Evaporation of multiple droplets

2021 ◽  
Vol 927 ◽  
Author(s):  
Hassan Masoud ◽  
Peter D. Howell ◽  
Howard A. Stone
Keyword(s):  
Experimental Studies ◽  
Accurate Estimate ◽  
Contact Angles ◽  
Single Droplet ◽  
Horizontal Substrate ◽  
Transport Problems ◽  
Multi Body ◽  
Theoretical Results

We derive an accurate estimate for the diffusive evaporation rates of multiple droplets of different sizes and arbitrary contact angles placed on a horizontal substrate. The derivation, which is based on a combination of Green's second identity and the method of reflections, simply makes use of the solution for the evaporation of a single droplet. The theoretical results can serve as a guide for future computational and experimental studies on the collective evaporation of arrays of droplets, as well as similar multi-body, diffusion-dominated transport problems.

Study of a Vibratory Feeder with Repulsive Surface Which Has Directional Characteristic

1980 ◽  
Vol 102 (1) ◽  
pp. 94-101 ◽  
Author(s):  
S. Okabe ◽  
Y. Yokoyama
Keyword(s):  
Experimental Studies ◽  
Directional Characteristic ◽  
Vibratory Feeder ◽  
The Mean ◽  
Theoretical Results

This paper treats the motion of a particle on a vibratory feeder whose track has directional characteristic in repulsive motion, for examples, obliquely bristled track, obliquely sliced track and so on. Under some assumptions, the practical equation for predicting the mean conveying velocity is shown and the relations between conveying condition and the mean conveying velocity are clarified theoretically. These relations are shown in various diagrams. Referring these diagrams, the optimum conveying conditions are discussed also. The theoretical results show that the mean conveying velocity is considerably larger than that of the ordinary feeder. The theoretical results are confirmed by experimental studies.

scholarly journals MHD-waves in the geomagnetic tail: A review

10.12737/7168 ◽  
2015 ◽  
Vol 1 (1) ◽  
pp. 4-22 ◽  
Author(s):  
Анатолий Леонович ◽  
Anatoliy Leonovich ◽  
Виталий Мазур ◽  
Vitaliy Mazur ◽  
Даниил Козлов ◽  
...  
Keyword(s):  
Numerical Models ◽  
Experimental Studies ◽  
Low Frequency ◽  
Detailed Comparison ◽  
Mhd Waves ◽  
Theoretical Studies ◽  
Geomagnetic Tail ◽  
Magnetopause Oscillations ◽  
Experimental And Theoretical Studies ◽  
Theoretical Results

This article presents the review of experimental and theoretical studies on ultra-low-frequency MHD oscillations of the geomagnetic tail. We consider the Kelvin–Helmholtz instability at the magnetopause, oscillations with a discrete spectrum in the “magic frequencies” range, the ballooning instability of coupled Alfvén and slow magnetosonic waves, and “flapping” oscillations of the current sheet of the geomagnetic tail. Over the last decade, observations from THEMIS, CLUSTER and Double Star satellites have been of great importance for experimental studies. The use of several spacecraft allows us to study the structure of MHD oscillations with high spatial resolution. Due to this, we can make a detailed comparison between theoretical results and those obtained from multi-spacecraft studies. To make such comparisons in theoretical studies, in turn, we have to use the numerical models closest to the real magnetosphere.

scholarly journals UNIVERSAL THREE-PHASE FERRORESONANCE STABILIZERS

2016 ◽  
Vol 19 (1) ◽  
Author(s):  
GEORGI GEORGIEV ◽  
NADEZHDA EVSTATIEVA
Keyword(s):  
Comparative Analysis ◽  
Experimental Studies ◽  
Voltage Stabilizer ◽  
Satisfactory Accuracy ◽  
Three Phase ◽  
Theoretical Results

A comparative analysis has been carried out on two options of three-phase parametric current sources (inductive-capacitive stabilizers). Their capacities to operate in voltage stabilizer mode have been studied. Such capacities were proven and their conditions were defined. Theoretical results were experimentally checked and confirmed with satisfactory accuracy. Based on theoretical and experimental studies it was proven that the considered systems can operate in both modes – as current and voltage stabilizers.

scholarly journals Contact lines over random topographical substrates. Part 1. Statics

2011 ◽  
Vol 672 ◽  
pp. 358-383 ◽  
Author(s):  
NIKOS SAVVA ◽  
GRIGORIOS A. PAVLIOTIS ◽  
SERAFIM KALLIADASIS
Keyword(s):  
Numerical Experiments ◽  
Random Variable ◽  
Contact Angles ◽  
Contact Lines ◽  
Substrate Roughness ◽  
Random Functions ◽  
Flat Substrate ◽  
The Subject ◽  
Influence Of Substrate ◽  
Theoretical Results

We investigate theoretically the statistics of the equilibria of two-dimensional droplets over random topographical substrates. The substrates are appropriately represented as families of certain stationary random functions parametrized by a characteristic amplitude and wavenumber. In the limit of shallow topographies and small contact angles, a linearization about the flat-substrate equilibrium reveals that the droplet footprint is adequately approximated by a zero-mean, normally distributed random variable. The theoretical analysis of the statistics of droplet shift along the substrate is highly non-trivial. However, for weakly asymmetric substrates it can be shown analytically that the droplet shift approaches a Cauchy random variable; for fully asymmetric substrates its probability density is obtained via Padé approximants. Generalization to arbitrary stationary random functions does not change qualitatively the behaviour of the statistics with respect to the characteristic amplitude and wavenumber of the substrate. Our theoretical results are verified by numerical experiments, which also suggest that on average a random substrate neither enhances nor reduces droplet wetting. To address the question of the influence of substrate roughness on wetting, a stability analysis of the equilibria must be performed so that we can distinguish between stable and unstable equilibria, which in turn requires modelling the dynamics. This is the subject of Part 2 of this study.

Convergence of a cylindrical liquid shell and the formation of a bore in a rotating fluid

1999 ◽  
Vol 400 ◽  
pp. 355-374
Author(s):  
V. K. KEDRINSKII ◽  
V. V. NIKULIN
Keyword(s):  
Cylindrical Cavity ◽  
Experimental Studies ◽  
Discontinuous Solution ◽  
Rotating Fluid ◽  
Rotationally Symmetric ◽  
Basic Parameters ◽  
Hollow Vortex ◽  
Long Wave Approximation ◽  
Theoretical Results ◽  
Unbounded Fluid

This paper presents the results of experimental studies of a collapsing cylindrical cavity (the convergence of a liquid shell) in a rotating fluid as well as the formation and propagation of a jump (bore) at the interface. The basic parameters of the liquid shell dynamics for a pulsed one-dimensional load are estimated using the equation of cylindrical cavity pulsation in an unbounded fluid. The theoretical model of a rotationally symmetric hydraulic jump moving along the free surface of a hollow vortex is constructed. The jump is simulated by a discontinuous solution of the equations in the long-wave approximation for tornado-like and hollow vortices. For comparison with the experimental data, basic theoretical results are obtained for flows in a hollow vortex with constant circulation and axial velocity varying along the radius of the rotating liquid shell.

scholarly journals Theoretical and Experimental Studies on the C15 Intermetallic Compound NbCr2

1994 ◽  
Vol 364 ◽  
Author(s):  
F. Chu ◽  
D. J. Thoma ◽  
Y. He ◽  
T. E. Mitchell ◽  
S. P. Chen ◽  
...  
Keyword(s):  
Total Energy ◽  
Elastic Moduli ◽  
Experimental Studies ◽  
Atomic Sphere ◽  
Solubility Range ◽  
Volume Curve ◽  
Lmto Method ◽  
Sphere Approximation ◽  
Structure Density ◽  
Theoretical Results

AbstractThe electronic structure and total energy of the C15 NbCr2 phase have been calculated using the linear muffin-tin orbital (LMTO) method with the atomic sphere approximation (ASA). The total energy vs. volume curve, band structure, density of states and Fermi surface were obtained. The calculated results were used to examine several features of the C15 phase, including the elastic properties, phase formation and stability, and solubility range of the C15 phase. The theoretical results are compared to experimental studies on NbCr2 For example, the elastic moduli, phase stability, and homogeneity range have been determined with a variety of experimental techniques. Comparison of the experimental and theoretical results will be discussed.

CHARACTERISTICS OF MESOSCOPIC PHASE TRANSITIONS IN TWO-DIMENSIONAL SIMPLE NANOSTRUCTURED MATERIALS

2003 ◽  
Vol 17 (25) ◽  
pp. 4539-4554 ◽  
Author(s):  
YOSHITAKE YAMAZAKI ◽  
HERBERT GLEITER ◽  
CHENXU WU ◽  
VLADISLAV ALYOSHIN ◽  
JULY KRASILNIKOVA ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Nanostructured Materials ◽  
Critical Phenomena ◽  
Experimental Studies ◽  
Inert Gas ◽  
Computational Results ◽  
Two Dimensional ◽  
Metropolis Monte Carlo ◽  
Renormalization Theory ◽  
Theoretical Results

In order to study nanostructured materials, a fundamental framework of the theory and the computer-experimental studies is established. The essential characteristics of the mesoscopic phase transitions and critical phenomena in these materials are evaluated by means of this approach. For nanostructured materials consisting of inert gas atoms, we study mesoscopic phase transitions and critical phenomena by generalizing the renormalization theory and the Metropolis Monte Carlo method. The results obtained by the both methods are reported in two papers: computational results in the present paper and the theoretical results in the paper which follows.

scholarly journals Runtime Analysis of Restricted Tournament Selection for Bimodal Optimisation

2021 ◽  
pp. 1-26
Author(s):  
Edgar Covantes Osuna ◽  
Dirk Sudholt
Keyword(s):  
Distance Measure ◽  
Experimental Studies ◽  
Window Size ◽  
Population Diversity ◽  
Single Individual ◽  
Niching Methods ◽  
Size Population ◽  
Tournament Selection ◽  
Theoretical Results ◽  
Shed Light

Abstract Niching methods have been developed to maintain the population diversity, to investigate many peaks in parallel and to reduce the effect of genetic drift. We present the first rigorous runtime analyses of restricted tournament selection (RTS), embedded in a (μ+1) EA, and analyse its effectiveness at finding both optima of the bimodal function TwoMax. In RTS, an offspring competes against the closest individual, with respect to some distance measure, amongst w (window size) population members (chosen uniformly at random with replacement), to encourage competition within the same niche. We prove that RTS finds both optima on TwoMax efficiently if the window size w is large enough. However, if w is too small, RTS fails to find both optima even in exponential time, with high probability. We further consider a variant of RTS selecting individuals for the tournament without replacement. It yields a more diverse tournament and is more effective at preventing one niche from taking over the other. However, this comes at the expense of a slower progress towards optima when a niche collapses to a single individual. Our theoretical results are accompanied by experimental studies that shed light on parameters not covered by the theoretical results and support a conjectured lower runtime bound.

scholarly journals On the spectrum of discrete-ordinates neutron transport problems

2021 ◽  
Vol 9 (2) ◽  
Author(s):  
Jesús Pérez Curbelo
Keyword(s):  
Discrete Spectrum ◽  
Neutron Transport ◽  
Anisotropic Scattering ◽  
Discrete Ordinates ◽  
High Anisotropy ◽  
Linear Transport Equation ◽  
The One ◽  
Transport Problems ◽  
Theoretical Results ◽  
Analytic Problem

Over the last six decades, the discrete spectrum of the neutron transport operator has been widely studied. Important theoretical results can be found in the literature regarding the one-speed linear transport equation with anisotropic scattering. In this work, the discrete-ordinates (SN) transport problem with anisotropic scattering has been considered and the discrete spectrum results in multiplying media have been corroborated. The numerical results obtained for the dominant SN eigenvalues agreed with the ones for the analytic problem reported in the literature up to a triplet scattering order. A compact methodology to perform the spectral analysis to multigroup SN problems with high anisotropy order in the scattering and fission reactions is also presented in this paper.

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