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1. Nevanlinna Analytical Continuation

   https://doi.org/10.1103/PhysRevLett.126.056402  

   Fei, Jiani; Yeh, Chia-Nan; Gull, Emanuel (February 2021, Physical Review Letters)

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2. Analytical sphere–thin rod interaction potential

   https://doi.org/10.1140/epje/s10189-025-00480-9  

   Wang, Junwen; Cheng, Shengfeng (April 2025, The European Physical Journal E)

   AbstractA compact analytical form is derived through an integration approach for the interaction between a sphere and a thin rod of finite and infinite lengths, with each object treated as a continuous medium of material points interacting by the Lennard-Jones 12-6 potential and the total interaction potential as a summation of the pairwise potential between material points on the two objects. Expressions for the resultant force and torque are obtained. Various asymptotic limits of the analytical sphere–rod potential are discussed. The integrated potential is applied to investigate the adhesion between a sphere and a thin rod. When the rod is sufficiently long and the sphere sufficiently large, the equilibrium separation between the two (defined as the distance from the center of the sphere to the axis of the rod) is found to be well approximated as$$a+0.787\sigma $$ $a+0.787\sigma$, whereais the radius of the sphere and$$\sigma $$ $\sigma$is the unit of length of the Lennard–Jones potential. Furthermore, the adhesion between the two is found to scale with$$\sqrt{a}$$ $\sqrt{a}$. Graphic abstract) 

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3. A New Analytical Approach for Bistable Composites

   https://doi.org/10.1115/SMASIS2021-68224  

   Deshpande, Vishrut; Myers, Oliver; Fadel, Georges; Li, Suyi (September 2021, Proceedings of the ASME 2021 Conference on Smart Materials, Adaptive Structures and Intelligent Systems)

   Structures with adaptive capabilities offer many potentials to achieve future needs in efficiency, reliability, and intelligence. To this end, bistable CFRP (Carbon Fibre Reinforced Polymers) composites with asymmetric fiber layout are a promising concept that has shown shape morphing capabilities that adapt to the changes in the environment such as external forces and moments. This adaptability opens them to endless application potentials, ranging from small micro-switches to large airfoil sections in airplane wings or wind turbine blades. To harness this potential, it is essential to predict these composites’ physical shapes and behavior accurately. To this end, Hyer and Dano devised the first analytical model based on the concepts of Classical Lamination Theory, and this model has become the cornerstone of almost all subsequent studies. However, this theory uses Kirchoff’s theory of thin plates that are limited by several assumptions. As a result, Hyer’s theory can predict the overall shape of these laminates but lacks accuracy. A reason for this model’s underperformance is that it ignores the inter-laminar stresses and strains, but such stresses/strains play a vital role in the balance of the overall stress field and are found significantly higher near the free edges. To overcome these fundamental limitations, we propose a new analytical approach by combining the Reissner-Mindlin theory with concepts from the Classical Lamination Theory. This new model introduces in-plane rotations as two additional degrees of freedom. Thus, it has five independent variables compared to only three in Hyer and Dano’s model and its derivatives. Hence, we have a more complex but more accurate model. This paper outlines our new analytical approach by 1) introducing these two additional degrees of freedom; 2) selecting appropriate polynomial approximations; 3) formulating inter-laminar stresses that are functions of these added rotations; and 4) incorporating these inter-laminar stresses in the potential energy equation. By comparing this model’s prediction with the finite element simulation results, we found the new model slightly under predicts the laminate deformation, but the overall accuracy is promising, as evidenced by high R-squared correlation. 

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4. Analytical methods for detection of Zika virus

   https://doi.org/10.1557/mrc.2017.20  

   Yang, Kai-Hung; Narayan, Roger J. (March 2017, MRS Communications)

   Due to the recent outbreak of the Zika virus (ZIKV) in several regions, rapid, and accurate methods to diagnose Zika infection are in demand, particularly in regions that are on the frontline of a ZIKV outbreak. In this paper, three diagnostic methods for ZIKV are considered. Viral isolation is the gold standard for detection; this approach can involve incubation of cell cultures. Serological identification is based on the interactions between viral antigens and immunoglobulin G or immunoglobulin M antibodies; cross-reactivity with other types of flaviviruses can cause reduced specificity with this approach. Molecular confirmation, such as reverse transcription polymerase chain reaction (RT–PCR), involves reverse transcription of RNA and amplification of DNA. Quantitative analysis based on real-time RT–PCR can be undertaken by comparing fluorescence measurements against previously developed standards. A recently developed programmable paper-based detection approach can provide low-cost and rapid analysis. These viral identification and viral genetic analysis approaches play crucial roles in understanding the transmission of ZIKV. 

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5. Synthesizing analytical SQL queries from computation demonstration

   https://doi.org/10.1145/3519939.3523712  

   Zhou, Xiangyu; Bodik, Rastislav; Cheung, Alvin; Wang, Chenglong (June 2022, PLDI 2022: Proceedings of the 43rd ACM SIGPLAN International Conference on Programming Language Design and Implementation)