Study on the Mechanics State of Concrete under Penetration and the Deceleration of Projectile

2011 ◽  
Vol 413 ◽  
pp. 1-6
Author(s):  
Tao Deng ◽  
Tao Ge
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Velocity Field ◽  
Boundary Conditions ◽  
Wave Front ◽  
Mass Conservation ◽  
Conservation Of Mass ◽  
Conservation Of Momentum ◽  
Coulomb Criterion ◽  
The Continuum

The concrete under penetration has a restricted deform and is in intrinsic friction state. By used conservation of mass, conservation of momentum and velocity expression on wave front, the velocity field of the pulverized zone near penetration is obtained. The boundary conditions and the continuum conditions were also considered for the obtained velocity field. The pulverized concrete near the penetration is described by Mohr-Coulomb criterion. Based on the conclusions above, cavity expand theory and the expand equation of inconsistent deform, the resistance of projectile is gained in intrinsic friction state. In according to movement differential equation, the deceleration model is built which can describe different phases for penetration and perforation. The decelerations of different size projectiles with different velocity were calculated and were contrasted with experimental data.

MULTICENTERED THEORY OF MOLECULAR PHOTOIONIZATION

2002 ◽  
Vol 09 (02) ◽  
pp. 1143-1148 ◽  
Author(s):  
A. S. BALTENKOV ◽  
V. K. DOLMATOV ◽  
S. T. MANSON
Keyword(s):  
Experimental Data ◽  
Wave Function ◽  
Boundary Conditions ◽  
Qualitative Agreement ◽  
Diatomic Molecules ◽  
Calculated Data ◽  
Angular Distributions ◽  
Molecular Photoionization ◽  
Photoelectron Angular Distributions ◽  
The Continuum

A new theory for near-threshold photoionization of inner electrons of atoms confined in multicentered atomic formations, e.g. molecules or clusters, is developed. The formulas for fixed-in-space molecules have been derived. The interaction of the photoelectron in the continuum with atoms that surround the atom being ionized, is replaced by the suitable boundary conditions imposed on the photoelectron wave function at the location of nuclei of these atoms in the molecule. The general formulas derived are used to calculate photoelectron angular distributions of diatomic molecules. The calculated data are in qualitative agreement with experimental data and results of other calculations.

scholarly journals Flow Near an Ice Divide: Analysis Problems and Data Requirements

1986 ◽  
Vol 8 ◽  
pp. 171-174 ◽  
Author(s):  
E.D. Waddington ◽  
D.A. Fisher ◽  
R.M. Koerner ◽  
W.S.B. Paterson
Keyword(s):  
Velocity Field ◽  
Boundary Conditions ◽  
Ice Cores ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Integrated Modelling ◽  
Planning Stage ◽  
Simple Boundary ◽  
Conservation Model ◽  
The Impact

Climate studies using ice cores require knowledge of the ice deformation at a detailed level, obtainable only by integrated surveying and flow modelling. Field programs should consider model abilities and requirements at the planning stage. Strain and topographic surveys should enclose the flowlines to all boreholes and extend beyond. Only then is it possible to (1) calculate representative slopes at the drill sites and (2) use simple boundary conditions at locations where they do not affect the calculated flow near the holes. Mass conservation models, which may include a parameterized velocity field, estimate the imbalance between integrated accumulation and ice discharge. Momentum conservation models find the actual velocity field, and can reveal a more detailed flow history, but require detailed survey information for boundary conditions. A mass conservation model suggested that flow near core sites at Agassiz Ice Cap, Ellesmere Island, had been steady for more than 3000 years; however, a momentum conservation model showed that either the present transverse strain rate is much smaller than required by the mass conservation model, or the ice is much stiffer than accepted values. It also revealed transients in the flow and microclimate οf which the impact on the derived climate still needs to be assessed by integrated modelling and surveying.

scholarly journals Manufactured analytical solutions for isothermal full-Stokes ice sheet models

2010 ◽  
Vol 4 (3) ◽  
pp. 285-311 ◽  
Author(s):  
A. Sargent ◽  
J. L. Fastook
Keyword(s):  
Boundary Conditions ◽  
Analytical Solutions ◽  
Variable Viscosity ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Mass Conservation ◽  
Ice Surface ◽  
Aspect Ratios ◽  
Conservation Of Momentum ◽  
Outflow Boundary

Abstract. We present the detailed construction of a manufactured analytical solution to time-dependent and steady-state isothermal full-Stokes ice sheet problems. The solutions are constructed for two-dimensional flowline and three-dimensional full-Stokes ice sheet models with variable viscosity. The construction is done by choosing for the specified ice surface and bed a velocity distribution that satisfies both mass conservation and the kinematic boundary conditions. Then a compensatory stress term in the conservation of momentum equations and their boundary conditions is calculated to make the chosen velocity distributions as well as the chosen pressure field into exact solutions. By substituting different ice surface and bed geometry formulas into the derived solution formulas, analytical solutions for different geometries can be constructed. The boundary conditions can be specified as essential Dirichlet conditions or as periodic boundary conditions. By changing a parameter value, the analytical solutions allow investigation of algorithms for a different range of aspect ratios as well as for different, frozen or sliding, basal conditions. The analytical solutions can also be used to estimate the numerical error of the method in the case when the effects of the boundary conditions are eliminated, that is, when the exact solution values are specified as inflow and outflow boundary conditions.

scholarly journals Flow Near an Ice Divide: Analysis Problems and Data Requirements

1986 ◽  
Vol 8 ◽  
pp. 171-174 ◽  
Author(s):  
E.D. Waddington ◽  
D.A. Fisher ◽  
R.M. Koerner ◽  
W.S.B. Paterson
Keyword(s):  
Velocity Field ◽  
Boundary Conditions ◽  
Ice Cores ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Integrated Modelling ◽  
Planning Stage ◽  
Simple Boundary ◽  
Conservation Model ◽  
The Impact

Climate studies using ice cores require knowledge of the ice deformation at a detailed level, obtainable only by integrated surveying and flow modelling. Field programs should consider model abilities and requirements at the planning stage. Strain and topographic surveys should enclose the flowlines to all boreholes and extend beyond. Only then is it possible to (1) calculate representative slopes at the drill sites and (2) use simple boundary conditions at locations where they do not affect the calculated flow near the holes. Mass conservation models, which may include a parameterized velocity field, estimate the imbalance between integrated accumulation and ice discharge. Momentum conservation models find the actual velocity field, and can reveal a more detailed flow history, but require detailed survey information for boundary conditions. A mass conservation model suggested that flow near core sites at Agassiz Ice Cap, Ellesmere Island, had been steady for more than 3000 years; however, a momentum conservation model showed that either the present transverse strain rate is much smaller than required by the mass conservation model, or the ice is much stiffer than accepted values. It also revealed transients in the flow and microclimate οf which the impact on the derived climate still needs to be assessed by integrated modelling and surveying.

scholarly journals Mathematic simulation of cutting unloading from the bunker

2019 ◽  
Vol 10 (7) ◽  
pp. 758 ◽  
Author(s):  
Serhii Yermakov ◽  
Taras Hutsol ◽  
Oleh Ovcharuk ◽  
Iryna Kolosiuk
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Velocity Field ◽  
Boundary Conditions ◽  
Gaseous Medium ◽  
Navier Stokes ◽  
Bulk Materials ◽  
Navier Stokes Equation ◽  
Planting Material ◽  
The Mathematical Model

The peculiarities of cutting movement at unloading them from the hopper are described. The analysis of the scientific researches on bulk materials movement and bridging is given. To develop the mathematical model of cutting unloading the layer should be described as a pseudoliquid, that consists of discrete components (cuttings) and gaseous medium (air). The Navier-Stokes equation can be applied to the process of cutting unloading and velocity field. The equation of pseudoliquid motion is a nonlinear integral and differential equation. The initial and boundary conditions for speed of cutting movement are identified. As a result of research has been theoretically obtained a formula, that evaluates the rate of planting material unloading, the adequacy of which has already been partially tested in experimental experiments carried out by the authors on the way to creating an automatic planting machine.

EELS white line intensities calculated for the 3d and 4d metals

1989 ◽  
Vol 47 ◽  
pp. 388-389
Author(s):  
C. C. Ahn ◽  
D. H. Pearson ◽  
P. Rez ◽  
B. Fultz
Keyword(s):  
Experimental Data ◽  
Line Intensity ◽  
Transition Probabilities ◽  
Initial Increase ◽  
White Line ◽  
Hartree Fock ◽  
Line Intensities ◽  
Integrated Intensity ◽  
X Ray Absorption ◽  
The Continuum

Previous experimental measurements of the total white line intensities from L2,3 energy loss spectra of 3d transition metals reported a linear dependence of the white line intensity on 3d occupancy. These results are inconsistent, however, with behavior inferred from relativistic one electron Dirac-Fock calculations, which show an initial increase followed by a decrease of total white line intensity across the 3d series. This inconsistency with experimental data is especially puzzling in light of work by Thole, et al., which successfully calculates x-ray absorption spectra of the lanthanide M4,5 white lines by employing a less rigorous Hartree-Fock calculation with relativistic corrections based on the work of Cowan. When restricted to transitions allowed by dipole selection rules, the calculated spectra of the lanthanide M4,5 white lines show a decreasing intensity as a function of Z that was consistent with the available experimental data.Here we report the results of Dirac-Fock calculations of the L2,3 white lines of the 3d and 4d elements, and compare the results to the experimental work of Pearson et al. In a previous study, similar calculations helped to account for the non-statistical behavior of L3/L2 ratios of the 3d metals. We assumed that all metals had a single 4s electron. Because these calculations provide absolute transition probabilities, to compare the calculated white line intensities to the experimental data, we normalized the calculated intensities to the intensity of the continuum above the L3 edges. The continuum intensity was obtained by Hartree-Slater calculations, and the normalization factor for the white line intensities was the integrated intensity in an energy window of fixed width and position above the L3 edge of each element.

DETERMINISTIC APPROACH TO WATERSHED MODELING

1971 ◽  
Vol 2 (3) ◽  
pp. 146-166 ◽  
Author(s):  
DAVID A. WOOLHISER
Keyword(s):  
Boundary Conditions ◽  
Watershed Modeling ◽  
Deterministic Approach ◽  
Mass Energy ◽  
Deterministic Models ◽  
Conservation Of Mass ◽  
Hydrologic Process ◽  
Theoretical Structure ◽  
Physically Based ◽  
Initial And Boundary Conditions

Physically-based, deterministic models, are considered in this paper. Physically-based, in that the models have a theoretical structure based primarily on the laws of conservation of mass, energy, or momentum; deterministic in the sense that when initial and boundary conditions and inputs are specified, the output is known with certainty. This type of model attempts to describe the structure of a particular hydrologic process and is therefore helpful in predicting what will happen when some change occurs in the system.

Stochastic model of nonideal mixer. Boundary conditions in batch system

1984 ◽  
Vol 49 (2) ◽  
pp. 490-505
Author(s):  
Vladimír Kudrna ◽  
Pavel Hasal ◽  
Jiří Vlček
Keyword(s):  
Experimental Data ◽  
Stochastic Model ◽  
Boundary Conditions ◽  
Closed System ◽  
Batch System ◽  
Ideal Mixer

The earlier proposed general approach for description of the non-ideal mixer is coupled with corresponding boundary conditions for the closed system. Some simplifications in this procedure result in relations which are in agreement with experimental data.

scholarly journals Experimental Validation of Falling Liquid Film Models: Velocity Assumption and Velocity Field Comparison

Polymers ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1205
Author(s):  
Ruiqi Wang ◽  
Riqiang Duan ◽  
Haijun Jia
Keyword(s):  
Experimental Data ◽  
Particle Image Velocimetry ◽  
Velocity Field ◽  
Experimental Validation ◽  
Particle Image ◽  
Velocity Fields ◽  
Number Range ◽  
Comparison Results ◽  
Image Velocimetry ◽  
Experimental Particle

This publication focuses on the experimental validation of film models by comparing constructed and experimental velocity fields based on model and elementary experimental data. The film experiment covers Kapitza numbers Ka = 278.8 and Ka = 4538.6, a Reynolds number range of 1.6–52, and disturbance frequencies of 0, 2, 5, and 7 Hz. Compared to previous publications, the applied methodology has boundary identification procedures that are more refined and provide additional adaptive particle image velocimetry (PIV) method access to synthetic particle images. The experimental method was validated with a comparison with experimental particle image velocimetry and planar laser induced fluorescence (PIV/PLIF) results, Nusselt’s theoretical prediction, and experimental particle tracking velocimetry (PTV) results of flat steady cases, and a good continuity equation reproduction of transient cases proves the method’s fidelity. The velocity fields are reconstructed based on different film flow model velocity profile assumptions such as experimental film thickness, flow rates, and their derivatives, providing a validation method of film model by comparison between reconstructed velocity experimental data and experimental velocity data. The comparison results show that the first-order weighted residual model (WRM) and regularized model (RM) are very similar, although they may fail to predict the velocity field in rapidly changing zones such as the front of the main hump and the first capillary wave troughs.

Large Time Behavior of Solutions to One Nonlinear Integro-Differential Equation

2008 ◽  
Vol 15 (3) ◽  
pp. 531-539
Author(s):  
Temur Jangveladze ◽  
Zurab Kiguradze
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Boundary Conditions ◽  
Large Time ◽  
Dirichlet Boundary ◽  
Large Time Behavior ◽  
Dirichlet Boundary Conditions ◽  
Time Behavior ◽  
Integro Differential Equation ◽  
Homogeneous Data

Abstract Large time behavior of solutions to the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. The rate of convergence is given, too. Dirichlet boundary conditions with homogeneous data are considered.

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