Balancing domain decomposition by constraints and perturbation

In this paper, we formulate and analyze a perturbed formulation of the balancing domain decomposition by constraints (BDDC) method. We prove that the perturbed BDDC has the same polylogarithmic bound for the condition number as the standard formulation. Two types of properly scaled zero-order perturbations are considered: one uses a mass matrix, and the other uses a Robin-type boundary condition, i.e, a mass matrix on the interface. With perturbation, the wellposedness of the local Neumann problems and the global coarse problem is automatically guaranteed, and coarse degrees of freedom can be defined only for convergence purposes but not well-posedness. This allows a much simpler implementation as no complicated corner selection algorithm is needed. Minimal coarse spaces using only face or edge constraints can also be considered. They are very useful in extreme scale calculations where the coarse problem is usually the bottleneck that can jeopardize scalability. The perturbation also adds extra robustness as the perturbed formulation works even when the constraints fail to eliminate a small number of subdomain rigid body modes from the standard BDDC space. This is extremely important when solving problems on unstructured meshes partitioned by automatic graph partitioners since arbitrary disconnected subdomains are possible. Numerical results are provided to support the theoretical findings.Peer ReviewedPostprint (published version

APPROXIMATING COMMON ELEMENTS OF FIXED POINTS OF BREGMAN TOTALLY QUASI-ASYMPTOTICALLY NONEXPANSIVE MAPPINGS AND SOLUTIONS OF A SYSTEM OF GENERALIZED MIXED EQUILIBRIUM PROBLEMS IN REFLEXIVE BANACH SPACES

In this paper, we introduce a hybrid iterative method for approximating common elements of common fixed points of a finite family of Bregman totally quasiasymptotically nonexpansive mappings and solutions of a finite system of generalized mixed equilibrium problems. After that, a strong convergence result for the proposed iterative method is established and proved in reflexive Banach spaces. By this result, we get some convergence results for generalized mixed equilibrium problems in reflexive Banach spaces. Furthermore, we give a numerical example to illustrate the obtained results. 

Controlling neural cell behavior with electric field stimulation across a conductive substrate

textElectrical stimulation of tissues induces cell alignment, directed migration, extended processes, differentiation, and proliferation, but the mechanisms involved remain largely unknown. To reveal effects of electric fields (EF) through the media on cell behavior, voltage (7.45 – 22 V), current density (36 – 106 mA/cm2), duration (2 – 24 hrs), and alternating currents (AC, 2 – 1000 Hz) were varied independently when exposed to cell cultures. It was determined that current density and duration are the primary attribute Schwann cells respond to when an EF is applied through the media. This implies that the number of charges moving across the cell surface may play a key role in EF-induced changes in cell behavior. Identical conditions were used to stimulate cells grown on the surface of a conductive substrate to examine if a scaffold can provide structural and EF cues. The effects of an EF through the substrate were examined by placing a protein gel on the surface during stimulation and observing the morphology of subsequent cell cultures and the physical topology of the gel. EFs were shown to create Ca2+ redistribution across gels and subtle changes in collagen I fibril banding. Stimulated gels were able to induce perpendicular Schwann cell alignment on newly seeded cultures days after initial EF exposure, and the cell response decreased when seeded at longer times, indicating the effects of EF on the matrix environment has a relaxation time. These findings were then integrated into a biodegradable, electrically conductive polypyrrole-poly-ε-caprolactone polymer developed by collaborators. Dorsal root ganglia placed in matrix gels on top of conducting polymer exhibited significantly longer axons when stimulated with DC and AC signals. The overall results demonstrate that EFs have a significant effect on the extracellular environment. The broad implication of this data grants researchers with the ability to physically and metabolically control cell behavior with EFs, including improved wound healing or reduced cancer metastasis.Biomedical Engineerin

Unraveling the Enigma of Black Swan Events: A Multidisciplinary Examination of Financial and Climatic Extremes : The factors contributing to Black Swan Events and their varying effects

Black Swan events (BSE) are events that are highly improbable, unforeseen, and, many times, completely unpredictable and unknowable. The term itself was popularized by Nassim Taleb in his book, The Black Swan: The Impact of the Highly Improbable (2010). The study of extreme events is something that has gained popularity recently, and we aim to add to the growing literature by examining cases of extreme financial events and extreme weather events. We use a Monte Carlo simulation to look at potential extreme weather events in Sindh, Pakistan, to see if there are any changes in the frequency and severity of certain variables given small changes in variable means. With a qualitative and quantitative look at Black Swan events, we find there are some similarities between different systems that can be helpful for preparation and future study of extreme events.nhhma

Durabilité des réparations à base cimentaire : analyse comparée de l'influence des propriétés mécaniques du matériau de réparation

Pour une structure réparée par la technique de rechargement mince adhérent à base cimentaire, le décollement de l'interface support-rechargement est la principale cause limitant la durabilité de l'application. Pour améliorer cette durabilité, il est nécessaire de contrer la cause qui est à l'origine de ce décollement : la fissuration de la couche de réparation. Dans ce but, l'utilisation d'un composite cimentaire possédant la capacité de supporter des déformations importantes avant localisation de la fissure est, potentiellement, une solution. L'objectif de cette thèse est de la valider. Pour répondre à l'objectif de l'étude, les matériaux étudiés sont des mortiers incorporant de granulats à faible rigidité et renforcés par des fibres. Les granulats utilisés sont en caoutchouc issu du broyage de pneus usagés, une contribution à la valorisation de ce sous-produit industriel. S'agissant du renforcement, des fibres métalliques adhérentes et inoxydable ont été retenues. Elles sont les plus efficaces pour contrôler la fissuration et peuvent être utilisées y compris dans les milieux les plus agressifs. Une bonne synergie entre les granulats caoutchouc et les fibres est bien démontrée : la capacité de déformation avant localisation de la macro-fissuration est nettement plus élevée et la capacité portante post-pic attendue du renfort par des fibres n'est pas remise en cause en présence de granulats caoutchouc. Ces matériaux sont ensuite utilisés comme matériaux de rechargement. Des essais de flexion trois points monotones ou de fatigue ont été effectués sur des éprouvettes composites support-rechargement. Ils ont permis d'étudier la réponse structurale de ces composites, en particulier le comportement de l'interface (force d'initiation et cinétique du décollement). En parallèle un travail de modélisation par éléments finis, basé sur un modèle déjà développé et validé sur des granulats minéraux au LMDC, est réalisé. Il s'agit de la simulation numérique du comportement mécanique des structures composites support-rechargement sous sollicitations monotones ou de fatigue. Une confrontation des résultats expérimentaux avec ceux issus du modèle permettent d'asseoir sa pertinence dans le cas des rechargements incorporant des granulats caoutchouc et renforcés par des fibres. En particulier les résultats numériques permettent de mettre en évidence l'influence des variations dimensionnelles empêchées du matériau de rechargement au niveau de l'interface sur le comportement de la structure réparée. L'ensemble des résultats montre que la synergie de l'association granulats caoutchouc-renfort par des fibres contribue à améliorer la durabilité de la réparation.Substrate-overlay composites should work monolithically. For this reason, the durability of a cement-based repair relies also on the durability of its bond with the substrate. To improve the durability of repair, it is necessary to prevent the original cause of debonding: cracks through the depth of the overlay. For this the use of a cement composite having an improved strain capacity should be considered as a suitable solution. The aim of this work is to validate this hypothesis. As repair materials, cement-based mortars incorporating low aggregate stiffness and with fibre reinforcement were used. Rubber aggregates obtained from grinding end of life tyres were used thus contributing to the recovery of an industrial byproduct. Stainless and high bond steel fibres were also used. They are effective to restrain the cracking and can be used in aggressive environment. A good synergy between rubber aggregates and fibres reinforcement is demonstrated: rubber aggregates improve the strain capacity of the composite before the macro-cracking localisation and residual post-peak strength due to the fibre reinforcement is not affected. Monotoneous and fatigue bending tests were carried out on specimens repaired by using these mortars. These tests allow the structural response, in particular the interface debonding, to be analysed (the load corresponding to the debonding initiation and debonding propagation). In parallel, a numerical modelling based on finite element method was conducted to simulate the mechanical response of the tested specimens. Comparison between experimental and numerical results shows the relevance of the numerical modeling which is suitable tool that highlights the effect of the restrained length change of the repair material at the interface on the debonding mechanisms. As ultimate findings, this study shows that a positive synergetic effect from rubber aggregate and fibre reinforcement contributes to enhance the durability of bonded cement-based overlays

Virtual Machine Management for Efficient Cloud Data Centers with Applications to Big Data Analytics

Infrastructure-as-a-Service (IaaS) cloud data centers offer computing resources in the form of virtual machine (VM) instances as a service over the Internet. This allows cloud users to lease and manage computing resources based on the pay-as-you-go model. In such a scenario, the cloud users run their applications on the most appropriate VM instances and pay for the actual resources that are used. To support the growing service demands of end users, cloud providers are now building an increasing number of large-scale IaaS cloud data centers, consisting of many thousands of heterogeneous servers. The ever increasing heterogeneity of both servers and VMs requires efficient management to balance the load in the data centers and, more importantly, to reduce the energy consumption due to underutilized physical servers. To achieve these goals, the key aspect is to eliminate inefficiencies while using computing resources. This dissertation investigates the VM management problem for efficient IaaS cloud data centers. In particular, it considers VM placement and VM consolidation to achieve effective load balancing and energy efficiency in cloud infrastructures. VM placement allows cloud providers to allocate a set of requested or migrating VMs onto physical servers with the goal to balance the load or minimize the number of active servers. While addressing the VM placement problem is important, VM consolidation is even more important to enable continuous reorganization of already-placed VMs on the least number of servers. It helps create idle servers during periods of low resource utilization by taking advantage of live VM migration provided by virtualization technologies. Energy consumption is then reduced by dynamically switching idle servers into a power saving state. As VM migrations and server switches consume additional energy, the frequency of VM migrations and server switches needs to be limited as well. This dissertation concludes with a sample application of distributed computing to big data analytics

SPREAD OF INTERACTION IN NANOCOMPOSITE HARD/SOFT NANOSTRUCTURED MAGNETS

In this study, the magnetic properties of 3D modeled two-phase hard/soft nanocomposite nanostructured magnets were simulated by means of the Monte-Carlo method. The dependences of the energy product and coercivity on the grain size and magnetically soft phase content were investigated. The influence of the interaction spreading in the soft phase on the magnetic properties was also discussed. The obtained results revealed that the energy product reaches an optimal value when the soft phase content ranges around 50 vol.%, and a strong magnetic interaction spreading locally along the Kneller-Hawig exchange length seems to be more important than a weak but widely spreading interaction

Fixed Point Theorems for g-Monotone Maps on Partially Ordered S-Metric Spaces

In this paper, we prove some fixed point theorems for g-monotone maps on partially ordered S-metric spaces. Our results generalize fixed point theorems in [1] and [7] for maps on metric spaces to the structure of S-metric spaces. Also, we give examples to demonstrate the validity of the results