HEAT AND MASS TRANSFER IN DISPERSE AND POROUS MEDIA
MATHEMATICAL SIMULATION OF ACOUSTIC AND GAS-DYNAMICAL
PROCESSES IN THE CHANNEL OF AN ACOUSTOCONVECTIVE DRYER
I. A. Fedorchenko and A. V. Fedorov UDC 532.72; 669.015.23
This paper presents and analyzes the data of numerical simulation of nonstationary fl ow in the channel of an
acoustoconvective dryer in which the acoustic fi eld is produced by a Hartmann generator. The gas-dynamical fl ow
fi eld and frequency characteristics of the problem are calculated in axisymmetric and three-dimensional formulations.
The jet outfl owing from the generator nozzle with change in the resonator length and in the jet pressure ratio was
investigated parametrically. The results of numerical calculations are compared with experimental data.
Keywords: acoustoconvective drying, numerical simulation, axisymmetric and three-dimensional fl ows.
METHOD FOR CALCULATING THE DURATION OF VACUUM DRYING OF A METAL-CONCRETE CONTAINER FOR SPENT NUCLEAR FUEL
Yu. E. Karyakin,a M. A. Nekhozhin,b and A. A. Pletneva UDC 621.039.743
A method for calculating the quantity of moisture in a metal-concrete container in the process of its charging with
spent nuclear fuel is proposed. A computing method and results obtained by it for conservative estimation of the
time of vacuum drying of a container charged with spent nuclear fuel by technologies with quantization and without
quantization of the lower fuel element cluster are presented. It has been shown that the absence of quantization in
loading spent fuel increases several times the time of vacuum drying of the metal-concrete container.
Keywords: spent nuclear fuel, "dry" storage, metal-concrete containers, quantization, vacuum drying.
SELF-SIMILAR APPROXIMATION FOR THE PROCESS OF FORMATION OF MICROPOROSITY IN ALLOYS OF LIGHT METALS
I. Saifutdinova and V. G. Lebedevb UDC 537.525
A physical and mathematical model is proposed for description of the formation of microporosity in an alloy within the
framework of the two-phase zone approximation with account for the real state diagram of the alloy. The formation
of microporosity in an Al–Si melt in the process of its solidifi cation as a result of the liberation of hydrogen from it
was investigated in the self-similar approximation. The infl uence of the parameters of solidifi cation of this alloy on
the formation of a gas microporosity in it was analyzed.
Keywords: solidifi cation of an aluminum alloy, hydrogen segregation, shrinkage porosity, gas porosity, self-similar
solution.
UNSTEADY MIXED CONVECTIVE FLOW AND HEAT TRANSFER IN A VERTICAL CORRUGATED CHANNEL WITH COMPOSITE POROUS MEDIA
J. C. Umavathi and M. Shekar UDC 536.25
An unsteady mixed convective fl ow and heat transfer in a vertical corrugated channel containing porous and fl uid
layers are considered. The equations of momentum and energy are solved under appropriate boundary and interface
conditions with the assumption that the solution consists of a mean part and a perturbed one. The exact solutions are
obtained in the long-wave approximation. Separate solutions are matched at the interface with the use of suitable
matching conditions. The effects of pertinent parameters, such as the Grashof number, viscosity ratio, width ratio,
conductivity ratio, frequency, and the wave parameter on the fl ow fi eld and heat transfer characteristics are studied.
Keywords: mixed convection, corrugated channel, porous and fl uid layers.
HEAT AND MASS TRANSFER IN MAGNETO-BIOFLUID FLOW THROUGH A NON-DARCIAN POROUS MEDIUM WITH JOULE EFFECT
B. K. Sharma,a A. Mishra,b and S. Guptab UDC 536.25
In the present study, a mathematical model for the hydromagnetic non-Newtonian biofl uid fl ow in the non-Darcy
porous medium with Joule effect is proposed. A uniform magnetic fi eld acts perpendicularly to the porous surface.
The governing nonlinear partial differential equations are transformed into linear ones which are solved numerically
by applying the explicit fi nite difference method. The effects of various parameters, like Reynolds number and
hydro-magnetic, Forchheimer, and Darcian parameters, Prandtl, Eckert, and Schmidt numbers, on the velocity,
temperature, and concentration are presented graphically. The results of the study can fi nd applications in surgical
operations, industrial material processing, and various heat transfer processes.
Keywords: biofl uid, porous medium, Joule effect, MHD.
TRANSFER PROCESSES IN LOW-TEMPERATURE PLASMA EVOLUTION OF A DROPLET MEDIUM IN A PLASMA-CHEMICAL REACTOR
V. A. Arkhipov,a S. S. Bondarchuk,b and A. S. Zhukova UDC 66.02/09+66.047.791.1+533.9.07.1
We modeled the plasma-chemical method of obtaining fi nely disperse powders by thermochemical decomposition of
liquid pulverized reagents in a high-temperature heat-transfer agent in a column-type direct-fl ow cylindrical reactor.
We consider the processes of working body motion in the reactor cavity and of thermochemical decomposition of
the original solution droplets, evaporation of volatile components, and of the formation of a solid residue. The
simulation of gas dynamics was made using the Reynolds equations; turbulent stresses were determined with the aid
of the k–ε model. In describing the formation of the solid residue, we took into account the processes of heating and
evaporation of droplets, diffusion, crystallization, and of salt thermolysis in the formation of the needed structure
of particles. An analysis of the results of numerical simulation of various operating conditions of the reactor is
performed.
Keywords: plasma-chemical synthesis, metal /salt solution, diffusion, evaporation, heat transfer, crystallization,
metallic oxides, morphology of particles.
TRANSFORMATION OF COPPER STRUCTURE ON EXPOSURE TO A NONEQUILIBRIUM LOW-TEMPERATURE AIR PLASMA
V. V. Azharonok,a A. G. Anisovich,b A. V. Basalai,b UDC 533.9:669.3
S. V. Goncharik,a I. I. Filatova,a and N. I. Chubrika
The change in the structure of M1 copper on exposure to a nonequilibrium low-temperature plasma produced by
a high-frequency capacitive discharge in air at a pressure of about 1 Torr was investigated. The infl uence of the
duration of plasma action on the structure and mechanical properties of copper has been studied. The increase in
the dispersity of copper and in the homogeneity of its structure under the action of plasma has been established. It is
shown that transformation of the copper structure is accompanied by the formation of static distortions of its crystal
lattice at a level of about 0.007·10–10 m.
Keywords: high-frequency capacitive discharge, nonequilibrium low-temperature plasma, microstructure, static
displacement of atoms.
INTENSIFICATION OF ENERGY EXCHANGE IN A HETEROGENEOUS PLASMA JET BY MODULATION OF THE ELECTRIC PARAMETERS
OF THE PLASMA-SPRAYING PROCESS
A. M. Kadyrmetov UDC 621.793.74:621.791.927.55
The possibility of intensifi cation of the energy exchange in a heterogeneous plasma jet produced by a plasma generator
with the use of artifi cial turbulization of this jet and generation of shock waves in it as a result of the modulation of
the electric parameters of the plasma-generator arc was proved. The infl uence of this modulation on the gas-dynamic
parameters of the plasma and the energy state of the sprayed particles was estimated. The possibility of increasing
the velocity of the particles of a dispersed material (by 60%) and the rate of their heating by generation of traveling
velocity waves and entropy temperature waves in the plasma jet is demonstrated.
Keywords: plasma spraying, plasma generator, plasma jet, plasma-generator arc, electric-parameter modulation,
sprayed particles, velocity and temperature of particles.
OCCURRENCE OF EROSION PROCESSES IN THE NEAR-SURFACE REGION OF METALS EXPOSED TO INTENSE NANOSECOND LASER PULSES
V. K. Goncharov, K. V. Kozadaev, V. V. Makarov, UDC 621.373.826.004.14
and D. V. Shchegrikovich
Using the method of laser probing, the time dependences of the transparency factor and integral luminescence
of erosional jets of metals appearing upon their exposure to intense nanosecond laser pulses, as well as of the
probing radiation component scattered by the jet, have been determined. Based on the results of laser probing, a
conclusion was drawn on the condensation nature of the process of liquid-droplet phase formation near the surface
of investigated metals in the considered conditions of laser effect on them.
Keywords: laser erosion of metals, nanosecond pulses of optical radiation, condensed phase of target material.
FORMATION OF THE CONDENSED PHASE OF METALS EXPOSED TO INTENSE NANOSECOND LASER PULSES AT ATMOSPHERIC PRESSURE
V. K. Goncharov, K. V. Kozadaev, V. V. Makarov, UDC 621.373.826.004.14
and D. V. Shchegrikovich
Using the method of laser probing, the basic laws governing the formation of a liquid-droplet phase of a number
of metals exposed to intense (108–109 W/cm2) nanosecond pulses have been determined. Deposited colloidal
nanoparticles have been investigated with the aid of scanning electron microscopy. The effect of smoothing the
surface relief of solid metal targets under the action of a laser pulse train has been demonstrated.
Keywords: erosion laser torch, nanosecond radiation pulses, laser probing, condensed phase of the metal, surface
relief of the metal.
HEAT CONDUCTION AND HEAT TRANSFER IN TECHNOLOGICAL PROCESSES HYDRODYNAMICS AND HEAT TRANSFER OF A WATER FLOW
WITH SUPERCRITICAL PARAMETERS IN A VERTICAL ASSEMBLY OF FUEL ELEMENTS
A. A. Avramenko, E. A. Kondrat′eva, M. M. Kovetskaya, UDC 536.24
and A. I. Tyrinov
Water fl ow in a hexahedral seven-rod fuel assembly at supercritical pressure has been modeled. Consideration
has been given to nonstationary regimes of this fl ow in the case of a stepwise increase in the heat fl ux on the fuelelement
surface and of a drop in the fl ow rate of the coolant at entry. Numerical investigation of the processes of
hydrodynamics and heat transfer was based on the RNG k–ε turbulence model; equations of state of the IF-97
formulation were used. Hydrodynamic and thermal characteristics of the coolant fl ow in the indicated assembly have
been obtained as a result of the modeling.
Keywords: supercritical parameters, modeling, fuel assembly, nuclear power plants, heat fl ux, drop in the coolant
fl ow rate, hydrodynamics, heat transfer.
MATHEMATICAL MODEL OF A NONLOCAL MEDIUM WITH INTERNAL STATE PARAMETERS
V. S. Zarubin, G. N. Kuvyrkin, and I. Yu. Savel′eva UDC 539.3:536.2
Using the relations of the rational thermodynamics of irreversible processes with internal state parameters, a
mathematical model of a nonlocal continuous medium is suggested and examples of calculations are presented.
Keywords: internal state parameters, nonlocal continuous medium, heat conduction equation, structural element.
HEAT EXCHANGE AND HYDRAULIC RESISTANCE OF LASER MIRROR COOLING SYSTEMS FROM CORRUGATIONS
Yu. I. Shanin and O. I. Shanin UDC 536.35:62-405.8;621.375
The hydrodynamics and heat exchange of cooling systems based on corrugated inserts have been investigated
analytically and experimentally. On the basis of the generalization of the data obtained, the fi elds of reasonable use
of such systems for cooling laser mirrors have been determined. Recommendations for improving the characteristics
of the above systems have been worked out.
Keywords: heat transfer, hydraulic resistance, cooling system, laser mirror, corrugated insert.
HEAT EXCHANGE AND HYDRAULIC RESISTANCE OF COMPACT LASER MIRROR COOLING SYSTEMS
Yu. I. Shanin and O. I. Shanin UDC 536.35:62-405.8;621.375
The hydraulic resistance of cooling systems for laser mirrors and the heat exchange in them have been investigated
experimentally. The data obtained have been generalized for several cooling systems with different porous elements.
Keywords: heat transfer, hydraulic resistance, cooling system, laser mirror, porous element.
NANOSTRUCTURES
MECHANOCHEMICAL TREATMENT, SPECIFIC FEATURES OF THE STRUCTURE AND PROPERTIES, AND REACTIVITY OF SHS SYSTEMS BASED ON NATURAL
MATERIALS. 1. MECHANOCHEMICAL SYNTHESIS OF DISPERSE NANOSTRUCTURED COMPOSITE QUARTZ-BASED SYSTEMS
Z. A. Mansurov, N. N. Mofa, and T. A. Shabanova UDC 541.17
This paper presents the results of experimental investigations of the dispersion of quartz particles with their
simultaneous modifi cation in a planetary-centrifugal dynamic mill depending on the variation of the time-force
regimes of mechanochemical treatment. Nitrogen- and carbon-containing compounds were used as modifi ers.
The laws of change in the dispersivity, imperfection, and transformation of the surface layer structure and the
morphological features of synthesized particles of the composite polymer/mineral structure in the process of
mechanochemical treatment have been established. We have shown the relationship between the mechanical action
and the piezoelectric response of the system to the process of modifi cation of the newly formed surface of quartz
particles and their capsulization into hetero-organic shells, whose composition and structure are determined by both
the quality of the material-base and the kind of the modifi er.
Keywords: mechanochemistry, surface modifi cation, nanocomposites, quartz, piezoeffect.
RELAXATION TRANSITIONS IN POLYVINYLCHLORIDE CONTAINING A NANODISPERSED MATERIAL
V. A. Sidletskii,a B. B. Kolupaev,b V. V. Klepko,b UDC 677.494.7:536.63
and E. V. Lebedevb
Results of experimental investigations and evaluations of the infl uence of the microstructure of polyvinylchloride
macromolecules on relaxation processes in heterogeneous systems containing nanodispersed copper powders have
been given. It has been shown that the relaxation β transition whose parameters are dependent on the content of the
fi ller in the composite is realized in the region 300 K ≤ T < 400 K. The interrelation between the β transition and
the cooperative glass α transition has been established. A derivatographic analysis of the distinctive features of the
process of splitting of the α maximum with allowance for the degree of ordering of the arrangement of segments in the
composite volume has been made. Calculated and experimental values of the sought quantities have been compared.
Keywords: structural relaxation, glass transition, segment, mobility, structural element.
INFLUENCE OF SIZE EFFECTS ON CHEMICAL REACTIONS INSIDE A NANOPARTICLE AND ON ITS SURFACE
V. V. Levdanskii,a J. Smolik,b V. Zdimal,b UDC 541.182
and P. Moravecb
The infl uence of size effects on the course of chemical reactions both inside a nanosized particle and on its surface
has been investigated theoretically.
Keywords: nanoparticle, chemical reaction, size effects.
COMPLEX OPTICAL METHOD OF EXPRESS DIAGNOSTICS OF TRANSPARENT MEDIA CONTAINING NANOPARTICLES OF NOBLE METALS
V. K. Goncharov and K. V. Kozadaev UDC 621.373.8; 543.42
A method is proposed for diagnostics of parameters of optically transparent ultrafi ne media containing particles of
noble metals (Au, Ag). In accordance with this method, parameters of small-sized gold and silver particles (their
effective diameter, concentration, and size-distribution dispersion) in optically transparent condensed media were
investigated using, in combination, the methods of laser probing and two-factor analysis of the surface-plasmon
resonance band on the basis of simulation of the dimension and spectral dependences of the effi ciency of extinction
and scattering of radiation by this medium in accordance with the Mie theory.
Keywords: laser probing of optically transparent media, effi ciency of extinction and scattering of radiation,
nanoparticles of noble metals, surface-plasmon resonance, Mie theory.
COMBUSTION OF HETEROGENEOUS SYSTEMS WITH A STOCHASTIC SPATIAL STRUCTURE NEAR THE PROPAGATION LIMITS
P. S. Grinchuk UDC 536.46
Extinction of a heterogeneous reactant mixture in the vicinity of thermal and concentration limits of propagation is
considered. The consideration is based on an analysis of analytical solutions of combustion-theory problems and
on their comparison with both the results of mathematical modeling and a number of experimental works on selfpropagating
high-temperature synthesis. It is shown that solid-phase-combustion models based on the approximation
of a continuous medium are only applicable away from the extinction limits. It is demonstrated that it is fl uctuations
of the spatial reactant distribution that play a decisive role on the limit of propagation of a combustion wave; these
fl uctuations must be allowed for, among other factors, when self-sustaining combustion waves are investigated. A
percolation model that enables one to explain a number of distinctive features found in the behavior of a combustion
wave near the propagation limit is presented.
Keywords: extinction limits, heterogeneous mixture, combustion waves, model.
SCREENING OF THERMAL RADIATION OF THE FLAME AT THE FIRE SITE BY A RADIAL WATER SHIELD
V. N. Gud′,a A. V. Lazarenko,b UDC 614.8.086.54:614.843.4
and V. I. Zhelyakb
The results of investigations of the absorption of thermal radiation from a combustion site by a radial water shield
are presented. The dependence of the screening coeffi cient on the scattering slit width has been established. It is
confi rmed experimentally that the screening properties of water depend on the composition of the combustion site
products.
Keywords: thermal radiation, screening of thermal radiation, water shield.
INFLUENCE OF DROPLET DISTRIBUTION IN A "WATER SLUG" ON THE TEMPERATURE AND CONCENTRATION OF COMBUSTION
PRODUCTS IN ITS WAKE
P. A. Strizhak UDC 536.4
A numerical study has been made of the infl uence of the droplet distribution in a “water slug” on the integral
characteristics of heat and mass transfer (temperature and concentration of the gases in its wake) in motion
through high-temperature combustion products of typical combustible wood. Limiting values of the parameters
characterizing the position of the droplets relative to the neighboring droplets in the ″water slug″ at which minimum
temperatures and concentrations of the combustion products in its wake are attained under the conditions of the
greatest possible completeness of water evaporation, have been established. It has been shown that a series-parallel
droplet distribution in the ″water slug″ is expedient for effi cient action on the high-temperature gases.
Keywords: fi nely atomized water, droplets,″water slug,″ combustion products, heat and mass transfer, evaporation.
HYDRODYNAMICS IN TECHNOLOGICAL PROCESSES DYNAMICS OF FINE PARTICLES DURING IMPINGEMENT OF JETS
ON A BODY WITH A NEEDLE
A.P. Alkhimov,* I. A. Bedarev, and A. V. Fedorov UDC 534.222
Numerical simulation of the impingement of a jet of a two-phase mixture of a gas with submicron metal particles on an
obstacle with a needle located in front of it is carried out. Th e structure of a separated fl ow formed on impingement of a
supersonic jet on a body with a needle has been studied. A comparison of various approximations for the law of resistance
of spherical particles is made. It is shown that particles whose size exceeds 5 μm practically have a rectilinear trajectory
and velocity suffi cient for cold gas-dynamical deposition, whereas particles of diameter less than 0.2 μm envelope the
separation zone being formed near the needle, and their velocity is much smaller than the critical one.
Keywords: two-phase supersonic jet, body with a needle, cold gas-dynamical deposition.
SELF-OSCILLATIONS (SURGING) OF A SINGLE-STAGE CENTRIFUGAL PUMP IN THE CAVITATION REGIME AND THEIR DAMPING
V. V. Gotsulenkoa and V. N. Gotsulenkob UDC 621.65.001:532.595.7
The self-oscillations (surging) of a single-stage centrifugal pump working in a hydraulic system in the cavitation
regime before the stall of the water feed were investigated. The character of change in these oscillations with
change in the value of the acoustic capacitance positioned at the input of the pump was determined. The damping
of the indicated self-oscillations with the use of an acoustic liquid damper connected to the hydraulic system was
investigated. The impossibility of realization of a model of cavitation self-oscillations for a single-stage impeller
pump was substantiated.
Keywords: cavitation self-oscillations, surging, pump-feed stall, cavitation branches, damping of selfoscillations.
ASYMPTOTIC LAW OF ATTENUATION OF OVERCOMPRESSED DETONATION WAVES IN GASES
E. S. Prokhorov UDC 534.222.2
Basic propositions of an isothermal detonation model used for a simplifi ed description of overcompressed detonation
waves in gases have been formulated. Within the framework of the present model, the author has derived an asymptotic
law of attenuation of plane overcompressed detonation up to the Chapman–Jouguet regime in accordance with
which the detonation-front velocity decreases more slowly than was considered to be the case before.
Keywords: detonation waves, degree of overcompression, detonation products, isothermal medium.
THE RIEMANN PROBLEM FOR THE MULTIVELOCITY MODEL OF A MULTICOMPONENT MEDIUM
V. S. Surov UDC 532.529.5
The solution of the Riemann self-similar problem on the decay of an arbitrary discontinuity in a multivelocity
multicomponent mixture is obtained using a model that takes into account the properties of the mixture as a whole.
Keywords: multicomponent
HEAT TRANSFER IN HORIZONTALLY ARRANGED BENT PIPES IN A TURBULENT REGIME OF MOTION AND AT SUPERCRITICAL
PRESSURES OF TOLUENE
R. F. Kelbaliev,a R. A. Sultanov,b I. M. Mamedov,c UDC 536.242.08
and B. F. Ragimovc
It has been established that the heat transfer of toluene in a turbulent regime of motion and at a supercritical pressure
in a horizontally arranged bent pipe changes nonuniformly along the perimeter of the cross section. The basic factors
are free convection and inertial forces. Computational equations for the heat-transfer coeffi cient are proposed.
Keywords: heat transfer, coil, horizontal pipe, supercritical pressure, turbulent regime, toluene.
MISCELLANEA
LASER SPECKLE TECHNOLOGY IN STOMATOLOGY. DIAGNOSTICS OF STRESSES AND STRAINS OF HARD BIOTISSUES
AND ORTHODONTIC AND ORTHOPEDIC STRUCTURES
Yu. L. Denisova,a N. B. Bazylev,b S. P. Rubnikovich,c UDC 615.8-7+615.832.3+535.211+535.341+536.37
and N. A. Fominb
We have investigated the formation and dynamics of speckle biofi elds formed by hard biotissues of the oral cavity
irradiated with low-intensity radiation. We present experimental methods for diagnosing the stressed-strained state
of the maxillodental system and orthodontic and orthopedic structures based on speckle technologies and crosscorrelation
analysis of speckle biofi elds.
Keywords: biospeckle fi eld, strain stress, hard biotissues, speckle technologies, cross-correlation analysis.
ANALYSIS OF THE INFLUENCE OF THERMAL CONDITIONS ON THE OPERATION OF OPTOELECTRONIC DEVICES
E. D. Ushakovskaya UDC 535.8;681.7.01
The optoelectronic device has been considered from the viewpoint of system analysis. It has been shown that thermal
conditions infl uence the transfer function of this system and, as a consequence, the desired signal. Moreover, the
self-radiation of the device′s elements, which also leads to a change in the output signal of the device, depends on
the thermal conditions.
Keywords: information and measurement optoelectronic devices, optoelectronic tracking and detecting devices, thermal noise, photon noise, temperature noise, measurement error, detection probability, image quality, thermal conditions, transfer function, desired signals, self-radiation.
UNDERWATER SHOCK WAVE RESEARCH APPLIED TO THERAPEUTIC
DEVICE DEVELOPMENTS
K. Takayama,a H. Yamamoto,b and H. Shimokawac UDC 532.5:535.8
The chronological development of underwater shock wave research performed at the Shock Wave Research Center
of the Institute of Fluid Science at the Tohoku University is presented. Firstly, the generation of planar underwater
shock waves in shock tubes and their visualization by using the conventional shadowgraph and schlieren methods are
described. Secondly, the generation of spherical underwater shock waves by exploding lead azide pellets weighing
from several tens of micrograms to 100 mg, that were ignited by irradiating with a Q-switched laser beam, and
their visualization by using double exposure holographic interferometry are presented. The initiation, propagation,
refl ection, focusing of underwater shock waves, and their interaction with various interfaces, in particular, with air
bubbles, are visualized quantitatively. Based on such a fundamental underwater shock wave research, collaboration
with the School of Medicine at the Tohoku University was started for developing a shock wave assisted therapeutic
device, which was named an extracorporeal shock wave lithotripter (ESWL). Miniature shock waves created by
irradiation with Q-switched HO:YAG laser beams are studied, as applied to damaged dysfunctional nerve cells in the
myocardium in a precisely controlled manner, and are effectively used to design a catheter for treating arrhythmia.
Keywords: underwater shock wave, medical application, water, silicon oil, microexplosion, double exposure
holographic interferometry, high-speed video recording, ESWL, soft tissue dissection, arrhythmia.
UNIVERSAL ALGORITHM FOR ESTIMATING THE MEASURED VALUE BY THE DATA OF A REPEATED EXPERIMENT AND ITS SIMPLIFICATION
E. V. Chernukho UDC 519.23:53.089.6
A universal solution of the problem of estimating parameters of an a priori given arbitrary distribution by the data of
a repeated experiment is presented. The properties of the solution with the structure of the uncertainty function have
been analyzed. The algorithm converting data of an n-fold experiment and a priori information given in the form of
a standardized distribution into estimates of the measured parameter value given as an uncertainty function has been
investigated. Variants of simplifying the algorithm in conformity with practical requirements have been considered.
Keywords: rank measure, estimation of parameters, repeated experiment.