Fast calibration of magnetic field coils in miniaturized NMRGs from Rabi oscillation of nuclear spins by Jinpeng Peng, Zhanchao Liu, Tengyue Wang, Yunkai Mao, Binquan Zhou

“…Through the numerical simulation of Bloch equations, we show that the behavior of My′ and Mz can be completely specified by two dimensionless quantities a and b, and we provide a ready-to-use selection criterion of b ≥ 24 for choosing the proper B1. …”
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Effect of Viscous Energy Dissipation on Transient Laminar Free Convective Flow of a Dusty Viscous Fluid through a Porous Medium by O. R. Jimoh, I. Ibrahim

“…The partial differential equations governing the phenomenon were non-dimensionalized using some dimensionless quantities. The dimensionless coupled non-linear partial differential equations were solved using harmonic solution technique. …”
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Dynamic Quality of an Aerostatic Thrust Bearing with a Microgroove and Support Center on Elastic Suspension by Vladimir Kodnyanko, Stanislav Shatokhin, Andrey Kurzakov, Lilia Strok, Yuri Pikalov, Iakov Pikalov, Olga Grigorieva, Maxim Brungardt

“…The calculations were carried out using dimensionless quantities, which made it possible to reduce the number of variable parameters. …”
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Dicke enhanced energy transfer via off resonant coupling y Christopher Black. by Black, Christopher (Christopher Mark), 1976-

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Insight into the Dynamics of Fractional Maxwell Nano-Fluids Subject to Entropy Generation, Lorentz Force and Heat Source via Finite Difference Scheme by Muhammad Imran Asjad, Muhammad Usman, Arfan Ali, Jan Awrejcewicz, Maksymilian Bednarek

“…The Bejan number is obtained following the suggested transformation of dimensionless quantities like entropy generation. A mathematical model of entropy generation, Bejan number, Nusselt number and skin friction are developed for nanofluids. …”
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Thermal and concentration diffusion impacts on MHD Maxwell fluid: A generalized Fourier's and Fick's perspective by Aziz Ur Rehman, Muhammad Bilal Riaz, Abdon Atangana, Fahd Jarad, Jan Awrejcewicz

“…The fractionalized model is transfromed into non-dimensional form by using some suitable dimensionless quantities. The non-dimensional developed fractional model for momentum, thermal and diffusion equations based on Prabhakar fractional operator has been solved analytically via Laplace transformation method and calculated solutions expressed in terms of Mittag-Leffler special functions. …”
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Two-dimensional numerical simulation of chimney fluidization in a granular medium using a combination of discrete element and lattice Boltzmann methods by Ngoma, Jeff, Philippe, Pierre, Bonelli, Stéphane, Radjaï, Farhang, Delenne, Jean-Yves

“…We also present quantitative findings about transient fluidization, for which several dimensionless quantities and scaling laws are proposed, and about the influence of the injection width, from localized to homogeneous fluidization. …”
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Microelongated Thermo-Elastodiffusive Waves of Excited Semiconductor Material under Laser Pulses Impact by Ismail M. Tayel, Kh. Lotfy, Alaa A. El-Bary, Jawdat Alebraheem, Mogtaba A. Y. Mohammed

“…The analytical linear solutions for the main quantities during thermoelastic (TD) and electronic (ED) deformation are obtained using Laplace transforms for dimensionless quantities. To obtain exact expressions of the important physical variables according to certain boundary surface conditions, numerical approximations solutions of the fundamental relevant relations are performed in the Laplace inverse time domain. …”
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Numerical study of a dissipative micropolar fluid flow past an inclined porous plate with heat source/sink by Shamshuddin MD, Thirupathi Thumma

“…For this purpose, the set of governing equations have been reframed and put into a dimensionless form under the assumption of low Reynolds number with appropriate dimensionless quantities that can fit into the finite element formulation. …”
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Comparing Physical and Electrochemical Properties of Different Weave Patterns for Carbon Cloth Electrodes in Redox Flow Batteries by Tenny, Kevin M, Forner-Cuenca, Antoni, Chiang, Yet-Ming, Brushett, Fikile R

“…Finally, we combine these findings to develop power law relations between relevant dimensional and dimensionless quantities and to calculate extensive mass transfer coefficients. …”
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Fundamental scaling laws for the direct-write chemical vapor deposition of nanoscale features: modeling mass transport around a translating nanonozzle by Drahushuk, Lee W, Govind Rajan, Ananth, Strano, Michael S

“…A Buckingham Π analysis identifies six dimensionless quantities crucial for the design and operation of the direct-write synthesis process. …”
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Hydrodynamic Effect On Low Field Gradient Magnetophoresis Of Superparamagnetic Nanoparticles by Leong, Sim Siong

“…Also, the separation mechanism of LGMS can be classified according to the range of three dimensionless quantities (Reynold number…”
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Numerical solution of mass transfer to micropolar fluid flow past a stenosed artery by A. Samad, Nursyafiqah

“…Then, all of the governing equations are written in dimensionless form by using dimensionless quantities in order to avoid difficulties. A radial coordinate transformation of the governing equation together with the set of initial and boundary are also needed in order to avoid interpolation error during discretization. …”
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Analysis of Nonlinear Convection–Radiation in Chemically Reactive Oldroyd-B Nanoliquid Configured by a Stretching Surface with Robin Conditions: Applications in Nano-Coating Manufa... by Muhammad Nasir, Muhammad Waqas, O. Anwar Bég, Hawzhen Fateh M. Ameen, Nurnadiah Zamri, Kamel Guedri, Sayed M Eldin

“…The influence of the emerging dimensionless quantities on the transport characteristics was comprehensively explained using appropriate data. …”
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Melting thermal transportation in bioconvection Casson nanofluid flow over a nonlinear surface with motile microorganism: Application in bioprocessing thermal engineering by Yijie Li, Aaqib Majeed, Nouman Ijaz, Kamal Barghout, Mohamed R. Ali, Taseer Muhammad

“…The graphs demonstrate the effects of various flows on dimensionless quantities. The current theoretic model might be used to increase heat transmission, engineering practices, and thermal energy.…”
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Do phenomenological dynamical paleoclimate models have physical similarity with Nature? Seemingly, not all of them do by M. Y. Verbitsky, M. Y. Verbitsky, M. Crucifix

“…</p> <p>The similarity parameters we advance here as the key dimensionless quantities are the ratio of the astronomical forcing amplitude to the terrestrial ice sheet mass influx and the so-called <span class="inline-formula"><i>V</i></span> number that is the ratio of the amplitudes of time-dependent positive and negative feedbacks. …”
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Fundamental scaling laws for the direct-write chemical vapor deposition of nanoscale features: modeling mass transport around a translating nanonozzle by Drahushuk, Lee W., Govind Rajan, Ananth, Strano, Michael S.

“…A Buckingham Π analysis identifies six dimensionless quantities crucial for the design and operation of the direct-write synthesis process. …”
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Triggering Rainfall of Large-Scale Landslides in Taiwan: Statistical Analysis of Satellite Imagery for Early Warning Systems by Tsai-Tsung Tsai, Yuan-Jung Tsai, Chjeng-Lun Shieh, John Hsiao-Chung Wang

“…Based on the concept of safety factor, two dimensionless quantities, rainfall/landslide depth (<i>R/D</i>) and friction angle/slope (<i>ϕ/θ</i>), were analyzed by linear regression. …”
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Semi-Analytical Approach and Green’s Function Method: A Comparison in the Analysis of the Interaction of a Moving Mass on an Infinite Beam on a Three-Layer Viscoelastic Foundation... by Zuzana Dimitrovová, Traian Mazilu

“…Additionally, a numerical algorithm based on the Green’s function and convolution integral written for dimensionless quantities is used to calculate the time series of the moving mass. …”
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Peristaltic motion of Jeffrey fluid with nonlinear mixed convection by S. Farooq, T. Shoaib, S.Z.B. Bukhari, A.S. Alqahtani, M.Y. Malik, S. Abdullaev, S.E. Alhazmi

“…These numerical results are used to discuss the flow quantities i.e., velocity, temperature and concentration against the sundry dimensionless quantities. Examining the results it comes to know that both thermal and concentration nonlinear mix convection have oppositely affecting the axial velocity. …”
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