Interface kinetics in phase field models: isothermal transformations in binary alloys and steps dynamics in molecular-beam-epitaxy

We present a unified description of interface kinetic effects in phase field models for isothermal transformations in binary alloys and steps dynamics in molecular-beam-epitaxy. The phase field equations of motion incorporate a kinetic cross-coupling between the phase field and the concentration field. This cross coupling generalizes the phenomenology of kinetic effects and was omitted until recently in classical phase field models. We derive general expressions (independent of the details of the phase field model) for the kinetic coefficients within the corresponding macroscopic approach using a physically motivated reduction procedure. The latter is equivalent to the so-called thin interface limit but is technically simpler. It involves the calculation of the effective dissipation that can be ascribed to the interface in the phase field model. We discuss in details the possibility of a non positive definite matrix of kinetic coefficients, i.e. a negative effective interface dissipation, although being in the range of stability of the underlying phase field model. Numerically, we study the step-bunching instability in molecular-beam-epitaxy due to the Ehrlich-Schwoebel effect, present in our model due to the cross-coupling. Using the reduction procedure we compare the results of the phase field simulations with the analytical predictions of the macroscopic approach

Achieving realistic interface kinetics in phase field models with a diffusional contrast

Phase field models are powerful tools to tackle free boundary problems. For phase transformations involving diffusion, the evolution of the non conserved phase field is coupled to the evolution of the conserved diffusion field. Introducing the kinetic cross coupling between these two fields [E. A. Brener, G. Boussinot, Phys. Rev. E {\bf 86}, 060601(R) (2012)], we solve the long-standing problem of a realistic description of interface kinetics when a diffusional contrast between the phases is taken into account. Using the case of the solidification of a pure substance, we show how to eliminate the temperature jump at the interface and to recover full equilibrium boundary conditions. We confirm our results by numerical simulations

Elastic and plastic effects on heterogeneous nucleation and nanowire formation

We investigate theoretically the effects of elastic and plastic deformations on heterogeneous nucleation and nanowire formation. In the first case, the influence of the confinement of the critical nucleus between two parallel misfitting substrates is investigated using scaling arguments. We present phase diagrams giving the nature of the nucleation regime as a function of the driving force and the degree of confinement. We complement this analytical study by amplitude equations simulations. In the second case, the influence of a screw dislocation inside a nanowire on the development of the morphological surface stability of the wire, related to the Rayleigh-Plateau instability, is examined. Here the screw dislocation provokes a torsion of the wire known as Eshelby twist. Numerical calculations using the finite element method and the amplitude equations are performed to support analytical investigations. It is shown that the screw dislocation promotes the Rayleigh-Plateau instability.Comment: 16 page

Kinetic cross coupling between non-conserved and conserved fields in phase field models

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

Resource Control for Synchronous Cooperative Threads

We develop new methods to statically bound the resources needed for the execution of systems of concurrent, interactive threads. Our study is concerned with a \emph{synchronous} model of interaction based on cooperative threads whose execution proceeds in synchronous rounds called instants. Our contribution is a system of compositional static analyses to guarantee that each instant terminates and to bound the size of the values computed by the system as a function of the size of its parameters at the beginning of the instant. Our method generalises an approach designed for first-order functional languages that relies on a combination of standard termination techniques for term rewriting systems and an analysis of the size of the computed values based on the notion of quasi-interpretation. We show that these two methods can be combined to obtain an explicit polynomial bound on the resources needed for the execution of the system during an instant. As a second contribution, we introduce a virtual machine and a related bytecode thus producing a precise description of the resources needed for the execution of a system. In this context, we present a suitable control flow analysis that allows to formulte the static analyses for resource control at byte code level

Fine-grained and coarse-grained reactive noninterference

International audienceWe study the security property of noninterference in a core synchronous reactive language that we call CRL. In the synchronous reactive paradigm, programs communicate by means of broadcast events, and their parallel execution is regulated by a notion of instant. We first show that CRL programs are indeed reactive, namely that they always converge to a state of termination or suspension ("end of instant") in a finite number of steps. We define two bisimulation equivalences on CRL programs, corresponding respectively to a fine-grained and to a coarse-grained observation of programs. We show that coarse-grained bisimilarity is more abstract than fine-grained bisimilarity, as it is insensitive to the order of generation of events and to repeated emissions of the same event during an instant. Based on these bisimulations, two properties of Reactive Noninterference (RNI) are introduced, formalising secure information flow. Both properties are time-insensitive and termination-insensitive. Again, coarse-grained RNI is more abstract than fine-grained RNI. Finally, a type system guaranteeing both security properties is presented. Thanks to a design choice of CRL, which offers two separate constructs for loops and iteration, and to refined typing rules, this type system allows for a precise treatment of termination leaks, which are an issue in parallel languages

Approximate Reachability for Dead Code Elimination in Esterel*

Esterel is an imperative synchronous programming language for the design of reactive systems. Esterel* extends Esterel with a non-instantaneous jump instruction (compatible with concurrency, preemption, etc.) so as to enable powerful source-to-source program transformations, amenable to formal verification. In this work, we propose an approximate reachability algorithm for Esterel* and use its output to remove dead code. We prove the correctness of our techniques

On affine usages in signal-based communication

We describe a type system for a synchronous pi-calculus formalising the notion of affine usage in signal-based communication. In particular, we identify a limited number of usages that preserve affinity and that can be composed. As a main application of the resulting system, we show that typable programs are deterministic

Grounding Synchronous Deterministic Concurrency in Sequential Programming

In this report, we introduce an abstract interval domain I(D; P) and associated fixed point semantics for reasoning about concurrent and sequential variable accesses within a synchronous cycle-based model of computation. The interval domain captures must (lower bound) and cannot (upper bound) information to approximate the synchronisation status of variables consisting of a value status D and an init status P. We use this domain for a new behavioural definition of Berry’s causality analysis for Esterel. This gives a compact and uniform understanding of Esterel-style constructiveness for shared-memory multi-threaded programs. Using this new domain-theoretic characterisation we show that Berry’s constructive semantics is a conservative approximation of the recently proposed sequentially constructive (SC) model of computation. We prove that every Berry-constructive program is sequentially constructive, i.e., deterministic and deadlock-free under sequentially admissible scheduling. This gives, for the first time, a natural interpretation of Berry-constructiveness for main-stream imperative programming in terms of scheduling, where previous results were cast in terms of synchronous circuits. It also opens the door to a direct mapping of Esterel’s signal mechanism into boolean variables that can be set and reset arbitrarily within a tick. We illustrate the practical usefulness of this mapping by discussing how signal reincarnation is handled efficiently by this transformation, which is of complexity that is linear in progra