Nucleation of austenite in mechanically stabilized martensite by localized heating

The nucleation of bcc austenite in a single crystal of a mechanically stabilized 2H-martensite of Cu-Al-Ni shape-memory alloy is studied. The nucleation process is induced by localized heating and observed by optical microscopy. It is observed that nucleation occurs after a time delay and that the nucleation points are always located at one of the corners of the sample (a rectangular bar in the austenite), regardless of where the localized heating is applied. Using a simplified nonlinear elasticity model, we propose an explanation for the location of the nucleation points, by showing that the martensite is a local minimizer of the energy with respect to localized variations in the interior, on faces and edges of the sample, but not at some corners, where a localized microstructure can lower the energy.Comment: Proceedings, ICOMAT 2011, Journal of Alloys and Compounds, in pres

Analysis of nonlinear constraints in CLP(R)

Solving nonlinear constraints over real numbers is a complex problem. Hence constraint logic programming languages like CLP(R) or Prolog III solve only linear constraints and delay nonlinear constraints until they become linear. This efficient implementation method has the disadvantage that sometimes computed answers are unsatisfiable or infinite loops occur due to the unsatisfiability of delayed nonlinear constraints. These problems could be solved by using a more powerful constraint solver which can deal with nonlinear constraints like in RISC-CLP(Real). Since such powerful constraint solvers are not very efficient, we propose a compromise between these two extremes. We characterize a class of CLP(R) programs for which all delayed nonlinear constraints become linear at run time. Programs belonging to this class can be safely executed with the efficient CLP(R) method while the remaining programs need a more powerful constraint solver

Turbine vane gas film cooling with injection in the leading edge region from a single row of spanwise angled holes

An experimental study of gas film cooling was conducted on a 3X size model turbine vane. Injection in the leading edge region was from a single row of holes angled in a spanwise direction. Measurements of the local heat flux downstream from the row of coolant holes, both with and without film coolant flow, were used to determine the film cooling performance presented in terms of the Stanton number ratio. Results for a range of coolant blowing ratio, M = 0 to 2.0, indicate a reduction in heat flux of up to 15 to 30 percent at a point 10 to 11 hole diameters downstream from injection. An optimum coolant blowing ratio corresponds to a coolant-to-freestream velocity ratio in the range of 0.5. The shallow injection angle resulted in superior cooling performance for injection closest to stagnation, while the effect of injection angle was insignificant for injection further from stagnation

Lazy unification with inductive simplification

Unification in the presence of an equational theory is an important problem in theorem-proving and in the integration of functional and logic programming languages. This paper presents an improvement of the proposed lazy unification methods by incorporating simplification with inductive axioms into the unification process. Inductive simplification reduces the search space so that in some case infinite search spaces are reduced to finite ones. Consequently, more efficient unification algorithms can be achieved. We prove soundness and completeness of our method for equational theories represented by ground confluent and terminating rewrite systems

Propositional Encoding of Constraints over Tree-Shaped Data

We present a functional programming language for specifying constraints over tree-shaped data. The language allows for Haskell-like algebraic data types and pattern matching. Our constraint compiler CO4 translates these programs into satisfiability problems in propositional logic. We present an application from the area of automated analysis of (non-)termination of rewrite systems

A debugging model for functional logic programs

This paper presents a box-oriented debugging model for the functional logic language ALF. Due to the sophisticated operational semantics of ALF which is based on innermost basic narrowing with simplification, the debugger must reflect the application of the different computation rules during program execution. Hence our debugging model includes not only one box type as in Byrd's debugging model for logic programs but several different kinds of boxes corresponding to the various computation rules of the functional logic language (narrowing, simplification etc.). Moreover, additional box types are introduced in order to allow skips over (sometimes) uninteresting program parts like proofs of the condition in a conditional equation. Since ALF is a genuine amalgamation of functional and logic languages, our debugging model subsumes operational aspects of both kinds of languages. As a consequence, it can be also used for pure logic languages, pure functional languages with eager evaluation, or functional logic languages with a less sophisticated operational semantics like SLOG or eager BABEL

Combining Static and Dynamic Contract Checking for Curry

Static type systems are usually not sufficient to express all requirements on function calls. Hence, contracts with pre- and postconditions can be used to express more complex constraints on operations. Contracts can be checked at run time to ensure that operations are only invoked with reasonable arguments and return intended results. Although such dynamic contract checking provides more reliable program execution, it requires execution time and could lead to program crashes that might be detected with more advanced methods at compile time. To improve this situation for declarative languages, we present an approach to combine static and dynamic contract checking for the functional logic language Curry. Based on a formal model of contract checking for functional logic programming, we propose an automatic method to verify contracts at compile time. If a contract is successfully verified, dynamic checking of it can be omitted. This method decreases execution time without degrading reliable program execution. In the best case, when all contracts are statically verified, it provides trust in the software since crashes due to contract violations cannot occur during program execution.Comment: Pre-proceedings paper presented at the 27th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur, Belgium, 10-12 October 2017 (arXiv:1708.07854

An abstract interpretation algorithm for residuating logic programs

Residuation is an operational mechanism for the integration of functions into logic programming languages. The residuation principle delays the evaluation of functions during the unification process until the arguments are sufficiently instantiated. This has the advantage that the deterministic nature of functions is preserved but the disadvantage of incompleteness: if the variables in a delayed function call are not instantiated by the logic program, this function can never be evaluated and some answers which are logical consequences of the program are lost. In order to detect such situations at compile time, we present an abstract interpretation algorithm for this kind of programs. The algorithm approximates the possible residuations and instantiation states of variables during program execution. If the algorithm computes an empty residuation set for a goal, then it is ensured that the concrete execution of the goal does not end with a nonempty set of residuations which cannot be evaluated due to insufficient instantiation of argument variables

From Boolean Equalities to Constraints

Although functional as well as logic languages use equality to discriminate between logically different cases, the operational meaning of equality is different in such languages. Functional languages reduce equational expressions to their Boolean values, True or False, logic languages use unification to check the validity only and fail otherwise. Consequently, the language Curry, which amalgamates functional and logic programming features, offers two kinds of equational expressions so that the programmer has to distinguish between these uses. We show that this distinction can be avoided by providing an analysis and transformation method that automatically selects the appropriate operation. Without this distinction in source programs, the language design can be simplified and the execution of programs can be optimized. As a consequence, we show that one kind of equational expressions is sufficient and unification is nothing else than an optimization of Boolean equality

Non-linear Pattern Matching with Backtracking for Non-free Data Types

Non-free data types are data types whose data have no canonical forms. For example, multisets are non-free data types because the multiset $\{a,b,b\}$ has two other equivalent but literally different forms $\{b,a,b\}$ and $\{b,b,a\}$. Pattern matching is known to provide a handy tool set to treat such data types. Although many studies on pattern matching and implementations for practical programming languages have been proposed so far, we observe that none of these studies satisfy all the criteria of practical pattern matching, which are as follows: i) efficiency of the backtracking algorithm for non-linear patterns, ii) extensibility of matching process, and iii) polymorphism in patterns. This paper aims to design a new pattern-matching-oriented programming language that satisfies all the above three criteria. The proposed language features clean Scheme-like syntax and efficient and extensible pattern matching semantics. This programming language is especially useful for the processing of complex non-free data types that not only include multisets and sets but also graphs and symbolic mathematical expressions. We discuss the importance of our criteria of practical pattern matching and how our language design naturally arises from the criteria. The proposed language has been already implemented and open-sourced as the Egison programming language