Microscopic chaos and diffusion

We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of models involving a single particle moving in two dimensions and colliding with fixed scatterers. We find that a number of microscopically nonchaotic models exhibit diffusion, and that the standard methods of chaotic time series analysis are ill suited to the problem of distinguishing between chaotic and nonchaotic microscopic dynamics. However, we show that periodic orbits play an important role in our models, in that their different properties in chaotic and nonchaotic systems can be used to distinguish such systems at the level of time series analysis, and in systems with absorbing boundaries. Our findings are relevant to experiments aimed at verifying the existence of chaoticity and related dynamical properties on a microscopic level in diffusive systems.Comment: 28 pages revtex, 14 figures incorporated with epsfig; see also chao-dyn/9904041; revised to clarify the definition of chaos and include discussion of a mixed model with both square and circular scatterer

Discrete dislocation and crystal plasticity analyses of load shedding in polycrystalline titanium alloys

The focus of this paper is the mechanistic basis of the load shedding phenomenon that occurs under the dwell fatigue loading scenario. A systematic study was carried out using a discrete dislocation plasticity (DDP) model to investigate the effect of crystallographic orientations, localised dislocation behaviour and grain combinations on the phenomenon. Rate sensitivity in the model arises from a thermal activation process at low strain rates, which is accounted for by associating a stress- and temperature-dependent release time with obstacles; the activation energy was determined by calibrating an equivalent crystal plasticity model to experimental data. First, the application of Stroh's dislocation pile-up model of crack nucleation to facet fracture was quantitatively assessed using the DDP model. Then a polycrystalline model with grains generated using a controlled Poisson Voronoi tessellation was used to investigate the soft-hard-soft rogue grain combination commonly associated with load shedding. Dislocation density and peak stress at the soft/hard grain boundary increased significantly during the stress dwell period, effects that were enhanced by dislocations escaping from pile-ups at obstacles. The residual stress after dwell fatigue loading was also found to be much higher compared to standard fatigue loading. Taylor (uniform strain) and Sachs (uniform stress) type assumptions in a soft-hard grain combination have been assessed with a simple bicrystal DDP model. Basal slip nucleation in the hard grain was found to be initiated by high stresses generated by strong pile ups in the soft grain, and both basal and pyramidal slip nucleation was observed in the hard grain when the grain boundary orientation aligned with that of an active slip system in the soft grain. The findings of this study give new insight into the mechanisms of load shedding and faceting associated with cold dwell fatigue in Ti alloys used in aircraft engines

Investigation of slip transfer across HCP grain boundaries with application to cold dwell facet fatigue

This paper addresses the role of grain boundary slip transfer and thermally-activated discrete dislocation plasticity in the redistribution of grain boundary stresses during cold dwell fatigue in titanium alloys. Atomistic simulations have been utilised to calculate the grain boundary energies for titanium with respect to the misorientation angles. The grain boundary energies are utilised within a thermally-activated discrete dislocation plasticity model incorporating slip transfer controlled by energetic and grain boundary geometrical criteria. The model predicts the grain size effect on the flow strength in Ti alloys. Cold dwell fatigue behaviour in Ti-6242 alloy is investigated and it is shown that significant stress redistribution from soft to hard grains occurs during the stress dwell, which is observed both for grain boundaries for which slip transfer is permitted and inhibited. However, the grain boundary slip penetration is shown to lead to significantly higher hard-grain basal stresses near the grain boundary after dwell, thus exacerbating the load shedding stress compared to an impenetrable grain boundary. The key property controlling the dwell fatigue response is argued to remain the time constant associated with the thermal activation process for dislocation escape, but the slip penetrability is also important and exacerbates the load shedding. The inclusion of a macrozone does not significantly change the conclusions but does potentially lead to the possibility of a larger initial facet

Fast and Lean Immutable Multi-Maps on the JVM based on Heterogeneous Hash-Array Mapped Tries

An immutable multi-map is a many-to-many thread-friendly map data structure with expected fast insert and lookup operations. This data structure is used for applications processing graphs or many-to-many relations as applied in static analysis of object-oriented systems. When processing such big data sets the memory overhead of the data structure encoding itself is a memory usage bottleneck. Motivated by reuse and type-safety, libraries for Java, Scala and Clojure typically implement immutable multi-maps by nesting sets as the values with the keys of a trie map. Like this, based on our measurements the expected byte overhead for a sparse multi-map per stored entry adds up to around 65B, which renders it unfeasible to compute with effectively on the JVM. In this paper we propose a general framework for Hash-Array Mapped Tries on the JVM which can store type-heterogeneous keys and values: a Heterogeneous Hash-Array Mapped Trie (HHAMT). Among other applications, this allows for a highly efficient multi-map encoding by (a) not reserving space for empty value sets and (b) inlining the values of singleton sets while maintaining a (c) type-safe API. We detail the necessary encoding and optimizations to mitigate the overhead of storing and retrieving heterogeneous data in a hash-trie. Furthermore, we evaluate HHAMT specifically for the application to multi-maps, comparing them to state-of-the-art encodings of multi-maps in Java, Scala and Clojure. We isolate key differences using microbenchmarks and validate the resulting conclusions on a real world case in static analysis. The new encoding brings the per key-value storage overhead down to 30B: a 2x improvement. With additional inlining of primitive values it reaches a 4x improvement

A fast analysis for thread-local garbage collection with dynamic class loading

Long-running, heavily multi-threaded, Java server applications make stringent demands of garbage collector (GC) performance. Synchronisation of all application threads before garbage collection is a significant bottleneck for JVMs that use native threads. We present a new static analysis and a novel GC framework designed to address this issue by allowing independent collection of thread-local heaps. In contrast to previous work, our solution safely classifies objects even in the presence of dynamic class loading, requires neither write-barriers that may do unbounded work, nor synchronisation, nor locks during thread-local collections; our analysis is sufficiently fast to permit its integration into a high-performance, production-quality virtual machine

Live Heap Space Analysis for Languages with Garbage Collection

The peak heap consumption of a program is the maximum size of the live data on the heap during the execution of the program, i.e., the minimum amount of heap space needed to run the program without exhausting the memory. It is well-known that garbage collection (GC) makes the problem of predicting the memory required to run a program difficult. This paper presents, the best of our knowledge, the first live heap space analysis for garbage-collected languages which infers accurate upper bounds on the peak heap usage of a program’s execution that are not restricted to any complexity class, i.e., we can infer exponential, logarithmic, polynomial, etc., bounds. Our analysis is developed for an (sequential) object-oriented bytecode language with a scoped-memory manager that reclaims unreachable memory when methods return. We also show how our analysis can accommodate other GC schemes which are closer to the ideal GC which collects objects as soon as they become unreachable. The practicality of our approach is experimentally evaluated on a prototype implementation.We demonstrate that it is fully automatic, reasonably accurate and efficient by inferring live heap space bounds for a standardized set of benchmarks, the JOlden suite

Digital Ecosystems: Ecosystem-Oriented Architectures

We view Digital Ecosystems to be the digital counterparts of biological ecosystems. Here, we are concerned with the creation of these Digital Ecosystems, exploiting the self-organising properties of biological ecosystems to evolve high-level software applications. Therefore, we created the Digital Ecosystem, a novel optimisation technique inspired by biological ecosystems, where the optimisation works at two levels: a first optimisation, migration of agents which are distributed in a decentralised peer-to-peer network, operating continuously in time; this process feeds a second optimisation based on evolutionary computing that operates locally on single peers and is aimed at finding solutions to satisfy locally relevant constraints. The Digital Ecosystem was then measured experimentally through simulations, with measures originating from theoretical ecology, evaluating its likeness to biological ecosystems. This included its responsiveness to requests for applications from the user base, as a measure of the ecological succession (ecosystem maturity). Overall, we have advanced the understanding of Digital Ecosystems, creating Ecosystem-Oriented Architectures where the word ecosystem is more than just a metaphor.Comment: 39 pages, 26 figures, journa