Numerical Investigation of Collision-Induced Breakup of Raindrops. Part II: Parameterizations of Coalescence Efficiencies and Fragment Size Distributions

2010 ◽  
Vol 67 (3) ◽  
pp. 576-588 ◽  
Author(s):  
Winfried Straub ◽  
Klaus Dieter Beheng ◽  
Axel Seifert ◽  
Jan Schlottke ◽  
Bernhard Weigand
Keyword(s):  
Fragment Size ◽  
Mass Conservation ◽  
Distribution Functions ◽  
Size Distributions ◽  
Independent State ◽  
Peak Structure ◽  
Binary Collisions ◽  
The One ◽  
Physical Quantities ◽  
Second Peak

Abstract Results of numerically investigated binary collisions of 32 drop pairs presented in Part I of this study are used to parameterize coalescence efficiencies and size distributions of breakup fragments of large raindrops. In contrast to the well-known results of Low and List, it is shown that coalescence efficiencies Ec can be described best by means of the Weber number We yielding Ec = exp(−1.15We). The fragment size distributions gained from our numerical investigations were parameterized by fitting normal, lognormal, and delta distributions and relating the parameters of the distribution functions to physical quantities relevant for the breakup event. Thus, this parameterization has formally a substantial similarity to the one of Low and List, although no reference is made to breakup modes such as filament, disk, and sheet. Additionally, mass conservation is guaranteed in the present approach. The parameterizations from Low and List, as well as the new parameterizations, are applied to compute a stationary size distribution (SSD) from solving the kinetic coagulation–breakup equation until a time-independent state is reached. Although with the parameterizations of Low and List, the SSD shows an often-reported three-peak structure, with the new parameterizations the second peak vanishes completely.

scholarly journals Numerical Investigation of Collision-Induced Breakup of Raindrops. Part I: Methodology and Dependencies on Collision Energy and Eccentricity

2010 ◽  
Vol 67 (3) ◽  
pp. 557-575 ◽  
Author(s):  
Jan Schlottke ◽  
Winfried Straub ◽  
Klaus Dieter Beheng ◽  
Hassan Gomaa ◽  
Bernhard Weigand
Keyword(s):  
Fragment Size ◽  
Calculated Data ◽  
Additional Parameter ◽  
Horizontal Distance ◽  
Size Distributions ◽  
Fall Velocity ◽  
Limit Value ◽  
Binary Collisions ◽  
Important Extension ◽  
Definite Limit

Abstract Binary collisions of large raindrops moving with terminal fall velocity are numerically investigated using FS3D, a direct numerical simulation (DNS) code based on the “volume of fluid” method. The result of this process can be a permanent coalescence or a temporal coalescence followed by a breakup of the coalesced system into smaller-sized remnants of the original raindrops and a number of fragment droplets of different sizes. In total, 32 drop pairs are studied with sizes chosen to cover nearly completely the entire size parameter range relevant to breakup. This is an important extension of investigations performed in 1982 by Low and List, who studied 10 drop pairs only. Moreover, eccentricity has been introduced as an additional parameter controlling the collision outcome. Eccentricity is defined as the horizontal distance of the initial drops’ centers with values equal to approximately 0 for centric and 1 for grazing collisions. The main results include numerically calculated data of coalescence efficiencies and fragment size distributions with emphasis on eccentricity effects. It is shown that eccentricity largely determines the appearance of specific breakup modes and consequently the respective fragment size distributions. Comparisons are made with the main findings of Low and List. Coalescence efficiency values larger than those derived by Low and List show up for very small Weber numbers. Additionally, the existence of their definite limit value of collision kinetic energy necessary for coalescence could not be confirmed. The fragment size distributions are in some cases similar to those measured by Low and List but there are also major differences for other cases. The presented results are used for parameterizations of coalescence efficiencies and fragment size distributions as well as for calculations of stationary drop spectra shown in Part II of this study.

Analysis of fragment size distributions in collisions of monocharged ions with the C60molecule

2005 ◽  
Vol 38 (7) ◽  
pp. 789-806 ◽  
Author(s):  
A Rentenier ◽  
P Moretto-Capelle ◽  
D Bordenave-Montesquieu ◽  
A Bordenave-Montesquieu
Keyword(s):  
Fragment Size ◽  
Size Distributions

Indentation of a Transversely Isotropic Thermoporoelastic Half-Space by a Rigid Circular Cylindrical Punch

2017 ◽  
Vol 84 (11) ◽  
Author(s):  
Yilan Huang ◽  
Guozhan Xia ◽  
Weiqiu Chen ◽  
Xiangyu Li
Keyword(s):  
Half Space ◽  
Original Problem ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
The Finite Element Method ◽  
Thermal Fields ◽  
Cylindrical Punch ◽  
The One ◽  
Physical Quantities ◽  
Potential Theory Method

Exact solutions to the three-dimensional (3D) contact problem of a rigid flat-ended circular cylindrical indenter punching onto a transversely isotropic thermoporoelastic half-space are presented. The couplings among the elastic, hydrostatic, and thermal fields are considered, and two different sets of boundary conditions are formulated for two different cases. We use a concise general solution to represent all the field variables in terms of potential functions and transform the original problem to the one that is mathematically expressed by integral (or integro-differential) equations. The potential theory method is extended and applied to exactly solve these integral equations. As a consequence, all the physical quantities of the coupling fields are derived analytically. To validate the analytical solutions, we also simulate the contact behavior by using the finite element method (FEM). An excellent agreement between the analytical predictions and the numerical simulations is obtained. Further attention is also paid to the discussion on the obtained results. The present solutions can be used as a theoretical reference when practically applying microscale image formation techniques such as thermal scanning probe microscopy (SPM) and electrochemical strain microscopy (ESM).

THE RESPONSE FUNCTION OF THE 4He, 16O AND 40Ca NUCLEI IN THE HARMONIC OSCILLATOR SHELL MODEL AND THE IMPULSE APPROXIMATIONS

2013 ◽  
Vol 22 (02) ◽  
pp. 1350011
Author(s):  
M. MODARRES ◽  
Y. YOUNESIZADEH
Keyword(s):  
Harmonic Oscillator ◽  
Shell Model ◽  
Momentum Distribution ◽  
Impulse Approximation ◽  
Distribution Functions ◽  
Heavy Nuclei ◽  
Momentum Distribution Function ◽  
Oscillator Shell ◽  
Nucleus Scattering ◽  
The One

In this work, the response functions (RFs) of the 4 He , 16 O and 40 Ca nuclei are calculated in the harmonic oscillator shell model (HOSM) and the impulse approximation (IA). First, the one-body momentum distribution and the one-body spectral functions for these nuclei are written in the HOSM configuration. Then, their RFs are calculated, in the two frameworks, namely the spectral and the momentum distribution functions, within the IA. Unlike our previous work, no further assumption is made to reduce the analytical complications. For each nucleus, it is shown that the (RF) evaluated using the corresponding spectral function has a sizable shift, with respect to the one calculated in terms of the momentum distribution function. It is concluded that for the heavier nuclei, this shift increases and reaches nearly to a constant value (approximately 62 MeV), i.e., similar to that of nuclear matter. It is discussed that in the nuclei with the few nucleons, the above shift can approximately be ignored. This result reduces the theoretical complication for the explanation of the ongoing deep inelastic scattering (DIS) experiments of 3 H or 3 H nucleus target in the Jefferson Laboratory. On the other hand, it is observed that in the heavier nuclei, the RF heights (width) decrease (increase), i.e., the comparison between the theoretical and the experimental electron nucleus scattering cross-section is more sensible for heavy nuclei rather than the light ones.

scholarly journals An investigation of processes controlling the evolution of the boundary layer aerosol size distribution properties at the Swedish background station Aspvreten

2004 ◽  
Vol 4 (4) ◽  
pp. 4507-4543 ◽  
Author(s):  
P. Tunved ◽  
J. Ström ◽  
H.-C. Hansson
Keyword(s):  
Size Distribution ◽  
Wet Deposition ◽  
Source Area ◽  
Aerosol Size Distribution ◽  
Back Trajectory ◽  
Main Process ◽  
Size Distributions ◽  
Back Trajectory Analysis ◽  
The One ◽  
Precipitating Clouds

Abstract. Aerosol size distributions have been measured at the Swedish background station Aspvreten (58.8° N, 17.4° E). Different states of the aerosol were determined using a novel application of cluster analysis. The analysis resulted in eight different clusters capturing the different stages of the aerosol lifecycle. The aerosol was interpreted as belonging to fresh, intermediate and aged type of size distribution and different magnitudes thereof. With aid of back trajectory analysis we present statistics concerning the relation of source area and different meteorological parameters using a non-lagrangian approach. Source area is argued to be important although not sufficient to describe the observed aerosol properties. Especially processing by clouds and precipitation is shown to be crucial for the evolution of the aerosol size distribution. As much as 60% of the observed size distributions present features likely related to cloud processes or wet deposition. The lifetime properties of different sized aerosols are discussed by means of measured variability. Processing by non-precipitating clouds most obviously affect aerosols in the size range 100 nm and larger. This indicates an approximate limit for activation in clouds to 100 nm in this type of environment. The aerosol lifecycle is discussed. Size distributions bearing signs of recent new particle formation (~30% of the observed size distributions) represent the first stage in the lifecycle. Aging may proceed in two directions: either growth by condensation and coagulation or processing by non-precipitating clouds. In both cases mass is accumulated. Wet removal is the main process capable of removing aerosol mass. Wet deposition is argued to be an important mechanism in reaching a state where nucleation may occur (i.e. sufficiently low aerosol surface area) in environments similar to the one studied.

scholarly journals Demographic Development of Russia in Geopolitical Coordinates of the XX – Early XXI Century

2021 ◽  
Vol 20 (3) ◽  
pp. 146-154
Author(s):  
Leonid L. Rybakovsky ◽  
◽  
Natalia I. Kozhevnikova ◽  
Keyword(s):  
Soviet Union ◽  
The State ◽  
Human Potential ◽  
Demographic Development ◽  
Independent State ◽  
Demographic Dynamics ◽  
The Soviet Union ◽  
History Of ◽  
English Speaking ◽  
The One

The article shows that due to the fact that Russia has the largest territory among the rest of the world, the richest natural resources, making it a self-sufficient, advantageous geographical position, as well as a kind of history of the creation and development of the state, in the past, and still causes hostile attitude to it a number of states. Thanks to sufficient human potential, Russia, constituting the core of a state united with other peoples in pre-revolutionary and Soviet times, was able to defend its homeland, even from such an enemy as Nazi Germany. The increase in the population of Russia has always been the most important factor in ensuring the security of the state. The paper provides a detailed description of the demographic development of Russia, both as part of the Soviet Union and as an independent state. The dynamics of the population of Russia is considered, on the one hand, in the group of countries with a predominance of the Slavic ethnos, and on the other hand, it is compared with the demographic dynamics of the English-speaking group of countries.

Fascism under Pressure

2009 ◽  
Vol 24 (1) ◽  
pp. 116-158 ◽  
Author(s):  
Ana Antic
Keyword(s):  
World War Ii ◽  
Racial Identity ◽  
Class Struggle ◽  
The Political ◽  
World War ◽  
Independent State ◽  
Anti Semitism ◽  
State And Society ◽  
National Boundaries ◽  
The One

This article analyzes how the ideological discourse of the Croatian fascist movement (the Ustaša) evolved in the course of World War II under pressures of the increasingly popular and powerful communist armed resistance. It explores and interprets the way the regime formulated its ideological responses to the political/ideological challenge of the leftist guerrilla and its propaganda in the period after the proclamation of the Ustaša Independent State of Croatia in 1941 until the end of the war. The author demonstrates that the regime, faced with its own political weakness and inability to maintain authority, shaped its rhetoric and ideological self-definition in a direct dialogue with the Marxist discourse of the communist propaganda, incorporating important Marxist concepts in its theory of state and society and redefining its concepts of national boundaries and racial identity to match the communists’ propaganda of inclusive, civic national Yugoslavism. This massive ideological renegotiation of the movement’s basic tenets and its consequent leftward shift reflected a change in an opposite direction from the one commonly encountered in narratives of other fascisms’ ideological evolution paths (most notably in Italy and Germany): as the movement became a regime, the Ustaša transformed from its initial conservatism, traditionalism (in both sociopolitical and cultural matters), pseudo-feudal worldview of peasant worship and antiurbanism, anti-Semitism, and rigid racialism in relation to nation and state into an ideology of increasingly inclusive, culture-based, and nonethnic nationalism and with an exceptionally strong leftist rhetoric of social welfare, class struggle, and the rights of the working class.

Fragment size distributions in brittle deformed rocks.

2021 ◽  
pp. 104496
Author(s):  
Alison Ord ◽  
Thomas Blenkinsop ◽  
Bruce Hobbs
Keyword(s):  
Fragment Size ◽  
Size Distributions

scholarly journals Evolution of fragment size distributions from the crushing of granular materials

2019 ◽  
Vol 99 (1) ◽  
Author(s):  
Pavel S. Iliev ◽  
Falk K. Wittel ◽  
Hans J. Herrmann
Keyword(s):  
Granular Materials ◽  
Fragment Size ◽  
Size Distributions

scholarly journals WAVE-CURRENT INTERACTION OVER SEABEDS WITH DIFFERENT ROUGHNESS: A STATISTICAL ANALYSIS

2017 ◽  
pp. 16
Author(s):  
Carla Faraci ◽  
Pietro Scandura ◽  
Enrico Foti
Keyword(s):  
Gaussian Distribution ◽  
Current Velocity ◽  
Mass Conservation ◽  
Distribution Functions ◽  
Wave Velocities ◽  
Velocity Statistics ◽  
Steady Current ◽  
Wave Effects ◽  
Current Interaction ◽  
Rippled Bed

Wave-current flow over seabeds covered with different roughness has been studied in order to deepen the knowledge on the statistical properties of the near-bed velocity. The results of three different experimental campaigns performed in the presence of a sandy bed, a gravel bed and a rippled bed, carried out superimposing a steady current onto an orthogonal wave, have been analysed. The statistics of the current velocity, including the wave effects on the steady current have been investigated. It has been observed that in the absence of waves, the fluctuations of the near-bed velocities closely follow a Gaussian distribution. When waves are also present, in order to obtain consistent near-bed velocity statistics, it is necessary to decouple the velocity events in the current direction by taking into account the sign of the wave velocities. In the latter case, the nature of the distribution functions is influenced by the mass conservation principle. A Gaussian distribution well describes the turbulent fluctuations obtained by removing the phase averaged velocity from the current velocity.

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