Multiscale Experimental Analysis in Plasticity: Linking Dislocation Structures to Continuum Fields

Plastic deformation in metals is a complex phenomenon and is result of competition between different complicated mechanisms, and among all, dislocation nucleation and motion are the most dominant ones. Dislocation evolution is known to be a multiscale phenomenon, and has been incorporated to crystal plasticity theories to analyze the size effect in metals for almost a decade ago. Although the theories suffice to predict the size effect in metals, they are largely phenomenological. Here a novel experimental method is developed to resolve the complexity in plastic deformation due to dislocations and to extract new material length scales that can be incorporated to numerical models. A continuum-based quantity: the geometrically necessary dislocation density (GND) that describes the signed part of the overall dislocations is measured on a nickel single crystal sample using recently developed high resolution electron backscatter diffraction (HR-EBSD) over different field of view, 90 μm^2 − 1mm^2 with various step sizes, 50 nm to 2, 500 nm . The net Burgers vector density, which includes the information of the direction of the overall dislocation motion and also quantifies the flux of atoms changing positions due to dislocations, is measured for the first time using continuum methods. A new parameter, β, that is extracted from the net Burger vector density to monitor dislocation activity on crystallographic slip planes is measured. Measurements reveals patterning in GND densities and a distribution of length scales rather than a single length scale as assumed. The length scales, such as dislocation spacing, and dislocation cell sizes are quantified. The linear relationship between dislocation spacing and dislocation cell size is obtained, where the slope of the linear fit varies with different crystallographic slip systems and the number of the active slip systems. The slope ranges between 23-29 for dominantly single slip regions, whereas it ranges between 13-16 for multislip regions, which agrees with the findings from TEM analysis in the literature showing how a continuum based method can be used to obtain same material parameters. The experimental measurements and the assumptions are elaborated in a detailed analysis. The effect of step size in EBSD results is presented, and the information loss with increasing the step size is shown. The uncertainty in GND density from the HR-EBSD measurements is found to be 10^13, which is two order of magnitude less than results from traditional diffraction methods. The effect of dislocation mobility on microstructure evolution has been also investigated, specifically tantalum single crystal specimens tested at 77 K and 293 K. The results unraveled occurrences of different deformation mechanisms: kink shear, and twinning at low temperatures. Interactions between dislocations and twin formations are observed and striking microstructure differences are examined. The dislocations density measurement results on tantalum are unique in the experimental sense and data can be used to extract length scale information. The experimental observations have been exploited to build the foundations of a numerical model. The effect of microstructure evolution on mechanical response has been investigated numerically based upon experimental observations. One of the main outcome of the experimental analysis -the variation of GND densities in cell walls- has been incorporated into a strain gradient plasticity framework. The proposed model is demonstrated with constrained shear and pure bending problems. The results presented show patterning in the GND density profile depending on the prescribed initial variation of the saturation value of GND densities and also change in overall mechanical response depending on the complexity of the prescribed profile

Optimal bundle formation and pricing of two products with limited stock

Cataloged from PDF version of article.In this study, we consider the stochastic modeling of a retail firm that sells two types of perishable products in a single period not only as independent items but also as a bundle. Our emphasis is on understanding the bundling practices on the inventory and pricing decisions of the firm. One of the issues we address is to decide on the number of bundles to be formed from the initial product inventory levels and the price of the bundle to maximize the expected profit. Product demands follow a Poisson Process with a price dependent rate. Customer reservation prices are assumed to have a joint distribution. We study the impact of reservation price distributions, initial inventory levels, product prices, demand arrival rates and cost of bundling. We observe that the expected profit decreases as the correlation between the reservation prices of two products increases. With negative correlation, bundling cost has a significant impact on the number of bundles formed. When the product prices are low, the retailer sells individual products as well as the bundle (mixed bundling), when they are high, the retailer sells only bundles (pure bundling). The expected profit and the number of bundles offered decrease as the variance of the reservation price distribution increases. For high starting inventory levels, the retailer reduces bundle price and offers more bundles. The number of bundle sales decreases and the number of individual product sales increases when the arrival rate increases since the need for bundling decreases. Impacts of substitutability and complementarity of products are also investigated. The retailer forms more bundles, or charges higher prices for the bundle or both as the products become more complementary and less substitutable. © 2009 Elsevier B.V. All rights reserved

Learning Multi-Object Symbols for Manipulation with Attentive Deep Effect Predictors

In this paper, we propose a concept learning architecture that enables a robot to build symbols through self-exploration by interacting with a varying number of objects. Our aim is to allow a robot to learn concepts without constraints, such as a fixed number of interacted objects or pre-defined symbolic structures. As such, the sought architecture should be able to build symbols for objects such as single objects that can be grasped, object stacks that cannot be grasped together, or other composite dynamic structures. Towards this end, we propose a novel architecture, a self-attentive predictive encoder-decoder network with binary activation layers. We show the validity of the proposed network through a robotic manipulation setup involving a varying number of rigid objects. The continuous sensorimotor experience of the robot is used by the proposed network to form effect predictors and symbolic structures that describe the interaction of the robot in a discrete way. We showed that the robot acquired reasoning capabilities to encode interaction dynamics of a varying number of objects in different configurations using the discovered symbols. For example, the robot could reason that (possible multiple numbers of) objects on top of another object would move together if the object below is moved by the robot. We also showed that the discovered symbols can be used for planning to reach goals by training a higher-level neural network that makes pure symbolic reasoning.Comment: 7 pages, 7 figure

Diffusion Policies for Out-of-Distribution Generalization in Offline Reinforcement Learning

Offline Reinforcement Learning (RL) methods leverage previous experiences to learn better policies than the behavior policy used for data collection. In contrast to behavior cloning, which assumes the data is collected from expert demonstrations, offline RL can work with non-expert data and multimodal behavior policies. However, offline RL algorithms face challenges in handling distribution shifts and effectively representing policies due to the lack of online interaction during training. Prior work on offline RL uses conditional diffusion models to represent multimodal behavior in the dataset. Nevertheless, these methods are not tailored toward alleviating the out-of-distribution state generalization. We introduce a novel method named State Reconstruction for Diffusion Policies (SRDP), incorporating state reconstruction feature learning in the recent class of diffusion policies to address the out-of-distribution generalization problem. State reconstruction loss promotes generalizable representation learning of states to alleviate the distribution shift incurred by the out-of-distribution (OOD) states. We design a novel 2D Multimodal Contextual Bandit environment to illustrate the OOD generalization and faster convergence of SRDP compared to prior algorithms. In addition, we assess the performance of our model on D4RL continuous control benchmarks, namely the navigation of an 8-DoF ant and forward locomotion of half-cheetah, hopper, and walker2d, achieving state-of-the-art results.Comment: 8 pages, 7 figure

Clinical Evaluation on Non-Functional Invasive Hypophysis Adenomas

Background There are ongoing studies to predetermine non-functional invasive pituitary adenomas which may show aggressive behavior. Our aim is to discuss whether there is a relationship between the immunohistochemical presence of GH, FSH, LH, PRL, ACTH, TSH and their aggressive clinical course in non-functional pituitary adenomas. Materials and Methods In this study, we evaluated retrospectively the files of the patients who were diagnosed with thesellar or parasellar tumor in our endocrinology clinic between the years of 2004-2014.The patients were divided into two groups as non-invasive pituitary adenomas and non-functional invasive pituitary adenomas. The immunohistochemical staining characteristics were compared between the two groups. Results In this study, we scanned the data of 70 patients who were followed for non-functional sellar or parasellar mass. 47.1% of the patients were female and 52.9% of the patients were male.39 patients had a non-functional pituitary adenoma.The rate of non-functional invasive adenoma was found to be 20.5%. There was a significant relationship between the immunohistochemical positivity of GH, FSH, LH andaggressive behavior of non-functional invasive adenomas. There was no a significant relationship between the immunohistochemicalpositivityof PRL, ACTH, TSH and aggressive behavior of non-functional invasive adenomas. Conclusion We found silent GH and gonadotropin adenomas as non-functional aggressive pituitary adenoma. More aggressive treatment and close clinical monitoring should be performed because atypical pituitary adenomas are characterized by invasive growth and aggressive clinical course

Discovering Predictive Relational Object Symbols with Symbolic Attentive Layers

In this paper, we propose and realize a new deep learning architecture for discovering symbolic representations for objects and their relations based on the self-supervised continuous interaction of a manipulator robot with multiple objects on a tabletop environment. The key feature of the model is that it can handle a changing number number of objects naturally and map the object-object relations into symbolic domain explicitly. In the model, we employ a self-attention layer that computes discrete attention weights from object features, which are treated as relational symbols between objects. These relational symbols are then used to aggregate the learned object symbols and predict the effects of executed actions on each object. The result is a pipeline that allows the formation of object symbols and relational symbols from a dataset of object features, actions, and effects in an end-to-end manner. We compare the performance of our proposed architecture with state-of-the-art symbol discovery methods in a simulated tabletop environment where the robot needs to discover symbols related to the relative positions of objects to predict the observed effect successfully. Our experiments show that the proposed architecture performs better than other baselines in effect prediction while forming not only object symbols but also relational symbols. Furthermore, we analyze the learned symbols and relational patterns between objects to learn about how the model interprets the environment. Our analysis shows that the learned symbols relate to the relative positions of objects, object types, and their horizontal alignment on the table, which reflect the regularities in the environment.Comment: arXiv admin note: text overlap with arXiv:2208.0102