A major challenge for our understanding of the mathematical basis of particle dynamics is the formulation of N-body and N-vortex dynamics on Riemann surfaces. In this paper, we show how the two problems are, in fact, closely related when considering the role played by the intrinsic geometry of the surface. This enables a straightforward deduction of the dynamics of point masses, using recently derived results for point vortices on general closed differentiable surfaces endowed with a metric . We find, generally, that Kepler's Laws do not hold. What is more, even Newton's First Law (the law of inertia) fails on closed surfaces with variable curvature (e.g. the ellipsoid).
Download full-text PDF |
Source |
|---|---|
| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5014100 | PMC |
| http://dx.doi.org/10.1098/rspa.2016.0020 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Cerebellar Transcranial AC Stimulation Produces a Frequency-Dependent Bimodal Cerebellar Output Pattern.
Cerebellum
January 2025
Department of Neuroscience and Physiology, Grossman School of Medicine, NYU Neuroscience Institute, New York University, New York, NY, 10016, USA.
Cerebellar transcranial alternating current stimulation (ctACS) has the potential to be an appealing, non-invasive treatment option for psychiatric and neurological disorders. However, realization of this potential has been limited by gaps in our knowledge of how ctACS affects cerebellar output on single cell and population levels. Previously, we showed that AC stimulation applied to the cerebellar surface produced a strong, frequency-dependent modulation of Purkinje cell (PC) and cerebellar nuclear (CN) cell activity.
View Article and Find Full Text PDFMonitoring the operational changes in surface reflectances after logging, based on popular indices over Sentinel-2, Landsat-8, and ASTER imageries.
Environ Monit Assess
January 2025
Forest Engineering, Faculty of Forestry, Kastamonu University, Kastamonu, Türkiye.
Revealing the status of forests is important for sustainable forest management. The basis of the concept lies in meeting the needs of future generations and today's generations in the management of forests. The use of remote-sensing (RS) technologies and geographic information systems (GIS) techniques in revealing the current forest structure and in long-term planning of forest areas with multipurpose planning techniques is increasing day by day.
View Article and Find Full Text PDFA Focal Traumatic Injury to the Neonatal Rodent Spinal Cord Causes an Immediate and Massive Spreading Depolarization Sustained by Chloride Ions, with Transient Network Dysfunction.
Cell Mol Neurobiol
January 2025
Neuroscience Department, International School for Advanced Studies (SISSA), Via Bonomea 265, Trieste, TS, Italy.
In clinics, physical injuries to the spinal cord cause a temporary motor areflexia below lesion, known as spinal shock. This topic is still underexplored due to the lack of preclinical spinal cord injury (SCI) models that do not use anesthesia, which would affect spinal excitability. Our innovative design considered a custom-made micro impactor that provides localized and calibrated strikes to the ventral surface of the thoracic spinal cord of the entire CNS isolated from neonatal rats.
View Article and Find Full Text PDFSelf-Assembly Behavior of Zein on Two Different Substrates Visualized by Atomic Force Microscopy.
Microsc Res Tech
January 2025
Centre for Opto/Bio-Nano Measurement and Manufacturing, Zhongshan Institute of Changchun University of Science and Technology, Zhongshan, China.
When protein molecules come into contact with different types of substrate materials, the surface properties of the substrate will have a significant effect on their self-assembly behavior. The purpose of this study was to investigate the self-assembly behavior of zein molecules on the two different substrates. Herein, the microstructure of zein molecules on the surface of two typical substrates, mica and glass, were characterized in detail by atomic force microscopy.
View Article and Find Full Text PDFPhase evolutions of sodium layered oxide cathodes during thermal fluctuations.
Chem Commun (Camb)
January 2025
College of Chemistry and Materials Engineering, Wenzhou University, Wenzhou 325035, China.
Layered transition metal oxide (NaTMO) cathodes are considered highly appropriate for the practical applications of sodium-ion batteries (SIBs) owing to their facile synthesis and high theoretical capacity. Generally, the phase evolution behaviors of NaTMO during solid-state reactions at high temperature closely related to their carbon footprint, prime cost, and the eventual electrochemical properties, while the thermal stability in various desodiated states associated with wide temperature fluctuations are extremely prominent to the electrochemical properties and safety of SIB devices. Therefore, in this review, the influences of sintering conditions such as pyrolysis temperature, soaking time, and cooling rates on the phase formation patterns of NaTMO are summarized.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!