Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 53 min ago
Peer-reviewedCC BY 4.0Nanomaterials

Differential Equations at the Nanoscale

  • Grzegorz Matyszczak1
  1. 1Faculty of Chemistry, Warsaw University of Technology, Noakowski Street 3, 00-664 Warsaw, Poland
Open at sourceDOICite

Abstract

Nanotechnology is a rapidly developing and relatively young subdiscipline of science and engineering. It mainly deals with the preparation, characterization and utilization of nanoparticles—particles of size ranging from 1 to 100 nm. The manipulation of such small objects is demanding and the phenomena involved on the nanoscale are relatively complex, and different, compared with their counterparts at both quantum- and macroscales. Further development of nanoscience requires applications and evolution of mathematical models of nanoscale phenomena, preferably with the aid of advanced mathematical methods such as the ordinary and partial differential equations. This review presents the methodology of usage, along with the applications, of differential equations of various types (ordinary, partial, stochastic) to the nanoscale phenomena, including nanoparticles growth, aggregation, properties, and applications.

Related

  1. Closed-form hard-sphere thermodynamics under nanoscale confinement: from equations of state to unmixing forces
    Jose M. G. Vilar, Leonor Saiz
    arXivPreprintarXiv licenceFull textPhysical chemistryCondensed matterarXiv
  2. Reconfigurable Nanoscale Material Display
    Yan Xiong, Shih-Ting Wang, Ashley Shay +3
    ChemRxivPreprintLicence not statedGeneral chemistryChemRxiv
  3. Nanoscale sensing of spatial correlations in nonequilibrium current noise
    Yifan Zhang, Rhine Samajdar, Sarang Gopalakrishnan
    Quantum Science and TechnologyPeer-reviewedLicence not statedFull text7 citedMaterials & polymersOpenAlex
  4. A high-sensitivity resistance bridge for nanoscale thermal microscopy
    Wilfrid Poirier, Victor Guillemot, Mohammed Mghalfi +2
    HALPreprintLicence not statedFull textMaterials & polymersHAL
  5. Ligand-Length Asymmetry Controls Nanoscale Heat Flow in Gold Janus Nanorods
    Chao Zeng, James D.E.T. Wilton-Ely, Fernando Bresme
    ChemRxivPreprintLicence not statedGeneral chemistryChemRxiv

Cite

BibTeXRIS
BibTeX
@article{matyszczak2026differential,
  title = {{Differential Equations at the Nanoscale}},
  author = {Grzegorz Matyszczak},
  journal = {Nanomaterials},
  year = {2026},
  month = oct,
  doi = {10.3390/nano16211380},
  url = {https://www.mdpi.com/2079-4991/16/21/1380},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Differential Equations at the Nanoscale
AU  - Grzegorz Matyszczak
PY  - 2026
DA  - 2026/10/28
JO  - Nanomaterials
DO  - 10.3390/nano16211380
UR  - https://www.mdpi.com/2079-4991/16/21/1380
AB  - Nanotechnology is a rapidly developing and relatively young subdiscipline of science and engineering. It mainly deals with the preparation, characterization and utilization of nanoparticles—particles of size ranging from 1 to 100 nm. The manipulation of such small objects is demanding and the phenomena involved on the nanoscale are relatively complex, and different, compared with their counterparts at both quantum- and macroscales. Further development of nanoscience requires applications and evolution of mathematical models of nanoscale phenomena, preferably with the aid of advanced mathematical methods such as the ordinary and partial differential equations. This review presents the methodology of usage, along with the applications, of differential equations of various types (ordinary, partial, stochastic) to the nanoscale phenomena, including nanoparticles growth, aggregation, properties, and applications.
SN  - 2079-4991
ER  -