Central limit theorem for exponentially quasi-local statistics of spin models on Cayley graphs

Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing conditions, and on the other hand, it does not seem easy to show central limit theorem for local statistics via quasi-associativity. In this work, we prove general central limit theorems for local statistics and exponentially quasi-local statistics of spin models on discrete Cayley graphs with polynomial growth. Further, we supplement these results by proving similar central limit theorems for random fields on discrete Cayley graphs and taking values in a countable space but under the stronger assumptions of {\alpha}-mixing (for local statistics) and exponential {\alpha}-mixing (for exponentially quasi-local statistics). All our central limit theorems assume a suitable variance lower bound like many others in the literature. We illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology, statistical physics and random networks. Examples of clustering spin models include quasi-associated spin models with fast decaying covariances like the off-critical Ising model, level sets of Gaussian random fields with fast decaying covariances like the massive Gaussian free field and determinantal point processes with fast decaying kernels. Examples of local statistics include intrinsic volumes, face counts, component counts of random cubical complexes while exponentially quasi-local statistics include nearest neighbour distances in spin models and Betti numbers of sub-critical random cubical complexes.Comment: Minor changes incorporated based on suggestions by referee

(How) did attack advertisements increase affordable care act enrollments?

We examine the effects of exposure to negative information in attack advertisements in the context of Affordable Care Act (ACA) and Common Core (CC) education standards and show that they lead to an increase in the ACA enrollments and support of the CC standards. To explain this effect, we rely on the knowledge-gap theory and show that individuals who were exposed to more attack advertisements were also more likely to independently seek information, become more knowledgeable, and consequently support these subjects. In addition to an observational study, to test our hypotheses on the link between exposure to negative information, curiosity, and shifts in knowledge and support levels, we design and conduct a randomized experiment using a sample of 300 unique individuals. Our multi-methods research contributes to marketing literature by documenting a rare occasion in which exposure to attack advertisements leads to increased demand and unveiling the mechanisms through which this effect takes place

Computational screening of magnetocaloric alloys

An exciting development over the past few decades has been the use of high-throughput computational screening as a means of identifying promising candidate materials for a variety of structural or functional properties. Experimentally, it is often found that the highest-performing materials contain substantial atomic site disorder. These are frequently overlooked in high-throughput computational searches however, due to difficulties in dealing with materials that do not possess simple, well-defined crystallographic unit cells. Here we demonstrate that the screening of magnetocaloric materials with the help of the density functional theory-based magnetic deformation proxy can be extended to systems with atomic site disorder. This is accomplished by thermodynamic averaging of the magnetic deformation for ordered supercells across a solid solution. We show that the highly non-monotonic magnetocaloric properties of the disordered solid solutions Mn(Co$_{1-x}$Fe$_x$)Ge and (Mn$_{1-x}$Ni$_x$)CoGe are successfully captured using this method.Comment: Main text: 8 pages, 6 figures. Supplemental Material: 2 pages, 2 figure

Multi-Material Ultrasonic Consolidation

Ultrasonic consolidation (UC) is a recently developed direct metal solid freeform fabrication process. While the process has been well-demonstrated for part fabrication in Al alloy 3003 H18, including with intricate cooling channels, some of the potential strengths of the process have not been fully exploited. One of them is its flexibility with build materials and the other is its suitability for fabrication of multi-material and functionally graded material parts with enhanced functional or mechanical properties. Capitalizing on these capabilities is critical for broadening the application range and commercial utilization of the process. In the current work, UC was used to investigate ultrasonic bonding of a broad range of engineering materials, which included stainless steels, Ni-base alloys, brass, Al alloys, and Al alloy composites. UC multimaterial part fabrication was examined using Al alloy 3003 as the bulk part material and the above mentioned materials as performance enhancement materials. Studies were focused on microstructural aspects to evaluate interface characteristics between dissimilar material layers. The results showed that most of these materials can be successfully bonded to Al alloy 3003 and vice versa using the ultrasonic consolidation process. Bond formation and interface characteristics between various material combinations are discussed based on oxide layer characteristics, material properties, and others.Mechanical Engineerin

Blade planform for a quiet helicopter

The effects of blade planform and tip speed on noise and performance for a Hughes 500 C rotor system were studied. A cursory examination of the effects of such planform shapes as regular, inverse, and no taper on the noise and performance of the rotor was conducted. It was found that a constant width wide chord planform at tower tip speed provided the best performance and lowest noise. The tapered planforms had lower performance figures due to the reduced solidity. However, some noise reductions were achieved

Further evidence for intra-night optical variability of radio-quiet quasars

Although well established for BL Lac objects and radio-loud quasars, the occurrence of intra-night optical variability (INOV) in radio-quiet quasars is still debated, primarily since only a handful of INOV events with good statistical significance, albeit small amplitude, have been reported so far. This has motivated us to continue intra-night optical monitoring of bona-fide radio-quiet quasars (RQQs). Here we present the results for a sample of 11 RQQs monitored by us on 19 nights. On 5 of these nights a given RQQ was monitored simultaneously from two well separated observatories. In all, two clear cases and two probable case of INOV were detected. From these data, we estimate an INOV duty cycle of $\sim$8% for RQQs which would increase to 19% if the `probable variable' cases are also included. Such comparatively small INOV duty cycles for RQQs, together with the small INOV amplitudes ($\sim$1%), are in accord with the previously deduced characteristics of this phenomenon.Comment: 15 Pages, 4 Tables, 24 Figures; Accepted in BAS

Improving Linear Weld Density in Ultrasonically Consolidated Parts

Ultrasonic consolidation is a novel additive manufacturing process with immense potential for fabrication of complex shaped three-dimensional metallic objects from metal foils. The proportion of bonded area to unbonded area along the layer interface, termed linear weld density (LWD), is perhaps the most important quality attribute of ultrasonically consolidated parts. Part mechanical properties largely depend on LWD and a high level of LWD must be ensured in parts intended for load-bearing structural applications. It is therefore necessary to understand what factors influence LWD or defect formation and devise methods to enhance bond formation during ultrasonic consolidation. The current work examines these issues and proposes strategies to ensure near 100% LWD in ultrasonically consolidated aluminum alloy 3003 parts. The work elucidates the effects of various process parameters on LWD and a qualitative understanding of the effects of process parameters on bond formation during ultrasonic consolidation is presented. The beneficial effects of using elevated substrate temperatures and its implications on overall manufacturing flexibility are discussed. A preliminary understanding of defect morphologies and defect formation is presented, based on which a method (involving surface machining) for minimizing defect incidence during ultrasonic consolidation is proposed and demonstrated. Finally, trade-offs between part quality and build time are discussed.Mechanical Engineerin

Process Parameters Optimization for Ultrasonically Consolidated Fiber-Reinforced Metal Matrix Composites

As an emerging rapid prototyping technology, Ultrasonic Consolidation (UC) has been used to successfully fabricate metal matrix composites (MMC). The intent of this study is to identify the optimum combination of processing parameters, including oscillation amplitude, welding speed, normal force, operating temperature and fiber orientation, for manufacture of long fiber-reinforced MMCs. The experiments were designed using the Taguchi method, and an L25 orthogonal array was utilized to determine the influences of each parameter. SiC fibers of 0.1mm diameter were successfully embedded into an Al 3003 metal matrix. Two methods were employed to characterize the bonding between the fiber and matrix material: optical/electron microscopy and push-out tests monitored by an acoustic emission (AE) sensor. SEM images and data from push-out tests were analyzed and optimum combinations of parameters were achieved.Mechanical Engineerin