We present a phase field model for isothermal transformations of two component alloys that includes Onsager kinetic cross coupling between the non-conserved phase field and the conserved concentration field. We also provide the reduction of the phase field model to the corresponding macroscopic description of the free boundary problem. The reduction is given in a general form. Additionally we use an explicit example of a phase field model and check that the reduced macroscopic description, in the range of its applicability, is in excellent agreement with direct phase field simulations. The relevance of the newly introduced terms to solute trapping is also discussed.
We derive diffusive macroscopic equations for the particle and energy density of a system whose time evolution is described by a kinetic equation for the one particle position and velocity function f(r,v,t) that consists of a part that conserves energy and momentum such as the Boltzmann equation and an external randomization of the particle velocity directions that breaks the momentum conservation. Rescaling space and time by epsilon and epsilon square respectively and carrying out a Hilbert expansion in epsilon around a local equilibrium Maxwellian yields coupled diffusion equations with spec…
We consider the kinetic theory of the quantum and classical Toda lattice models. A kinetic equation of Bethe-Boltzmann type is derived for the distribution function of conserved quasiparticles. Near the classical limit, we show that the kinetic theory depends smoothly on Planck's constant, and explicitly characterise the leading quantum corrections to classical behaviour. The classical kinetic theory is compared with direct numerical simulations and shows excellent agreement. Finally, we connect the Bethe-Boltzmann approach with the classical inverse scattering method, by identifying conserved…
We study the early time dynamics of bimodal spin systems on $2d$ lattices evolving with different microscopic stochastic updates. We treat the ferromagnetic Ising model with locally conserved order parameter (Kawasaki dynamics), the same model with globally conserved order parameter (nonlocal spin exchanges), and the voter model. As already observed for non-conserved order parameter dynamics (Glauber dynamics), in all the cases in which the stochastic dynamics satisfy detailed balance, the critical percolation state persists over a long period of time before usual coarsening of domains takes o…
We present a comprehensive Monte Carlo study of domain growth in the random-bond XY model with non-conserved kinetics. The presence of quenched disorder slows down domain growth in d = 2; 3. In d = 2, we observe power-law growth with a disorder-dependent exponent on the time-scales of our simulation. In d = 3, we see the signature of an asymptotically logarithmic growth regime. The scaling functions for the real-space correlation function are seen to be independent of the disorder. However, the same does not apply for the two-time autocorrelation function, demonstrating the breakdown of superu…
After a sudden quench from the disordered high-temperature $T_0\to\infty$ phase to a final temperature below the critical point $T_F \ll T_c$, the non-conserved order parameter dynamics of the two-dimensional ferromagnetic Ising model on a square lattice (2dIM) initially approaches the critical percolation state before entering the coarsening regime. This approach involves two timescales associated with the first appearance (at time $t_{{\rm p}_1}>0$) and stabilization (at time $t_{\rm p}>t_{{\rm p}_1}$) of a giant percolation cluster, as previously reported. However, the microscopic mechanism…
The statistical mechanics of a one-dimensional Ising model in thermal equilibrium is well-established, textbook material. Yet, when driven far from equilibrium by coupling two sectors to two baths at different temperatures, it exhibits remarkable phenomena, including an unexpected 'freezing by heating.' These phenomena are explored through systematic numerical simulations. Our study reveals complicated relaxation processes as well as a crossover between two very different steady-state regimes.
We present Monte Carlo (MC) simulation studies of phase separation in binary (AB) mixtures with bond-disorder that is introduced in two different ways: (i) at randomly selected lattice sites and (ii) at regularly selected sites. The Ising model with spin exchange (Kawasaki) dynamics represents the segregation kinetics in conserved binary mixtures. We find that the dynamical scaling changes significantly by varying the number of disordered sites in the case where bond-disorder is introduced at the randomly selected sites. On the other hand, when we introduce the bond-disorder in a regular fashi…
We consider a kinetic model whose evolution is described by a Boltzmann-like equation for the one-particle phase space distribution $f(x,v,t)$. There are hard-sphere collisions between the particles as well as collisions with randomly fixed scatterers. As a result, this evolution does not conserve momentum but only mass and energy. We prove that the diffusively rescaled $f^\varepsilon(x,v,t)=f(\varepsilon^{-1}x,v,\varepsilon^{-2}t)$, as $\varepsilon\to 0$ tends to a Maxwellian $M_{ρ, 0, T}=\fracρ{(2πT)^{3/2}}\exp[{-\frac{|v|^2}{2T}}]$, where $ρ$ and $T$ are solutions of coupled diffusion equat…
We study a totally asymmetric simple exclusion process equipped with Langmuir kinetics with boundaries connected to a common reservoir. The total number of particles in the system is conserved and controlled by filling factor $μ$. Additionally, crowding of reservoir is taken into account which regulates the entry and exit of particles from both boundary as well as bulk. In the framework of mean-field approximation, we express the density profiles in terms of Lambert-W functions and obtain phase diagrams in $α-β$ parameter space. Further, we elucidate the variation of phase diagram with respect…
Albert-Ludwigs-Universität Freiburg（弗莱堡大学）；Laboratoire de Physique et Chimie Théoriques (CNRS UMR 7019), Université de Lorraine Nancy（洛林大学南锡物理与理论化学实验室（CNRS UMR 7019））；Centre for Fluid and Complex Systems, Coventry University（考文垂大学流体与复杂系统中心）；Centro de Física Teórica e Computacional, Universidade de Lisboa（里斯本大学理论与计算物理中心）
