal region in one-dimensional martensitic phase transitions ⋮ A low-order approximation for viscous-capillary phase transition dynamics ⋮ Relative energy for the Korteweg theory and related Hamiltonian flows in gas dynamics ⋮ Symmetry group classification for two-dimensional elastodynamics problems in nonlocal elasticity ⋮ Homoclinic solutions to an integral equation: Existence and stability ⋮ Parabolic approximations of diffusive-dispersive equations

Cites Work

• Translation of J. D. van der Waals' ``The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density
• Structured phase transitions on a finite interval
• An analysis of a phase field model of a free boundary
• A nonlocal model for the exchange energy in ferromagnetic materials
• Nonlocal superconductivity
• Continuum theory of thermally induced phase transitions based on an order parameter
• Dynamic solid-solid transitions with phase characterized by an order parameter
• Linear integral equations
• Direct methods in the calculus of variations
• Unnamed Item
• Unnamed Item