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Advancing triage of acute lymphoblastic leukaemia subtypes diagnosis: label-free Raman spectroscopy for precise single-cell phenotyping and subtype classification

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Analyst, 2024, 149,5443-5454
DOI: 10.1039/D4AN00956H, Paper
Patrycja Leszczenko, Anna M. Nowakowska, Patrycja Dawiec, Karolina Czuja, Justyna Jakubowska, Marta Zabczynska, Agata Pastorczak, Kinga Ostrowska, Szymon Tott, Wojciech Mlynarski, Malgorzata Baranska, Katarzyna Majzner
Acute lymphoblastic leukaemia (ALL) is a complex disease in pediatric oncology, necessitating accurate diagnostic strategies for effective treatment planning.
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Electrochemical and imaging evaluations of electrochemically activated screen-printed gold electrodes

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Analyst, 2024, 149,5401-5410
DOI: 10.1039/D4AN00990H, Paper
Nor Dyana Zakaria, Ibrahim Luqman Salih, Hairul Hisham Hamzah, Turgut Sönmez, Muhamad Huzaifah Omar, Noorhashimah Mohamad Nor, Khairunisak Abdul Razak, Venugopal Balakrishnan
The graphic abstract displays the integration of the SPGE measurement system with an electrochemical cell-based 3D printing to evaluate the electrochemical behaviors and 3D images of both unactivated and activated SPGEs.
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Differentiation of oligosaccharide isomers by direct infusion multidimensional mass spectrometry

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Analyst, 2024, 149,5504-5517
DOI: 10.1039/D4AN01142B, Paper
Open Access
Enoch Amoah, Taghi Sahraeian, Ayesha Seth, Abraham K. Badu-Tawiah
Halide adduction enables the generation of diagnostic fragments ions for oligosaccharide isomers enabling multi-dimensional mass spectrometry analysis without prior separation.
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Effects of media composition and light exposure on the electrochemical current response during scanning electrochemical microscopy live cell imaging

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Analyst, 2024, 149,5555-5562
DOI: 10.1039/D4AN01075B, Paper
Nikita Thomas, Mengzhen Lyu, Jadon Khouv, Dhésmon Lima, Sabine Kuss
The cellular electrochemical current response is impacted by media composition and light exposure during scanning electrochemical microscopy (SECM).
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Material-agnostic characterization of spatially offset Raman spectroscopy in turbid media via Monte Carlo simulations

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Analyst, 2024, 149,5463-5475
DOI: 10.1039/D4AN01044B, Paper
Zuriel Erikson Joven, Piyush Raj, Ishan Barman
Monte Carlo simulations of spatially offset Raman spectroscopy (SORS) produce widely-applicable, quantitative frameworks for optimizing and interpreting SORS experiments.
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Imaging specific proteins in living cells with small unnatural amino acid attached Raman reporters

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Analyst, 2024, 149,5476-5481
DOI: 10.1039/D4AN00758A, Paper
Erli Cai, Yage Chen, Jing Zhang, Haozheng Li, Yiran Li, Shuai Yan, Zhiyong He, Quan Yuan, Ping Wang
For living HeLa cells, we report a small and minimally-invasive Raman reporter (about 2 aa and <1 kDa), which can be site-specifically introduced into proteins by genetic codon expansion combined with tetrazine ligation.
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A gold nanomaterial-integrated distance-based analytical device for uric acid quantification in human urine samples

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Analyst, 2024, 149,5518-5526
DOI: 10.1039/D4AN01139B, Paper
Tapparath Leelasattarathkul, Thithawat Trakoolwilaiwan, Kawin Khachornsakkul
A simple and low-cost distance-based paper analytical device (dPAD) was combined with gold nanomaterials for uric acid quantification.
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Acoustic levitation and manipulation of columns of droplets with integrated optical detection for parallelisation of reactions

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Analyst, 2024, 149,5546-5554
DOI: 10.1039/D4AN01096E, Paper
Open Access
  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.
Ruchi Gupta, Nicholas J. Goddard
In this work, acoustically levitated droplets serve as wells of microtitre plates and are acoustically manipulated to perform chemical and biological reactions in a non-contact fashion.
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Liquid saliva-based Raman spectroscopy device with on-board machine learning detects COVID-19 infection in real-time

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Analyst, 2024, 149,5535-5545
DOI: 10.1039/D4AN00729H, Paper
Open Access
Katherine J. I. Ember, Nassim Ksantini, Frédérick Dallaire, Guillaume Sheehy, Trang Tran, Mathieu Dehaes, Madeleine Durand, Dominique Trudel, Frédéric Leblond
Raman spectroscopy and machine learning is used in combination to detect COVID-19 positive saliva in liquid form.
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An improved cancer diagnosis algorithm for protein mass spectrometry based on PCA and a one-dimensional neural network combining ResNet and SENet

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Analyst, 2024, Advance Article
DOI: 10.1039/D4AN00784K, Paper
Liang Ma, Wenqing Gao, Xiangyang Hu, Dongdong Zhou, Chenlu Wang, Jiancheng Yu, Keqi Tang
An improved cancer diagnosis algorithm for protein mass spectrometry based on PCA and 1D neural network combining ResNet and SENet is proposed and successfully applied to the diagnosis of ovarian cancer with high accuracy and strong fitting ability.
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Impact of blue light on cutaneous barrier structures and properties: NPLC/HR-MSn and Raman analyses

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Analyst, 2024, Advance Article
DOI: 10.1039/D4AN01244E, Paper
Léa Habib, Rime Michael-Jubeli, Marie Abboud, Roger Lteif, Ali Tfayli
Blue light alters lipids and proteins in the reconstructed human epidermis.
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Molecularly imprinted polymer sensors for biomarker detection in cardiovascular diseases

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Analyst, 2024, Advance Article
DOI: 10.1039/D4AN01103A, Critical Review
Wenteng Tang, Junlei Han, Wenhong Zhang, Huimin Li, Jun Chen, Wei Song, Li Wang
Molecularly imprinted polymer sensors, combined with electrochemical, optical, thermal, and acoustic detection technologies, detect biomarkers for key cardiovascular diseases: coronary artery disease, acute myocardial infarction, and heart failure.
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Exploring gunshot residue detection in fingerprints by functionalized particle-coupled matrix-assisted laser desorption/ionization mass spectrometry

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Analyst, 2024, Advance Article
DOI: 10.1039/D4AN01260G, Paper
Sunil S. Adav, Yan Wen Crystal Tan, Choon Teck Low, Song Wei Loo, Ridhwan Yusoff, Archana Gautam, Yuk Lin Yong, Chiew Yung Yang, Chin Chin Lim, Kee Woei Ng
In firearm forensic investigations, detecting gunshot residue (GSR) is crucial for linking firearms to suspects and determining firing distance for forensic reconstruction.
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Generation, manipulation, detection and biomedical applications of magnetic droplets in microfluidic chips

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Analyst, 2024, Advance Article
DOI: 10.1039/D4AN01175A, Minireview
Chenyang Xu, Huanhuan Shi, Zhongjian Tan, Yun Zheng, Weizheng Xu, Zhengxian Dan, Jiacong Liao, Zhiying Dai, Yali Zhao
This review discusses the formation and manipulation of magnetic droplets on microfluidic chips and classifies related detection techniques. Applications in biomedicine were reviewed. Future development of this emerging field is provided.
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Structural determination of fructooligosaccharides and raffinose family oligosaccharides using logically derived sequence tandem mass spectrometry

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Analyst, 2024, Advance Article
DOI: 10.1039/D4AN00872C, Paper
Chia Yen Liew, Wun-Long Li, Chi-Kung Ni
Logical procedures for structural determination of fructooligosaccharides and raffinose family oligosaccharides.
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Areca influences many

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Published On :: Thu, 21 Feb 2013 12:57:35 +0530


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  • A J Vinayak
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Pran and…, mannerisms

By www.thehindubusinessline.com
Published On :: Sat, 13 Apr 2013 16:53:07 +0530


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  • A J Vinayak
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The efficient triplet states formation of Se-modified PDI dimers and tetramers in solvents

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Phys. Chem. Chem. Phys., 2024, 26,27325-27331
DOI: 10.1039/D4CP00954A, Paper
Feijun Huang, Wenli Su, Yubo Yang, Hang Wang, Zhishan Bo, Pengfei Jing, Wenkai Zhang
The Se-modified PDI oligomers experience triplet states formation in the solvents, but there are differences in the efficiency of triplet state generation due to variations in molecular structure.
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Spintronic performance of bent zigzag phosphorene nanoribbons: effects of mechanical deformation and gate voltage

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Phys. Chem. Chem. Phys., 2024, 26,27363-27370
DOI: 10.1039/D4CP03470H, Paper
Rouhollah Farghadan
This study explores how bending and gate voltage tune the spintronic properties of zigzag phosphorene nanoribbons (ZPNRs) for advanced applications.
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Magneto-optical properties of heavily Fe-doped GaAs: a density functional approach

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Phys. Chem. Chem. Phys., 2024, 26,27510-27518
DOI: 10.1039/D4CP03101F, Paper
J. Zarpellon, D. H. Mosca, J. Varalda
Heavily Fe-doped GaAs, investigated using a DFT approach, reveals a spin polarized electronic band structure correlated with magnetic circular dichroism and complex Kerr and Faraday rotation angles in agreement with some previous experiments.
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Densification of sodium and magnesium aluminosilicate glasses at ambient temperature: structural investigations by solid-state nuclear magnetic resonance and molecular dynamics simulations

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Phys. Chem. Chem. Phys., 2024, 26,27348-27362
DOI: 10.1039/D4CP02431A, Paper
Millena Logrado, Yara Hellen Firmo Gomes, Tomiki Inoue, Shingo Nakane, Yoshinari Kato, Hiroki Yamazaki, Akihiro Yamada, Hellmut Eckert
Superposition of 17O triple-quantum magic-angle spinning NMR spectra of 20MgO–20Al2O3–60SiO2 (MAS**) and 20Na2O–20Al2O3–60SiO2 (NAS**) glasses prepared at ambient pressure (AP) and pressurized and decompressed at 25 GPa at room temperature (HP(25)).
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Structural and sorption characteristics of an aerogel composite material loaded with flufenamic acid: insights from MAS NMR and high-pressure NOESY studies

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Phys. Chem. Chem. Phys., 2024, 26,27301-27313
DOI: 10.1039/D4CP03217A, Paper
Valentina V. Sobornova, Valeriya V. Mulloyarova, Konstantin V. Belov, Alexey A. Dyshin, Peter M. Tolstoy, Mikhail G. Kiselev, Ilya A. Khodov
The structural and sorption characteristics of a composite material consisting of a silica aerogel loaded with flufenamic acid were investigated using a variety of nuclear magnetic resonance techniques.
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Oxidation of fine aluminum particles: thermally induced transformations in particle shells and kinetics of oxide nucleation

By pubs.rsc.org
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Phys. Chem. Chem. Phys., 2024, 26,27602-27616
DOI: 10.1039/D4CP03355H, Paper
Andrey V. Korshunov
A submicron aluminum particle during oxidation is a shrinking spherical segment due to the growth of a single γ-Al2O3 nucleus.
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Machine-learning-accelerated structure prediction of PtSnO nanoclusters under working conditions

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Phys. Chem. Chem. Phys., 2024, 26,27624-27632
DOI: 10.1039/D4CP03769C, Paper
Fanke Zeng, Wanglai Cen
Credible property calculations based on the structure prediction of multi-component catalyst clusters under working conditions via a machine-learning-accelerated genetic algorithm and ab initio thermodynamics approach.
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Experimental and theoretical study of the Sn–O bond formation between atomic tin and molecular oxygen

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Phys. Chem. Chem. Phys., 2024, 26,27763-27771
DOI: 10.1039/D4CP03687E, Paper
Iakov A. Medvedkov, Anatoliy A. Nikolayev, Shane J. Goettl, Zhenghai Yang, Alexander M. Mebel, Ralf I. Kaiser
In this article, we combine state-of-art electronic structure calculations and crossed beam experiments to expose the reaction dynamics of 120Sn(3Pj) + 16O2(X3Σ−g) → 120Sn16O(X1Σ+) + 16O(3P) reaction that involve extensive ISC.
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Diffracting molecular matter-waves at deep-ultraviolet standing-light waves

By pubs.rsc.org
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Phys. Chem. Chem. Phys., 2024, 26,27617-27623
DOI: 10.1039/D4CP03059A, Paper
Open Access
  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.
Ksenija Simonović, Richard Ferstl, Alfredo Di Silvestro, Marcel Mayor, Lukas Martinetz, Klaus Hornberger, Benjamin A. Stickler, Christian Brand, Markus Arndt
We demonstrate an optical 266 nm beamsplitter for molecular matter-waves, observing effects of optical molecular properties in the gas phase such as absorption cross section and polarisability.
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Simulated conformality of atomic layer deposition in lateral channels: the impact of the Knudsen number on the saturation profile characteristics

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Phys. Chem. Chem. Phys., 2024, Advance Article
DOI: 10.1039/D4CP00131A, Paper
Open Access
  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.
Christine Gonsalves, Jorge A. Velasco, Jihong Yim, Jänis Järvilehto, Ville Vuorinen, Riikka L. Puurunen
Systematic analysis of saturation profile characteristics allowed development of an extended slope method that relates the slope of the adsorption front to the sticking coefficient for any Knudsen number.
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Hydrogen tunneling with an atypically small KIE measured in the mediated decomposition of the Co(CH3COOH)+ complex

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Phys. Chem. Chem. Phys., 2024, 26,27741-27750
DOI: 10.1039/D4CP02722A, Paper
Open Access
Simon U. Okafor, Gabriele Pinto, Michael Brdecka, William Smith, Tucker W. R. Lewis, Michael Gutierrez, Darrin J. Bellert
Rate-limiting hydrogen/deuterium tunneling rate constants are measured in the photon initiated decay of Co(CH3COOH)+ with small KIE values.
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Two-dimensional Janus XWZAZ' (X = S, Se, Te; A = Si, Ge; Z, Z' = N, P, As): candidates for photocatalytic water splitting and piezoelectric materials

By pubs.rsc.org
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Phys. Chem. Chem. Phys., 2024, 26,27314-27324
DOI: 10.1039/D4CP03503H, Paper
Zhen Gao, Hongbo Wu, Yao He, Kai Xiong
Janus two-dimensional (2D) materials exhibit strong light absorption and high solar-to-hydrogen conversion efficiency, making them promising candidates for photocatalytic water splitting applications.
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Dynamics of ionic liquids by means of nuclear magnetic resonance relaxation – overview of theoretical approaches

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Phys. Chem. Chem. Phys., 2024, 26,27248-27259
DOI: 10.1039/D4CP03183K, Review Article
Danuta Kruk, Elzbieta Masiewicz, Roksana Markiewicz, Rajendra Kumar Singh
Nuclear magnetic resonance relaxometry probes the translational and rotational dynamics of ionic liquids. To take advantage of this unique experimental potential, appropriate theoretical models are needed.
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On the peculiar EPR spectra of P1 centers at high (12–20 T) magnetic fields

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Phys. Chem. Chem. Phys., 2024, 26,27633-27647
DOI: 10.1039/D4CP03055A, Paper
Open Access
  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.
Orit Nir-Arad, Eyal Laster, Mais Daksi, Nurit Manukovsky, Ilia Kaminker
State mixing at a high magnetic field in the well-studied nitrogen substitutions in diamonds leads to unique electron spin spectral properties.
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Effects of oxidizer concentration and abrasive type on interfacial bonding and material removal in 4H-SiC polishing processes

By pubs.rsc.org
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Phys. Chem. Chem. Phys., 2024, 26,27791-27806
DOI: 10.1039/D4CP03544E, Paper
Yuqi Zhou, Kezhong Xu, Yuhan Gao, Ziniu Yu, Fulong Zhu
Two different modes of material removal are defined based on the difference in the mode of atom removal, i.e., mechanical removal and removal associated with interfacial bonding.
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Performance of functionalized graphene oxide with organic radical scavengers in proton exchange membranes

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Phys. Chem. Chem. Phys., 2024, 26,27817-27828
DOI: 10.1039/D4CP03151B, Paper
Yu Hu, Jiaxing Wang, Shuai Wang, Yuan Feng
A diazonium salt reaction is used to prepare benzoic acid-functionalized graphene oxide as a bi-functional filler for a Nafion membrane, and the corresponding composite membrane has improved chemical durability and proton conductivity.
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Synthesis and modification of boron nitride nanomaterials for gas sensors: from theory to application

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Phys. Chem. Chem. Phys., 2024, Advance Article
DOI: 10.1039/D4CP02137A, Review Article
Yan Zhang, Yan Wang, Cong Qin, Jianliang Cao
The synthesis and modification of BN based nanomaterials for gas sensors is summarized from theory to application.
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Morphology optimization via pre-aggregation and miscibility matching in PM6:L8-BO ternary organic solar cells

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Phys. Chem. Chem. Phys., 2024, Advance Article
DOI: 10.1039/D4CP03206C, Paper
Chuyue Wei, Junwei Zhang, Jing Deng, Xiangyan Yang, Jiahui Luo, Zixiao Xu, Lin Zhang, Shuaishuai Yuan, Weihua Zhou
Pre-aggregation and miscibility matching accounting for morphology optimization in ternary organic solar cells based on a PM6:L8-BO system.
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Insight into the potential of M–NbS2 (M = Pd, Ti and V) monolayers as anode materials for alkali ion (Li/Na/K) batteries

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Phys. Chem. Chem. Phys., 2024, Advance Article
DOI: 10.1039/D4CP03744H, Paper
Meixia Xiao, Shuling Xu, Haiyang Song, Zhifei Sun, Jiaying Bi, Beibei Xiao
First-principles calculations were conducted to explore the effects of Pd, Ti and V doping on the performance of NbS2 monolayers as electrode materials for alkali ion batteries.
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Lattice thermal conductivity reduction in Ca3AlSb3 and Ca5Al2Sb6 by manipulating the covalent tetrahedral chain

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Phys. Chem. Chem. Phys., 2024, Advance Article
DOI: 10.1039/D4CP03574G, Paper
Chi Zhang, Wenya Zhai, Jingyu Li, Jianbo Zhu, Zengfu Ou, Lanwei Li, Peng-Fei Liu, Xiaobing Liu, Yuli Yan, Yongsheng Zhang
Exploring the origins of low thermal conductivity in Ca–Al–Sb compounds reveals structural interactions that enhance phonon scattering. Strategies involve substituting heavier atoms to disrupt covalent chains, thereby reducing thermal conductivity.
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Ballistic transport in sub-10 nm monolayer InAs transistors for high-performance applications

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Phys. Chem. Chem. Phys., 2024, Advance Article
DOI: 10.1039/D4CP03789H, Paper
Tianruo Xie, Yuliang Mao
The modelling of double gate MOSFETs of monolayer InAsH2 is shown in (a). The corresponding transfer characteristics are shown for (b) n-type and (c) p-type, in which various doping concentrations are chosen.
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A Comprehensive Guide for Accurate Conformational Energies of Microsolvated Li+ Clusters with Organic Carbonates

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Phys. Chem. Chem. Phys., 2024, Accepted Manuscript
DOI: 10.1039/D4CP03487B, Paper
Arseniy A. Otlyotov, Andrey Moshchenkov, Timofey P. Rozov, Anna A. Tuma, Alexander S. Ryzhako, Yury Minenkov
Organic carbonates and their mixtures are frequently used in electrolyte solutions in lithium-ion batteries. Rationalization and tuning of the related Li+ solvation processes are rooted in the proper identification of...
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High Chern number quantum anomalous Hall effect in monolayer Co3X3SSe (X = Sn, Pb) kagomes

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Phys. Chem. Chem. Phys., 2024, Advance Article
DOI: 10.1039/D4CP03625E, Paper
Xiang Yin, Li Deng, Fei Wang, Yanzhao Wu, Junwei Tong, Xianmin Zhang
Two-dimensional stable kagome ferromagnets Co3Sn3SSe and Co3Pb3SSe can realize the QAHE with a high Chern number of |C| = 3, and present intriguing possibilities for advancing intrinsic high Chern number QAH devices.
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Structural Distortion Driven Polaronic Transport and Table-like Magnetocaloric Properties in Polycrystalline Tb0.7Sr0.3MnO3 compound

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Phys. Chem. Chem. Phys., 2024, Accepted Manuscript
DOI: 10.1039/D4CP03760J, Paper
Dipak Mazumdar, I. Das, Kalipada Das
This research mainly explores the structural, magnetic, magneto-transport, and magnetocaloric properties of the polycrystalline Tb0.7Sr0.3MnO3 compound. The results reveal a significant modification of the compound’s ground state with increasing the...
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Electronic Relaxation Pathways in Thio-Acridone and Thio-Coumarin: Two Heavy-Atom-Free Photosensitizers Absorbing Visible Light

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Phys. Chem. Chem. Phys., 2024, Accepted Manuscript
DOI: 10.1039/D4CP03720K, Paper
Open Access
Chris Acquah, Sean J. Hoehn, Sarah E. Krul, Steffen Jockusch, Shudan Yang, Sourav Kanti Seth, Eric Lee, Han Xiao, Carlos E. Crespo-Hernández
Heavy-atom-free photosensitizers (HAF-PSs) have emerged as a new class of photosensitizers aiming to broaden their applicability and versatility across various fields of the photodynamic therapy of cancers. The strategy involves...
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Intermolecular interaction potential maps from energy decomposition for interpreting reactivity and intermolecular interactions

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Phys. Chem. Chem. Phys., 2024, Advance Article
DOI: 10.1039/D4CP03237C, Paper
Amin Kiani, Wentong Zhou, Lawrence M. Wolf
The development and application of intermolecular interaction potential maps to rationalize a range of interactions at the DFT level using suitable probes is described.
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Simulation study of the conformation and dynamics of substrate-supported ring and linear polymer films

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Phys. Chem. Chem. Phys., 2024, Advance Article
DOI: 10.1039/D4CP02794A, Paper
Jianhua Huang, Hongzhu Ji, Jin Zhang, Zhunpeng Wang
Ring polymers in substrate-supported films exhibit stronger adsorbability, less deformation, and similar dynamics suppression compared to linear polymers.
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Deciphering the spectroscopic and thermodynamic aspects of binding of biologically important antioxidants with the alkali induced state of human serum albumin

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Phys. Chem. Chem. Phys., 2024, Advance Article
DOI: 10.1039/D4CP03636K, Paper
Anjali Maheshwari, Nand Kishore
Protein–ligand interactions are crucial for developing and identifying novel therapeutic targets.
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Deciphering nonlinear optical properties in functionalized hexaphyrins via explainable machine learning

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Phys. Chem. Chem. Phys., 2024, Advance Article
DOI: 10.1039/D4CP03303E, Paper
Eline Desmedt, Michiel Jacobs, Mercedes Alonso, Freija De Vleeschouwer
The NLO response of hexaphyrins is traced back to its driving forces using kernel ridge regression and explainable machine learning. Orbital and charge-transfer based features play a key role, as opposed to aromaticity and geometrical descriptors.
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Correlating Negative Thermal Expansion and Thermal Conductivity in Two-dimensional Carbon-based Materials

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Phys. Chem. Chem. Phys., 2024, Accepted Manuscript
DOI: 10.1039/D4CP03776F, Paper
Soumya Mondal, Ayan Datta
Negative thermal expansion (NTE) is a fascinating phenomenon where certain materials contract upon heating. The phonon transport properties of two-dimensional carbon-based allotropes are poorly understood in terms of their NTE...
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Magnetic field enhanced discharge and water activation of atmospheric pressure plasma jet: effect of assistance region and underlying physico-chemical mechanism

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Phys. Chem. Chem. Phys., 2024, Accepted Manuscript
DOI: 10.1039/D4CP03938F, Paper
Xiongfeng Zhou, Bin Chen, Hua Liao, Kun Liu
Magnetic field-assistance holds the promise of becoming a new or complementary approach to enhance the efficiency of atmospheric pressure plasma jet (APPJ), but there is currently a lack of research...
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Uniaxial Tensile Strain Impact on 1T-NbS2 Monolayers as Cathode Material for Lithium-Sulfur Batteries

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Phys. Chem. Chem. Phys., 2024, Accepted Manuscript
DOI: 10.1039/D4CP03156C, Paper
Shanling Ren, Xiaocong Tan, Xin Huang, zhihong yang, Yunhui Wang
In this work, we report our study on asymmetrical Janus TiSSe monolayers as cathode materials for lithium-sulfur batteries by first-principles calculations, encompassing adsorption, catalytic, and conductive properties. The results indicate...
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Breaking the Brownian Barrier: Models and Manifestations of Molecular Diffusion in Complex Fluids

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Phys. Chem. Chem. Phys., 2024, Accepted Manuscript
DOI: 10.1039/D4CP01813C, Perspective
H. Srinivasan, Veerendra Kumar Sharma, Subhankur Mitra
Over a century ago, Einstein formulated a precise mathematical model for describing Brownian motion. While this model adequately explains the diffusion of micron-sized particles in fluids, its limitations become apparent...
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