scholarly journals The shape of dendritic tips

2020 ◽  
Vol 378 (2171) ◽  
pp. 20190243 ◽  
Author(s):  
Dmitri V. Alexandrov ◽  
Peter K. Galenko
Keyword(s):  
Experimental Data ◽  
Power Law ◽  
Dendritic Growth ◽  
Binary Systems ◽  
Fractional Power ◽  
Power Laws ◽  
Theme Issue ◽  
Special Case ◽  
Dendritic Shape ◽  
Good Agreement

The present article is focused on the shapes of dendritic tips occurring in undercooled binary systems in the absence of convection. A circular/globular shape appears in limiting cases of small and large Péclet numbers. A parabolic/paraboloidal shape describes the tip regions of dendrites whereas a fractional power law defines a shape behind their tips in the case of low/moderate Péclet number. The parabolic/paraboloidal and fractional power law shapes are sewed together in the present work to describe the dendritic shape in a broader region adjacent to the dendritic tip. Such a generalized law is in good agreement with the parabolic/paraboloidal and fractional power laws of dendritic shapes. A special case of the angled dendrite is considered and analysed in addition. The obtained results are compared with previous experimental data and the results of numerical simulations on dendritic growth. This article is part of the theme issue ‘Patterns in soft and biological matters’.

scholarly journals Emergence of power laws in the pharmacokinetics of paclitaxel due to competing saturable processes.

2008 ◽  
Vol 11 (3) ◽  
pp. 77 ◽  
Author(s):  
Jack A Tuszynski ◽  
Rebeccah E. Marsh ◽  
Michael B. Sawyer ◽  
Kenneth J.E. Vos
Keyword(s):  
Power Law ◽  
Fractional Power ◽  
Area Under The Curve ◽  
Power Laws ◽  
Dose Dependence ◽  
Power Exponent ◽  
Least Squares Regression ◽  
Time Data ◽  
Concentration Time ◽  
Wide Range

Purpose: This study presents the results of power law analysis applied to the pharmacokinetics of paclitaxel. Emphasis is placed on the role that the power exponent can play in the investigation and quantification of nonlinear pharmacokinetics and the elucidation of the underlying physiological processes. Methods: Forty-one sets of concentration-time data were inferred from 20 published clinical trial studies, and 8 sets of area under the curve (AUC) and maximum concentration (Cmax) values as a function of dose were collected. Both types of data were tested for a power law relationship using least squares regression analysis. Results: Thirty-nine of the concentration-time curves were found to exhibit power law tails, and two dominant fractal exponents emerged. Short infusion times led to tails with a single power exponent of -1.57 ± 0.14, while long infusion times resulted in steeper tails characterized by roughly twice the exponent. The curves following intermediate infusion times were characterized by two consecutive power laws; an initial short slope with the larger alpha value was followed by a crossover to a long-time tail characterized by the smaller exponent. The AUC and Cmax parameters exhibited a power law dependence on the dose, with fractional power exponents that agreed with each other and with the exponent characterizing the shallow decline. Computer simulations revealed that a two- or three-compartment model with both saturable distribution and saturable elimination can produce the observed behaviour. Furthermore, there is preliminary evidence that the nonlinear dose-dependence is correlated with the power law tails. Conclusion: Assessment of data from published clinical trials suggests that power laws accurately describe the concentration-time curves and non-linear dose-dependence of paclitaxel, and the power exponents provide insight into the underlying drug mechanisms. The interplay between two saturable processes can produce a wide range of behaviour, including concentration-time curves with exponential, power law, and dual power law tails.

scholarly journals Sn-Ni-Bi liquid phase thermodynamic properties

2011 ◽  
Vol 9 (1) ◽  
pp. 149-156 ◽  
Author(s):  
Nikolina Milcheva ◽  
Jolanta Romanowska ◽  
Gueorgui Vassilev
Keyword(s):  
Experimental Data ◽  
Liquid Phase ◽  
Thermodynamic Properties ◽  
Binary Systems ◽  
Isopiestic Method ◽  
Miscibility Gap ◽  
Calphad Approach ◽  
Activity Data ◽  
General Solution Model ◽  
Good Agreement

AbstractExperimental data of bismuth activity coefficients at 1773 K were obtained by isopiestic method and compared to calculated values. Thermodynamic properties of the Sn-Ni-Bi liquid phase were estimated by means of the general solution model and by the methods of Kohler. Description of the ternary liquid phase (Gibbs excess energy dependence on the temperature and the composition) was achieved by using available thermodynamic data of the constitutive binary systems (Ni-Bi, Sn-Bi, Sn-Ni). A comparison between calculated quantities and experimental data wasconducted. The present assessment with thermodynamically optimized values of the system Sn-Ni-Bi (obtained by the CALPHAD approach) was in good agreement. The suggested appearance of a liquid phase miscibility gap at high temperatures is in agreement with the experimental bismuth activity data and with the assessed thermochemical functions.

Analysis of a Power Law and Log Law for a Turbulent Wall Jet Over a Transitional Rough Surface: Universal Relations

2011 ◽  
Vol 133 (9) ◽  
Author(s):  
Noor Afzal ◽  
Abu Seena
Keyword(s):  
Experimental Data ◽  
Rough Surface ◽  
Power Law ◽  
Power Laws ◽  
Velocity Profiles ◽  
Wall Jet ◽  
Log Law ◽  
Jet Velocity ◽  
Turbulent Wall ◽  
Momentum Integral

The power law and log law velocity profiles and an integral analysis in a turbulent wall jet over a transitional rough surface have been proposed. Based on open mean momentum Reynolds equations, a two layer theory for large Reynolds numbers is presented and the matching in the overlap region is carried out by the Izakson-Millikan-Kolmogorov hypothesis. The velocity profiles and skin friction are shown to be governed by universal log laws as well as by universal power laws, explicitly independent of surface roughness, having the same constants as a fully smooth surface wall jet (or fully rough surface wall jet, as appropriate). The novel scalings for stream-wise variations of the flow over a rough wall jet have been analyzed, and best fit relations for maximum wall jet velocity, boundary layer thickness at maxima of wall jet velocity, the jet half width, the friction factor, and momentum integral are supported by the experimental data. There is no universality of scalings in traditional variables, and different expressions are needed for transitional roughness. The experimental data provides very good support to our universal relations proposed in terms of alternate variables.

Prediction of Solid-Liquid Interface Stability and Dendritic Growth in Multi-Component Alloys with Calphad Method

2005 ◽  
Vol 475-479 ◽  
pp. 2721-2724
Author(s):  
Rui Jie Zhang ◽  
Zhi He ◽  
Wan Qi Jie
Keyword(s):  
Experimental Data ◽  
Present Method ◽  
Dendritic Growth ◽  
Calphad Method ◽  
Liquid Interface ◽  
Interface Stability ◽  
Calculation Results ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Good Agreement

A method to predict the solid-liquid interface stability and the constrained dendrite growth of multi-component alloys was developed based on the Calphad method. The method was applied to several industrial Al-Si-Mg alloys, and the predicted results were compared with some former experimental data. The good agreement between the calculation results and the experimental data demonstrates the superiority of the present method to the classical one based on constant parameter assumptions.

An Alternative Approach for Modeling the Hot Carrier Degradation of the Si/SiO2 Interface

1998 ◽  
Vol 513 ◽  
Author(s):  
Zhi Chen ◽  
Jinju Lee ◽  
Joseph W. Lyding
Keyword(s):  
Experimental Data ◽  
Theoretical Model ◽  
Power Law ◽  
Interface Trap ◽  
Hot Carrier ◽  
Alternative Approach ◽  
Physical Insight ◽  
Insight Into ◽  
Good Agreement ◽  
Hot Carrier Degradation

ABSTRACTAn alternative approach for modeling the hot carrier degradation of the Si/SiO2 interface based on the dispersive characteristics of the interface trap generation has been proposed. The timedependent interface trap generation has been modeled using the stretched exponential expression. The conventional power law of degradation is just the approximation of this general form. Very good agreement has been found between the theoretical model and the experimental data. This approach gives more physical insight into the understanding of the mechanism for the interface trap generation.

scholarly journals Power Law Duality in Classical and Quantum Mechanics

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 409
Author(s):  
Akira Inomata ◽  
Georg Junker
Keyword(s):  
Quantum Mechanics ◽  
Green Function ◽  
Power Law ◽  
Ad Hoc ◽  
Fractional Power ◽  
Power Laws ◽  
Energy Coupling ◽  
Arbitrary Power ◽  
Dual Symmetry ◽  
The Green Function

The Newton–Hooke duality and its generalization to arbitrary power laws in classical, semiclassical and quantum mechanics are discussed. We pursue a view that the power-law duality is a symmetry of the action under a set of duality operations. The power dual symmetry is defined by invariance and reciprocity of the action in the form of Hamilton’s characteristic function. We find that the power-law duality is basically a classical notion and breaks down at the level of angular quantization. We propose an ad hoc procedure to preserve the dual symmetry in quantum mechanics. The energy-coupling exchange maps required as part of the duality operations that take one system to another lead to an energy formula that relates the new energy to the old energy. The transformation property of the Green function satisfying the radial Schrödinger equation yields a formula that relates the new Green function to the old one. The energy spectrum of the linear motion in a fractional power potential is semiclassically evaluated. We find a way to show the Coulomb–Hooke duality in the supersymmetric semiclassical action. We also study the confinement potential problem with the help of the dual structure of a two-term power potential.

scholarly journals Empirical Estimation of Ethanol-Methylcellulose based Green Gel Propellant Viscosity at Varying Temperature

2021 ◽  
Vol 23 (07) ◽  
pp. 1293-1302
Author(s):  
Saugata Mandal ◽  
◽  
Balaguru Pandian ◽  
Rajarshi Das ◽  
◽  
...  
Keyword(s):  
Experimental Data ◽  
Power Law ◽  
Empirical Model ◽  
Rheological Behavior ◽  
Empirical Estimation ◽  
Propulsion Systems ◽  
Shear Rates ◽  
Temperature Range ◽  
Shear Thinning Fluids ◽  
Good Agreement

The rheological behavior of the Ethanol based green gels for use in propulsion systems at temperature range of 100C – 500C is investigated by employing a novel empirical model developed. The study is conducted at various shear rates. Empirically predicted results were observed to be in good agreement with experimental data at higher shear rates for both pure and energized gel system (>100 s-1). Considering the results, the present empirical model is deemed suitable for those Non Newtonian shear thinning fluids which obey Power law.

scholarly journals Prediction of phase equilibria in the In-Sb-Pb system

2008 ◽  
Vol 73 (3) ◽  
pp. 377-384
Author(s):  
Dusko Minic ◽  
Dragan Manasijevic ◽  
Dragana Zivkovic ◽  
Nada Strbac ◽  
Zvonimir Stankovic
Keyword(s):  
Experimental Data ◽  
Phase Diagram ◽  
Phase Equilibria ◽  
Binary Systems ◽  
Equilibrium Phase ◽  
Calculated Phase Diagram ◽  
Equilibrium Phase Diagram ◽  
Thermodynamic Prediction ◽  
Calculated Liquidus ◽  
Good Agreement

Binary thermodynamic data, successfully used for phase diagram calculations of the binary systems In-Sb, Pb-Sb and In-Pb, were used for the prediction of the phase equilibria in the ternary In-Sb-Pb system. The predicted equilibrium phase diagram of the vertical Pb-InSb section was compared with the results of differential thermal analysis (DTA) and optical microscopy. The calculated phase diagram of the isothermal section at 300 ?C was compared with the experimentally (SEM, EDX) determined composition of phases in the chosen alloys after annealing. Very good agreement between the binary-based thermodynamic prediction and the experimental data was found in all cases. The calculated liquidus projection of the ternary In-Sb-Pb system is also presented.

scholarly journals Solidification thermal parameters and dendritic growth during the horizontal directional solidification of Al-7wt.%Si alloy

2014 ◽  
Vol 67 (3) ◽  
pp. 265-270 ◽  
Author(s):  
Diego de Leon Brito Carvalho ◽  
Thiago Antônio Paixão de Sousa Costa ◽  
Antonio Luciano Seabra Moreira ◽  
Maria Adrina Paixão de Souza da Silva ◽  
José Marcelino Dias Filho ◽  
...  
Keyword(s):  
Experimental Data ◽  
Growth Rate ◽  
Comparative Study ◽  
Directional Solidification ◽  
Power Law ◽  
Dendritic Growth ◽  
Primary Dendrite ◽  
Thermal Parameters ◽  
Hypoeutectic Alloy ◽  
Power Law Function

The main purpose of this work is to investigate the influence of thermal parameters such as growth rate (V L) and cooling rate (T R) on the primary dendrite arm spacings (λ1) during the horizontal transient directional solidification of Al-7wt.%Si hypoeutectic alloy. The primary dendrite spacings were measured along the length of the samples and correlated with these thermal parameters. The variation of dendrite spacings is expressed as a power law function of V L and T R given by the formulas λ1 = 55(V L)-1.1 and λ1 = 212 (T R)-0.55, respectively. A comparative study between the results of this work and those from the literature proposed to investigate these dendrite spacings during the upward and downward vertical directional solidification of Al-7wt.%Si alloy is also conducted. Finally, the experimental data are compared with some predictive dendritic models from the literature.

Fechner's Psychophysical Law as a Special Case of Stevens' Three-Parameter Power Law

1992 ◽  
Vol 75 (3_suppl) ◽  
pp. 1205-1206 ◽  
Author(s):  
Tarald O. Kvålseth
Keyword(s):  
Experimental Data ◽  
Power Law ◽  
Additional Parameter ◽  
Response Variable ◽  
The Cost ◽  
Special Case ◽  
Extra Parameter

This paper shows that Fechner's law of psychophysics is a special case of Stevens' power law with three parameters. Consequently, at least as good over-all fit to experimental data is always obtained, at the cost of one additional parameter, by using Stevens' power law involving an extra parameter added to the response variable.

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