This paper reports the derivation of a relationship between some elements of the cumulant matrix of the second-order reduced density matrix and the elements of the spin-density matrix. This relationship turns out to be very useful to determine local spins through the partitioning of the spin expectation value of an N-electron system. The procedure enables expression of both one- and two-center contributions only in terms of one-electron matrix elements, the elements of the spin-density matrix. We report numerical determinations of local spins in the Hilbert space of atomic orbitals in selected molecules and radicals in triplet and doublet states.
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Sci Adv
January 2025
Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA.
Tissues form during development through mechanical compaction of their extracellular matrix (ECM) and shape morphing, processes that result in complex-shaped structures that contribute to tissue function. While observed in vivo, control over these processes in vitro to understand both tissue development and guide tissue formation has remained challenging. Here, we use combinations of mesenchymal stromal cell spheroids and hydrogel microparticles (microgels) with varied hydrolytic stability to fabricate programmable and dynamic granular composites that control compaction and tissue formation over time.
View Article and Find Full Text PDFJ Anat
January 2025
Bonn Institute of Organismal Biology, Paleontology, University of Bonn, Bonn, Germany.
Current understanding of the histology of the dermoskeleton of tetrapods comes from fossilized and recent remains of skulls, osteoderms, carapace, plastron and other postcranial material which were always investigated using linear cross polarized light (LCPL) microscopy. The pectoral girdle of vast majority of non-amniote tetrapods, including temnospondyls evolved large ventrally located dermal bones- the interclavicle and a pair of clavicles. Despite that, there is a lack of information about the bone tissue structure from these postcranial dermal bones.
View Article and Find Full Text PDFPLoS One
January 2025
Shenzhen Yingshisheng Information Technology Co., Ltd., Shenzhen, Guangdong, China.
This study delves into neutral-type systems (NTSs), emphasizing the critical role of defining precise reachable set (RS) boundaries for safe and efficient system design and operation. The investigation notably addresses the challenges posed by time-varying delays, applying Lyapunov's direct method alongside advanced matrix inequality techniques to identify minimized and more accurate ellipsoidal boundaries of the RS in NTSs influenced by bounded and nonlinear disturbances. Our findings, verified through numerical simulations and comparisons with existing literature, demonstrate enhanced control and management capabilities for complex systems, thus underscoring the substantial theoretical and practical value of incorporating delay elements in NTSs.
View Article and Find Full Text PDFPLoS One
January 2025
School of Mechanical Engineering, Liaoning Technical University, Fuxin, China.
Titanium alloy is known for its low thermal conductivity, small elastic modulus, and propensity for work hardening, posing challenges in predicting surface quality post high-speed milling. Since surface quality significantly influences wear resistance, fatigue strength, and corrosion resistance of parts, optimizing milling parameters becomes crucial for enhancing service performance. This paper proposes a milling parameter optimization method utilizing the snake algorithm with multi-strategy fusion to improve surface quality.
View Article and Find Full Text PDFNeural Netw
December 2024
Department of Earth Science and Engineering, Imperial College London, Prince Consort Road, London SW7 2BP, UK; Centre for AI-Physics Modelling, Imperial-X, White City Campus, Imperial College London, W12 7SL, UK.
Machine learning (ML) has benefited from both software and hardware advancements, leading to increasing interest in capitalising on ML throughout academia and industry. There have been efforts in the scientific computing community to leverage this development via implementing conventional partial differential equation (PDE) solvers with machine learning packages, most of which rely on structured spatial discretisation and fast convolution algorithms. However, unstructured meshes are favoured in problems with complex geometries.
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